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A book has a width of 2.5 decimeters. What is the width of the book in centimeters?
- A. 0.25 centimeters
- B. 25 centimeters
- C. 250 centimeters
- D. 0.025 centimeters
Correct Answer: B
Rationale: To convert decimeters to centimeters, we use the conversion factor that 1 decimeter is equal to 10 centimeters. Setting up the proportion: 1/0.1 = x/2.5. Solving for x gives 2.5 = 0.1x, x = 25. Therefore, the width of the book in centimeters is 25. Choices A, C, and D are incorrect because they do not correctly convert decimeters to centimeters. A and D have decimal placement errors, and C has an incorrect magnitude of centimeters.
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Arrange the following numbers from least to greatest: 7/3, 9/2, 10/9, 7/8
- A. 10/9, 7/3, 9/2, 7/8
- B. 9/2, 7/3, 10/9, 7/8
- C. 7/3, 9/2, 10/9, 7/8
- D. 7/8, 10/9, 7/3, 9/2
Correct Answer: D
Rationale: To arrange the numbers from least to greatest, first convert them to decimals:
1. 7/3 is approximately 2.33
2. 9/2 equals 4.5
3. 10/9 is approximately 1.11
4. 7/8 equals 0.875
Now, arrange the decimals from least to greatest: 0.875 (7/8), 1.11 (10/9), 2.33 (7/3), 4.5 (9/2). Therefore, the correct order is 7/8, 10/9, 7/3, 9/2. Choice A is incorrect because it doesn't follow the correct order. Choice B is incorrect as it places 9/2 before 7/3, which is not the right arrangement. Choice C is incorrect as it places 7/3 before 9/2 and 10/9, which is incorrect. Thus, the correct answer is choice D.
In a research study, a researcher collects data on the number of hours spent studying and the grades students received. Which of the following is the dependent variable?
- A. The number of hours spent studying
- B. The grades students received
- C. The subjects students studied
- D. The number of students in the study
Correct Answer: B
Rationale: The correct answer is B: 'The grades students received.' In this scenario, the grades students received are the dependent variable because they are influenced by the number of hours spent studying. The grades are the outcome that is being measured based on the manipulation or observation of the independent variable, which in this case is the number of hours spent studying. Choices A, C, and D are incorrect. The number of hours spent studying is the independent variable being manipulated or observed, the subjects students studied is not directly related to the dependent variable, and the number of students in the study is not the variable being measured or influenced by the independent variable.
Simplify the following expression:
3 (1/6) - 1 (5/6)
- A. 2 (1/3)
- B. 1 (1/3)
- C. 2 (1/9)
- D. 5/6
Correct Answer: B
Rationale: To simplify:
First, subtract the whole numbers: 3 - 1 = 2.
Then, subtract the fractions: (1/6) - (5/6) = - (4/6) = - (2/3).
Now, subtract (2 - 2/3) = 1 (1/3).
Curtis is taking a road trip through Germany, where all distance signs are in metric. He passes a sign that states the city of Dusseldorf is 45 kilometers away. Approximately how far is this in miles?
- A. 42 miles
- B. 37 miles
- C. 28 miles
- D. 16 miles
Correct Answer: C
Rationale: To convert kilometers to miles, you can use the conversion factor of approximately 0.62 miles per kilometer. Therefore, 45 kilometers 0.62 miles/kilometer = 27.9 miles, which is approximately 28 miles away. Choice A (42 miles), Choice B (37 miles), and Choice D (16 miles) are incorrect as they do not reflect the accurate conversion from kilometers to miles.
A mathematics test has a 4:2 ratio of data analysis problems to algebra problems. If the test has 18 algebra problems, how many data analysis problems are on the test?
- A. 24
- B. 28
- C. 36
- D. 38
Correct Answer: C
Rationale: The ratio of 4:2 simplifies to 2:1. This means that for every 2 algebra problems, there is 1 data analysis problem. If there are 18 algebra problems, we can set up a proportion: 2 algebra problems correspond to 1 data analysis problem. Therefore, 18 algebra problems correspond to x data analysis problems. Solving the proportion, x = 18 * 1 / 2 = 9. Hence, there are 9 data analysis problems on the test. Therefore, the total number of data analysis problems on the test is 18 (algebra problems) + 9 (data analysis problems) = 27.