Write the integral and solve for the area under the curve:

Write The Integral And Solve For The Area Under The Curve:

Answers

Answer 1

Answer:

Integral: [tex]\int\limits^\pi _0 {3sinx} \, dx[/tex]

Area: 6

Step-by-step explanation:

[tex]\int\limits^\pi _0 {3sinx} \, dx = -3[cosx]_{0} ^{\pi} = 6[/tex]


Related Questions

Need number 7 the answer please.

Answers

Answer:

h(x) = -2|x+2| + 2

Step-by-step explanation:

let me know if you want an explanation :))

Mama bear wants to bake a cake with chocolate frosting for her twins birthday party. She uses a package containing 495 grams of coco powder for the frosting. What will be the weight of the chocolate frosting if it is 55% cocoa powder?

Answers

The weight of the chocolate frosting if it is 55% cocoa powder will be 272.25 grams.

What is the percentage?

The quantity of anything is stated as though it were a fraction of a hundred.

Mama bear wants to bake a cake with chocolate frosting for her twin's birthday party.

She uses a package containing 495 grams of cocoa powder for the frosting.

Then the weight of the chocolate frosting if it is 55% cocoa powder will be

⇒ 0.55 × 495

⇒ 272.25 grams

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Hamish and Harry work as plumbers. harry earns a dollar more than 5/4 the amount Hamish earns per hour. the amount Harry earns per hour is 2$ less than 7/5 the amount Hamish earns per hour. how much to both of them earn per hour? ​

Answers

Answer:

Hamish earns $20 per hour, and Harry earns $26 per hour.

Step-by-step explanation:

Harry earns

$1+(5/4)•x and also (7/5)•x-$2

$1+(5/4)•x = (7/5)•x-$2

$1+$2= (7/5)•x-(5/4)•x

3=(7•4•x-5•5•x)/20

3=3x/20

3•20=3x

X=20, Hamish earns $20

Substitute x in one of the expressions

1+(5/4)•20=1+25=26, Harry earns $26

work hours

frequency

0 - <10

45

10 - <20

33

20 - <30

20

30 - <40

7

40 - <50

8

Use your calculator to find the mean and standard deviation

Answers

The mean and the standard deviation are 16.15 and 12.03, respectively

How to determine the mean and the standard deviation?

The table of values is given as:

Work hours           Frequency

0 - <10                        45

10 - <20                      33

20 - <30                     20

30 - <40                       7

40 - <50                      8

Start by rewriting the table using the midpoint of each class

x      f

5     45

15    33

25    20

35    7

45    8

The mean is then calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

This gives

[tex]\bar x = \frac{5 * 45 + 15 * 33 + 25 * 20 35 * 7 + 45 * 8}{45 + 33 + 20 + 7 + 8}[/tex]

Evaluate the sum and the products

[tex]\bar x = \frac{1825}{113}[/tex]

Divide

[tex]\bar x = 16.15[/tex]

The standard deviation is:

[tex]\sigma =\sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]

This gives

[tex]\sigma= \sqrt{\frac{45 * (5 - 16.15)^2 + 33 * (15 - 16.15)^2 + 20 * (25 - 16.15)^2 + 7 * (35 - 16.15)^2 + 8 * (45 - 16.15)^2 }{45 + 33 + 20 + 7 + 8}}[/tex]

Evaluate the sum and the products

[tex]\sigma= \sqrt{\frac{16350.4425}{113}}[/tex]

Divide

[tex]\sigma= \sqrt{144.694181416}[/tex]

Take the square root

[tex]\sigma= 12.03[/tex]

Hence, the mean and the standard deviation are 16.15 and 12.03, respectively

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Expert Mathematicians, please help!

