What is the volume of the following cylinder?



150.72 in. 3
301.44 in. 3
75.36 in. 3
602.88 in. 3

Answer:

a) The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.

b) Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.

c) 37 cars would have to be sampled.

Step-by-step explanation:

Question a:

We have the sample standard deviation, and thus, the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{6.2}{\sqrt{15}} = 3.4[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 26.7 - 3.4 = 23.3 mpg.

The upper end of the interval is the sample mean added to M. So it is 26.7 + 3.4 = 30.1 mpg.

The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.

b. What would happen to the interval if you increased the confidence level from 95% to 99%? Explain

Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.

c. The lead engineer is not happy with the interval you constructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?

Width is twice the margin of error, so a margin of error of 2 would be need. To solve this, we have to consider the population standard deviation as [tex]\sigma = 6.2[/tex], and then use the z-distribution.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

How many cars would you have to sample to create the interval the engineer is requesting?

This is n for which M = 2. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]2 = 1.96\frac{6.2}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 1.96*6.2[/tex]

[tex]\sqrt{n} = \frac{1.96*6.2}{2}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*6.2}{2})^2[/tex]

[tex]n = 36.9[/tex]

Rounding up:

37 cars would have to be sampled.

The given graph is a line and he line is the distance between two points.  The required equation of the line is y = 0.5x + 5

The given graph is a line and he line is the distance between two points. The equation of a line is represented as;

y = mx+ b

Given the coordinate points (-5, 4) and (1, 7)

Get the slope

Slope = 7-4/1-(-5)

Slope = 3/6

Slope = 0.5

The intercept is 5 (the point where the line cuts the y-axis)

Determine the required equation

y = 0.5x + 5

Hence the required equation of the line is y = 0.5x + 5

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Answer:

40

Step-by-step explanation:

range is the difference between the highest and lowest number.

60 is the highest and 20 is the lowest

60-20=40

Answer:

The student's GPA is of 0.82.

Step-by-step explanation:

GPA:

To find the student's GPA, we find his weighed mean.

Grades:

7 hours worth 3(B)

6 hours worth 1(D)

20 hours worth 0(F). So

[tex]M = \frac{7*3 + 6*1 + 20*0}{7+6+20} = 0.82[/tex]

The student's GPA is of 0.82.

Answer:

I think its C:37

Step-by-step explanation:

And if im wrong sorry :/

Answer:

-6

Step-by-step explanation:

f(x) = -2x - 7 and g(x) = -4x + 6

Find f(-5)

f(-5) = -2(-5) -7 = 10-7 = 3

The find g(3)

g(3) = -4(3) +6

     = -12 +6 =-6

g(f(-5)) = -6

Answer:

15

Step-by-step explanation:

The figure has total 15 faces, the correct option is A.

A hexagon is a polygon with six sides.

A hexagonal pyramid has 8 faces

From (2 hexagonal base + 6 lateral surfaces)

A hexagonal prism has 7 faces

From ( A hexagonal base + 6 lateral faces)

Total faces the figure has is 8 +7 = 15

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Answer:

a)

[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.

[tex]|z| > 2.054[/tex]: Reject the null hypothesis.

b) [tex]z = 2.81[/tex]

c) Reject.

d) The p-value is 0.005.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and the subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Population 1:

Sample of 42, standard deviation of 3.3, mean of 101, so:

[tex]\mu_1 = 101[/tex]

[tex]s_1 = \frac{3.3}{\sqrt{42}} = 0.51[/tex]

Population 2:

Sample of 53, standard deviation of 3.6, mean of 99, so:

[tex]\mu_2 = 99[/tex]

[tex]s_2 = \frac{3.6}{\sqrt{53}} = 0.495[/tex]

H0 : μ1 = μ2

Can also be written as:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

H1 : μ1 ≠ μ2

Can also be written as:

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error .

a. State the decision rule.

0.04 significance level.

Two-tailed test(test if the means are different), so between the 0 + (4/2) = 2nd and the 100 - (4/2) = 98th percentile of the z-distribution, and looking at the z-table, we get that:

[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.

[tex]|z| > 2.054[/tex]: Reject the null hypothesis.

b. Compute the value of the test statistic.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = \mu_1 - \mu_2 = 101 - 99 = 2[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.51^2 + 0.495^2} = 0.71[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{2 - 0}{0.71}[/tex]

[tex]z = 2.81[/tex]

c. What is your decision regarding H0?

[tex]|z| = 2.81 > 2.054[/tex], which means that the decision is to reject the null hypothesis.

d. What is the p-value?

Probability that the means differ by at least 2, either plus or minus, which is P(|z| > 2.81), which is 2 multiplied by the p-value of z = -2.81.

Looking at the z-table, z = -2.81 has a p-value of 0.0025.

2*0.0025 = 0.005

The p-value is 0.005.

Answer:

[tex]4x-1[/tex]

Step-by-step explanation:

This value is approximate.

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

Explanation:

We have a normal distribution with these parameters

The goal is to find the area under the curve from x = 68 to x = 158, where x is the number of text messages sent per day. So effectively, we want to find P(68 < x < 158).

Let's convert the score x = 68 to its corresponding z score

z = (x-mu)/sigma

z = (68-128)/30

z = -60/30

z = -2

This tells us that the score x = 68 is exactly two standard deviations below the mean mu = 128.

Repeat for x = 158

z = (x-mu)/sigma

z = (158-128)/30

z = 30/30

z = 1

This value is exactly one standard deviation above the mean

-------------------------------------------

The problem of finding P(68 < x < 158) can be rephrased into P(-2 < z < 1)

We do this because we can then use the Empirical rule as shown in the diagram below.

We'll focus on the regions between z = -2 and z = 1. This consists of the blue 13.5% on the left, and the two pink 34% portions. So we will say 13.5% + 34% + 34% = 81.5%

Approximately 81.5% of the the population sends between 68 and 158 text messages per day. This value is approximate because the percentages listed in the Empirical rule below are approximate.

Answer:

C. 81.5%

Step-by-step explanation:

Answer:

Logx(1/8) = -3/2

x = 4

Answered by GAUTHMATH

Answer:-10

-3+-4+-3

-3-4=-7

-7+-3=-7-3

=-10

Answer:

65% of 27.69 is 18.

Step-by-step explanation:

Formula = Number x 100

Percent = 18 x 100

65 = 27.69

Following shows the steps on how to derive this formula

Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.

18

65% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

65Y = 18 x 100

65Y = 1800

Y = 1800

100 = 27.69

Terms given

No of terms=8

We know

[tex]\boxed{\sf Mean=\dfrac{Sum\;of\:terms}{No\;of\:terms}}[/tex]

[tex]\\ \sf\longmapsto Mean=\dfrac{40+35+32+39+34+35+35+37}{8}[/tex]

[tex]\\ \sf\longmapsto Mean=\dfrac{270}{8}[/tex]

[tex]\\ \sf\longmapsto Mean=35[/tex]

Final Answer:

35

Step-by-step explanation:

-median is the middle number in the data set-

arrange the data set from least to greatest:

40, 30, 32, 39, 34, 35, 35, 37 ⇒ 30, 32, 34, 35, 35, 37, 39, 40

we start from the lowest number and the highest  number and work your way to the middle:

30, 32, 34, 35, 35, 37, 39, 40

notice that there is no middle number:

30, 32, 34, 35, ?, 35, 37, 39, 40

so what we do is add both 35's and then divide it by 2

35 + 35 = 70 ÷ 2 = 35

median: 35

Answer:  Choice D

HG= 11 square root 3/3 and HI = 22 square root 3/3

In other words, [tex]\text{HG} = \frac{11\sqrt{3}}{3} \ \text{ and } \ \text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex]

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

Explanation:

Let's say that x is the short leg and y is the long leg

For any 30-60-90 triangle, we have this connection: [tex]y = x\sqrt{3}[/tex]

The long leg y is exactly sqrt(3) times longer compared to the short leg x.

