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A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. The radius of the dartboard is 18in, and the radius of the shaded region is 6in.Use the value 3.14 for π. Round your answer to the nearest hundredth.18in6in

Question

A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. The radius of the dartboard is 18in, and the radius of the shaded region is 6in.Use the value 3.14 for π. Round your answer to the nearest hundredth.18in6in

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Solution

To solve this problem, we need to find the areas of both the entire dartboard and the shaded region, and then divide the area of the shaded region by the area of the entire dartboard.

Step 1: Find the area of the entire dartboard. The formula for the area of a circle is πr², where r is the radius of the circle. In this case, the radius of the dartboard is 18 inches. So, the area of the dartboard is:

π * (18in)² = 3.14 * (324in²) = 1017.36 square inches.

Step 2: Find the area of the shaded region. The radius of the shaded region is 6 inches. So, the area of the shaded region is:

π * (6in)² = 3.14 * (36in²) = 113.04 square inches.

Step 3: Find the probability that the dart lands in the shaded region. The probability is the ratio of the area of the shaded region to the area of the entire dartboard:

113.04in² / 1017.36in² = 0.111 or 11.1% when rounded to the nearest hundredth.

So, the probability that the dart lands in the shaded region is approximately 0.11 or 11.1%.

This problem has been solved

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