Answers

Answer:

Two functions which satisfies the H(x) are f(x) = 2x - 4, (x)    = x⁵  and

f(x)  = 2x,  g(x)  = x⁵ - 2

Step-by-step explanation:

The given question is based on the decomposition of a given function into two functions

Decomposition of a function :- functional decomposition is the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed from those parts by function composition

so the function given in the question is H(x) = 2x⁵ - 4

now by using the concept of decomposition of a function we can find two functions f and g

therefore,

f(x) = 2x - 4

and    g(x)    = x⁵

similarly we can find another pair which satisfies the function H(x)

f(x)  = 2x

and g(x)  = x⁵ - 2

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enita is factoring the expression 32 a b minus 8 b. She determines the GCF and writes the factored expression as 8 b (4 a minus 0). Which best describes Venita’s error?
a. She incorrectly determined the GCF.
b. She subtracted the GCF from the second term in the expression instead of dividing.
c. She divided the GCF into the first term in the expression instead of subtracting.
d. She divided each piece of the expression by different factors.

Answers

This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.

Greatest common factor

Given the following expression

32ab - 8

Find the factors of each terms

32ab = 8 * 4. * a * b

8 = 8 * 1

Since 8 is common to both factors, hence

32ab - 8 = 8(4ab -1)

This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.

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1.9^4 × 10 × 2.9 x 10^1

Answers

3779.309 is the answer....

Are you sure the question isn’t 1.9 x 10^4 x 2.9 x 10^1 = (1.9 x 2.9) x (10^4 x 10^1) = 5.51 x 10^5

Raul's pet store has a play area that can fit up to 30 cats and dogs. His son is allergic to cats so the pet store never has more than 8 cats in the play areas.

How many of each type of pet can they have at the
pet store?
Write a system of inequalities.

Answers

Answer:

Step-by-step explanation:

Let :

C = number of cats

D = number of dogs

Raul's pet store has a play area that can fit up to 30 cats and dogs.

C + D = 30

The pet store never has more than 8 cats in the play areas.

C < 9

(there can never be 9 or more cats)

As or the number of dogs :

C + D = 30

C = 30 - D

Since we know that C < 9. To get the number of dogs allowed, we just plug in 30 - D for C.

30 - D < 9

30 - 9 < D

or

D > 21

(dogs have to be 22 or more)

The equation for the pH of a substance is pH = -log[H*], where H+ is the concentration of hydrogen ions. A basic
solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentratic
of hydrogen ions between the two solutions?
1.6x10-9
O4.0x10-3
O 6.7x10-1
O 1.6x10¹11

Answers

The approximate difference in the concentration of hydrogen ions between the two solutions is 4.0×10⁻³

What is pH value?

The pH of a solution is a measurement of the concentration of hydrogen ions in the solution, as well as its acidity or alkalinity. Normally, the pH scale ranges from 0 to 14.

pH value for basic solution = 11.2

pH value for acidic solution = 2.4

Concentration for a basic solution:

[tex]\rm = 10^{-11.2}[/tex]

[tex]= 6.309\times10^{-12}[/tex]

Concentration for an acidic solution:

[tex]\rm = 10^{-2.4}[/tex]

[tex]= 3.981\times10^{-3}[/tex]

Difference between the concentration:

[tex]= 3.981\times10^{-3}- 6.309\times10^{-12}[/tex]

[tex]= 3.98\times10^{-3}[/tex]

[tex]= 4\times10^{-3}[/tex]

Thus, the approximate difference in the concentration of hydrogen ions between the two solutions is 4.0×10⁻³

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how would i solve this problem

Answers

Answer:

30

Step-by-step explanation:

1500/50=30

Rewrite exponential expressions
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!

Answers

Answer:

Step-by-step explanation:

What are the zeros of the quadratic function f(x)=6x^2+12x-7?


(Please pick from one of the options in the photo)

Answers

The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.

The missing options are given below.

What is the solution of the quadratic equation by formula method?

The quadratic equation is given as ax² + bx + c = 0.

