a researcher records the repair cost for 1313 randomly selected stereos. a sample mean of $85.52$⁢85.52 and standard deviation of $10.81$⁢10.81 are subsequently computed. determine the 90�% confidence interval for the mean repair cost for the stereos. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.

Answers

Answer 1

The mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.

What is the critical factor?

The critical factor for a 90% confidence interval for the true mean repair cost for stereos is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

We have been given that a researcher records the repair cost for 13 randomly selected stereos. a sample mean of $⁢85.52 and a standard deviation of $10.81 are subsequently computed.

Since we don't know the population standard deviation, we used t statistics to create the 90% confidence interval in this case.

So, the 90% confidence interval for the true mean repair cost, μ is ;

⇒ P(-2.015 < t₅ < 2.015) = 0.90  

{As the critical value of t at 5 degrees of  freedom are -2.015 & 2.015 with P = 5%}

⇒ P(-2.015 < (x-μ)/(s/√n) < 2.015) = 0.90

⇒ P(-2.015×(s/√n) < (x-μ) < 2.015×(s/√n)) = 0.90

⇒ P(x - 2.015×(s/√n) < μ < x + 2.015×(s/√n)) = 0.90

90% confidence interval for

⇒ μ = (x - 2.015×(s/√n) , x + 2.015×(s/√n))

Here, x = $85.52, s  = $10.81, and n = 13

⇒ μ = (85.52 - 2.015×(10.81/√13) , 85.52 + 2.015×(10.81/√13))

⇒ μ = (79.47, 91.56)

Hence, the mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.

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Related Questions

find the solution to this equation:5(x-6)+8=7x-10

Answers

Answer:

x = -6

Step-by-step explanation:

Distribute where possible

5x - 30 + 8 = 7x - 10

Combine like terms

5x - 22 = 7x - 10

Subtract 7x from both sides and add 22 to both sides

-2x = 12

x = -6

Answer is 70 according to my calculator

jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. the area of the smaller lawn is 144 square feet. in the equation (x – 8)2

Answers

The dimensions of original lawn are a. 4 feet by 4 feet.

As per the equation and information mentioned in question, x represents the dimension of original lawn. The equation in question represents the relation between area of lawn at side of reduced lawn and it's area. We will solve this equation to find the value of x.

[tex](x - 8)^{2} = 144[/tex]

The expression on Left Hand Side is same as [tex](a - b)^{2}[/tex]. We know, on expansion, we write it as [tex]a^{2} + b^{2} - 2ab[/tex]. Thus, new equation will be -

[tex]x^{2} + 8^{2} - 2*x*8 = 144[/tex]

[tex]x^{2} + 64 + 16x = 144[/tex]

[tex]x^{2} + 16x + 64 - 144 = 0[/tex]

[tex]x^{2} + 16x - 80 = 0[/tex]

[tex]x^{2} + 20x - 4x - 80 = 0[/tex]

x (x + 20) -4 (x + 20) = 0

(x + 20) (x - 4) = 0

So, the two values of x that we get are:

x = 4 and -20.

The dimensions of lawn can not be negative. Hence, the value of x will be x.

Therefore, the dimensions of original lawn are a. 4 feet by 4 feet.

The complete question is -

Jillian is trying to save water, so she reduces the size  of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation [tex](x - 8)^{2} = 144[/tex], x represents the side measure of the original lawn. What were the dimensions of the original lawn?

a. 4 feet by 4 feet

b. 8 + [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

c. 8 - [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

d. 20 feet by 20 feet

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A forest covers 61,000 acres. A survey finds that 0.4​% of the forest is​ old-growth trees. How many acres of​ old-growth trees are​ there?

Answers

Answer:

2,440 acres of old-growth trees.

Step-by-step explanation:

61,000*0.04=2,440

There are 2,440 acres of old-growth trees.

Hope this helps!

Please mark as brainliest if correct!

Given the definitions of f(x) and g(x) below, find the value of (gof)(-2).
f(x) = -2x + 7
g(x) = x² - 6x + 5

Answers

The value of (gof)(-2) for the given values of f(x) and g(x) is 60.

A Composite function may be defined as a function which is formed from the operation of combination of two functions. If f(x) and g(x) are two functions, then the composite functions of the given functions are fog(x) that is f(g(x)) and gof(x) that is g(f(x)).

It is given in the question that f(x) = -2x + 7 and g(x) = x² - 6x + 5.

Now, gof(x) = g(f(x)) = (-2x + 7)² - 6(-2x + 7) + 5

gof(x) = 4x² + 49 - 28x + 12x - 42 + 5

gof(x) = 4x² - 16x + 12

gof(-2) = 4(-2)² - 16(-2) + 12

gof(-2) = 16 + 32 + 12

=>gof(-2) = 60

Therefore, the value of gof(-2) is equal to 60.

