One way to check on how representative a survey is of the population from which it was drawn is to compare various characteristics of the sample with the population characteristics. A typical variable used for this purpose is age. The 2010 GSS of the American adult population found a mean age 49.28 years and a standard deviation of 17.21 for its sample of 4,857 adults. Assume that we know from Census data that the mean age of all American adults is 37.2 years.

Required:
a. State the research and the null hypothesis setting for a two-tailed test.
b. Calculate the t statistics and test the null hypothesis setting alpha at .01. What did you find?
c. What is your decision about the null hypothesis? What does this tell us about how representative the sample is of the American adult population?

Answer:

upper bound for the error, | Error |  ≤ 0.0032

Step-by-step explanation:

Given the data in the question;

[tex]e^{0.4[/tex] < e < 3

Using Taylor's Error bound formula

| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]

where m = [tex]| f^{N+1 }(x) |[/tex]

so we have

| Error |  ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]

| Error |  ≤ ( 0.125 ) 0.0256

| Error |  ≤ 0.0032

Therefore, upper bound for the error, | Error |  ≤ 0.0032

The area of the shaded region is 294.5 m².

The area of the entire circle is calculated as follows;

A = πr²

where;

A = π ( 11.1² )

A = 387.1 m²

The area of the sector is calculated as follows;

A = ( θ/360 ) πr²

A = ( 130/360 ) x π ( 11.1² )

A = 139.8 m²

The area of the triangle is calculated as follows;

A = ¹/₂ ( sinθ )r²

A = ¹/₂ ( sin 130 ) (11.1²)

A = 47.2 m²

Area of the unshaded region is calculated as;

A' = 139.8 m²  -  47.2 m²

A' = 92.6 m²

The area of the shaded region is calculated as follow;

A'' = 387.1 m² - 92.6 m²

A'' = 294.5 m²

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tan graph and its tax because tax=0

Answer:

x=70

Step-by-step explanation:

First, we know that the mode is the number that is the most common. As each value in the set so far only has one of each number, we know that x must be one of the current numbers, making that the mode.

Next, because x is the mode and has to be the median as well, and our number line so far is

(10, 70, 80, 120), x must be either 70 or 80 to make it the median. This is because if x is 10 or 120, we would end up with (10, 10, 70, 80, 120) with 70 as the median or (10, 70, 80, 120, 120) with 80 as the median.

Finally, to calculate the mean, we have

mean = sum / count

The mean must be x, as it is equal to the mode, so we have

x = (10+70+80+120 + x)/5 (as there are 5 numbers including x)

multiply both sides by 5 to remove the denominator

5 * x = 10+70+80+120+x

5 * x = 280 + x

subtract x from both sides to isolate the x and the coefficient

4 * x = 280

divide both sides by 4 to get x

x= 70

We see that x is 70 or 80 and is one of the current numbers, checking off all boxes.

Answer: Interior angle: 150 degrees Exterior angle: 30 degrees

Step-by-step explanation:

We use the angle formula to find the value of an interior angle: 180*(12-2)/12 = 150 degrees. Since an exterior angle is the supplement of an interior angle, the measure of an exterior angle is 180 - 150 = 30 degrees

Answer:

Step-by-step explanation:

the ratio of 24 to 36 is the same as  x to 12

[tex]\frac{24}{36}[/tex] = [tex]\frac{x}{12}[/tex]

then

12*([tex]\frac{24}{36}[/tex])=x

[tex]\frac{24}{3}[/tex] = x

8 = x  

that's it :)

Answer:

it can not cleared clear but it can not cleared

Answer:

D)

[tex]an = -6 \times {( \frac{1}{4} )}^{n - 1} [/tex]

Step-by-step explanation:

(See the picture)

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

The general explicit formula for a geometric sequence is expressed as:

Given the following recursive functions:

[tex]a_1=-6\\ a_n=a_{n-1}\cdot\frac{1}{4} [/tex]

Get the next two terms:

[tex]a_2=a_{1}\cdot\frac{1}{4} \\ a_2=-6\cdot\frac{1}{4} \\ a_2=\frac{-3}{2} [/tex]

For the third term:

[tex]a_3=a_{2}\cdot\frac{1}{4} \\ a_3=\frac{-3}{2} \cdot\frac{1}{4} \\ a_3=\frac{-3}{8} [/tex]

The common ratio for the sequence will be [tex]\frac{1}{4} [/tex]

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

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Answer:

f(6) = 3

f'(6) = 1/6

Step-by-step explanation:

Remember that for a function f(x), we define f'(x) as the slope of the tangent line to the point (x, f(x))

We know that:

y = f(x) passes through the point (6, 3)

Then we already know that:

f(6) = 3.