Then the solution is given as

[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The quadratic function is given below.

f(x) = 6x² + 12x – 7

Then the zeroes of the quadratic function will be

[tex]\rm x = \dfrac{-12\pm \sqrt{12^2 - 4 * 6 * (-7)}}{2 * 6}\\\\\\\rm x = \dfrac{-12\pm \sqrt{312}}{12}\\\\\\\rm x = -1 \pm \sqrt{\dfrac{13}{6}}\\\\\\x = -1 - \sqrt{\dfrac{13}{6}} , -1 + \sqrt{\dfrac{13}{6}}[/tex]

Then the correct option is A.

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need help with this please

Answers

The values of x and y at t=3 are -4.95 and 0.423 respectively.

The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.

The value of the tangent slope at t=3 is 4.21.

The speed at t=3 is 3.05 units/sec.

Given the equation of x as the function of t is

x= 5 cos t

similarly, the equation of y as the function of t is

y= 3 sin t

At t=3 the value of x will be

x (at t=3) = 5 cos 3= 5(-0.989)= -4.95

At t=3 the value of y will be

y (at t=3) = 3 sin 3= 3(0.141)= 0.423

The derivative of the function of x with respect to t will be

dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t

at t=3 the value of dx/dt will be

dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71

The derivative of the function of y with respect to t will be

dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t

at t=3 the value of dy/dt will be

dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97

The tangent slope is dy/dx which can be calculated by

dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t=  (-3/5) cot t

at t=3 the value of tangent slope will be

dy/dx (at t=3) = (-3/5) cot 3= 4.21

The speed at t=3 will be

speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]

= √(dx/dt)²+(dy/dt)²

at t=3

= √(0.71)²+(-2.97)²

= √9.325

= 3.05 unit/sec

Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.

The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.

The value of the tangent slope at t=3 is 4.21.

The speed at t=3 is 3.05 units/sec.

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Use a calculator to graph the functions y=-3x-21 and y=x³-3x-3. How many points of intersection do the
functions share?
0
1
2
3

Answers

Answer:

1

Step-by-step explanation:

When you graph the functions they intersect at one point

(-3.368119, -31.10436)

what is ⅛ in a percentage form​

Answers

Answer:

12.5%

Step-by-step explanation:

1/8 × 100% = 12.5%

So 9f you multiply an eighth by one hundred percent and simplify accurately you'll get 12.5%

Determine the equation of the tangent line in both cases


1. x^2/x+2 at (2,1)


2. x^3+2y^2=10y at (2,1)

Answers

Differentiate the function/equation with respect to x and solve for the derivative, dy/dx. The value of dy/dx at the given point is the slope of the tangent line to the curve at that point. Then use the point-slope formula to get the equation of the tangent.

1.

[tex]y = \dfrac{x^2}{x+2} \implies \dfrac{dy}{dx} = \dfrac{2x\times(x+2) - x\times1}{(x+2)^2} = \dfrac{x(x+4)}{(x+2)^2}[/tex]

When x = 2, the derivative is

[tex]\dfrac{dy}{dx}\bigg|_{x=2} = \dfrac{2(2+4)}{(2+2)^2} = \dfrac34[/tex]

Then the equation of the tangent line at (2, 1) is

[tex]y - 1 = \dfrac34 (x - 2) \implies \boxed{y = \dfrac{3x}4 - \dfrac12}[/tex]

2.

[tex]x^3 + 2y^2 = 10y \implies 3x^2 + 4y \dfrac{dy}{dx} = 10 \dfrac{dy}{dx} \implies \dfrac{dy}{dx} = \dfrac{3x^2}{10-4y}[/tex]

When x = 2 and y = 1, the derivative is

[tex]\dfrac{dy}{dx}\bigg|_{(x,y)=(2,1)} = \dfrac{3\times2^2}{10-4\times1} = 2[/tex]

Then the tangent at (2, 1) has equation

[tex]y - 1 = 2 (x - 2) \implies \boxed{y = 2x - 3}[/tex]

