If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same, what is the formula to find the modified surface area?

The answer is

Step-by-step explanation:

In order to determine the formula, we have to know the expression of the volume of a rectangular prism.

I have attached an image that shows two formulas about the rectangular prism.

Therefore, using the same notation of the image:

L=length of the rectangular prism

W=width of the rectangular prism

H=height of the rectangular prism

So, the original surface area is:

Then, if the width and height of the rectangular prism are each shrunk to one seventh of the original size but the length remains the same, the new surface area is:

Finally, the formula of the modified surface area is

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

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: