Mathematics

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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.

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What is the length of the unknown leg of a right triangle that has one leg measuring 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth)

  • A. 40 feet
  • B. 4 feet
  • C. 14.4 feet
  • D. 8.9 feet
Correct Answer: D

Rationale: To find the length of the unknown leg of a right triangle, you can use the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse (12 feet) is equal to the sum of the squares of the other two sides. Let x be the length of the unknown leg. So, 12^2 = 8^2 + x^2. Solving for x gives x = √(12^2 - 8^2) = √(144 - 64) = √80 ≈ 8.9 feet. Therefore, the length of the unknown leg is approximately 8.9 feet.

What is the decimal equivalent of 7/25?

  • A. 0.28
  • B. 3.4
  • C. 0.18
  • D. 3.57
Correct Answer: A

Rationale: To convert a fraction to a decimal, divide the numerator by the denominator. For 7/25, the calculation would be 7 · 25 = 0.28. Therefore, the decimal equivalent of 7/25 is 0.28. This process involves dividing the numerator by the denominator to represent the fraction as a decimal number.

What is the equivalent weight of 50 kg in pounds (1 kg = 2.2 lb)?

  • A. 110 lb
  • B. 220 lb
  • C. 52.2 lb
  • D. 22.7 lb
Correct Answer: A

Rationale: To convert 50 kg to pounds, we need to multiply by the conversion factor 2.2 lb/kg. Therefore, 50 kg * 2.2 lb/kg = 110 lb. The correct answer is A, which is 110 lb. The provided conversion factor (1 kg = 2.2 lb) is used to convert kilograms to pounds. By multiplying 50 kg by the conversion factor, we get the equivalent weight in pounds, which is 110 lb.

In a local community college, there are 800 students enrolled in four allied programs as illustrated in the pie chart. What is the number of students enrolled in the respiratory care program?

  • A. 336
  • B. 168
  • C. 152
  • D. 144
Correct Answer: C

Rationale: To find the number of students in the respiratory care program, you need to calculate 19% of 800, which represents the proportion of students in this program. To do this, multiply 0.19 by 800 to get 152. Therefore, there are 152 students enrolled in the respiratory care program. The pie chart visually represents the distribution of students among the programs, with the respiratory care program accounting for 19% of the total student population.

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.

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