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The area of a parallelogram may be found by multiplying the base by the height. What is the area, in square inches, of the parallelogram below?
- a)27
- b)36
- c)45
- d)48
- e)81
Correct answer is option 'B'. Can you explain this answer?
The area of a parallelogram may be found by multiplying the base by the height. What is the area, in square inches, of the parallelogram below?
a)
27
b)
36
c)
45
d)
48
e)
81
|
Ayesha Joshi answered |
The height, h, can be found using the Pythagorean Theorem (c2 = a2 + b2):
52 = 32 + h2
25 = 9 + h2
h2 = 16, or h = 4.
Thus, when you multiply the base of the parallelogram by its height, the area of the parallelogram is 9 x 4 = 36.
52 = 32 + h2
25 = 9 + h2
h2 = 16, or h = 4.
Thus, when you multiply the base of the parallelogram by its height, the area of the parallelogram is 9 x 4 = 36.
On the blueprint for Roger’s house, 1/4 inch represents an actual length of 1 foot. What is the area, in square feet, of Roger’s rectangular living room, which is 3 inches by 
inches on the blueprint?- a)51
- b)104
- c)144
- d)204
- e)244
Correct answer is option 'D'. Can you explain this answer?
On the blueprint for Roger’s house, 1/4 inch represents an actual length of 1 foot. What is the area, in square feet, of Roger’s rectangular living room, which is 3 inches by inches on the blueprint?
inches on the blueprint?a)
51
b)
104
c)
144
d)
204
e)
244
|
|
Ayesha Joshi answered |
Since 1/4 inch on the blueprint represents an actual length of 1 foot, 1 inch on the blue print represents an actual length of 4 feet. When the room is 3 inches by 1/4 inches on the blueprint, it is actually 4(3) feet by 
feet. Because the room is rectangular, the area is equal to length times width, so the area is 
feet. Because the room is rectangular, the area is equal to length times width, so the area is In the figure below, l1 is parallel to l2, and l3 is parallel to l4. Which of the following angles is NOT equal to angle x?
- a)α
- b)b
- c)c
- d)d
- e)e
Correct answer is option 'C'. Can you explain this answer?
In the figure below, l1 is parallel to l2, and l3 is parallel to l4. Which of the following angles is NOT equal to angle x?
a)
α
b)
b
c)
c
d)
d
e)
e
|
|
Ayesha Joshi answered |
The correct answer is C. The best approach to this problem is to identify the relationships between the angles. Since a and b are vertical angles formed from the intersection of parallel lines and transversals, they are equal in measure. Since the same transversal (l1) creates angle x, angle x is equal to angles a and b. Eliminate answer choices A and B. Angle c is a supplementary to angle x, which means that angle c + angle x = 180◦.
There are no right angles in the figure, so angle c is NOT equal to angle x; answer choice C is correct.
There are no right angles in the figure, so angle c is NOT equal to angle x; answer choice C is correct.
Directions: Read the passages and choose the best answer to each question.
Passage
Scientists have observed rapid eutrophication of a local lake, at a rate much higher than that of other lakes in the area.
Eutrophication is the aging of a lake, resulting in increased levels of plant life and accumulated sediments, brought on by a build-up of nutrients such as nitrates and phosphates.
Rapid eutrophication is harmful, as it leads to the dying off of cold water fish such as trout. Researchers performed the following experiments to determine the possible source of the increased nitrates and phosphates.
Experiment 1
Scientists suspected that one source of nutrients was a feeder stream which intercepts run-off from farmland where pesticides and animal waste are found. Water samples were obtained over several days from that stream (Feeder A) as well as another feeder stream (Feeder B) not near the farm. Results are displayed in Table 1.
Experiment 2
The scientists also surmised that another possible source of harmful nutrients entering the lake was run-off from a golf course adjacent to the lake where fertilizers were applied.
Water samples were obtained from the lake at various distances (0 meters, 100 meters and 200 meters) from the golf course on four successive days, and the levels of chlorophyll, phosphates, and nitrates were measured. The results are depicted in Table 2.
Q. What was the scientists’ hypothesis concerning lake eutrophication in Experiment 1?- a)Run-off from farmland increases levels of phosphates and nitrates, speeding up the eutrophication process.
- b)Fertilizer used on the golf course increases phosphate and nitrate levels in lake water.
- c)Pesticides and animal waste entering the lake through a feeder stream hinder the eutrophication process.
- d)Increases in phosphate and nitrate concentration lead to more plant and algae growth, increasing chlorophyll levels in the lake.
Correct answer is option 'A'. Can you explain this answer?
Directions: Read the passages and choose the best answer to each question.
Passage
Scientists have observed rapid eutrophication of a local lake, at a rate much higher than that of other lakes in the area.
Eutrophication is the aging of a lake, resulting in increased levels of plant life and accumulated sediments, brought on by a build-up of nutrients such as nitrates and phosphates.
Rapid eutrophication is harmful, as it leads to the dying off of cold water fish such as trout. Researchers performed the following experiments to determine the possible source of the increased nitrates and phosphates.
Experiment 1
Scientists suspected that one source of nutrients was a feeder stream which intercepts run-off from farmland where pesticides and animal waste are found. Water samples were obtained over several days from that stream (Feeder A) as well as another feeder stream (Feeder B) not near the farm. Results are displayed in Table 1.
Passage
Scientists have observed rapid eutrophication of a local lake, at a rate much higher than that of other lakes in the area.
Eutrophication is the aging of a lake, resulting in increased levels of plant life and accumulated sediments, brought on by a build-up of nutrients such as nitrates and phosphates.
Rapid eutrophication is harmful, as it leads to the dying off of cold water fish such as trout. Researchers performed the following experiments to determine the possible source of the increased nitrates and phosphates.
Experiment 1
Scientists suspected that one source of nutrients was a feeder stream which intercepts run-off from farmland where pesticides and animal waste are found. Water samples were obtained over several days from that stream (Feeder A) as well as another feeder stream (Feeder B) not near the farm. Results are displayed in Table 1.
Experiment 2
The scientists also surmised that another possible source of harmful nutrients entering the lake was run-off from a golf course adjacent to the lake where fertilizers were applied.
Water samples were obtained from the lake at various distances (0 meters, 100 meters and 200 meters) from the golf course on four successive days, and the levels of chlorophyll, phosphates, and nitrates were measured. The results are depicted in Table 2.
The scientists also surmised that another possible source of harmful nutrients entering the lake was run-off from a golf course adjacent to the lake where fertilizers were applied.
Water samples were obtained from the lake at various distances (0 meters, 100 meters and 200 meters) from the golf course on four successive days, and the levels of chlorophyll, phosphates, and nitrates were measured. The results are depicted in Table 2.
Q. What was the scientists’ hypothesis concerning lake eutrophication in Experiment 1?
a)
Run-off from farmland increases levels of phosphates and nitrates, speeding up the eutrophication process.
b)
Fertilizer used on the golf course increases phosphate and nitrate levels in lake water.
c)
Pesticides and animal waste entering the lake through a feeder stream hinder the eutrophication process.
d)
Increases in phosphate and nitrate concentration lead to more plant and algae growth, increasing chlorophyll levels in the lake.
|
|
Ayesha Joshi answered |
The best answer is a. According to Experiment 1, “Scientists suspected that one source of nutrients was a feeder stream which intercepts run-off from farmland where pesticides and animal waste are found.” This information suggests that the scientists believed that the high rate of eutrophication was caused by the run-off from the farmland, which best supports answer choice a.
Answer choice b and d can be eliminated because they contain information not present in Experiment 1. Answer choice c is incorrect because scientists believed that the eutrophication process was accelerated, not hindered, by farmland run-off.
Answer choice b and d can be eliminated because they contain information not present in Experiment 1. Answer choice c is incorrect because scientists believed that the eutrophication process was accelerated, not hindered, by farmland run-off.
The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate plane below are 2 vertices of triangle RST, which has a right angle at S. Which of the following could be the third vertex, T ?
- a)(5, 7)
- b)(5, -5)
- c)(4, 6)
- d)(4, 9)
- e)(4, 9/2)
Correct answer is option 'A'. Can you explain this answer?
The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate plane below are 2 vertices of triangle RST, which has a right angle at S. Which of the following could be the third vertex, T ?
a)
(5, 7)
b)
(5, -5)
c)
(4, 6)
d)
(4, 9)
e)
(4, 9/2)
|
|
Ayesha Joshi answered |
Because there is a right angle at S, the point T will lie along the line through S that is perpendicular to the segment RS. To solve this problem, find the equation for the line through S that is perpendicular to the segment RS and try each answer choice to find one that lies on the line. Since the line is perpendicular to segment RS, it will have a slope that is the opposite reciprocal of the slope of RS. Since slope is rise/run, the slope of RS is 
The slope of a line perpendicular to that is -4. Because a point and the slope of the line are known, the point-slope form of the equation can be utilized. A line through point (h, -k) with slope m has equation y - k = m(x - h). Thus the line through S (6,-3) that is perpendicular to the segment RS has equation y - 3 = -4(x - 6). Distributing and adding like terms, the result is y = -4x + 27. Of the answer choices, only the point (5, 7) falls on the line.
The slope of a line perpendicular to that is -4. Because a point and the slope of the line are known, the point-slope form of the equation can be utilized. A line through point (h, -k) with slope m has equation y - k = m(x - h). Thus the line through S (6,-3) that is perpendicular to the segment RS has equation y - 3 = -4(x - 6). Distributing and adding like terms, the result is y = -4x + 27. Of the answer choices, only the point (5, 7) falls on the line.Directions: In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also find questions about a particular section of the passage, or about the entire passage. These questions will be identified either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.Passage
Puzzling Numbers
The Japanese number game Sudoku has taken the world (1) with storm. While crossword puzzles seem to be the game of choice, (2) they need only sit in an airport or doctor’s office in any city to see how Sudoku is slowly overtaking the popular word game.
In the most common game of Sudoku, the player is faced with a nine-by-nine space grid with a total of 81 spaces. The solution to the puzzle requires a number, one through nine, to be placed in each box. (3) Each number must appear only once in each row and only once in each column. A Sudoku puzzle will begin with a few digits already in place. The solver’s (4) task, is to figure out which numeral belongs in the remaining empty spaces. While being a math whiz is no requirement for this seemingly simple process, a level of logic and reasoning (5) is necessary in order to choose the correct number for each space. As with most such activities, practice makes perfect with Sudoku. The puzzles that seem impossible at first glance (6) eventual become more manageable.
The name Sudoku is derived from the phrase single number in the Japanese language. (7) Nevertheless, its definition refers to the placement or allotment of a single number. This puzzle is aptly (8) named, since the misplacement of a single number spells the beginning of an incorrect solution. For this reason, Sudoku (9) should have been played using a pencil with a good eraser.
It is nearly impossible to discern (10) which number the solver has placed incorrectly once an error is discovered. If you don’t have a pencil, use a pen to write the digit as a series of light dots. This way, (11) should you make a mistake, you can retrace your steps to locate and correct the original errant placement.
There are certain strategies involved in solving a Sudoku puzzle, including the process of elimination. For example, if a row of nine spaces already has the number 4, that row cannot contain another 4. This goes for columns as well. The solver can use these clues and a bit of deduction to limit the possible combinations of numbers. By attacking the puzzle using (12) logic, you can turn the process into an amusing challenge rather than an impossible task.
1. The origin of Sudoku is attributed to Leonhard Euler, the Swiss mathematician who (13) sometimes developed the game Magic Squares in 1783.
2. In fact, Euler’s game was actually based on a game derived from Chinese folklore.
3. The primary difference between Magic Squares and Sudoku is that Euler’s game has no grid dividing the puzzle and it is somewhat easier to solve, since there are multiple possibilities for a solution.
4. In true Sudoku, each puzzle has only one solution.
5. The puzzle’s difficulty varies according to the number of digits that are initially provided.
6. When faced with a puzzle with only one 3 provided, for example, you can be sure that it will be more difficult to solve than a puzzle that already has half of the numbers placed in the correct boxes. (14)
One has only to examine a local newspaper to ascertain the popularity of this addictive brain teaser. Where comics and crossword puzzles reign supreme, it is often easy to locate a grid of spaces and numbers tucked off in a corner, or even sitting boldly next to the time-honored crossword.Q. (3) The writer is considering deleting the preceding sentence. Should this sentence be kept or deleted?- a)Kept, because the reader needs to understand the process by which he or she can solve the puzzle.
- b)Kept, because it helps the reader visualize the solution to a specific puzzle in a magazine.
- c)Deleted, because it is not relevant to the preceding sentence.
- d)Deleted, because it is unnecessarily wordy.
Correct answer is option 'A'. Can you explain this answer?
Directions: In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also find questions about a particular section of the passage, or about the entire passage. These questions will be identified either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.
Passage
Puzzling Numbers
The Japanese number game Sudoku has taken the world (1) with storm. While crossword puzzles seem to be the game of choice, (2) they need only sit in an airport or doctor’s office in any city to see how Sudoku is slowly overtaking the popular word game.
In the most common game of Sudoku, the player is faced with a nine-by-nine space grid with a total of 81 spaces. The solution to the puzzle requires a number, one through nine, to be placed in each box. (3) Each number must appear only once in each row and only once in each column. A Sudoku puzzle will begin with a few digits already in place. The solver’s (4) task, is to figure out which numeral belongs in the remaining empty spaces. While being a math whiz is no requirement for this seemingly simple process, a level of logic and reasoning (5) is necessary in order to choose the correct number for each space. As with most such activities, practice makes perfect with Sudoku. The puzzles that seem impossible at first glance (6) eventual become more manageable.
The name Sudoku is derived from the phrase single number in the Japanese language. (7) Nevertheless, its definition refers to the placement or allotment of a single number. This puzzle is aptly (8) named, since the misplacement of a single number spells the beginning of an incorrect solution. For this reason, Sudoku (9) should have been played using a pencil with a good eraser.
It is nearly impossible to discern (10) which number the solver has placed incorrectly once an error is discovered. If you don’t have a pencil, use a pen to write the digit as a series of light dots. This way, (11) should you make a mistake, you can retrace your steps to locate and correct the original errant placement.
There are certain strategies involved in solving a Sudoku puzzle, including the process of elimination. For example, if a row of nine spaces already has the number 4, that row cannot contain another 4. This goes for columns as well. The solver can use these clues and a bit of deduction to limit the possible combinations of numbers. By attacking the puzzle using (12) logic, you can turn the process into an amusing challenge rather than an impossible task.
1. The origin of Sudoku is attributed to Leonhard Euler, the Swiss mathematician who (13) sometimes developed the game Magic Squares in 1783.
