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mckenzieandjesus

  • one year ago

A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

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  1. mckenzieandjesus
    • one year ago
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  2. mckenzieandjesus
    • one year ago
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    about 70% about 60% about 90% about 80%

  3. mckenzieandjesus
    • one year ago
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    @jim_thompson5910

  4. mckenzieandjesus
    • one year ago
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    How do I find the probability?

  5. SolomonZelman
    • one year ago
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    basically, you need the ratio between the square, and a circle that is subscribed in it.

  6. SolomonZelman
    • one year ago
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    lets define the side of a square using s.

  7. SolomonZelman
    • one year ago
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    The side of a the square is equivalent to the diameter of the circle. The area of the square is just A=s². The area of the circle however is a little bit harder.

  8. mckenzieandjesus
    • one year ago
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    ok

  9. SolomonZelman
    • one year ago
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    The radius is s/2 (considering the fact that diameter =s) Now, the formula for the area of the circle is `A=π • r²` `A=π • (s/2)² = πs² /4 ` or alternatively `= (π/4) • s² `

  10. mckenzieandjesus
    • one year ago
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    are of a circle is A=pi r^2

  11. mckenzieandjesus
    • one year ago
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    ok

  12. SolomonZelman
    • one year ago
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    the probability that the point in the whole square that you randomly choose is \(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}\)

  13. SolomonZelman
    • one year ago
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    good luck....

  14. SolomonZelman
    • one year ago
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    if you have questions, you are always welcome to ask

  15. mckenzieandjesus
    • one year ago
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    There is no lengths or anything so im kinda confused

  16. SolomonZelman
    • one year ago
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    that sentence is supposed to say the probability that the point in the whole square that you randomly `will lay on the shaded part ` choose is (the part in gray I left out. apologize)

  17. SolomonZelman
    • one year ago
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    there is length. length for what don't you see?

  18. SolomonZelman
    • one year ago
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    radius = s/2 side of the square = diameter of the circle = s

  19. mckenzieandjesus
    • one year ago
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    but i dont know the side of the square or diameter of the circle to figure it out. Sorry im lost

  20. SolomonZelman
    • one year ago
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    (this probability that they ask you for, and that we will find, is true for any side length of the square, this is why the side of the square isn't given to us.)

  21. mckenzieandjesus
    • one year ago
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    So i make up a side length and a diameter of the circle?

  22. SolomonZelman
    • one year ago
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    Yes, that is what I showed

  23. SolomonZelman
    • one year ago
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    I denoted the length with letter s.

  24. SolomonZelman
    • one year ago
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    And now the probability of a randomly selected point, to lay on a circle is `A(circle) ÷ A(square)`

  25. SolomonZelman
    • one year ago
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    our area of the circle is πs²/4 area of the square is s²

  26. SolomonZelman
    • one year ago
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    still confused?

  27. mckenzieandjesus
    • one year ago
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    so 5^2=25 and 3.14*5^2 = 78 1/2

  28. SolomonZelman
    • one year ago
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    no, you don't make up a length. Not that it would matter, but you are not asked or meant to do this. I am sorry.

  29. mckenzieandjesus
    • one year ago
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    i thought u said i do

  30. SolomonZelman
    • one year ago
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    We are just using any side-length "s" (regardless of what "s" is - of course, as long as s>0)

  31. SolomonZelman
    • one year ago
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    I said that we use any sidelength 's'. we show or work, for why is it so, that this probability is blank in this case? if they wanted to, they would have given you the side. but they did not- for a reason.

  32. SolomonZelman
    • one year ago
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    But, do you understand my previous replies, how I found the area of a square and a circle in terms of s, or should I go over that again?

  33. mckenzieandjesus
    • one year ago
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    i know the formulas

  34. SolomonZelman
    • one year ago
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    ok, now divide the area of circle, by area of the square.

  35. SolomonZelman
    • one year ago
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    \(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}=\frac{\frac{\pi}{4}{\rm s}^2}{{\rm s}^2}=~...?\)

  36. SolomonZelman
    • one year ago
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    (the s² cancels on top and bottom, and you remain with ?)

  37. mckenzieandjesus
    • one year ago
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    pi/4?

