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Ratio and Proportion: 3 : 10 :: 12 : X
- A. X = 3.6
- B. X = 40
- C. X = 0.27
- D. X = 2.5
Correct Answer: B
Rationale: To solve this proportion, set up the equation: 3/10 = 12/X. Cross-multiply to get 3X = 120. Dividing both sides by 3 gives X = 40. Therefore, the correct answer is B. X equals 40 to maintain the proportional relationship. The ratio 3:10 is equivalent to the ratio 12:40, hence X equals 40.
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In Mr. Garcia's class, two-thirds of the students are boys. If there are 27 students in the class, how many of them are girls?
- A. 1
- B. 9
- C. 12
- D. 20
Correct Answer: B
Rationale: If two-thirds of the students are boys, then one-third must be girls. To find the number of girls, we calculate one-third of the total number of students. Since the total number of students is 27, one-third of 27 is 9. Therefore, there are 9 girls in Mr. Garcia's class.
Convert 0.75 to a ratio in simplest form.
- A. 5:07
- B. 3:04
- C. 7:05
- D. 0.09375
Correct Answer: B
Rationale: To convert 0.75 to a ratio in simplest form, we first need to express 0.75 as a fraction, which is 75/100 or 3/4. The ratio form of 3/4 is 3:4. Therefore, the correct answer is B. Choice A (5:07) is incorrect as it doesn't represent the correct ratio. Choice C (7:05) is also incorrect because it doesn't match the simplified form of 0.75. Choice D (0.09375) is incorrect as it is not in ratio form and does not represent the given decimal value correctly.
Express 0.004 as a ratio.
- A. 3:5
- B. 10:20
- C. 5:250
- D. 20:40
Correct Answer: C
Rationale: To convert 0.004 to a ratio, we first express it as a fraction, which is 4/1000. Simplifying this fraction by dividing the numerator and denominator by their greatest common factor, which is 4, we get 1/250. Therefore, the ratio of 0.004 is 1:250. Remember that to express a decimal as a ratio, you need to convert it to a fraction first, simplify the fraction, and then express it in the form of a ratio.
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.
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.