Question

the table below summarizes the 225 members of a voluntary society by their majors. the information is also presented as a circle graph. find the central angle measure, ( x^{circ} ), for the business slice in the circle graph. do not round.

Explanation:

Step1: Calculate the percentage of Business

Since the total percentage of all majors should be \(100\%\), we can find the percentage of Business by subtracting the sum of the percentages of other majors from \(100\%\).
The sum of the given percentages: \(12\%+28\%+28\%+12\%+8\%+12\% = 100\%\) (Wait, no, there is a mistake. Let's recalculate. The sum of the percentages of non - Business majors: \(12 + 28+28 + 12+8+12=100\). But this is wrong. Wait, no, the total is \(100\%\). Let's assume that the percentage of Business is \(x\%\). Then \(x\%=100-(12 + 28+28 + 12+8+12)\). Wait, no, looking at the table, if we assume that the percentage of Business is \(x\%\), and the sum of all percentages is \(100\%\). But actually, in a circle graph (pie chart), the central angle of a sector is given by the formula \(\theta=\frac{p}{100}\times360^{\circ}\), where \(p\) is the percentage of the category.
If we assume that the percentage of Business is \(8\%\) (by re - checking the sum \(12 + 28+28 + 12+8+12 = 100\) is wrong. Wait, no, \(12+28 + 28+12+8+12=100\) (if Business is \(8\%\)).

Step2: Calculate the central angle

The formula for the central angle \(\theta\) of a sector in a circle graph is \(\theta=\frac{p}{100}\times360^{\circ}\), where \(p\) is the percentage of the category.
If \(p = 8\%\), then \(\theta=\frac{8}{100}\times360^{\circ}\)

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Answer:

\(28.8\)