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MATH / A point with coordinates (x, y) is randomly selected such that 0≤x≤10 and 0≤y≤10. What is the probability that the coordinates of the point will satisfy 2x+5y≥20? Express your answ…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
A point with coordinates is randomly selected such that and . What is the probability that the coordinates of the point will satisfy ? Express your answer as a common fraction.
[asy]
size(5cm,5cm);
draw((-2,0)--(12,0),Arrows);
draw((0,-2)--(0,12),Arrows);
pair a,b,x;
x=(0,0);
a=(10,0);
b=(0,10);
add(pathticks(x--a,2,0.1,0,25));
add(pathticks(x--a,2,0.2,0,25));
add(pathticks(x--a,2,0.3,0,25));
add(pathticks(x--a,2,0.4,0,25));
add(pathticks(x--a,2,0.5,0,25));
add(pathticks(x--a,2,0.6,0,25));
add(pathticks(x--a,2,0.7,0,25));
add(pathticks(x--a,2,0.8,0,25));
add(pathticks(x--a,2,0.9,0,25));
add(pathticks(x--a,2,1,0,25));
add(pathticks(x--b,2,0.1,0,25));
add(pathticks(x--b,2,0.2,0,25));
add(pathticks(x--b,2,0.3,0,25));
add(pathticks(x--b,2,0.4,0,25));
add(pathticks(x--b,2,0.5,0,25));
add(pathticks(x--b,2,0.6,0,25));
add(pathticks(x--b,2,0.7,0,25));
add(pathticks(x--b,2,0.8,0,25));
add(pathticks(x--b,2,0.9,0,25));
add(pathticks(x--b,2,1,0,25));
[/asy]
Plain-text mathematical notation (without MathML)
A point with coordinates (x, y) is randomly selected such that 0≤x≤10 and 0≤y≤10. What is the probability that the coordinates of the point will satisfy 2x+5y≥20? Express your answer as a common fraction. [asy] size(5cm,5cm); draw((-2,0)--(12,0),Arrows); draw((0,-2)--(0,12),Arrows); pair a,b,x; x=(0,0); a=(10,0); b=(0,10); add(pathticks(x--a,2,0.1,0,25)); add(pathticks(x--a,2,0.2,0,25)); add(pathticks(x--a,2,0.3,0,25)); add(pathticks(x--a,2,0.4,0,25)); add(pathticks(x--a,2,0.5,0,25)); add(pathticks(x--a,2,0.6,0,25)); add(pathticks(x--a,2,0.7,0,25)); add(pathticks(x--a,2,0.8,0,25)); add(pathticks(x--a,2,0.9,0,25)); add(pathticks(x--a,2,1,0,25)); add(pathticks(x--b,2,0.1,0,25)); add(pathticks(x--b,2,0.2,0,25)); add(pathticks(x--b,2,0.3,0,25)); add(pathticks(x--b,2,0.4,0,25)); add(pathticks(x--b,2,0.5,0,25)); add(pathticks(x--b,2,0.6,0,25)); add(pathticks(x--b,2,0.7,0,25)); add(pathticks(x--b,2,0.8,0,25)); add(pathticks(x--b,2,0.9,0,25)); add(pathticks(x--b,2,1,0,25)); [/asy]
Original LaTeX notation
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. [asy] size(5cm,5cm); draw((-2,0)--(12,0),Arrows); draw((0,-2)--(0,12),Arrows); pair a,b,x; x=(0,0); a=(10,0); b=(0,10); add(pathticks(x--a,2,0.1,0,25)); add(pathticks(x--a,2,0.2,0,25)); add(pathticks(x--a,2,0.3,0,25)); add(pathticks(x--a,2,0.4,0,25)); add(pathticks(x--a,2,0.5,0,25)); add(pathticks(x--a,2,0.6,0,25)); add(pathticks(x--a,2,0.7,0,25)); add(pathticks(x--a,2,0.8,0,25)); add(pathticks(x--a,2,0.9,0,25)); add(pathticks(x--a,2,1,0,25)); add(pathticks(x--b,2,0.1,0,25)); add(pathticks(x--b,2,0.2,0,25)); add(pathticks(x--b,2,0.3,0,25)); add(pathticks(x--b,2,0.4,0,25)); add(pathticks(x--b,2,0.5,0,25)); add(pathticks(x--b,2,0.6,0,25)); add(pathticks(x--b,2,0.7,0,25)); add(pathticks(x--b,2,0.8,0,25)); add(pathticks(x--b,2,0.9,0,25)); add(pathticks(x--b,2,1,0,25)); [/asy]
level
Level 4
type
Counting & Probability
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