Suppose that a nonzero constant b is added to every value of a generic sample dataset 1 2 3 { , , , , }n x x x x , to produce a new dataset 1 2 3 { , , , , } n x b x b x b x b . Provide a formal mathematical (i.e., algebraic) proof for what happens to the mean, variance, and standard deviation. (Hint: Think of the dotplot for informal motivation.)

Answers

Answer 1

Answer:

Step-by-step explanation:

Suppose there is the addition of a constant "b" to each generic dataset, then, new mean = old mean + b. This will affect the variance and the standard deviation of the resulting dataset to remain the same:

From the information given:

[tex]\mathbf{x_1,x_2,x_3...x_n \ have \ mean \ \overline x }[/tex]

Proof:

If c is added to each data set:

Then,

[tex]\mathbf{x_1+c,x_2+c,x_3+c...x_n+c \ and \ the \ new \ mean \ \overline x = \overline x + c}[/tex]

also;

[tex]\mathbf{New \ Sd^2 = \dfrac{(x_1+c -(\overline x+c))^2+ (x_2+c -(\overline x+c))^2 +...+ (x_3+c -(\overline x+c))^2}{n}}[/tex]

[tex]\mathbf{New \ Sd^2 = \dfrac{(x_1+c -\overline x+c)^2+ (x_2+c -\overline x+c)^2 +...+ (x_3+c -\overline x+c)^2}{n}}[/tex]

[tex]\mathbf{New \ Sd^2 = (x_1- \overline x)^2+ (x_2- \overline x)^2+ ... +(x_n- \overline x)^2}[/tex]

[tex]\mathbf{New \ Sd^2 = old \ sd^2}[/tex]


Related Questions

What is the quotient? (32h12 – 48h18) ÷ –16h6

32h12 + 3h12


–2h18 + 3h24


32h12 + 3h24


–2h6 + 3h12

Answers

The quotient of this mathematical expression (32h12 – 48h18) ÷ –16h6 include the following: D. –2h6 + 3h12.

What is a quotient?

In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

By writing the given mathematical expression as a division of a number (numerator) by another number (denominator), we have the following:

Quotient = (32h12 – 48h18)/–16h6

Quotient = -2h6 - (-3h12)

Quotient = –2h6 + 3h12.

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1/4 of 24 is 6, so 3/4 or 24 =

Answers

Answer:8

Step-by-step explanation:

18

can i have Brainliest?

if George put $6,000 into a savings account that pays 3.5 percent in compound how many years would it take for him to have 18,000 dollars if no money is added or withdrawn during this time?(Round to the nearest tenth)

Answers

Answer:

57.1 years

Step-by-step explanation:

multiply the money put into savings by the interest rate 6000×.035=210

divide the total earned by the annual interest earned

12000÷210=57.1428571428

rounded to the nearest tenth is 57.1

True or false: Removing the parenthesis from will change the result.

Answers

Answer:

true

Step-by-step explanation:

the steps won't be the same

Answer:

True

Step-by-step explanation:

In a equation with parenthesis it is VERY important to never take them out of the equation. The only reason for that is that the parentthesis are signaling you to solve what is in the parentthesis first. And if you where to move the parenthesis out your answer would be totally different. Hope this helped. (Brainliest?)

what is the slope of the line passing through points (x,y) and (p,q)​

Answers

Step-by-step explanation:

Let (x1,y1) = ( x, y)

(x2 , y2) = (p, q)

Then

Slope (m)

= (y2 - y1) / (x2 - x1)

= ( q - y) / ( p - x)

Hope it will help :)

help i will give brainliest

Answers

Answer:

the first one

Step-by-step explanation:

What is the area of one trapezoidal face of the figure

Answers

there is no area jdhdiebs

Problem:

Ford cut a whole pizza into 8 equal parts. He gave 2 slices to each
brothers and ate the rest. What part did each one get?

Question:

1.)To whom did Ford give the 2 slices of pizza?

2.)How did he divide the pizza?

3.) What do you call a part of it?









plzzz....
i follow you​

Answers

Answers:

1. his brothers :)

2. Into 8 equal parts

3. a fraction of the pizza, a slice

Answer:

1. his brothers

2. in 8 equal pieces

3. a slice

Step-by-step explanation:

PLEASE HELP ME ASAP!

Answers

Answer:

D. local maximum at the point (4, 18)

Step-by-step explanation:

Check the critical points and end points to test for any absolute extrema over the given interval.

