The figure is formed by a square, a parallelogram with a height of 11 inches and a right triangle. Mariam found that the area of the figure is 204 square inches and that the perimeter is 88 inches. Which statement is true? A:Both Are Correct, B:Both Her Answers are Incorrect, C:Only her Perimeter is Correct, or D:Only Her AREa

Answer:

Step-by-step explanation: First you do 5*5 and get 25. Then you do 25/8 and get 3 1/8.

The expressions that represent the derivative of the function y = f(x) are dy/dx, l'(x), and lim h->0 [f(x+h) - f(x)]/h. These expressions show the rate of change of y with respect to x at any given point on the function.

The other expressions, such as S(x) + f(h), xth dh/dx, lim 10 f(x) + f(h) x+h, and lim 1-0 F(x +h)-f(x)/h, are not equivalent to the derivative of the function. It is important to understand and use the correct expressions for the derivative in order to accurately analyze and interpret the behavior of a given function.

The expressions that represent the derivative of the function y = f(x) are:

1. lim (x→0) [f(x + h) - f(x)] / h
2. dy/dx
3. f'(x)
4. dh/dx

These expressions are used to describe the rate of change of the function y = f(x) with respect to the variable x. They can be used to find the slope of the tangent line to the curve at any given point or to analyze the behavior of the function.

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Answer:

Booker:  $103.50 profit

Finley:  $34.50 profit

Step-by-step explanation:

b = # of candles Booker sold

f = # of candles Finley sold

1)  b = 3f

2) f = b - 12    substitute b=3f into this equation to get an expression all in terms of f, then solve for f

f = 3f - 12

-2f = -12

f = -12/2 = 6    now plug this into either equation and solve for b

b = 3(6) = 18

Booker:  18 candles x $5.75 profit/candle = $103.50 profit

Finley:  6 candles x $5.75 profit/candle = $34.50 profit

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

its 5.

Step-by-step explanation:

Given any real number x, the ceiling of x, denoted as ⌈x⌉, is the smallest integer n such that n is greater than or equal to x.

In other words, ⌈x⌉ is the unique integer n that satisfies the following two conditions:

n is greater than or equal to x

n is the smallest integer that satisfies condition 1

For example, if x = 2.4, then ⌈x⌉ = 3 because 3 is the smallest integer that is greater than or equal to 2.4. Similarly, if x = -1.9, then ⌈x⌉ = -1 because -1 is the smallest integer that is greater than or equal to -1.9.

The ceiling function is useful in various mathematical and computational contexts, such as in rounding up numbers, calculating the smallest integer greater than or equal to a given value, and approximating functions.

It is a fundamental concept in discrete mathematics and is used in many applications, including computer science, optimization, and operations research.

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The formula for calculating the amount of money after compounding for a period of time is expressed as;

A = P(1+r/n)^nt

P is the principal (amount deposited)

r is the rate

t is the time

n is the time of compounding

Given

P = 200.00

r = 9% = 0.09

t = 2 years

n = 1 year

Substitute the given parameters into the formula

A = 200(1+0.09/1)^1(2)

A = 200(1.09)^2

A = 200(1.1881)

A = 237.62

Hence he will be able to spend 237.62 on the bike

Answer: D.

Step-by-step explanation:

For an absolute value function, the vertex of \(f(x) = |x+h| + k\) is defined as the point (-h, k) for the coordinate (x, y).

When x is equal to negative h, the value for x and value for h effectively cancel out, and only the positive k remains, hence the vertex being (-h, k).

The function given has a vertex at (2, 3). We know that the vertex of an absolute function is (-h, k), so h must equal -2 and k must equal 3.

The equation:

\(f(x) = |x-2| + 3\)

By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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Answer:

C) 4/25

Please mark me brainliest

♥️❤️♥️❤️♥️

Answer:

c

Step-by-step explanation:

:)

Answer:

Faraday's law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force —a phenomenon known as electromagnetic induction.

Step-by-step explanation:

The angle at which golf ball should be hit to land in the hole is 13.65°.

