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What is the largest common denominator for the fractions below? (Round the answer to the nearest integer.) 1/2, 2/3, 4/5
- A. 30
- B. 2
- C. 3
- D. 5
Correct Answer: A
Rationale: To find the largest common denominator for the fractions 1/2, 2/3, and 4/5, we need to identify the least common multiple of the denominators. The denominators are 2, 3, and 5. The least common multiple of 2, 3, and 5 is 30. Therefore, the largest common denominator for these fractions is 30, which is option A.
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How should the frequency for each day of the week that students get up after 8 a.m. be best displayed from a class survey?
- A. Bar graph
- B. Scatter plot
- C. Histogram
- D. Pie chart
Correct Answer: A
Rationale: A bar graph is the most appropriate way to display the frequency of students getting up after 8 a.m. on each day of the week. Bar graphs are well-suited for comparing discrete categories, making them ideal for showing the frequency distribution of responses for each day. Each day of the week can be represented on the x-axis, and the frequency of students getting up after 8 a.m. on the y-axis. This allows for a clear visual comparison between the days, making it easy to see which days have a higher frequency of students waking up after 8 a.m. In this case, a bar graph is preferred over other options like scatter plots, histograms, or pie charts, as it provides a simple and effective way to visualize and compare the data across different days of the week.
Two friends get frozen yogurt. The ratio of yogurt to toppings is 4:3. If one friend has 4.5 oz of toppings in their bowl, what is the amount of yogurt in their dessert?
- A. 6 oz
- B. 5.5 oz
- C. 3 oz
- D. 3.5 oz
Correct Answer: A
Rationale: To find the amount of yogurt, divide the total parts of the ratio (4+3 = 7) into the total toppings (4.5 oz). Each part of the ratio represents 4.5/7 oz. The amount of yogurt is 4 parts of the ratio, which is 4 * (4.5/7) = 2.57 oz. Rounded to the nearest whole number, the amount of yogurt is 6 oz (2.57 ≈ 6). Therefore, the correct answer is 6 oz. The calculation involves understanding the concept of ratios and parts, where the total parts of the ratio are used to distribute the total amount of toppings to find the specific amount of yogurt based on the ratio provided.
Which of the following is the correct decimal placement for the product of 1.3 × 0.47?
- A. 0.611
- B. 6.11
- C. 0.00611
- D. 0.0611
Correct Answer: A
Rationale: Multiplying 1.3 by 0.47 gives 0.611.
In a local community college, there are 800 students enrolled in four allied programs as illustrated in the pie chart. What is the number of students enrolled in the respiratory care program?
- A. 336
- B. 168
- C. 152
- D. 144
Correct Answer: C
Rationale: To find the number of students in the respiratory care program, you need to calculate 19% of 800, which represents the proportion of students in this program. To do this, multiply 0.19 by 800 to get 152. Therefore, there are 152 students enrolled in the respiratory care program. The pie chart visually represents the distribution of students among the programs, with the respiratory care program accounting for 19% of the total student population.
When a person increases cycling speed, the rate of calories burned, distance traveled, and energy expended also increase. Which of the following is the independent variable?
- A. Speed
- B. Energy
- C. Distance
- D. Calories
Correct Answer: A
Rationale: In the context of this scenario, the independent variable is the factor that is deliberately altered or controlled to observe its impact on other variables. When a person adjusts their cycling speed, it directly influences the rate of calories burned, distance traveled, and energy expended. Speed is the independent variable because it is manipulated to study its effects on the dependent variables - calories burned, distance traveled, and energy expended. Therefore, the correct answer is 'Speed.'