Digital SAT Mock Test - 1 - SAT MCQ

Choice 4 is the best answer because it provides a detail about Elinor that is established in the text. The text indicates that although Elinor is “only nineteen,” she gives good advice and exhibits such a high level of understanding and judgment that she serves as “the counsellor of her mother.” Thus, Elinor is mature beyond her years.
Choice 1 is incorrect because it isn’t supported by the text: although the text says that Elinor advises her mother and often counteracts her mother’s impulses, there’s no mention of Elinor arguing with her mother or failing to change her mother’s mind.
Choice 2 is incorrect because it isn’t supported by the text: although the text mentions that Elinor has strong feelings, it doesn’t indicate that she’s excessively sensitive when it comes to family issues.
Choice 3 is incorrect because it isn’t supported by the text: there’s no mention of what Elinor thinks about her mother and no suggestion that she thinks her mother is a bad role model. Because she’s described as having “an excellent heart,” Elinor likely doesn’t think ill of her mother.

Choice 4 is the best answer because it most accurately states the main idea of the text. According to the text, conceptual artists Gins and Arakawa have designed an apartment building that is disorienting because of several unconventional elements, such as uneven kitchen counters and “a door to nowhere.” The text goes on to suggest that there may be benefits to this kind of design because filmmaker Yamaoka lived in the apartment building for four years and reported health benefits. Thus, although the design is impractical, it may improve the well-being of the apartment building’s residents.
Choice 1 is incorrect. Although the text mentions that Yamaoka lived in the apartment for four years, it doesn’t address how long someone can beneficially live in a home surrounded by fanciful features or whether doing so can be sustained.
Choice 2 is incorrect. Although the text mentions the potential benefits of living in a home with disorienting design features, it doesn’t suggest that this is the most effective method to create a physically stimulating environment.
Choice 3 is incorrect because the text refers to Yamaoka to support the claim that Gins and Arakawa’s apartment building design may be beneficial, but the text doesn’t indicate that Yamaoka supports the designs of other conceptual artists.

Choice C is the best answer. The fact that Henry VIII commissioned a survey of church holdings just before enacting the Dissolution of the Monasteries suggests that he was interested in the potential profits from claiming their assets. This supports the historians’ assertion.
Choice A is incorrect. This choice describes a potential effect of the Dissolution of the Monasteries. The decrease in the proportion of monks in England isn’t relevant to the question of Henry VIII’s motivations. Choice B is incorrect. Details about how the monks were treated during the dissolution don’t address Henry VIII’s motivations for enacting the policy in the first place. That the monks could keep the content of their cells (their rooms) and sell off the timber they’d harvested has no impact on the value of the monasteries’ estates—their land holdings. Choice D is incorrect. This choice mentions one impact that the Dissolution of the Monasteries contributed to, two years after it happened. But it doesn’t help explain why Henry VIII might have wanted to enact the policy in the first place.

Choice 3 is the best answer. If REM sleep were homeostatically regulated in fur seals, then all the seals would compensate with REM levels significantly over baseline after going weeks without REM. We’d also expect the seals to maintain those elevated REM levels for some time. Since seals B and C return very quickly to baseline REM levels, this suggests that REM sleep in fur seals may not be regulated homeostatically.

Choice 1 is incorrect. This doesn’t support the conclusion. If REM sleep were homeostatically regulated in fur seals, then we’d suspect the seals to sustain REM levels well above baseline for a prolonged period in order to compensate for weeks of REM deprivation while in the water. Whether or not there’s a reduction in REM sleep from day 1 to day 2 doesn’t tell us how REM sleep on those days relates to baseline, which is where our focus should be.

Choice 2 is incorrect. The y-axis of this graph doesn’t depict baseline levels of REM sleep, but rather shows REM sleep as a percent of baseline.

