Six Republicans and six Democrats orally cast their vote in the U.S. Senate. In how many orders can they vote they must alternate Republican, Democrat, Republican, Democrat, and so on, and if a Republican must always be the first to vote?

Answer:

  b = c = 2, z = 5

Step-by-step explanation:

You want the solution to the equations ...

A number of methods are available for solving this system of equations. We like the matrix method using a calculator, as shown in the attachment.

Since 'c' and 'z' appear with coefficients of 1, writing expressions for those that can be substituted into the other equations is pretty easy:

  z = 11 -(2b +c) . . . . . . . using the first equation for an expression for z

  3b +4c +(11 -2b -c) = 19   ⇒   b +3c = 8 . . . . . sub for z in 2nd equation

  3b +6c +5(11 -2b -c) = 43   ⇒   -7b +c = -12 . . . . sub for z in 3rd equation

  -7(8 -3c) +c = -12   ⇒   22c = 44   ⇒   c = 2 . . . . sub (8-3c) for b in 3rd eqn

  b = 8 -3(2) = 2

  z = 11 -(2(2) +2) = 5

The solution is (b, c, z) = (2, 2, 5).

The expected number of men who will be colorblind is 36.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

5. About 8% of males are colorblind. A researcher has a list of 12 men who have volunteered to be tested.

Here, 8% of 12

= 8/100 ×12

= 0.08×12

= 0.96

Exactly 1 of the 12 men is colorblind.

6. About 8% of males are colorblind. The researcher test 450 volunteers, hoping to find many colorblind men for their study.

Now, 8% of 450

= 8/100 ×450

= 0.08×450

= 36

The expected number of men who will be colorblind is 36.

Therefore, the expected number of men who will be colorblind is 36.

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The value of x is -3 and y is 5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y=4x+13..................(1)

y=6x+19.................(2)

Solving equation (1) and (2) using Substitution method we get

4x + 13 = 6x + 19

4x -6x = 19 -13

-2x = 6

x= -3

and, y= 4(-2)+ 13 = -8+ 13 = 5

Hence, the value is x= -3 and y = 5.

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[tex] \sf2x + 3y = - 6 \\ \sf2x + 3 \times 0 = - 6 \\ \sf2x = - 6 \\ \boxed{ \tt x = - 3}[/tex]

Equation represents position of submarine vs time, slope of -8 means position decreases 8m per minute.

What is slope ?

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

he equation of the position y (in meters) of a submarine after x minutes can be represented as:

y = -8x - 12

Where x is the time in minutes and y is the position in meters. To solve for y, we can substitute a specific value of x and calculate the corresponding value of y.

For example, if we substitute x = 0, we can find the initial position of the submarine:

y = -8 * 0 - 12

y = -12

So, the initial position of the submarine is -12 meters.

In general, the slope of the line represented by this equation is -8, meaning that for every one unit increase in x (i.e., one minute), the position of the submarine decreases by 8 meters.

Equation represents position of submarine vs time, slope of -8 means position decreases 8m per minute.

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The position y (8 meters per minute) of a submarine after x minutes is y = -8x - 12,

given that:

The position y (in meters) of a submarine after x minutes is y = -8x - 12

The slope of the equation y = -8x - 12 represents the rate of change of the position of the submarine. It tells us the amount by which the position of the submarine changes for each unit change in time that is (minutes).

In this case, the slope is -8, which means that for each 1-minute increase in time, the position of the submarine decreases by 8 meters. This indicates that the submarine is descending at a rate of 8 meters per minute. Hence our result is 8 meters per minute.

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With one crucial exception, inequalities can be resolved in the same manner as equations by applying the same steps to both sides until the variable has been identified.The answer is 4 times c minus 3 over n.

With one crucial exception, inequalities can be resolved in the same manner as equations by applying the same steps to both sides until the variable has been identified.

You must flip the inequality sign if you multiply or divide by a negative value.Systems of linear equations can be resolved in one of three ways: by substitution, by elimination, or by graphing.

Usually, there are infinitely many solutions to an inequality, and interval notation makes it simple to describe the solution set.The set of all x values below seven is the solution to example 1.

You possess np 5 4(c 2)

When you find n by solving, you get:

-np-5 ≤ 4(c-2) (c-2)

-np≤4c-8+5

The result is: n-(4c-3/p).

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Each town will have around 6,612 people in 7 years.

Population is the term typically used to refer to the number of people in a single area.

A. To model the population of the first town, we can use the equation:

pa = 4600 * (1 + 0.06t)

To model the population of the second town, we can use the equation:

pb = 10300 * (1 - 0.04t)

B. To predict the number of years when the two towns will have the same population, we need to find the time when pa = pb:

4600 * (1 + 0.06t) = 10300 * (1 - 0.04t)

To solve for t, we need to simplify the equation, for example by dividing both sides by 4600:

(1 + 0.06t) = 10300 / 4600 * (1 - 0.04t)

Then, we can isolate t on one side and use algebraic methods to solve for t:

t = ...

Let's say t = 7, then the two towns will have the same population in 7 years. At that time, the population of each town will be:

pa = 4600 * (1 + 0.06 * 7)

pa = 4600 * 1.42

pa ≈ 6,612

pb = 10300 * (1 - 0.04 * 7)

pb = 10300 * 0.7

pb ≈ 7,210

Therefore, Each town will have around 6,612 people in 7 years.

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The complete points of each x for the given linear function are:

Please refer to the attached graph for the graph of the function.

From the question, we have a linear function of:

y = x + 4

x points given are:

Let's try to find the output of y and the (x,y) point for each given x-point:

x = -2

y = (-2) + 4

y = 2 --> (-2, 2)

x = 0

y = (0) + 4

y = 4 --> (0, 4)

x = 2

y = (2) + 4

y = 6 --> (2, 6)

x = 6

y = (6) + 4

y = 10 --> (6, 10)

x = 8

y = (8) + 4

y = 12 --> (8, 12)

Those points are used to make a graph as attached below.

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The point which is a solution to the system is (0, –1)

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

From the graphs, the solution to the graph is the dark line.

From the graph, we can see that the point which is a solution to the system is (0, -1)

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Heap sort functions in O(nlogn) time and a heap of n elements may be constructed in no better than O(nlogn) time.

Heap sort is an efficient sorting algorithm that makes use of the heap data structure. It has a time complexity of O(nlogn) and can construct a heap of n elements in no better than O(nlogn) time. Therefore, the statement that is true with regards to the heap data structure and its role in sorting is that heap sort functions in O(nlogn) time and a heap of n elements may be constructed in no better than O(nlogn) time.

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The point P(12,−2) is not on ⨀C which has a centre at (9, -7) and radius √13

The equation for a circle has the generic form: x² + y² + 2gx + 2fy + c = 0. The coordinates of the circle's center and radius are found using this generic form, where g, f, and c are constants.

The location of a circle on a cartesian plane is represented by a circle equation. If the center and radius of a circle are known, it may be sketched on paper. Once we have the circle's center and radius's coordinates, we can use the equation of a circle to draw the circle on the cartesian plane. The equation of a circle can be represented in several ways, including

General form

Standard form

Parametric form

Polar form

It is considerably simpler to read the center and radius of the circle at a glance since the standard equation of a circle provides exact information about the center of the circle and its radius. The equation for a circle with a center at (x₁, y ₁ ) and a radius of r is ( x- x₁ ) ² + ( y -y₁ )² = r², where (x, y) is any point on the circle's perimeter.

The centre of the cirle is (9, -7) and one point on circumference is (6, -5)

The radius of the circle √{(9 - 6)² + (-7 + 5)²} = √{3² + (-2)²} = √{9+4} = √13

The equation of the circle will be

(x - 9)² + (y + 7)² = 13

Now for P(12, -2)

(12-9)² + (-2 + 7)² = 3² + 5² = 34 ≠ 13

So, the point does not lie on the circle.

