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Which of the following percentages is equivalent to 5 1/4?
- A. 525%
- B. 514%
- C. 5.14%
- D. 5.25%
Correct Answer: A
Rationale: To convert 5 1/4 to a percentage, first convert the mixed number to an improper fraction. 5 1/4 is equal to 21/4. To find the equivalent percentage, multiply 21/4 by 100%. This gives 525%, making choice A the correct answer.
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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.
Translate the phrase 'Five less than twice the number' into a mathematical expression.
- A. 5x-2
- B. 2x-5
- C. 2-5x
- D. 5-2x
Correct Answer: B
Rationale: To translate 'Five less than twice the number' into a mathematical expression, you first calculate twice the number (2x) and then subtract 5 from it. This gives you 2x-5. Therefore, choice B, 2x-5, accurately represents the mathematical expression for 'Five less than twice the number.' The phrase 'Five less than' implies subtraction, and 'twice the number' is represented by 2x. Thus, when you subtract 5 from twice the number, the correct expression is 2x-5.
A new professional saw 841 clients during the first year of practice and 1072 clients during the second year of practice. Which of the following represents the approximate percentage increase in client volume?
- A. 127%
- B. 27%
- C. 22%
- D. 78%
Correct Answer: B
Rationale: To calculate the percentage increase in client volume, subtract the initial number of clients from the final number, then divide the result by the initial number and multiply by 100. The increase is 1072 - 841 = 231 clients. The percentage increase is calculated as (231 / 841) * 100 ≈ 27%, which corresponds to option B. Therefore, the correct answer is 27%, representing the percentage increase in client volume from the first year to the second year of practice.
Given x/y - 3x = rw, solve for x in the equation above.
- A. x = rw y + z
- B. x = rw y - z
- C. x = rw(y - z)
- D. None of the Above
Correct Answer: D
Rationale: To solve for x in the equation x/y - 3x = rw, you need to isolate x. This equation involves a term with x on both sides and a division by y, making it challenging to find a direct solution for x. By combining these complexities, there is no single correct expression for x. Therefore, 'None of the Above' is the correct answer as there is no straightforward solution for x in this particular equation.
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.