The number 686 can be expressed as a product of prime factors in the form p x qr. The value of p+q+r is _________. Work must be shown.

Answers

Answer 1

Answer:

p + q + r is 12.

Step-by-step explanation:

Prime factors of a number is the expression of the number in terms of the product of its factors that are prime numbers only.

The prime factor of 686 = 2 x 7 x 7 x 7. Which can be expressed in the form;

p × [tex]q^{r}[/tex] as 2 × [tex]7^{3}[/tex].

So that, p = 2, q = 7 and r = 3.

p + q + r = 2 + 7  + 3

              = 12

Therefore, the sum of p, q, and r is 12.


Related Questions

Caleb types 100 words in 5 minutes what is the unit rate

Answers

Basically, the unit rate is known as the simplest form of something. In this case, you're trying to figure out how many words he types in 1 minute.

Here's the work:

100 words = 5 minutes

100/5 = 5/5

20 words = 1 minute.

Please vote my answer the Brainliest if it helped! Don't be afraid to ask questions if you didn't understand!

Answer:

20 words per minute

A polynomial is factored using algebra tiles. An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 15 tiles are in the Product spot in 3 columns with 5 rows: 1 is labeled + x squared, 2 are labeled + x, the 4 tiles below + x squared are labeled negative x, and the 8 tiles below the + x tiles are labeled negative. Which polynomial was factored? x2 – 2x – 8 x2 + 2x – 8 x2 – 2x – 4 x2 + 2x – 4

Answers

Answer:

x² - 2x - 8

Step-by-step explanation:

Algebra tiles are tiles used to represent variables or numbers and are rectangular or square shaped.

1 is labeled + x squared, this gives x²

2 are labeled + x, this gives +x × 2 = +2x

4 tiles below + x squared are labeled negative x, this gives - x × 4 = - 4x

8 tiles below the + x tiles are labeled negative, this gives -1 × 8 = -8

Therefore to get the polynomial that was factored, we add all the terms. This gives :

+x² + (+ 2x) + (-4x) + (-8) = x² + 2x - 4x - 8 = x² - 2x - 8

Answer:

The answer is A, and if edge is being weird the answer is x^2-2x-8, Have fun dreamers!

Step-by-step explanation:

Brian set his compass equal to the radius of circle C and drew two circles centered at points A and B on circle C. He labeled the points of intersection of the two circles as shown. To complete his construction, Brian only needs to use his straightedge to draw some chords of circle C. Which figures could Brian be constructing? equilateral triangle MNQ inscribed in circle C equilateral triangle ANP inscribed in circle C regular hexagon AMNBPQ inscribed in circle C square MNPQ inscribed in circle C square ANBQ inscribed in circle C

Answers

Answer:

equilateral triangle ANP inscribed in circle C

regular hexagon AMNBPQ inscribed in circle C

Step-by-step explanation:

By looking through our choices, we can eliminate which choices could be wrong and which choices could be right.

Δ MNQ does form a triangle, however, it DOES NOT form a equilateral triangle.

Δ ANP does form a triangle and it is ALSO an equilateral triangle.

Hexagon AMNBPQ does form a hexagon and it is ALSO a regular polygon as we can see all the sides and angles within the polygon are congruent to one another.

MNPQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.

ANBQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.

By looking through our observations, we can conclude that Δ ANP and hexagon AMNBPQ are the correct choices.

- 2022 Edmentum

The equilateral triangle ANP inscribed in circle C  and the regular hexagon AMNBPQ inscribed in circle C. Then the correct options are B and C.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Brian set his compass equal to the radius of circle C and drew two circles centered at points A and B on circle C.

He labeled the points of intersection of the two circles as shown.

The equilateral triangle ANP inscribed in circle C  and the regular hexagon AMNBPQ inscribed in circle C.

Then the correct options are B and C.

The complete question is attached below.

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ5

0.00045-2.5*10^-5 in scientific notation?