2. In fact, Euler’s game was actually based on a game derived from Chinese folklore.
3. The primary difference between Magic Squares and Sudoku is that Euler’s game has no grid dividing the puzzle and it is somewhat easier to solve, since there are multiple possibilities for a solution.
4. In true Sudoku, each puzzle has only one solution.
5. The puzzle’s difficulty varies according to the number of digits that are initially provided.
6. When faced with a puzzle with only one 3 provided, for example, you can be sure that it will be more difficult to solve than a puzzle that already has half of the numbers placed in the correct boxes. (14)
One has only to examine a local newspaper to ascertain the popularity of this addictive brain teaser. Where comics and crossword puzzles reign supreme, it is often easy to locate a grid of spaces and numbers tucked off in a corner, or even sitting boldly next to the time-honored crossword.
Puzzling Numbers
The Japanese number game Sudoku has taken the world (1) with storm. While crossword puzzles seem to be the game of choice, (2) they need only sit in an airport or doctor’s office in any city to see how Sudoku is slowly overtaking the popular word game.
In the most common game of Sudoku, the player is faced with a nine-by-nine space grid with a total of 81 spaces. The solution to the puzzle requires a number, one through nine, to be placed in each box. (3) Each number must appear only once in each row and only once in each column. A Sudoku puzzle will begin with a few digits already in place. The solver’s (4) task, is to figure out which numeral belongs in the remaining empty spaces. While being a math whiz is no requirement for this seemingly simple process, a level of logic and reasoning (5) is necessary in order to choose the correct number for each space. As with most such activities, practice makes perfect with Sudoku. The puzzles that seem impossible at first glance (6) eventual become more manageable.
The name Sudoku is derived from the phrase single number in the Japanese language. (7) Nevertheless, its definition refers to the placement or allotment of a single number. This puzzle is aptly (8) named, since the misplacement of a single number spells the beginning of an incorrect solution. For this reason, Sudoku (9) should have been played using a pencil with a good eraser.
It is nearly impossible to discern (10) which number the solver has placed incorrectly once an error is discovered. If you don’t have a pencil, use a pen to write the digit as a series of light dots. This way, (11) should you make a mistake, you can retrace your steps to locate and correct the original errant placement.
There are certain strategies involved in solving a Sudoku puzzle, including the process of elimination. For example, if a row of nine spaces already has the number 4, that row cannot contain another 4. This goes for columns as well. The solver can use these clues and a bit of deduction to limit the possible combinations of numbers. By attacking the puzzle using (12) logic, you can turn the process into an amusing challenge rather than an impossible task.
1. The origin of Sudoku is attributed to Leonhard Euler, the Swiss mathematician who (13) sometimes developed the game Magic Squares in 1783.
2. In fact, Euler’s game was actually based on a game derived from Chinese folklore.
3. The primary difference between Magic Squares and Sudoku is that Euler’s game has no grid dividing the puzzle and it is somewhat easier to solve, since there are multiple possibilities for a solution.
4. In true Sudoku, each puzzle has only one solution.
5. The puzzle’s difficulty varies according to the number of digits that are initially provided.
6. When faced with a puzzle with only one 3 provided, for example, you can be sure that it will be more difficult to solve than a puzzle that already has half of the numbers placed in the correct boxes. (14)
One has only to examine a local newspaper to ascertain the popularity of this addictive brain teaser. Where comics and crossword puzzles reign supreme, it is often easy to locate a grid of spaces and numbers tucked off in a corner, or even sitting boldly next to the time-honored crossword.
Q. (3) The writer is considering deleting the preceding sentence. Should this sentence be kept or deleted?
a)
Kept, because the reader needs to understand the process by which he or she can solve the puzzle.
b)
Kept, because it helps the reader visualize the solution to a specific puzzle in a magazine.
c)
Deleted, because it is not relevant to the preceding sentence.
d)
Deleted, because it is unnecessarily wordy.
|
Orion Classes answered |
The sentence in question is important because it explains how to play the game of Sudoku, and Sudoku is the subject of the passage. Answer choice B is incorrect because it does not provide a solution to any particular game.
Answer choices C and D are incorrect because the sentence is both relevant and to the point.
Answer choices C and D are incorrect because the sentence is both relevant and to the point.
Directions: In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also find questions about a particular section of the passage, or about the entire passage. These questions will be identified either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.
The following paragraphs may or may not be in the most logical order. You may be asked questions about the logical order of the paragraphs, as well as where to place sentences logically within any given paragraph.Passage
Care with Cards
[1] Does anyone have a real hobby anymore? I must admit I was disheartened when my brother, younger by 10 years, didn’t want to go into the sports card shop with me. (1) We went to a department store instead. Every boy (2) which I have known as a kid had a box in his (3) room, brimming, with cards. Some boys were into basketball and football cards, but my passion was for baseball cards. I couldn’t believe the shocked look on my brother’s face when he saw some of the expensive offerings in the shop’s window display. He just couldn’t appreciate the history behind the cards and the care taken to preserve them over the decades. For him, no piece of cardboard (4) are worth any sum of money. He would rather have a video screen to distract him.
[2] 1. (5) I appreciate the arguments in favor of television, video games, and other electronic entertainment.
2. The technology is dynamic (6) and, for the most part, engaging.
3. There’s indeed something for everyone.
4. I also believe, however, that these new forms of entertainment have taken time away from “unplugged” fun.
5. (7) A good hands-on hobby should be an important part of any childhood.
6. Instead of simple story books, toddlers have interactive learning computers that read for them.
7. When children aren’t watching satellite television, they have console games to entertain them.
8. It seems to me that more and more of the joys of childhood are being lost to the allure of the video screen.
[3] Building a sports card collection is a rewarding endeavor for children and adults (8) alike that is fun for everyone. It teaches quality lessons, such as patience and organization. For young fingers, it develops a careful touch. I remember how hard I tried to slide each card into a plastic sleeve without damaging the delicate corners of the card. Nearly (9) all weekend, there was a card show at the local mall where I learned to bargain and trade for all the cards that I needed to fill the gaps in my collection. Although I very much enjoyed spending time alone looking at the cards, (10) I often shared the experience with others. Card collecting is a social activity (11) too encouraging the old and young to swap cards and stories. Today’s electronic entertainment, however, keeps people apart and does little to benefit developing minds. The video screen silences spectators as it holds their attention (12) to the screen. Television and video games deliver instant gratification. Tune a channel or insert a disc and off you go. Hours and hours of sedentary satisfaction are at (13) their fingertips!
[4] I am concerned that this trend toward electronics will lead to less physical activity and make the fun in life
effortless and (14) instant available. The younger generation needs to know that pleasure can also come from a hobby that demands patience, care, hard work, and concentration.Q. (4)- a)no change
- b)has
- c)was
- d)could of been
Correct answer is option 'C'. Can you explain this answer?
Directions: In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also find questions about a particular section of the passage, or about the entire passage. These questions will be identified either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.
The following paragraphs may or may not be in the most logical order. You may be asked questions about the logical order of the paragraphs, as well as where to place sentences logically within any given paragraph.
The following paragraphs may or may not be in the most logical order. You may be asked questions about the logical order of the paragraphs, as well as where to place sentences logically within any given paragraph.
Passage
Care with Cards
[1] Does anyone have a real hobby anymore? I must admit I was disheartened when my brother, younger by 10 years, didn’t want to go into the sports card shop with me. (1) We went to a department store instead. Every boy (2) which I have known as a kid had a box in his (3) room, brimming, with cards. Some boys were into basketball and football cards, but my passion was for baseball cards. I couldn’t believe the shocked look on my brother’s face when he saw some of the expensive offerings in the shop’s window display. He just couldn’t appreciate the history behind the cards and the care taken to preserve them over the decades. For him, no piece of cardboard (4) are worth any sum of money. He would rather have a video screen to distract him.
[2] 1. (5) I appreciate the arguments in favor of television, video games, and other electronic entertainment.
2. The technology is dynamic (6) and, for the most part, engaging.
3. There’s indeed something for everyone.
4. I also believe, however, that these new forms of entertainment have taken time away from “unplugged” fun.
5. (7) A good hands-on hobby should be an important part of any childhood.
6. Instead of simple story books, toddlers have interactive learning computers that read for them.
7. When children aren’t watching satellite television, they have console games to entertain them.
8. It seems to me that more and more of the joys of childhood are being lost to the allure of the video screen.
[3] Building a sports card collection is a rewarding endeavor for children and adults (8) alike that is fun for everyone. It teaches quality lessons, such as patience and organization. For young fingers, it develops a careful touch. I remember how hard I tried to slide each card into a plastic sleeve without damaging the delicate corners of the card. Nearly (9) all weekend, there was a card show at the local mall where I learned to bargain and trade for all the cards that I needed to fill the gaps in my collection. Although I very much enjoyed spending time alone looking at the cards, (10) I often shared the experience with others. Card collecting is a social activity (11) too encouraging the old and young to swap cards and stories. Today’s electronic entertainment, however, keeps people apart and does little to benefit developing minds. The video screen silences spectators as it holds their attention (12) to the screen. Television and video games deliver instant gratification. Tune a channel or insert a disc and off you go. Hours and hours of sedentary satisfaction are at (13) their fingertips!
[4] I am concerned that this trend toward electronics will lead to less physical activity and make the fun in life
effortless and (14) instant available. The younger generation needs to know that pleasure can also come from a hobby that demands patience, care, hard work, and concentration.
Care with Cards
[1] Does anyone have a real hobby anymore? I must admit I was disheartened when my brother, younger by 10 years, didn’t want to go into the sports card shop with me. (1) We went to a department store instead. Every boy (2) which I have known as a kid had a box in his (3) room, brimming, with cards. Some boys were into basketball and football cards, but my passion was for baseball cards. I couldn’t believe the shocked look on my brother’s face when he saw some of the expensive offerings in the shop’s window display. He just couldn’t appreciate the history behind the cards and the care taken to preserve them over the decades. For him, no piece of cardboard (4) are worth any sum of money. He would rather have a video screen to distract him.
[2] 1. (5) I appreciate the arguments in favor of television, video games, and other electronic entertainment.
2. The technology is dynamic (6) and, for the most part, engaging.
3. There’s indeed something for everyone.
4. I also believe, however, that these new forms of entertainment have taken time away from “unplugged” fun.
5. (7) A good hands-on hobby should be an important part of any childhood.
6. Instead of simple story books, toddlers have interactive learning computers that read for them.
7. When children aren’t watching satellite television, they have console games to entertain them.
8. It seems to me that more and more of the joys of childhood are being lost to the allure of the video screen.
[3] Building a sports card collection is a rewarding endeavor for children and adults (8) alike that is fun for everyone. It teaches quality lessons, such as patience and organization. For young fingers, it develops a careful touch. I remember how hard I tried to slide each card into a plastic sleeve without damaging the delicate corners of the card. Nearly (9) all weekend, there was a card show at the local mall where I learned to bargain and trade for all the cards that I needed to fill the gaps in my collection. Although I very much enjoyed spending time alone looking at the cards, (10) I often shared the experience with others. Card collecting is a social activity (11) too encouraging the old and young to swap cards and stories. Today’s electronic entertainment, however, keeps people apart and does little to benefit developing minds. The video screen silences spectators as it holds their attention (12) to the screen. Television and video games deliver instant gratification. Tune a channel or insert a disc and off you go. Hours and hours of sedentary satisfaction are at (13) their fingertips!
[4] I am concerned that this trend toward electronics will lead to less physical activity and make the fun in life
effortless and (14) instant available. The younger generation needs to know that pleasure can also come from a hobby that demands patience, care, hard work, and concentration.
Q. (4)
a)
no change
b)
has
c)
was
d)
could of been
|
|
Orion Classes answered |
The simple plural past tense is correct here. No piece is a singular subject, and cannot be referred to by answer choice A.
Answer choice B would not make sense in the sentence.
Answer choice B would not make sense in the sentence.
The figure below shows part of a circle whose circumference is 40. If arcs of length 4 and length s continue to alternate around the entire circle so that there are 8 arcs of each length, what is the degree measure of each of the arcs of length s?
- a)6°
- b)9°
- c)12°
- d)18°
- e)36°
Correct answer is option 'B'. Can you explain this answer?
The figure below shows part of a circle whose circumference is 40. If arcs of length 4 and length s continue to alternate around the entire circle so that there are 8 arcs of each length, what is the degree measure of each of the arcs of length s?
a)
6°
b)
9°
c)
12°
d)
18°
e)
36°
|
|
Ayesha Joshi answered |
First, find the value of s. Since there are 8 arcs of each length, it follows that there are 8 arcs of length (4 + s). Since the circumference is 40, then 8(4 + s) = 40. Solve for s: 32 + 8s = 40 and s = 1. Now that you know the value of each length, you can solve for the degree measure of each of the arcs of length s. You know that the entire circle has 360°. You
also know that the length of the smaller arc (s) is 1/4 the length of the larger arc. Therefore, you can set up the following equation:
where x is the degree measure corresponding to each arc of length 4 and 
is the degree measure corresponding to each arc of length s = 1. Now you have 
which is 10x = 360°. So x = 36°. Recall that x is the degree measure corresponding to each arc of length 4. The degree measure corresponding to each arc of length s is 
also know that the length of the smaller arc (s) is 1/4 the length of the larger arc. Therefore, you can set up the following equation:
where x is the degree measure corresponding to each arc of length 4 and is the degree measure corresponding to each arc of length s = 1. Now you have which is 10x = 360°. So x = 36°. Recall that x is the degree measure corresponding to each arc of length 4. The degree measure corresponding to each arc of length s is For which of the following functions is f(−5) > f(5)?- a)f(x) = 6x2
- b)f(x) = 6
- c)f(x) = 6/x
- d)f(x) = 6 − x3
- e)f(x) = x6 + 6
Correct answer is option 'D'. Can you explain this answer?
For which of the following functions is f(−5) > f(5)?
a)
f(x) = 6x2
b)
f(x) = 6
c)
f(x) = 6/x
d)
f(x) = 6 − x3
e)
f(x) = x6 + 6
|
Oliver Ramirez answered |
Comparison of Function Values at -5 and 5:
- When comparing the function values at -5 and 5 for each given function, we need to substitute x = -5 and x = 5 into the functions and compare the results.
Functions:
a) f(x) = 6x^2
- f(-5) = 6*(-5)^2 = 150
- f(5) = 6*5^2 = 150
b) f(x) = 6
- f(-5) = 6
- f(5) = 6
c) f(x) = 6/x
- f(-5) = 6/(-5) = -1.2
- f(5) = 6/5 = 1.2
d) f(x) = 6 - x^3
- f(-5) = 6 - (-5)^3 = 31
- f(5) = 6 - 5^3 = -19
e) f(x) = x^6 + 6
- f(-5) = (-5)^6 + 6 = 15631
- f(5) = 5^6 + 6 = 15631
Conclusion:
The only function for which f(-5) > f(5) is d) f(x) = 6 - x^3. This is because f(-5) = 31 is greater than f(5) = -19.
