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Algebra Difficulty 2.5 Junior Find the answer Canada

Three numbers have a mean (average) of 7. The mode of these three numbers is 9. What is the smallest of these three numbers?

Pick one

Solution

Since $PQ$ passes through centre $O$ , then it is a diameter of the circle.

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Since $\angle QOT=90\degree$ , then $\angle POT=180\degree-90\degree=90\degree$ .

Thus, the area of sector $POT$ is $\frac{90\degree}{360\degree}=\frac{1}{4}$ or 25% of the area of the circle.

Since the areas labelled $R$ and $S$ are equal, then each is

$25\%\div 2=12.5\%$ of the area of the circle.
Therefore, a spin will stop on the shaded region $12.5\%$ of the time.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.