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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.
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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mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0about 70% about 60% about 90% about 80%

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0How do I find the probability?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1basically, you need the ratio between the square, and a circle that is subscribed in it.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1lets define the side of a square using s.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1The 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.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1The 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
 one year ago
Best ResponseYou've already chosen the best response.0are of a circle is A=pi r^2

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1the 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
 one year ago
Best ResponseYou've already chosen the best response.1if you have questions, you are always welcome to ask

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0There is no lengths or anything so im kinda confused

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1that 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
 one year ago
Best ResponseYou've already chosen the best response.1there is length. length for what don't you see?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1radius = s/2 side of the square = diameter of the circle = s

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0but i dont know the side of the square or diameter of the circle to figure it out. Sorry im lost

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(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
 one year ago
Best ResponseYou've already chosen the best response.0So i make up a side length and a diameter of the circle?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that is what I showed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I denoted the length with letter s.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And now the probability of a randomly selected point, to lay on a circle is `A(circle) ÷ A(square)`

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1our area of the circle is πs²/4 area of the square is s²

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0so 5^2=25 and 3.14*5^2 = 78 1/2

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1no, 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
 one year ago
Best ResponseYou've already chosen the best response.0i thought u said i do

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1We are just using any sidelength "s" (regardless of what "s" is  of course, as long as s>0)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I 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
 one year ago
Best ResponseYou've already chosen the best response.1But, 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
 one year ago
Best ResponseYou've already chosen the best response.0i know the formulas

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1ok, now divide the area of circle, by area of the square.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}=\frac{\frac{\pi}{4}{\rm s}^2}{{\rm s}^2}=~...?\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(the s² cancels on top and bottom, and you remain with ?)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(and again, that is regardless of the value of s, for all real values of s that are greater than 0)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.13.14/4 (if you use that approximation, then you might want to rewrite the fraction, reduce it... or you know...) i would perhaps go: 3.14/4= 314/500= 157/250

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0i did 3.14/4 = 157/200

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0ok so 157/250

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435286362761:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1An alternative is to think of the square with side length 2r so the radius of each circle is r dw:1435286688332:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1area 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
 one year ago
Best ResponseYou've already chosen the best response.0what do i put for r

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1r can be any number you want the 'r's will cancel, so it really doesn't matter

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1same with the 's's following SolomonZelman's method

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0so i could do 3.14*5^2/4*5^2?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, I guess to find the answer you can of course give the side of the square any length like 3.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I was just thinking that it asked for a complete prove that shows the probability of π/4 for all positive s.

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0or 3.14*5^2/4*2^2= 78 1/2 now what?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1once you pick a number for r, you have to stick with it

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and I should have used parenthesis (pi*r^2)/(4r^2)

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0so (3.14*5^2)/(4*5^2)?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what format do they want the answer? as a fraction? or decimal?

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0about 70% about 60% about 90% about 80%

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1convert the fraction you have to a decimal then convert that decimal to a percent

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1convert 0.785 to a percent

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0well that was confusing lol thanku

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0whats a minor arc in a circle?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1http://mathworld.wolfram.com/MinorArc.html any arc that is smaller than 180 degrees

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1an arc is just a piece of the whole circumference

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0ok so it be PS?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1that's one minor arc

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0MY CHOICES: PS, SO, SQ, PSR

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0the others didnt look right

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah PS is the only minor arc SO isn't even an arc (it's a radius)

mckenzieandjesus
 one year ago
Best ResponseYou've already chosen the best response.0thats what i thought
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