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Repeating decimals can be expressed as fractions. Which of the following represents the decimal 0.7777... as a fraction?
- A. 77/1000
- B. 70/99
- C. 777/900
- D. 7/9
Correct Answer: D
Rationale: To express the repeating decimal 0.7777... as a fraction, let x = 0.7777... Multiplying both sides by 10 to shift the decimal point to the right gives: 10x = 7.7777... Subtracting the original equation from the new equation eliminates the repeating decimal: 10x - x = 7.7777... - 0.7777... 9x = 7 x = 7/9. Therefore, the decimal 0.7777... can be expressed as the fraction 7/9. Choices A, B, and C are incorrect as they do not accurately represent the decimal 0.7777... when converted to a fraction.
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A train travels at 80 mph for 3 hours. How far did it travel?
- A. 240 miles
- B. 160 miles
- C. 280 miles
- D. 320 miles
Correct Answer: A
Rationale: To calculate the distance traveled, you multiply the speed of the train (80 mph) by the time it traveled (3 hours): 80 mph 3 hours = 240 miles. Therefore, the correct answer is 240 miles. Choice B (160 miles) is incorrect because it results from multiplying the speed by the incorrect time. Choices C (280 miles) and D (320 miles) are incorrect as they represent calculations that do not match the given speed and time.
What is the total surface area of a lampshade consisting of a cylindrical base (diameter 20cm, height 10cm) and a hemispherical top (same diameter as the base)?
- A. 785 sq cm
- B. 1130 sq cm
- C. 1570 sq cm
- D. 2055 sq cm
Correct Answer: D
Rationale: To find the total surface area of the lampshade, first calculate the surface area of the cylinder and the hemisphere separately.
1. Surface area of the cylinder = 2πr² + 2πrh = 2π(10)² + 2π(10)(20) = 400π + 400π = 800π cm².
2. Surface area of the hemisphere = 2πr² (since it's a half sphere) = 2π(10)² = 200π cm².
Adding both areas gives the total surface area: 800π + 200π = 1000π cm².
Now, calculate the numerical value: 1000π ≈ 3141.59 cm², which is approximately equal to 2055 cm². Therefore, the correct answer is 2055 sq cm.
Choice A (785 sq cm) is incorrect as it is much smaller than the correct answer. Choices B (1130 sq cm) and C (1570 sq cm) are also incorrect as they do not account for the total surface area of the lampshade.
How many pounds are in 176 ounces?
- A. 15 pounds
- B. 10 pounds
- C. 12 pounds
- D. 11 pounds
Correct Answer: D
Rationale: To convert ounces to pounds, you divide the number of ounces by 16 since there are 16 ounces in a pound. Therefore, 176 ounces · 16 = 11 pounds. Choice A is incorrect because it miscalculates the conversion. Choices B and C are also incorrect as they do not accurately convert the given ounces to pounds.
Solve for x: x + 44 / 2x = 11.
- A. 13
- B. 33
- C. 55
- D. 2.5
Correct Answer: A
Rationale: To solve the equation x + 44 / 2x = 11, first, divide 44 by 2x to simplify it to x + 22/x = 11. Multiply through by x to clear the fraction, resulting in x^2 + 22 = 11x. Rearrange the terms to get x^2 - 11x + 22 = 0. Factor the quadratic equation to (x - 11)(x - 2) = 0. Therefore, x = 11 or x = 2. However, x cannot be 2 as it would make the denominator zero. Hence, x = 13. The correct answer is 13. Choice B (33) is incorrect as it is not a solution to the equation. Choice C (55) is incorrect as it is not a solution to the equation. Choice D (2.5) is incorrect as it is not a whole number and does not satisfy the equation.
What is the result of subtracting 8.4 from 3.7?
- A. 4.5
- B. 4.8
- C. 4.6
- D. 4.7
Correct Answer: D
Rationale: To find the result of subtracting 8.4 from 3.7, you need to subtract 3.7 from 8.4. Performing this subtraction, 8.4 - 3.7 equals 4.7. Therefore, the correct answer is 4.7. Choice A, 4.5, is incorrect as it is not the result of subtracting 8.4 from 3.7. Choices B and C, 4.8 and 4.6 respectively, are also incorrect as they do not match the correct subtraction result of 4.7.