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miss Akunina [59]
1 year ago
7

If Raj randomly chooses a point in the square below, what is the probability that point is not in the circle? Assume that pi = 3

.14 and round to the nearest tenth of a percent. A circle inside of a square. The radius of the circle is 4 units. The side of the square is 10 units.
Mathematics
1 answer:
hodyreva [135]1 year ago
6 0

Answer:

49.7%

Step-by-step explanation:

A cdircle is located within a square.

<u>Area of the circle</u>

Area = \pir^{2}, where r = 4 units.

Area Circle = 50.3 units^2

<u>Area of the square</u>

Area = l*w or l^2 for a square, since l = w

Area = (10 units)^2

Area = 100 units^2

<u>Area in the square but outside the circle</u>

This is the difference [Square minus Circle Areas]

Square minus Circle Areas = 100 - 50.3  or <u>49.7 units^2</u>

<u>Probability</u>

The probability of picking a point in the square that is not in the circle is the ration of the two areas:  <u>[Outside Circle/Square]x100%</u>

<u></u>

<u>(</u>49.7 units^2)/(100 units^2)x100% = 49.7%

<u></u>

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Answer:

Option A)   Inside the circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The radius is equal to the distance from the center to any point on the circle

the formula to calculate the distance between two points is equal to

d\sqrt{(y2-y1)^2+(x2-x1)^2 }

we have

A(-5,-8),M(-1,-3)

substitute the values

r=\sqrt{(-3+8)^{2}+(-1+5)^{2}}

r=\sqrt{(5)^{2}+(4)^{2}}

r=\sqrt{41}\ units

step 2

Find the distance from the center to point V

we know that

If the distance from the center to point V is equal to the radius, then the point V lie on the circle

If the distance from the center to point V is less than the radius, then the point V lie inside the circle

If the distance from the center to point V is greater than the radius, then the point V lie outside the circle

we have

A(-5,-8),V(-11,-6)

substitute in the formula

d=\sqrt{(-6+8)^{2}+(-11+5)^{2}}

d=\sqrt{(2)^{2}+(-6)^{2}}

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so

\sqrt{40}\ units< \sqrt{41}\ units

The distance from the center to point V is less than the radius

therefore

The point V lie inside the circle

Hope that helped :)

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In a radio station contest, the first prize is $2,000 and the second prize is $500. The probability of winning the first prize i
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