<span>The area of the base is x^2> The height is h. Each side of the box has area xh. There are 4 sides of the box so the total surface area of the box is x^2+4xh and that is equal to 1000. Solve that equation for h:
x^2+4xh = 1000 h = (1000-x^2)/4x so the Volume = x^2[(1000-x^2)/4x]
Simplify and get V = 250x-x^3/4
The volume will be a maximum when its first derivative is 0.
V' = 250-3/4x^2
Set to 0 and solve. x=18.26
Now plug into the volume function to find the maximum volume:
V=250(18.26)-(18.26)^3/4
V= 4564.35 - 1522.10 =3042.25</span>
-4.16 is your answer and I have to fill up space to submit this
Answer:
0.3085,0.2417,0.0045
Step-by-step explanation:
Given that X, the amount of money spent at shopping centers between 4 P.M. and 6 P.M. on Sundays has a normal distribution with mean $85 and with a standard deviation of $20.
X is N(85, 20)
To convert into std normal variate we use the following formula

a) the probability that he has spent more than $95 at the mall
=
b. the probability that he has spent between $95 and $115 at the mall
=
c. If two shoppers are randomly selected, what is the probability that both shoppers have spent more than $115 at the mall
=product of two probabilities since independent
= 
the answer is a because complement angles have a sum of 90 degrees