It is believed that the average starting salary for a 21-25 year old college grad exceeds $52,000 per year. Hence, it is desired to test H0: µ ≤ 52,000 versus H1 : µ > 52,000. Assume σ = $5,745 and a SRS of size 65 is taken. We reject H0 when X > 53,460. The significance level α is:

Answer: The value of the sine of ∠C is 0.28.

Step-by-step explanation:

Let's draw a triangle again (see the picture below).

Remember SOHCAHTOA? It's:

-sin = opposite/hypotenuse

-cos = adjacent/hypotenuse

-tan = opposite/adjacent.

We need to use sin in here.

The sin of C is [tex]\frac{7}{25}[/tex], which in a calculator, gives [tex]0.28[/tex]

Given Information:

Population size = N = 210

Mean height of women population = μ = 64.4 in.

Standard deviation of height of women population = σ = 2.9 in.

Sample size = n = 36

Required Information:

Sample mean = μx = ?

Sample standard deviation = σx = ?

Answer:

Sample mean = μx = 64.4 in.

Sample standard deviation = σx = 0.44 in.

Step-by-step explanation:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

The mean of the sample will be same as population mean that is

μ = μx = 64.4 in

Whereas the sample standard deviation is given by

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \cdot \sqrt{\frac{N-n}{N-1} }[/tex]

Where σ is the standard deviation of height of women population, N is the population size and n is the sample size.

The term [tex]\sqrt{\frac{N-n}{N-1} }[/tex] is known as finite population correction factor and is used since the sampling is done without replacement.

[tex]\sigma_{x} = \frac{2.9}{\sqrt{36} } \cdot \sqrt{\frac{210-36}{210-1} }\\\sigma_{x} = 0.483 \cdot \sqrt{\frac{174}{209} }\\\sigma_{x} = 0.483 \cdot 0.912\\\sigma_{x} = 0.44[/tex]

Therefore, the standard deviation of sample is 0.44 in.

To find the mean (mu Subscript x overbar) and standard deviation (sigma Subscript x overbar) of the population of sample means, use the formulas provided.

To find the mean (mu Subscript x overbar) and standard deviation (sigma Subscript x overbar) of the population of sample means, we use the formulas:

In this case, the population mean (mu) = 64.4 inches, the population standard deviation (sigma) = 2.9 inches, and the sample size (n) = 36.

Using these values, we can calculate:

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Step-by-step explanation:

2 ( 8 - 3c) = 4c - 34

16 - 6c = 4c - 34

6c + 4c = 16 + 34

10c = 50

c = 50/ 10

therefore c = 5

Hope it will help :)

Answer: B, E, and F

Step-by-step explanation: :)

Answer:

No. The frequencies and probabilities for red and green segments might change in the next experiment.

Step-by-step explanation:

I just did it and it said my answer was right

Answer:

Step-by-step explanation:

No. The frequencies and probabilities for red and green segments might change in the next experiment.

i just did it and got it right so i hope you do too

Answer:

Hypothesis test on a proportion.

There is no enough evidence to support the claim that the proportion of business executives in the sample differs from the national magazine poll.

Step-by-step explanation:

We should test the hypothesis of the proportion, with a z-statistic.

The claim is that the proportion of business executives in the sample differs from the national magazine poll.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.26\\\\H_a:\pi<0.26[/tex]

The significance level is assumed to be 0.05.

The sample, of size n=100, has a proportion p=0.19.

The standard error for the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.26*0.74}{100}}=\sqrt{0.001924}=0.044[/tex]

Then, the z-statistic can be calculated as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.19-0.26+0.5/100}{0.044}=\dfrac{-0.065}{0.044}=-1.477[/tex]

The P-value for this one-tailed test is:

[tex]P-value=P(z<-1.477)=0.07[/tex]

As the P-value is bigger than the significance level, the effect is not significant. The null hypothesis failed to be rejected.

There is no enough evidence to support the claim that the proportion of business executives in the sample differs from the national magazine poll.

Answer:

11.55 ft

Step-by-step explanation:

tan 60° = 20 / x

x = 20 / tan 60° = 20 / √3 = 11.55

The length of the shadow will be 11.55 ft. It is found by the help of the tangent formula of trigonometry.

Angle of depression is the angle formed by the horizontal and the place where your head came to a halt.

You keep your gaze level with the ground. When you need to keep an eye on anything, though, you raise your head and lower your gaze.

The given data in the problem is;

Angle of depression = 60°

Length of the shadow(x) = ?

Height of  flagpole = 20 ft

From trigonometry formula of tanΘ is;

[tex]\rm tan \theta = \frac{P}{B} \\\\ tan60^0=\frac{20}{x} \\\\ x= \frac{20}{tan60^0} \\\\ x= \frac{20}{\sqrt{3} } \\\\ x=11.55 \ ft[/tex]

Hence, the length of the shadow will be 11.55 ft.

