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An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?
Correct answer is '50'. Can you explain this answer?
Most Upvoted Answer
An online store receives customer satisfaction ratings between 0 and 1...
The correct answer is 50.
The mean of a data set is the sum of the values in the data set divided by the number of values in the data set.
The mean of 75 is obtained by finding the sum of the first 10 ratings and dividing by 10.
Thus, the sum of the first 10 ratings was 750.
In order for the mean of the first 20 ratings to be at least 85, the sum of the first 20 ratings must be at least (85)(20) = 1700.
Therefore, the sum of the next 10 ratings must be at least 1700 − 750 = 950.
The maximum rating is 100, so the maximum possible value of the sum of the 12th through 20th ratings is 9 × 100 = 900.
Therefore, for the store to be able to have an average of at least 85 for the first 20 ratings, the least possible value for the 11th rating is 950 − 900 = 50.
The mean of a data set is the sum of the values in the data set divided by the number of values in the data set.
The mean of 75 is obtained by finding the sum of the first 10 ratings and dividing by 10.
Thus, the sum of the first 10 ratings was 750.
In order for the mean of the first 20 ratings to be at least 85, the sum of the first 20 ratings must be at least (85)(20) = 1700.
Therefore, the sum of the next 10 ratings must be at least 1700 − 750 = 950.
The maximum rating is 100, so the maximum possible value of the sum of the 12th through 20th ratings is 9 × 100 = 900.
Therefore, for the store to be able to have an average of at least 85 for the first 20 ratings, the least possible value for the 11th rating is 950 − 900 = 50.
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An online store receives customer satisfaction ratings between 0 and 1...
Given information:
- The online store receives customer satisfaction ratings between 0 and 100, inclusive.
- The average of the first 10 ratings is 75.
Objective:
- Find the least value the store can receive for the 11th rating and still have an average of at least 85 for the first 20 ratings.
Approach:
To find the least value the store can receive for the 11th rating, we need to maximize the ratings for the first 10 ratings while still maintaining an average of at least 85 for the first 20 ratings.
Step 1: Maximizing the first 10 ratings:
To maximize the first 10 ratings, we can assume that all the ratings are equal to the maximum value of 100. This is because if any rating is less than 100, the average will be lower than if all the ratings were 100.
Step 2: Calculating the sum of the first 10 ratings:
Since all the first 10 ratings are assumed to be 100, the sum of these ratings would be 10 * 100 = 1000.
Step 3: Finding the minimum value for the 11th rating:
To find the minimum value for the 11th rating, we need to calculate the minimum sum of the first 20 ratings that would result in an average of at least 85.
Since we want an average of at least 85 for the first 20 ratings, the minimum sum of the first 20 ratings would be 20 * 85 = 1700.
Step 4: Calculating the maximum sum of the first 11 ratings:
To find the maximum sum of the first 11 ratings, we subtract the sum of the first 10 ratings (1000) from the minimum sum of the first 20 ratings (1700).
Maximum sum of the first 11 ratings = 1700 - 1000 = 700.
Step 5: Finding the minimum value for the 11th rating:
To find the minimum value for the 11th rating, we subtract the sum of the first 10 ratings (1000) from the maximum sum of the first 11 ratings (700).
Minimum value for the 11th rating = 700 - 1000 = -300.
However, since the ratings are between 0 and 100, inclusive, the minimum value for the 11th rating cannot be negative. Therefore, the least value the store can receive for the 11th rating and still have an average of at least 85 for the first 20 ratings is 0.
Conclusion:
The least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings is 0.
- The online store receives customer satisfaction ratings between 0 and 100, inclusive.
- The average of the first 10 ratings is 75.
Objective:
- Find the least value the store can receive for the 11th rating and still have an average of at least 85 for the first 20 ratings.
Approach:
To find the least value the store can receive for the 11th rating, we need to maximize the ratings for the first 10 ratings while still maintaining an average of at least 85 for the first 20 ratings.
Step 1: Maximizing the first 10 ratings:
To maximize the first 10 ratings, we can assume that all the ratings are equal to the maximum value of 100. This is because if any rating is less than 100, the average will be lower than if all the ratings were 100.
Step 2: Calculating the sum of the first 10 ratings:
Since all the first 10 ratings are assumed to be 100, the sum of these ratings would be 10 * 100 = 1000.
Step 3: Finding the minimum value for the 11th rating:
To find the minimum value for the 11th rating, we need to calculate the minimum sum of the first 20 ratings that would result in an average of at least 85.
Since we want an average of at least 85 for the first 20 ratings, the minimum sum of the first 20 ratings would be 20 * 85 = 1700.
Step 4: Calculating the maximum sum of the first 11 ratings:
To find the maximum sum of the first 11 ratings, we subtract the sum of the first 10 ratings (1000) from the minimum sum of the first 20 ratings (1700).
Maximum sum of the first 11 ratings = 1700 - 1000 = 700.
Step 5: Finding the minimum value for the 11th rating:
To find the minimum value for the 11th rating, we subtract the sum of the first 10 ratings (1000) from the maximum sum of the first 11 ratings (700).
Minimum value for the 11th rating = 700 - 1000 = -300.
However, since the ratings are between 0 and 100, inclusive, the minimum value for the 11th rating cannot be negative. Therefore, the least value the store can receive for the 11th rating and still have an average of at least 85 for the first 20 ratings is 0.
Conclusion:
The least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings is 0.
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An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?Correct answer is '50'. Can you explain this answer?
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An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?Correct answer is '50'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?Correct answer is '50'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?Correct answer is '50'. Can you explain this answer?.
An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?Correct answer is '50'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?Correct answer is '50'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?Correct answer is '50'. Can you explain this answer?.
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