15. A survey about the student's government program at a school finds the following results:
110 students like the program
120 students think the program is unnecessary.
210 students plan on running for student government next year.
If a circle graph were made from this data, what would the measure of the central angle be for the group that thinks the program is unnecessary?
A. 98
B.27
C.90
D.172
To find the measure of the central angle for the group that thinks the program is unnecessary, we need to first calculate the total number of students surveyed. We can do this by adding up all the students who responded:
110 (like the program) + 120 (think the program is unnecessary) + 210 (plan on running for student government next year) = 440
Next, we can calculate the percentage of students who think the program is unnecessary:
120 ÷ 440 × 100% ≈ 27.27%
To convert this percentage to an angle in degrees, we can use the formula:
Angle = Percentage ÷ 100% × 360°
Angle = 27.27 ÷ 100% × 360°
Angle ≈ 98°
Therefore, the answer is A. 98.
To find the measure of the central angle for the group that thinks the program is unnecessary, we need to determine the percentage of students in that group and then convert it to degrees.
First, we need to add the number of students who like the program and the number of students who think the program is unnecessary:
110 students (like the program) + 120 students (think program is unnecessary) = 230 students.
To determine the percentage of students who think the program is unnecessary, we divide the number of students in that group by the total number of students and multiply by 100:
(120 students / 230 students) * 100 = 52.17%.
To convert the percentage to degrees, we multiply it by 360:
52.17% * 360 = 187.42 degrees.
Therefore, the measure of the central angle for the group that thinks the program is unnecessary is approximately 187.42 degrees.
The closest option is D. 172.