Choice 4 is incorrect. The graph doesn’t depict REM sleep while in the water for the seals in the study. Additionally, we’re told fur seals get no REM sleep while in the water, which is significantly different to the values shown in the graph for after they return to land.

Choice 1 is the best answer because it most logically completes the text’s discussion of the evolution of bipedalism in humans. According to the text, one potential explanation for humans walking upright on two legs is that the behavior evolved from an ancestor that mostly stayed on the ground and walked on four limbs, as modern chimpanzees and gorillas do. However, the finding that orangutans, also a relative of humans, sometimes stand on two legs in trees while using their arms to balance and reach for fruits suggests another possible explanation: perhaps a tree-dwelling ancestor of humans began moving on two legs because it offered an advantage, such as access to certain foods.
Choice 2 is incorrect because the finding that modern orangutans (a relative of humans) sometimes stand on two legs in trees doesn’t offer any insight into when either bipedalism or tree-climbing behavior emerged in human ancestors. Additionally, the text indicates that one theory is that bipedalism evolved from a mostly ground-based ancestor that was already practicing knuckle-walking, not that bipedalism and knuckle-walking developed at the same time.
Choice 3 is incorrect because the finding that orangutans (a relative of humans) sometimes stand on two legs in trees doesn’t offer any insight into how difficult it would’ve been to move between the ground and the trees without bipedalism; there’s no suggestion that climbing or moving in trees depends on the ability to walk on two legs rather than four, even if that ability might be helpful in certain circumstances.
Choice 4 is incorrect because the finding that orangutans (a relative of humans) sometimes stand on two legs in trees doesn’t suggest that a knuckle-walking human ancestor could’ve easily moved on two legs in trees. Although the text indicates that bipedalism may have evolved from a human ancestor that mostly stayed on the ground and walked on four limbs, it gives no indication of how easy it would’ve been for such an ancestor to move bipedally in trees.

Choice 3 is the best answer because it effectively uses data from the table to complete the statement, providing an example of how the people of the Navajo Nation can experience different climate conditions depending on where they live. The table shows the average highest temperatures and average lowest temperatures in four locations in the Navajo Nation in July. According to the table, Ramah’s average highest temperature for July was 83°, whereas Cameron’s average highest temperature was much higher, at 99°. This difference illustrates the statement that the people of the Navajo Nation can experience different climate conditions depending on where they live.

Choice 1 is incorrect because it states that Cameron and Teec Nos Pos had the same average lowest temperature (65°) for July, which suggests a similarity in climate conditions in those locations rather than a difference. Choice 2 is incorrect because it misrepresents the data from the table, which shows that the average highest temperature in July for Tuba City was 83°, not 94°, and for Teec Nos Pos it was 94°, not 93°. Even if the cited data accurately reflected the data in the table, the similarity between the two values for average highest temperature would suggest that people in the two locations likely experience similar climate conditions, not different climate conditions.
Choice 4 is incorrect because it states that Ramah and Tuba City had the same average lowest temperature (50°) for July, which suggests a similarity in climate conditions in those locations rather than a difference.

Choice 4 is the best answer. The text asks us to provide examples of several states that saw rapid growth in copper production from the 1890s onward. The graph depicts Arizona, Michigan, and Montana all experiencing such rapid growth during this time period.

Choice 1 is incorrect. The claim is about states experiencing rapid growth in copper production. This statement only discusses one state and does not provide evidence of rapid growth—in fact, it discusses a slow-down of growth.

Choice 2 is incorrect. The claim is about states experiencing rapid growth in copper production, and this statement provides a comparison of production rates between states, rather than an example of rapid growth. Choice 3 is incorrect. The claim is about several states experiencing rapid growth in copper production. This statement only discusses one state and does not provide evidence of growth in copper production.

Choice 4 is the best answer because it states why Wang and his team’s discovery of the Terropterus xiushanensis fossil was significant. The text explains that up until Wang and his team’s discovery, the only fossil evidence of mixopterids came from the paleocontinent of Laurussia. Wang and his team, however, identified fossil remains of a mixopterid species from the paleocontinent Gondwana. Therefore, the team’s discovery was significant because the fossil remains of a mixopterid species were outside of the paleocontinent Laurussia.