- When comparing the function values at -5 and 5 for each given function, we need to substitute x = -5 and x = 5 into the functions and compare the results.
Functions:
a) f(x) = 6x^2
- f(-5) = 6*(-5)^2 = 150
- f(5) = 6*5^2 = 150
b) f(x) = 6
- f(-5) = 6
- f(5) = 6
c) f(x) = 6/x
- f(-5) = 6/(-5) = -1.2
- f(5) = 6/5 = 1.2
d) f(x) = 6 - x^3
- f(-5) = 6 - (-5)^3 = 31
- f(5) = 6 - 5^3 = -19
e) f(x) = x^6 + 6
- f(-5) = (-5)^6 + 6 = 15631
- f(5) = 5^6 + 6 = 15631
Conclusion:
The only function for which f(-5) > f(5) is d) f(x) = 6 - x^3. This is because f(-5) = 31 is greater than f(5) = -19.
What is the distance in the standard (x,y) coordinate plane between the points (0,1) and (4,4)?- a)√7
- b)3
- c)4
- d)5
- e)√27
Correct answer is option 'D'. Can you explain this answer?
What is the distance in the standard (x,y) coordinate plane between the points (0,1) and (4,4)?
a)
√7
b)
3
c)
4
d)
5
e)
√27
|
Zachary Barnes answered |
The distance between two points in the standard (x,y) coordinate plane can be found using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, (x1,y1) = (0,1) and (x2,y2) = (4,4).
So, the distance is:
d = √[(4 - 0)^2 + (4 - 1)^2]
= √[16 + 9]
= √25
= 5
Therefore, the distance in the standard (x,y) coordinate plane between the points (0,1) and (4,4) is 5 units.
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, (x1,y1) = (0,1) and (x2,y2) = (4,4).
So, the distance is:
d = √[(4 - 0)^2 + (4 - 1)^2]
= √[16 + 9]
= √25
= 5
Therefore, the distance in the standard (x,y) coordinate plane between the points (0,1) and (4,4) is 5 units.
Directions: Read the passages and choose the best answer to each question.
Passage
NATURAL SCIENCE: Those Jellystone Bears
Over the years, there have been countless fans
of the classic Hanna-Barbera cartoon character Yogi
Bear. The cartoon series enjoyed by young and old
alike revolved mostly around the misadventures of this
(5) loveable bear and his sidekick Boo-Boo as they
attempted to snag “pic-a-nic” baskets in the made-up
land of Jellystone Park. It’s not often that people think
about where the ideas for these cartoons characters
come from, which brings up an interesting point: do
(10) bears actually search for food left in picnic baskets
and unattended campsites? Anyone who has watched
an episode of Yogi Bear can see that the bears’ behav-
ior goes far beyond the limits of what is natural. The
thing which must be explored, then, is which of those
(15) humorous antics were license on the part of Hanna-
Barbera, and which were actually based on the bear’s
normal behaviors.
Remarkably enough, bears have been known to
seek out food from some unlikely sources, including
(20) picnic baskets, on top of their usual diet of berries,
insects, and fish. Bears work throughout the summer
and fall to build up fat stores so as to have energy
enough to last them through their winter hibernations.
Related to this is their need to replenish their depleted
(25) reserves when they wake up in the spring. Food is gen-
erally scarce in the early spring, and consequently they
will gladly indulge in any foods that are high in pro-
teins or fats. This is the main reason for many incidents
involving bears entering campsites in search of food.
(30) Although this behavior may seem strange, it is
no more than the result of nature equipping bears with
a variety of traits that allow them to remain well fed
in increasingly human-populated habitats. Specifically,
the American black bear, Ursus americanus, has color
(35) vision and has been observed by scientists using its
color vision to distinguish between varying food items
at close range. On top of this, all bears have an acute
sense of smell and can use their especially sensitive lips
to locate food. These sensory talents contribute to the
(40) bears’ remarkably high intelligence and curiosity, giv-
ing them the ability to open closed containers if they
believe food is inside. Their exploratory and naviga-
tional skills are also worthy of note—most bears will
maintain vast territories in order to obtain food from
(45) a variety of sources. Bears may even vary their sleep
cycles in areas where there is a large degree of human
activity, either feasting on road-side garbage during the
day or scouring campsites for leftovers at night.
Yet another strange but true comparison is that
(50) Yogi and Boo-Boo have developed a social relationship
much like the ones that will form between wild bears
when several animals find themselves sharing a limited
number of food sources. Generally solitary, black bears
will create a hierarchical order in situations where paths
(55) cross in pursuit of food, so as to assure that all animals
remain adequately fed. While it is unlikely that any
black bears in nature would actually send a cub after a
camper’s lunch, the behavioral relationships that might
inspire the creation of such a story are indeed real.
(60) Though many of the features of the comical Yogi
Bear are likely the result of pure imagination, there
is scientific fact behind at least some of his activities.
Despite his apperance as a brown bear, the distinctive
feeding behaviors of the American black bear match
(65) remarkably well with the habits of the cartoonish cul-
prit. The uncanny truth behind little known scientific
facts such as these should make everyone think twice
the next time they sit down to watch Saturday morning
cartoons.Q. With which of the following statements would the author most likely agree?- a)Bears are particularly resourceful.
- b)Bears cannot tolerate human food.
- c)Bears eat voraciously throughout the winter.
- d)Bears have only one method of obtaining food.
Correct answer is option 'A'. Can you explain this answer?
Directions: Read the passages and choose the best answer to each question.
Passage
NATURAL SCIENCE: Those Jellystone Bears
Over the years, there have been countless fans
of the classic Hanna-Barbera cartoon character Yogi
Bear. The cartoon series enjoyed by young and old
alike revolved mostly around the misadventures of this
(5) loveable bear and his sidekick Boo-Boo as they
attempted to snag “pic-a-nic” baskets in the made-up
land of Jellystone Park. It’s not often that people think
about where the ideas for these cartoons characters
come from, which brings up an interesting point: do
(10) bears actually search for food left in picnic baskets
and unattended campsites? Anyone who has watched
an episode of Yogi Bear can see that the bears’ behav-
ior goes far beyond the limits of what is natural. The
thing which must be explored, then, is which of those
(15) humorous antics were license on the part of Hanna-
Barbera, and which were actually based on the bear’s
normal behaviors.
Remarkably enough, bears have been known to
seek out food from some unlikely sources, including
(20) picnic baskets, on top of their usual diet of berries,
insects, and fish. Bears work throughout the summer
and fall to build up fat stores so as to have energy
enough to last them through their winter hibernations.
Related to this is their need to replenish their depleted
(25) reserves when they wake up in the spring. Food is gen-
erally scarce in the early spring, and consequently they
will gladly indulge in any foods that are high in pro-
teins or fats. This is the main reason for many incidents
involving bears entering campsites in search of food.
(30) Although this behavior may seem strange, it is
no more than the result of nature equipping bears with
a variety of traits that allow them to remain well fed
in increasingly human-populated habitats. Specifically,
the American black bear, Ursus americanus, has color
(35) vision and has been observed by scientists using its
color vision to distinguish between varying food items
at close range. On top of this, all bears have an acute
sense of smell and can use their especially sensitive lips
to locate food. These sensory talents contribute to the
(40) bears’ remarkably high intelligence and curiosity, giv-
ing them the ability to open closed containers if they
believe food is inside. Their exploratory and naviga-
tional skills are also worthy of note—most bears will
maintain vast territories in order to obtain food from
(45) a variety of sources. Bears may even vary their sleep
cycles in areas where there is a large degree of human
activity, either feasting on road-side garbage during the
day or scouring campsites for leftovers at night.
Yet another strange but true comparison is that
(50) Yogi and Boo-Boo have developed a social relationship
much like the ones that will form between wild bears
when several animals find themselves sharing a limited
number of food sources. Generally solitary, black bears
will create a hierarchical order in situations where paths
(55) cross in pursuit of food, so as to assure that all animals
remain adequately fed. While it is unlikely that any
black bears in nature would actually send a cub after a
camper’s lunch, the behavioral relationships that might
inspire the creation of such a story are indeed real.
(60) Though many of the features of the comical Yogi
Bear are likely the result of pure imagination, there
is scientific fact behind at least some of his activities.
Despite his apperance as a brown bear, the distinctive
feeding behaviors of the American black bear match
(65) remarkably well with the habits of the cartoonish cul-
prit. The uncanny truth behind little known scientific
facts such as these should make everyone think twice
the next time they sit down to watch Saturday morning
cartoons.
Passage
NATURAL SCIENCE: Those Jellystone Bears
Over the years, there have been countless fans
of the classic Hanna-Barbera cartoon character Yogi
Bear. The cartoon series enjoyed by young and old
alike revolved mostly around the misadventures of this
(5) loveable bear and his sidekick Boo-Boo as they
attempted to snag “pic-a-nic” baskets in the made-up
land of Jellystone Park. It’s not often that people think
about where the ideas for these cartoons characters
come from, which brings up an interesting point: do
(10) bears actually search for food left in picnic baskets
and unattended campsites? Anyone who has watched
an episode of Yogi Bear can see that the bears’ behav-
ior goes far beyond the limits of what is natural. The
thing which must be explored, then, is which of those
(15) humorous antics were license on the part of Hanna-
Barbera, and which were actually based on the bear’s
normal behaviors.
Remarkably enough, bears have been known to
seek out food from some unlikely sources, including
(20) picnic baskets, on top of their usual diet of berries,
insects, and fish. Bears work throughout the summer
and fall to build up fat stores so as to have energy
enough to last them through their winter hibernations.
Related to this is their need to replenish their depleted
(25) reserves when they wake up in the spring. Food is gen-
erally scarce in the early spring, and consequently they
will gladly indulge in any foods that are high in pro-
teins or fats. This is the main reason for many incidents
involving bears entering campsites in search of food.
(30) Although this behavior may seem strange, it is
no more than the result of nature equipping bears with
a variety of traits that allow them to remain well fed
in increasingly human-populated habitats. Specifically,
the American black bear, Ursus americanus, has color
(35) vision and has been observed by scientists using its
color vision to distinguish between varying food items
at close range. On top of this, all bears have an acute
sense of smell and can use their especially sensitive lips
to locate food. These sensory talents contribute to the
(40) bears’ remarkably high intelligence and curiosity, giv-
ing them the ability to open closed containers if they
believe food is inside. Their exploratory and naviga-
tional skills are also worthy of note—most bears will
maintain vast territories in order to obtain food from
(45) a variety of sources. Bears may even vary their sleep
cycles in areas where there is a large degree of human
activity, either feasting on road-side garbage during the
day or scouring campsites for leftovers at night.
Yet another strange but true comparison is that
(50) Yogi and Boo-Boo have developed a social relationship
much like the ones that will form between wild bears
when several animals find themselves sharing a limited
number of food sources. Generally solitary, black bears
will create a hierarchical order in situations where paths
(55) cross in pursuit of food, so as to assure that all animals
remain adequately fed. While it is unlikely that any
black bears in nature would actually send a cub after a
camper’s lunch, the behavioral relationships that might
inspire the creation of such a story are indeed real.
(60) Though many of the features of the comical Yogi
Bear are likely the result of pure imagination, there
is scientific fact behind at least some of his activities.
Despite his apperance as a brown bear, the distinctive
feeding behaviors of the American black bear match
(65) remarkably well with the habits of the cartoonish cul-
prit. The uncanny truth behind little known scientific
facts such as these should make everyone think twice
the next time they sit down to watch Saturday morning
cartoons.
Q. With which of the following statements would the author most likely agree?
a)
Bears are particularly resourceful.
b)
Bears cannot tolerate human food.
c)
Bears eat voraciously throughout the winter.
d)
Bears have only one method of obtaining food.
|
|
Orion Classes answered |
The best answer is a. Throughout the passage the author refers to the feeding habits of bears as being varied and discusses a variety of methods that they use to secure food, such as keeping “vast territories,” “varying sleep cycles,” and “creating a hierarchical order.” These behaviors are somewhat outside the norm of typical animal behavior, so the author would likely call them resourceful.
The other answer choices are not supported by the passage.
The other answer choices are not supported by the passage.
What is the slope-intercept form of 10x - y - 8 = 0?- a)y = -2x
- b)y = -10x - 8
- c)y = -10x + 8
- d)y = 10x - 8
- e)y = 10x + 8
Correct answer is option 'D'. Can you explain this answer?
What is the slope-intercept form of 10x - y - 8 = 0?
a)
y = -2x
b)
y = -10x - 8
c)
y = -10x + 8
d)
y = 10x - 8
e)
y = 10x + 8
|
|
Orion Classes answered |
The slope-intercept form of the equation for a line is y = mx + b; isolate y on the left side of the equation, as follows:
10x − y − 8 = 0
10x − y = 8
− y = −10x + 8
y = 10x − 8
10x − y − 8 = 0
10x − y = 8
− y = −10x + 8
y = 10x − 8
If x and y are positive integers such that the greatest common factor of x2y2 and xy3 is 27, then which of the following could y equal?- a)81
- b)27
- c)18
- d)9
- e)3
Correct answer is option 'E'. Can you explain this answer?
If x and y are positive integers such that the greatest common factor of x2y2 and xy3 is 27, then which of the following could y equal?
a)
81
b)
27
c)
18
d)
9
e)
3
|
|
Ayesha Joshi answered |
The correct answer is E. You could take a “bruteforce” approach and test all the given values of y and see if you could find an x that worked. For aenxdamxple, if y = 9, then the two numbers are x2 × 92 × 93. You can see that 92 is a factor of these 2 numbers, so 27 cannot be the greatest common factor.
It might be more efficient to be more general and avoid testing all 5 values of x. Notice that xy2 is a common factor of both x2y2 and xy3. Because it is a factor, xy2 must also be a factor of 27. Well, 27 factors as 3 × 32, so it seems natural to see = 3 and y = 3 are possible solutions. In this case the two numbers from the problem are 32 × 32 and 33 × 3 and the g
It might be more efficient to be more general and avoid testing all 5 values of x. Notice that xy2 is a common factor of both x2y2 and xy3. Because it is a factor, xy2 must also be a factor of 27. Well, 27 factors as 3 × 32, so it seems natural to see = 3 and y = 3 are possible solutions. In this case the two numbers from the problem are 32 × 32 and 33 × 3 and the g
Directions: Read the passages and choose the best answer to each question.
