Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x)

Answer:

The worst-case probability is 0.05

Step-by-step explanation:

The given significance level ([tex]\alpha[/tex]) = 0.05

since Probability of a type I error is [tex]\alpha[/tex]

∴ P (type I error) = 0.05

0.05 will be the worst-case probability of a type I error in at least one of the tests.

Answer:

It is less  than 3000 ft^3 by 450 ft^3

Step-by-step explanation:

The volume of the bin

V = l*w*h

V = 17*15*10

V =2550 ft^3

If it less than 3000 ft^3

V = 3000- 2550 =450 ft^3

If is less by 450 ft^3

Answer:

Let’s first multiply all the numbers given

Since it wants the volume we need to use the formula

LxWxH

17x15x10=2,550

Part A: yes the bin is under 3,000

Part B: by 450 more because if you subtract 3,000 and 2,550 you will get 450

Hope this helps! :)

Answer:

First answer.

Step-by-step explanation:

Multiply everything by 10, to get rid of the decimals.

Answer:

-16-5q

Step-by-step explanation:

-6+4q-6q-6+4q-6q-6+4q-6q= -18-6q

Answer:C

Step-by-step explanation: 100% correct I did it on Khan Academy

Answer:

The hypothesis test is right-tailed

Step-by-step explanation:

To identify a one tailed test, the claim in the case study tests for the either of the two options of greater or less than the mean value in the null hypothesis.

While for a two tailed test, the claim always test for both options: greater and less than the mean value.

Thus given this: H0:X=10.2, Ha:X>10.2, there is only the option of > in the alternative claim thus it is a one tailed hypothesis test and right tailed.

A test with the greater than option is right tailed while that with the less than option is left tailed.

Answer:

Please help with questions on my profile somebody

Step-by-step explanation:

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

In the question equation is missing so, the equation and its solution can be defined as follows:

[tex]B={b_1,b_2}\\\\b_1= \left[\begin{array}{c}5&5\end{array}\right] \ \ \ \ \b_2= \left[\begin{array}{c}2&-5\end{array}\right] \ \ \ \ \x= \left[\begin{array}{c}-7&-35\end{array}\right][/tex]

[tex]\left[\begin{array}{c}a&c\end{array}\right] =?[/tex]

[tex]\to \left[\begin{array}{c}-7&-35\end{array}\right]= a\left[\begin{array}{c}5&5\end{array}\right]+c \left[\begin{array}{c}2&-5\end{array}\right] \\[/tex]

[tex]\to \left[\begin{array}{c}-7&-35\end{array}\right]= \left[\begin{array}{c}5a+2c&5a-5c\end{array}\right]\\\\\to 5a+2c=-7....(1)\\\\\to 5a-5c=-35....(2)\\\\[/tex]

subtract equation 1 from equation 2:

[tex]\to 7c=28\\\\\to c=\frac{28}{7}\\\\\to c= 4\\\\[/tex]

put the value of c in equation 1

[tex]\to 5a+2(4)=-7\\\to 5a+8=-7\\\to 5a=-7-8\\\to 5a=-15\\\to a= -3[/tex]

coordinate  value is [-3,4].

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▹ Answer

12

▹ Step-by-Step Explanation

[tex]7/\frac{7}{12} \\\\= 7 * \frac{12}{7} \\\\= \frac{84}{7} \\\\= 12[/tex]

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

Step-by-step explanation:

pt=700 is basically evaluate it form the bottom to the top and u must mark me as brainly

Answer:

The graph of g is the graph of f shifted up by 3 units.

Step-by-step explanation:

Consider the graph of a function r with real numbers k and h.

Transformation Effect

r(x) + k shifts the graph up k units

r(x) - k shifts the graph down k units

r(x + h) shifts the graph to the left h units

r(x - h) shifts the graph to the right h units

It is given that g(x) = f(x) + 3. Therefore, the graph of g is the graph of f shifted up by 3 units.

Answer:

3.22222......  = [tex]\frac{29}{9}[/tex]

Step-by-step explanation:

In this question we have to convert the number given in recurrent decimals into fraction.