Choice 1 is incorrect. Although the text states that Wang and his team identified fossilized remains of a mixopterid species that lived more than 400 million years ago, it doesn’t indicate that mixopterid fossils previously found by scientists dated to a more recent period than that.
Choice 2 is incorrect. Although the text states that mixopterids are related to modern arachnids and horseshoe crabs, it doesn’t suggest that the fossil discovered by Wang and his team confirmed that this relationship is closer than scientists had previously thought.
Choice 3 is incorrect because the team’s fossil established the presence of mixopterids on Gondwana, not on Laurussia. Moreover, the text only discusses the fossil in relation to the geographical distribution of mixopterids, not in relation to their evolution.

Choice 1 is the best answer. The text says that corals produce bright colors to block sunlight and encourage algae to recolonize after “an environmental stressor.” From this, we can infer that corals that produce bright colors have probably been subjected to an environmental stressor.

Choice 2 is incorrect. The text says that corals produce bright colors to block intense sunlight, which protects the light-sensitive algae that keep the coral healthy. In other words, bright colors make the coral’s health less vulnerable to intense sunlight.
Choice 3 is incorrect. The text says that corals produce bright colors to encourage algae to recolonize, not that they have recovered without the assistance of algae colonies.
Choice 4 is incorrect. The text never compares the likelihood of differently colored corals surviving without algae colonies.

Choice 1 is the best answer. The narrator is “embarrassed” about the route he took, which ends up leaving him lost and confused about how to get to his destination for the evening.

Choice 2 is incorrect. This choice doesn’t match the passage. The narrator is embarrassed, rather than fond, and he doesn’t describe the beauty of the place.
Choice 3 is incorrect. This choice doesn’t match the passage. We don’t know from this excerpt whether or not the narrator has visited this part of New York multiple times.
Choice 4 is incorrect. This choice doesn’t match the passage. The narrator doesn’t explain how he overcame being lost in this excerpt.

Choice 1 is the best answer because it presents the quotation that most directly illustrates the claim that Cather portrays Alexandra as having a deep emotional connection to her natural surroundings. This quotation states that the country meant a great deal to Alexandra and then goes on to detail several ways in which her natural surroundings affect her emotionally: the insects sound like “the sweetest music,” she feels as though “her heart were hiding” in the grass “with the quail and the plover,” and near the ridges she feels “the future stirring.”

Choice 2 is incorrect because the quotation doesn’t suggest that Alexandra had a deep emotional connection to her natural surroundings but instead describes how she interacts with the people around her to learn more about crops, poultry, and experiments with clover hay.
Choice 3 is incorrect because the quotation doesn’t suggest that Alexandra has a deep emotional connection to her natural surroundings but instead describes her nighttime departure in a wagon. The quotation says nothing about Alexandra’s emotional state.
Choice 4 is incorrect because the quotation doesn’t convey Alexandra’s deep emotional connection to her natural surroundings; instead, this quotation describes how well she understands the markets and livestock.

• Choice B is the best answer because it most logically completes the text’s discussion of Jacob Lawrence’s artistic process. In this context, “observant” means watchful and perceptive. The text emphasizes that the “close attention” Lawrence paid to “all the details” of his neighborhood allowed him to reflect subtle elements of “the beauty and vitality of the Black experience” in his artwork. This context indicates that being observant of his surroundings was an important part of Lawrence’s work as an artist.
• Choice A is incorrect because the text gives no indication that Lawrence was “skeptical,” or had an attitude of doubt in general or about particular things, let alone that skepticism was important to him as an artist. Rather than indicating that he was skeptical, the text focuses on how Lawrence paid careful attention to everything around him and reflected his observations in his artwork.
• Choice C is incorrect because the text gives no indication that Lawrence was “critical,” which in this context would mean inclined to criticize harshly or unfairly. Rather than indicating that Lawrence found fault in things, the text suggests that he paid careful attention to everything around him and that his artwork reflects this careful attention.
• Choice D is incorrect because the text doesn’t suggest that Lawrence was “confident,” or self-assured. Rather than addressing how Lawrence felt about himself and how that feeling affected his artistic process, the text emphasizes the careful attention Lawrence paid to everything around him— attention that allowed him to capture subtle elements of a particular place and time in his artwork.