Passage
SOCIAL SCIENCE: This passage discusses some social and economic issues regarding liquid natural gas as an energy source.
Although oil and gasoline remain important
energy sources, it is natural gas that currently supplies
around 25 percent of America’s energy needs. A recent
study shows that natural gas use was roughly 22 trillion
(5) cubic feet (TCF) annually. Natural gas demand is
increasing at phenomenal rates because of its ability
to create cleaner fuel for electrical power. Experts pre-
dict that annual demand is likely to increase to almost
32 TCF in less than a decade. At a consumption rate
(10) of 32 TCF per year, the United States would only have
about a five-year supply of natural gas. Known natural
gas reserves in North America are quickly becoming
exhausted. In fact, in the past thirty years, known sup-
plies have dwindled from almost 300 TCF to around
(15) 150 TCF.
It is no wonder that natural gas has become a con-
troversial and critical topic of discussion among politi-
cians, business leaders,
and consumers. It is apparent
that the United States will need to drastically increase
(20) imports of natural gas to relieve shortages. One way
that economists believe this can be done is by importing
liquid natural gas. Experts predict that liquid natural
gas imports will increase by almost 500 percent in a few
short years. Currently, the country imports very little
(25) liquid natural gas. The process of transporting liquid
natural gas is complicated and expensive. This is the
most obvious reason why America has been reluctant
to choose liquid natural gas over other energy sources.
Converting natural gas into liquid natural gas involves
(30) cooling natural gas as it is collected to −260◦F. This
transforms the gas into a liquid, which is then injected
into a specially designed vessel for transport. When
the liquid natural gas reaches its destination, the liquid
is reheated into its original gaseous state and allowed
(35) to flow into a pipeline. Even though new technology
has considerably decreased transportation costs for liq-
uid natural gas, it is still often uneconomical. This is
especially true for nations with other energy sources.
One of the largest misconceptions about liquid
(40) natural gas is that it is an abundant source of natural
gas. While liquid natural gas imports continue to
increase, the public demand for natural gas increases
at an even higher rate. Even though the United States
has several facilities that can process liquid natural gas,
(45) these facilities are consistently unable to obtain enough
liquid natural gas to operate at their fullest capacity.
Even when liquid natural gas is obtainable, there is a
fear that low natural gas prices in the United States will
make liquid natural gas uneconomical. Most business
(50) leaders and politicians are reluctant to create new facili-
ties to process liquid natural gas because these facilities
are expensive and risky. This limits the capacity to pro-
cess liquid natural gas even if it becomes more readily
available.
(55) The United States also faces competition from
Asia in securing liquid natural gas. Competition for
liquid natural gas will most likely become even more
ferocious as other populous countries like Japan and
China become more desperate for fuel sources. Some
(60) of the more daring politicians and business leaders
believe that building new liquid natural gas facilities
will help companies and consumers take advantage of
future increased liquid natural gas imports. Currently,
Canada is the largest liquid natural gas supplier for
(65) the United States. However, liquid natural gas imports
from Canada will decrease considerably in the next
decade as Canadian consumption increases and sup-
plies of natural gas dwindle. Therefore, consumers and
business leaders should not rely on liquid natural gas
(70) to solve America’s energy needs and consumers should
continue to expect high prices as demand grows and
supplies decline.Q. According to the passage, current known North American supplies of natural gas are:- a)sufficient to provide the United States with natural gas for the next thirty years.
- b)down approximately 50 percent from thirty years ago.
- c)decreasing at a rate of 25 percent per year.
- d)extremely difficult to access.
Correct answer is option 'B'. Can you explain this answer?
Directions: Read the passages and choose the best answer to each question.
Passage
SOCIAL SCIENCE: This passage discusses some social and economic issues regarding liquid natural gas as an energy source.
Although oil and gasoline remain important
energy sources, it is natural gas that currently supplies
around 25 percent of America’s energy needs. A recent
study shows that natural gas use was roughly 22 trillion
(5) cubic feet (TCF) annually. Natural gas demand is
increasing at phenomenal rates because of its ability
to create cleaner fuel for electrical power. Experts pre-
dict that annual demand is likely to increase to almost
32 TCF in less than a decade. At a consumption rate
(10) of 32 TCF per year, the United States would only have
about a five-year supply of natural gas. Known natural
gas reserves in North America are quickly becoming
exhausted. In fact, in the past thirty years, known sup-
plies have dwindled from almost 300 TCF to around
(15) 150 TCF.
It is no wonder that natural gas has become a con-
troversial and critical topic of discussion among politi-
cians, business leaders,
and consumers. It is apparent
that the United States will need to drastically increase
(20) imports of natural gas to relieve shortages. One way
that economists believe this can be done is by importing
liquid natural gas. Experts predict that liquid natural
gas imports will increase by almost 500 percent in a few
short years. Currently, the country imports very little
(25) liquid natural gas. The process of transporting liquid
natural gas is complicated and expensive. This is the
most obvious reason why America has been reluctant
to choose liquid natural gas over other energy sources.
Converting natural gas into liquid natural gas involves
(30) cooling natural gas as it is collected to −260◦F. This
transforms the gas into a liquid, which is then injected
into a specially designed vessel for transport. When
the liquid natural gas reaches its destination, the liquid
is reheated into its original gaseous state and allowed
(35) to flow into a pipeline. Even though new technology
has considerably decreased transportation costs for liq-
uid natural gas, it is still often uneconomical. This is
especially true for nations with other energy sources.
One of the largest misconceptions about liquid
(40) natural gas is that it is an abundant source of natural
gas. While liquid natural gas imports continue to
increase, the public demand for natural gas increases
at an even higher rate. Even though the United States
has several facilities that can process liquid natural gas,
(45) these facilities are consistently unable to obtain enough
liquid natural gas to operate at their fullest capacity.
Even when liquid natural gas is obtainable, there is a
fear that low natural gas prices in the United States will
make liquid natural gas uneconomical. Most business
(50) leaders and politicians are reluctant to create new facili-
ties to process liquid natural gas because these facilities
are expensive and risky. This limits the capacity to pro-
cess liquid natural gas even if it becomes more readily
available.
(55) The United States also faces competition from
Asia in securing liquid natural gas. Competition for
liquid natural gas will most likely become even more
ferocious as other populous countries like Japan and
China become more desperate for fuel sources. Some
(60) of the more daring politicians and business leaders
believe that building new liquid natural gas facilities
will help companies and consumers take advantage of
future increased liquid natural gas imports. Currently,
Canada is the largest liquid natural gas supplier for
(65) the United States. However, liquid natural gas imports
from Canada will decrease considerably in the next
decade as Canadian consumption increases and sup-
plies of natural gas dwindle. Therefore, consumers and
business leaders should not rely on liquid natural gas
(70) to solve America’s energy needs and consumers should
continue to expect high prices as demand grows and
supplies decline.
Passage
SOCIAL SCIENCE: This passage discusses some social and economic issues regarding liquid natural gas as an energy source.
Although oil and gasoline remain important
energy sources, it is natural gas that currently supplies
around 25 percent of America’s energy needs. A recent
study shows that natural gas use was roughly 22 trillion
(5) cubic feet (TCF) annually. Natural gas demand is
increasing at phenomenal rates because of its ability
to create cleaner fuel for electrical power. Experts pre-
dict that annual demand is likely to increase to almost
32 TCF in less than a decade. At a consumption rate
(10) of 32 TCF per year, the United States would only have
about a five-year supply of natural gas. Known natural
gas reserves in North America are quickly becoming
exhausted. In fact, in the past thirty years, known sup-
plies have dwindled from almost 300 TCF to around
(15) 150 TCF.
It is no wonder that natural gas has become a con-
troversial and critical topic of discussion among politi-
cians, business leaders,
and consumers. It is apparent
that the United States will need to drastically increase
(20) imports of natural gas to relieve shortages. One way
that economists believe this can be done is by importing
liquid natural gas. Experts predict that liquid natural
gas imports will increase by almost 500 percent in a few
short years. Currently, the country imports very little
(25) liquid natural gas. The process of transporting liquid
natural gas is complicated and expensive. This is the
most obvious reason why America has been reluctant
to choose liquid natural gas over other energy sources.
Converting natural gas into liquid natural gas involves
(30) cooling natural gas as it is collected to −260◦F. This
transforms the gas into a liquid, which is then injected
into a specially designed vessel for transport. When
the liquid natural gas reaches its destination, the liquid
is reheated into its original gaseous state and allowed
(35) to flow into a pipeline. Even though new technology
has considerably decreased transportation costs for liq-
uid natural gas, it is still often uneconomical. This is
especially true for nations with other energy sources.
One of the largest misconceptions about liquid
(40) natural gas is that it is an abundant source of natural
gas. While liquid natural gas imports continue to
increase, the public demand for natural gas increases
at an even higher rate. Even though the United States
has several facilities that can process liquid natural gas,
(45) these facilities are consistently unable to obtain enough
liquid natural gas to operate at their fullest capacity.
Even when liquid natural gas is obtainable, there is a
fear that low natural gas prices in the United States will
make liquid natural gas uneconomical. Most business
(50) leaders and politicians are reluctant to create new facili-
ties to process liquid natural gas because these facilities
are expensive and risky. This limits the capacity to pro-
cess liquid natural gas even if it becomes more readily
available.
(55) The United States also faces competition from
Asia in securing liquid natural gas. Competition for
liquid natural gas will most likely become even more
ferocious as other populous countries like Japan and
China become more desperate for fuel sources. Some
(60) of the more daring politicians and business leaders
believe that building new liquid natural gas facilities
will help companies and consumers take advantage of
future increased liquid natural gas imports. Currently,
Canada is the largest liquid natural gas supplier for
(65) the United States. However, liquid natural gas imports
from Canada will decrease considerably in the next
decade as Canadian consumption increases and sup-
plies of natural gas dwindle. Therefore, consumers and
business leaders should not rely on liquid natural gas
(70) to solve America’s energy needs and consumers should
continue to expect high prices as demand grows and
supplies decline.
Q. According to the passage, current known North American supplies of natural gas are:
a)
sufficient to provide the United States with natural gas for the next thirty years.
b)
down approximately 50 percent from thirty years ago.
c)
decreasing at a rate of 25 percent per year.
d)
extremely difficult to access.
|
|
Ayesha Joshi answered |
The best answer is B. As stated in the passage, “in the past 30 years, known supplies have dwindled from almost 300 TCF to around 150 TCF,” or known supplies have decreased by about 50 percent. Answer choice A is incorrect because the passage states that at predicted rates of consumption, the United States’ natural gas supply would be exhausted in approximately five years.
Answer choice C is incorrect because natural gas provides for roughly 25 percent of America’s energy needs, which has nothing to do with the decrease in supply. Answer choice D is incorrect because the passage states that it is extremely difficult to obtain natural gas from other countries, not from within the US.
Answer choice C is incorrect because natural gas provides for roughly 25 percent of America’s energy needs, which has nothing to do with the decrease in supply. Answer choice D is incorrect because the passage states that it is extremely difficult to obtain natural gas from other countries, not from within the US.
Kate rode her bicycle to visit her grandmother. The trip to Kate’s grandmother’s house was mostly uphill, and took m minutes. On the way home, Kate rode mostly downhill and was able to travel at an average speed twice that of her trip to her grandmother’s house. Which of the following expresses the total number of minutes that Kate bicycled on her entire trip?- a)3m
- b)2m
- c)m + 1/2
- d)3m/2
- e)m/2
Correct answer is option 'D'. Can you explain this answer?
Kate rode her bicycle to visit her grandmother. The trip to Kate’s grandmother’s house was mostly uphill, and took m minutes. On the way home, Kate rode mostly downhill and was able to travel at an average speed twice that of her trip to her grandmother’s house. Which of the following expresses the total number of minutes that Kate bicycled on her entire trip?
a)
3m
b)
2m
c)
m + 1/2
d)
3m/2
e)
m/2
|
|
Orion Classes answered |
The correct answer is d. According to the problem, Kate traveled distance d in m minutes on the way to her grandmother’s house, and she traveled distance d in 1/2 m minutes (because she went twice as fast, it took her half as long) on the way back.
The total number of minutes traveled would be equal to the number of minutes Kate traveled to her grandmother’s house and back:
The total number of minutes traveled would be equal to the number of minutes Kate traveled to her grandmother’s house and back:
Which of the following is equivalent to the inequality 3x - 6 > 6x + 9?- a)x > -5
- b)x < -5
- c)x > -2
- d)x < 3
- e)x > 3
Correct answer is option 'B'. Can you explain this answer?
Which of the following is equivalent to the inequality 3x - 6 > 6x + 9?
a)
x > -5
b)
x < -5
c)
x > -2
d)
x < 3
e)
x > 3
|
|
Orion Classes answered |
Inequalities can be solved like equations, by isolating the variable on one side. Remember, though, that when you multiply an inequality by a negative number, you must reverse the sign:
3x − 6 > 6x + 9
−3x > 15
x < −5
3x − 6 > 6x + 9
−3x > 15
x < −5
In the standard (x, y) coordinate plane, what is the y-intercept of the line given by the equation 3x + 5y = 8?- a)3
- b)5/3
- c)8/5
- d)
- e)-3
Correct answer is option 'C'. Can you explain this answer?
In the standard (x, y) coordinate plane, what is the y-intercept of the line given by the equation 3x + 5y = 8?
a)
3
b)
5/3
c)
8/5
d)
e)
-3
|
|
Ayesha Joshi answered |
To solve, convert the equation of the line to slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept). If 3x + 5y = 8, then:
3x + 5y − 3x = 8 − 3x
Since the equation
is in slope-intercept form, the y-intercept is 8/5.
3x + 5y − 3x = 8 − 3x
Since the equation
is in slope-intercept form, the y-intercept is 8/5.The ratio of the side lengths for a triangle is exactly 15 : 14 : 12. In a second triangle similar to the first, the longest side is 10 inches long. To the nearest tenth of an inch, what is the length of the shortest side of the second triangle?- a)6.4
- b)8.0
- c)9.3
- d)12.0
- e)Cannot be determined from the given information
Correct answer is option 'B'. Can you explain this answer?
The ratio of the side lengths for a triangle is exactly 15 : 14 : 12. In a second triangle similar to the first, the longest side is 10 inches long. To the nearest tenth of an inch, what is the length of the shortest side of the second triangle?
a)
6.4
b)
8.0
c)
9.3
d)
12.0
e)
Cannot be determined from the given information
|
|
Alexander Blake answered |
Understanding the Problem:
The problem provides us with the ratio of side lengths for a triangle (15:14:12) and tells us that the longest side of a similar triangle is 10 inches long. We need to find the length of the shortest side of the second triangle.