Recurrent decimal number is 3.22222.......

Let x = 3.2222.........   -------(1)

Multiply this expression by 10.

10x = 32.2222........... -------(2)

Now subtract the expression (1) from (2),

10x = 32.22222.....

   x = 3.22222.......

9x = 29

x = [tex]\frac{29}{9}[/tex]

Therefore, recurrent decimal number can be written as [tex]\frac{29}{9}[/tex] which is in the form of [tex]\frac{p}{q}[/tex].

Answer:

A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Step-by-step explanation:

We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.

For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.

Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;

                     P.Q.  =  [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~  [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15

[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06

[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11

[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09

[tex]n_1[/tex] = sample of 25-mil film = 8

[tex]n_2[/tex] = sample of 20-mil film = 8

[tex]\mu_1[/tex] = population mean speed for the 25-mil film

[tex]\mu_2[/tex] = population mean speed for the 20-mil film

Also,  [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005

Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.

So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;

P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98  {As the critical value of t at 14 degrees of

                                             freedom are -2.624 & 2.624 with P = 1%}  

P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98

P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] <  ) = 0.98

P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98

98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]

= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]

 = [-0.042, 0.222]

Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.

Answer:

A) 64 observations

B) analytic study

Step-by-step explanation:

Given:  

There are 3 number of factors i.e. armature length, spring load, and bobbin depth.

There are 4 levels i.e. low, fair, moderate, and high

There is a single i.e. 1 observation on flow made for each combination of levels.

A)

To find:

Number of observations.

There are 4 levels so these 4 levels are to be considered for each factor.

Number of observations = 4.4.4 = 64

For example if we represent low fair moderate and high as L,F,M,H

and factors armature length, spring load, and bobbin depth as a,s,b

Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]

So resulting data set has 64 observations.  

B)

This is analytic study.

The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.

Answer:

x = 50

Step-by-step explanation:

Since the triangle has 2 congruent sides then it is isosceles, thus the base angles are congruent, that is x and x

The sum of the angles in a triangle = 180°, thus

x + x + 80 = 180

2x + 80 = 180 ( subtract 80 from both sides )

2x = 100 ( divide both sides by 2 )

x = 50

surface area of a equilateral by hand a 140.4 cm and 9cm

Answer:

vol = 96

Step-by-step explanation:

Area of a triangle = 1/2 * b * h

b = 4

h = 6

A = 0.5 * 4 * 6

A = 12

length = 8

vol = Area * length

vol = 12 * 8

vol = 96

Answer:

(104 + 16 sqrt 13)

Step-by-step explanation:

i did this on my school, it was correct

Answer:

74w+10

Step-by-step explanation:

That's the answer

Answer:

4.12 kg

Step-by-step explanation:

Regular cakes:

1 dozen normal sponge cakes: 264 g plain flour

Vegetarian cakes:

1 dozen cakes: 264 g plain flour

4 eggs are replaced by 4 * 30 g of flour = 120 g flour

total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g

Proportion for regular cakes:

12 cakes to 264 g flour = 100 cakes to x grams flour

12/264 = 100/x

12x = 26400

x = 2200

2200 g flour for 100 regular cakes

Proportion for vegetarian cakes:

12 cakes to 384 g flour = 60 cakes to y grams flour

12/384 = 60/y

12y = 384 * 60

12y = 23040

y = 1920

1920 g flour for 60 vegetarian cakes

Total flour needed:

2200 g + 1920 g = 4120 g

4120 g * 1 kg/(1000 g) = 4.12 kg

Answer: 4.12 kg

Answer:

[tex]z=(-\sqrt{3}+i)^6[/tex] = -64

Step-by-step explanation:

You have the following complex number:

[tex]z=(-\sqrt{3}+i)^6[/tex]       (1)

The Demoivres theorem stables the following:

[tex]z^n=r^n(cos(n\theta)+i sin(n\theta))[/tex]      (2)

In this case you have n=6

In order to use the theorem you first find r and θ, as follow:

[tex]r=\sqrt{3+1}=2\\\\\theta=tan^{-1}(\frac{1}{\sqrt{3}})=30\°[/tex]

Next, you replace these values into the equation (2) with n=6:

[tex]z^6=(2)^6[cos(6*30\°)+isin(6*30\°)]\\\\z^6=64[-1+i0]=-64[/tex]

Then, the solution is -64

Answer:

A) -64

Step-by-step explanation:

Edge 2021

Complete question :

a store specializing in mountain bikes is to open in one of two malls if the first mall is selected the store anticipates a yearly profit of $825,000 if successful a yearly loss of 275,000 otherwise the probability of success is 1/2 if the second mall is selected it is an estimated that the yearly profit will be 550,000 if successful otherwise the annual loss will be 165,000 the probability of success at the second mall is three Fourth (3/4).

What is the expected profit of thesecond mall?

Answer:

$453,750

Step-by-step explanation:

Given the following :

First mall:

Profit if successful = $825,000

Loss if otherwise = $275000

Probability of success = 1/2

Second mall:

Profit if successful = $550,000

Loss if otherwise = $165,000

Probability of success = 3/4

Expected profit of second mall:

If probability of profit ' P(profit)' = 3/4

Then,

Probability of loss P(loss) = 1 - P(profit)

P(loss) = 1 - 3/4 = 1/4

Expected profit:

[P(profit) * profit] + [P(loss) * loss])

(0.75 * $550,000) + (0.25 * (-$165,000))

$412,500 - $41,250 = $453,750

Answer: Its coefficient of variation = 0.316

Step-by-step explanation:

The formula to find the coefficient of variations:

Coefficient of variation: [tex](\dfrac{\sqrt{\text{variance}}}{\text{return}})[/tex]

Given: Asset X has

Variance = 10

Expected return = 10

then, coefficient of variation [tex]=\dfrac{\sqrt{10}}{10}=\dfrac{1}{\sqrt{10}}\approx0.316[/tex]

Hence, its coefficient of variation = 0.316

Answer:

x = 64

Step-by-step explanation:

A circle equal 360 degrees

180 + 90 + x + 26 = 360

Combine like terms

296+x = 360

Subtract 296 from each side

296+x-296 = 360-296

x = 64

Answer:

The p-value is 2.1%.

Step-by-step explanation:

We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.

The sample average age was 24.2 with a standard deviation of 3.7.

Let [tex]\mu[/tex] = true average age a "child" moves permanently out of his parents' home in the United States.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 23      {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 23      {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                            T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average age = 24.2

            s = sample standard deviation =3.7

            n = sample of U.S. Adults = 43

So, the test statistics =  [tex]\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }[/tex]  ~  [tex]t_4_2[/tex]

                                    =  2.127

The value of t-test statistics is 2.127.

Now, the p-value of the test statistics is given by;

         P-value = P( [tex]t_4_2[/tex] > 2.127) = 0.021 or 2.1%

Answer:

Range of wages is £140 to £525.

Mean wage = £226

Step-by-step explanation:

Given:

Weekly wages paid to the staff are :

£245, £140, £525, £163, £195, £174 and £140.

To find:

Range of these wages = ?

Mean wage = ?

Solution:

First of all, let us learn about the range of wages and mean wage.

Range of wages has a minimum pay and a maximum pay.

Here, if we have a look £140 is the minimum pay and

£525 is the maximum pay.

So, range of wages is £140 to £525.

Mean wage means the average of all the wages given to the staff.

Mean is defined as the formula:

[tex]\text{Average/Mean =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]

Here, Sum of all observations mean sum of the wages of all the staff members.

Number of observations mean the number of staff members i.e. 7 here.

Applying the formula:

[tex]\text{Average/Mean =} \dfrac{\text{245+140+525+163+195+174+140}}{\text{7}} \\\Rightarrow \text{Average/Mean =} \dfrac{\text{1582}}{\text{7}}\\\Rightarrow \text{Average/Mean =} 226[/tex]

So, the answer is:

Range of wages is £140 to £525.

