A1 be the event that the receiver functions properly throughout the warranty period, A2 be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A1) 5 .95, P(A2) 5 .98, and P(A3) 5 .80. a. What is the probability that all three components function properly throughout the warranty period

0.7448

Step-by-step explanation:

P(A1) =0.95

P(A2) =0.98

P(A3) =0.8

We have to find P( all three components function properly)=P(A1∩A2∩A3).

We know that the these three events are independent so,

P( all three components function properly)=P(A1∩A2∩A3)=P(A1)*P(A2)*P(A3)

P( all three components function properly)=P(A1∩A2∩A3)=0.95*0.98*0.80

P( all three components function properly)=P(A1∩A2∩A3)=0.7448

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2