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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.
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A couple dining at a restaurant receives a bill for $38.40. They wish to leave a 15% gratuity. What is the estimated gratuity amount?
- A. $4.00
- B. $5.76
- C. $5.00
- D. $7.00
Correct Answer: B
Rationale: To calculate a 15% gratuity on a $38.40 bill, you multiply $38.40 by 0.15 (15%). This calculation results in $5.76, which is the estimated gratuity amount. Therefore, the correct answer is $5.76 (Choice B). Leaving a 15% gratuity is a common practice to show appreciation for the service provided by the restaurant staff.
If X represents the width of a rectangle and the length is four less than three times the width, which of the following expressions represents the length of the rectangle in terms of X?
- A. 3x - 4
- B. 4x - 3
- C. 4 - 3x
- D. 3 - 4x
Correct Answer: A
Rationale: To determine the expression for the length of the rectangle in terms of X, we need to consider that the length is four less than three times the width. This can be mathematically represented as 3 times X minus 4, which simplifies to 3x - 4 (choice A). Therefore, choice A correctly represents the length of the rectangle in terms of X, making it the correct answer.
A circle has an area of 49Ï€ square inches. What is the circumference of the circle in terms of pi?
- A. 7Ï€ inches
- B. 28Ï€ inches
- C. 14Ï€ inches
- D. 3.5Ï€ inches
Correct Answer: C
Rationale: To find the circumference of a circle with an area of 49π square inches, you first need to find the radius using the area formula A = πr^2. Given the area is 49π, then 49π = πr^2, which simplifies to r^2 = 49, resulting in r = 7. The circumference formula is C = 2πr. Substituting r = 7 gives C = 2π(7) = 14π. Therefore, the correct circumference of the circle in terms of pi is 14π inches.
Simplify the expression [2(3 + 5 × 3)] / (12 ÷ 2)
- A. 12
- B. 1
- C. 8
- D. 6
Correct Answer: D
Rationale: To simplify: Calculate 5 × 3 = 15; then 3 + 15 = 18. So, 2 × 18 = 36. Then, 12 ÷ 2 = 6. Finally, 36 ÷ 6 = 6.
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.