CAN SOMEONE HELP WITH THIS QUESTION?✨

CAN SOMEONE HELP WITH THIS QUESTION?

Answers

Answer 1

the rate of change of the angle of elevation teta is  ∅ = tan⁻¹ 2.1275

What is angle of elevation?

Angle of Elevation is an equation used in math to describe the angle formed between the horizontal line and the line of sight when an observer looks upwards. It is always at a height that is greater than the height of the observer

Using ∅ = tan⁻¹ (x/2000)

Then we are to find the angle teta

Where x = 4255 ( substitution)

∅ = tan⁻¹ (4255/2000)

∅ = tan⁻¹ 2.1275

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Related Questions

Combine like terms: -4x+3-7x-8
A. -7x-5
B. -11x-5
C. -3x -11
D. none of the above

Answers

Answer:

answer is B

Step-by-step explanation:

-4x-7x=-11x

+3-8=-5

=-11x-5

answer: B -11x-5

[tex] \sf \implies \: - 4x +3 - 7x - 8[/tex]

[tex] \sf \implies \: - 11x +3 - 8[/tex]

[tex] \sf \implies \: - 11x - 5[/tex]

Hence, Option B is correct!!

Need Help (25 Points)

Answers

1. opposite
2. addition
3. division
4. inverse

Answer:

Opposite
(or a any synonyms)
Addition
(Or sum)
division
inverse

Step-by-step explanation:

The first one is the most complicated, theres so many words can fit. Probably try with an synonyms of reverse like "Opposite"  
For the 2nd,3rd and 4th options:

Addition (Or sum) since is the reverse of subtraction
division  since is the reverse of multiplication
inverse
since those functions (Exponent and radicals) are also inverse of each other

What is the intercept give your answer to three decimal places

Answers

A. The intercept does not have a practical interpretation and is not statistically meaningful.

What is line regression?

Linear regression is a statistical method used to model the relationship between a dependent variable (also called the response or target variable) and one or more independent variables (also called predictors or explanatory variables) in a linear fashion.

B. The intercept is 4.62 mpg.

C. The value of the intercept represents the predicted city mileage for Highway gas mileage of 0 mpg. However, such a car does not exist, so the intercept is not statistically meaningful.

The intercept represents the value of the dependent variable (highway gas mileage) when the independent variable (city gas mileage) is equal to 0. However, in this case, it is not possible for a car to have 0 city gas mileage and still be in operation.

Therefore, The intercept does not have a practical interpretation and is not statistically meaningful.

In fact, the intercept can be considered as a theoretical value that is not meaningful in the context of the data.

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You are trying to develop a strategy for investing in two different stocks The anticipated annual return for a 1,000 investment in each stock under four different economic conditions has the probability distribution shown to the right Complete parts ( ) through ( ) below

Answers

The first step in developing a strategy for investing in two different stocks is to perform research on the stocks and their respective industries.

What is stock?

Stock is a type of security that signifies ownership in a company and represents a claim on part of the company's assets and earnings. It is a share of ownership in a company. It is bought and sold on a stock exchange, and the price of the stock is determined by the supply and demand of the stock.

This can be done by looking at the company’s financials, track record, industry trends, and more. This research can help you to determine which stock is more likely to perform better in any given economic condition. By doing this, you can maximize your return while also minimizing your risk. This can be done by using a risk-adjusted return metric such as the Sharpe Ratio.

Finally, you must decide how to allocate funds across the two stocks. This will depend on your risk tolerance and investment goals. For example, if you are a conservative investor, you may want to allocate more funds to the stock with the highest expected return under all economic conditions. On the other hand, if you are a more aggressive investor, you may want to allocate more funds to the stock with the highest expected return under one or two of the economic conditions.

Overall, developing a strategy for investing in two different stocks takes into account several factors, including research, expected returns, and risk tolerance. By doing this, you can maximize your return while also minimizing your risk.

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given the lengths of two sides of a triangle , write an inequaluty to indicate between which two number the lengths of the third side must fall. 8 and 13

Answers

Answer:

5 < x < 21

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

13 - 8 < x < 13 + 8 , then

5 < x < 21

Write an inequality to describe each situation. a. The minimum age for voting in the United States is 18 years old. Let a represent a voter's age. b. A theater seats up to 275 people. Let p represent the number of people attending a performance in the theater.​

Answers

According to this inequality, the number of persons attending a theatrical inequality  play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.

