Mathematics

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A homeowner has hired two individuals to mow his lawn. If person A is able to mow the lawn in 2 hours by himself, and person B is able to mow the lawn in 3 hours by himself, how long would it take for both person A and person B to mow the lawn together?

  • A. 5 hours
  • B. 1 hour
  • C. 2.5 hours
  • D. 1.2 hours
Correct Answer: D

Rationale: To find out how long it would take for both person A and person B to mow the lawn together, we can use the formula: 1 / (1/A + 1/B), where A and B represent the individual times taken by each person. Substituting A = 2 hours and B = 3 hours into the formula: 1 / (1/2 + 1/3) = 1 / (5/6) = 6/5 = 1.2 hours. Therefore, it would take both person A and person B 1.2 hours to mow the lawn together.

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What is the mean of the test scores listed below? 100, 78, 47, 84, 93, 78

  • A. 96
  • B. 78
  • C. 80
  • D. 82
Correct Answer: C

Rationale: To find the mean of a set of numbers, you add up all the numbers and then divide by the total count of numbers. In this case, (100 + 78 + 47 + 84 + 93 + 78) / 6 = 480 / 6 = 80. Therefore, the mean of the given test scores is 80. The correct answer is C, 80, as it represents the average of the test scores provided.

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.

What is the best decimal approximation of 10 times the positive square root of 207?

  • A. 100
  • B. 44.7
  • C. 200
  • D. 89.4
Correct Answer: D

Rationale: To find the decimal approximation of 10 times the positive square root of 207, we first approximate the square root of 207 to be around 14.4. Multiplying this by 10 gives us 144. Among the choices, 89.4 is the closest value to this approximation, making it the correct answer. Therefore, the best decimal approximation of 10 times the positive square root of 207 is 89.4.

A temperature gauge reads 95F. Which of the following is the correct conversion to degrees Celsius? (Note: C = 5/9[F - 32])

  • A. 113C
  • B. 63C
  • C. 35C
  • D. 21C
Correct Answer: C

Rationale: To convert F to C, use the formula: C = 5/9(95 - 32) = 5/9(63) = 35C.

A soccer field is rectangular in shape and measures 100 meters in length and 75 meters in width. The hectare is a metric unit of area often used to measure large areas. Given that 1 hectare = 10,000 square meters, what is the soccer field's area in hectares?

  • A. 7,500 hectares
  • B. 7.5 hectares
  • C. 75,000,000 hectares
  • D. 0.75 hectares
Correct Answer: D

Rationale: To find the area of the soccer field in square meters, multiply its length by its width: 100 meters * 75 meters = 7500 square meters. To convert square meters to hectares, divide the area in square meters by 10,000 (since 1 hectare = 10,000 square meters): 7500 square meters / 10,000 = 0.75 hectares. Therefore, the soccer field's area in hectares is 0.75 hectares.

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