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Which of the following options correctly orders the numbers below from least to greatest? 235.971, 145.884, -271.906, -193.823
- A. -271.906, -193.823, 145.884, 235.971
- B. -271.906, 235.971, -193.823, 145.884
- C. 145.884, -193.823, 235.971, -271.906
- D. -193.823, -271.906, 145.884, 235.971
Correct Answer: A
Rationale: To correctly order the numbers from least to greatest, we start with the smallest number, which is -271.906, followed by -193.823, 145.884, and finally 235.971. Therefore, the correct order is -271.906, -193.823, 145.884, 235.971. Choice A is correct. Choice B is incorrect as it incorrectly places 235.971 before -193.823. Choice C is incorrect as it starts with the largest number, 145.884. Choice D is incorrect as it starts with -193.823, which is not the smallest number in the list.
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Four friends are sharing a pizza. One friend eats half of the pizza. The other three friends equally divide the rest among themselves. What portion of the pizza did each of the other three friends receive?
- A. 1/5
- B. 1/3
- C. 1/4
- D. 1/6
Correct Answer: D
Rationale: After one friend eats half of the pizza, there is half left. This remaining half is divided equally among three friends. To find the portion each of the other three friends receives, we divide 1/2 by 3, which equals 1/6. Therefore, each of the other three friends receives 1/6 of the pizza. Choice A, 1/5, is incorrect because the correct portion is 1/6. Choice B, 1/3, is incorrect as each of the three friends receives 1/6. Choice C, 1/4, is incorrect as well since the correct portion is 1/6.
Which of the following relationships represents no correlation between two variables?
- A. As a student's class attendance decreases, the student's overall grade remains the same
- B. As the number of hours a person exercises decreases, the weight of that person increases
- C. As the number of miles driven increases, the amount of gasoline in the tank decreases
- D. As the amount of water a plant receives increases, the growth rate of the plant increases
Correct Answer: A
Rationale: Choice A represents no correlation between two variables as it states that as a student's class attendance decreases, the student's overall grade remains the same. This scenario shows no relationship between class attendance and grade. In contrast, choices B, C, and D show clear correlations between the variables mentioned. Choice B indicates a negative correlation between exercise hours and weight gain, choice C indicates a negative correlation between miles driven and gasoline in the tank, and choice D indicates a positive correlation between water intake and plant growth rate, making them all examples of correlated relationships.
What is any number raised to the power of zero?
- A. One
- B. Itself
- C. Zero
- D. Two
Correct Answer: A
Rationale: The correct answer is A: One. Any number raised to the power of zero is always equal to 1. This is a fundamental property of exponentiation. Choice B, 'Itself,' is vague and does not specify a numerical value. Choice C, 'Zero,' is incorrect as any nonzero number raised to the power of zero is 1, not 0. Choice D, 'Two,' is incorrect as any number raised to the power of zero is 1, not 2.
What is the best estimate in meters for the average width of a doorway?
- A. 0.5
- B. 1
- C. 10
- D. 3
Correct Answer: B
Rationale: The correct answer is B: 1. The average width of a doorway typically ranges from 0.8 to 1.2 meters, making 1 meter a reasonable estimate. Choice A (0.5) is too narrow for a standard doorway. Choice C (10) is too wide for a typical doorway. Choice D (3) is also wider than the standard width of a doorway.
As a company's stocks increase, production, sales, and investments also increase. Which of the following is the independent variable?
- A. Sales
- B. Stocks
- C. Production
- D. Investments
Correct Answer: B
Rationale: The independent variable in this scenario is 'Stocks.' An independent variable is the one that is manipulated or controlled by the experimenter. In this case, stocks are the factor that is changing and influencing the other variables - production, sales, and investments. Production, sales, and investments are dependent on the changes in stocks; hence, they are the dependent variables. While production, sales, and investments may increase as a result of changes in stocks, the stocks themselves are the driving force behind these changes, making them the independent variable.