Amanufacturer knows that their items have a normally distributed lifespan, with a mean of 7.4 years, and standard deviation of 2.3 years. if you randomly purchase one item, what is the probability it will last longer than 4 years?

0.9306

Step-by-step explanation:

Given : A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.4 years, and standard deviation of 2.3 years.

i.e.

Let x denotes the lifespan of the items.

Then, the probability it will last longer than 4 years will be :-

Hence , our required probability =  0.9306

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17