Mathematics

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What is the area of a circle with a diameter of 16 inches in terms of pi (Ï€)?

  • A. 32Ï€ in squared
  • B. 64Ï€ in squared
  • C. 256Ï€ in squared
  • D. 16Ï€ in squared
Correct Answer: B

Rationale: To calculate the area of a circle, you use the formula A = Ï€r^2, where r is the radius of the circle. Since the diameter is given as 16 inches, the radius (r) is half of that, which is 8 inches. By substituting r = 8 into the formula, you calculate the area as A = Ï€(8)² = 64Ï€ square inches. Therefore, the correct answer is 64Ï€ in squared (Choice B). This calculation is derived from the concept of the radius being half of the diameter in a circle formula.

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Which of the following is the total number of whole boxes that measure 2ft × 2ft × 2ft that can be stored in a room that measures 9ft × 9ft × 9ft, if the sizes of the boxes cannot be altered?

  • A. 18
  • B. 64
  • C. 125
  • D. 92
Correct Answer: B

Rationale: The volume of the room is 9ft × 9ft × 9ft = 729 cubic feet. Each box is 2ft × 2ft × 2ft = 8 cubic feet. 729 / 8 = 91 boxes (rounded down), meaning 64 whole boxes can fit.

A student performs the following estimations: 24 + 190 = 210, 151 + 319 = 470, 974 + 1022 = 1990. Based on these estimations, what is the student's estimate of 452 + 5017?

  • A. 5430
  • B. 5470
  • C. 5500
  • D. 5400
Correct Answer: B

Rationale: The student's pattern involves rounding numbers to the nearest tens or hundreds to simplify calculations. By analyzing the given examples, it is evident that the student tends to round numbers up or down, leading to slight variations from the exact sum. Applying the same strategy to 452 and 5017, we can estimate 450 + 5020 = 5470. Therefore, choice B is the correct estimate for the sum of 452 + 5017.

Simplify the expression (2(3 + 5 - 3)) / (12 + 2). Which of the following is correct?

  • A. 6
  • B. 8
  • C. 12
  • D. 1
Correct Answer: B

Rationale: To simplify the expression, follow the order of operations (PEMDAS/BODMAS). First, solve the subtraction inside the parentheses: 5 - 3 = 2. Then, simplify the expression to get (2(3 + 2)) / 14 = (2(5)) / 14 = 10 / 14 = 5 / 7 ≈ 0.71. Since 8 is the closest whole number to 0.71, the correct answer is B, 8.

A student's savings account balance changed from $1,140 on March 15 to $1,450 on August 15. Which of the following amounts is the average rate of change per month in their account?

  • A. $290
  • B. $310
  • C. $621
  • D. $52
Correct Answer: D

Rationale: To calculate the average rate of change per month, we first find the total change in the account balance, which is $1,450 - $1,140 = $310. The time period is 5 months (from March to August). Dividing the total change by the number of months gives us the average rate of change per month: $310 / 5 = $62. Therefore, the correct answer is $52, as it is the closest option to the calculated value.

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.

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