What is the domain of this function?

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?

timama [110]

The Mean Value Theorem:
If a function is continuous on [ a, b ] and differentiable on ( a , b ) than there is a point c in ( a, b ) such that:
f ` ( c )= ( f ( b ) - f ( a ) ) / ( b - a )
f ` ( c ) = ( f ( 2 ) - f ( 0 ) ) / ( 2 - 0 )
f `( x ) = 10 x - 3
f ` ( c ) = 10 c - 3
2 f ` ( c ) = 16 - 2
f ` ( c ) = 7
7 = 10 c - 3
c = 1
Answer:
Yes, the function is continuous on [ 0, 2 ] and differentiable on ( 0, 2 ).

4 0

3 years ago

Which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13

saw5 [17]

Answer:

a) The null and alternative hypothesis are:

$H_0: \mu=13.04\\\\H_a:\mu< 13.04$

b) P-value = 0.0151

c) We reject the null hypothesis.

We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean cost of a restaurant meal is significantly less than fixing a comparable meal at home.

Then, the null and alternative hypothesis are:

$H_0: \mu=13.04\\\\H_a:\mu< 13.04$

The significance level is 0.05.

The sample has a size n=100.

The sample mean is M=12.6.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{100}}=0.2$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{12.6-13.04}{0.2}=\dfrac{-0.44}{0.2}=-2.2$

The degrees of freedom for this sample size are:

$df=n-1=100-1=99$

This test is a left-tailed test, with 99 degrees of freedom and t=-2.2, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.0151) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean cost of a restaurant meal is significantly less than fixing a comparable meal at home.

6 0

3 years ago

-8y=-800<br> what is y?<br> Plz with the explanation...

solniwko [45]

Answer:

-100

Step-by-step explanation:

8*-100=-800

4 0

3 years ago

Read 2 more answers

PLEASE HELP ME ASAP!!!!!

slavikrds [6]

First find the circumference of the wheel ( the length around the outside).
Circumference = 2 x PI x Radius

Circumference = 2 x 3.14 x 14 = 87.92 feet.

This would be the distance it traveled in one full rotation.

To find the distance traveled in 96 degrees, multiply total distance by 96/360 ( this is the fraction of a full rotation it travels).

87.92 x 96/360 = 23.4 feet

5 0

3 years ago

Days on the market are shown for the 36 most recent home sales in the city of Sonando Hills. 16546208818045851658823266716813621

Volgvan

Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given data

$\begin{gathered} 165,46,20,88,180,45,85,165,8,8,23,26,67,168,136,21,143,8,84,22,106,131,16,152,171,64,33,116,151,117,99,61,159 \\ 73,51,136 \end{gathered}$

STEP 2: Find the mean

$\begin{gathered} mean=\frac{sum\text{ of data values}}{number\text{ of data values}} \\ sum\text{ of data values}=3144 \\ Number\text{ of data values}=36 \\ mean=\frac{3144}{36}=87.33333333\approx87.33 \end{gathered}$

mean is 87.33

STEP 3: Find the median

$undefined$

5 0

1 year ago