• Choice C is the best answer because it presents a finding that, if true, would support the researchers’ claim that archaeologists are unlikely to be replaced by certain computer models. The text explains that although archaeologists hold that categorizing pottery fragments relies on both objective criteria and instinct developed through direct experience, researchers have found that a computer model can categorize the fragments with the same degree of accuracy as the humans can—a finding that has caused some archaeologists to worry that their own work won’t be needed any longer. If survey results indicate that categorizing pottery fragments limits the amount of time archaeologists can dedicate to other important tasks that only human experts can do, that would mean that computer models aren’t able to do all of the important things archaeologists do, thus supporting the researchers’ claim that computer models are unlikely to replace human archaeologists.
• Choice A is incorrect because if it were true that the computer model could categorize the pottery fragments much more quickly than the archaeologists could, that would weaken the researchers’ claim that archaeologists are unlikely to be replaced by certain computer models, since it would demonstrate that the models could conduct the archaeologists’ work not only with equal accuracy but also at a faster pace.
• Choice B is incorrect because the inability of both the computer model and the archaeologists to accurately categorize all of the pottery fragments presented wouldn’t support the researchers’ claim that archaeologists are unlikely to be replaced by certain computer models. The text indicates that some archaeologists are worried because the computer model’s accuracy is equal to their own, and that could be the case whether both were perfectly accurate or were unable to achieve complete accuracy.
• Choice D is incorrect because survey results showing that few archaeologists received special training in properly categorizing pottery fragments wouldn’t support the researchers’ claim that archaeologists are unlikely to be replaced by certain computer models. The amount of special training in categorizing pottery fragments that archaeologists have received has no direct bearing on whether computer models’ success at categorizing fragments will lead to the models replacing the archaeologists.

• Choice C is the best answer. The convention being tested is the use of finite and nonfinite verb forms within a sentence. The nonfinite present participle “forcing” is correctly used to form a participial phrase that supplements the main clause “those...cover,” describing the effects on monkeys of the lack of food sources.
• Choice A is incorrect because the finite present tense verb “forces” can’t be used in this way to supplement the main clause (“those...cover”).
• Choice B is incorrect. While the nonfinite to-infinitive “to force” could be used to form a subordinate clause that supplements the main clause (“those...cover”), to-infinitives conventionally express purpose, and nothing in the sentence suggests that the food sources become unavailable for the purpose of forcing monkeys to hunt marine animals.
• Choice D is incorrect because the finite past tense verb “forced” can’t be used in this way to supplement the main clause (“those...cover”).

• Choice A is the best answer because it most accurately states the main purpose of the text. In the first part of the text, the speaker addresses Paul Laurence Dunbar’s ability to understand people (he has “read the hearts and souls of men” and written of their “joy and mirth”). In the second part of the text, the speaker describes Dunbar’s thorough understanding of the natural world (he has read “the language of the flowers” and engaged with “the little brook”). Thus, the text mainly praises Dunbar for being especially perceptive about people and nature.
• Choice B is incorrect because the speaker describes Dunbar as having read the “hearts and souls of men” and the “language of flowers” to convey Dunbar’s ability to comprehend people and nature, not to suggest that Dunbar has literally read any of these things or has read a great deal about them.
• Choice C is incorrect because the text notes how well Dunbar has made sense of the topics he’s written about but doesn’t address any specific parts of Dunbar’s writing process beyond the suggestion that he used a pen.
• Choice D is incorrect because the text focuses on Dunbar’s understanding of people and nature as expressed in his writing. Nothing in the text suggests that the speaker is recalling a particular afternoon actually spent in nature with Dunbar; even if there had been a shared experience, the text isn’t focused on reminiscing.