What is inequality?

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. We resuming our current status quo. Yet a variety of things lead to inequality: Negative values on both sides are split or added.

a. The disparity in representing the voting age in the United States is as follows:

a ≥ 18

In order to be eligible to vote, a voter's age, denoted by a, must be more than or equal to 18 years old.

b. The inequality used to depict a theater's seating capacity is:

p ≤ 275

According to this inequality, the number of persons attending a theatrical play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.

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The demand equation for a certain commodity is given by the
following equation.
p= =1/2+². - 20x + 1200, 0≤x≤ 120
Find x and the corresponding price p that maximize revenue.
The maximum value of R(x) occurs at x =0.

Answers

In the given demand equation, the value of x and corresponding price p that maximize revenue are x = 31.8 and p = $514.60.

How to Solve the Equation?

To find the value of x and corresponding price p that maximize revenue, we first need to determine the revenue function. Revenue (R) is given by the product of price (p) and quantity demanded (x), so:

R(x) = xp

Substituting the given demand equation for p, we get:

R(x) = x(1/2 + ² - 20x + 1200)

Simplifying and rearranging:

R(x) = 1/2x + ²x - 20x² + 1200x

R(x) = -20x² + (1200 + ²)x + 1/2x

To find the value of x that maximizes revenue, we take the derivative of R(x) with respect to x, set it equal to zero, and solve for x:

dR/dx = -40x + (1200 + ²) + 1/2 = 0

Solving for x:

x = (1200 + ² + 1/2) / 40

x = 31.8

To find the corresponding price, we substitute this value of x back into the demand equation for p:

p = 1/2 + ² - 20(31.8) + 1200

p = $514.60

Therefore, the value of x and corresponding price p that maximize revenue are x = 31.8 and p = $514.60.

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From the sum of 8a-2b+8 and -2a+6b,subtract 5b-6a ?​

Answers

Therefore , the solution of the given problem of expressions comes out to be b + 8 when 8a-2b+8 and -2a+6b are added together.

Expression : what is it ?

There is a need for calculations like joining, random variable division, variable multiplication, and removal. If they were united, the following would happen: A mathematical equation, some data, and a formula. A statement of truth is composed of numerical data, formulae, components, and mathematical operations like additions, subtractions, errors, and segmentations. One can assess and analyse words and sentences.

Here,

The formula is as follows:

=> 8a - 2b + 8 - 2a + 6b - (5b - 6a)

By combining similar words to make the expression shorter, we get:

=> (0a - b + 8 = -b + 8)

=>  (8a - 2a - 6a) + (-2b + 6b - 5b)

Therefore, the answer is b + 8 when 8a-2b+8 and -2a+6b are added together.

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Identify the slope and Y intercept of the line whose equation is given right the white intercept as an ordered pair remember the slope intercept formula is Y equals MX plus BQ equals two minus are

Answers

Answer:

The correct answer is: slope= -1;  y-intercept (0,2)

Step-by-step explanation:

The given equation is:   [tex]q=2-r[/tex]

Assuming [tex]q[/tex] and [tex]r[/tex] as [tex]y[/tex] and [tex]x[/tex] respectively, the equation becomes:  [tex]y=2-x[/tex]

Rearranging the terms in right side:  [tex]y=-x+2[/tex]

Comparing this above equation with the slope-intercept form [tex]y=mx+b[/tex], we will get.....

[tex]mx=-x[/tex] ⇒ [tex]m=\frac{-x}{x} =-1[/tex]

[tex]and[/tex]

[tex]b=2[/tex]

So, the slope is -1 and y-intercept is (0, 2)

for the following right triangle. find the side length x. round your answer to the nearest hundreth.

Answers

Answer:

answer is 11.60

Step-by-step explanation:  

formula is C^2 = a^2 + b^2

c = 13

a = 8

b = ?

169 = 64 + x^2

135 = x^2

I hope this helps!

Solve the indicated quantity​

Answers

The solutions to the indicated quantities are x = 25, MIK = 25 and KIE = 50 degrees

How to solve the indicated quantities

The value of x

From the question, we have the following angle that can be used in our computation:

Angle MIE = 75

Using the above as a guide, we have the following:

x + 2x = 75

Evaluate

3x = 75

So, we have

x = 25

The angle MIK

From the figure, we have

MIK = x

So, we have

MIK = 1 * 25

MIK = 25

The angle KIE

From the figure, we have

KIE = 2x

So, we have

KIE = 2 * 25

KIE = 50

Hence, the measure of angle KIE is 50 degrees

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Given: If A AND B, then C. Given: The if-then statement's reverse isalso correct. If A is True, B is True, what is C?