Explain

Don’t use for points or I’ll take it back and report

Answers

Answer:

answer is 27 degrees

Step-by-step explanation:

first of all interior angles of a right sided add up-to 180 degrees and you were given 2 angles already

90 + 63 + x = 180

153 -153 +x = 180 -153

x = 27

hope that helps

a rectangular field is 0.45 kilometers long and 0.3 kilometers wide what is the area of the field in square meters?

Answers

Answer:135000

Step-by-step explanation:

Answer:

The field has an area of 135,000 m².

Step-by-step explanation:

We first convert the measurements from kilometers to meters by multiplying by 1000.

- - - - - - - - - - - - - Length: 0.45 km = (0.45 × 1000) m = 450 m.

- - - - - - - - - - - - - Width: - - 0.3 km = (0.3 × 1000) m = 300 m.

So the field is a rectangle 450 meters long and 300 meters wide.

To compute the are of this rectangle, we multiply its length by its width.

- - - - - - - - - - - - - - Area = 450 × 300 = 135,000 m².

so the answer is 135,000 m².

Your next-door neighbor, Bob, decides to find out how the community feels about the cleanliness of the community pool in your housing tract. The survey has two choices: good (clean) or bad (dirty). He places one in every mailbox on the street where he lives. About a quarter of the neighbors return the survey, and 60% of those say that the pool is bad. There may be many types of problems here, but which problem probably causes the most damage

Answers

Answer:

the survey population is very isolated

Step-by-step explanation:

There is not much information to go on but from the information provided we can say that the biggest problem is that the survey population is very isolated. Bob gave the survey to every single individual in his block, this does not represent the entire population of the people that use the community pool. Therefore, the data would not represent the entire population. Instead, Bob should have randomly chosen mailboxes from the entire community to give them the survey.

what is the quotient of x^2 + 7x +12 and x +4?

Answers

Answer:

The Answer/Quotient is x+3

Which phrase best describes the scatter plot below

Answers

Answer:

strong negative correlation

Step-by-step explanation:

find the center and radius of this circle (x+13)^2+(y+2)^2=81

Answers

Answer:

center (-13,2)   radius=9

Step-by-step explanation:

(x+13)^2+(y+2)^2=81

x=-13

y=-2

r=sq rt of 81

The center and radius of this circle [tex](x+13)^{2} +(y+2)^{2} = 81[/tex] is (h, k) = (-13, -2) and r = 9.

What is a circle and equation of the circle?

A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center.

The equation of a circle in standard form,

[tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex]

Given equation of circle

[tex](x+13)^{2} +(y+2)^{2} = 81[/tex]..................(1)

By comparing the standard form of circle with equation 1, we get

(h, k) = (-13, -2) and

[tex]r^{2} = 81[/tex]

⇒ [tex]r = \sqrt{81}[/tex]

⇒ r = 9

Hence, the center and radius of this circle [tex](x+13)^{2} +(y+2)^{2} = 81[/tex] is (h, k) = (-13, -2) and r = 9.

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Assume you are buying a $15,000 car, with a 12 month loan at 5% interest, a net down payment of $2,500, and
a $40 (non-taxable) fee with 6% in sales tax.
What will be your monthly payment?
A. Between $1000 and $1049
B. Between $1050 and $1099
C. Between $1100 and $1149
D. Between $1150 and $1200

Answers

The answer would be C

3x-2y=10. 4x-y=6. solve each of the pair of simultaneous linear equation by substitution method ​

Answers

Answer:

x = 2/5, y= -22/5

Step-by-step explanation:

4x−y=6;3x−2y=10

Step: Solve4x−y=6for y:

4x−y+−4x=6+−4x(Add -4x to both sides)

−y=−4x+6

-y/-1 = -4x +6 over -1 (Divide both sides by -1)

y=4x−6

Step: Substitute4x−6for y in 3x−2y=10:

3x−2y=10

3x−2(4x−6)=10

−5x+12=10(Simplify both sides of the equation)

−5x+12+−12=10+−12(Add -12 to both sides)

−5x=−2

-5x/-5 = -2/5 (Divide both sides by -5)

x=  2 /5

Step: Substitute  2/ 5  for x in y=4x−6:

y=4x−6

y=4 ( 2/ 5 ) −6

y=  −22 /5

(Simplify both sides of the equation)

x = 2/5, y= -22/5

Simplify the expression
3 (x+4) -2x
X+4
x+12
3x+10
7-x
3x+12

Answers

Answer:

x+12

Step-by-step explanation:

3 (x+4) -2x

Distribute

3x+12 -2x

Combine like terms

x+12

Answer:Move

11

3

to the left side of the equation by subtracting it from both sides.