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A number d is decreased by 5 and then doubled

Answers

Let us assume the given number is x.

If it is decreased by 5 and then doubled, then we can represent that event with an algebraic expression as:

= (x-5) × 2

Formation of equation:

The number decreased by 5 can be written as: x - 5

Now, to double it, we will multiply it by 2 = (x-5) × 2

Therefore, we have the algebraic form of the given condition as :

= (x-5) × 2

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in a random sample of 77 residents of the state of texas, the mean waste recycled per person per day was 1.01.0 pounds with a standard deviation of 0.290.29 pounds. determine the 98�% confidence interval for the mean waste recycled per person per day for the population of texas. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.

Answers

Answer:

(0.63789 ; 1.38211 ) is the 98% confidence interval for the mean waste recycled per person per day for the population of texas and  Tcritical = 3.143

In a random sample of 7 residents of the state of texas ,the mean waste recycled per person per day was 1.01 pounds and standard deviation 0.29 pounds

we have to find the 98% confidence interval for the mean waste recycled per person per day for the population of texas

Mean, xbar = 1.01

Standard deviation, s = 0.29

Sample size, n = 7

Confidence interval  : xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Degree of freedom (df) = n - 1 = 7 - 1 = 6

Hence Tcritical = 3.143

Margin of Error = 3.143 * 0.29/sqrt(6)

Margin of error = 0.37211

Lower boundary = (1.01 - 0.37211) = 0.63789

Upper boundary = (1.01 + 0.37211) = 1.38211

(0.63789 ; 1.38211 )

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25 points plus brainliest

Answers

Answer:

The first answer is correct

Step-by-step explanation:

y = mx + b is the slope intercept form of a line

15x - 5y = 30  Subtract 15x from both sides

-5y = -15x + 60  Divide both sides by -5

y = 3x -6  The -6 is your y-intercept.  It is the point (0.-6)  We could stop here because that is the only choice that shows (0,-6), but let's find the x intercept.

The x-intercept is when y = 0

y = 3x -6

0 = 3x - 6 Add 6 to both sides

6 = 3x  Divide both side by 3

2 = x This is the point (2,0)

We could have taken the original equation and set x=0 and y=0

15x - 5y = 30

15(0) - 5y = 30

-5y = 30  Divide both sides by -5

y = -6

15x -5y = 30

15x - 5(0) = 30

15x = 30  Divide both sides by 15

x = 2

-

what is this equations value for x? |5-2x|>5

Answers

The value of equation for x is x > 0.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

|5-2x| > 5

To solve for let us take x on one side.

So, Subtracting 5 both the side we get,

|5 - 2x - 5| > 5 - 5

Simplifying we get,

|-2x| > 0

Extracting mod we get,

2x > 0

Now since 2 > 0 which is true,

Thus, x > 0

So, the value of equation for x is x > 0.

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Select all the expressions that are equivalent to –24 [tex]\frac{1}{2}[/tex] + 16.15 – 4.

Answers

The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex]  .

In the question,

the given expression is [tex]-24\frac{1}{2} +16.15-4[/tex] , solving further we get

= -49/2 + 16.15 - 4       ...(as [tex]24\frac{1}{2} = \frac{49}{2}[/tex]  )

= -24.5 + 12.15

= -12.35

In option(A) we have ,

=[tex]24\frac{1}{2} -16.15+4[/tex]

= 49/2 -16.15 +4

= 24.5 -16.15 +4

= 8.35 + 4

= 12.35

In option(B) we have ,

= 16.15 - 28.5

= -12.35

In option(C) we have ,

= -28.5 + 16.15

= -12.35

In option(D) we have ,

[tex]=-20\frac{1}{2} +16.5[/tex]

= -41/2 + 16.5     ...( as [tex]20\frac{1}{2} = \frac{41}{2}[/tex] )

= -20.5 + 16.5

= -4

In option(E) we have ,

[tex]=12.15-24\frac{1}{2}[/tex]

= 12.15 - 49/2

= 12.15 - 24.5

= -12.35

As we can see that from all the option , only option(B), option(C) and option(E) matches with the given expression .

Therefore , The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex]  .

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what is the value of 32 ⅗ ?​

Answers

Answer:

8

Step-by-step explanation:

I attached my answer........

Mrs. Genebe worked all year and earned $23,400. How much did she earn per week?

Answers

Answer:

$448.766754 per week or $448

Step-by-step explanation:

i gotchu

theres 52.1429 weeks

divide 23,400 by 52.1429

u get $448.766754 per week

17/21 + 1/3 - 5/7 thank you!

