A production facility contains two machines that are used to reworkitems that are initially defective.

LetXbe the number of hours that the firstmachine is in use, and letYbe the number of hours that the second machine isin use, on a randomly chosen day.

Assume that X and Y have joint probabilitydensity function given by, f(x, y) ={32(x2+y2)0< x <1 and 0< y <10 otherwise

What is the probability that both machines are in operation for more than half an hour?

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.

b

step-by-step explanation: