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Which of the following relationships represents a positive correlation between two variables?
- A. As the amount of water a plant receives increases,
- B. As the number of hours a person exercises decrease
- C. As a student class attendance decreases, the stude
- D. As the number of mile driven increases, the amount
Correct Answer: A
Rationale: A positive correlation means both variables increase together. As the amount of water a plant receives increases, the plant's health typically improves.
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A baker is using a cookie recipe that calls for 2 ? cups of flour to yield 36 cookies. How much flour will the baker need to make 90 cookies using the same recipe?
- A. 5 ? cups
- B. 6 ? cups
- C. 4 ? cups
- D. 10 ? cups
Correct Answer: B
Rationale: To find the amount of flour needed for 90 cookies, first calculate the flour per cookie: (2 ? cups / 36 cookies) = (8/36) = (2/9) cups per cookie. Then multiply by 90: (2/9) × 90 = 20 cups.
What is the value of x in the equation below? 18x - 4 = -10
- A. x = -2 or x = 1
- B. x = -1/3 or x = 2
- C. x = -1/2 or x = 3/2
- D. x = -3/2 or x = 1/2
Correct Answer: B
Rationale: To solve the equation 18x - 4 = -10, first, add 4 to both sides to get 18x = -6. Then, divide by 18 to isolate x, which gives x = -1/3. Therefore, the correct answer is x = -1/3 or x = 2. It's crucial to double-check the solutions in relation to the original equation to ensure accuracy. The error in the original solution is the incorrect value provided for x = -1 which should have been x = -1/3 instead. Hence, the correct solution is x = -1/3 or x = 2.
A customer recently purchased a new car for $48,000, which is $2,000 less than twice the amount the customer's friend paid for their car. What is the amount that the friend paid for their car?
- A. 50,000
- B. 23,000
- C. 25,000
- D. 46,000
Correct Answer: C
Rationale: Let x be the amount the friend paid for their car. According to the information given, 2x - 2000 = 48000. By solving this equation, we find 2x = 50000, x = 25000. Therefore, the friend paid $25,000 for their car. Thus, option C, $25,000, is the correct answer. The customer paid $48,000, which is $2,000 less than twice the amount the friend paid, confirming the calculation.
What is the mean of the test scores listed below? 100, 78, 47, 84, 93, 78
- A. 80
- B. 78
- C. 81
- D. 96
Correct Answer: A
Rationale: To find the mean of a set of numbers, you need to sum all the numbers together and then divide by the total count of numbers. In this case, the sum of the test scores is 100 + 78 + 47 + 84 + 93 + 78 = 480. Since there are 6 test scores in total, you divide the sum by 6 to get the mean. Therefore, the mean = 480 · 6 = 80. Hence, the correct answer is A, which is 80. It represents the average test score among the provided values.
What is the mean of the test scores listed below? 100, 78, 47, 84, 93, 78
- A. 96
- B. 78
- C. 80
- D. 82
Correct Answer: C
Rationale: To find the mean of a set of numbers, you add up all the numbers and then divide by the total count of numbers. In this case, (100 + 78 + 47 + 84 + 93 + 78) / 6 = 480 / 6 = 80. Therefore, the mean of the given test scores is 80. The correct answer is C, 80, as it represents the average of the test scores provided.