• Choice C is the best answer because it most logically completes the text’s discussion of the factors that influence peoples’ decisions to move to a different state. As used in this context, “overshadowed by” means to be surpassed by or caused to seem less important than other factors affecting a move. The text indicates that, according to a US tax policy expert, when people think about an interstate move, state taxes have little effect on their decisions, while employment opportunities, housing availability, and climate have a very strong effect. This context suggests that people consider these other factors to be more important than state taxes.
• Choice A is incorrect because the text indicates that state taxes aren’t as important a consideration as other factors when people are thinking of moving to another state. The context doesn’t suggest that state taxes are “consistent with,” or in agreement with these other factors.
• Choice B is incorrect because it wouldn’t make sense in context to say that state taxes are “representative of,” or typical of, other factors. Taxes aren’t an example of employment opportunities, housing availability, and climate, which are the other factors listed in the text.
• Choice D is incorrect because it wouldn’t make sense in context to say that state taxes are “irrelevant to,” or unconnected or unimportant to other factors. State taxes are irrelevant to peoples’ decisions, not to other factors. In other words, although the text suggests that state taxes may be irrelevant to people considering a move to another state, the other factors mentioned in the text, such as employment opportunities, are unable to have an opinion about state taxes. Furthermore, the text indicates that significant differences in state taxes have almost no effect on peoples’ choices to move, but they aren’t completely unimportant.

• Choice D is the best answer. The sentence uses information from the notes to make a generalization about the kind of study Glickman, Brown, and Song conducted. Specifically, the sentence indicates that the study was of a kind that used statistical methods to address questions of authorship within the field of music.
• Choice A is incorrect because the sentence summarizes the methodology and findings of a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted.
• Choice B is incorrect because the sentence mentions the data and conclusion of a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted.
• Choice C is incorrect because the sentence focuses on a specific conclusion from a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted.

• Choice C is the best answer because it most logically completes the text’s discussion of the kinds of mammals alive during the Mesozoic era. As used in this context, “diverse” means to have a significant amount of variety. The text indicates that some scientists have suggested that Mesozoic mammals can’t be characterized in a certain way, then contrasts the view put forward by those scientists with Luo’s research, which shows that Mesozoic mammals “weren’t all ground-dwelling insectivores” and instead were “various.” This context suggests that some scientists have viewed Mesozoic mammals as being all alike, or not a very diverse group.
• Choice A is incorrect because it wouldn’t make sense to say that some scientists have suggested that Mesozoic mammals weren’t very “predatory,” or that they didn’t prey on other animals, since the text establishes a contrast between what some scientists have suggested and Luo’s research showing that Mesozoic mammals “weren’t all ground-dwelling insectivores.” This context suggests that some scientists have regarded Mesozoic mammals as all being insectivores, or animals that prey on insects, not that some scientists have suggested that Mesozoic mammals didn’t prey on other animals.
• Choice B is incorrect because it wouldn’t make sense to say that some scientists have suggested that Mesozoic mammals weren’t very “obscure,” or concealed or not well known, since the text establishes a contrast between what some scientists have suggested and Luo’s research showing that Mesozoic mammals were a varied group. There’s no contrast between saying that the mammals weren’t concealed or well known and the mammals being varied.
• Choice D is incorrect because it wouldn’t make sense to say that some scientists have suggested that Mesozoic mammals weren’t very “localized,” or confined to a particular area, since the text establishes a contrast between what some scientists have suggested and Luo’s research showing that Mesozoic mammals were a varied group. There’s no contrast between saying that the mammals weren’t localized and the mammals being varied. Although the text mentions mammal fossils found in China, nothing in the discussion of Luo’s research addresses the limits of Mesozoic mammal habitats.

