Mathematics

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What is the best estimate of the number of centimeters (cm) in 1 yard? (Note: 1 yard = 3 feet; 1 foot = 12 inches; 1 inch = 2.54 cm)

  • A. 180 cm
  • B. 72 cm
  • C. 36 cm
  • D. 90 cm
Correct Answer: D

Rationale: To convert 1 yard to centimeters, we need to follow the conversion steps provided: 1 yard = 3 feet, 1 foot = 12 inches, and 1 inch = 2.54 cm. Therefore, 1 yard = 3 feet = 36 inches = 36 * 2.54 cm = 90 cm. Thus, the correct answer is D, which is 90 cm. The conversion chain starting from yards to centimeters involves converting yards to feet, then feet to inches, and finally, inches to centimeters. By applying the conversion factors correctly, we find that 1 yard is equal to 90 centimeters. Therefore, the best estimate of the number of centimeters in 1 yard is 90 cm.

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Which term best describes the data set below: 1, 1, 2, 2, 2, 2, 3, 3, 7, 7, 8, 8, 8, 8, 9, 9?

  • A. Uniform
  • B. Bimodal
  • C. Right-skewed
  • D. Left-skewed
Correct Answer: B

Rationale: A bimodal distribution is characterized by two peaks or distinct values that occur most frequently in the data set. In this specific data set, the values '2' and '8' appear more frequently than other values, indicating two modes, making it a bimodal distribution. The presence of two prominent peaks or modes distinguishes it from a uniform, right-skewed, or left-skewed distribution. In a uniform distribution, all values have similar frequencies, which is not the case here. Right-skewed and left-skewed distributions have a single peak but differ in the tail direction; however, this data set does not exhibit such characteristics.

What is the most likely weight of a pencil?

  • A. 25 mg
  • B. 25 g
  • C. 25 kg
  • D. 25 cm
Correct Answer: B

Rationale: The weight of a pencil is typically measured in grams. Milligrams (mg) and kilograms (kg) are not commonly used units to measure the weight of a pencil. Centimeters (cm) are a unit of length, not weight. Therefore, 25g is the most appropriate measurement for the weight of a pencil.

If a force of 132 Newtons stretched a coil by 0.007 meters, what force would be needed to stretch the coil by 0.1 meter? Round to the nearest tenth.

  • A. 92.4N
  • B. 136.0N
  • C. 188.6N
  • D. 1885.7N
Correct Answer: D

Rationale: To find the force needed to stretch the coil by 0.1 meters, we can use the concept of direct proportionality where the force to stretch remains constant. Setting up a proportion: (132N / 0.007m) = (x / 0.1m). Solving for x, we get x = (132N / 0.007m) * 0.1m = 1885.7N. Therefore, the force required to stretch the coil by 0.1 meters is 1885.7 Newtons.

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.

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.

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