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 the area of the rectangle

The area formula for a rectangle is $A = l\times w$. Here, $l = 20$ in and $w=16$ in, so $A_{rectangle}=20\times16 = 320$ square - inches.

Step2: Calculate the area of the circles

The area formula for a circle is $A=\pi r^{2}$.
For the two small circles with $r = 5$ in, the combined area of the two small circles is $2\times\pi\times5^{2}=2\times25\pi = 50\pi$ square - inches.
For the large circle with $r = 9$ in, its area is $A_{large - circle}=\pi\times9^{2}=81\pi$ square - inches.
The total area of the shaded circles is $A_{circles}=50\pi + 81\pi=131\pi$ square - inches.

Step3: Calculate the probability

The probability $P$ that a dart lands in the shaded region is the ratio of the area of the shaded region to the area of the entire rectangle.
$P=\frac{A_{circles}}{A_{rectangle}}=\frac{131\pi}{320}$.
Substitute $\pi\approx3.14$: $P=\frac{131\times3.14}{320}=\frac{411.34}{320}\approx1.2854375$.
To convert to a percentage, multiply by 100: $P\approx128.54375\%\approx128.5\%$.

Answer:

$128.5\%$