Given information is,
Horizontal distance of golf ball from hole = 420 ft or 140 yd
Height of golf ball from hole = 55 ft
Initial velocity of golf ball = 120 ft/s
Let, Angle at which golf ball should be hit to land in the hole is θ.The range of golf ball is given by:
R = u²/g × sin2θ
Where,u = Initial velocity of golf ball
g = acceleration due to gravity= 32 ft/s²
R = Range of golf ball
Therefore,420 = 120²/g × sin2θ
By solving this equation, the value of sin2θ is obtained,2 sinθ cosθ = 8400/g
The value of sinθ can be determined by solving the above equation, sinθ = (8400/g)/√(4 + (8400/g)²)
Therefore,θ = 0.5sin⁻¹(8400/g√(4 + (8400/g)²))
The value of θ can be calculated,θ = 0.5sin⁻¹(8400/32√(4 + (8400/32)²))= 0.5sin⁻¹(8400/32√(4 + 2625))= 0.5sin⁻¹(8400/32√(2629))= 0.5sin⁻¹(8400/181.33)= 0.5sin⁻¹(46.337)= 0.5 × 27.31= 13.65°

Therefore, the angle at which golf ball should be hit to land in the hole is 13.65°.

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The derivative of \(f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)\) is \(f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}\).

In this question we shall use the following derivative rules:

Derivative of a sum of functions

\(\frac{d}{dt}(f(t) + g(t)) = \frac{df(t)}{dt} + \frac{dg(t)}{dt}\) (1)

Derivative of a product of functions

\(\frac{d}{dt}(f(t)\cdot g(t)) = \frac{df(t)}{dt}\cdot g(t) + f(t)\cdot \frac{dg(t)}{dt}\) (2)

Derivative of a constant

\(\frac{d}{dt}(k) = 0\), \(\forall k \in \mathbb{R}\) (3)

Derivative of a function multiplied by a constant

\(\frac{d}{dt}(c\cdot f(t)) = c\cdot \frac{df(t)}{dt}\), \(\forall\, c\in \mathbb{R}\) (4)

Derivative of the cosine function

\(\frac{d}{dt} \cos t = -\sin t\) (5)

Derivative of the tangent function

\(\frac{d}{dt}\tan t = \sec^{2} t\) (6)

Chain rule

\(\frac{d}{dt}f[u(t)] = \frac{df(u)}{du}\cdot \frac{du(t)}{dt}\) (7)

Let be \(f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)\), then the derivative of \(f(x)\) is:

\(f'(x) = \sec^{2}x\cdot (4 + 3\cdot \cos x) + (3+\tan x)\cdot (-3\cdot \sin x)\)

\(f'(x) = 4\cdot \sec^{2}x+3\cdot \sec x -9\cdot \sin x -3\cdot \sin x\cdot \tan x\)

\(f'(x) = \frac{4+3\cdot \cos x}{\cos^{2}x} -\frac{9\cdot \sin x \cdot \cos x+3\cdot \sin^{2}x}{\cos x}\)

\(f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}\)

The derivative of \(f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)\) is \(f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}\).

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Answer:

6.5 feet

Step-by-step explanation:

the formula for the area is A=l*w   l=length  w=width

A=l*w

78=l*12

Divide both sides by 12

78/12=6.5

Answer:

Step-by-step explanation:

a=0.5

Answer:

32.36

Step-by-step explanation:

Answer:

32.36

Step-by-step explanation:

Answer:

x = 40

Step-by-step explanation:

We have to find,

→ the value of x in the equation.

The equation is,

→ (x/2) + 3 = 23

Now the value of x will be,

→ (x/2) + 3 = 23

→ x/2 = 23 - 3

→ x/2 = 20

→ x = 20 × 2

→ [ x = 40 ]

Hence, the value of x is 40.

Answer:

44 square units

Step-by-step explanation:

We can split the figure into 4 separate figures :

Area of the left triangle

Area of the right triangle

Area of the rectangle

Area of the right triangle

Area of the figure

Answer:

\(8\sqrt{5}+3\sqrt{30}\)

Step-by-step explanation:

When we have any quantity being multiplied to an expression, we can use the distributive property.  The distributive property says that \(a(b+c)=ab+ac\).  In other words, we can distribute the outer number inside the parentheses.  

Using the distributive property, we can then simplify the given equation as follows:

\(\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}\)

Finally, you should recall that when multiplying square roots, you can simply bring all the numbers inside of one root.  For instance, \(\sqrt{2}*\sqrt{3}=\sqrt{2*3}=\sqrt{6}\) (note, this does not work for addition or subtraction, only multiplication or division).  Therefore, we can simplify \(\sqrt{6}\sqrt{5}=\sqrt{6*5}=\sqrt{30}\).  

