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Minchanka [31]
3 years ago
8

a point is chosen at random in the circle. What percent of the time will the point be in the square? Round to the nearest tenth

of a percent.
Mathematics
1 answer:
sergejj [24]3 years ago
6 0

Answer:

P = 0.637

Step-by-step explanation:

By a small online search, i've found that the image is a circle of radius R = 1in, and a square inside of the circle, such that the distance between the center of the square and the one vertex of the square is one inch.

To solve this problem, we need to find the area of each figure.

The area of a circle of radius R is:

A = 3.14*R^2

Then the area of our circle is:

A = 3.14*(1in)^2 = 3.14 in^2

Now for the square.

If the distance between the center and one vertex is 1 inch, then the distance between two opposite vertex is twice that: 2 inches.

Now we can think of a triangle rectangle, where both catheti are equal to L, the side length of the square, and the hypotenuse is 2 inches.

Using the Pythagoreans theorem, we get:

L^2 + L^2 = (2in)^2

2*L^2 = (2in)^2

L^2 = (2in)^2/2 = 2 in^2

L = √(2 in^2) = √2 in

And the area of a square of side length L, the area is:

A = L^2

Then the area of our square is:

A = (√2 in) = 2 in^2

Then:

Area of the circle = 3.14 in^2

Area of the square = 2 in^2

The area of the circle represents the 100% (if a point is chosen at random in the circle, the probability that the point will be inside the circle is P = 1)

The probability that the point will be inside the square is equal to the quotient between the area of the square and the area of the circle, this is:

P = (2 in^2)/(3.14 in^2) = 0.637

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Step-by-step explanation:

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2 years ago
Can anyone help me with this question? <br>what is 6y+8x=24
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6y=-8x+24

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3 years ago
Each pack of batteries cost $21. How many i can buy if i have $63?
Rashid [163]

Each pack of batteries cost $21 each.
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Answer: 3


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6 0
3 years ago
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It takes 15 electricians 24 days to wire a new housing subdivision. how many days would 18 electricians require to do the same j
Romashka [77]
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now, there were 15 electricians on any given day though, since each one of them worked the whole day that one day, so the "days work worth" on a day is 15, so the house gets 15days worth of work because of that.

so how many "days worth" did all 15 do on the 24 days, well, 15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15+15, namely 15 * 24, or 360 days worth of work.

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3 years ago
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two positive integers are 3 units apart on a number line. their product is 180. wich equation can be used to solve for m, the gr
3241004551 [841]

Answer:

m^2-3m-180=0

m=15

Step-by-step explanation:

greater integer = m

small integer = n

we know that m = n+3 or n = m-3

we also know that n*m = 180

replace n for m-3

(m-3)*m=180

or

m^2-3m-180 = 0

(m-15)(m+12)=0

so m = 15 or -12, but since problem states positive, m=15

5 0
3 years ago
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