Answers

Answer:

The answer is 4.25*10^−4

Step-by-step explanation:

First convert 2.5*10^-5 into decimal form

That's

2.5*10^-5 = 0.000025

0.00045 - 0.000025 = 0.000425

= 4.25*10^−4 in scientific notation

Hope this helps

Answer:

4.25*10^−4

Step-by-step explanation:

khan

John is standing at the point (-4,-8) and his friend Victor is standing at the point (-4,12). Find the distance between them. A. 20 units
B. -20 units
C. 28 units
D. -28 units

Answers

Answer:

20 units

solution,

Let the points be A and B

A(-4,-8)--->(X1,y1)

B(-4,12)---->(x2,y2)

Now,

[tex]ab = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \: \: \: = \sqrt{ {( - 4 - ( - 4)}^{2} + 12 - ( - 8) ^{2} } \\ \: \: \: \: = \sqrt{ {( - 4 + 4)}^{2} + {(12 + 8)}^{2} } \\ = \: \: \: \: \sqrt{ {(0)}^{2} + {(20)}^{2} } \\ \: \: \: \: = \sqrt{0 + 400} \\ \: \: \: = \sqrt{400} \\ \: \: = \sqrt{ {(20)}^{2} } \\ \: \: = 20 \: units[/tex]

Hope this helps..

Good luck on your assignment...

please help thanks !

Answers

Answer:

point slope form: y-3=[tex]-\frac{3}5}[/tex](x+2)

slope-intercept form: y=[tex]-\frac{3}{5}[/tex]x+[tex]\frac{9}{5}[/tex]

Step-by-step explanation:

so to find point-slope form, you first have to find the slope of the line

--slope =[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]=[tex]\frac{0-3}{3+2} =-\frac{3}{5}[/tex] (you have to use the two points shown: (-2,3) and (3,0) to plug in for y1, y2, x1, and x2 to find the slope.)

so your slope is [tex]-\frac{3}{5}[/tex].

Now all you have to do is use one of the points (-2,3) to sub in for y1 and x1 in the point-slope form equation.

Therefore, you get y-3=[tex]-\frac{3}{5}[/tex](x+2) for point-slope form.

Now for slope-intercept form, you already have the slope because you found it to complete the equation for point slope form

slope = [tex]-\frac{3}{5}[/tex]

Now slope intercept form is y=mx+b, where m is the slope and b is the y-intercept.

So, far we have y=[tex]-\frac{3}{5}[/tex]x+b

the easiet point to use for the x and y values is (3,0)

so, lets substitute: 0=[tex]-\frac{3}{5}[/tex](3)+b, which becomes 0=[tex]-\frac{9}{5}[/tex]+b

add [tex]-\frac{9}{5}[/tex] to both sides to get b=[tex]\frac{9}{5}[/tex]

Now you have both the slope and the y-intercept so you can now write the line in slope-intercept form.

You get [tex]y=-\frac{3}{5}x +\frac{9}{5}[/tex].

10. If there is a crossword that has four squares that need to be filed, how many possible four letter arrangements are there (assuming they do not have to make a real word)?

Answers

Answer:

See Explanation

Step-by-step explanation:

The question didn't specify if letter can be repeated or not;

I'll solve for both;

Given

Number of Letters = 26

Number of squared = 4

If Repetition is allowed;

The four squares can take any of the 26 letters in any order

The first letter can be any of 26; Same with the second, third and fourth letters;

Number of Arrangement = 26 * 26 * 26 * 26

Number of Arrangement = 26⁴

Number of Arrangement = 456976

If Repetition is not allowed;

The first square can be filled with any of the 26 letters;

The second can take any of (26 - 1) letters

The third can take any of (26 - 2) letters

The fourth can take any of (26 - 3) letters

Number of Arrangement = 26 * (26 - 1) * (26 - 2) * (26 - 3)

Number of Arrangement = 26 * 25 * 24 * 23

Number of Arrangement = 358800

Answer:

26!/22!