30

3x-12

+

1

x-4

-

11

3

=0

Step-by-step explanation:

help me on my geometry homework? :/

Answers

Answer:

You could use a graphing calculator I just used Desmos. Origin is (0, 0). Rotate 90 degrees about the origin.

I used triangles

The rotated point would be at (1, 2)

ANSWER: the question mark = 1

How to figure out diameter

Answers

Answer:

If you are given the area of a circle, the diameter is equal to the square root of four times the area divided by pi (diameter = √ (4 x area) / pi).

Answer:

A diameter of a circle is twice its radius!

Hope that helps!

Step-by-step explanation:

Karen pumped 7 gallons of water out of her pool each minute for 28 minutes. What was the total change in the amount of water in the pool?

Answers

There was a total of 196 gallons pumped out at the end of 28 minutes if 7 gallons was pumped each minute.
(Is this what you were asking?)

I dance I sing I am perfect I am I am a believer that I am a discoverer. PLEASE ANSWER I'LL MARK AND BRAINLIEST

Answers

Answer:

not sure if its a song or not but you do you, gg <3

Answer:

YAZZ You are amazing :> remind yourself everyday!!!

A car depreciates at a rate of 15% of its value annually. Carl purchased a new car for $25,000 and wants to know how many years it
will take until the car is worth a specific amount.
a) Formulate a logarithmic function that would find the number of years t it will take for the car to be worth x dollars.
Then
b) How many years will Carl have until he new car is worth about $5000?

Answers

Answer:

(a) (log X - log 25000)/log 0.85 = t

(b) about 9.9 years

Step-by-step explanation:

(a)   Let X = value and t = elapsed years since purchase; X in dollars

X = 25000 x 0.85 x 0.85 x 0.85 ... with a factor of 0.85 for every year

(If you lose 15% of value, you have 85% left, right?)

So if you do it for t years, you have t as the exponent on the 0.85 factor.

[tex]X = 25000(0.85)^t[/tex]  is a good equation, but not logarithmic like they ask.

[tex]log X = log 25000 + log [(0.85)^t][/tex]    because the log of a product is the sum of the logs of the factors

log X = log 25000 + t*log 0.85  because the log of a power is power times log

log X - log 25000 = t* log 0.85    just algebra, subtracting from both sides

(log X - log 25000)/log 0.85 = t   just algebra, dividing both sides

(b)  If we let X = $5000

t = (log 5000 - log 25000)/log 0.85

 = (3.69897 - 4.39794)/-0.07058

 =  9.90

So t = 9.9 years is a good estimate

Carl will have approximately 5.06 years until his new car is worth about $5000.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Let V(t) be the value of the car t years after it was purchased.

We know that the car depreciates at a rate of 15% annually, so the value of the car after t years can be expressed as:

[tex]V(t) = 25000 \times (1 - 0.15)^t[/tex]

Simplifying this equation, we get:

[tex]V(t) = 25000 \times 0.85^t[/tex]

Now suppose Carl wants to know how many years it will take for the car to be worth x dollars.

We can set V(t) equal to x and solve for t:

[tex]25000 \times 0.85^t = x[/tex]

log0.85(25000) +[tex]log0.85(0.85^t)[/tex] = log0.85(x)

Since log0.85(25000) is a constant, we can subtract it from both sides of the equation:

[tex]log0.85(0.85^t)[/tex]= log0.85(x) - log0.85(25000)

Divide both sides of the equation by log0.85(0.85) = 1:

t = [log0.85(x) - log0.85(25000)] / log0.85(0.85)

Therefore, the logarithmic function that would find the number of years t it will take for the car to be worth x dollars is:

t = [log0.85(x) - log0.85(25000)] / log0.85(0.85)

b) We want to find the number of years it will take for the car to be worth $5000.

Substituting x = 5000 into the formula derived in part (a), we get:

t = [log0.85(5000) - log0.85(25000)] / log0.85(0.85)

t = 5.06

Therefore, Carl will have approximately 5.06 years until his new car is worth about $5000.