Question 6 of 15
Gloria invested $1200 in an account that earns 2.5% interest, compounded
annually. The formula for compound interest is A(t) = P(1 + i)t. How
much did Gloria have in the account after 5 years?
O A. $3662.11
OB. $6150.00
OC. $1470.00
OD. $1357.69

Answers

Answer:

D

Step-by-step explanation:

[tex]1200( {1.025}^{5} ) = 1357.69[/tex]

Question 9 of 10
For what value of x is the rational expression below equal to zero?
3x + 15
6-x
OA. -5
OB. 5
O C. 6
OD. -6
UBMIT

Answers

Answer:

A. -5

Explanation:

For (3x + 15)/(6 - x) to be equal to zero. Set the equation to 0.

Doing so:

(3x + 15)/(6 - x) = 0

3x + 15 = 0(6 - x)

3x + 15 = 0

3x = -15

 x = -15/3

 x = -5

Therefore, the value of x is -5 to equal to zero.

the data below shows the number of workers employed in the various section s of each a construction company in the Lagos

Carpenter 24
plumber 12
labourers 27
plasterers 15
painters 9
Messengers 3
bricklayers 18

if the Worker is retrenched, what is the probability that he is a plumber or a plasterer?​

Answers

If the Worker is retrenched, the probability that he is a plumber or a plasterer will be  0.0152.

What is probability?

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

The probability that the employee is a plumber;

[tex]\rm P(plumber)= \frac{No \ of \ plumber}{Total \ number \ of \ employ} \\\\ P(plumber)=\frac{12}{108} \\\\\ P(plumber)= 0.11[/tex]

The probability that the employee is a plasterer;

[tex]\rm P(plasterers )= \frac{No \ of \ plasterers }{Total \ number \ of \ employ} \\\\ P(plasterers )=\frac{15}{108} \\\\\ P(plasterers )= 0.13[/tex]

The probability that he is a plumber or a plasterer:

P = 0.13 × 0.11

P= 0.0152

Hence, if the worker is retrenched, the probability that he is a plumber or a plasterer will be  0.0152.

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The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.

Answers

The true statement is:

"The range of the function is all real numbers less than or equal to 9."

Which statements are true?

Here we have the quadratic function:

[tex]f(x) = -x^2 - 4x + 5[/tex]

And we want to see which of the given statements are true.

The first one is:

"The domain is al real numbers less than or equal to -2"

This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).

The second statement is:

" The domain of the function is all real numbers less than or equal to 9."

Also false

Third one:

" The range of the function is all real numbers less than or equal to −2"

The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.

In this case, the quadratic function is:

[tex]f(x) = -x^2 - 4x + 5[/tex]

So the vertex is at:

[tex]x = 4/(2*-1) = -2\\[/tex]

Then the y-value of the vertex is:

[tex]f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9[/tex]

So the range is the set of all real numbers less than or equal to 9.

So the above statement is false, and the final one:

"The range of the function is all real numbers less than or equal to 9."

Is the true statement.

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What is the length of leg s of the triangle below? 45 √32 45° A. √4 B. 1.5 C. 16 ​

Answers

Answer:

s = 4 units

Step-by-step explanation:

Given is isosceles right triangle, since its interior angles are 45°, 45° and 90°.

The missing length is therefore same as the length of the other leg:

s = 4

Note: This is not included in the answer choices.

Answer:

4 units

Step-by-step explanation:

We can use the converse theorem of the isosceles triangle to find the missing leg.

Converse Isosceles triangle theorem: If two angles are congruent in a triangle, then sides opposite to those angles are also congruent.

Therefore,

As there are two 45° angles, the opposite sides to those are also congruent.

∴ s = 4

50 cm
1.5
Path
Vegetables
50 cm
50 cm
2
5.5m
This plan shows a vegetable garden.
The width of the path is 50 cm throughout.
4.5m

Answers

Step-by-step explanation:

b because you have to multiply

This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!

