the graph shows data relating sodium per serving and price per serving of different brands of peanut butter, Using this model, predict the amount of sodium in Peanut Butter that costs $.35 per serving.

The Graph Shows Data Relating Sodium Per Serving And Price Per Serving Of Different Brands Of Peanut

Answers

Answer 1

A linear model that best fits the overall pattern of points is given by the

regression line of the data.

a. Please find attached the graph showing the linear model of the scatter plot created with MS Excel.

b. The slope of the line is -6.2173.

c. The relationship is as the price per Serving increases by 1 cent, the sodium per Serving decreases by -6.2173 mg.

Reasons:

a. Points on the graph are;

(6, 218),

The slope, b, regression line equation is given by the following formula;

[tex]b = \mathbf{\dfrac{\sum \left(x_i - \overline x\right) \times \left(y_i - \overline y\right) }{\sum \left(x_i - \overline x\right )^2 }}[/tex]

The regression line equation is; [tex]\overline y = b \cdot \overline x + a[/tex]

Where;

[tex]\overline x[/tex] = 18.732

[tex]\overline y[/tex] = 187.24

[tex]\sum \left(x_i - \overline x\right) \times \left(y_i - \overline y\right)[/tex] = -4926.59

[tex]\sum \left(x_i - \overline x\right )^2[/tex] = 792.3944

Therefore;

[tex]b = \dfrac{-4926.59}{792.3944 } \approx -6.2173[/tex]

[tex]a = \overline y - b \cdot \overline x[/tex]

Which gives;

a = 187.24 - (-6.2173) × 18.732 ≈ 303.70

The equation of the line is therefore; [tex]\overline y = \mathbf{-6.2173 \cdot \overline x + 303.70}[/tex]

Using the above regression line equation, the linear model of the scatter

plot can be drawn as presented in the graph created with MS Excel.

b. The slope of the line is b = -6.2173

c. The relationship between price per serving and sodium per serving is

as follows;

When the price per serving increases by 1 cent, the sodium per serving

decreases by 6.2173 mg.

Learn more about the regression line formula here:

https://brainly.com/question/14747095

The Graph Shows Data Relating Sodium Per Serving And Price Per Serving Of Different Brands Of Peanut

Related Questions

Find the quotient.
3/8÷ 2/7

3/28
1 5/16
16/21
1 3/28

Answers

Answer:

B

Step-by-step explanation:

[tex] \frac{3}{8} \div \frac{2}{7 } \\ = \frac{3}{8} \times \frac{7}{2 } \\= \frac{21}{16} \\ = 1 \frac{5}{16} [/tex]

1 less then the quotent of a number n and 6

Answers

" the quotient " means divide

(n/6) - 1 <== ur expression

Ellie and Isaiah are helping their friend Nora move. If Ellie can move 4 boxes for
every 16 boxes that Isaiah moves, then how many boxes can Isaiah move for every
box that Ellie moves?

Answers

Answer:

Isaiah can move 4 boxes for every box Ellie moves.

Pls give brainliest. :D

1. When two lines cross, the opposite angles are ___________ angles and are congruent. *
Straight Angle
Adjacent Angles
Angle Addition Postulate
Vertical Angles
2. Two angles that share a side and a vertex but do not overlap. *
Straight Angle
Adjacent Angles
Angle Addition Postulate
Vertical Angles
3. Two angles whose measures add up to 180 degrees. *
Angle Addition Postulate
Adjacent Angles
Supplementary Angles
Vertical Angles

Answers

Answer:

1. vertical angles

2. Adjacent angles

3. Supplementary angles

Step-by-step explanation:

WILL GIVE BRAINLIEST

Answers

Answer:the slope of the line is 5/3

The y-intercept is 0

Step-by-step explanation:

Answer:

C and E

Step-by-step explanation:

25% of Santa's 9 reindeer were playing reindeer games. How many of Santa's reindeer were NOT playing reindeer
games?

