5) Suppose hospital employees are required to take lie detector tests. Suppose that the probability is 0.05 that the lie detector concludes that a person is lying who, in fact, is telling the truth. Suppose that any pair of tests is independent.

a) What is the probability that the lie detector will conclude that each of three employees is lying when all are telling the truth?
b) What is the probability that the lie detector will conclude that at least one of three employees is lying when all are telling the truth?

a)Binomial Problem with n = 3 and p = 0.05

P(all telling truth) = 0.05^3 = 0.000125

b) P(at least one true) = 1 - P(says zero are lying when all tell truth)

= 1 -0.95^3

= 0.1426

Step-by-step explanation:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2