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A composite figure is composed of a semicircle whose radius measures 5 inches added to a square whose side measures 10 inches. A point within the figure is randomly chosen.

What is the probability that the randomly selected point is in the semicircular region?

Enter your answer rounded to the nearest tenth in the box.

%

User HotN
by
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1 Answer

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To solve this problem, we need to find the total area of the composite figure and the area of the semicircular region, and then divide the area of the semicircular region by the total area to get the probability that the randomly selected point is in the semicircular region.

The area of a semicircle with radius r is (1/2)πr^2, and the area of a square with side s is s^2. Therefore, the total area of the composite figure is:

Total area = (1/2)π(5^2) + 10^2 = 25π/2 + 100

The area of the semicircular region is (1/2)π(5^2) = 25π/2.

The probability of selecting a point in the semicircular region is:

Probability = Area of semicircular region / Total area
Probability = (25π/2) / (25π/2 + 100)
Probability = 0.198 (rounded to the nearest tenth)

Therefore, the probability that the randomly selected point is in the semicircular region is approximately 0.2, or 20%.
User Yogsototh
by
8.0k points

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