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Answer:

I think it is A and B. Not one hundred percent sure but,50 percent sure.

Step-by-step explanation:

Answer:

B.) and D.)

Step-by-step explanation:

Answer:

50 degrees

Step-by-step explanation:

Answer:

Length of the longest metal rod which can be carried horizontally around the right-angle turn is 21.21ft

Step-by-step explanation:

Length of the longest metal rod which can be carried horizontally around the right-angle turn, can be determined at the point at where the distance between one end of rod and the 7feet corridor is same as the distance between other end of the rod and the 8feet corridor. How do I mean.

The length of longest metal rod will be determined when distance between the one end of rod and the 7feet corridor and the distance between other end of the rod and the 8feet corridor are both 15ft (7ft + 8ft).

See attachment for illustration.

Therefore using Pythagoras theorem we can find the length of longest metal rod that can be carried horizontally around the right angle turn

See illustration in attachment

i.e

Hyp² = opp²+adj²

Hyp = √(15²+15²)

Hyp = √450

Hyp = 21.21ft

Answer:

Scalene Triangles

Step-by-step explanation:

Isosceles triangles have one pair of equivalent edges, and equilateral triangles of course have all equivalent edges, it would obviously be the scalene triangles.

I am joyous to assist you at any time.

Answer:

P-value of the test statistic: P=0.0266.

Step-by-step explanation:

Hypothesis test on a proportion.

The claim is that the percentage of residents who favor annexation is above 72% This is going to be stated in the alternative hypothesis.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.72\\\\H_a:\pi>0.72[/tex]

The sample size is n=900 and the sample proportion is p=0.75.

The standard devaition is calculated as:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.72*0.28}{900}}=\sqrt{0.000224}=0.015[/tex]

Then, the z-statistic is:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.75-0.72-0.5/900}{0.015}=\dfrac{0.029}{0.015} = 1.9333[/tex]

For this right tailed test, the P-value is:

[tex]P-value=P(z>0.1933)=0.0266[/tex]

Answer:

Step-by-step explanation:

Answer:

The Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables

= -3072uv

Step-by-step explanation:

Step :-(i)

Given  x = 1 6 (u + v)  …(i)

  Differentiating equation (i) partially with respective to 'u'

               [tex]\frac{∂x}{∂u} = 16(1)+16(0)=16[/tex]

  Differentiating equation (i) partially with respective to 'v'

              [tex]\frac{∂x}{∂v} = 16(0)+16(1)=16[/tex]

  Differentiating equation (i)  partially with respective to 'w'

               [tex]\frac{∂x}{∂w} = 0[/tex]

Given  y = 1 6 (u − v) …(ii)

  Differentiating equation (ii) partially with respective to 'u'

               [tex]\frac{∂y}{∂u} = 16(1) - 16(0)=16[/tex]

 Differentiating equation (ii) partially with respective to 'v'

               [tex]\frac{∂y}{∂v} = 16(0) - 16(1)= - 16[/tex]

Differentiating equation (ii)  partially with respective to 'w'

               [tex]\frac{∂y}{∂w} = 0[/tex]

Given   z = 6uvw   ..(iii)

Differentiating equation (iii) partially with respective to 'u'

               [tex]\frac{∂z}{∂u} = 6vw[/tex]

Differentiating equation (iii) partially with respective to 'v'

               [tex]\frac{∂z}{∂v} =6 u (1)w=6uw[/tex]

Differentiating equation (iii) partially with respective to 'w'

               [tex]\frac{∂z}{∂w} =6 uv(1)=6uv[/tex]

Step :-(ii)

The Jacobian ∂(x, y, z)/ ∂(u, v, w) =

                                                         [tex]\left|\begin{array}{ccc}16&16&0\\16&-16&0\\6vw&6uw&6uv\end{array}\right|[/tex]

   Determinant       16(-16×6uv-0)-16(16×6uv)+0(0) = - 1536uv-1536uv

                                                                                 = -3072uv

Final answer:-

The Jacobian ∂(x, y, z)/ ∂(u, v, w) = -3072uv

Answer: p-value  = 0.1085 and we will not reject the null hypothesis.

Step-by-step explanation:

Since we have given that

Hypothesis are :

[tex]H_0:p=0.3\\\\H_1:p>0.3[/tex]

Here, n = 200

x = 68

So, [tex]\hat{p}=\dfrac{68}{200}=0.34[/tex]

So, the test statistic value would be :

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.34-0.3}{\sqrt{\dfrac{0.3\times 0.7}{200}}}\\\\z=\dfrac{0.04}{0.0324}\\\\z=1.234[/tex]

So, the value of statistic value is 1.234.