Now we also know that the tangent at this point, also passes through (0, 2)

Remember that a line can be written as:

y = a*x + b

Where in this case, a = f'(6)

so we just want to find the slope of this line.

Remember that for a line that passes through (x₁, y₁) and (x₂, y₂) the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

And we know that the tangent line passes through the points (0, 2) and (6, 3)

Then the slope is:

a = (3 - 2)/(6 - 0)  = 1/6

Then we have:

a =  f'(6)  =1/6

Answer:

y=(2/3)x+10

Hope it helps!

My graph isn't really clear

The slope-intercept of the line that passes through the point (-9, 4) and has a slope of 2/3 will be y = (2/3)x + 10.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A line is given as y = mx + c

Here m is the slope,

Put m = 2/3 and  (-9, 4)

4 = (2/3)(-9) + c

c = 10

Thus equation will be y = (2/3)x + 10.

Hence "Y = (2/3)x + 10 is the slope-intercept of the line passing through the point (-9, 4), which has a slope of 2/3".

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Answer:

A

Step-by-step explanation:

graph is 6 units to the right

if it had been (x+6)^2

it would have been 6 units to left

Answer:

s = -4

Step-by-step explanation:

Your goal is to manipulate the equation so you can isolate s

9s + 20 = -16

Subtract 20 from both sides to get:

9s = -36

Divide both sides by 9 so s is alone

you end up with s = -4

Answer:

s  = -4

Step-by-step explanation:

9s+20=−16

Subtract 20 from each side

9s +20 -20 = -16 -20

9s = -36

Divide by 9

9s/9 = -36/9

s  = -4

Answer:

[tex](a)\ \bar x = 1.19[/tex]

[tex](b)\ \sigma_x = 0.18[/tex]

Step-by-step explanation:

Given

[tex]n = 4[/tex]

[tex]x: 1.45\ 1.19\ 1.05\ 1.07[/tex]

Solving (a): The mean

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{1.45 + 1.19 + 1.05 + 1.07}{4}[/tex]

[tex]\bar x = \frac{4.76}{4}[/tex]

[tex]\bar x = 1.19[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}[/tex]

So, we have:

[tex]\sigma_x = \sqrt{\frac{(1.45 -1.19)^2 + (1.19 -1.19)^2 + (1.05 -1.19)^2 + (1.07 -1.19)^2}{4 - 1}}[/tex]

[tex]\sigma_x = \sqrt{\frac{(0.1016}{3}}[/tex]

[tex]\sigma_x = \sqrt{0.033867}[/tex]

[tex]\sigma_x = 0.18[/tex]

Answer:

C. 37.8 units

Step-by-step explanation:

ED = 17/ cos(38°) = 17 / 0.7880 = 21.6 units

DF = 17× tan (38°) = 17× 0.7813 = 13.3 units

CD = 10/13.3 × 21.6 = 16.2 units

so, the length of CE = 21.6+16.2 = 37.8 units

Answer

500,000 + 500,000 = 1,000,000

Step-by-step explanation:

Answer:

(3) [tex]x = 7.5[/tex] and [tex]y = 51[/tex]

(4) [tex]x = 6[/tex]

Step-by-step explanation:

Question 3

Required

Solve for x and y

We have:

[tex]16x - 18 + 10x +3 = 180[/tex] --- angle on a straight line

Collect like terms

[tex]16x + 10x = 180 + 18 - 3[/tex]

[tex]26x = 195[/tex]

Solve for x

[tex]x = 195/26[/tex]

[tex]x = 7.5[/tex]

Also:

[tex]16x - 18 = 2y[/tex] ---- opposite angles

So, we have:

[tex]16 * 7.5 - 18 = 2y[/tex]

[tex]120 - 18 = 2y[/tex]

[tex]102 = 2y[/tex]