Solution:
- We know that the ratio of side lengths of the two similar triangles is the same.
- Let the shortest side of the second triangle be x.
- Using the ratio 15:14:12, we can set up the proportion: 15/14 = 10/x.
- Cross multiplying, we get 15x = 140.
- Solving for x, we find x = 140/15 = 9.3 inches.
Therefore, to the nearest tenth of an inch, the length of the shortest side of the second triangle is 9.3 inches, which corresponds to option B.
The problem provides us with the ratio of side lengths for a triangle (15:14:12) and tells us that the longest side of a similar triangle is 10 inches long. We need to find the length of the shortest side of the second triangle.
Solution:
- We know that the ratio of side lengths of the two similar triangles is the same.
- Let the shortest side of the second triangle be x.
- Using the ratio 15:14:12, we can set up the proportion: 15/14 = 10/x.
- Cross multiplying, we get 15x = 140.
- Solving for x, we find x = 140/15 = 9.3 inches.
Therefore, to the nearest tenth of an inch, the length of the shortest side of the second triangle is 9.3 inches, which corresponds to option B.
Directions: Read the passages and choose the best answer to each question.
Passage
Earth’s habitability is sustained by the sun. Currently, the sun provides enough light and warmth to maintain temperature conditions that can support life on our planet. It is undisputed that the sun is a star. All stars go through phases where they change in size, temperature, and brightness. Two scientists present their views on how long Earth will remain habitable.
Scientist 1
Earth’s sun has another 7 billion years before it enters the Red Giant phase. Currently, Earth could not sustain human life during the Red Giant phase. However, it is important not to believe that human life on Earth will immediately cease to exist as we know it in 7 billion years. Technology has played a huge role in helping humans adapt to conditions on this planet. We humans have 7 billion years to advance technology and find solutions to adapt to the atmospheric changes the Red Giant phase would bring. For instance, creating a large sunshade to protect Earth would allow life to continue even when the sun enters the Red Giant phase. Another solution would be to develop technology that would stir the sun and bring new hydrogen to the sun’s core. This would greatly extend the current phase that our sun is in. There is enough time and incentive to discover ways to thwart the natural progress of nature. Therefore, I believe that human life on this planet will exist indefinitely.
Scientist 2
The sun will enter its Red Giant phase in about 7 billion years. However, new models suggest that Earth has less than a billion years before atmospheric carbon dioxide levels drop to levels that can no longer support photosynthesis.
This would lead to a dramatic temperature increase. Once Earth’s average temperature rises to above 70◦ C, the oceans will evaporate and Earth’s water sources will be almost completely eliminated. One billion years is not long enough for humans to evolve in order to meet large atmospheric and environmental changes, or to develop the technology needed to make Earth habitable. In a billion years, atmospheric changes will eliminate all life on Earth as we know it. Humans need to accept the reality that advanced life flourishes for only a limited period of time. Science fiction— inspired plans to create space colonies or massive sunshades are unrealistic and will not likely be developed in the next billion years.Q. Studies show that Venus may once have had an atmosphere and environment almost identical to Earth’s. Now, Venus has no water on its surface or in its atmosphere.How would Scientist 2 most likely explain the change in Venus’s atmosphere and environment?- a)Venus’s living beings were not able to stir the sun to bring new hydrogen to its core.
- b)Venus’s sun entered its Red Giant phase much earlier in the planet’s development.
- c)The carbon dioxide levels in the atmosphere dropped to levels that no longer supported photosynthesis.
- d)Venus’s location to the sun made it more vulnerable to atmospheric and environmental change
Correct answer is option 'C'. Can you explain this answer?
Directions: Read the passages and choose the best answer to each question.
Passage
Earth’s habitability is sustained by the sun. Currently, the sun provides enough light and warmth to maintain temperature conditions that can support life on our planet. It is undisputed that the sun is a star. All stars go through phases where they change in size, temperature, and brightness. Two scientists present their views on how long Earth will remain habitable.
Scientist 1
Earth’s sun has another 7 billion years before it enters the Red Giant phase. Currently, Earth could not sustain human life during the Red Giant phase. However, it is important not to believe that human life on Earth will immediately cease to exist as we know it in 7 billion years. Technology has played a huge role in helping humans adapt to conditions on this planet. We humans have 7 billion years to advance technology and find solutions to adapt to the atmospheric changes the Red Giant phase would bring. For instance, creating a large sunshade to protect Earth would allow life to continue even when the sun enters the Red Giant phase. Another solution would be to develop technology that would stir the sun and bring new hydrogen to the sun’s core. This would greatly extend the current phase that our sun is in. There is enough time and incentive to discover ways to thwart the natural progress of nature. Therefore, I believe that human life on this planet will exist indefinitely.
Scientist 2
The sun will enter its Red Giant phase in about 7 billion years. However, new models suggest that Earth has less than a billion years before atmospheric carbon dioxide levels drop to levels that can no longer support photosynthesis.
This would lead to a dramatic temperature increase. Once Earth’s average temperature rises to above 70◦ C, the oceans will evaporate and Earth’s water sources will be almost completely eliminated. One billion years is not long enough for humans to evolve in order to meet large atmospheric and environmental changes, or to develop the technology needed to make Earth habitable. In a billion years, atmospheric changes will eliminate all life on Earth as we know it. Humans need to accept the reality that advanced life flourishes for only a limited period of time. Science fiction— inspired plans to create space colonies or massive sunshades are unrealistic and will not likely be developed in the next billion years.
Passage
Earth’s habitability is sustained by the sun. Currently, the sun provides enough light and warmth to maintain temperature conditions that can support life on our planet. It is undisputed that the sun is a star. All stars go through phases where they change in size, temperature, and brightness. Two scientists present their views on how long Earth will remain habitable.
Scientist 1
Earth’s sun has another 7 billion years before it enters the Red Giant phase. Currently, Earth could not sustain human life during the Red Giant phase. However, it is important not to believe that human life on Earth will immediately cease to exist as we know it in 7 billion years. Technology has played a huge role in helping humans adapt to conditions on this planet. We humans have 7 billion years to advance technology and find solutions to adapt to the atmospheric changes the Red Giant phase would bring. For instance, creating a large sunshade to protect Earth would allow life to continue even when the sun enters the Red Giant phase. Another solution would be to develop technology that would stir the sun and bring new hydrogen to the sun’s core. This would greatly extend the current phase that our sun is in. There is enough time and incentive to discover ways to thwart the natural progress of nature. Therefore, I believe that human life on this planet will exist indefinitely.
Scientist 2
The sun will enter its Red Giant phase in about 7 billion years. However, new models suggest that Earth has less than a billion years before atmospheric carbon dioxide levels drop to levels that can no longer support photosynthesis.
This would lead to a dramatic temperature increase. Once Earth’s average temperature rises to above 70◦ C, the oceans will evaporate and Earth’s water sources will be almost completely eliminated. One billion years is not long enough for humans to evolve in order to meet large atmospheric and environmental changes, or to develop the technology needed to make Earth habitable. In a billion years, atmospheric changes will eliminate all life on Earth as we know it. Humans need to accept the reality that advanced life flourishes for only a limited period of time. Science fiction— inspired plans to create space colonies or massive sunshades are unrealistic and will not likely be developed in the next billion years.
Q. Studies show that Venus may once have had an atmosphere and environment almost identical to Earth’s. Now, Venus has no water on its surface or in its atmosphere.How would Scientist 2 most likely explain the change in Venus’s atmosphere and environment?
a)
Venus’s living beings were not able to stir the sun to bring new hydrogen to its core.
b)
Venus’s sun entered its Red Giant phase much earlier in the planet’s development.
c)
The carbon dioxide levels in the atmosphere dropped to levels that no longer supported photosynthesis.
d)
Venus’s location to the sun made it more vulnerable to atmospheric and environmental change
|
|
Orion Classes answered |
The best answer is c. According to Scientist 2, a significant drop in carbon dioxide levels could lead to the end of photosynthesis, which, in turn would result in dramatic temperature increases.
Once the temperature reaches a certain point, the water on the surface and in the atmosphere will evaporate. This information best supports answer choice c.
Once the temperature reaches a certain point, the water on the surface and in the atmosphere will evaporate. This information best supports answer choice c.
The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?- a)(ab)642
- b)(ab)643
- c)a642b
- d)a643b
- e)ab642
Correct answer is option 'E'. Can you explain this answer?
The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?
a)
(ab)642
b)
(ab)643
c)
a642b
d)
a643b
e)
ab642
|
Julian Sullivan answered |
Given information:
- First term of geometric sequence: a
- Second term of geometric sequence: ab
Formula for the nth term of a geometric sequence:
The nth term of a geometric sequence is given by: \(a_n = a \cdot r^{(n-1)}\), where
- a is the first term of the sequence
- r is the common ratio of the sequence
Finding the common ratio (r):
The second term of the sequence is a * r, so we have:
\(ab = a \cdot r\)
\(r = b\)
Calculating the 643rd term:
The 643rd term of the sequence can be written as:
\(a_{643} = a \cdot (b)^{642} = ab^{642}\)
Therefore, the 643rd term of the geometric sequence is \(ab^{642}\), which is option E.
- First term of geometric sequence: a
- Second term of geometric sequence: ab
Formula for the nth term of a geometric sequence:
The nth term of a geometric sequence is given by: \(a_n = a \cdot r^{(n-1)}\), where
- a is the first term of the sequence
- r is the common ratio of the sequence
Finding the common ratio (r):
The second term of the sequence is a * r, so we have:
\(ab = a \cdot r\)
\(r = b\)
Calculating the 643rd term:
The 643rd term of the sequence can be written as:
\(a_{643} = a \cdot (b)^{642} = ab^{642}\)
Therefore, the 643rd term of the geometric sequence is \(ab^{642}\), which is option E.
The hypotenuse of the right triangle LMN shown below is 22 feet long. The cosine of angle L is 3/4. How many feet long is the segment LM?
- a)18.4
- b)16.5
- c)11.0
- d)6.7
- e)4.7
Correct answer is option 'B'. Can you explain this answer?
The hypotenuse of the right triangle LMN shown below is 22 feet long. The cosine of angle L is 3/4. How many feet long is the segment LM?
a)
18.4
b)
16.5
c)
11.0
d)
6.7
e)
4.7
|
|
Ayesha Joshi answered |
The correct answer is b. To find the length of the segment LM in ΔLMN, where the length of the hypotenuse is 22 and the cosine of angle L is 3/4, use the definition of cosine, which is the ratio of the length of the adjacent side to the length of the hypotenuse. In ΔLMN, the cosine of angle L is the ratio of the length of segment LM to the length of the hypotenuse. Substitute the length of the hypotenuse and solve for LM, as follows:
3/4 = LM/22
4 x LM = 22 x 3
LM = 66/4, or 16.5, answer choice G.
3/4 = LM/22
4 x LM = 22 x 3
LM = 66/4, or 16.5, answer choice G.
The lengths of the sides of a triangle are 3 consecutive even integers. If the perimeter of the triangle is 48 inches, what is the length, in inches, of the longest side?- a)12
- b)14
- c)16
- d)18
- e)24
Correct answer is option 'D'. Can you explain this answer?
The lengths of the sides of a triangle are 3 consecutive even integers. If the perimeter of the triangle is 48 inches, what is the length, in inches, of the longest side?
a)
12
b)
14
c)
16
d)
18
e)
24
|
|
Ayesha Joshi answered |
To solve this problem, first remember that perimeter is equal to the distance around an object. Therefore, the perimeter of a triangle is simply the sum of the lengths of its sides. You are given that the lengths of the sides of the triangle are 3 consecutive even integers. Set the first length (the shortest side) equal to x, the second length equal to x + 2, and the third length (the longest side) equal to x + 4. Now, create an equation and solve for x, as follows:
x + (x + 2) + (x + 4) = 48
3x + 6 = 48
x = 14
You now know that the length of the shortest side is 14, so the length of the longest side must be 14 + 4 = 18.
x + (x + 2) + (x + 4) = 48
3x + 6 = 48
x = 14
You now know that the length of the shortest side is 14, so the length of the longest side must be 14 + 4 = 18.
The temperature, t, in degrees Fahrenheit, in a certain city on a certain spring day satisfies the inequality |t - 34| < 40. Which of the following temperatures, in degrees Fahrenheit, is NOT in this range?- a)74
- b)16
- c)0
- d)-6
- e)-8
Correct answer is option 'E'. Can you explain this answer?
The temperature, t, in degrees Fahrenheit, in a certain city on a certain spring day satisfies the inequality |t - 34| < 40. Which of the following temperatures, in degrees Fahrenheit, is NOT in this range?
a)
74
b)
16
c)
0
d)
-6
e)
-8
|
Elizabeth Morgan answered |
To properly complete the inequality, we would need the rest of the information after the inequality symbol. Please provide the complete inequality.
What is the y-coordinate of the point in the standard (x, y) coordinate plane at which the 2 lines y = 3x + 4 and y = 2x + 6 intersect?- a)1
- b)2
- c)4
- d)6
- e)10
Correct answer is option 'E'. Can you explain this answer?
What is the y-coordinate of the point in the standard (x, y) coordinate plane at which the 2 lines y = 3x + 4 and y = 2x + 6 intersect?
a)
1
b)
2
c)
4
d)
6
e)
10
|
|
Orion Classes answered |
You are given that the two lines intersect at a certain point, which means that the lines cross at the same point in the (x, y) coordinate plane, so at that point, the equations of those lines is equal. Set up the following equation and solve for x:
3x + 4 = 2x + 6
x = 2
Now, substitute 2 for x in either equation and find y, as follows:
y = 3x + 4
y = 3(2) + 4
y = 6 + 4 = 10
3x + 4 = 2x + 6
x = 2
Now, substitute 2 for x in either equation and find y, as follows:
y = 3x + 4
y = 3(2) + 4
y = 6 + 4 = 10
If 5 times a number x is subtracted from 15, the result is negative. Which of the following gives the possible value(s) for x?- a)All x < 3
- b)All x > 3
- c)10 only
- d)3 only
- e)0 only
Correct answer is option 'B'. Can you explain this answer?
If 5 times a number x is subtracted from 15, the result is negative. Which of the following gives the possible value(s) for x?
a)
All x < 3
b)
All x > 3
c)
10 only
d)
3 only
e)
0 only
|
|
Orion Classes answered |
To solve this problem, first convert the information in the question into its mathematical equivalent, as follows:
5 times a number x = 5x
Subtracting 5x from 15 yields a negative result, so
15 - 5x < 0.
Now, solve the inequality for x:
15 - 5x < 0
- 5x < -15
Divide both sides by -5 and reverse the inequality to get x > 3.
