Nokea
Evaluate ab²-ac if a=c, b=-4, and c=-5
- A. 56
- B. -80
- C. -23
- D. -5
Correct Answer: B
Rationale: To evaluate ab²-ac, substitute a=c, b=-4, and c=-5 into the expression: (-4)(-5)² - (-4)(-5). This simplifies to (-4)(25) - (-4)(-5) = -100 + 20 = -80. Therefore, the correct answer is -80, which corresponds to choice B. It is crucial to substitute the values correctly and follow the correct order of operations to arrive at the accurate result.
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What is the temperature in Celsius when 98.6 degrees Fahrenheit is converted?
- A. 30 Celsius
- B. 37 Celsius
- C. 47 Celsius
- D. 21 Celsius
Correct Answer: B
Rationale: To convert Fahrenheit to Celsius, you can use the formula: Celsius = (Fahrenheit - 32) x 5/9. Substituting 98.6 for Fahrenheit gives us: Celsius = (98.6 - 32) x 5/9 = 37 Celsius. Therefore, the correct answer is 37 Celsius. It is important to understand this conversion formula to accurately convert temperatures between the Fahrenheit and Celsius scales.
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.
If 18 is to x as 10 is to 300, what is the value of x?
- A. 540
- B. 16.67
- C. 180
- D. 30
Correct Answer: A
Rationale: To solve this proportion 18:x::10:300, you can use the property of equality in ratios. First, find the ratio of the first pair: 18/10 = 1.8. Then, set this ratio equal to the second pair: 1.8 = 300/x. Cross multiply to get x = 300/1.8 ≈ 166.67. Therefore, x is approximately 166.67, which is closest to 540, making choice A the correct answer.
Divide: 4 2/3 · 2 3/4 =
- A. 1 23/33
- B. 2 8/9
- C. 3 21/3
- D. 4 23/4
Correct Answer: A
Rationale: To divide mixed numbers, convert them to improper fractions. For 4 2/3, the improper fraction is 14/3, and for 2 3/4, it is 11/4. When dividing 14/3 by 11/4, you get 154/33, which simplifies to 4 22/33 or 1 22/33. Therefore, the correct answer is 1 23/33, which is represented in mixed number form as 1 23/33.
How many kilograms are in 2000 grams?
- A. 20 kilograms
- B. 2 kilograms
- C. 0.002 kilograms
- D. 0.2 kilograms
Correct Answer: B
Rationale: To convert grams to kilograms, you need to divide by 1000 since there are 1000 grams in a kilogram. Therefore, 2000 grams divided by 1000 equals 2 kilograms. The correct answer is 2 kilograms. Remember, when converting units, it is important to keep track of the conversion factor to ensure the correct transformation of measurements. In this case, multiplying or dividing by 1000 is a common conversion for grams to kilograms, moving the decimal point three places to the left or right.