Question

determine the probability that a dart that lands on a random part of the target will land in the shaded scoring section. assume that all squares in the figure and all circles in the figure are congruent unless otherwise marked. round your answer to the nearest tenth of a percent, if necessary. the area of the square is 100 square inches. the area of the

enter the answer in the space provided. use numbers instead of words.

%

Explanation:

Step1: Calculate area of one circle

The diameter of each circle in the second - figure is \(d = 10\) inches (since \(20\div2 = 10\)), so the radius \(r = 5\) inches. The area of a single - circle is \(A_{circle}=\pi r^{2}=\pi\times(5)^{2}=25\pi\) square inches.

Step2: Calculate total area of three circles

The total area of the three congruent circles is \(A_{total - circles}=3\times25\pi = 75\pi\) square inches.

Step3: Calculate area of the square

The area of the square is \(A_{square}=20\times20 = 400\) square inches.

Step4: Calculate the probability

The probability \(P\) that a dart lands in the shaded region is the ratio of the area of the shaded region (area of the three circles) to the area of the entire square. \(P=\frac{A_{total - circles}}{A_{square}}=\frac{75\pi}{400}=\frac{3\pi}{16}\).

Step5: Convert to percentage and round

\(P=\frac{3\pi}{16}\times100\%=\frac{300\pi}{16}\% \approx 58.9\%\)

Answer:

58.9%