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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.
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A student gets 42 questions out of 48 correct on a quiz. What is the percentage of questions that the student answered correctly?
- A. 1.14%
- B. 82.50%
- C. 85.00%
- D. 87.50%
Correct Answer: D
Rationale: To find the percentage of questions answered correctly, divide the number of correct questions by the total number of questions: 42/48 = 0.875. Multiply the result by 100 to express it as a percentage, which gives 87.5%. Therefore, the correct answer is 87.50%. Choice A (1.14%) is incorrect as it does not reflect the correct percentage. Choices B (82.50%) and C (85.00%) are also incorrect as they do not align with the calculation based on the given information.
Adam is painting the outside of a 4-walled shed. The shed is 5 feet wide, 4 feet deep, and 7 feet high. Which of the following is the amount of paint Adam will need for the four walls?
- A. 80 ft²
- B. 126 ft²
- C. 140 ft²
- D. 560 ft²
Correct Answer: B
Rationale: To find the amount of paint needed for the four walls of the shed, calculate the total area of the four walls. The shed has two pairs of identical walls. The area of one pair of walls is 5 feet (width) x 7 feet (height) + 4 feet (depth) x 7 feet (height) = 35 ft² + 28 ft² = 63 ft². Since there are two pairs of walls, the total area for the four walls is 2 x 63 ft² = 126 ft². Therefore, Adam will need 126 ft² of paint for the four walls. Choice A, 80 ft², is incorrect as it does not account for the total surface area of all four walls. Choice C, 140 ft², is incorrect as it overestimates the area required. Choice D, 560 ft², is incorrect as it significantly overestimates the amount of paint needed for the shed.
Which of the following is not a negative value?
- A. (−3)(−1)(2)(−1)
- B. 14 - 7 + (−7)
- C. 7 - 10 + (−8)
- D. −5(−2)(−3)
Correct Answer: B
Rationale: To identify the negative value, simplify each expression. A) simplifies to 6 which is positive. B) simplifies to 0 which is neither positive nor negative. C) simplifies to -11 which is negative. D) simplifies to -30 which is negative. Therefore, only choice B results in a non-negative value, making it the correct answer.
Solve the equation 8x − 6 = 3x + 24. Which of the following is the correct solution?
- A. x = 2.5
- B. x = 3.6
- C. x = 5
- D. x = 6
Correct Answer: D
Rationale: To solve the equation 8x − 6 = 3x + 24, start by adding 6 to both sides: 8x − 6 + 6 = 3x + 24 + 6, which simplifies to 8x = 3x + 30. Next, subtract 3x from both sides to get 5x = 30. Finally, divide both sides by 5 to solve for x: x = 6. Therefore, the correct solution is x = 6. Choices A, B, and C are incorrect because they do not result from the correct algebraic manipulation of the equation.
A dry cleaner charges $3 per shirt, $6 per pair of pants, and an extra $5 per item for mending. Annie drops off 5 shirts and 4 pairs of pants, 2 of which need mending. Assuming the cleaner charges an 8% sales tax, what will be the amount of Annie's total bill?
- A. $45.08
- B. $49.00
- C. $52.92
- D. $88.20
Correct Answer: C
Rationale: To determine the total cost before tax, calculate: 5 shirts $3/shirt + 4 pants $6/pair of pants + 2 items mended $5/item mended = $49. Now, multiply this amount by 1.08 to include the 8% sales tax: $49 1.08 = $52.92. Therefore, Annie's total bill will be $52.92. Choice A, $45.08, is incorrect as it does not include the correct calculation for the total bill. Choice B, $49.00, is wrong because it is the total cost before tax and does not consider the added sales tax. Choice D, $88.20, is incorrect as it does not accurately calculate the total bill including the sales tax.