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If two lines l and m have equations y = -x + 6 and y = -2x + 8, what is the probability that a point randomly selected in the 1st quadrant and below l will fall between l and m? Express your answer as a decimal to the nearest hundredth.

 Nov 12, 2020
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Look at the graph, here  : https://www.desmos.com/calculator/40z8d53zzr

 

The triangle  formed by  L   has a base of  6  and a height of 6...so....its area = (1/2) (6)(6)  = 36/2  = 18

 

The two lines intersect at (2,4)

 

So.....the  area  between  L and M   and below L  is a triangle with a base of 2 and a height of 4

 

And this area  =  (1/2)(2) (4)  =  8/2  = 4

 

So....the probability of a point  being below L and between L and M  =   4/18  = 2/9   ≈ 0.22

 

 

cool cool cool

 Nov 12, 2020

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