5 times a number x = 5x
Subtracting 5x from 15 yields a negative result, so
15 - 5x < 0.
Now, solve the inequality for x:
15 - 5x < 0
- 5x < -15
Divide both sides by -5 and reverse the inequality to get x > 3.
The minimum fine for driving in excess of the speed limit is $25. An additional $6 is added to the minimum fine for each mile per hour (mph) in excess of the speed limit. Rachel was issued a $103 fine for speeding in a 55-mph speed limit zone. For driving at what speed, in mph, was Rachel fined?- a)48
- b)52
- c)62
- d)68
- e)78
Correct answer is option 'D'. Can you explain this answer?
The minimum fine for driving in excess of the speed limit is $25. An additional $6 is added to the minimum fine for each mile per hour (mph) in excess of the speed limit. Rachel was issued a $103 fine for speeding in a 55-mph speed limit zone. For driving at what speed, in mph, was Rachel fined?
a)
48
b)
52
c)
62
d)
68
e)
78
|
|
Orion Classes answered |
The correct answer is D. You are given that Rachel paid a total of $103 for her speeding ticket, and that the basic fine for speeding is $25. This means that Rachel was charged an additional $78 (103 – 25).
If the charge for each mile per hour over the speed limit is $6, then Rachel was driving 13 mph over the 55-mph speed limit (78/6 = 13), or 68 mph.
If the charge for each mile per hour over the speed limit is $6, then Rachel was driving 13 mph over the 55-mph speed limit (78/6 = 13), or 68 mph.
Members of the fire department lean a 26-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?- a)12
- b)15
- c)20
- d)22
- e)24
Correct answer is option 'E'. Can you explain this answer?
Members of the fire department lean a 26-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?
a)
12
b)
15
c)
20
d)
22
e)
24
|
William Hunt answered |
Solution:
Given:
- Length of the ladder = 26 feet
- Distance of the base of the ladder from the building = 10 feet
Using the Pythagorean theorem:
- Let the height reached by the ladder on the building be 'h'
- According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.
- Therefore, we have: \( 10^2 + h^2 = 26^2 \)
- \( 100 + h^2 = 676 \)
- \( h^2 = 676 - 100 \)
- \( h^2 = 576 \)
- \( h = \sqrt{576} \)
- \( h = 24 \) feet
Therefore, the ladder reaches 24 feet up the building.
So, the correct answer is option 'E' (24).
Given:
- Length of the ladder = 26 feet
- Distance of the base of the ladder from the building = 10 feet
Using the Pythagorean theorem:
- Let the height reached by the ladder on the building be 'h'
- According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.
- Therefore, we have: \( 10^2 + h^2 = 26^2 \)
- \( 100 + h^2 = 676 \)
- \( h^2 = 676 - 100 \)
- \( h^2 = 576 \)
- \( h = \sqrt{576} \)
- \( h = 24 \) feet
Therefore, the ladder reaches 24 feet up the building.
So, the correct answer is option 'E' (24).
The ratio of the side lengths for a triangle is exactly 7:11:13. In a second triangle similar to the first, the shortest side is 9 inches long. To the nearest tenth of an inch, what is the length of the longest side of the second triangle?- a)14.1
- b)15
- c)16.7
- d)17.3
- e)Cannot be determined from the given information.
Correct answer is option 'C'. Can you explain this answer?
The ratio of the side lengths for a triangle is exactly 7:11:13. In a second triangle similar to the first, the shortest side is 9 inches long. To the nearest tenth of an inch, what is the length of the longest side of the second triangle?
a)
14.1
b)
15
c)
16.7
d)
17.3
e)
Cannot be determined from the given information.
|
|
Orion Classes answered |
The correct answer is C. To find the length of the longest side of the second triangle, use ratios of corresponding sides of each triangle. For example, 9/7 = x/13, where x is the longest side of the second triangle. Cross-multiply to arrive at 117 = 7x.
Divide by 7 to get x = about 16.7.
If you selected answer choice B, the most common incorrect answer, you might have noticed that the difference in lengths of the smallest sides was 2 and then simply added 2 to the longest side of the first triangle to get 15 for the longest side of the second triangle.
Divide by 7 to get x = about 16.7.
If you selected answer choice B, the most common incorrect answer, you might have noticed that the difference in lengths of the smallest sides was 2 and then simply added 2 to the longest side of the first triangle to get 15 for the longest side of the second triangle.
What is the value of b in the solution to the system of equations below?
3a - b = 18
a + 3b = -4- a)-10
- b)-3
- c)3
- d)6
- e)cannot be determined with the given information
Correct answer is option 'B'. Can you explain this answer?
What is the value of b in the solution to the system of equations below?
3a - b = 18
a + 3b = -4
3a - b = 18
a + 3b = -4
a)
-10
b)
-3
c)
3
d)
6
e)
cannot be determined with the given information
|
|
Ayesha Joshi answered |
To solve this problem, add the two equations, or multiples of them, so that cancellation occurs and you can solve for the b variable. If the equation a + 3b = -4 is multiplied by -3, the result is -3a - 9b = 12. The addition of -3a - 9b = 12 to the second equation is shown below:
3a - b = 18
-3a - 9b = 12
-10b = 30
By canceling out the a terms, you can solve for b:
b = 30/-10 = -3.
3a - b = 18
-3a - 9b = 12
-10b = 30
By canceling out the a terms, you can solve for b:
b = 30/-10 = -3.
Directions: Read the passages and choose the best answer to each question.
Passage
Students debate 4 hypotheses regarding the origin of the asteroid belt located between Mars and Jupiter, based on the following observations.
Observations
Observation 1- If all of the asteroids were gathered together into one object, the diameter of the object formed would be less than half the diameter of Earth’s Moon.
Observation 2- The total mass of the asteroid belt is only 4% that of the Moon. One asteroid alone, Ceres, contains 1/3 of the total mass of the asteroid belt.
Observation 3- Asteroids are largely composed of silicate, with some deposits of iron and nickel, a composition proportionately similar to that of the terrestrial planets.
Some asteroids also contain carbon and other elements.
Observation 4- There is a strong orbital resonance (overlapping gravity) with Jupiter in the region of the asteroid belt, which keeps the asteroids in an orbit around the sun.
Observation 5- In reality, asteroids within the belt are very far apart, not clustered together.
Observation 6- Within the early solar system, the velocity of collisions within the region of the asteroid belt was much higher than it is currently.
Hypothesis 1 All of the material that makes up the asteroids in the asteroid belt is similar to that of the material that makes up the terrestrial planets. The velocity of collisions in the early solar system was at one time high enough to break apart planets as they formed. Since one asteroid, Ceres, has 1/3 the total mass of the belt, the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.
Hypothesis 2 The material that composes the asteroids is similar to that of the terrestrial planets. The belt likely formed during the same time that the planets were forming, and due to the strong orbital resonance with the gas giant Jupiter and high velocity collisions, chunks of the material were pulled away from various planets and trapped within orbit. This also explains the varying composition of the asteroids throughout the belt.
Hypothesis 3 The asteroids could not once have been a planet, because there is not enough material within the entire belt to form a planet-sized object. The lack of material, shown by the total diameter and mass of the objects within the belt, is proof that the asteroids are no more than large particles left over from the formation of the terrestrial planets from a single cloud of material.
Hypothesis 4 The asteroids most likely came from somewhere outside the solar system. As they passed through space at varying intervals, they were trapped by the large orbital resonance of Jupiter and formed a “belt.” The vast distances between most of the asteroids in the belt are evidence that they did not come from a singular source, but arrived at different points in the belt’s development.Q. Which of the following assumptions regarding the asteroid belt’s origins is implicit in Hypothesis 1?- a)The asteroid’s composition is identical to that of the Moon.
- b)The asteroids have several different sources of origin.
- c)The asteroid belt is older than Jupiter.
- d)The asteroid belt is younger than Jupiter.
Correct answer is option 'D'. Can you explain this answer?
Directions: Read the passages and choose the best answer to each question.
Passage
Students debate 4 hypotheses regarding the origin of the asteroid belt located between Mars and Jupiter, based on the following observations.
Observations
Observation 1- If all of the asteroids were gathered together into one object, the diameter of the object formed would be less than half the diameter of Earth’s Moon.
Observation 2- The total mass of the asteroid belt is only 4% that of the Moon. One asteroid alone, Ceres, contains 1/3 of the total mass of the asteroid belt.
Observation 3- Asteroids are largely composed of silicate, with some deposits of iron and nickel, a composition proportionately similar to that of the terrestrial planets.
Some asteroids also contain carbon and other elements.
Observation 4- There is a strong orbital resonance (overlapping gravity) with Jupiter in the region of the asteroid belt, which keeps the asteroids in an orbit around the sun.
Observation 5- In reality, asteroids within the belt are very far apart, not clustered together.
Observation 6- Within the early solar system, the velocity of collisions within the region of the asteroid belt was much higher than it is currently.
Hypothesis 1 All of the material that makes up the asteroids in the asteroid belt is similar to that of the material that makes up the terrestrial planets. The velocity of collisions in the early solar system was at one time high enough to break apart planets as they formed. Since one asteroid, Ceres, has 1/3 the total mass of the belt, the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.
Hypothesis 2 The material that composes the asteroids is similar to that of the terrestrial planets. The belt likely formed during the same time that the planets were forming, and due to the strong orbital resonance with the gas giant Jupiter and high velocity collisions, chunks of the material were pulled away from various planets and trapped within orbit. This also explains the varying composition of the asteroids throughout the belt.
Hypothesis 3 The asteroids could not once have been a planet, because there is not enough material within the entire belt to form a planet-sized object. The lack of material, shown by the total diameter and mass of the objects within the belt, is proof that the asteroids are no more than large particles left over from the formation of the terrestrial planets from a single cloud of material.
Hypothesis 4 The asteroids most likely came from somewhere outside the solar system. As they passed through space at varying intervals, they were trapped by the large orbital resonance of Jupiter and formed a “belt.” The vast distances between most of the asteroids in the belt are evidence that they did not come from a singular source, but arrived at different points in the belt’s development.
Passage
Students debate 4 hypotheses regarding the origin of the asteroid belt located between Mars and Jupiter, based on the following observations.
Observations
Observation 1- If all of the asteroids were gathered together into one object, the diameter of the object formed would be less than half the diameter of Earth’s Moon.
Observation 2- The total mass of the asteroid belt is only 4% that of the Moon. One asteroid alone, Ceres, contains 1/3 of the total mass of the asteroid belt.
Observation 3- Asteroids are largely composed of silicate, with some deposits of iron and nickel, a composition proportionately similar to that of the terrestrial planets.
Some asteroids also contain carbon and other elements.
Observation 4- There is a strong orbital resonance (overlapping gravity) with Jupiter in the region of the asteroid belt, which keeps the asteroids in an orbit around the sun.
Observation 5- In reality, asteroids within the belt are very far apart, not clustered together.
Observation 6- Within the early solar system, the velocity of collisions within the region of the asteroid belt was much higher than it is currently.
Hypothesis 1 All of the material that makes up the asteroids in the asteroid belt is similar to that of the material that makes up the terrestrial planets. The velocity of collisions in the early solar system was at one time high enough to break apart planets as they formed. Since one asteroid, Ceres, has 1/3 the total mass of the belt, the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.
Hypothesis 2 The material that composes the asteroids is similar to that of the terrestrial planets. The belt likely formed during the same time that the planets were forming, and due to the strong orbital resonance with the gas giant Jupiter and high velocity collisions, chunks of the material were pulled away from various planets and trapped within orbit. This also explains the varying composition of the asteroids throughout the belt.
Hypothesis 3 The asteroids could not once have been a planet, because there is not enough material within the entire belt to form a planet-sized object. The lack of material, shown by the total diameter and mass of the objects within the belt, is proof that the asteroids are no more than large particles left over from the formation of the terrestrial planets from a single cloud of material.
Hypothesis 4 The asteroids most likely came from somewhere outside the solar system. As they passed through space at varying intervals, they were trapped by the large orbital resonance of Jupiter and formed a “belt.” The vast distances between most of the asteroids in the belt are evidence that they did not come from a singular source, but arrived at different points in the belt’s development.
Q. Which of the following assumptions regarding the asteroid belt’s origins is implicit in Hypothesis 1?
a)
The asteroid’s composition is identical to that of the Moon.
b)
The asteroids have several different sources of origin.
c)
The asteroid belt is older than Jupiter.
d)
The asteroid belt is younger than Jupiter.
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|
Ayesha Joshi answered |
The best answer is d. The best way to answer this question is to plug each statement into the hypothesis to see if it fits with the information presented.
Answer choice a and b can be eliminated, because their topics are not talked about in Hypothesis 1, which says, “the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.” In order for the asteroid to become trapped in an orbit between Mars and Jupiter, both Mars and Jupiter must have already formed. This information supports answer choice d.
Answer choice a and b can be eliminated, because their topics are not talked about in Hypothesis 1, which says, “the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.” In order for the asteroid to become trapped in an orbit between Mars and Jupiter, both Mars and Jupiter must have already formed. This information supports answer choice d.
In the figure showing ΔPQR below, line l is parallel to line m. Which one of the following angles must be congruent to ∠y?
- a)∠1
- b)∠2
- c)∠3
- d)∠4
- e)∠5
Correct answer is option 'D'. Can you explain this answer?
In the figure showing ΔPQR below, line l is parallel to line m. Which one of the following angles must be congruent to ∠y?
a)
∠1
b)
∠2
c)
∠3
d)
∠4
e)
∠5
|
|
Ayesha Joshi answered |
When parallel lines are cut by a transversal (such as segment PR in this problem), “alternate interior angles” are congruent.
In this problem, ∠y and ∠4 are alternate interior angles, and so you can conclude that they are congruent.
In this problem, ∠y and ∠4 are alternate interior angles, and so you can conclude that they are congruent.
Considering all values of α and b for which α + b is at most 9, α is at least 2, and b is at least -2, what is the minimum value of b - α?- a)0
- b)-7
- c)-11
- d)-13
- e)-15
Correct answer is option 'D'. Can you explain this answer?
Considering all values of α and b for which α + b is at most 9, α is at least 2, and b is at least -2, what is the minimum value of b - α?
a)
0
b)
-7
c)
-11
d)
-13
e)
-15
|
|
Ayesha Joshi answered |
The correct answer is d. The first step in solving this problem is to rewrite the information in mathematical terms, as follows:
α + b is at most 9 means that α + b < 9
α is at least 2 means that α > 2
b is at least -2 means that b > -2
Given the information above, the value of b - α will be least when b is at its minimum value of -2. In that case, since α + b < 9, then α + (-2) < 9, and a < 11. Therefore, at its minimum, b - α is equivalent to -2 - 11, or -13.
