The problem is asking for the probability that a dart lands in the shaded region of a dartboard. The probability of an event is calculated by dividing the number of successful outcomes by the total number of outcomes. In this case, the successful outcome is the dart landing in the shaded region, and the total outcomes are any point on the dartboard.

1. First, we need to 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. The radius of the dartboard is given as 6 inches. So, the area of the dartboard is π(6in)² = 3.14 * 36in² = 113.04 square inches.

2. Next, we need to find the area of the shaded region. The radius of the shaded region is given as 3 inches. So, the area of the shaded region is π(3in)² = 3.14 * 9in² = 28.26 square inches.

3. Now, we can find the probability. The probability is the area of the shaded region divided by the area of the entire dartboard. So, the probability is 28.26in² / 113.04in² = 0.25.

4. Finally, we round our answer to the nearest hundredth, which gives us a probability of 0.25. So, the probability that the dart lands in the shaded region is 0.25, or 25%.

Question

The problem is asking for the probability that a dart lands in the shaded region of a dartboard. The probability of an event is calculated by dividing the number of successful outcomes by the total number of outcomes. In this case, the successful outcome is the dart landing in the shaded region, and the total outcomes are any point on the dartboard.

1. First, we need to 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. The radius of the dartboard is given as 6 inches. So, the area of the dartboard is π(6in)² = 3.14 * 36in² = 113.04 square inches.

2. Next, we need to find the area of the shaded region. The radius of the shaded region is given as 3 inches. So, the area of the shaded region is π(3in)² = 3.14 * 9in² = 28.26 square inches.

3. Now, we can find the probability. The probability is the area of the shaded region divided by the area of the entire dartboard. So, the probability is 28.26in² / 113.04in² = 0.25.

4. Finally, we round our answer to the nearest hundredth, which gives us a probability of 0.25. So, the probability that the dart lands in the shaded region is 0.25, or 25%.

Knowee AI · Accepted Answer

The problem is asking for the probability that a dart lands in the shaded region of a dartboard. The probability of an event is calculated by dividing the number of successful outcomes by the total number of outcomes. In this case, the successful outcome is the dart landing in the shaded region, and the total outcomes are any point on the dartboard.

1. First, we need to 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. The radius of the dartboard is given as 6 inches. So, the area of the dartboard is π(6in)² = 3.14 * 36in² = 113.04 square inches.

2. Next, we need to find the area of the shaded region. The radius of the shaded region is given as 3 inches. So, the area of the shaded region is π(3in)² = 3.14 * 9in² = 28.26 square inches.

3. Now, we can find the probability. The probability is the area of the shaded region divided by the area of the entire dartboard. So, the probability is 28.26in² / 113.04in² = 0.25.

4. Finally, we round our answer to the nearest hundredth, which gives us a probability of 0.25. So, the probability that the dart lands in the shaded region is 0.25, or 25%.

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 6in, and the radius of the shaded region is 3in.Use the value 3.14 for π. Round your answer to the nearest hundredth.6in3in

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