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You are an entrepreneur and selling handmade kites. Your company Kites-R-Fun has been contacted by a customer in Alaska who wants to purchase several of your best-selling kites and wants you to ship them to her. You have already established the cost at $4 each and it's only going to cost you $8 to ship these items to Alaska. Your competitor Windy Kites sells the same items, but charges half of your price. However, if the customer buys from your competitor, she will be charged $20 in shipping costs.
Write two equations to represent the customer's total cost based on how many kites she purchases from each company where y is the total cost and x is the number of kites purchased.
1. Total cost for Kites-R-Fun *
y = 4x + 8
y = 4x + 20
y = 8x + 4
y = 8x + 20
2. Total Cost for Windy Kites *
y = 2x + 10
y = 2x + 20
y = 8x + 20
y = 20x + 4

3. If the customer in Alaska wants to buy 4 kits, who should she buy from? *
Kites-R-Fun
Windy Kites
4. If the customer in Alaska wants to buy 10 kits, who should she buy from? *
Kites-R-Fun
Windy Kites

Answers

Answer:

do you have the answers i’m taking this rn i’m gonna literally cry lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm not sure if I am correct or incorrect but these are my answers, I'm pretty sure they're correct but I'm not sure as I didn't turn it in yet

1. Fill in the table to find customer costs from each seller.

2. Write an equation to represent the customer's total cost to purchase from Kite-R-Fun.

Y = 4x + 8

3. Write an equation to represent the customer's total cost to purchase from Windy Kites.

Y = 2x + 20

4. Based on your table, if the Alaskan customer wants to buy 4 kites, who charges the least?

Kites - R - Fun

5. If the Alaskan customer wants to buy 10 kites, who charges the least?

Windy Kites

6. (6, 32)

7. Looking at your graph, find the solution and explain what it means in this situation

This point represented where prices have intersected

Find the measure and solve for x

Answers

Answer:

14

Step-by-step explanation:

Number of sides (n) = 10

Sum of all angles of polygon = (n - 2 )* 180

                                                = 8 * 180 = 1440

As this is a regular polygon,

measurement of each angle = 1440/10 = 144

10x + 4 = 144

       10x = 144- 4

       10x = 140

           x = 140/10

           x = 14

3 pizzas are shared equally between 10 people. What fraction of a pizza does each person receive?

Answers

Answer:

7

Step-by-step explanation:

and beetween 10-3 7 pizza

Find the value of x.

Answers

Answer:

D

Step-by-step explanation:

So first you know that the angles are across for each other meaning that they are equal.

Therefore the equation would be 7x-13 = 48

Simply do order of operations meaning you subtract 13 from 48 giving you 35.

Then do 35 divided by 7 which means X equals 5 which makes it D.  

Answer:

Umm I am pretty sure this answer is 3

Step-by-step explanation:

Por su asistencia y puntualidad, dos empleadas
de una fábrica textil recibieron como estímulo
vales de despensa y dinero en efectivo. A Sandra le dieron 8 vales y $60.00 en efectivo; a
Bertha le entregaron seis vales más $160.00. Si
los vales son de la misma denominación y ambas
reciben la misma cantidad de dinero, ¿qué valor
tiene cada vale?
A) 100 pesos
B) 75 pesos
C) 50 pesos
D) 25 pesos​

Answers

Anwser

El valor de cada vale 50 por eso es que sandra y Bertha recibieron cada una $460

Step-by-step explanation:

x son lo que cuestan los vales

Sandra 8 × +$60

Bertha 6x+$120

Each voucher has a value of 50 pesos.

Option C is the correct answer.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's represent the value of each voucher with the variable "v".

Then we can set up two equations based on the given information:

8v + 60 = 6v + 160 (both employees receive the same amount of money)

8v - 6v = 160 - 60

2v = 100

v = 50

Therefore,

Each voucher has a value of 50 pesos.

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The complete question:

For their attendance and punctuality, two employees

from a textile factory received as encouragement

grocery vouchers and cash. Sandra was given 8 vouchers and $60.00 in cash; to

Bertha was given six vouchers plus $160.00. Yeah

the vouchers are of the same denomination and both

receive the same amount of money, what is the value

does each voucher have?

A) 100 pesos

B) 75 pesos

C) 50 pesos

D) 25 pesos

The figure shows the dimensions of a backyard
Find the area
8 yd
eccles
30 yd
15 yd
30 yd
The area of the backyard is
square yards.

Answers

answer:

570yd^2

step by step:

Split the backyard into 2 different rectangles and add the areas together. I did 8x30 and 15x22.
Answer: 570yd^2


Explaining: The area can be found by using the base and the height. Fist I will split the figure into two piece to make it easier to find. The first piece is solved by 30•15=450. The second figure can be solved by 8•15=120. Now add the total numbers together and you get 570yd^2

Question 5 of 12
The orthocenter of a triangle may lie outside the triangle since the
may not intersect any side of the triangle.
A. angle bisector
B. perpindicular bisector
C. altitude
D. median
SUBMIT

Answers

The perpendicular bisector
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