• Choice D is the best answer because it most logically completes the text’s discussion of the Three Sisters intercropping system. As used in this context, “intricate” would mean made up of complexly related elements. The text indicates that in the Three Sisters system, maize, squash, and beans form a “web of relations” in which the crops interact in various ways. The text’s description of these interactions—the bean vines growing on the maize stalks, the squash vines keeping weeds away, and the beans adding nutrients that the maize and squash use—provides context suggesting that this “web of relations” is intricate.
• Choice A is incorrect because describing the relationship among the crops in the Three Sisters system as “indecipherable,” or impossible to comprehend, would not make sense in context. Although the text presents the relationship as complex, the text’s description of the role that each crop plays makes it clear that the relationship is well understood, not indecipherable.
• Choice B is incorrect because the text discusses the practical benefits that each plant in the Three Sisters system provides to other members of the system, showing that the relationship among the crops that make up the system is not “ornamental,” or mainly serving a decorative purpose.
• Choice C is incorrect because describing the relationship among the crops in the Three Sisters system as “obscure,” or unknown or poorly understood, would not make sense in context. Although the text presents the relationship as complex, the text’s description of the role that each crop plays makes it clear that the relationship is well understood, not obscure.

• Choice C is the best answer because it uses data from the graph to effectively complete the example of Eludoyin and his colleagues’ findings concerning female farmers in some regions of Ondo State, Nigeria. The graph presents values for the percentage of Ondo State small-scale farmers who are female, by type of crop and region. The graph shows that of the farmers mainly cultivating nonroot vegetables, approximately 57% in north Ondo and approximately 54% in south Ondo are female; in other words, most of those farmers are female, which exemplifies the idea that female farmers make up the majority (more than half) of the farmers cultivating specific types of crops in some regions.
• Choice A is incorrect because it inaccurately cites data from the graph: the graph shows that in south Ondo, most of the farmers mainly cultivating non-root vegetables are women (approximately 54%), but that only about 35% (less than half) of the farmers mainly cultivating cereals are women.
• Choice B is incorrect because it inaccurately cites data from the graph: the graph shows that more women in central Ondo mainly cultivate cereals than mainly cultivate root crops (approximately 36% and 20%, respectively). Additionally, it doesn’t effectively complete the example because the graph shows that female farmers don’t make up the majority (more than half) of the farmers for any type of crop in central Ondo.
• Choice D is incorrect because it doesn’t effectively complete the example; it simply states that a relatively equal proportion of women across the three regions mainly cultivate cereals, which doesn’t address the value for that proportion and thus doesn’t show that a majority (more than half) of the farmers cultivating certain crops are female.

• Choice A is the best answer. The convention being tested is subject-verb agreement. The singular verb “has enhanced” agrees in number with the singular subject “A Sheaf Gleaned in French Fields,” which is the title of a book of poems.
• Choice B is incorrect because the plural verb “are enhancing” doesn’t agree in number with the singular subject “A Sheaf Gleaned in French Fields.”
• Choice C is incorrect because the plural verb “have enhanced” doesn’t agree in number with the singular subject “A Sheaf Gleaned in French Fields.”
• Choice D is incorrect because the plural verb “enhance” doesn’t agree in number with the singular subject “A Sheaf Gleaned in French Fields.”

