Question

1. before a school dance, the organizing committee did a survey of students to find out their music preferences. the graph below shows the number of students who prefer each type of music. survey results: music preferences a) how many people were surveyed? b) what percentage of the people prefer rock music? c) calculate the number of degrees in the circle that represent those who prefer r&b music.

Explanation:

Step1: Calculate total surveyed people

Add all the numbers: \(6 + 14+52 + 65\)
$$6+14 + 52+65=(6 + 14)+(52 + 65)=20+117 = 137$$

Step2: Calculate percentage of rock - music preferers

Number of rock - music preferers is \(52\). Use the formula \(\text{Percentage}=\frac{\text{Part}}{\text{Whole}}\times100\). So \(\frac{52}{137}\times100\)
$$\frac{52}{137}\times100=\frac{5200}{137}\approx 37.96\%$$

Step3: Calculate degrees for R&B

Number of R&B preferers is \(14\). A circle has \(360^{\circ}\). Use the formula \(\text{Degrees}=\frac{\text{Part}}{\text{Whole}}\times360\). So \(\frac{14}{137}\times360\)
$$\frac{14\times360}{137}=\frac{5040}{137}\approx 36.8^{\circ}$$

Answer:

a) \(137\) people were surveyed.
b) Approximately \(37.96\%\) of the people prefer rock music.
c) Approximately \(36.8^{\circ}\) represent those who prefer R&B music.