Answers

The conclusion is that if A is true, B is true, then C must be true as well.

What is statement ?

In logic and mathematics, a statement is a declarative sentence that is either true or false. It is an assertion about a fact or a relationship between facts. A statement can be a simple sentence, such as "The sun is shining," or a complex one, such as "If it rains tomorrow, I will stay indoors."

If the statement "If A AND B, then C" is true, and if its reverse statement is also true, then the converse of the statement is "If C, then A AND B."

If A is true and B is true, then A AND B is also true. Therefore, by the original statement, C must also be true.

Therefore, the conclusion is that if A is true, B is true, then C must be true as well.

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8. Daisy is trying to figure out how much negotiating room she has in purchasing a new car. The car has an MSRP of $34,995.99. She has learned from an industry insider that most car dealerships have a 20% markup on selling price. What does she estimate the dealership paid for the car?

Answers

Answer:

To estimate the dealership's cost for the car, we need to first calculate the dealership's selling price. We know that the car has an MSRP of $34,995.99, and we know that dealerships typically have a 20% markup on selling price.

So, to find the dealership's selling price, we can use the formula:

Selling price = MSRP + (Markup percentage * MSRP)

Substituting the values we have:

Selling price = $34,995.99 + (20% * $34,995.99)

Selling price = $34,995.99 + $6,999.20

Selling price = $41,995.19

Therefore, we estimate that the dealership paid $41,995.19 - the 20% markup - for the car.

To check this estimate, we can calculate the dealership's cost using the formula:

Cost = Selling price - Markup

Substituting the values we have:

Cost = $41,995.19 - (20% * $41,995.19)

Cost = $41,995.19 - $8,399.04

Cost = $33,596.15

This is very close to the MSRP of $34,995.99, which suggests that our estimate is reasonable.

Farmer Ed has 1,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

Answers

Answer:

Step-by-step explanation:

Farmer Ed has 1,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

**Jackie took out a mortgage loan for $90,000 at an interest rate of 10% for 25 years. If Jackie had not filed a bankruptcy, which damaged her credit score a lot, her payments could have been much lower at $527.16 per month. How much is Jackie paying in additional interest over the life of the loan?
Hint: 1st, use minimum monthly payment formula: to calculate the monthly payment at 10% interest rate, where PV = 90,000, i = 0.10/12, and n = 300 (because that is how many months there are in 25 years).
2nd, once you find P multiply it by 300 months to find how much Jackie paid for the lifetime of the loan for the mortgage.
3rd, finally, subtract $90,000 to find out how much interest she paid in total.
4th, how much would Jackie have paid for the lifetime of the loan if her monthly payments were $527.16 (if she had not filed bankruptcy)? Remember, this is the monthly payment, so you don't have to use the formula, just multiply it by 300 months to find the cost of the lifetime loan.
5th, subtract $90,000 from the answer you got in step 4. That is how much interest Jackie would have paid if the monthly loan payments were smaller.
Finally, what is the difference between the interest you found in step 3 and step 5?

a.
$49,200.00
b.
$87,201.20
c.
$68,148.00
d.
$56,809.00

Please select the best answer from the choices provided.

Answers

The difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is $83,421.

What is the interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

First, we need to calculate the monthly payment at a 10% interest rate for 25 years:

PV = 90,000

i = 0.10/12

n = 25*12 = 300

Using the formula for the monthly payment of a mortgage loan, we get:

[tex]P = i PV / (1 - (1 + i)^{(-n)})[/tex]

= 805.23

So, if Jackie paid the minimum monthly payment, she would pay $805.23 per month. The total amount paid over the lifetime of the loan would be:

Total amount paid = P * n = 805.23 * 300 = $241,569

The amount of interest paid would be:

Interest paid = Total amount paid - PV = 241,569 - 90,000 = $151,569

If Jackie had made payments of $527.16 per month, the total amount paid over the lifetime of the loan would be:

Total amount paid = 527.16 * 300 = $158,148

The amount of interest paid would be:

Interest paid = Total amount paid - PV = 158,148 - 90,000 = $68,148

Therefore, the difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is: $151,569 - $68,148 = $83,421

hence, the answer is not one of the choices provided.