Answers

Step-by-step explanation:

[tex] \frac{5 {}^{ - 4x + 7} }{125 {}^{x} } [/tex]

[tex] \frac{5 {}^{ - 4x + 7} }{5 {}^{3x} } [/tex]

[tex]5 {}^{ - 4x + 7 - 3x} [/tex]

[tex]5 {}^{ - 7x + 7} [/tex]

Which graph shows y=1/2⌈x⌉?

Answers

The correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.

What is a graph?

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the equation y =1/2x is represented in the answer below we can see in the graph that at every value of y the value of x is double for example if we put y = 1 then the value of x will be 2.

y = 1/2 x

at x = 2

y = 1/2 x 2

x = 1

Therefore the correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.

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in need of assistance

Answers

Answer:

60

Step-by-step explanation:

_---&$'_-4$':/-&$$--(:'##4--&&4___&$$_666&4&&&&&

Answer: 489.8 in

Step-by-Step Explanation:

Diameter (d) = 26 in
Radius (r) = 26/2 = 13 in

No. Of Revolutions = 6

We know, that the length around the tire is nothing but the perimeter of the tire.

Perimeter = 2πr

Therefore,
= 2πr
= 2 * π * r
= 2 * 3.14 * 13
= 6.28 * 13
=> 81.64

Perimeter = 81.64 in

Distance Travelled after 6 Revolutions of the Tire = Perimeter * 6

Therefore,
= 81.64 * 6
=> 489.8

Distance Travelled after 6 Revolutions of the Tire = 489.8 in

Integration by Parts Evaluate e-2x cos(2x) dx.​

Answers

Let

[tex]I = \displaystyle \int e^{-2x} \cos(2x) \, dx[/]tex

Integrate by parts:

[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]

with

[tex]u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \cos(2x) \, dx \implies v = \dfrac12 \sin(2x)[/tex]

Then

[tex]\displaystyle I = \frac12 e^{-2x} \sin(2x) + \int e^{-2x} \sin(2x) \, dx + C[/tex]

Integrate by parts again, this time with

[tex]u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \sin(2x) \, dx \implies v = -\dfrac12 \cos(2x)[/tex]

so that

[tex]\displaystyle I = \frac12 e^{-2x} \sin(2x) - \frac12 e^{-2x} \cos(2x) - \int e^{-2x} \cos(2x) \, dx + C\\\\ \implies I = \frac{\sin(2x)-\cos(2x)}{2e^{2x}} - I + C \\\\ \implies 2I = \frac{\sin(2x) - \cos(2x)}{2e^{2x}} + C \\\\ \implies I = \boxed{\frac{\sin(2x) - \cos(2x)}{4e^{2x}} + C}[/tex]

Which of the following statements is true?

Answers

Answer:

B

Step-by-step explanation:

1/9 can be simplified to 1/3 as 1/3 x 1/3 = 1/9  and 49/25 can be simplified to 7/5 as 7/5 x 7/5 = 49/25.

Now looking at both the fraction 1/3 and 7/5

1/3 simplifies to 0.34

It is an irrational value as the 3 keeps repeating.

7/5 simplifies to 1.4

It is a rational value as the decimal value is not repeating.

Thus making the second option the answer.

Given a function described by the table below, what is y when x is 5?
XY
26
48
59
612

Answers

Answer:

y = x + 4

when x is 5, y is 9

Step-by-step explanation:

the pattern from the table is that the y value is 4 more than the x value, so the equation would be y = x + 4.

if you plug in x = 5, then this would be y = 5 + 4 = 9

PLEASE HELP!!!!!!!!!

Answers

Answer:

correct answer is B.

Step-by-step explanation:

for more information see the attachment.

Answer:

no 2/B is the correct answer


the answer to this question

Answers

From indices : when you have a fraction like 3⁶/5

we can also write it as (5√3)^6

and we were given (c√a )^b

meaning that anywhere the letters are, we put them as the numbers there.

therefore: a = 3 , b = 6 , c = 5

Hope this helps and you understood it.

you're super free to ask any more questions eh.

Good luck ✅.