Answers

Answer:

75%, or 7

Step-by-step explanation:

100-25=75

75% of 9 is 6.75 (because 9x0.75)

so we can round to 7, unless there's a decapitated reindeer involved

Answer: 6.75

Step-by-step explanation:

for this math problem we need to find the percentage and subtract that from the original number ( 9 ) . . .

what is 25% if 9 ? 2.25

what is 9 - 2.25 ? 6.75

x + 7 when x = -11
What is the answer

Answers

-3!!!!!!!! Is the answer have fun and I hope you get this right

Evaluate g(10) of g(x) =1/2x -4

Answers

Answer:

g(x)= 1

Step-by-step explanation:

[tex]g(x) = \frac{1}{2} x - 4 \\g(10) = \frac{1}{2} (10) = 5 \\ 5 - 4 = 1[/tex]

Convert 5 square meters to square centimeters. Explain

Answers

Answer:

5 sq m = 50,000 sq cm

5 sq m = 5 sq m

Step-by-step explanation:

To convert a square meter measurement to a square centimeter measurement, multiply the area by the conversion ratio.

Since one square meter is equal to 10,000 square centimeters, you can use this simple formula to convert:

square centimeters = square meters × 10,000

Answer:

50000 square centimeters.

Step-by-step explanation:

pls help me . Eleven family members are going on a trip together. They have cars that fit only 4
people. How many cars will they need to take? help

Answers

Answer:

3.

Step-by-step explanation:

Since there are 11 family members and only 4 people fit in a car, they will have to take 3 cars.

4 x 3 = 12,

Also, even though there is going to be 1 seat extra you cannot squeeze 3 people in. Ps. (Just a safety note) In real life it is illegal to drive with extra passengers in a vehicle.

Hope that helps. x

Answer:

3

Step-by-step explanation:

3×4=12 so will still have one vacant seat on one of the cars

I need help. I have to find X to solve the equation.

Answers

Answer:

x=17.333

Step-by-step explanation:

3x+8=60

3x=60-8

3x=52

x=52\3

x=17.333

HURRY!

Given the function ƒ = {(1 , 2), (2 , 3), (3 , 4)} write the set of ordered pairs representing ƒ -1.
Select one:
a. {(1, 2), (3, 2), (4, 3)}
b. {(2,1), (3, 2), (4, 3)}
c. {(2, 1), (2, 3), (3, 4)}

Answers

C is s the answer because your just repeating

The set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1, which is the correct answer that would be an option (C).

What is an ordered pair?

An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.

Given the function ƒ = {(1 , 2), (2 , 3), (3 , 4)}

According to option (A),

The set of ordered pairs is {(1, 2), (3, 2), (4, 3)}

This represents ƒ -3,

According to option (B),

The set of ordered pairs is {(2,1), (3, 2), (4, 3)}

This represents ƒ -2,

According to option (C),

The set of ordered pairs is {(2, 1), (2, 3), (3, 4)}

This represents ƒ -1,

Thus, the set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1.

Hence, the correct answer would be option (C).

Learn more about the set of ordered pairs here:

https://brainly.com/question/10197233

#SPJ2

Ben made some apple pies. For every 4 cups of butter, he added 3 cups of water. The ratio of butter to water in Ben's apple pies is ____. (5 points)

Question 1 options:

1)



2)



3)

3

4)

4

Answers

Answer:

4 Trust me

Step-by-step explanation:

A gardener measures the dimensions of a rectangular garden that is 9 meters wide by 12 meters long. If the gardener draws a blueprint of the garden, where each meter is equivalent to
inch, which statements are true?
Select ALL that apply.
The area of the blueprint is square inches
The area of the blueprint is 108 square inches
The length of the blueprint is 6 meters
The perimeter of the blueprint is 28 inches.
The width of the blueprint is 8 meters
Calculator

Answers

Answer:

Catalog Name:*Shimmering Chic Earrings*

Base Metal: Alloy

Plating: Gold Plated

Stone Type: Cubic Zirconia/American Diamond

Type: Jhumkhas

Multipack: 1

Easy Returns Available In Case Of Any Issue

*Proof of Safe Delivery! Click to know on Safety Standards of Delivery Partners- https://ltl.sh/y_nZrAV3

The statements are true:

The area of the blueprint is square inches

The area of the blueprint is 108 square inches

What is Area of rectangle?

The Area of Rectangle is product of its length to its width.

So, Area of Rectangle = length x width

Given:

length= 12 inch

and width= 9 inch

Area of Blue print = l x w

                              = 12 x 9

                              = 108 square inches.