Mean wage = £226

Answer: 0.0548

Step-by-step explanation:

Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.

Let [tex]\overline{X}[/tex] represents the sample mean GPA for each student.

Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:

[tex]P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z<1.6)\\\\=1-0.9452=0.0548[/tex]

hence, the required probability is 0.0548.

Answer:

sin⁴x - sin²x = cos⁴x - cos²x

Solve the right hand side of the equation

That's

sin⁴x - sin²x

From trigonometric identities

So we have

sin⁴x - ( 1 - cos²x)

sin⁴x - 1 + cos²x

sin⁴x = ( sin²x)(sin²x)

That is

( sin²x)(sin²x)

So we have

( 1 - cos²x)(1 - cos²x) - 1 + cos²x

Expand

1 - cos²x - cos²x + cos⁴x - 1 + cos²x

1 - 2cos²x + cos⁴x - 1 + cos²x

Group like terms

That's

cos⁴x - 2cos²x + cos²x + 1 - 1

Simplify

We have the final answer as

So we have

Since the right hand side is equal to the left hand side the identity is true

Hope this helps you

Answer:

A. 4.4 units²

Step-by-step explanation:

Area of a Triangle: A = 1/2bh

sin∅ = opposite/hypotenuse

cos∅ = adjacent/hypotenuse

Step 1: Draw the altitude down the center of the triangle

- We should get a perpendicular bisector that creates 90° ∠ and JM = KM

- We should also see that we use sin∅ to find the h height of the triangle and that we use cos∅ to find length of JM to find b base of the triangle

Step 2: Find h

sin70° = h/3.7

3.7sin70° = h

h = 3.47686

Step 3: Find b

cos70° = JM/3.7

3.7cos70° = JM

JM = 1.26547

Step 4: Find entire length base JK

JM + KM = JK

JM = KM (Definition of Perpendicular bisector)

2(JM) = JK

2(1.26547) = 2.53095

b = 2.53095

Step 5: Find area

A = 1/2(3.47686)(2.53095)

A = 4.39988

A ≈ 4.4

Answer:

[tex]\boxed{13}[/tex] pages

Step-by-step explanation:

Divide the total number of pages by 5 to get how many sets of every 5 pages will contain 2/3 of a page of advertisements.

[tex]\frac{98}{5} = 19.6[/tex]

Multiply this value by [tex]\frac{2}{3}[/tex] to get the total number of pages.

[tex]19.6 * \frac{2}{3} \approxeq 13[/tex] pages

Answer:

The GCF is the largest expression that is factor of all expressions

Answer:

The GCF of two expressions is the greatest expression that is a factor of both the expressions.

Step-by-step explanation:

For example 7x² and 14x.

7x² = 1, 7, x, x

14x = 2, 7, x

The greatest common factor of the two expressions is 7x.

Answer:

First, a absolute value function is something like:

y = f(x) = IxI

remember how this work:

if x ≥ 0, IxI = x

if x ≤ 0, IxI = -x

Notice that I0I = 0.

And the range of this function is all the possible values of y.

For example for the parent function IxI, the range will be all the positive reals and the zero.

First, if A is the value of the vertex of the absolute function, then we know that A is the maximum or the minimum value of the function.

Now, if the arms of the graph open up, then we know that A is the minimum of the function, and the range will be:

y ≥ A

Or all the real values equal to or larger than A.

if the arms of the graph open downwards, then A is the maximum of the function, and we have that the range is:

y ≤ A

Or "All the real values equal to or smaller than A"

Answer:

x = √(-1) = i

Since the value of √(-1) is not real.

The system has no real solution.

Step-by-step explanation:

The solution to the system of equations is at the point where they intercept each other.

y1 = y2

For the given equation;

y=x^2-2x and y=-2x-1

To get the where they intercept, we will equal both equations;

y=x^2-2x = -2x-1

x^2 - 2x = -2x - 1

x^2 - 2x + 2x + 1 =0

x^2 +1 = 0

x^2 = -1

x = √(-1) = i

Since the value of √(-1) is not real.

The system has no real solution.