Choice B is correct. This equation can be solved using the quadratic formula or factoring. The quadratic formula approach is left as an exercise for students. We will show first how to solve this equation using simple factoring and then will show how to solve it using both the structure of the equation and factoring.
Since 7x = 10x - 3x, the given equation can be rewritten as 2x² + (10x - 3x) - 15 = 0. Regrouping the terms so that the left side of the equation is in the factored form gives (2x - 3)(x + 5) = 0, from which it follows that 2x - 3 = 0 or x + 5 = 0. Thus, the
quadratic equation has solutions 3/2 and - 5. Since r and s are solutions to the quadratic equation and r > s, we can conclude that r = 3/2 and s = -5; therefore,
 
Alternatively: Multiplying the original equation by 2, we can rewrite it in terms of 2x as follows: (2x)² + 7(2x) - 30 = 0. Since the two numbers whose sum is -7 and whose product is -30 are -10 and 3, the equation will be factored as (2x - 3)(2x + 10) - 0, generating 3/2 and -5 as solutions. Since r and s are solutions to the quadratic equation and r > s, we can conclude that r = 3/2 and s = -5; therefore,
Choices A, C, and D are incorrect and could result from calculating the value of expressions given in terms of the solutions r and s, but are not equivalent to the difference r - s of these solutions. For example, 15/2 is the value of -rs, not the value of r - s.

Dividing each side of the equation d = rt by t results in an equation that expresses r in terms of the other variables: r = d/t
Choices B, C, and D are incorrect and may result from algebraic errors when rewriting the given equation.

If shipment A is 30% polyester and x represents the total weight of shipment A, then 0.3x represents the weight of polyester in shipment A. By the same reasoning, 0.5y represents the weight of polyester in shipment B. These two weights have a sum of 130, so 0.3x + 0.5y = 130. 

If x is the number of cookies the PTA sells and y is the number of brownies it sells, the total number of baked items that the PTA sells is x + y. They want this total to be at least 55, so x + y ≥ 55. The money they make from cookies equals the price of each cookie multiplied by the number of cookies they sell, 1.50x, and, by the same reasoning, the money they make from brownies will equal 2.25y. The total amount of money they bring in will equal 1.50x + 2.25y, and they want to make at least $100, so they can represent this goal with the inequality 1.50x + 2.25y ≥ 100. 

The graph indicates that Rebecca started her hike at 10:00 a.m. and stopped for lunch at 11:45 a.m. (The horizontal segment indicates when she is not moving, so that represents her 1-hour lunch break.) This first part of her hike, therefore. took 1 hour 45 minutes, or 105 minutes. The return hike began at 12:45 and lasted until 2:00 p.m., for a time of 1 hour 15 minutes, or 75 minutes. The difference is 105 - 75 = 30 minutes.

The graph of the line y = mx - 4 has a slope of m and a y-intercept of -4. Since m > 0, this slope is positive. We are told that this line intersects the x-axis at an angle of θ, where cos θ = 3/√58. This gives us enough information to sketch a fairly detailed graph:

Notice that this information lets us construct a right triangle that includes θ, in which the adjacent side has length 3 and the hypotenuse has length √58 (remember cos θ = adjacent/hypotenuse). This triangle is particularly handy because it depicts the rise and the run for a portion of the line, which will enable us to find the slope. We simply have to find the rise with the
Pythagorean Theorem: 3² + rise² = (√58)
Simplify: 9 + rise² = 58
Subtract 9: rise² = 49
Take square root: rise = 7
Therefore, the slope of the line is m = rise/run = 7/3 or 2.33

Although solving for y and z isn't hard, it is even simpler to just express (yz)⁶ in terms of y³ and z², using the Laws of Exponentials
Original expression: (yz)⁶
Law of Exponentials #5: y⁶ z⁶
Law of Exponentials #8: (y³)²(z²)³
Substitute y³ = 20 and z² = 10: (20)²(10)³
Substitute 20 = (2)(10): (2)²(10)²(10)³
Combine terms with like bases with Law of Exponents #4: 2²(10)⁵
Simplify: 4 x 10⁵

(A) (6b) (6b) = 36b²
(B) 12b(b) = 12b²
(C) b(√12)²) = (b√12 )b√12) = 12b²
(D) 6b² + 6b² = b²(6 + 6) = 12b²