Divide by 2

[tex]51 = y[/tex]

[tex]y = 51[/tex]

Question 4:

Required

Solve for x

We have:

[tex]11x - 2 + 5x - 4 = 90[/tex] ---- angle at right-angled

Collect like terms

[tex]11x + 5x = 90 +2 + 4[/tex]

[tex]16x = 96[/tex]

Divide by 16

[tex]x = 6[/tex]

Pentagon has sum of 540°

Answer:

Hence, the roots of the polynomial equation are:

-2, 1, 4

Step-by-step explanation:

We are asked to find the roots of the polynomial equation:

We can also equate this equation to y to obtain a system of equation as:

and

Hence, the roots of the polynomial; equation are the x-values of the point of intersections of the graph of the system of equations.

Hence, the point of intersection of the two graphs are:

(-2,4), (1,-5) and (4,40)

Hence, the roots of the polynomial equation are:

-2, 1, 4

the answer is c i just had this question your welcome

Answer:

SECOND ONE

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The definition of a function is that any input will only have one output. Here, the input is the number of years, and the output is the value of the car. We know this because the question is asking why the value of the car is a function of the number of years. Therefore, based on the number of years, the value of the car is given.

Going back to the definition of a function, we can apply this year to say that any number of years will only have one car value. Another way to say this is that each time is associated with exactly one car value.

Answer:

8/9

Step-by-step explanation:

Find what fraction of their goal they have raised by adding the amounts from last year and this year together:

7/9 + 1/9

= 8/9

So, they have raised 8/9 of their goal

Answer:

μ = 170 customers per day

σ = 45 customers per day

n = 31

[tex]\mu_x = 170[/tex]

[tex]\sigma_x = 8[/tex]

Step-by-step explanation:

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.

She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers.

This means that [tex]\mu = 170, \sigma = 45[/tex]

Suppose she takes a random sample of 31 days.

This means that [tex]n = 31[/tex]

For the sample:

By the Central Limit Theorem, the mean is [tex]\mu_x = 170[/tex] and the standard deviation is [tex]\sigma_x = \frac{45}{\sqrt{31}} = 8[/tex]

Answer:

the operating characteristics have been solved below

Step-by-step explanation:

we have an average of 10 minutes per customers

μ = mean service rate = 60/10 = 6 customers in one hr

the average number of customers that are waiting in line

mean arrival λ = 2.5

μ = 6

[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]

= 6.25/21

= 0.2976

we calculate the average number of customers that are in the system

[tex]L=Lq+\frac{2.5}{6}[/tex]

= 0.2976+0.4167

= 0.7143

we find the average time that a customer spends in waiting

[tex]Wq=\frac{0.2976}{2.5}[/tex]

= 0.1190 hours

when converted to minutes = 0.1190*60 = 7.1424 minutes

[tex]0.1190+\frac{1}{6}[/tex]

=0.2857

probability that arriving customers would wait for the service

= 2.5÷6 = 0.4167

Answer:

B."5, -3, -4, 1, -1, 6, -4"

Step-by-step explanation:

We are given that

13,5,4,9,7,14,4

We have to find the deviation.

Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]

Using the formula

[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]

[tex]Mean,\mu=\frac{56}{7}=8[/tex]

Deviation=[tex]x_i-\mu[/tex]

         [tex]x_i-\mu[/tex]

13          5

5           -3

4           - 4

9            1

7             -1

14            6

4            - 4

Hence, option  B is correct.

Answer:

your selected answer is right

Answer:

Step-by-step explanation:

I don't think so. This equation has but one definite answer and the left and right sides don't produce the same result.

subtract 5m from both sides

6 = 4m - 5m

6 = - m                 Multiply both sides by - 1

-6 = m

An identity is something like 4x + 5x = 9x

It doesn't matter what x is. Any value of x will make the right side = to the left side. This becomes more important when you will study trigonometry.

Answer:

Option C: QT < TR

Step-by-step explanation:

From the triangle, we can see that UX bisects RS into two equal parts and so it is a perpendicular bisector.

TZ Is a mid segment and it means that T bisects QR into 2 equal parts as well as QS into 2 equal parts.

Thus;

QT = QR

And QZ = SZ

So Option C is not correct because QT = QR