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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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Convert 2/5 to a decimal.
- A. 0.5
- B. 0.25
- C. 0.4
- D. 0.5
Correct Answer: C
Rationale: To convert 2/5 to a decimal, you divide the numerator (2) by the denominator (5): 2 · 5 = 0.4. Therefore, the correct decimal representation of 2/5 is 0.4. Choice A (0.5) is incorrect because it represents 1/2, not 2/5. Choice B (0.25) is incorrect as it represents 1/4, not 2/5. Choice D (0.5) is incorrect as it also represents 1/2, not 2/5.
If a marathon runner burns 2276 calories in 21.4 miles, what is their rate of calories burned per mile?
- A. 107.5
- B. 106.4
- C. 105.6
- D. 109.3
Correct Answer: B
Rationale: To find the rate of calories burned per mile, divide the total calories burned by the total miles run: 2276 · 21.4 ≈ 106.4 calories per mile. This calculation gives the average number of calories burned for each mile of the marathon. Choice A, 107.5, is incorrect as it does not match the precise calculation result. Choices C and D are also incorrect as they are not the accurate rate of calories burned per mile based on the given data.
A circular bandage has a diameter of 6cm. What is the area covered by the bandage (area of a circle = πr^2)?
- A. 9π cm^2
- B. 18π cm^2
- C. 27π cm^2
- D. 36π cm^2
Correct Answer: C
Rationale: Rationale:
- The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
- The diameter of the circular bandage is 6 cm, so the radius (r) is half of the diameter, which is 6/2 = 3 cm.
- Substitute the radius (r = 3 cm) into the formula for the area of a circle: A = π(3)^2 = 9π cm^2.
- Therefore, the area covered by the bandage is 9π cm^2.
What is the probability of rolling an odd number on a six-sided die?
- A. 50%
- B. 66.70%
- C. 33.30%
- D. 25%
Correct Answer: A
Rationale: A six-sided die has three odd numbers (1, 3, 5) out of six possible outcomes. To calculate the probability, divide the number of favorable outcomes (odd numbers) by the total number of outcomes: 3/6 = 0.5 or 50%. Therefore, the probability of rolling an odd number on a six-sided die is 50%. Choice A is correct. Choice B (66.70%) is incorrect as it does not represent the correct probability of rolling an odd number on a six-sided die. Choice C (33.30%) is incorrect as it represents the probability of rolling an even number. Choice D (25%) is incorrect as it does not reflect the correct probability of rolling an odd number on a six-sided die.
A die is rolled. What is the probability of getting 5?
- A. 16.67%
- B. 20%
- C. 50%
- D. 83.33%
Correct Answer: A
Rationale: The correct answer is A: 16.67%. When rolling a standard 6-sided die, each face has an equal probability of 1/6. Therefore, the probability of rolling a 5 specifically is 1/6, which is approximately 16.67% when converted to a percentage. Choices B, C, and D are incorrect because they do not reflect the correct probability of rolling a 5 on a standard die.