Nokea
A new professional saw 841 clients during the first year of practice and 1072 clients during the second year of practice. Which of the following represents the approximate percentage increase in client volume?
- A. 127%
- B. 27%
- C. 22%
- D. 78%
Correct Answer: B
Rationale: To calculate the percentage increase in client volume, subtract the initial number of clients from the final number, then divide the result by the initial number and multiply by 100. The increase is 1072 - 841 = 231 clients. The percentage increase is calculated as (231 / 841) * 100 ≈ 27%, which corresponds to option B. Therefore, the correct answer is 27%, representing the percentage increase in client volume from the first year to the second year of practice.
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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.
Solve the equation 2(4x + 3) = 7x + 5 for x. Which of the following is correct?
- A. -1
- B. 1
- C. 11
- D. 2
Correct Answer: A
Rationale: To solve the equation, first distribute the 2 on the left side: 8x + 6 = 7x + 5. Next, move all terms involving x to one side by subtracting 7x from both sides: x + 6 = 5. Then, subtract 6 from both sides to isolate x: x = -1. Therefore, the correct answer is A, -1, as it satisfies the equation 2(4*(-1) + 3) = 7*(-1) + 5. Substituting x = -1 back into the original equation gives 2(4*(-1) + 3) = 7*(-1) + 5, which simplifies to -2 + 6 = -7 + 5, and finally to 4 = -2, proving that -1 is indeed the correct solution.
Which of the following translates the phrase '5 less than 2 times a number' into a mathematical expression?
- A. 5 - 2x
- B. 5x - 2
- C. 2x - 5
- D. 2 - 5x
Correct Answer: C
Rationale: To translate the phrase '5 less than 2 times a number' into a mathematical expression, you first express '2 times a number' as 2x. Then, '5 less than' indicates subtracting 5 from the result, leading to 2x - 5. Therefore, choice C, 2x - 5, correctly represents the given phrase in a mathematical expression.
In the graph above, which represents the amount of rainfall in a particular state by month, what is the total rainfall for the first 3 months of the year?
- A. 3 1/2 inches
- B. 2 inches
- C. 4 inches
- D. 1 1/2 inches
Correct Answer: A
Rationale: To calculate the total rainfall for the first 3 months of the year, you need to add the rainfall amounts for January (1 inch), February (1/2 inch), and March (2 inches) together. This sum gives a total of 3 1/2 inches, making choice A the correct answer.
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.