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A line contains points M(1, 3) and N(5, 0). What is the slope of MN?negative StartFraction 4 Over 3 EndFractionnegative StartFraction 3 Over 4 EndFractionStartFraction 3 Over 4 EndFractionStartFraction 4 Over 3 EndFraction You have loaned a friend %100 and will charge him 5% annual simple interest when he pay it back. Suppose a households income increases from $2500 to $3000 and quantity demanded changes from 190 to 150. What is the income elasticity? a.0.6b.$500c.-1.05d.2.5 you're using a linux distribution that uses rpm for package management. which command would you use to install httpd, the apache http server package, and all its dependencies? In the early part of the twentieth century, ________ argued forcefully for the idea of continental drift. Which cells are present during acute inflammation? Read the following sentence: Because he had such a logical mind, Bernie usually had autilitarian solution that was reasonable and worked for every problem. Use context clues to determine which of the following words would best replace the word utilitarian.practicalfoolishAll of the choices are correct.clearGunaware When Korker was born, her family realised that the Shape of her nose resembled that of her mother and her skin Colour resembled that of her of her father. Explain the principle behind this occurrence Describe the benefits of understanding marginal analysis as an individual a paperweight has height 4cm and volume 38.4cm3. a mathematically similar paperweight has height 7cm. calculate the volume of this paperweight. See photo for questions. Read the excerpt from Jane Eyre by Charlotte Bront.from fanMy head still ached and bled with the blow and fall Ihad received: no one had reproved John for wantonlystriking me; and because I had turned against him toavert farther irrational violence, I was loaded withgeneral opprobrium [harsh criticism]."Unjust!-unjust!" said my reason, forced by theagonising stimulus into precocious though transitorypower.What is revealed about Jane by the juxtaposition ofJane's feelings with those of the rest of her household?O She is upset when she is criticized.O She is not affected by the way others treat her.She has a strong sense of what is right.OO She has trouble seeing things from another point ofview. Read the excerpt from "Deucalion and Pyrrha by Ovid.Here is the worldwith its glorious lands from east to west; and here are we,an inglorious crowd of two. All else belongs to the sea.As yet, indeed, we can hardly be certain the life that we haveis safely assured. These clouds still fill me with fear and foreboding.How would you now be feeling, my poor dear love, if Ihad been lost and you had been snatched from death?Read the excerpt from the adaptation "The Flood by James Baldwin.But Deucalion and Pyrrha were very sad, for they knew that they were the only persons who were left alive in all the land. At last they started to walk down the mountain side towards the plain, wondering what would become of them now, all alone as they were in the wide world.How does Baldwins decision to describe the characters feelings change the tone from Ovids original?from a feeling of disappointment and sadness to one of relieffrom a feeling of fear to one of despair and significant lossfrom a feeling of betrayal to one of camaraderiefrom a feeling of joy and pride to one of bewilderment What wave in an ECG tracing depicts ventricular repolarization? Rhonda gave the cashier $20 to pay for 3 pairs of socks. The cashier gave her $5.12. Each pair of socks cost the same amount. What is the cost in dollars and cents for each pair of socks? The Carter family just left the local pet store with Rex, their new family dog. The pet store owner told the Carter family that for the next 6 months, Rex would grow at an average rate of 9 pounds per month. Currently, Rex is 2 months old and weighs 6 pounds. Age, in months 2 3 4 5 6 7 8 Weight, in pounds 6 Part A: Complete the given table that represents Rexs current weight, in pounds, as a function of his age, in months Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points. Part C: Create a linear model that represents the Rexs current weight, in pounds, as a function of his age, in months. Part D: If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old? Upload your table, graph, and solution below. How many eight-digit numbers can be formed if the leading digit cannot be a zeroand the last number cannot be 1 or 0? What is pasteurization, and how is it used? If y=4 when x=12, find y when x=-24 If s(x) = 2 x and t(x) = 3x, which value is equivalent to (sof)(-7)?-439-141153443