α + b is at most 9 means that α + b < 9
α is at least 2 means that α > 2
b is at least -2 means that b > -2
Given the information above, the value of b - α will be least when b is at its minimum value of -2. In that case, since α + b < 9, then α + (-2) < 9, and a < 11. Therefore, at its minimum, b - α is equivalent to -2 - 11, or -13.
All sides of a rhombus are the same length, as shown below.
If one diagonal is 12 inches long and the other is 32 inches long, how many inches long, to the nearest hundredth of an inch, is a side of the rhombus?- a)8.54
- b)17.09
- c)34.17
- d)35.78
- e)48.00
Correct answer is option 'B'. Can you explain this answer?
All sides of a rhombus are the same length, as shown below.
If one diagonal is 12 inches long and the other is 32 inches long, how many inches long, to the nearest hundredth of an inch, is a side of the rhombus?
If one diagonal is 12 inches long and the other is 32 inches long, how many inches long, to the nearest hundredth of an inch, is a side of the rhombus?
a)
8.54
b)
17.09
c)
34.17
d)
35.78
e)
48.00
|
|
Orion Classes answered |
The diagonals of a rhombus intersect at their midpoints and form right angles as shown below.
Since the diagonals meet at their midpoints and form right angles, they form a right triangle with legs 12/2 = 6 and 32/2 = 16. To find the length of a side of the rhombus, you can simply use the Pythagorean Theorem and solve where the side of the rhombus, s, is the hypotenuse: s2 = 62 +162 = 292; s is approximately equal to 17.09.
Since the diagonals meet at their midpoints and form right angles, they form a right triangle with legs 12/2 = 6 and 32/2 = 16. To find the length of a side of the rhombus, you can simply use the Pythagorean Theorem and solve where the side of the rhombus, s, is the hypotenuse: s2 = 62 +162 = 292; s is approximately equal to 17.09.
If a system of 2 linear equations in 2 variables has NO solution, and 1 of the equations is graphed in the (x, y) coordinate plane below, which of the following could be the equation of the other line?
- a)y = −2
- b)
- c)y = −2x − 4
- d)
- e)y = 4x − 4
Correct answer is option 'D'. Can you explain this answer?
If a system of 2 linear equations in 2 variables has NO solution, and 1 of the equations is graphed in the (x, y) coordinate plane below, which of the following could be the equation of the other line?
a)
y = −2
b)
c)
y = −2x − 4
d)
e)
y = 4x − 4
|
|
Ayesha Joshi answered |
In order for a system of 2 linear equations to have no solutions, the graphs of the equations must be parallel. Parallel lines have the same slope. To find the equation whose graph is parallel to the line in the figure, you must find the slope of the line between the points (0, −4) and (3, −0). Since slope is rise/run the slope is 4/3. The only equation with the correct slope of 
Let x x y = (x − 2y)2 for all integers x and y. Which of the. following is the value of 5 x (−3)?- a)121
- b)64
- c)41
- d)1
- e)-31
Correct answer is option 'A'. Can you explain this answer?
Let x x y = (x − 2y)2 for all integers x and y. Which of the. following is the value of 5 x (−3)?
a)
121
b)
64
c)
41
d)
1
e)
-31
|
|
Orion Classes answered |
The correct answer is A. You are given that x ◦ y = (x − 2y)2 and are asked to solve 5 x (−3). To do this, simply replace x with 5, and y with −3, as follows:
x x y = (x − 2y)2
5 x (−3) = (5 − 2(−3))2
5 x (−3) = (5 − (−6))2
5 x (−3) = (5 + 6)2
5 x (−3) = (11)2
5 x (−3) = 121
x x y = (x − 2y)2
5 x (−3) = (5 − 2(−3))2
5 x (−3) = (5 − (−6))2
5 x (−3) = (5 + 6)2
5 x (−3) = (11)2
5 x (−3) = 121
Directions: Read the passages and choose the best answer to each question. Passage
Because fish live in water they are exposed to any bacteria that exist in the water. Table 1 lists the habitat choices of 7 species of fish in a local pond and the fish’s ability to combat the effects of the bacteria found in the water.
Figure 1 shows the percent of fish that survive to adulthood in the lab for the 7 species, after exposure to water with bacteria present or exposure to water with the bacteria removed.
Figure 2 shows predicted bacteria levels over time in 4 geographic regions with fish populations.
Q. According to the data in Figure 1, which species showed the greatest difference between the percent of fish that survived to adulthood after exposure to unfiltered water, and the percent of fish that survived to adulthood after exposure to filtered water?- a)Species A
- b)Species C
- c)Species E
- d)Species G
Correct answer is option 'B'. Can you explain this answer?
Directions: Read the passages and choose the best answer to each question.
Passage
Because fish live in water they are exposed to any bacteria that exist in the water. Table 1 lists the habitat choices of 7 species of fish in a local pond and the fish’s ability to combat the effects of the bacteria found in the water.
Figure 1 shows the percent of fish that survive to adulthood in the lab for the 7 species, after exposure to water with bacteria present or exposure to water with the bacteria removed.
Figure 2 shows predicted bacteria levels over time in 4 geographic regions with fish populations.
Because fish live in water they are exposed to any bacteria that exist in the water. Table 1 lists the habitat choices of 7 species of fish in a local pond and the fish’s ability to combat the effects of the bacteria found in the water.
Figure 1 shows the percent of fish that survive to adulthood in the lab for the 7 species, after exposure to water with bacteria present or exposure to water with the bacteria removed.
Figure 2 shows predicted bacteria levels over time in 4 geographic regions with fish populations.
Q. According to the data in Figure 1, which species showed the greatest difference between the percent of fish that survived to adulthood after exposure to unfiltered water, and the percent of fish that survived to adulthood after exposure to filtered water?
a)
Species A
b)
Species C
c)
Species E
d)
Species G
|
|
Ayesha Joshi answered |
To answer this question, you must look at the difference between the light gray and dark gray bars for each species in Figure 1. Answer choice D can be eliminated because the percent of fish that survived with and without exposure to bacteria are almost identical.
Species C has the greatest difference in percent between the two, answer choice B.
Species C has the greatest difference in percent between the two, answer choice B.
The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?- a)5(2a + 9) + 2a = 74
- b)5(2a - 9) + 2a = 74
- c)(4a + 9) + 5a = 74
- d)2(2a + 9) + 5a = 74
- e)2(2a - 9) + 5a = 74
Correct answer is option 'D'. Can you explain this answer?
The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?
a)
5(2a + 9) + 2a = 74
b)
5(2a - 9) + 2a = 74
c)
(4a + 9) + 5a = 74
d)
2(2a + 9) + 5a = 74
e)
2(2a - 9) + 5a = 74
|
|
Ayesha Joshi answered |
To solve this problem, first convert the information given into its mathematical equivalent, as follows (use b to represent the larger number):
The larger of two numbers exceeds twice the smaller number by nine: b = 2a + 9
The sum of twice the larger and five times the smaller number is 74: 2b + 5a = 74
Now, simply substitute the value of b into the second equation in order to solve for a: 2(2a + 9) + 5a = 74
The larger of two numbers exceeds twice the smaller number by nine: b = 2a + 9
The sum of twice the larger and five times the smaller number is 74: 2b + 5a = 74
Now, simply substitute the value of b into the second equation in order to solve for a: 2(2a + 9) + 5a = 74
The area of a rectangular kitchen is 80 square feet. If the length of the floor is 4 feet less than four times the width. what is the width of the floor in feet?- a)4
- b)5
- c)8
- d)16
- e)17
Correct answer is option 'B'. Can you explain this answer?
The area of a rectangular kitchen is 80 square feet. If the length of the floor is 4 feet less than four times the width. what is the width of the floor in feet?
a)
4
b)
5
c)
8
d)
16
e)
17
|
Charlotte Turner answered |
Problem:
The area of a rectangular kitchen is 80 square feet. If the length of the floor is 4 feet less than four times the width, what is the width of the floor in feet?
Solution:
Let's assume the width of the floor is 'x' feet.
Step 1: Find the equation representing the given information.
According to the problem statement, the length of the floor is 4 feet less than four times the width. So, the length can be represented as (4x - 4) feet.
The area of a rectangle is given by the formula: Area = Length * Width.
We are given that the area of the rectangular kitchen is 80 square feet. So, we can write the equation as:
80 = (4x - 4) * x
Step 2: Solve the equation for 'x'.
To solve the equation, we need to simplify and rearrange it.
80 = (4x - 4) * x
80 = 4x^2 - 4x
4x^2 - 4x - 80 = 0
Step 3: Factor or use the quadratic formula to solve the equation.
To factor the quadratic equation, we can first divide the equation by 4 to simplify it:
x^2 - x - 20 = 0
Now, we need to find two numbers whose product is -20 and whose sum is -1 (the coefficient of 'x'). The numbers are -5 and 4.
So, we can factor the equation as:
(x - 5)(x + 4) = 0
Setting each factor equal to zero, we get:
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
Step 4: Determine the valid solution.
Since the width of the floor cannot be negative, we can discard the solution x = -4.
Therefore, the width of the floor is x = 5 feet.
Thus, the correct answer is option 'B' (5).
The area of a rectangular kitchen is 80 square feet. If the length of the floor is 4 feet less than four times the width, what is the width of the floor in feet?
Solution:
Let's assume the width of the floor is 'x' feet.
Step 1: Find the equation representing the given information.
According to the problem statement, the length of the floor is 4 feet less than four times the width. So, the length can be represented as (4x - 4) feet.
The area of a rectangle is given by the formula: Area = Length * Width.
We are given that the area of the rectangular kitchen is 80 square feet. So, we can write the equation as:
80 = (4x - 4) * x
Step 2: Solve the equation for 'x'.
To solve the equation, we need to simplify and rearrange it.
80 = (4x - 4) * x
80 = 4x^2 - 4x
4x^2 - 4x - 80 = 0
Step 3: Factor or use the quadratic formula to solve the equation.
To factor the quadratic equation, we can first divide the equation by 4 to simplify it:
x^2 - x - 20 = 0
Now, we need to find two numbers whose product is -20 and whose sum is -1 (the coefficient of 'x'). The numbers are -5 and 4.
So, we can factor the equation as:
(x - 5)(x + 4) = 0
Setting each factor equal to zero, we get:
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
Step 4: Determine the valid solution.
Since the width of the floor cannot be negative, we can discard the solution x = -4.
Therefore, the width of the floor is x = 5 feet.
Thus, the correct answer is option 'B' (5).
A triangle, ΔABD, is reflected across the line y = x to have the image ΔA'B'D' in the standard (x, y) coordinate plane: thus A reflects to A'. The coordinates of point A are (m, n). What are the coordinates of point A'?- a)(-m, n)
- b)(m, -n)
- c)(-m, -n)
- d)(n, m)
- e)Cannot be determined from the given information.
Correct answer is option 'D'. Can you explain this answer?
A triangle, ΔABD, is reflected across the line y = x to have the image ΔA'B'D' in the standard (x, y) coordinate plane: thus A reflects to A'. The coordinates of point A are (m, n). What are the coordinates of point A'?
a)
(-m, n)
b)
(m, -n)
c)
(-m, -n)
d)
(n, m)
e)
Cannot be determined from the given information.
|
|
Olivia Anderson answered |
In geometry, is a polygon with three sides and three angles. The sum of the three interior angles of a triangle is always 180 degrees.Triangles can be classified based on their side lengths and angles. Types of triangles based on side lengths include equilateral (all sides are equal in length), isosceles (two sides are equal in length), and scalene (no sides are equal in length). Types of triangles based on angles include acute (all angles are less than 90 degrees), right (one angle is 90 degrees), and obtuse (one angle is greater than 90 degrees).Triangles are commonly used in various mathematical problems and real-world applications, such as in architecture, engineering, and navigation.
Which of the following is the set of all real numbers x such that x - 3 < x - 5?- a)The empty set
- b)The set containing only zero
- c)The set containing all nonnegative real numbers
- d)The set containing all negative real numbers
- e)The set containing all real numbers
Correct answer is option 'A'. Can you explain this answer?
Which of the following is the set of all real numbers x such that x - 3 < x - 5?
a)
The empty set
b)
The set containing only zero
c)
The set containing all nonnegative real numbers
d)
The set containing all negative real numbers
e)
The set containing all real numbers
|
Max Long answered |
The question seems to be incomplete. Could you please provide the rest of the equation or inequality involving x?
If 6x − 5 = 3x − 16, then x = ?- a)-11
- b)-7
- c)
- d)11/3
- e)7
Correct answer is option 'C'. Can you explain this answer?
If 6x − 5 = 3x − 16, then x = ?
a)
-11
b)
-7
c)
d)
11/3
e)
7
|
|
Orion Classes answered |
To solve this problem, since the equations equal each other, you must combine like terms and solve for x:
6x − 5 = 3x − 16
6x − 5 − 3x = 3x − 16 − 3x
3x − 5 + 5 = −16 + 5
6x − 5 = 3x − 16
6x − 5 − 3x = 3x − 16 − 3x
3x − 5 + 5 = −16 + 5
Which of the following operations will produce the smallest result when substituted for the blank in the expression: 2/3 ____ − 3?- a)plus
- b)minus
- c)multiplied by
- d)divided by
- e)averaged with
Correct answer is option 'A'. Can you explain this answer?
Which of the following operations will produce the smallest result when substituted for the blank in the expression: 2/3 ____ − 3?
a)
plus
b)
minus
c)
multiplied by
d)
divided by
e)
averaged with
|
|
Ayesha Joshi answered |
To solve, calculate the result for each operation and select the smallest result.
The smallest result is
which was obtained by adding.
The smallest result is
which was obtained by adding.The measure of the vertex angle of an isosceles triangle is (a + 30)°. The base angles each measure (2a - 15)°. What is the measure in degrees of one of the base angles?- a)36°
- b)45°
- c)57°
- d)66°
- e)90°
Correct answer is option 'C'. Can you explain this answer?
The measure of the vertex angle of an isosceles triangle is (a + 30)°. The base angles each measure (2a - 15)°. What is the measure in degrees of one of the base angles?
a)
36°
b)
45°
c)
57°
d)
66°
e)
90°
|
Lucy Jenkins answered |
The measure of the vertex angle of an isosceles triangle is always equal to (180 - 2a) degrees, where "a" is the measure of each base angle.
What is the smallest possible value for the product of 2 integers that differ by 7?- a)8
- b)0
- c)-6
- d)-10
- e)-12
Correct answer is option 'E'. Can you explain this answer?
