Help 10 pts!
If a point is randomly selected from the rectangular area of the graph, what is the probability that it will be in the blue region?
Round answer to the nearest whole percentage?
A. 49%
B. 59%
C. 69%
D. 79%

Answer:

D. 79%

Step-by-step explanation:

Took the the on USA Test prep

If a point is randomly selected from the rectangular area of the graph, the probability that it will be in the blue region is 79%.

The ratio of the number of favorable outcomes to the total number of outcomes of an event is known as probability.

It is given that, the length=20, the width=10, and the radius of half circle=10.

Calculate the area of the rectangle.

Knows the area of the rectangle is the product of length and width.

So,

[tex]\Rightarrow \text{Area of rectangle}=\text{10}\times \text{20} \\ \Rightarrow \text{Area of rectangle}=200 \\[/tex]

Calculate the area of the half-circle.

Knows the area of the half-circle[tex]=\frac{\pi r^{2} }{2}[/tex].

So,

[tex]& \Rightarrow \text{Area of half circle}=\frac{3.14\times 10\times 10}{2} \\ & \Rightarrow \text{Area of half circle}=\frac{314}{2} \\ & \Rightarrow \text{Area of half circle}=157 \\[/tex]

Calculate the probability that it will be in the blue region.

Knows the formula for the probability, [tex]\text{Probability}\left( \text{Event} \right)=\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}[/tex]

So,

[tex]& \Rightarrow \text{Probability}=\frac{\text{157}}{200} \\ & \Rightarrow \text{Probability}=0.78539 \\ & \therefore \text{Probability }\%=79\% \\[/tex]

Thus, the correct answer is an option (D). i.e., 79%.

Learn more about the probability, here

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