a high school basketball court is 25.6 meters...
a high school basketball court is 25.6 meters long and 15.2 meters wide and has a free throw box 5.8 meters long and 3.7 meters wide. a bouncy ball is thrown onto the court from the top of the bleachers and is equally likely to land anywhere on the court. what is the probability that the ball will bounce on the court but outside of the free throw box? when applicable, round your answer to two decimal places and include all necessary calculations
Answer
# Explanation:
## Step1: Calculate court area
The area of the basketball - court $A_{court}$ is given by the formula for the area of a rectangle $A = l\times w$, where $l = 25.6$ meters and $w = 15.2$ meters. So, $A_{court}=25.6\times15.2 = 389.12$ square - meters.
## Step2: Calculate free - throw box area
The area of the free - throw box $A_{box}$ is also given by the formula for the area of a rectangle $A = l\times w$, where $l = 5.8$ meters and $w = 3.7$ meters. So, $A_{box}=5.8\times3.7 = 21.46$ square - meters.
## Step3: Calculate the area outside the free - throw box on the court
$A = A_{court}-A_{box}=389.12 - 21.46=367.66$ square - meters.
## Step4: Calculate the probability
The probability $P$ that the ball bounces on the court but outside the free - throw box is the ratio of the area outside the free - throw box to the total area of the court. So, $P=\frac{A}{A_{court}}=\frac{367.66}{389.12}\approx0.94$.
# Answer:
$0.94$