Question

each student in a school was asked, \what is your favorite color?\ the circle graph below shows how they answered. (a) which color was chosen by approximately one - eighth of the students? (b) approximately what percentage of the students chose purple or green? 20% 40% 60% 80%

Explanation:

Step1: Find one - eighth of the circle

A full circle is \(360^{\circ}\). One - eighth of a circle has an angle measure of \(\frac{1}{8}\times360^{\circ}=45^{\circ}\). Looking at the circle graph, the "Purple" section has an angle close to \(45^{\circ}\) (since one - eighth of the circle represents one - eighth of the students).

Step2: Calculate the percentage for Purple or Green

The "Purple" section is approximately \(\frac{1}{8}\) of the circle (\(12.5\%\)) and the "Green" section is also relatively small. Let's assume the "Purple" is \(12.5\%\) and the "Green" is about \(7.5\%\). The sum of Purple and Green is \(12.5\%+7.5\% = 20\%\)

Answer:

(a) Purple; (b) \(20\%\)