Perimeter of Blue print = 2 ( l+ w)

                                       = 2( 12+ 9)

                                       = 42 inches

Learn more about Area of rectangle here:
https://brainly.com/question/20693059

#SPJ2

Good evening my daughter needs help with the following. thank you ​

Answers

Answer:

3 x 9 = 3 x (5 + 4)

= 15 + 12

= 27

Step-by-step explanation:  First you split 9 into 2 parts and ask what plus what equals 9?  5 + 4 = 9 so you got the first equation 3 x (5 + 4).

Then 3 x 5 = 15 and 3 x 4 = 12 so you got the equation 15 + 12 = 27

which graph shows the Same and behaviour as the Graph of F(x) = 2X^6=2x²2-5​

Answers

Given function:-

 f(x) = 2x6 – 2x2 – 5.

In order to find the end behavior of the graph, we need to find the degree of the given function and the leading coefficent.

Degree of the given function is the highest power of the variable.

We have variable x there.

Highest power of x is 6.

So, we can say:

Degree = 6 ( an even degree)

And leading coefficent is the coefficent of highest power term.

We have highest power term is 2x^6.

So, the leading coefficent is : 2 (Positive number)

For even degree and positive leading coefficent, end behaviour is

x --> ∞  f(x) = +∞

x-->-∞   f(x) = +∞

Expression:
Simplify 2s - s + 6s

Please explain step by step how I get the answer to get marked as brainliest

Answers

Answer:

7s.

Step-by-step explanation:

2s - s + 6s (Given)

Rembember that - s is the same as - 1s because there is an invisible 1.

So, 2s - 1s =  1s or s.

1s + 6s = 7s.

2s - s + 6s (Given)

7s (Combine like terms)

Describe how to find all the points on a baseball field that are equidistant from second base and third base.

In the figure, m∠DBE=50. Find each of the following.

m∠BEDm angle b e d
m∠BEAm angle b e eh
x
y
BE
BC

Answers

From the given diagram, the following statements are true:

AB = BC

3y = 5y - 22

3y - 5y = -22

-2y = -22

y = 11

Similarly, m<DBE = 50 degrees

m<BED = 90 - m<DBE

m<BED = 90 - 50

m<BED = 40 degrees

Since BE = BC = 3y

BE = BC = 3(11) = 33

Also, 7x  - 2 = 40

7x = 40 + 2

7x = 42

x = 6

Get the measure of m<BEA

m<BEA = 7x - 2

m<BEA = 7(6) - 2

m<BEA = 40 degrees

Learn more on angles here: https://brainly.com/question/16281260

If sin A = 3/4, then the value of tan A

Answers

[tex]sinA=\frac{3}{4}[/tex]  ⇒  ∠A ≈ 49°

tanA ≈ 1.15

ok done. Thank to me :>

A middle school took all of its 6th grade students on a field trip to see a play. The students filled 1917 seats, which was 45% of the total number of seats in the theater. How many total seats were in the theater?

Answers

Answer:

4260 seats in the theater

Step-by-step explanation:

We write the equation 0.45x=1917, with x representing the total number of seats.

Multiply both sides by 100, we get 45x=191700.

Divide both sides by 45, we get x=191700/45

x=4260.

There are 4260 seats in the theater.

The total number of seats is the theater is 4,260.

Percentage:

The percentage is a ratio or fraction of 100 and can be calculated with the formula

Percentage = [tex]\frac{parts}{whole}.100[/tex]

How to calculate percentage?

Here we have given that the 1917 seats is 45% of the total seats

Let the total number of seats available in theater is = x

Then 45 % of x = 1917

0.45 x = 1917

Multiply both the sides by 100 we have

45 x = 1917x100

x = [tex]\frac{191700}{45}=4260[/tex]

The final answer is 4,260 seats

Learn more about Percentage here-

https://brainly.com/question/843074

#SPJ2

6^9+6^8)/(6^8*6^-9)
HELP PLS​

Answers

Step-by-step explanation:

Question:-To simplify the expression

Expression:-[tex] \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]Solution :-

[tex] = \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]

[In numerator we take 6^8 common]

[tex] = \frac{ {6}^{8} ( {6} + 1)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]

[On Simplification]

[tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]

[In denominator as we know, a^x × a^y = a^(x+y)]

[tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8 + ( -9)} )} [/tex]

[On Simplification]