Step-by-step explanation:

I just took the quiz I got it right



Use the given information to draw a box-and-whisker plot of the data set

Minimum – 28

Maximum – 54

Lower Quartile – 32

Upper Quartile – 40

Answers

Answer:

The box-and-whisker plot of this distribution is presented in the attached image to this solution.

Step-by-step explanation:

A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.

A box and whiskers plot shows 5 major information about the distribution of data. It shows:

- The maximum variable.

- The minimum variable.

- The Median.

- The first quartile.

- The third quartile.

Further info such as the range and Inter quartile range can then be obtained from this 5-number summary.

The elements of the box plot are described thus;

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.

The horizontal line inside the box is the median.

The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.

The required boxplot for this question is given in the attached image to this solution.

The median for the boxplot isn't provided, but it was assumed to be midway between the first and third quartile.

Hope this Helps!!!

Help me !!! please 50 points!!


A system of equations is shown below: 1. Equation A: 4c = d − 8 Equation B: c = 5d + 8 Which of the following steps should be performed to eliminate variable d first? (5 points)


Multiply equation B by 4. Multiply equation A by −5. Multiply equation A by 4. Multiply equation B by 5. 2 . A system of equations is shown below: n = 3m + 7 n − 2m = 1 What is the solution, in the form (m, n), to the system of equations? (5 points)


(3, 7) (1, 8) (−3, −2) (−6, −11) 3. A system of two equations is shown below: Equation C: a = 3b + 6 Equation D: a = 7b − 1 What value of a can be substituted into equation D to solve the system of equations? (5 points)

Answers

Answer:

the first step to eliminate d is to multiply equation B by 5

second :(m,n) (-6,-11)

value of a can be substituted into equation D to solve the system of equations is 7b-1

Step-by-step explanation:

first equation:

4c=d-8 or 4c-d=-8

c=5d+8 or c-5d=8

so the first step to eliminate d is to multiply equation B by 5

second equation :

n=3m+7 or n-3m=7

n-2m=1

n-3m=7

solve :

1-eliminate n by subtracting two equation : : n-2m-(n-3m)=1-7

-2m+3m=-6

m=-6

substitute m: n-3(-6)=7 , then n+18=7

n=7-18=-11

third :

a=3b+6 or a-3b=6

a=7b-1

find a

a-3b=6

value of a can be substituted into equation D to solve the system of equations is 7b-1

Angles that measure between 0 and 90 degrees are called_?

Answers

Answer:

Acute angles.

Step-by-step explanation:

Acute angles are from 0-90 degrees.

Hope this helps :)

Answer:

Acute angles

Step-by-step explanation:

Acute angles are measured between 0 and 90 degrees.

Which point is located at (4, -2)?
y
5
ТА
4
3
2+
1
2 3
Х
-5 -4 -3 -2 -11
-2
4 5
B
-4
D
b

Answers

Answer:

Point B of 4the quertant

A magazine has 96 pages. There are ads on 75% of the pages. How many pages don't have ads?

Answers

Hey there! :)

Answer:

24 pages.

Step-by-step explanation:

Calculate how many pages 75% of 96 is:

96 × 0.75 = 72 pages.

Find how many pages do not have ads by subtracting the amount that have ads from the total:

96 - 72 = 24 pages.

Therefore, 1/4 of 96 or 24 pages do not have ads.

Clara would like to buy a toy for her baby sister that sells for
$12.49. How much will the toy cost after 13% tax? (Round to the nearest
cent)

Answers

So all you need to do is to multiply 12.49 by 1.13 ( since 1.00 is the price and 0.13 is the added tax rate), which gives you $14.11

Approximately how many seconds would it take for the Mississippi River( 16,790 cubic meters per second) to fill the volume of the Gulf of Mexico(2,434,000,000,000,000)? Choice A : 1 *10^9 Choice B : 1* 10^10 Choice C : 1 * 10^11

Answers

Answer:

1 * 10^11

Step-by-step explanation:

Take the gulf of mexico and divide by the rate to get the number of seconds

2,434,000,000,000,000 / 16790

Change each to scientific notation

2 * 10 ^15/ 1.6 *10^ 4

Rounding

2 * 10^15 / 2 * 10^4

Dividing the numbers 2/2 =1

Dividing the exponents means subtracting the powers = 10 ^(15-4) = 10 ^1

1 * 10^11

What is the distance from point (-5,-4) to (9,2)?

