Mathematics

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Which of the following statements demonstrates a negative correlation between two variables?

  • A. Cars that are older tend to have higher mileage
  • B. Tennis balls that are older tend to have less bounce
  • C. Shorter people tend to weigh less than taller people
  • D. People who play baseball more tend to have more hits
Correct Answer: B

Rationale: A negative correlation exists when one variable increases as the other variable decreases. In the statement 'Tennis balls that are older tend to have less bounce,' as the age of the tennis balls increases, the bounce decreases, establishing a negative correlation. This demonstrates an inverse relationship where increased age is associated with reduced bounce. Hence, choice B showcases a negative correlation between the variables, making it the correct answer.

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There are 80 calories in one serving of salad dressing, and 87.5% of those calories are from fat. One serving of salad dressing is 2 tablespoons. Which of the following amounts is the number of calories from fat per tablespoon of salad dressing?

  • A. 40
  • B. 70
  • C. 35
  • D. 45
Correct Answer: A

Rationale: To find the calories from fat per tablespoon, first, calculate the total calories from fat: 80 calories * 0.875 = 70 calories from fat. Then, divide by the number of tablespoons in a serving (2): 70 / 2 = 35 calories per tablespoon. Therefore, the correct answer is 35 calories, which is closest to 40.

The Americans with Disabilities Act (ADA) requires the slope of a wheelchair ramp to be no greater than 1:12. What is the minimum length of the ramp needed to provide access to a door that is 2.5 feet above the sidewalk?

  • A. 25 feet
  • B. 30 feet
  • C. 32.5 feet
  • D. 14.5 feet
Correct Answer: B

Rationale: To determine the minimum length of the ramp needed to provide access to a door elevated 2.5 feet above the sidewalk, we divide the vertical rise (2.5 feet) by the slope ratio (1:12). This calculation results in 2.5 feet divided by 1/12, which equals 30 feet. Therefore, a 30-foot ramp is required to meet the ADA requirement of a 1:12 slope, ensuring proper wheelchair access to a door elevated 2.5 feet above the sidewalk.

A person weighed themselves at 180 lb. Three months later they weighed themselves at 160 lb. Which of the following is the percent of weight the person lost over 3 months? (Round to the nearest percent.)

  • A. 13%
  • B. 20%
  • C. 10%
  • D. 5%
Correct Answer: B

Rationale: The percent lost is calculated as 180?160180×100?11.1%\frac{180 - 160}{180} \times 100 \approx 11.1\%180180?160?×100?11.1%, which rounds to 11%.

A temperature gauge reads 95F. Which of the following is the correct conversion to degrees Celsius? (Note: C = 5/9[F - 32])

  • A. 113C
  • B. 63C
  • C. 35C
  • D. 21C
Correct Answer: C

Rationale: To convert F to C, use the formula: C = 5/9(95 - 32) = 5/9(63) = 35C.

How many feet are in 6 yards?

  • A. 2 feet
  • B. 9 feet
  • C. 36 feet
  • D. 18 feet
Correct Answer: D

Rationale: To convert yards to feet, remember that 1 yard is equal to 3 feet. To find how many feet are in 6 yards, you multiply 6 by 3, which equals 18 feet. Therefore, the correct answer is 18 feet. Understanding this conversion is essential for accurate measurements in various situations such as construction, crafting, or any activity involving distance calculations.

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