[tex] = \frac{( {6}^{8} \times 7)}{( {6}^{ - 1} )} [/tex]

[As we know, 1/a^-1 = a ]

[tex] = {6}^{8} \times 7 \times 6[/tex]

[On further multiplying of 6]

[tex] = {6}^{9} \times 7[/tex]

Result:-

In exponential form:

[tex] = {6}^{9} \times {7}^{1} (ans)[/tex]

In numerical form:

70,543,872 (Ans)

[tex] \huge \: \bf \: Question:—[/tex]

[tex] \sf \longmapsto6^9+6^8)/(6^8 \times 6^{-9})[/tex]

[tex]\huge\bf Solution:—[/tex]

[tex]\sf \longmapsto \: \dfrac{ {6}^{9} + {6}^{8} }{ {6}^{8} \times {6}^{ - 9} } [/tex]

[tex]\sf \longmapsto \dfrac{10077696 + {6}^{8} } { {6}^{8} \times {6}^{ - 9} } [/tex]

[tex]\sf \longmapsto \dfrac{10077696+1679616}{ {6}^{8} \times {6}^{ - 9} } [/tex]

[tex]\sf \longmapsto \: \dfrac{11757312}{{6}^{8} \times {6}^{ - 9}} [/tex]

[tex]\sf \longmapsto \dfrac{11757312}{1679616(6 {}^{ - 9} )} [/tex]

[tex] \boxed{\bf \: As \: a^{-n} = 1/a(n) \: ,}[/tex]

[tex]\sf \longmapsto \dfrac{11757312}{1679616 \bigg(\dfrac{1}{10077696} \bigg )} [/tex]

[tex]\sf \longmapsto \dfrac{11757312}{ \dfrac{1}{6} } [/tex]

[tex]\sf \longmapsto \: \: 70543872[/tex]

[tex] \boxed{\bf \: \: \: Convert\: 70543872 \: to\: scientific \: notation}[/tex]

[tex] \sf \longmapsto \: 7.0543872 × 10 {}^{7} [/tex]

[tex]\boxed{ \bf \: \: Convert\: 70543872 \: to\: exponent}[/tex]

[tex]\sf\longmapsto {6}^{9} \times 7 [/tex]

_________________________________

[tex] \boxed{\bf \: Answer\: in\: Number}:—[/tex]

[tex] \boxed{\bf \: 70543872}[/tex]

[tex]\boxed{ \bf \: Answer\: in\: Exponent:—}[/tex]

[tex] \boxed{\bf \: {6}^{9} \times 7}[/tex]

[tex]\boxed{\bf Answer\: in\: Scientific\: Notation:—}[/tex]

[tex]\boxed{ \bf \: 7.0543872 × 10 {}^{7} }[/tex]

HELP PLEASE!!! 50 POINTS INCORRECT ANSWERS WILL BE REPORTED.

Answers

Congruent means same so the equation is
5x+24=9x-17
Subtract 5x on both sides
24=4x-17
Add 17 to both sides
41=4x
Divide by 4
10.25

Write the following fraction as percent 7/10

Answers

the fraction version of 7/10 is 70% :))
7/10 is equal to 70%

At a video arcade, the action video games this week cost $25, which is 125% of last week's price. What was its price last week?

A. $20

B. $15

C. $40

D. $25

Answers

Answer:

A

Step-by-step explanation:

125% of 25 is the same as 5/4 of 25.

Divide by 5 and you get 5. 1/4 is 5, so 100% or 4/4 is 20

Answer:

it's a

Step-by-step explanation:

trust

Homework: Ch 5.2
Question 1, 5.2.3
HW Score: 25%, 2 of 8 points
O Points: 0 of 1
Save
A recipe for 14 banana-nut mutins calls for 1 cup of flour. The number of muffins that can be made varios directly with the amount of flour used. There are 2.2 cups of flour available. How many muffins can be made?

Answers

Answer:

  30 muffins

Step-by-step explanation:

2.2 cups of flour is 2.2 times the 1 cup quantity required for 14 muffins. Since muffins are proportional to flour, that means 2.2 times 14 muffins can be made. That is ...

  2.2×14 = 30.8

30 whole muffins can be made.