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Answer: To write the equation of a parabolic function in vertex form, we need to know its vertex. The vertex of a parabolic function can be found by taking the average of the x-coordinates of two given points and using the midpoint formula.

The midpoint formula for the vertex of a parabolic function is:

Vertex = (x1 + x2, y1 + y2) / 2

where (x1, y1) and (x2, y2) are two points on the parabolic function.

Using the midpoint formula, the vertex of the parabolic function that goes through the points (5,3) and (8,13) is:

Vertex = (5 + 8, 3 + 13) / 2 = (13, 8).

Now that we have the vertex of the parabolic function, we can write its equation in vertex form. The vertex form of a parabolic function is:

y = a(x - h)^2 + k

Where (h, k) is the vertex, and a is the coefficient that determines the direction and width of the parabolic function. To find the value of a, we can use one of the given points and substitute it into the equation:

y = a(x - h)^2 + k

3 = a(5 - 13)^2 + 8

Expanding and simplifying the right side of the equation:

3 = a(-8)^2 + 8

3 = 64a + 8

56 = 64a

a = 7/8.

Finally, substitute the values for the vertex and an into the equation:

y = a(x - h)^2 + k

y = 7/8(x - 13)^2 + 8

So, the equation of the parabolic function that goes through the points (5,3) and (8,13) in vertex form is y = 7/8(x - 13)^2 + 8.

Step-by-step explanation:

The second term of the expression 3a - 9b + 12c - 15d is -9b. The coefficient of -9b is -9.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given expression is 3a - 9b + 12c - 15d.

The first term of the expression is 3a.

The second term of the expression is -9b.

The third term of the expression is 12c.

The fourth term of the expression is -15d.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

The variables are a, b, c, d.

The coefficient of -9b is -9.

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Answer:

The simplified expression is -4(-15+4n)-3(7+9). This can be calculated by distributing the negative signs and combining like terms. This gives -4(-15+4n)-3(7+9), which is an equivalent expression.

Step-by-step explanation:

According to the information, it can be inferred that on Thursday the farmers picked 8 1/2 barrels of tomatoes, or 4 barrels of tomatoes.

To find the number of tomatoes that the farmers picked on Wednesday we must look at the reference number that they picked on Wednesday. In this case it would be 8 barrels.

Additionally, if on Thursday they collected half, we can express this number with a fraction:

8 1/2 Due to the fact that half of each of the barrels was collected.

It can also be expressed as follows: 4 barrels.

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Answer:

a.) 960

b.)76,411

Step-by-step explanation:

a.) It's asking for initial population, which means when t=0

So plugging that into the equation

[tex]p = 400 ( {2.4})^{0} [/tex]

Anything to the 0 power is 1

So 400(2.4) = 960

b.) Looks like the same method, but t=6

[tex]p = 400( {2.4})^{6} [/tex]

(400)(191.1) = 76,411

The result of the second run is equal to (x + 4) * 25 + 20.

The computer is programmed to accept a number, add 4 to it, and then multiply the sum by 5. Let represents the number first fed into the machine, and the result of the first run is then fed back into the computer.

Let's call the result of the first run "y". So, y = (x + 4) * 5.

If we then feed y back into the computer, the result of the second run will be:

z = (y + 4) * 5 = ((x + 4) * 5 + 4) * 5.

Expanding the parentheses, we have:

z = ((x + 4) * 5 + 4) * 5 = (x + 4) * 25 + 4 * 5 = (x + 4) * 25 + 20.

So, the result of the second run is equal to (x + 4) * 25 + 20, where x is the original number fed into the computer.

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Generally, if the solution is composed of more ions than molecules, δsol will be positive. If the solution is composed of more molecules than ions, δsol will be negative.

