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anonymous

  • one year ago

The figure below shows a shaded circular region inside a larger circle: A shaded circle is shown inside another larger circle. The radius of the smaller circle is labeled as r and the radius of the larger circle is labeled as R. On the right side of the image is written r equal to 4 inches and below r equal to 4 inches is written R equal to 5 inches. What is the probability that a point chosen inside the larger circle is not in the shaded region?

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  1. anonymous
    • one year ago
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    pic

  2. anonymous
    • one year ago
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    24% 36% 50% 64%

  3. anonymous
    • one year ago
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    one of these is answer ^

  4. mathstudent55
    • one year ago
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    You need to find what percentage of the large circle is the unshaded area. The unshaded region is the difference in the areas of the circles. First, find the areas of the two circles.

  5. mathstudent55
    • one year ago
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    Do you know hoe to find the area of a circle?

  6. mathstudent55
    • one year ago
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    Here is the formula: \(\large A_{circle} = \pi r^2\)

  7. anonymous
    • one year ago
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    so pi times 5?

  8. mathstudent55
    • one year ago
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    pi times 5 squared pi times 4 squared

  9. mathstudent55
    • one year ago
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    Remember the radius is squared in the formula for the area of a circle.

  10. mathstudent55
    • one year ago
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    This is how you find the areas of the circles: pi * 5 * 5 pi * 4 * 4

  11. anonymous
    • one year ago
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    so its 78.5 and 50.24?

  12. anonymous
    • one year ago
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    @mathstudent55 so its 78.5 and 50.24?

  13. mathstudent55
    • one year ago
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    Good. Now let's find the unshaded area. Subtract the smaller area form the larger area.

  14. anonymous
    • one year ago
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    @mathstudent55 so 28.26?

  15. mathstudent55
    • one year ago
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    Correct. Now you need to calculate what percentage of the large circle is the unshaded area.

  16. mathstudent55
    • one year ago
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    The unshaded area if the part. The large circle is the whole. To find what percent a part is of a whole, divide the part by the whole and multiply by 100.

  17. anonymous
    • one year ago
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    i dont get it :(

  18. mathstudent55
    • one year ago
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    Here is an example. Do you know that 50% means half?

  19. anonymous
    • one year ago
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    yeah

  20. mathstudent55
    • one year ago
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    Ok. Now I'm going to follow the rule above of finding a percent and show you how 50% means half. Since you already know that 50% means half, you'll understand this more easily. Then we can try the problem again.

  21. mathstudent55
    • one year ago
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    5 is half of 10. Since we know that 50% means half, we know that 5 is 50% of 10. What if we had to find what percentage of 10 is 5? We follow the rule above. 5 is the part. 10 is the whole. To find a percentage, divide the part by the whole and multiply by 100. 5/10 * 100 = 0.5 * 100 = 50 This shows us that 5 is 50% of 10.

  22. mathstudent55
    • one year ago
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    Here is a second example. We know that 25% is a quarter. 6 is a quarter of 24, so 6 must be 25% of 24. Let's calculate it to see how it's done. 6 is the part 24 is the whole 6/24 * 100 = 0.25 * 100 = 25 This shows that 6 is 25% of 24

  23. anonymous
    • one year ago
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    sorry i already finished it :P my brother answered it for me

  24. mathstudent55
    • one year ago
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    Now we can do the same with your problem. We have the unshaded area, 28.26. This is the part. The whole is 78.5. The percentage is: 28.26/78.5 * 100 = 36 The answer is 36%

  25. mathstudent55
    • one year ago
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    Did your brorther get 36%?

  26. anonymous
    • one year ago
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    yeah :P

  27. anonymous
    • one year ago
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    thanks anyway

  28. mathstudent55
    • one year ago
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    Great. If your brother can help you, that's great. It's easier to help if you're there than through a computer.

  29. mathstudent55
    • one year ago
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    You're welcome.

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