_____

Additional comment

If each muffin is made about 0.6% smaller than for the standard recipe, then 31 muffins could be made from 2.2 cups of flour. Usually, this change in size will not be noticeable.

hlep me pls daddddddddddddddddddddddddddddddddy

Answers

Answer:

The equation would be 2(n+3)-6. So A.

Step-by-step explanation:

It is asking you to subtract first and you cannot do that without  parentheses.

Answer:

First ONE

Step-by-step explanation:

First you are adding 3

n+3

then you mulitply by 2

so, its 2(n+3), you have to put in bracket because you want to do addition first

then you subtract everything by 6

its 2(n+3)-6

How to find the derivative???

Answers

Answer:

[tex]y'= \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]

Step-by-step explanation:

We have [tex]e^{2x} = \ln(y^3)[/tex] and we want the implicit differentiation [tex]\dfrac{dy}{dx}f(x) = y'[/tex]

Therefore, we want to separate the [tex]y[/tex] from the equation.

[tex]\ln(y^3) =e^{2x} \implies 3 \ln(y) = e^{2x} \implies \ln(y) = \dfrac{e^{2x} }{3}[/tex]

[tex]\implies e^{\ln(y)} = e^{e^{2x}/3} \implies \boxed{y = e^{e^{2x}/3}}[/tex]

Now we can calculate the derivative. By the chain rule,

[tex]y' = \dfrac{d}{dx}\left(e^{e^{2x}/3}\right) = e^{e^{2x}/3}\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right)[/tex]

Now

[tex]\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right) =\dfrac{1}{3}\dfrac{d}{dx}\left(e^{2x}\right) = \dfrac{2}{3}e^{2x}[/tex]

Therefore

[tex]y' = e^{e^{2x}/3}\cdot \dfrac{2}{3}e^{2x} = \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]

Shayna pays 20 for 5 bottles of juice. What is the unit price for the bottles of juice?

Answers

20/5 = 4
therefore the unit price for the bottles of juice is 4

HELP!!!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the multiplication expressions to the exponential expressions.

Answers

Answer:

Step-by-step explanation:

the product of seven non-zero factors. of which only three are positive. is

a) positive
B) negative
c) null​

Answers

The answer is A

Step-by-step explanation: This is one of those sneaky questions where you think there is no definite answer, but don't despair. There is an answer. You have 7 numbers 3 of them are positive which means greater than 0. Let's pick them 345 = 60 That part's easy. Those 3 numbers give a plus result. Now try the other 4 numbers -3 -2 - 1-4 Do you see what's going to happen. You have -3* - 2 = 6 then you get - 1*-4 = 4 All of a sudden you get a positive result 6 * 4 = 24 60 * 24 = 1440 So the answer is any 3 plus numbers multiplied by 4 minus numbers gives a plus result.

Of 7 non-zero factors, 3 are positive, so the other 4 are negative. Multiplying two negatives gives a positive number. So on its own, the product of all the negatives is positive, and multiplying by the other 3 positive numbers makes the overall product positive.

