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nadezda [96]
1 year ago
9

t hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular regio

n. Each side of the dartbozn, and the radius of the shaded region Is 2 in.the value 3.14 for T. Round your answer to the nearest hundredth.

Mathematics
1 answer:
masha68 [24]1 year ago
6 0

Given:

Required:

To find the probability that the dart land will be in the shaded region.

Explanation:

Area of the circle is given by the formula:

A=\pi r^2

Where r = radius

Thus the area of the circular region

\begin{gathered} =(3.14)\times(2)^2 \\ =3.14\times4 \\ =12.56\text{ square in.} \end{gathered}

The area of the square is given by the formula:

=(side)^2

Thus the area of the given square

\begin{gathered} =(6)^2 \\ =36\text{ square in.} \end{gathered}

The probability of an event is given by the formula:

P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}

The probability that the dart land will be in the shaded region

=\frac{Area\text{ of the shaded region}}{Area\text{ of the square}}

Thus probability

\begin{gathered} P=\frac{12.56}{36} \\ P=0.3488 \\ P=0.349 \end{gathered}

Final answer:

Thus the probability that the dart land will be in the shaded region is 0.349.

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