What is the smallest possible value for the product of 2 integers that differ by 7?
a)
8
b)
0
c)
-6
d)
-10
e)
-12
|
|
Julian Sullivan answered |
Explanation:
Product of Two Integers:
When two integers differ by 7, we can represent them as x and x+7, where x is the smaller integer.
Product Calculation:
The product of these two integers is calculated as:
x * (x + 7)
Finding the Smallest Value:
To find the smallest possible value for the product, we need to determine the smallest value of x.
Calculating the Product:
Let's substitute the smallest value of x into the product formula:
-2 * (-2 + 7) = -2 * 5 = -10
Answer:
Therefore, the smallest possible value for the product of 2 integers that differ by 7 is -10, which corresponds to option 'E'.
Product of Two Integers:
When two integers differ by 7, we can represent them as x and x+7, where x is the smaller integer.
Product Calculation:
The product of these two integers is calculated as:
x * (x + 7)
Finding the Smallest Value:
To find the smallest possible value for the product, we need to determine the smallest value of x.
Calculating the Product:
Let's substitute the smallest value of x into the product formula:
-2 * (-2 + 7) = -2 * 5 = -10
Answer:
Therefore, the smallest possible value for the product of 2 integers that differ by 7 is -10, which corresponds to option 'E'.
Directions: Read the passages and choose the best answer to each question.
Passage
Tenebrio molitor is an arthropod insect which, like 90% of all insects, undergoes the process of complete metamorphosis, meaning that it passes through four life stages: egg, larva, pupa, and adult. In the larval stage the insect is commonly known as a mealworm; as a full adult it is a darkling beetle. Figure 1 shows the four stages of the T . molitor life cycle (x-axis), as well as data for minimum and maximum days spent in each stage of metamorphosis (y-axis) for T. molitor that were raised by students in a lab.
Table 1 includes data recorded for four different colonies of T. molitor raised by students in a lab, including the type of food each colony was given, beginning larval length, duration of time in larval and pupal stages, and final adult length. It was decided that the colonies would be given only one type of food source: either a fruit, a vegetable, or one of two whole grains. Apple was chosen as the fruit, carrot for the vegetable, and oats and wheat for the two whole grains.
Q. A Tenebrio molitor specimen has been in the same metamorphic stage for 12 days. According to Figure 1, in which stage is it possible for the specimen to be?
I. Egg stage
II. Larval stage
III. Pupal stage
IV. Adult stage- a)II only
- b)I and II only
- c)IV only
- d)II and IV only
Correct answer is option 'D'. Can you explain this answer?
Directions: Read the passages and choose the best answer to each question.
Passage
Tenebrio molitor is an arthropod insect which, like 90% of all insects, undergoes the process of complete metamorphosis, meaning that it passes through four life stages: egg, larva, pupa, and adult. In the larval stage the insect is commonly known as a mealworm; as a full adult it is a darkling beetle. Figure 1 shows the four stages of the T . molitor life cycle (x-axis), as well as data for minimum and maximum days spent in each stage of metamorphosis (y-axis) for T. molitor that were raised by students in a lab.
Table 1 includes data recorded for four different colonies of T. molitor raised by students in a lab, including the type of food each colony was given, beginning larval length, duration of time in larval and pupal stages, and final adult length. It was decided that the colonies would be given only one type of food source: either a fruit, a vegetable, or one of two whole grains. Apple was chosen as the fruit, carrot for the vegetable, and oats and wheat for the two whole grains.
Passage
Tenebrio molitor is an arthropod insect which, like 90% of all insects, undergoes the process of complete metamorphosis, meaning that it passes through four life stages: egg, larva, pupa, and adult. In the larval stage the insect is commonly known as a mealworm; as a full adult it is a darkling beetle. Figure 1 shows the four stages of the T . molitor life cycle (x-axis), as well as data for minimum and maximum days spent in each stage of metamorphosis (y-axis) for T. molitor that were raised by students in a lab.
Table 1 includes data recorded for four different colonies of T. molitor raised by students in a lab, including the type of food each colony was given, beginning larval length, duration of time in larval and pupal stages, and final adult length. It was decided that the colonies would be given only one type of food source: either a fruit, a vegetable, or one of two whole grains. Apple was chosen as the fruit, carrot for the vegetable, and oats and wheat for the two whole grains.
Q. A Tenebrio molitor specimen has been in the same metamorphic stage for 12 days. According to Figure 1, in which stage is it possible for the specimen to be?
I. Egg stage
II. Larval stage
III. Pupal stage
IV. Adult stage
I. Egg stage
II. Larval stage
III. Pupal stage
IV. Adult stage
a)
II only
b)
I and II only
c)
IV only
d)
II and IV only
|
|
Ayesha Joshi answered |
The best answer is D. According to Figure 1, the maximum time that the Tenebrio molitor beetle can be in the egg stage is approximately 7.5 days.
The maximum time the beetle can be in the pupa stage is approximately 10 days. Therefore, the beetle specimen cannot be in either of these two stages, so eliminate answer choices A and B. The beetle can be in either the larval or adult stage, answer choice D.
The maximum time the beetle can be in the pupa stage is approximately 10 days. Therefore, the beetle specimen cannot be in either of these two stages, so eliminate answer choices A and B. The beetle can be in either the larval or adult stage, answer choice D.
The speed of a car exceeds twice the speed of a truck by 15 mph. If t is the speed of the truck, which of the following expresses the speed, in miles per hour, of the car?- a)t + 15
- b)t + 30
- c)t - 30
- d)2t + 15
- e)2t + 30
Correct answer is option 'D'. Can you explain this answer?
The speed of a car exceeds twice the speed of a truck by 15 mph. If t is the speed of the truck, which of the following expresses the speed, in miles per hour, of the car?
a)
t + 15
b)
t + 30
c)
t - 30
d)
2t + 15
e)
2t + 30
|
|
Ayesha Joshi answered |
If t is the speed of the truck, then twice the speed of the truck can be written as 2t. If the speed of the car exceeded twice the speed of the truck by 15 mph, the car’s speed was 2t + 15.
On a map, 1/4 inch represents 12 miles. If a road is 66 miles long, what is its length, in inches, on the map?- a)5 1/2
- b)5 1/8
- c)1 1/2
- d)1 3/8
- e)7/8
Correct answer is option 'D'. Can you explain this answer?
On a map, 1/4 inch represents 12 miles. If a road is 66 miles long, what is its length, in inches, on the map?
a)
5 1/2
b)
5 1/8
c)
1 1/2
d)
1 3/8
e)
7/8
|
Sofia Bennett answered |
To solve this question, we can set up a proportion using the given information. We know that 1/4 inch on the map represents 12 miles in reality. Let's set up the proportion:
1/4 inch = 12 miles
We need to find the length of the road in inches on the map, so let's call that length "x". We can set up the proportion as follows:
1/4 inch = 12 miles
x inches 66 miles
To solve for x, we can use cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the denominator of the first fraction by the numerator of the second fraction:
(1/4) * 66 = 12 * x
66/4 = 12x
Now, we can simplify the left side of the equation:
16.5 = 12x
To solve for x, divide both sides of the equation by 12:
16.5/12 = x
x = 1.375
So the length of the road on the map is 1.375 inches.
To find the answer choice that corresponds to this length, we can convert 1.375 into a mixed number or fraction.
1.375 is equivalent to 1 and 375/1000. Simplifying the fraction gives us 1 and 3/8.
Therefore, the length of the road on the map is 1 3/8 inches, which corresponds to option D.
1/4 inch = 12 miles
We need to find the length of the road in inches on the map, so let's call that length "x". We can set up the proportion as follows:
1/4 inch = 12 miles
x inches 66 miles
To solve for x, we can use cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the denominator of the first fraction by the numerator of the second fraction:
(1/4) * 66 = 12 * x
66/4 = 12x
Now, we can simplify the left side of the equation:
16.5 = 12x
To solve for x, divide both sides of the equation by 12:
16.5/12 = x
x = 1.375
So the length of the road on the map is 1.375 inches.
To find the answer choice that corresponds to this length, we can convert 1.375 into a mixed number or fraction.
1.375 is equivalent to 1 and 375/1000. Simplifying the fraction gives us 1 and 3/8.
Therefore, the length of the road on the map is 1 3/8 inches, which corresponds to option D.
A survey is conducted among 700 high-school students to see who their favorite college basketball teams are. If 250 students like the Hawks, 200 students like the Vikings, 50 students like the Bears, and the remaining students like the Warriors, approximately what percentage of the 700 high school students answered that the Warriors were their favorite team? (round to the nearest tenth of a percentage point)- a)14.3%
- b)28.6%
- c)42.9%
- d)56.2%
- e)78.6%
Correct answer is option 'B'. Can you explain this answer?
A survey is conducted among 700 high-school students to see who their favorite college basketball teams are. If 250 students like the Hawks, 200 students like the Vikings, 50 students like the Bears, and the remaining students like the Warriors, approximately what percentage of the 700 high school students answered that the Warriors were their favorite team? (round to the nearest tenth of a percentage point)
a)
14.3%
b)
28.6%
c)
42.9%
d)
56.2%
e)
78.6%
|
|
Orion Classes answered |
The correct answer is B. To find the percentage of the 700 high-school students who answered that the Warriors were their favorite team, divide the number of students who answered Warriors by 700 and multiply by 100%. To find the number of students who answered Warriors, add the total number of students who answered that they liked a different team and subtract that quantity from 700. Thus the percentage of students who answered
approximately 28.6%.
approximately 28.6%.
In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two points on the line defined by the equation y = 4x + 5, then t =?- a)4
- b)5
- c)8
- d)9
- e)11
Correct answer is option 'C'. Can you explain this answer?
In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two points on the line defined by the equation y = 4x + 5, then t =?
a)
4
b)
5
c)
8
d)
9
e)
11
|
|
Ayesha Joshi answered |
To solve this problem, you need to recognize that the slope of the line is equal to 4. In the standard equation for a line, y = mx + b, m is equivalent to the slope. The slope is equal to the change in y-values over the change in x-values; set up the following equation to solve for t:
slope = (s + t) − s/(r + 2) − r
4 = t /2
8 = t
slope = (s + t) − s/(r + 2) − r
4 = t /2
8 = t
A bag contains only quarters, dimes, and nickels. The probability of randomly selecting a quarter is 1/6. The probability of randomly selecting a nickel is 1/4. Which of the following could be the total number of coins in the bag?- a)15
- b)24
- c)30
- d)32
- e)40
Correct answer is option 'B'. Can you explain this answer?
A bag contains only quarters, dimes, and nickels. The probability of randomly selecting a quarter is 1/6. The probability of randomly selecting a nickel is 1/4. Which of the following could be the total number of coins in the bag?
a)
15
b)
24
c)
30
d)
32
e)
40
|
|
Elizabeth Morgan answered |
Problem:
A bag contains only quarters, dimes, and nickels. The probability of randomly selecting a quarter is 1/6. The probability of randomly selecting a nickel is 1/4. Which of the following could be the total number of coins in the bag?
Solution:
To solve this problem, we need to consider the probabilities given and determine the possible number of coins in the bag. Let's analyze each answer option one by one.
a) 15 coins:
If there are 15 coins in the bag, the probability of randomly selecting a quarter would be 1/15, which is not equal to 1/6. Therefore, option (a) is not possible.
b) 24 coins:
If there are 24 coins in the bag, the probability of randomly selecting a quarter would be 1/24, which is not equal to 1/6. However, we can calculate the probability of randomly selecting a nickel. Let's assume there are q quarters, d dimes, and n nickels in the bag. According to the given probabilities, we have the following equations:
q/(q + d + n) = 1/6 (probability of selecting a quarter)
n/(q + d + n) = 1/4 (probability of selecting a nickel)
Simplifying the equations, we get:
q = (q + d + n)/6
n = (q + d + n)/4
Multiplying both equations by 6 and 4 respectively, we get:
6q = q + d + n
4n = q + d + n
Rearranging the equations, we have:
5q - d - n = 0
- q - d + 3n = 0
Solving these equations, we find that q = 12, d = 12, and n = 8. Therefore, it is possible to have 24 coins in the bag. Option (b) is correct.
c) 30 coins:
If there are 30 coins in the bag, the probability of randomly selecting a quarter would be 1/30, which is not equal to 1/6. Therefore, option (c) is not possible.
d) 32 coins:
If there are 32 coins in the bag, the probability of randomly selecting a quarter would be 1/32, which is not equal to 1/6. Therefore, option (d) is not possible.
e) 40 coins:
If there are 40 coins in the bag, the probability of randomly selecting a quarter would be 1/40, which is not equal to 1/6. Therefore, option (e) is not possible.
Conclusion:
Based on the analysis, the only possible number of coins in the bag is 24. Therefore, option (b) is the correct answer.
A bag contains only quarters, dimes, and nickels. The probability of randomly selecting a quarter is 1/6. The probability of randomly selecting a nickel is 1/4. Which of the following could be the total number of coins in the bag?
Solution:
To solve this problem, we need to consider the probabilities given and determine the possible number of coins in the bag. Let's analyze each answer option one by one.
a) 15 coins:
If there are 15 coins in the bag, the probability of randomly selecting a quarter would be 1/15, which is not equal to 1/6. Therefore, option (a) is not possible.
b) 24 coins:
If there are 24 coins in the bag, the probability of randomly selecting a quarter would be 1/24, which is not equal to 1/6. However, we can calculate the probability of randomly selecting a nickel. Let's assume there are q quarters, d dimes, and n nickels in the bag. According to the given probabilities, we have the following equations:
q/(q + d + n) = 1/6 (probability of selecting a quarter)
n/(q + d + n) = 1/4 (probability of selecting a nickel)
Simplifying the equations, we get:
q = (q + d + n)/6
n = (q + d + n)/4
Multiplying both equations by 6 and 4 respectively, we get:
6q = q + d + n
4n = q + d + n
Rearranging the equations, we have:
5q - d - n = 0
- q - d + 3n = 0
Solving these equations, we find that q = 12, d = 12, and n = 8. Therefore, it is possible to have 24 coins in the bag. Option (b) is correct.
c) 30 coins:
If there are 30 coins in the bag, the probability of randomly selecting a quarter would be 1/30, which is not equal to 1/6. Therefore, option (c) is not possible.
d) 32 coins:
If there are 32 coins in the bag, the probability of randomly selecting a quarter would be 1/32, which is not equal to 1/6. Therefore, option (d) is not possible.
e) 40 coins:
If there are 40 coins in the bag, the probability of randomly selecting a quarter would be 1/40, which is not equal to 1/6. Therefore, option (e) is not possible.
Conclusion:
Based on the analysis, the only possible number of coins in the bag is 24. Therefore, option (b) is the correct answer.
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