A factory manager collected data on the number of breakdowns per day. From these data, he derived the probability distribution for X, the number of breakdowns on a given day:

X 0 1 2
prob 0.80 0.15 0.05

1)The mean of X is (exact answer)

2)The standard deviation of X is (to three places after the decimal)

3)On average, how many breakdowns are there per day?

4)Assuming there are weekend shifts in the factory (work goes on every day), about how many breakdowns are expected during a one-year period. (non-leap year, and round to the nearest whole number).

a) 0.25

b) 0.536

c) 0.25

d) 91

Step-by-step explanation:

We are given the following in the question:

X:         0         1          2

P(x) : 0.80     0.15    0.05

a) The mean of X

b) The standard deviation of X

c) breakdowns are there per day

On average, there are 0.25 breakdowns per day.

d) breakdowns are expected during a one-year period

Thus, there are approximately 91 breakdowns during a one-year period.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation: