The value of -4^2 is _____?<br><br> 16<br><br> -16<br><br> 8<br><br> -8

Find all values of c in the open interval (a, b) such that f'(c)=(f(b)-f(a))/(b-a)

timama [110]

<h3>Answer: c = 7/4</h3>

================================================

Work Shown:

Compute the function value at the endpoints

$f(x) = \sqrt{4-x}\\\\f(-5) = \sqrt{4-(-5)} = 3\\\\f(4) = \sqrt{4-4} = 0\\\\$

With a = -5 and b = 4, we have

$f'(c) = \frac{f(b)-f(a)}{b-a}\\\\f'(c) = \frac{f(4)-f(-5)}{4-(-5)}\\\\f'(c) = \frac{0-3}{9}\\\\f'(c) = -\frac{1}{3}\\\\$

So,

$f(x) = \sqrt{4-x}\\\\f'(x) = -\frac{1}{2\sqrt{4-x}}\\\\f'(c) = -\frac{1}{3}\\\\-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\$

Use algebra to solve for c

$-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\\frac{1}{2\sqrt{4-c}} = \frac{1}{3}\\\\3 = 2\sqrt{4-c}\\\\2\sqrt{4-c} = 3\\\\\sqrt{4-c} = \frac{3}{2}\\\\4-c = \frac{9}{4}\\\\c = 4-\frac{9}{4}\\\\c = \frac{16-9}{4}\\\\c = \frac{7}{4}\\\\$

6 0

3 years ago

Dwayne is trying to find the fraction represented by the repeating decimal 0.5. He completes the three steps shown:

Studentka2010 [4]

Answer:

Step-by-step explanation:

10x = 5.5

9x = 5

x = 5/9

therefore, the answer is C. 5/9

8 0

3 years ago

Hey yall what would the solution to the system be?

tamaranim1 [39]

Answer:

~-~-~-~-(6, 2)-~-~-~-~

6 0

3 years ago

Maya bought 16 boxes of cookies and each box has 13 cookies. She needs to place an equal number of cookies in 8 containers.

aev [14]

Answer:

first you multiply the boxes and how much are in the boxes then you have that answer and you divide it by 8

5 0

3 years ago

Read 2 more answers

The CEO of a large electric utility claims that more than 75 percent of his customers are very satisfied with the service they r

vichka [17]

Answer:

$z=\frac{0.77-0.75}{\sqrt{\frac{0.75(1-0.75)}{100}}}=0.462$

Now we can find the p value using the alternative hypothesis with this probability:

$p_v =P(z>0.462)=0.322$

Since the p value is large enough, we have evidence to conclude that the true proportion for this case is NOT significanctly higher than 0.75 since we FAIL to reject the null hypothesis at any significance level lower than 30%

Step-by-step explanation:

Information provided

n=100 represent the random sample selected

$\hat p=0.77$ estimated proportion of students that are satisfied

is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to verify if more than 75 percent of his customers are very satisfied with the service they receive, then the system of hypothesis is.:

Null hypothesis: $p\leq 0.75$

Alternative hypothesis: $p > 0.75$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.77-0.75}{\sqrt{\frac{0.75(1-0.75)}{100}}}=0.462$

Now we can find the p value using the alternative hypothesis with this probability:

$p_v =P(z>0.462)=0.322$

Since the p value is large enough we have evidence to conclude that the true proportion for this case is NOT significanctly higher than 0.75 since we FAIL to reject the null hypothesis at any significance level lower than 30%

4 0

3 years ago

The value of -4^2 is _____? 16 -16 8 -8