A survey about the student government program at a school finds that of 245 students:
-218 students like the program
-27 students think the program is unnecessary
If a circle graph were made from this data, what would the measure of the central angle be for the group that likes the program? Round your answer to the nearest whole number.
How would I solve this step by step?
218/245 = .889 ≈ 89%
There are 360° in a circle, so this section would be
..889 * 360 = 320°
That means the other slice would be 360-320 = 40°
Thank you very much!
To find the measure of the central angle for the group that likes the student government program, we need to determine the percentage of students who like the program and then convert that into an angle.
Step 1: Calculate the percentage of students who like the program:
- Divide the number of students who like the program (218) by the total number of students surveyed (245).
- 218 / 245 = 0.8918 (rounded to four decimal places).
Step 2: Convert the percentage into an angle:
- Multiply the percentage by 360 degrees (a full circle) to find the measure of the central angle for the group that likes the program.
- 0.8918 * 360 = 320.4288 degrees (not rounded).
Step 3: Round the angle to the nearest whole number:
- The measure of the central angle for the group that likes the program is 320 degrees (rounded to the nearest whole number).
Therefore, the measure of the central angle for the group that likes the student government program, when represented in a circle graph, would be 320 degrees.
To solve this problem step by step, you need to calculate the measure of the central angle for the group that likes the program based on the given data.
Step 1: Calculate the total number of students who participated in the survey.
- Given that 245 students responded to the survey, the total number of students is 245.
Step 2: Calculate the number of students who like the program.
- Given that 218 students like the program, the number of students who like the program is 218.
Step 3: Calculate the percentage of students who like the program.
- Divide the number of students who like the program by the total number of students and multiply by 100 to get the percentage.
- (218 / 245) * 100 = 88.98
Step 4: Calculate the measure of the central angle for the group that likes the program.
- The measure of the central angle can be determined by multiplying the percentage obtained in Step 3 by 360 (as there are 360 degrees in a circle).
- 88.98 * 360 = 32032.8
Step 5: Round the measure of the central angle to the nearest whole number.
- Rounding 32032.8 to the nearest whole number gives you 32033.
Therefore, the measure of the central angle for the group that likes the program, when represented in a circle graph, would be approximately 32033 degrees.