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Find the value of x.

Answers

Answer: 19

Step-by-step explanation:

(5x + 30) = 125   (opposite angles are equal)

5x = 95

x = 19

ANSWER RIGHT NOW PLEASE

Answers

Answer:

0.19^9

0.19 to the 9th power

Step-by-step explanation:

Use Exponent Rules:

If you are multiplying terms with the same base, then ADD the exponents.

see image

As economy of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.02 worth of coal, $0.30 worth of electricity, and 0.30 worth of steel, the electric industry needs $0.04 worth of coal, $0.04 worth of electricity, and 0.02 worth worth of steel, and the steel industry needs $0.10 worth of coal and $0.04 worth of steel. The sales demand is estimated to be $1 billion for coal, $1 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and demand for coal doubles, whereas the demand for for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand.

Answers

Answer:

Step-by-step explanation:

Let’s denote the production levels of coal, electricity and steel as x, y and z respectively. We can set up a system of equations to represent the inter-industry demand for each industry’s output.

For coal: 0.02x + 0.04y + 0.10z = x For electricity: 0.30x + 0.04y = y For steel: 0.30x + 0.02y + 0.04z = z

Solving this system of equations gives us x = (50/3)y and z = (25/2)y.

The new sales demand for coal is $2 billion (double the original), for electricity is $3 billion (triple the original) and for steel is $6 billion (an increase of 50%). Substituting these values into our equations gives us:

(50/3)y = $2 billion y = $3 billion (25/2)y = $6 billion

Solving these equations gives us y = $3 billion, x = $5 billion and z = $18.75 billion.

So to satisfy the new demand, the coal industry should produce at a level of $5 billion, the electric industry should produce at a level of $3 billion and the steel industry should produce at a level of $18.75 billion.

find the diffrence. enter your answer in simplest terms using the slash (/) as a faction bar

Answers

Answer: Fraction Form: 9/56
Decimal form: 0.16071428…

Answer:

7/8 - 5/7 =

49-40/56 =

9/56

What is the distance between the points (15,-17) and (-10,-17) in the coordinate plane?
A. 12.5 units
B. 25 units
C. 32 units
D. 5 units

Answers

Hello and Regards zoecenters91522.

Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.

Step-by-step explanation:

The distance between two points is the measure of the length of the straight line that joins them. On a Cartesian plane, the distance between two points is calculated using the Euclidean distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is equal to the square root of the sum of the squares of the differences of their coordinates:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

This formula can be used to calculate the distance between two points on any plane, such as a three-dimensional plane or Euclidean space of any dimension.

Now we locate the points of x and y.

x₁ = 15, y₁ = -17x₂ = -10, y₂ = -17

We substitute the points in the formula and solve:

[tex]\huge \boxed{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]

[tex]\huge \boxed{d=\sqrt{(-10-15)^2+(-17-(-17))^2 } }[/tex]

[tex]\huge \boxed{d=\sqrt{(-25)^2+0^2}=\sqrt{625+0} }[/tex]

[tex]\huge \boxed{d=\sqrt{625}=25 \ units }[/tex]

Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.

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Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.


How many boxes of cookies did Jane sell last year?

Answers

Jane sold 27 boxes of cookies last year if Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given ,

Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.

Let's assume the number of boxes Jane sold last year as x.

As per the given condition, 50 = 2x - 4

Adding 4 on both sides, we get:

50 + 4 = 2x - 4 + 4

54 = 2x

Dividing by 2 on both sides, we get:

x = 27

Therefore, Jane sold 27 boxes of cookies last year.

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Batteries are sold in packs
and boxes.
There are 8 batteries in each
pack.
There are 30 batteries in
each box.
Emily buys p packs of
batteries and b boxes of
batteries.
Write down an expression,
in terms of pand b, for the
total amount of batteries
that Emily buys.

Answers

Answer:

The total number of batteries that Emily buys can be expressed as:

8p + 30b

Here, 8p represents the total number of batteries in the packs that Emily buys, and 30b represents the total number of batteries in the boxes that Emily buys. By adding these two terms together, we can find the total number of batteries that Emily buys.