Finally, we can combine our answer into \(\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}=8\sqrt{5}+3\sqrt{30}\)

The equation of the tangent line at (6, 0) is y = 1/6e⁶x - e⁶

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

6x - 5x⁸y⁷ = 36e⁶y

Calculate the slope of the line by differentiating the function

So, we have

\(dy/dx = \frac{-6 + 40x^7y^7}{-36e^6 - 35x^8y^6}\)

The point of contact is given as

(x, y) = (6, 0)

So, we have

\(dy/dx = \frac{-6 + 40 * 6^7 * 0^7}{-36e^6 - 35 * 6^8 * 0^6}\)

dy/dx = 1/6e⁶

The equation of the tangent line can then be calculated using

y = dy/dx * x + c

So, we have

y = 1/6e⁶x + c

Using the points, we have

1/6e⁶ * 6 + c = 0

Evaluate

e⁶ + c = 0

So, we have

c = -e⁶

So, the equation becomes

y = 1/6e⁶x - e⁶

Hence, the equation of the tangent line is y = 1/6e⁶x - e⁶

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4x - 2y = 14

y = 0.5x - 1

2y = x - 2

4x - x + 2 = 14

3x = 12

x = 4

y = 1

( 4, 1 )

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Answer:

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The Markov Chain Model is the best model to predict what activity people will do in two days based on the current weather. It is suitable for predicting outcomes based on probabilities over time, and it considers only the current weather conditions and the probabilities of the different activities.

To predict what activity people will do in two days based on the current weather, I would use a Markov Chain Model. This model is suitable for predicting outcomes based on probabilities over time. In this case, the model would use the current weather (sunny) and the probabilities of the different activities (going for a walk, shopping, or staying home and cleaning) to predict the probability of each activity in two days. The Markov Chain Model assumes that the probability of an activity depends only on the current weather, and not on any previous or future weather conditions.

A Markov Chain Model is the most appropriate model to predict what activity people will do in two days based on the current weather. This model is suitable for predicting outcomes based on probabilities over time, and it would use the current weather (sunny) and the probabilities of the different activities (going for a walk, shopping, or staying home and cleaning) to predict the probability of each activity in two days. The Markov Chain Model assumes that the probability of an activity depends only on the current weather, and not on any previous or future weather conditions.

In conclusion, the Markov Chain Model is the best model to predict what activity people will do in two days based on the current weather. It is suitable for predicting outcomes based on probabilities over time, and it considers only the current weather conditions and the probabilities of the different activities. By using this model, we can make accurate predictions about what people are likely to do in the future, based on the current weather conditions.

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By applying the knowledge of similar triangles, the lengths of AE and AB are:

a. \(\mathbf{AE = 3.9 $ cm}\\\\\)

b. \(\mathbf{AB = 2.05 $ cm} \\\\\)

See the image in the attachment for the referred diagram.

This implies that:

Given:

\(EC = 8.1 $ cm\\\\DC = 5.4 $ cm\\\\DB = 2.6 cm\\\\AC = 6.15 $ cm\)

a. Find the length of AE:

EC/DC = AE/DB

\(\frac{8.1}{5.4} = \frac{AE}{2.6}\)

\(5.4 \times AE = 8.1 \times 2.6\\\\5.4 \times AE = 21.06\)

\(AE = \frac{21.06}{5.4} = 3.9 $ cm\)

b. Find the length of AB:

\(AB = AC - BC\)

AC = 6.15 cm

To find BC, use AC/BC = EC/DC.

\(\frac{6.15}{BC} = \frac{8.1}{5.4}\)

\(BC \times 8.1 = 6.15 \times 5.4\\\\BC = \frac{6.15 \times 5.4}{8.1} \\\\BC = 4.1\)

\(AB = AC - BC\)

\(AB = 6.15 - 4.1\\\\AB = 2.05 $ cm\)

Therefore, by applying the knowledge of similar triangles, the lengths of AE and AB are:

a. \(\mathbf{AE = 3.9 $ cm}\\\\\)

b. \(\mathbf{AB = 2.05 $ cm} \\\\\)

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The insurance policy's anticipated value is -$81 for the one year life insurance policy.

Consider the various factors and the man's potential benifits.

-$165 because he already paid that sum.

The beneficiary could earn as a potential profit.

140000-165 = $139835

The probability of surviving is 0.9994.

The likelihood of not living is 0.0006.

The expected value is given by;

E(v) = (-165)(0.9994) + (139835)(0.0006)

E(v) = -164.901 + 83.901

E(v) = -81.

Thus, the insurance policy's anticipated value is -$81.

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Answer:

63 inches

Step-by-step explanation:

1 foot = 12 inches

5 feet = 60 inches

60+3 = 63 inches

x = oz of 100% acid

y = oz of 4% acid

the first solution is 100% acid, if the amount of ounces in it is "x", how much only acid is there?  well, (100/100) * x = 1.0x.

likewise, how much only acid is there in the 4% solution?  well, (4/100) * y = 0.04y.

