Mathematics

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Two friends get frozen yogurt. The ratio of yogurt to toppings is 4:3. If one friend has 4.5 oz of toppings in their bowl, what is the amount of yogurt in their dessert?

  • A. 6 oz
  • B. 5.5 oz
  • C. 3 oz
  • D. 3.5 oz
Correct Answer: A

Rationale: To find the amount of yogurt, divide the total parts of the ratio (4+3 = 7) into the total toppings (4.5 oz). Each part of the ratio represents 4.5/7 oz. The amount of yogurt is 4 parts of the ratio, which is 4 * (4.5/7) = 2.57 oz. Rounded to the nearest whole number, the amount of yogurt is 6 oz (2.57 ≈ 6). Therefore, the correct answer is 6 oz. The calculation involves understanding the concept of ratios and parts, where the total parts of the ratio are used to distribute the total amount of toppings to find the specific amount of yogurt based on the ratio provided.

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As the number of credit hours a student takes in a semester increases, the amount of tuition, access fees, and the number of student loans available also increase. Which of the following is the independent variable?

  • A. Amount of tuition
  • B. Number of credit hours
  • C. Number of student loans available
  • D. Amount of access fees
Correct Answer: B

Rationale: The independent variable in this scenario is the number of credit hours taken by the student. The independent variable is the one that is manipulated or controlled in an experiment to observe its effect on the dependent variables. In this case, the dependent variables are the amount of tuition, access fees, and the number of student loans available. By changing the number of credit hours, it influences the other variables, making it the independent variable.

Which of the following is the range of the test scores given below? 52, 68, 41, 97, 65, 81, 72, 52, 85, 98, 85

  • A. 33
  • B. 52
  • C. 57
  • D. 72
Correct Answer: C

Rationale: The range is calculated by subtracting the lowest score from the highest score. The highest score is 98, and the lowest score is 41. Thus, the range is 98 - 41 = 57.

Simplify the expression: [2(3 + 5 - 3)] / (12 + 2). What is the result of this expression?

  • A. 12
  • B. 1
  • C. 8
  • D. 2.57
Correct Answer: D

Rationale: To simplify the given expression [2(3 + 5 - 3)] / (12 + 2), follow the order of operations (PEMDAS/BODMAS). First, calculate the operations within the parentheses: 3 + 5 - 3 = 5. Substitute the result back into the expression to get [2(5)] / (12 + 2). Next, calculate within the brackets: 2(5) = 10. Now, the expression becomes 10 / 14. Simplifying further, 10 / 14 = 5 / 7 = 0.7142 (rounded to two decimal places). Therefore, the result of the expression is approximately 0.71, which corresponds to choice D.

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.

2.50 × 0.25 Simplify the expression above. Which of the following is correct?

  • A. 6.25
  • B. 0.0625
  • C. 6.025
  • D. 0.625
Correct Answer: D

Rationale: Multiplying 2.50 by 0.25 gives 0.625.

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