EASY (NEED HELP)
Find the function that is finally graphed after the following transformations are applied to the graph

1) Reflect about the x axis
2) shift up 9 units
3) shift left 9 units

Answers

After reflection and shifts, all three transformations gives us the final function: y = -√(x+9) + 9. This function starts at the point (-9,9) and decreases as x increases. The graph of this function is a reflection of the original graph of y = √x about the x-axis, shifted up by 9 units, and shifted left by 9 units.

What is the function after reflection about x - axis

This function starts at the origin (0,0) and increases as x increases.

1. Reflect about the x axis:

A reflection about the x-axis takes every point on the graph of y = √x and maps it to a new point with the same x-coordinate, but the opposite y-coordinate. For example, the point (1,1) on the graph of y = √x would be reflected to the point (1,-1) on the new graph. This transformation effectively flips the graph upside down.

2. Shift up 9 units:

This transformation moves the entire graph up by 9 units. Every point on the graph is shifted vertically by 9 units. For example, the point (1,-1) on the reflected graph would be shifted up to the point (1,8) on the new graph.

3. Shift left 9 units:

This transformation moves the entire graph to the left by 9 units. Every point on the graph is shifted horizontally by 9 units. For example, the point (1,8) on the shifted graph would be shifted left to the point (-8,8) on the final graph.

Combining all three transformations gives us the final function: y = -√(x+9) + 9.

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Pat needs to paint an 8 ft × 36 ft rectangular wall. What is the area that needs to be painted?
A) 300 ft2
B) 288 ft2
C) 282 ft2
D) 276 ft2

Answers

Area of rectangle = wl
W= 8 ft
L = 36
A = 8*36
= 288 ft^2

A tree on a hillside casts a shadow c = 235 ft down the hill. If the angle of inclination of the hillside is b = 26° to the horizontal and the angle of elevation of the sun is a = 56°, find the height of the tree. (Round your answer to the nearest foot.)

Answers

The height of the tree is equal to 210 ft to the nearest foot using the sine rule.

What is the sine rule

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

angle opposite of the tree = 56 - 26 = 30

angle opposite of the shadow = 180 - 90 - 56= 34

by application of sine rule:

sin 30/h = sin 34/235

h = (235 × sin 30)/sin 34 {cross multiplication}

h = 117.5/0.5592

h = 210.1216 ft.

Therefore, the height of the tree is equal to 210 ft to the nearest foot using the sine rule.

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Find the volume of the right circular cone with r=22.1 mm and h=5.91 mm.

Answers

Answer:

radius r = 22.1 m

height h = 5.91 m

slant height s = 22.8765841 m

volume V = 3022.73898 m^3

lateral surface area L = 1588.30288 m^2

base surface area B = 1534.38527 m^2

total surface area A = 3122.68815 m^2

Step-by-step explanation:

help me pleaseeee!!!

Answers

Answer: -5/6

Step-by-step explanation:

Hopefully this helps, my friend, best of luck to you :)

help again asapppppp

Answers

Answer:

[tex]\mathrm{y\:=\:\frac{3}{2}x\:+\:7}[/tex]

Step-by-step explanation:

To find the equation of a line parallel to -4y = 32 - 6x, we first need to rewrite this equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

-4y = 32 - 6x

Divide both sides by -4:

y = -8 + (3/2)x

So the slope of this line is 3/2. Since we want a line parallel to this one, it will have the same slope of 3/2.

Now we can use the point-slope form of a linear equation to find the equation of the line that passes through (0,7) with a slope of 3/2:

y - y1 = m(x - x1)

where m = 3/2 and (x1,y1) = (0,7)

y - 7 = (3/2)(x - 0)

Simplifying:

y - 7 = (3/2)x

y = (3/2)x + 7

So the equation of the line parallel to -4y = 32 - 6x that passes through the point (0,7) is y = (3/2)x + 7.

i need help with question 6

Answers

The company's expense budget for 2009 was $189,785.

Standard Scores

Use both the Student ID and Distance to Work variables.
List the Student ID at TESU in ascending order of Distance to Work.
Calculate the z-scores associated with each student (use the sample standard deviation for this calculation).
Identify potential outliers and explain your reasoning.

Confidence Intervals/Samples

Take a sample of the first four data points for the variable Distance to Work (unsorted - use the original order in the dataset).
Determine the 95% and 99% confidence intervals using the same size of 4.
Describe and compare the two intervals.