And the p-value = 0.1085 at 5% level of significance.

So, 0.1085 <  1.234,

So, we will not reject the null hypothesis.

Hence, p-value  = 0.1085 and we will not reject the null hypothesis.

The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. To calculate the p-value, we compare the observed proportion to the target percentage using a one-sample proportion test. The statistical decision when alpha = 0.05 is to reject the null hypothesis if the p-value is less than 0.05.

A. The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. It represents the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

B. To calculate the p-value for the test statistic in this case, we need to perform a hypothesis test. We compare the proportion of viewers who would see the movie again (68/200 = 34%) to the target percentage of 30% using a one-sample proportion test.

C. The statistical decision when alpha = 0.05 is to reject the null hypothesis if the p-value is less than 0.05. This indicates strong evidence against the null hypothesis.

D. The managerial conclusion for this situation would depend on the p-value obtained. If the p-value is less than 0.05, we can conclude that there is strong evidence to suggest that more than 30% of the viewers would see the movie again. Otherwise, we cannot make a definitive conclusion.

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Complete Question:

Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 69%. He examines a random sample of 500 emails received at an email server, and finds that 365 of the messages are spam. Can you conclude that greater than 69% of emails are spam? Use both a=0.01 and a=0.05 levels of significance and the -value method with the table.

(a) State the appropriate null and alternate hypotheses.

(b) Compute the -value.

(c) At the a=0.01, can you conclude that greater than 69% of emails are spam?

(d) At the a=0.05, can you conclude that greater than 69% of emails are spam?

Answer and step-by-step explanation:

a)

The required hypothesis are                                          

H₀: [tex]\mu[/tex] = 0.69

H₁: [tex]\mu[/tex] > 0.69

additional solutions are attached in the image below

Answer:

a) No

B) Yes

Step-by-step explanation:

Calculating the p-value, we have;

z = (p-bar) -p/√(p(1-p)/n)

But p-bar = 365/500

               = 0.73

Therefore,

z = 0.73 -0.69/√0.69(1-0.69)/500

   = 0.04/√0.2139/500

   = 0.04/√0.0004278

   = 0.04/0.02068

   = 1.93

p-value = p(z ≥1.93) = 0.0268

(a) Can you conclude that the percentage of emails that are spam is greater than 69% ?

No, because the p- value is greater than α. That is p-value⊃ 0.01

(b) Can you conclude that the percentage of emails that are spam is greater than 69%

Yes, since p-value ∠ 0.05

Answer:

i think you may have to use sin or cos

Step-by-step explanation:

Answer:

9m (You were correct!!!!)

Step-by-step explanation:

Use Pythagorean Theorem:

[tex]a^{2} +b^{2} = c^{2}[/tex]

⬆️  ⬆️   ⬆️

  legs    hypotenuse

x² + 12² = 15²

x² + 144 = 225

x² = 81

x = 9

Answer:quasi experiment

Step-by-step explanation:

Because it is basically for comparison usually by measuring outcomes if a program by participants and non participants

Answer:

B. One solution

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

-6y + 13 + 9y = 8y - 3

Step 2: Solve for y

∴ We can see by solving the equation, we get 1 solution only.

The linear equation has one solution after simplifying and isolating the variable y, which results in y = 16/5.

When solving the given linear equation −6y + 13 + 9y = 8y − 3, the first step is to simplify and collect like terms. Begin by combining the terms with y on the left side: 3y + 13 = 8y − 3. Next, move the terms with y to one side by subtracting 3y from both sides: 13 = 5y − 3. Lastly, isolate y by adding 3 to both sides and then dividing by 5: y =  rac{16}{5}. Since we have successfully isolated y and found a specific value for it, the equation has one solution.

Answer:   This is the Communitve Property because the equation has the same thing on both sides, but the numbers "flip flopped" or switched around.

The y-intercept is the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis.

The slope(m) is:

[tex]m=\frac{rise}{run}[/tex]

"rise" is the number of units you go up(+) or down(-) from each point

"run" is the number of units you go to the right from each point

You know:

y-intercept = -6 or (0, -6)

m = 2 or [tex]\frac{2}{1}[/tex] , so from each point you go up 2 units and to the right 1 unit to get to the next point.

#1: Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

This is true

#2: Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.

This isn't accurate because the slope doesn't move left.

#3: Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

This isn't accurate because (-6, 0) isn't the y-intercept or a point on the y-axis

#4: Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.

This isn't accurate because (-6, 0) isn't the y-intercept or a point on the y-axis, and the slope doesn't move to the left.

Answer:

tis be A my friends

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

got 100 on quiz

The maximum height of the firework is 40 feet.

'The maximum height of the object is the highest vertical position along its trajectory.'

According to the given problem,

y = -16x²+32x+24

For maximum height,

The slope of y with respect to x has to be 0.