Answers

Answer:3/7

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation:

change all denominators to 21

{21 is the lcd of all the numbers)

17/21 x 1= 17/21

1/3 x 7 = 7/21

5/7 x 3 = 15/21

17/21 + 7/21 - 15/21

24/21-5/21

9/21

reduce by three

9/21÷3

3/7

please help!! (answer is NOT undefined)

Answers

[tex]-8\sqrt{-165} \\ \\ =-8\sqrt{-1}\sqrt{165} \\ \\ =\boxed{-8i\sqrt{165}}[/tex]

write the algebraic expression for two less than for times a number
PLEASE SHOW WORK

Answers

two less=-2
four times a number(x)=4x
Combine it
4x-2 is the right answer

Another circular section of the island to be used to count marine iguanas has
a'radius of 1 kilometer. Researchers will sample this area to draw conclusions
about the iguana population on the entire island. What is the area of this
section? Use an approximation of n to two decimal places. Place your
approximation of the area in the orange chart below.

Answers

The area of the circular section is 3.14 square units

How to determine the area of the circular section?

The given parameters are:

Radius, r = 1 kilometre

Rewrite the above properly as follows

So, we have

r = 1 kilometre

The area of the circular section is:

A = πr^2

So, we have

A = 3.14 * 1^2

Evaluate the exponent

So, we have

A = 3.14 * 1

Evaluate the product

So, we have

A = 3.14

Hence, the area of the circular section is 3.14 square units

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Simplify:
4(10+2³-5)
O a. 52
O b. 44
O c. 6892
O d. 17

Answers

Answer:

A. 52 is your answer

Step-by-step explanation:

Explained below

Answer:

Ans is a

First you solve the inside of the bracket u will get 4(13)

which will give u 52

The expression for the nth term of a sequence is 5n^2

work out the third term in this sequence

Answers

Answer:45

Step-by-step explanation:

5n²

5(3)²

5(9)

∴ The third term in the sequence 5n² is 45

donald is studying the buying habits of all women attending his store. he samples the population by dividing the women into groups by age and randomly selecting a proportionate number of women from each group. he then collects data from the sample. which type of sampling is used?

Answers

According to the statement Donald is using Stratified sampling to collects data from the sample.

The correct option is A.

Briefing:

A simple random sample is then taken from each separate or subgroup using the stratified sampling survey method, which first divides the population being studied into distinct subgroups or groups known as strata.

The ability to reduce the sample size needed to obtain reliable results is one of the main benefits of stratified sampling.

What accomplishes stratified sampling?

When attempting to evaluate data from various subgroups or strata, researchers frequently use stratified random sampling. They can quickly find a population sample that most accurately reflects the entire population they are studying.

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I understand that the question you are looking for is:

Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?

a. Systematic sampling

b. Convenience sampling

c. Stratified sampling

d. Cluster sampling

Find the total amount given the original price and tax rate. Round to the nearest hundredth if necessary. Original price: $123.28 Tax rate: 7.5%

Answers

7.5% = 0.075

0.075 x 123.28 = 9.246

So, the tax will be $9.20.

Total cost would be $132.48.

Simplify the ABSOLUTE VALUE of the number
sentence to solve:

| -4 | + | 1 |=

3

5

-5

-3

Answers

Answer:

5

Step-by-step explanation:

Every number from the absolute sign will be positive.

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form..

Answers

Answer:

y = 4/5x + 27/5

or 5y = 4x + 27

or 5y - 4x = 27

Step-by-step explanation:

Look at (-3,3) and (2,7)

So the line rises 4 units and runs 5 units, then slope is 4/5

using m = 4/5, y = 3, x = -3

y = mx + b

3 = 4/5(-3) + b

3 = -12/5 + b

b = 15/5 + 12/5 = 27/5

so y = 4/5x + 27/5

or 5y = 4x + 27

or 5y - 4x = 27

Find the distance between -55 and 63.

Answers

Answer:

The distance would be 118

Step-by-step explanation:

The easiest way I solve the distance between a negative number and a positive number is by adding the negative (but making it a positive) and the positive together. If you add 55 and 63 you would get 118. And 118 is the distance between -55 and 63.

I hope this helps!! :)

Prove that cos 4θ = 8 cos⁴ θ - 8 cos² θ + 1

Answers

Answer:

Step-by-step explanation:

Answer is in the pic.

Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\ \\$\sin^2 \theta + \cos^2 \theta=1$\\\end{minipage}}[/tex]

Use the trigonometric identities to prove the given equation:

[tex]\begin{aligned} \implies \cos 4 \theta & = \cos (2 \theta +2 \theta)\\& = \cos 2 \theta \cos 2 \theta - \sin 2 \theta \sin 2 \theta\\& = \cos^2 2 \theta - \sin^2 2 \theta\\& = \cos^2 2 \theta - (1-\cos^2 2 \theta)\\& = 2\cos^2 2 \theta - 1\\ & = 2\left(\cos 2 \theta \right)^2-1\\& = 2\left(\cos\theta \cos\theta-\sin \theta\sin \theta\right)^2-1\\& = 2\left(\cos^2\theta-\sin ^2\theta\right)^2-1\\& = 2\left(\cos^2\theta-(1-\cos^2\theta)\right)^2-1\\& = 2\left(2\cos^2\theta-1\right)^2-1\\\end{aligned}[/tex]

                 [tex]\begin{aligned}& = 2\left(4\cos^4\theta-4\cos^2\theta+1\right)-1\\& =8\cos^4\theta-8\cos^2\theta+2-1\\ & =8\cos^4\theta-8\cos^2\theta+1 \end{aligned}[/tex]

Problem: Chrissy has 3 cats. Each cat weighs differently. The first and second cat weigh 7 kg altogether. The second and third cat weigh 8 kg altogether. The third and first cat weigh 11 kg altogether. What is the weight of each cat?

Answers

Answer:its a

Step-by-step explanation:

the annual salaries of all employees at a financial company are normally distributed with a mean mu

Answers

The value of the Z - Score is a -1.5.

According to the statement

We have to find that the z-score of the company.

So, For this purpose, we know that the

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

From the given information:

The annual salaries of all employees at a financial company are normally distributed with a mean Mu = $34,000 and a standard deviation Sigma = $4,000.

Then

Let X = annual salaries of all employees at a financial company

And

The z score probability distribution for the normal distribution is given by:

Z - Score = Annual salary - mean / s.d.

Then substitute the values

Z - Score = 28,000 - 34,000/ 4000

Z -Score = -6/4

Z -Score = -1.5.

So, The value of the Z - Score is a -1.5.

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A scientist created a scatter plot to represent the heights of four plants over time. Then, she found a line of best-fit to model the height in centimeters of each plant after x days. The equations of each trend line are given in the table.


Trend Line Equations
Plant
Equation of trend line
1
y = three-halves x + three-halves
2
y = 2 x + 1
3
y = one-half x + 3
4
y = three-halves x + 1

According to the trend line equations, which plants are growing at the same rate per day?

Answers

The plants which are growing at the same rate are Plant 1 and Plant 4.

Both the plants are growing at the same rate because they have same slope when their growth rate is expressed in the form of equation. Slope may be defined as the amount of steepness of the graph when plotted on graph paper. The slope-intercept form of equation of line is given by y = mx + c where m is the slope of the line and c is the intercept formed by the line. The slope-intercept form of the growth rate equation of Plant 1 is given by y = 3/2x + 3/2 and the slope-intercept form of the growth rate equation of Plant 4 is given by y = 3/2x + 1.

If we compare them from the slope-intercept form of line, then both the Plants have same slope and thus their growth rate is same.

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Answer:

B. 1 and 4

Step-by-step explanation:

Edge 2023

A football team gained 6 yards on a first down, lost 15 yards on the second down, and gained 12 yards on the third down. How many yards did the team gain or lose?

9 yards

33 yards

21 yards

3 yards

Answers

The answer is 3 yards
Answer is + 3 yards gained

First you gained
+6 yards
Then you lost
- 15 yards
Then you gained
+ 12 yards
_________
+ 3 yards gained

Insert <,>,or = to make the following sentence true. square root of 17 and 4

Answers

we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4

we have to solve the following sentence

[tex]\sqrt{17}[/tex] --- 4     ( insert <,>, = to make the following sentence true)

what is square root ?

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is  [tex]\sqrt{}[/tex] .

we know that

square root of 17 is 4.12310563

which is 4+ 0.12310563

that is if we add 4+0.12310563 we get 4.12310563

therefore square root of 17 is greater than 4

that is [tex]\sqrt{17}[/tex] > 4  

since 4.12310563 > 4

hence,   we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4

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AYUDA!! SE ME OLVIDO COMO RESOLVER GEOMETRÍA ​

Answers

P = 180 - (125 + 30)

P = 180 - 155

P = 25 degrees

Thus :

P = 25/180 n radian

P = 5/36 n

Which mean the first option is the correct answer.

what is the difference of - 3 - ( - 10)

Answers

Answer
(-3) - (-10) = 7

|7| = 7

7

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