Take a sample of the first seven data points for the variable Distance to Work (unsorted - use the original order in the dataset).
Determine the 95% confidence interval. Use the same mean and SD, but change the sample size to 20 and determine the 95% confidence interval.
Describe and compare the two intervals.




STUDENT DATA TABLE
ID School Enrolled Months enrolled Birthday month Distance to Work Height Foot Size Hand Size Sleep Homework
1 Arts and Sciences 12 January 0 60 8 5 360 30
2 Applied Science and Technology 6 February 0 62 7 6 400 45
3 Business and Management 8 April 5 66 10 7 420 60
4 Nursing 10 June 10 68 12 8 440 15
5 Public Service 48 July 15 68 14 8 540 75
6 Arts and Sciences 48 June 30 70 12 9 480 120
7 Applied Science and Technology 36 October 32 72 12 8 320 80
8 Applied Science and Technology 32 November 36 75 14 7 440 60
9 Nursing 6 July 8 63 9 7 300 90
10 Arts and Sciences 22 May 22 80 14 9 420 30
11 Business and Management 15 February 10 65 8 6 500 60
12 Public Service 20 April 4 71 10 8 400 20
13 Applied Science and Technology 11 March 15 66 9 7 440 60
14 Arts and Sciences 18 November 28 64 9 7 300 30
15 Arts and Sciences 29 January 12 72 10 8 360 80
16 Nursing 13 December 6 63 8 6 480 100
17 Business and Management 49 August 0 79 13 9 410 25
18 Applied Science and Technology 16 April 10 74 12 8 430 15
19 Business and Management 24 September 30 66 10 6 330 60
20 Arts and Sciences 8 May 0 65 9 7 480 30

Answers

For the sample size of 20, the 95% confidence interval is (-4.87, 27.16), which is narrower than the previous interval due to the larger sample size.

What is mean?

In statistics, mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total number of values in the set. Mean is also commonly referred to as the arithmetic mean. It is a commonly used statistical measure in many fields including finance, economics, social sciences, and more.

Here,

To calculate the z-scores associated with each student, we first need to calculate the sample mean and standard deviation for the Distance to Work variable:

Sample mean: (0+0+5+10+15+30+32)/7 = 10.71

Sample standard deviation: √(((0-10.71)² + (0-10.71)² + (5-10.71)² + (10-10.71)² + (15-10.71)² + (30-10.71)² + (32-10.71)²)/6) = 10.72

Now we can calculate the z-scores for each student:

Student 1: (0 - 10.71) / 10.72 = -0.94

Student 2: (0 - 10.71) / 10.72 = -0.94

Student 3: (5 - 10.71) / 10.72 = -0.53

Student 4: (10 - 10.71) / 10.72 = -0.07

Student 5: (15 - 10.71) / 10.72 = 0.40

Student 6: (30 - 10.71) / 10.72 = 1.80

Student 7: (32 - 10.71) / 10.72 = 1.98

Student 8: (8 - 10.71) / 10.72 = -0.25

Student 9: (36 - 10.71) / 10.72 = 2.37

Student 10: (9 - 10.71) / 10.72 = -0.16

Student 11: (22 - 10.71) / 10.72 = 1.05

Student 12: (10 - 10.71) / 10.72 = -0.07

Student 13: (15 - 10.71) / 10.72 = 0.40

Student 14: (28 - 10.71) / 10.72 = 1.54

Student 15: (12 - 10.71) / 10.72 = 0.12

Student 16: (6 - 10.71) / 10.72 = -0.44

Student 17: (0 - 10.71) / 10.72 = -0.94

Student 18: (10 - 10.71) / 10.72 = -0.07

Student 19: (30 - 10.71) / 10.72 = 1.80

Student 20: (0 - 10.71) / 10.72 = -0.94

To identify potential outliers, we can look for z-scores that are more than 2 standard deviations away from the mean (i.e., greater than 2 or less than -2). From the list above, we can see that Students 6, 7, 9, and 19 have z-scores greater than 2, indicating that they may be potential outliers.

For the second sample of seven data points (0, 0, 5, 10, 15, 30, 32), the mean is 11.14 and the standard deviation is 12.05. Using a t-distribution with 6 degrees of freedom (n-1), the 95% confidence interval is (-7.54, 29.82).

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