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Which of the following weights is equivalent to 3.193 kilograms?
- A. 3,193 grams
- B. 3,193,000 grams
- C. 319.3 grams
- D. 0.003193 grams
Correct Answer: C
Rationale: To convert kilograms to grams, you multiply by 1000. Therefore, 3.193 kilograms is equivalent to 319.3 grams. When converting from kilograms to grams, the decimal point is moved three places to the right to get the equivalent weight in grams. In this case, 3.193 kilograms, when converted to grams, becomes 319.3 grams.
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Elevation above sea level and temperature are negatively correlated variables. Which of the following statements describes the relationship between the variables?
- A. As elevation decreases, temperature decreases
- B. As elevation decreases, temperature remains the same
- C. As elevation increases, temperature increases
- D. As elevation increases, temperature decreases
Correct Answer: D
Rationale: When two variables are negatively correlated, as one variable increases, the other decreases. In this case, as elevation above sea level increases, the temperature decreases. This relationship is often observed due to changes in atmospheric pressure and temperature with altitude. As altitude rises, the air becomes less dense, leading to lower temperatures. Therefore, the correct statement is 'As elevation increases, temperature decreases.' This relationship is crucial in understanding climate patterns, especially in mountainous regions where temperature changes significantly with elevation.
Which of the following relationships represents a positive correlation between two variables?
- A. As the amount of water a plant receives increases,
- B. As the number of hours a person exercises decrease
- C. As a student class attendance decreases, the stude
- D. As the number of mile driven increases, the amount
Correct Answer: A
Rationale: A positive correlation means both variables increase together. As the amount of water a plant receives increases, the plant's health typically improves.
Of the numbers listed above, which number is the greatest? The numbers are 2/3, -0.7, -1.3, and -4/3.
- A. 2/3 (0.67)
- B. -0.7 (-0.7)
- C. -1.3 (-1.3)
- D. -4/3 (-1.33)
Correct Answer: A
Rationale: To compare these numbers, convert them to a common form. 2/3 is equivalent to approximately 0.67. -0.7, -1.3, and -4/3 are negative numbers. Among these choices, 2/3 (0.67) is the only positive number, making it greater than all the negative numbers (-0.7, -1.3, -4/3). Therefore, 2/3 is the greatest number among the options provided.
What is the value of x in the equation below? 18x - 4 = -10
- A. x = -2 or x = 1
- B. x = -1/3 or x = 2
- C. x = -1/2 or x = 3/2
- D. x = -3/2 or x = 1/2
Correct Answer: B
Rationale: To solve the equation 18x - 4 = -10, first, add 4 to both sides to get 18x = -6. Then, divide by 18 to isolate x, which gives x = -1/3. Therefore, the correct answer is x = -1/3 or x = 2. It's crucial to double-check the solutions in relation to the original equation to ensure accuracy. The error in the original solution is the incorrect value provided for x = -1 which should have been x = -1/3 instead. Hence, the correct solution is x = -1/3 or x = 2.
Simplify the expression [2(3 + 5 × 3)] / (12 ÷ 2)
- A. 12
- B. 1
- C. 8
- D. 6
Correct Answer: D
Rationale: To simplify: Calculate 5 × 3 = 15; then 3 + 15 = 18. So, 2 × 18 = 36. Then, 12 ÷ 2 = 6. Finally, 36 ÷ 6 = 6.