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anonymous

  • 5 years ago

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  1. anonymous
    • 5 years ago
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    Find the probability that a randomly chosen point in the figure lies in the shaded region...

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  2. anonymous
    • 5 years ago
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    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.

  3. anonymous
    • 5 years ago
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    huh???

  4. anonymous
    • 5 years ago
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    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?

  5. anonymous
    • 5 years ago
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    6.5

  6. anonymous
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    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?

  7. anonymous
    • 5 years ago
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    so 3.14*6.5?

  8. anonymous
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    20.41

  9. anonymous
    • 5 years ago
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    Close, but remember that the radius is squared.

  10. anonymous
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    132.67

  11. anonymous
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    Also recall that 6.5 is the diameter, not the radius. The radius is half the diameter or 3.25.

  12. anonymous
    • 5 years ago
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    so 33.17

  13. anonymous
    • 5 years ago
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    Correct. So the area of 4 circles would be?

  14. anonymous
    • 5 years ago
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    33.17*4=132.68

  15. anonymous
    • 5 years ago
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    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?

  16. anonymous
    • 5 years ago
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    how would it be set up?

  17. anonymous
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    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?

  18. anonymous
    • 5 years ago
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    so 132.68+6.5?

  19. anonymous
    • 5 years ago
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    139.18

  20. anonymous
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    \[A_{total} = 169\] \[A_{circles} = 132.68\] What is \[A_{not\ circles}\]

  21. anonymous
    • 5 years ago
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    36.32

  22. anonymous
    • 5 years ago
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    Indeed. Now divide that area by the total area to find the probability for a random point to be in that area.

  23. anonymous
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    36.32/169

  24. anonymous
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    .2149112

  25. anonymous
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    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.

  26. anonymous
    • 5 years ago
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    21.49%

  27. anonymous
    • 5 years ago
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    Yep.

  28. anonymous
    • 5 years ago
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    thank you

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