  38. mckenzieandjesus
    • one year ago
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    3.14/4?

  39. SolomonZelman
    • one year ago
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    yes π/4 :)

  40. SolomonZelman
    • one year ago
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    (and again, that is regardless of the value of s, for all real values of s that are greater than 0)

  41. mckenzieandjesus
    • one year ago
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    okay

  42. SolomonZelman
    • one year ago
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    3.14/4 (if you use that approximation, then you might want to re-write the fraction, reduce it... or you know...) i would perhaps go: 3.14/4= 314/500= 157/250

  43. mckenzieandjesus
    • one year ago
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    i did 3.14/4 = 157/200

  44. mckenzieandjesus
    • one year ago
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    ok so 157/250

  45. jim_thompson5910
    • one year ago
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    |dw:1435286362761:dw|

  46. jim_thompson5910
    • one year ago
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    An alternative is to think of the square with side length 2r so the radius of each circle is r |dw:1435286688332:dw|

  47. mckenzieandjesus
    • one year ago
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    ok

  48. jim_thompson5910
    • one year ago
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    area of square = (2r)*(2r) = 4r^2 area of circle = pi*r^2 divide the area of the circle by the area of the square = pi*r^2/4r^2 = pi/4 either way you get the same answer

  49. mckenzieandjesus
    • one year ago
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    what do i put for r

  50. jim_thompson5910
    • one year ago
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    r can be any number you want the 'r's will cancel, so it really doesn't matter

  51. jim_thompson5910
    • one year ago
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    same with the 's's following SolomonZelman's method

  52. mckenzieandjesus
    • one year ago
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    so i could do 3.14*5^2/4*5^2?

  53. SolomonZelman
    • one year ago
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    yes, I guess to find the answer you can of course give the side of the square any length like 3.

  54. SolomonZelman
    • one year ago
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    I was just thinking that it asked for a complete prove that shows the probability of π/4 for all positive s.

  55. mckenzieandjesus
    • one year ago
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    or 3.14*5^2/4*2^2= 78 1/2 now what?

  56. jim_thompson5910
    • one year ago
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    once you pick a number for r, you have to stick with it

  57. jim_thompson5910
    • one year ago
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    and I should have used parenthesis (pi*r^2)/(4r^2)

  58. mckenzieandjesus
    • one year ago
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    so (3.14*5^2)/(4*5^2)?

  59. mckenzieandjesus
    • one year ago
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    = 157/200

  60. mckenzieandjesus
    • one year ago
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    now what?

  61. jim_thompson5910
    • one year ago
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    what format do they want the answer? as a fraction? or decimal?

  62. mckenzieandjesus
    • one year ago
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    about 70% about 60% about 90% about 80%

  63. jim_thompson5910
    • one year ago
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    oh ok

  64. jim_thompson5910
    • one year ago
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    convert the fraction you have to a decimal then convert that decimal to a percent

  65. mckenzieandjesus
    • one year ago
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    0.785

  66. jim_thompson5910
    • one year ago
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    convert 0.785 to a percent

  67. mckenzieandjesus
    • one year ago
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    78.5%

  68. mckenzieandjesus
    • one year ago
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    about 80%?

  69. jim_thompson5910
    • one year ago
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    correct

  70. mckenzieandjesus
    • one year ago
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    well that was confusing lol thanku

  71. mckenzieandjesus
    • one year ago
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    whats a minor arc in a circle?

  72. jim_thompson5910
    • one year ago
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    http://mathworld.wolfram.com/MinorArc.html any arc that is smaller than 180 degrees

  73. jim_thompson5910
    • one year ago
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    an arc is just a piece of the whole circumference

  74. mckenzieandjesus
    • one year ago
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    ok so it be PS?

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  75. jim_thompson5910
    • one year ago
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    that's one minor arc

  76. mckenzieandjesus
    • one year ago
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    MY CHOICES: PS, SO, SQ, PSR

  77. mckenzieandjesus
    • one year ago
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    the others didnt look right

  78. jim_thompson5910
    • one year ago
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    yeah PS is the only minor arc SO isn't even an arc (it's a radius)

  79. mckenzieandjesus
    • one year ago
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    thats what i thought

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