A survey about the student 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 the data, what is the measure of the central angle for the group that plans on running for student government next year?
A. 39°
B. 90°
C. 98°
D. 172°
To find the measure of the central angle for the group that plans on running for student government next year, we need to first calculate the total number of students surveyed. This is simply the sum of the number of students in each category:
Total = 110 (like) + 120 (unnecessary) + 210 (running) = 440
Next, we can find the fraction of students who plan on running for student government next year by dividing the number of students in that category by the total number of students:
210/440 = 0.4773 (rounded to four decimal places)
This means that the central angle for the "running" category would be equal to 0.4773 times the total central angle of the circle graph (which is 360 degrees).
Central angle for "running" category = 0.4773 x 360 = 171.228 degrees
Rounding to the nearest degree, we get that the central angle for the "running" category is approximately 171 degrees, which corresponds to answer choice D.
To find the measure of the central angle for the group that plans on running for student government next year, we need to calculate the percentage of students in that group out of the total number of students surveyed.
The total number of students surveyed is the sum of the students who like the program and the students who think the program is unnecessary: 110 + 120 = 230.
The percentage of students planning on running for student government next year can be found by dividing the number of students in that group by the total number of students and multiplying by 100: (210/230) * 100 = 91.3%.
To find the measure of the central angle, we can use the proportion: the percentage is to 360 degrees as the number of students planning on running for student government is to the central angle.
Let x be the measure of the central angle:
91.3/100 = 210/x
Cross-multiplying:
(91.3 * x) = (210 * 100)
91.3x = 21000
Dividing both sides by 91.3:
x = 21000 / 91.3
x = 229.98 ≈ 230
Therefore, the measure of the central angle for the group planning on running for student government next year is approximately 230 degrees.
None of the provided answer choices match the calculated measure, so the answer is not given.
To find the measure of the central angle for the group that plans on running for student government next year, we need to first calculate the percentage of students who plan on running for student government.
To do this, we divide the number of students planning to run (210) by the total number of students surveyed (110 + 120 + 210):
210 / (110 + 120 + 210) = 210 / 440 ≈ 0.4773 or 47.73%
The central angle for the group that plans on running for student government next year will be equal to 47.73% of the total angle in the circle graph.
To find this angle measure, we multiply the percentage by 360° (since a circle is 360°):
0.4773 * 360° = 171.732°
So, the measure of the central angle for the group that plans on running for student government next year is approximately 171.732°.
Since the given answer choices are rounded to the nearest whole number, the closest option is D. 172°.