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After taxes, a worker earned $15,036 in 7 months. What is the amount the worker earned in 2 months?
- A. $2,148
- B. $4,296
- C. $6,444
- D. $8,592
Correct Answer: B
Rationale: To find the amount earned in 2 months, set up a proportion using two ratios relating amount earned to months: (15,036/7) = (x /2). Cross-multiply and solve for x: 7x = 30,072, x = 4,296. Therefore, the worker earned $4,296 in 2 months. Choice A, $2,148, is incorrect as it is half of the correct answer. Choices C and D, $6,444 and $8,592, are incorrect as they do not correspond to the calculated proportion.
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What is the area of a triangle with a base of 10 cm and a height of 7 cm?
- A. 70 cm²
- B. 35 cm²
- C. 140 cm²
- D. 100 cm²
Correct Answer: B
Rationale: To find the area of a triangle, you use the formula A = 1/2 base height. Substituting the given values: A = 1/2 10 cm 7 cm = 35 cm². Therefore, the correct answer is B. Choice A (70 cm²) is incorrect as it seems to be the product of the base and height rather than the area formula. Choice C (140 cm²) is incorrect as it appears to be twice the correct answer, possibly a result of a miscalculation. Choice D (100 cm²) is incorrect as it does not reflect the correct calculation based on the given base and height values.
Which statement about the following set is true? {60, 5, 18, 20, 37, 37, 11, 90, 72}
- A. The median and the mean are equal.
- B. The mean is less than the mode.
- C. The mode is greater than the median.
- D. The median is less than the mean.
Correct Answer: D
Rationale: To find the median, we first need to arrange the set in ascending order: {5, 11, 18, 20, 37, 37, 60, 72, 90}. The median is the middle value, which is 37 in this case. The mean is calculated by adding all numbers and dividing by the total count, which gives a mean greater than 37. Therefore, the statement that the median is less than the mean is correct. Choice A is incorrect because the median and mean are not equal in this set. Choice B is incorrect as the mean is greater than the mode in this set. Choice C is incorrect as the mode is 37, which is equal to the median, not greater.
What is the result of (4.71 10^3) - (2.98 10^2)? Which of the following is the correct simplified expression?
- A. 1.73 10
- B. 4.412 10^2
- C. 1.73 10^3
- D. 4.412 10^3
Correct Answer: D
Rationale: The correct answer is D: 4.412 10^3. To simplify the expression, rewrite 4.71 10^3 as 47.1 10^2. Subtract the values in front of 10^2: 47.1 - 2.98 = 44.12. Rewriting this gives 44.12 10^2 = 4.412 10^3. Choice A is incorrect as it does not account for the correct subtraction result. Choice B is incorrect as it does not correctly simplify the expression. Choice C is incorrect as it provides an incorrect power of 10 in the simplified expression.
Simplify the expression. Which of the following is the value of x? (5(4x - 5) = (3/2)(2x - 6))
- A. −(2/7)
- B. −(4/17)
- C. (16/17)
- D. (8/7)
Correct Answer: C
Rationale: To solve the given proportion 5(4x - 5) = (3/2)(2x - 6), first distribute to get 20x - 25 = 3x - 9. Then, simplify the linear equation by isolating x: 20x - 3x = 25 - 9, which leads to 17x = 16. Finally, solving for x gives x = 16/17. Choice A is incorrect as it does not match the calculated value of x. Choice B is incorrect as it does not correspond to the correct solution for x. Choice D is incorrect as it does not align with the accurate value of x obtained from solving the equation.
Simplify the expression. What is the value of x? (5/4)x = 20
- A. 8
- B. 16
- C. 24
- D. 32
Correct Answer: D
Rationale: To solve for x, multiply both sides by the reciprocal of 5/4 to isolate x. (4/5)(5/4)x = (4/5)20; x = 16. Therefore, the correct answer is 32. Choice A (8), Choice B (16), and Choice C (24) are incorrect as they do not represent the correct value of x obtained after correctly simplifying the expression.