Other Questions
Complete the first step of the indirect proof of the following statement:"4X+3>12"Assume temporarily that 4x+3 12.>O 4x+3y=7 what is the coefficients Niccolo is invited to help a program where, even though not mandated by the external environment, management requires teams to make big, up-front, and detailed scope commitments for every release. What three things can Niccolo do to best coach the decision-makers Many feel that AIDS went largely undetected because it impacted the homosexual and drug using communities first, and these groups often face prejudice. If this was the case, which groups in society would get the most attention if a pandemic impacted them? Since 1976, the National Association of Legal Assistants (NALA) has administered aA)rigorous ethics exam.B)two-day comprehensive exam.C)temporary certificate that is good until the candidate completes a bachelor's degree. What is The output of full-wave rectifier with filter PLEASE HELP2.How many atoms are in 3.35 moles of Aluminum?3.How many moles of CO2 gas are in a 101.25 L container filled with CO2 gas?4.What is the mass of 13.7 moles of N2 gas? What can you conclude about the domain and range of a relation if a verticals line at x=5 passes through 2 points? 1 point? No Points? I need this answer ASAP! Remainder of 52,259 divided by 215 Any ideas for this? V. Answer the following questions logically with complete sentences in Spanish. (12 points)1. Cundo te pones [t] triste?2. Dnde se yen Uds. en efcampus?3. Quin es el ms simptico de tus amigos?4. Estn repitiendo los verbos Diana y Roberto? Pleaseee HELPPPPPP HELPPPPP PLEASE Is this answer corrrect if not what is the correct answer? Why is air temperature above land warmer than the air temperature above water in the same location during the summer? How long did the Aztecs fight against Corts and his soldiers?a.1 yearb.5 yearsc.80 daysd.2 weeks Simplify the expression 4(-y+2) -3y Chang made $156 for 13 hours of work at the same rate, how many hours would he have to work to make $108? 5. Linda earns $95 per day. If she works of a day, how much will she earn? Match each shape with its area formula. 1. A roller coaster with a mass of 800 kg sits stationary at the top of a section of track, 75 m abovethe ground as shown. When the brake is released, it starts to roll down the track2. For each height represented in the diagram, calculate the gravitational potential energy usingEp = mgh. Show ONE SAMPLE calculation in the calculations section below and fill in Table 1 foreach of the heights of the roller coaster. (6 marks)3. Assuming there is no friction, determine the mechanical kinetic energy using Ek = Etotal - Ep.Show ONE SAMPLE calculation in the calculations section below and fill in Table 1 for each ofthe heights of the roller coaster. (6 marks)4. For each height represented in the diagram, calculate the velocity using = 2 . Show ONESAMPLE calculation in the calculations section below and fill in Table 1 for each of the heights ofthe roller coaster. (6 marks)5. Use your answers to graph how gravitational potential energy, mechanical kinetic energy, andvelocity change as the roller coaster changes height. Use different colours for the three lines onthe graph. Graph paper is provided below. (3 marks)6. Repeat steps 1 5 above for a roller coaster cart that has a mass of 300 kg and enter yourresults in Table 2.Calculations:800 kg roller coaster cart:Sample calculation for gravitational potential energy:Sample calculation for Mechanical kinetic energy:Sample calculation for velocity:300 kg roller coaster cart:Sample calculation for gravitational potential energy:Sample calculation for mechanical kinetic energy:Sample calculation for velocity:Results:Table 1: Potential energy, kinetic energy, total energy, and velocity of the 800 kg roller coaster cartTable 2: Potential energy, kinetic energy, total energy, velocity of the 300 kg roller coaster cart.Graphs:Its graphing time. These graphs are a bit different than the ones you did in thedata analysis assignment at the beginning of the course. In this case you havethree things to graph on each graph. (One graph for the 800 kg roller coaster cartand one graph for the 300 kg roller coaster cart.) You need to graph thegravitational potential energy with respect to height, the mechanical kineticenergy vs height, and the velocity vs height.Lets look at the energy graphs first. In this case both kinetic energy andmechanical energy cover the same range of values. This means they can use thesame scale on the y-axis. So, you will use the left y-axis and the x-axis to graphthe kinetic energy vs height and the potential energy vs height. You will need alegend to explain which line is which. Colour coding is a nice way to highlight this.The velocity values are much different than the energy values. This means youneed a totally different scale. So, your left y-axis wont work. You need to make asecond scale on the right y-axis for your velocity values. You will plot the pointsthe same way as normal, but you will use the numbers on the right-hand scaleinstead. Again, be sure to add your velocity line to the legend with a separatecolour code.Discussion Questions:1. Describe the relationship between the gravitational potential energy and the mechanical kineticenergy of the roller coaster on your graph. (2 marks)2. Describe the shapes of each of the three lines in the graph. Explain why the velocity is different.(4 marks)3. Describe how mass affects the speed at the bottom of the roller coaster. (2 marks)4. Describe how mass affects the gravitational potential energy and the mechanical kinetic energyof the roller coaster. (2 marks)5. At what point does the roller coaster have a maximum value for the following? Justify youranswer by explaining why. (2 marks each)a. Gravitational potential energyb. Mechanical energyc. Velocity6. In your calculations, you assumed that the roller coaster was frictionless. All real roller coastersencounter friction. Describe how the actual values of the variables would differ, or not differ,from your calculated values for a real roller coaster. (Hint: what form of energy would some ofthe total energy be converted to if there was friction in the system?) (4 marks)How you will be graded:Grades will be based on answering questions to demonstrate an understanding of the material coveredin this unit. Point form answers are okay if ideas are complete and use vocabulary (Word Bank)provided. For questions out of 4 marks, there are 4 responses expected.