Let's solve for x and then plug in y = 11

[tex]y = x\sqrt{3}\\\\x = \frac{y}{\sqrt{3}}\\\\x = \frac{y*\sqrt{3}}{\sqrt{3}*\sqrt{3}}\\\\x = \frac{y\sqrt{3}}{3}\\\\x = \frac{11\sqrt{3}}{3}\\\\[/tex]

Side HG, the shorter leg, has an exact length of [tex]\text{HG} = \frac{11\sqrt{3}}{3}\\\\[/tex]

------------------

Once we know the short leg, we double that expression to get the length of the hypotenuse. Like before, this only applies to 30-60-90 triangles.

[tex]\text{hypotenuse} = 2*(\text{short leg})\\\\\text{HI} = 2*\text{HG}\\\\\text{HI} = 2*\frac{11\sqrt{3}}{3}\\\\\text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex]

------------------

Since [tex]\text{HG} = \frac{11\sqrt{3}}{3}\\\\[/tex] and [tex]\text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex], this shows that choice D is the final answer.

GIVEN -> Triangles r similar

so sides r in ratio

[tex] \frac{2.4}{3} = \frac{2.8}{x} \\ 0.8 = \frac{2.8}{x} \\ x = \frac{2.8}{0.8} \\ x = \frac{28}{8} \\ x = 3.5 \: \: ans[/tex]

Answer:

3.5

Step-by-step explanation:

We can write a ratio to solve

2.4      2.8

----- = --------

3         x

Using cross products

2.4x = 3(2.8)

2.4x =8.4

Divide each side by 2.4

2.4x /2.4 = 8.4/2.4

x = 3.5

Answer:

The answer is Line Segment SR.

Answer:

[11.906 ; 12.894]

Step-by-step explanation:

Given :

Sample mean, xbar = 12.4

Sample standard deviation, s = 1.7

Sample size, n = 48

We use the T distribution since we are using the sample standard deviation;

α - level = 95% ; df = n - 1 = 48 - 1 = 47

Tcritical = T(1 - α/2), 47 = 2.012

Using the confidence interval for one sample mean

Xbar ± Tcritical * s/√n

12.4 ± (2.012 * 1.7/√48)

12.4 ± 0.4936922

C. I = [11.906 ; 12.894]

Answer:

Check the photo for the answer

Answer:

side AC is 5

Step-by-step explanation:

by using th pythagorean theorm you would square both sides add them together and the square root the sum to get you answer.

AB =3 BC=4

9+16=25

25 square root is 5

makeing AC=5

Answer:

False

Step-by-step explanation:

Answer:

30 and 270 respectively

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*4=1200 and (x-y)*5=1200. Solving it, we get x=270 and y=30

Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.

g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]

Option C

Hope this helps!

Answer:

The missing segment length is 20.

Step-by-step explanation:

2 is multiplied by 4 to get to 8, so 5 must be multiplied by 4 to get to 20.

Answer:

Political stability is a variable of great importance in a country's evolution since, across time, it was identified as causing law level of economic growth, but also it was presented as a consequence of poor economic development.

Answer:

There is not enough evidence to support the claim that the bags are under filled.

Step-by-step explanation:

Given :

Population mean, μ = 433

Sample size, n = 26

xbar = 427

Variance, s² = 324 ; Standard deviation, s = √324 = 18

The hypothesis :

H0 : μ = 433

H0 : μ < 433

The test statistic :

(xbar - μ) ÷ (s/√(n))

(427 - 433) / (18 / √26)

-6 / 3.5300904

T = -1.70

The Pvalue :

df = 26-1 = 25 ; α = 0.05

Pvalue = 0.0508

Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled

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

Explanation:

Add up the values to get

1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54

Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.

So the mean is approximately 1.8876923

---------------------

Now make a spreadsheet as shown below

We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.

After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.

That sum is approximately 0.04403076924

Next, we divide that over n-1 = 13-1 = 12

0.04403076924 /12 = 0.00366923077

That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.

sqrt(0.00366923077) = 0.06057417576822

This rounds to 0.061 which is the final answer.