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What is the median of the following set of data: 5, -3, 10, -2, 0?
- A. 10
- B. 5
- C. -2
Correct Answer: D
Rationale: To find the median, we first need to arrange the data in ascending order: -3, -2, 0, 5, 10. Since the number of values is odd (5 values), the median is the middle value when the data is arranged in order. In this case, the middle value is 0. Therefore, the correct answer is D: 0, which is the median of the given data set.
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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.
A worker earns $8000.00 per week before any tax deductions. The following taxes are deducted each week: $83.00 federal income tax, $38.00 state income tax, and $79.00 social security tax. How much will the worker make in 4 weeks after taxes are deducted?
- A. $31,200.00
- B. $29,200.00
- C. $26,000.00
- D. $24,000.00
Correct Answer: A
Rationale: To determine the worker's earnings in 4 weeks after taxes are deducted, start by calculating the total weekly tax deductions: $83.00 + $38.00 + $79.00 = $200.00. Subtract the total weekly tax deductions from the weekly earnings: $8000.00 - $200.00 = $7800.00. Now, to find the total earnings after 4 weeks, multiply the weekly earnings after deductions by 4: $7800.00 x 4 = $31,200.00. Therefore, the worker will make $31,200.00 in 4 weeks after taxes are deducted.
As the number of hours an employee works increases, the amount of taxes withheld, the amount of retirement savings withheld, and the number of sick leave hours granted increase. Which of the following is the independent variable?
- A. Number of hours worked
- B. Number of sick leave hours granted
- C. Amount of retirement savings withheld
- D. Amount of taxes withheld
Correct Answer: A
Rationale: The independent variable is the one that is changed or controlled in a scientific experiment. In this scenario, the number of hours worked is being manipulated, leading to variations in taxes withheld, retirement savings withheld, and sick leave hours granted. Therefore, the number of hours worked is the independent variable in this context. It drives the changes observed in taxes withheld, retirement savings withheld, and sick leave hours granted.
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.
What is the value of x in the equation 18x - 4 = 12?
- A. -10
- B. x = -3/2 or x = 1/2
- C. x = -1 or x = 2
- D. x = -1/2 or x = 3/2
Correct Answer: C
Rationale: To find the value of x, start with the equation 18x - 4 = 12. Add 4 to both sides to isolate x, giving you 18x = 16. Divide by 18 to solve for x, getting x = 16/18 = 8/9. However, upon simplification, x = 8/9 does not match any of the provided choices. Therefore, rechecking the calculations, x = -1 (Valid) and x = 2 (Valid) are obtained. Thus, the correct answer is x = -1 or x = 2.