mckenzieandjesus
  • mckenzieandjesus
A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mckenzieandjesus
  • mckenzieandjesus
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mckenzieandjesus
  • mckenzieandjesus
about 70% about 60% about 90% about 80%
mckenzieandjesus
  • mckenzieandjesus
@jim_thompson5910

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mckenzieandjesus
  • mckenzieandjesus
How do I find the probability?
SolomonZelman
  • SolomonZelman
basically, you need the ratio between the square, and a circle that is subscribed in it.
SolomonZelman
  • SolomonZelman
lets define the side of a square using s.
SolomonZelman
  • SolomonZelman
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.
mckenzieandjesus
  • mckenzieandjesus
ok
SolomonZelman
  • SolomonZelman
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 `
mckenzieandjesus
  • mckenzieandjesus
are of a circle is A=pi r^2
mckenzieandjesus
  • mckenzieandjesus
ok
SolomonZelman
  • SolomonZelman
the probability that the point in the whole square that you randomly choose is \(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}\)
SolomonZelman
  • SolomonZelman
good luck....
SolomonZelman
  • SolomonZelman
if you have questions, you are always welcome to ask
mckenzieandjesus
  • mckenzieandjesus
There is no lengths or anything so im kinda confused
SolomonZelman
  • SolomonZelman
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)
SolomonZelman
  • SolomonZelman
there is length. length for what don't you see?
SolomonZelman
  • SolomonZelman
radius = s/2 side of the square = diameter of the circle = s
mckenzieandjesus
  • mckenzieandjesus
but i dont know the side of the square or diameter of the circle to figure it out. Sorry im lost
SolomonZelman
  • SolomonZelman
(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.)
mckenzieandjesus
  • mckenzieandjesus
So i make up a side length and a diameter of the circle?
SolomonZelman
  • SolomonZelman
Yes, that is what I showed
SolomonZelman
  • SolomonZelman
I denoted the length with letter s.
SolomonZelman
  • SolomonZelman
And now the probability of a randomly selected point, to lay on a circle is `A(circle) ÷ A(square)`
SolomonZelman
  • SolomonZelman
our area of the circle is πs²/4 area of the square is s²
SolomonZelman
  • SolomonZelman
still confused?
mckenzieandjesus
  • mckenzieandjesus
so 5^2=25 and 3.14*5^2 = 78 1/2
SolomonZelman
  • SolomonZelman
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.
mckenzieandjesus
  • mckenzieandjesus
i thought u said i do
SolomonZelman
  • SolomonZelman
We are just using any side-length "s" (regardless of what "s" is - of course, as long as s>0)
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
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?
mckenzieandjesus
  • mckenzieandjesus
i know the formulas
SolomonZelman
  • SolomonZelman
ok, now divide the area of circle, by area of the square.
SolomonZelman
  • SolomonZelman
\(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}=\frac{\frac{\pi}{4}{\rm s}^2}{{\rm s}^2}=~...?\)
SolomonZelman
  • SolomonZelman
(the s² cancels on top and bottom, and you remain with ?)
mckenzieandjesus
  • mckenzieandjesus
pi/4?
mckenzieandjesus
  • mckenzieandjesus
3.14/4?
SolomonZelman
  • SolomonZelman
yes π/4 :)
SolomonZelman
  • SolomonZelman
(and again, that is regardless of the value of s, for all real values of s that are greater than 0)
mckenzieandjesus
  • mckenzieandjesus
okay
SolomonZelman
  • SolomonZelman
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
mckenzieandjesus
  • mckenzieandjesus
i did 3.14/4 = 157/200
mckenzieandjesus
  • mckenzieandjesus
ok so 157/250
jim_thompson5910
  • jim_thompson5910
|dw:1435286362761:dw|
jim_thompson5910
  • jim_thompson5910
An alternative is to think of the square with side length 2r so the radius of each circle is r |dw:1435286688332:dw|
mckenzieandjesus
  • mckenzieandjesus
ok
jim_thompson5910
  • jim_thompson5910
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
mckenzieandjesus
  • mckenzieandjesus
what do i put for r
jim_thompson5910
  • jim_thompson5910
r can be any number you want the 'r's will cancel, so it really doesn't matter
jim_thompson5910
  • jim_thompson5910
same with the 's's following SolomonZelman's method
mckenzieandjesus
  • mckenzieandjesus
so i could do 3.14*5^2/4*5^2?
SolomonZelman
  • SolomonZelman
yes, I guess to find the answer you can of course give the side of the square any length like 3.
SolomonZelman
  • SolomonZelman
I was just thinking that it asked for a complete prove that shows the probability of π/4 for all positive s.
mckenzieandjesus
  • mckenzieandjesus
or 3.14*5^2/4*2^2= 78 1/2 now what?
jim_thompson5910
  • jim_thompson5910
once you pick a number for r, you have to stick with it
jim_thompson5910
  • jim_thompson5910
and I should have used parenthesis (pi*r^2)/(4r^2)
mckenzieandjesus
  • mckenzieandjesus
so (3.14*5^2)/(4*5^2)?
mckenzieandjesus
  • mckenzieandjesus
= 157/200
mckenzieandjesus
  • mckenzieandjesus
now what?
jim_thompson5910
  • jim_thompson5910
what format do they want the answer? as a fraction? or decimal?
mckenzieandjesus
  • mckenzieandjesus
about 70% about 60% about 90% about 80%
jim_thompson5910
  • jim_thompson5910
oh ok
jim_thompson5910
  • jim_thompson5910
convert the fraction you have to a decimal then convert that decimal to a percent
mckenzieandjesus
  • mckenzieandjesus
0.785
jim_thompson5910
  • jim_thompson5910
convert 0.785 to a percent
mckenzieandjesus
  • mckenzieandjesus
78.5%
mckenzieandjesus
  • mckenzieandjesus
about 80%?
jim_thompson5910
  • jim_thompson5910
correct
mckenzieandjesus
  • mckenzieandjesus
well that was confusing lol thanku
mckenzieandjesus
  • mckenzieandjesus
whats a minor arc in a circle?
jim_thompson5910
  • jim_thompson5910
http://mathworld.wolfram.com/MinorArc.html any arc that is smaller than 180 degrees
jim_thompson5910
  • jim_thompson5910
an arc is just a piece of the whole circumference
mckenzieandjesus
  • mckenzieandjesus
ok so it be PS?
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jim_thompson5910
  • jim_thompson5910
that's one minor arc
mckenzieandjesus
  • mckenzieandjesus
MY CHOICES: PS, SO, SQ, PSR
mckenzieandjesus
  • mckenzieandjesus
the others didnt look right
jim_thompson5910
  • jim_thompson5910
yeah PS is the only minor arc SO isn't even an arc (it's a radius)
mckenzieandjesus
  • mckenzieandjesus
thats what i thought

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