anonymous
  • anonymous
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Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Find the probability that a randomly chosen point in the figure lies in the shaded region...
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anonymous
  • anonymous
What is the area of the whole square? What is the area of one of the circles? What is 4 times the area of one circle? What is the area of the whole square minus 4 times the area of one circle? The answer to these questions should provide some insight into the solution. If you have questions or problems about how these areas are related post back and I can try to clarify.
anonymous
  • anonymous
huh???

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anonymous
  • anonymous
What is the area of the entire square? Area of a rectangle = length * width. The length is 13, and the width is also 13. Therefore the area is 13*13 = 169. So assuming that each circle has a diameter of 1/2 of 13, what is the area of one of the circles?
anonymous
  • anonymous
6.5
anonymous
  • anonymous
6.5 would be the diameter. Half of that would be the radius. \[ A_{Circle} = \pi r^2\] Where r is the radius of the circle. So what is the area of one circle?
anonymous
  • anonymous
so 3.14*6.5?
anonymous
  • anonymous
20.41
anonymous
  • anonymous
Close, but remember that the radius is squared.
anonymous
  • anonymous
132.67
anonymous
  • anonymous
Also recall that 6.5 is the diameter, not the radius. The radius is half the diameter or 3.25.
anonymous
  • anonymous
so 33.17
anonymous
  • anonymous
Correct. So the area of 4 circles would be?
anonymous
  • anonymous
33.17*4=132.68
anonymous
  • anonymous
Correct. So the probability of not being in any circles, is the area of the part of the square not in the circles, divided by the total area of the square. If the total area of the square is 169, and the area of all the circles together is 132.68, what is the area of the portion of the square outside the circles?
anonymous
  • anonymous
how would it be set up?
anonymous
  • anonymous
Which? The area of the non-circle part? \[A_{total} = A_{circles} + A_{not\ circles}\] We have calculated the total Area, and the circular areas, so what is the non-circular area?
anonymous
  • anonymous
so 132.68+6.5?
anonymous
  • anonymous
139.18
anonymous
  • anonymous
\[A_{total} = 169\] \[A_{circles} = 132.68\] What is \[A_{not\ circles}\]
anonymous
  • anonymous
36.32
anonymous
  • anonymous
Indeed. Now divide that area by the total area to find the probability for a random point to be in that area.
anonymous
  • anonymous
36.32/169
anonymous
  • anonymous
.2149112
anonymous
  • anonymous
Yep. Remember that probability of a situation is the number of ways that situation can occur divided by the total possible situations you can have. In this case we're working with areas, in the other example we were using lengths, but the process is the same.
anonymous
  • anonymous
21.49%
anonymous
  • anonymous
Yep.
anonymous
  • anonymous
thank you

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