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45:x=35:105. Find the value of X. (Enter the whole number only.)
- A. 100
- B. 135
- C. 75
- D. 175
Correct Answer: B
Rationale: To find the value of x in the proportion 45:x=35:105, we can cross multiply to solve for x.
45 * 105 = 35 * x
x = (45 * 105) / 35
x = 135
Therefore, the correct answer is B: 135.
Explanation: The correct answer is found by cross multiplying in a proportion. Choice A (100) is incorrect as it doesn't satisfy the proportion. Choice C (75) and Choice D (175) are also incorrect as they do not align with the calculated value of x (135) from the given proportion.
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What is the temperature in Fahrenheit when converted from 50°C? (Enter a numeric value only. If rounding is necessary, round to the nearest whole number.)
- A. 150°F
- B. 122°F
- C. 120°F
- D. 145°F
Correct Answer: B
Rationale: To convert Celsius to Fahrenheit, you can use the formula: F = (C — 9/5) + 32. Plugging in 50°C gives us (50 — 9/5) + 32 = 122°F. Therefore, the correct answer is 122°F. When converting temperatures between Celsius and Fahrenheit, it's important to remember the formula and apply it correctly. In this case, by substituting 50°C into the formula, it results in 122°F when rounded to the nearest whole number.
Ratio and Proportion: 100:2 :: 60:X. Find X.
- A. 1.2
- B. 2
- C. 3
- D. 30
Correct Answer: A
Rationale: To find the value of X when the ratio 100:2 is equivalent to 60:X, set up the proportion: 100/2 = 60/X. Cross-multiply to get 100X = 120. Divide by 100 to isolate X, so X = 120/100 = 1.2. Therefore, X equals 1.2, and the correct answer is A. In this scenario, the correct answer is calculated through cross-multiplication of the given ratio and solving for the unknown value. This method is commonly used to solve ratio and proportion problems. It is essential to understand the concept of ratios and proportions to solve mathematical problems efficiently.
Ratio and Proportion: 4:10 :: 5:X
- A. X = 10.5
- B. X = 20
- C. X = 12.5
- D. X = 25
Correct Answer: C
Rationale: To solve for X in the given ratio and proportion, set up the proportion: (4/10) = (5/X). Cross-multiply to get 4X = 50, leading to X = 12.5. So, the correct answer is X = 12.5, making choice C the correct option.
Subtract 3/5 - 2/7 =
- A. 1/2
- B. 3/35
- C. -1/2
- D. 11/35
Correct Answer: D
Rationale: To subtract fractions, you need a common denominator. In this case, the common denominator of 5 and 7 is 35. Rewrite the fractions with the common denominator: 3/5 = 21/35 and 2/7 = 10/35. Subtract: 21/35 - 10/35 = 11/35. Therefore, the correct answer is D, 11/35. Remember, when subtracting fractions, always ensure to find a common denominator to perform the operation accurately.
Express 0.9% as a decimal.
- A. 0.009
- B. 90
- C. 9
- D. 0.09
Correct Answer: A
Rationale: To convert a percentage to a decimal, divide by 100. In this case, 0.9% = 0.9 · 100 = 0.009. Therefore, the correct answer is A) 0.009, which represents 0.9% in decimal form.