The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x)=x(60x^2+30x), where x is the amunt of cheese sold, in hundreds of pounds. The "profit" is -$80 when no cheese is sold. a. Find the profit functionb. Find the profit from selling 200lbs of Brie Cheese

a)

b) The profit from selling 200lbs of Brie Cheese is $240.

Step-by-step explanation:

a. Find the profit function

We have that:

The profit function is P(x), which is the integral of P'(x).

So

There, I applied the integral rules of sum and power.

Since P(0) = -80, K = -80

Then

b. Find the profit from selling 200lbs of Brie Cheese

200 lbs is 200/100 = 2 hundreds of pounds.

So this is P(2).

The profit from selling 200lbs of Brie Cheese is $240.

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560