⇒ [tex]\frac{dy}{dx}[/tex] = 0

Now, [tex]\frac{d(-16x^{2} +32x+24)}{dx}[/tex] = -32x +32

⇒-32x + 32 = 0

⇒ 32 = 32x

⇒1 = x or x = 1 second

Therefore after 1 second, the firework reaches maximum height.

Now, we put the value of x = 1 second in the equation: y = -16x²+32x+24

⇒ -16(1)² + 32(1) +24

= -16+32+24

= 40 feet

Hence, we can conclude that after 1 second, the firework reaches a maximum height of 40 feet.

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Answer:

18

Step-by-step explanation:

I meant 6x3=18 -2=16 sorry for confusion

To find the value of x, you need to isolate/get the variable "x" by itself in the equation:

3x - 2 = 16       Add 2 on both sides

3x - 2 + 2 = 16 + 2

3x = 18         Divide 3 on both sides to get "x" by itself

[tex]\frac{3x}{3} =\frac{18}{3}[/tex]

x = 6

PROOF

3x - 2 = 16      Substitute/plug in 6 into "x" since x = 6

3(6) - 2 = 16

18 - 2 = 16

16 = 16

Answer:

A Vertical Angle

Step-by-step explanation:

Answer:

vertical angles

Step-by-step explanation:

Answer:

x = 29 cm

Step-by-step explanation:

An isosceles triangle has two equal sides that have equal angles at the bases

Since the 80 degree angles are at the bases of the 29 cm side, the length of x must be 29 cm

Answer:

29 cm

Step-by-step explanation:

Because both angles are 80 degrees. If your angles are the same so are your sides.

Answer:

just look it up on m..a.t.h. w.a.y.!!

Step-by-step explanation:

it works for me

Answer:

Let the 1st group be of students and 2nd group be of faculty.

n1 = 18

\bar{x}_{1} = 8.4

s1 = 7.3

n2 = 15

\bar{x}_{2} = 4.2

s2 = 3.8

1.

H0: =

HA: >

2.

Equality of variance test:

F = s12/s22

= 53.29/14.44

= 3.69

df-num = n1-1 = 17

df-den = n2-1 = 14

p-value = 0..008 < 0.05 i.e.H0 can be rejected and hence we can say that both populations do not have the same variances.

So, test-statistic will be calculated as follows:

[ Find the solution of this part in the attachment]

3.

df = 26

p-value = 0.0217

4.

E. It confirms the community college results because the p-value is much smaller.

Answer:

3(7x2 + 5) (x − 3)  took the quiz :)

Step-by-step explanation:

Answer:

C- 3(7x2 + 5) (x − 3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the sample data

Pre-test... 12 14 11 12 13

Post-Test 15 17 11 13 12

The mean of pre-test

x = ΣX / n

x = (12+14+11+12+13) / 5

x = 12.4

The standard deviation of pre-test

S.D = √Σ(X-x)² / n

S.D = √[(12-12.4)²+(14-12.4)²+(11-12.4)²+(12-12.4)²+(13-12.4)² / 5]

S.D = √(5.2 / 5)

S.D = 1.02.

The mean of post-test

x' = ΣX / n

x' = (15+17+11+13+12) / 5

x' = 13.6

The standard deviation of post-test

S.D' = √Σ(X-x)² / n

S.D' = √[(15-13.6)²+(17-13.6)²+(11-13.6)²+(13-13.6)²+(12-13.6)² / 5]

S.D = √(23.2 / 5)

S.D = 2.15

Test value

t = (sample difference − hypothesized difference) / standard error of the difference

t = [(x-x') - (μ- μ')] / (S.D / n — S.D'/n)

t = (12.4-13.6) - (μ-μ')/ (1.02/5 - 2.15/5)

-1.5 = -1.2 - (μ-μ') / -0.226

-1.5 × -0.226 = -1.2 -(μ-μ')

​0.339 = -1.2 - (μ-μ')

(μ-μ') = -1.2 -0.339

μ-μ' = -1.539

Then, μ ≠ μ'

We can calculate our P-value using table.

This is a two-sided test, so the P-value is the combined area in both scores.

The p-value is 0.172

The p value > 0.1

Using the t-distribution, it is found that the p-value is of 0.086.

At the null hypothesis, it is tested if there is no improvement, that is, the subtraction of the mean of the grades on test 1 by the mean of the grades on test 2 is of at least 0, that is:

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

At the alternative hypothesis, it is tested if there is improvement, that is, the grades on the second test were greater than on the first, hence:

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

We can find the standard deviation for the samples, hence, the t-distribution is used.

The p-value is found using a left-tailed test, as we are testing if the variable is less than a value, with 5 + 5 - 2 = 8 df and t = -1.5, using a calculator, the p-value is of 0.086.

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