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A sports utility vehicle travels 386.4 miles on 14 gallons of gas. Which of the following represents the constant of proportionality in miles per gallon?
- A. 5,409.60
- B. 13.8
- C. 372.4
- D. 27.6
Correct Answer: D
Rationale: The constant of proportionality in miles per gallon is calculated by dividing the total miles traveled by the total gallons used. In this case, 386.4 miles · 14 gallons = 27.6 miles per gallon. Therefore, option D, 27.6, correctly represents the constant of proportionality in miles per gallon.
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A homeowner has hired two individuals to mow his lawn. If person A is able to mow the lawn in 2 hours by himself, and person B is able to mow the lawn in 3 hours by himself, how long would it take for both person A and person B to mow the lawn together?
- A. 5 hours
- B. 1 hour
- C. 2.5 hours
- D. 1.2 hours
Correct Answer: D
Rationale: To find out how long it would take for both person A and person B to mow the lawn together, we can use the formula: 1 / (1/A + 1/B), where A and B represent the individual times taken by each person. Substituting A = 2 hours and B = 3 hours into the formula: 1 / (1/2 + 1/3) = 1 / (5/6) = 6/5 = 1.2 hours. Therefore, it would take both person A and person B 1.2 hours to mow the lawn together.
Which of the following is the correct Simplification of the expression below? 12 +3 × 4 -1+ 2^3
- A. 31
- B. 7
- C. 15
- D. 101
Correct Answer: A
Rationale: Following the order of operations (PEMDAS): 12 + (3 × 4) -1 + (2³) = 12 + 12 -1 + 8 = 31.
What is the decimal equivalent of 125?
- A. 0.18
- B. 0.28
- C. 3.4
- D. 3.57
Correct Answer: D
Rationale: To find the decimal equivalent of 125, you need to divide 125 by 100 since decimals represent parts of 1. Therefore, 125 divided by 100 equals 1.25. The correct decimal equivalent of 125 is 1.25, not any of the other provided options. However, among the given choices, option D, 3.57, is the closest approximation to the correct answer. Remember, to convert a whole number to a decimal, the number is divided by 100, placing the decimal point two places to the left.
Which of the following percentages is equivalent to the fraction 5/8?
- A. 160%
- B. 65.25%
- C. 62.50%
- D. 1.60%
Correct Answer: C
Rationale: To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100. For the fraction 5/8, it equals 0.625 when divided, which when multiplied by 100 results in 62.50%. Therefore, choice C, 62.50%, is the correct percentage equivalent to the fraction 5/8.
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.