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What is the result of multiplying 20.3 by 2? (Enter a numerical value only.)
- A. 40.5
- B. 40.6
- C. 41
- D. 39.5
Correct Answer: B
Rationale: To find the result of multiplying 20.3 by 2, you simply multiply the two numbers: 20.3 x 2 = 40.6. When multiplying decimals, multiply as if they were whole numbers and then adjust the decimal point in the product. In this case, the product is 40.6. Therefore, the correct answer is 40.6, rounded to the nearest tenth.
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Multiply: 39/54 x 6/13, reduced to lowest terms =
- A. 3\7
- B. 2\9
- C. 1\3
- D. 13\27
Correct Answer: C
Rationale: To multiply fractions, multiply the numerators together and the denominators together.
(39/54) x (6/13) = (39 x 6) / (54 x 13) = 234 / 702.
Reduce the fraction to lowest terms by dividing both numerator and denominator by their greatest common divisor, which is 234.
234 ÷ 234 = 1 and 702 ÷ 234 = 3.
So, the final answer is 1/3 (Choice C).
Choices A, B, and D are incorrect because they do not simplify to 1/3. Option A simplifies to 3/7, Option B to 2/9, and Option D to 13/27.
What is the result of subtracting 3.54 from 27?
- A. 24.56
- B. 23.46
- C. 33.3
- D. 24.54
Correct Answer: B
Rationale: To find the result of subtracting 3.54 from 27, you need to subtract the two numbers. 27 - 3.54 equals 23.46. Therefore, the correct answer is B. When subtracting a smaller number from a larger number, the result will be smaller than the original number. In this case, subtracting 3.54 from 27 results in 23.46, not 24.56, 33.3, or 24.54. Therefore, the only correct answer choice is B.
Which number system is commonly used in the United States?
- A. Tertiary
- B. Decimal
- C. Napoleonic
- D. Binary
Correct Answer: B
Rationale: The correct answer is B: Decimal. The decimal number system, based on powers of 10, is the most commonly used number system in the United States and many other parts of the world. It employs 10 digits (0-9) and is used for everyday calculations, commerce, and representation of numbers in various contexts. The use of the decimal system simplifies arithmetic operations and aligns with the way people count using their ten fingers, making it intuitive and widely adopted.
A young adult is running a 24-mile course. If they run the first 6 miles in 1 hour, the second 6 miles in 1.2 hours, the third 6 miles in 1.5 hours, and the fourth 6 miles in 1.6 hours, how long will it take them to complete the run? (Round to the nearest tenth.)
- A. 5.3
- B. 5.6
- C. 5.8
- D. 6
Correct Answer: A
Rationale: To find the total time taken to complete the 24-mile run, add the times for each segment: 1 + 1.2 + 1.5 + 1.6 = 5.3 hours. Therefore, it will take them 5.3 hours to finish the 24-mile course. The correct answer is A, 5.3 hours.
Ratio and Proportion: 125:5::75:X
- A. X=3
- B. X=75
- C. X=125
- D. X=5
Correct Answer: A
Rationale: To find the value of X in the given ratio 125:5::75:X, we need to maintain the same ratio relationship between the numbers. The ratio 125:5 simplifies to 25:1. Similarly, we can simplify 75:X as 15:X. Therefore, X must be such that 15 is to X as 25 is to 1, which means X=3 (15 divided by 5 equals 3). Choice A is correct as X=3 maintains the correct ratio relationship. Choices B, C, and D are incorrect as they do not follow the established ratio pattern.