The density function of the continuous random variable x, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is given below: f(x) = { x, 0 < x < 1 8 − x, 1 ≤ x < 2 0, otherwise Find the average number of hours per year that families run their vacuum cleaners?

answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

can i get the link to the assignment?

step-by-step explanation:

2

step-by-step explanation:

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