Answers

Answer:

radical 232

Step-by-step explanation:

14^2+6^2=x^2

196+36= 232

radical 232

Answer: Distance is 15.2

Step-by-step explanation:

[tex]d = √((x2-x1)2 + (y2-y1)2)[/tex]

[tex](x2-x1) = (9 - -5) = 14[/tex]

[tex](y2-y1) = (2 - -4) = 6[/tex]

[tex](14)2 + (6)2 = 196 + 36 = 232[/tex]

[tex]\sqrt{232} =15.2315[/tex]

round to the nearest 10th

What is the value of x in the equation -X = 3 - 4x + 6?
0-9
0-3
03
09

Answers

Answer:

x=3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

I took the test!

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Everything to the right of the line is shaded. Which linear inequality is represented by the graph?

Answers

Answer:

y<= 1/3x-4

Step-by-step explanation:

Its an inequality thats why

Of the four choices given, which two, when written as a system, have a solution of (–4, 5)? A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 5. Column 2 is labeled y with entries 2, negative 1, negative 2, negative 4. 2 x + y = negative 3 Negative 2 x + y = negative 3 A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 7. Column 2 is labeled y with entries 0, negative 3, negative 4, negative 8. 2 x + y = negative 3 and A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 5. Column 2 is labeled y with entries 2, negative 1, negative 2, negative 4. Negative 2 x + y = negative 3 and A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 5. Column 2 is labeled y with entries 2, negative 1, negative 2, negative 4. 2 x + y = negative 3 and A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 7. Column 2 is labeled y with entries 0, negative 3, negative 4, negative 8. Negative 2 x + y = negative 3 and A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 3, 7. Column 2 is labeled y with entries 0, negative 3, negative 4, negative 8.

Answers

Answer:

The answer is a.

Step-by-step explanation:

Hope this helps!

Answer:

It's A)

Step-by-step explanation:

Each unit on the coordinate grid represents 1 yard. The rectangular pool and triangular hot tub shown are both in need of covers. How much total material is needed to cover both? square yards

Answers

Answer:

29 square yards

Step-by-step explanation:

see attachment for the graph

Vertices of rectangular pool are A(3,2),B(7,8),C (4,10), and D (0,4).

AB=[tex]\sqrt{(7-3)^{2}+(8-2)^{2}}= \sqrt{16+36}=\sqrt{52}[/tex] yard=CD

BC= [tex]\sqrt{(7-4)^{2}+(8-10)^{2}}=\sqrt{9+4}=\sqrt{13}[/tex]yard=DA

In order to find the area of rectangular pool =Length × Breadth

                                        =√52 ×√13=13×2=26 sq. yard

Vertices of triangle given are: P(5,2),Q(7,2) and R(7,5).

PQ= 2 units, QR= 3 units

Area of right triangle PQR=1/2 ×PQ×PR

                                           =1/2×2×3= 3 sq. yards

Next is to find total material needed to cover( that includes bot rectangular pool and triangular hot tub)

       = Area of rectangle + Area of right triangle

       =26+3=29 square yards

Answer:

29

Step-by-step explanation:

I just did my homework

Which is the graph of f(x)=2(3) to the x power?

Answers

Answer:

Use a graphing calc.

Step-by-step explanation:

Explain how to determine the solutions to a quadratic equation, graphically.

Answers

Answer:

In a nutshell, you have to graph the parabola. Where the parabola intersects the x-axis is the solutions to the quadratic equation.

cot(45-A)=tan2A+ sec2A​

Answers

Answer:

See picture.

