Let

. Then

, and differentiating both sides with respect to

gives


Now, when

, you get

You have

, so

and

. So
Answer:
-45/4 or -11.25
I'm pretty sure this is right hope it helps
Answer:
24
Step-by-step explanation:
all odd numbers possible: 1, 3, 5, 7
__ __ __ __
there are 4 possibilities for the first blank
for the second blank there are 4-1 = 3 possibilities as one of the numbers will have been used
for the third blank there are 4-2 = 2 possibilities as 2 of the numbers have been used
for the last blank there is only 1 possibility
so the number of solutions possible is 4 x 3 x 2 x 1 = 24
Answer:
(a) 0.2824
(b) 0.0002441
Step-by-step explanation:
Assuming that the population is large enough to behave as a binomial distribution (between whites and non-whites), the probability of 12 out of 12 juros being white is:

Where p(w) is the proportion of the population that is white:
(a) for p = 0.90

The probability is 0.2824.
(b) for p = 0.50

The probability is 0.0002441.
The pump moves 6 gallons per minute. Hope this is what you wanted.