Which of the following is a perfect square<br> A. 13<br> B. 100<br> C. 127<br> D. 102

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that s

kupik [55]

Step-by-step explanation:

$\qquad\sf {:}\longrightarrow f (-4)=(-4)^3-4 (-4)^2-16 (-4)+9$

$\qquad\sf {:}\longrightarrow -64-64+64+9$

$\qquad\sf {:}\longrightarrow -64+9$

$\qquad\sf {:}\longrightarrow -55$

8 0

2 years ago

Read 2 more answers

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if

topjm [15]

Answer:

a) The expected value is $\frac{-1}{15}$

b) The variance is $\frac{49}{45}$

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is $\binom{10}{2}$ .

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is $\binom{5}{2}$ . Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is $\binom{5}{1}\cdot \binom{5}{1}$ . So, we define the following probabilities.

Probability of winning: $\frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}$

Probability of losing $\frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}$

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing = $1.10\cdot \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}$

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing = $1.10^2\cdot \frac{4}{9}+\frac{5}{9}=\frac{82}{75}$

We will use the following formula

$Var(X) = E(X^2)-E(X)^2$

Thus

Var(X) = $\frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}$

7 0

3 years ago

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for

patriot [66]

100-0.0124=99.9876

10%=1/10
1/10P=P(0.999876)^t
divide both sides by P
1/10=0.999876^t
take ln of both sides
ln(1/10)=t (ln(0.999876))
divide both sides by (ln(0.999876))
ln(1/10)/(ln(0.999876))=t
use calculator
18568.08=t
about 18568 years

5 0

2 years ago

Find the area of a triangle with sides 8 equals 5 b equals 8 and C equals 11

IceJOKER [234]

I round the answer to the second digit and get 18.33

4 0

3 years ago

Find the measure of angle A

kow [346]

Answer:

A=45

Step-by-step explanation:

If you take a pencil and put it in the middle of the line it looks like it could be half of the other side

180-45=135

8 0

2 years ago

Which of the following is a perfect square A. 13 B. 100 C. 127 D. 102