(a) let (x, y ) denote a uniformly chosen random point inside the unit square

[0,1]^2 =[0,1]×[0,1]={(x, y): 0≤x, y≤1}.

let 0 ≤ a < b ≤ 1. find the probability p(a < x < b), that is, the probability that the x-coordinate x of the chosen point lies in the interval (a, b).

(b) what is the probability p (|x−y|≤1/4) ?

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950