An open box is to be made from a flat piece of material 19 inches long and 4 inches wide by cutting equal squares of length x from the corners and folding up the sides. write the volume vof the box as a function of x. leave it as a product of factors, do not multiply out the factors. v= if we write the domain of the box as an open interval in the form (a, b), then what is a=? a= and what is b=? b=

Answer with Step-by-step explanation:

We are given that

Length of flat piece of material =19 inches

Width of flat piece=4 inches

An open box  is to be made from a flat piece by cutting equal squares of length  x from the corners and folding up the sides

Therefore, length of open box= inches

Width of open box=

Height of box=

Volume of box=

Substitute the values then we get

Volume of box=

Because volume of open box is always greater than  zero.

Then ,

Substitute

By adding 19 on both sides

Dividing by 2 on both sides

It means

Substitute

Adding 4 on both sides then we get

Dividing by 2 on both sides

Then,

Therefore, domain of the box =

Then ,a=0 and b=2

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: