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When a person increases cycling speed, the rate of calories burned, distance traveled, and energy expended also increase. Which of the following is the independent variable?
- A. Speed
- B. Energy
- C. Distance
- D. Calories
Correct Answer: A
Rationale: In the context of this scenario, the independent variable is the factor that is deliberately altered or controlled to observe its impact on other variables. When a person adjusts their cycling speed, it directly influences the rate of calories burned, distance traveled, and energy expended. Speed is the independent variable because it is manipulated to study its effects on the dependent variables - calories burned, distance traveled, and energy expended. Therefore, the correct answer is 'Speed.'
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A new professional saw 841 clients during the first year of practice and 1072 clients during the second year of practice. Which of the following represents the approximate percentage increase in client volume?
- A. 127%
- B. 27%
- C. 22%
- D. 78%
Correct Answer: B
Rationale: To calculate the percentage increase in client volume, subtract the initial number of clients from the final number, then divide the result by the initial number and multiply by 100. The increase is 1072 - 841 = 231 clients. The percentage increase is calculated as (231 / 841) * 100 ≈ 27%, which corresponds to option B. Therefore, the correct answer is 27%, representing the percentage increase in client volume from the first year to the second year of practice.
A baker is using a cookie recipe that calls for 2 1/4 cups of flour to yield 36 cookies. How much flour will the baker need to make 90 cookies using the same recipe?
- A. 6 1/4 cups
- B. 4 3/4 cups
- C. 5 5/8 cups
- D. 10 1/8 cups
Correct Answer: C
Rationale: To determine how much flour is needed for 90 cookies using the same recipe, start by calculating the amount of flour required per cookie in the original recipe. The original recipe uses 2 1/4 cups of flour for 36 cookies. To find the amount per cookie, divide the total flour by the number of cookies: 2 1/4 / 36 = 1/16 cup per cookie. Next, multiply the amount per cookie by the new number of cookies: 1/16 * 90 = 5 5/8 cups. Therefore, the baker will need 5 5/8 cups of flour to make 90 cookies following the same recipe.
A pharmaceutical company's stock price was $50.33 on Monday. On Tuesday, the price increased by $2.35. On Wednesday, the price decreased by $1.07 from Tuesday's price. On Thursday, the price increased by $0.75 from Wednesday's price. What was the final price on Thursday?
- A. $53.43
- B. $54.50
- C. $52.36
- D. $50.85
Correct Answer: C
Rationale: To find the final price on Thursday, start with $50.33 (Monday's price) and apply the changes: +$2.35 (Tuesday's increase), -$1.07 (Wednesday's decrease), and +$0.75 (Thursday's increase). Calculate the total by adding and subtracting the price changes: $50.33 + $2.35 - $1.07 + $0.75 = $52.36. Therefore, the final price on Thursday was $52.36. The correct answer is $52.36, as calculated from the given price changes throughout the week.
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.
A macaroni and cheese recipe calls for 1/2 cup of flour for every 1 1/2 cups of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?
- A. 3 8/15 cups
- B. 2 11/15 cups
- C. 7 1/15 cups
- D. 6 cups
Correct Answer: A
Rationale: To determine the amount of milk needed for 2 cups of flour, we first establish the ratio of flour to milk in the recipe: 1/2 cup of flour requires 1 1/2 cups of milk. Then, we calculate the amount of milk needed for 2 cups of flour by applying this ratio: 2 cups of flour * (1 1/2 cups of milk / 1/2 cup of flour) = 2 * 3 = 6 cups of milk. Therefore, for the bigger batch using 2 cups of flour, the chef would need 6 cups of milk, which is equivalent to 3 8/15 cups.