+0  
 
+1
229
1
avatar+753 

A point with coordinates $(x,\ y)$ is randomly selected such that $0\leq x \leq10$ and $0\leq y \leq10$. What is the probability that the coordinates of the point will satisfy $2x+5y \geq 20$? Express your answer as a common fraction.

Lightning  Mar 30, 2018
 #1
avatar+89781 
+2

\(0\leq x \leq10 and 0\leq y \leq10\)

 

\(2x+5y \geq 20 \)

 

The first  two conditions set  up  a square that is  10 units  on a side ....so the total area  is  10^2  =

100 units^2  (1)

 

The area below  the  inequality   2x  + 5y  ≥ 20  [ but still within the square ]  forms a triangle  with a base  of 10 and a height of 4

 

Its  area  =  10  * 4 / 2  = 20 units^2

 

Then  the area  above the inequality  [ but still within the square is 100 - 20 ]  =  80 units^2   (2)

 

So....the probability that  the coordinates of a point satisfy all three conditions  is

 

(2) / (1)    =     80 / 100    =   4/5

 

Here's a graph : https://www.desmos.com/calculator/ome3jb01pa

 

 

cool cool cool

CPhill  Mar 30, 2018

34 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.