\(\begin{array}{lcccl} &\stackrel{\stackrel{oz}{solution}}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of acid }}{amount}\\ \cline{2-4}&\\ \textit{first solution}&x&1.00&1.0x\\ \textit{second solution}&y&0.04&0.04y\\ \cline{2-4}&\\ mixture&480&0.08&38.4 \end{array}~\hfill \begin{cases} x+y=480\\\\ x+0.04y=38.4 \end{cases}\)

\(x+y=480\implies y=480-x~\hfill \stackrel{\textit{substituting on the 2nd equation}}{x+0.04(480-x)=38.4} \\\\\\ x+19.2-0.04x=38.4\implies 0.96x+19.2=38.4\implies 0.96x=19.2 \\\\\\ x=\cfrac{19.2}{0.96}\implies \boxed{x=20}~\hfill \boxed{\stackrel{480-20}{y=460}}\)

The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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This is because the values of f(x) in the table match the corresponding values obtained by evaluating the polynomial function for the given input values of the function represented by the data a polynomial function is represented by the data is f(x) = x^3 - x^2 - 24.

A polynomial is an expression with more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable. A polynomial function is a function that includes a polynomial expression with an independent variable (x) that can only take on integer values because of its discrete nature.

Choose the function represented by the data: The polynomial function represented by the data is f(x) = x^3 - x^2 - 24.

A table representing the function f(x) = x^3 - x^2 - 24 is shown below:

x | f(x)

0 | -24

1 | -14

2 | 0

4 | 40

Therefore, the function represented by the data is f(x) = x^3 - x^2 - 24.

The provided table displays the values of the function f(x) for different input values of x. By substituting the corresponding values of x into the function, we can observe the corresponding output values. This allows us to identify the pattern and equation that represents the function.

In this case, the table shows that when x is 0, the value of f(x) is -24. When x is 1, f(x) is -14. When x is 2, f(x) is 0. And when x is 4, f(x) is 40.

Based on these data points, we can conclude that the function represented by the data is f(x) = x^3 - x^2 - 24.

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We find that Option 2, f(x) = \((x^3)/4 + 2x^2 - 24\), matches the data given in the table.

Based on the data given in the table, we need to determine the polynomial function that represents the data.
To do this, we can compare the values of f(x) in the table with the given options for the polynomial functions. We are looking for a function that matches the given data points.

Let's evaluate each option using the x-values from the table:
Option 1: f(x) = \(x^3 - x^2 - 24\)
For x = 0,\(f(0) = 0^3 - 0^2 - 24 = -24\) (matches the data)
For x = 1, \(f(1) = 1^3 - 1^2 - 24 = -24 - 1 - 24 = -49\) (does not match the data)
For x = 2,\(f(2) = 2^3 - 2^2 - 24 = 8 - 4 - 24 = -20\) (does not match the data)
Option 2: \(f(x) = (x^3)/4 + 2x^2 - 24\)
For x = 0,\(f(0) = (0^3)/4 + 2(0^2) - 24 = 0 - 0 - 24 = -24\) (matches the data)
For x = 1,\(f(1) = (1^3)/4 + 2(1^2) - 24 = 1/4 + 2 - 24 = -20.75\)(does not match the data)
For x = 2, \(f(2) = (2^3)/4 + 2(2^2) - 24 = 8/4 + 8 - 24 = -14\)(matches the data)
Option 3: f(x) = -24 - 14(3/3)(3/4)
Simplifying, f(x) = -24 - 14(1)(3/4) = -24 - 14(3/4) = -24 - 10.5 = -34.5 (does not match the data)
Option 4: \(f(x) = -2 1/4 * x^2 + 24\)
For x = 0, \(f(0) = -2 1/4 * 0^2 + 24 = 24\) (does not match the data)
For x = 1,\(f(1) = -2 1/4 * 1^2 + 24 = -2 1/4 + 24 = 21.75\) (does not match the data)
For x = 2,\(f(2) = -2 1/4 * 2^2 + 24 = -2 1/4 * 4 + 24 = -9 + 24 = 15\) (does not match the data)
Option 5: \(f(x) = 3/4 * x^2 - 3x + 24\)
For x = 0, \(f(0) = 3/4 * 0^2 - 3(0) + 24 = 24\) (does not match the data)
For x = 1, \(f(1) = 3/4 * 1^2 - 3(1) + 24 = 3/4 - 3 + 24 = 21.75\) (does not match the data)
For x = 2,\(f(2) = 3/4 * 2^2 - 3(2) + 24 = 3/4 * 4 - 6 + 24 = 3 - 6 + 24 = 21\)(matches the data)

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