Step-by-step explanation:

If the four lines are extended, which system would have only one solution? On a coordinate plane, lines a and b would intersect. Lines c and d are the same line. line a and line b line b and line c line b and line d line c and line d

Answers

Answer:

a

Step-by-step explanation:

took the quiz

Answer:

A

Step-by-step explanation:

took the quiz

Uma caixa na forma de um cubo tem medidas de arestas igual a 10,5 cm. O volume dessa caixa corresponde à: * 1 ponto a) 1157,625cm³ b) 1157,6cm³ c) 11,5627cm³ d) 115,7625cm³

Answers

Answer:

(A) [tex]1157,625$ cm^3[/tex]

Step-by-step explanation:

s = 10,5 cm.

Volume do cubo = [tex]s^3[/tex]

[tex]=10,5^3\\=1157,625$ cm^3[/tex]

O volume do cubo é  [tex]1157,625$ cm^3[/tex]

What is the result of subtracting the second equation from the first? 8x-4y=-4 -3x+4y=5

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

(x, y) = (14/5, 87/20)

▹ Step-by-Step Explanation

8x - 4y = -4 - 3x + 4y = 5

8x - 4y = 5

-4 - 3x + 4y = 5

8x - 4y = 5

-3x + 4y = 9

5x = 14

x = 14/5

-3 * 14/5 + 4y = 9

y = 87/20

(x, y) = (14/5, 87/20)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

11x−8y=−9

Step-by-step explanation:

khan

hi can you help me i can’t move forward if i skip this question.

Answers

4.5x > 125+100
4.5x > 225
X>225\4.5
X>50

can someone help me answer this

Answers

Answer:

A

Step-by-step explanation:

A is the answe hope this helps

The​ half-life of a certain tranquilizer in the bloodstream is 47 hours. How long will it take for the drug to decay to 93​% of the original​ dosage? Use the exponential decay​ model, Upper A equals Upper A 0 e Superscript kt​, to solve.

Answers

Answer:

It will take 4.84 hours for the drug to decay to 93​% of the original​ dosage.

Step-by-step explanation:

We are given that the half-life of a certain tranquilizer in the bloodstream is 47 hours.

The given exponential model is: [tex]A = A_0 e^{kt}[/tex]

Now, we know that A becomes half after 47 hours which means that;

[tex]A = 0.5 A_0[/tex]

Using this in the above equation we get;

[tex]A = A_0 e^{kt}[/tex]

[tex]0.5 A_0 = A_0 e^{(k\times 47)}[/tex]  where t = 47 hours

[tex]\frac{0.5 A_0}{A_0} = e^{(47k)}[/tex]

[tex]0.5 = e^{47k}[/tex]

Taking log on both sides we get;

[tex]ln(0.5) = ln(e^{47k})[/tex]

[tex]ln(0.5) =47k[/tex]

[tex]k = \frac{ln(0.5)}{47}[/tex]

k = -0.015

Now, the time it will take for the drug to decay to 93​% of the original​ dosage is given by;

[tex]0.93 = e^{kt}[/tex]  where t is the required time

[tex]0.93 = e^{(-0.015 \times t)}[/tex]

Taking log on both sides we get;

[tex]ln(0.93) = ln(e^{-0.015t})[/tex]

[tex]ln(0.93) =-0.015t[/tex]

[tex]t = \frac{ln(0.93)}{-0.015}[/tex]

t = 4.84 hours

Hence, it will take 4.84 hours for the drug to decay to 93​% of the original​ dosage.

Solve for f. -11f=7(1-2f)+5

Answers

Answer:

4

Step-by-step explanation:

Our equation is -11f= 7*(1-2f)+5

-11f=7*(1-2f)+5 7*(1-2f)+5+11f=07-14f+5+11f=012-3f=0f=12/4f=4

Need help solving. Prefer you show each step in solving.

Answers

Answer:

55

Step-by-step explanation:

For PQ and RS to be parallel, the two degrees must be equal.

3x - 65 = 2x - 10

(3x - 65) + 65 = (2x - 10) + 65

3x = 2x + 55

(3x) - 2x = (2x + 55) - 2x

x = 55

Other Questions
help will give brainliest True or False: The people of ancient Egypt and Nubia were completely isolated from others because of the surrounding dessert?? A stone is thrown towards a wall with an initial velocity of v0=19m/s and an angle = 71 with the horizontal, as illustrated in the figure below. The stone reaches point A at the top of the wall, t=3.5s after being thrown. Determine (a) the height h of the wall, (b) the maximum height H of the path of the stone, (c) the horizontal distance between the launching point and point A and (d) the horizontal reach of the stone if the wall did not exist Good communication occurs only when the recipient ________. A) agrees with the sender's message B) does what the speaker asks C) understands the speaker's meaning D) makes eye contact with the speaker What is the tendency of a material to oppose the flow of charge? what is meant by amoeba and what is the name of its parts Which diagram shows lines that must be parallel lines cut by a transversal? 2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the bottom left angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 65 degrees. 2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the bottom left angle is 115 degrees and the bottom right angle is 65 degrees. 2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the top right angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 115 degrees. 2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the uppercase left angle is 65 degrees and the bottom right angle is 65 degrees. A metalsmith is mixing two molten metals, each containing different percentages of silver. The table shows the amount of each molten metal used. Which two expressions are both equivalent to t, the total number of grams of silver in the mixture? A: (15)(0.75) and 0.7(15 x) + 0.9x B: (15)(0.75) and 0.7(15 x)(0.9x) C: 15 + 0.75 and 0.7(15 x) + 0.9x D: 15 + 0.75 and 0.7(15 x)(0.9x) The tank on a petrol lorry is a cylinder 2m in diameter and 7cm longa.Calculate its volume in m3.b.Find its capacity in kilolitres WILL AWARD BRAINLIEST PLEASE HELP!!! Which excerpt from the prologue of Free the Children reflects what is happening in this frame? With the help of a human-rights organization, Iqbal was able to escape and go to school. Iqbal completed two grade levels that first year. In exchange, Iqbal, said to be only four years old at the time, was forced to join several other child weavers squatting before looms in the owner's factory. The man had not only the right to Iqbal's labour, but also, if he wished, the right to sell him to any other factory owner. He learned quickly not to bring on the wrath of the factory owner. If he made mistakes, fines were added to the sum owed by his parents. Sara has a goal to improve her cardiorespiratory fitness. She is new to working out. List the words that the acronym SPORT stands for then explain how she can use the SPORT principles to ensure she is getting a safe and effective workout. Please help me :) Ill give you extra points and name your answer as the brainliest :) Until 1973, homosexuality was considered a psychological disorder by the American Psychological Association. Which sociological perspective would be most concerned with why this was considered an illness, and what effect that diagnosis had on society write an inequality for the graphA. x > -3B. x < -3c. x > -3 _ Which Native American tribe lived in the Northeast, where there were cool winters and warm summers?A. the CherokeeB. the PuebloC. the MakahD the Iroquois Si busco informacin acerca de los lugares de inters en Buenos Aires, solicito la ayuda de: A) un agente de viajes B) un director de mercadotecnia C) un contador D) un gerente Which attributes are true about the five pillars of the Lets Move! program? Check all that apply. An increase in household saving causes consumption to a. fall and aggregate demand to increase. b. rise and aggregate demand to increase. c. rise and aggregate demand to decrease. d. fall and aggregate demand to decrease. In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each participant is notied if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree," and these are assigned the numbers 1 or 1, respectively. Participants responses to the survey are encoded as a vector in R4, where coordinates correspond to their answers to each question. Here are the questions: Identify one simple machine used at your home and explain how it makes your work easier