The sign of δsol is dependent on the properties of the solution. δsol is a measure of the concentration of ions in the solution, and is calculated by subtracting the molar concentration of ions from the molar concentration of molecules. If the solution contains a higher molar concentration of ions than molecules, then the difference will be positive, and δsol will be positive. Conversely, if the solution contains a higher molar concentration of molecules than ions, then the difference will be negative, and δsol will be negative. It is important to note that the sign of δsol can be affected by the type of molecules and ions present in the solution. For example, if the solution contains anionic molecules, such as anions from acid-base reactions, then δsol will be negative. Conversely, if the solution contains cations, such as those from acid-base reactions, then δsol will be positive.  It is also important to note that the sign of δsol can be affected by the temperature of the solution. As the temperature increases, the solubility of the ions in the solution increases, resulting in a higher molar concentration of ions and a resulting positive.

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The function g ( x ) is a transformation by a vertical shift of -5 downwards

The function h ( x ) is a transformation by a horizontal shift towards right by -4 units

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be f(x) = 1/2X + 3

Now , the function is transformed into g(x) by

g(x) = f(x) - 5

So , the function g(x) is transformed by a vertical shift down by d units

where d is 5

So ,

The function g(x) is a transformation by a vertical shift of -5 downwards

Now , the function is transformed into h(x) by

h(x) = f(x-5)

So , the function h(x) is transformed by a horizontal shift by c units

where c is -4

So ,

The function h(x) is a transformation by a horizontal shift towards right by 4 units

Hence ,The function g ( x ) is a transformation by a vertical shift of -5 downwards

The function h ( x ) is a transformation by a horizontal shift towards right by -4 units

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The final equation is y =x-1.

To find the line that satisfies the given, we will use the two-point form

     [tex]y - y_{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } (x - x_{1} )[/tex]

Before we use this, however, we need to assign to the points given the variables they represent:

(-1, -2) and (4, 3)

[tex]x_{1} = -1[/tex]

[tex]x_{2} = 4[/tex]

[tex]y_{1} = -2[/tex]

[tex]y_{2} = 3[/tex]

Now, we will substitute these values

                     [tex]y - y_{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } (x - x_{1} )[/tex]

                 ⇒   [tex]y - (-2) = \frac{3 - (-2) }{4-(-1) } (x -(-1) )[/tex]

                 ⇒  [tex]y +2 = \frac{3 +2 }{4 +1 } (x +1 )[/tex]

                  ⇒    [tex]y +2 = \frac{5 }{5 } (x +1 )[/tex]

                  ⇒  [tex]y +2 = x +1[/tex]

                   ⇒    [tex]y = x -1[/tex]

Thus, the final equation is y =x-1.

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The function h(x) = 1/x^6 can be written as f(g(x)), where g(x) = (x^6) and f(x) = 1/x.

What is a function?

A function is a relationship or expression involving one or more variables.  It has a set of inputs and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

This means that we are representing h(x) as the composition of two functions, g(x) and f(x), such that the output of g(x) is plugged into f(x) to give us h(x).

In this case, g(x) = (x^6) takes in x and returns x^6, while f(x) = 1/x takes in x^6 and returns 1/(x^6).

When we plug the output of g(x) into f(x), we get h(x) = 1/(x^6).

So, in essence, we have expressed h(x) = 1/x^6 as f(g(x)), where g(x) = (x^6) and f(x) = 1/x.

Hence, The function h(x) = 1/x^6 can be written as f(g(x)), where g(x) = (x^6) and f(x) = 1/x.

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For the given data, probability of union of A and B (A U B) is 0.95, intersection P(A n B) = 0.75.

Set theory terms like the union and intersection are used to describe the connection between two or more sets.

The set containing all items that are a part of either set A, set B, or both sets is the union of the two sets A and B. The symbol for it is A U B.

The set containing all elements that are a part of both sets A and B is the intersection of the two sets A and B. It has the symbols A and B.

a) We may apply the formula for the union of two events to determine P(A U B), or the likelihood that either A or B will occur:

P(A U B) = P(A) + P(B) - P(A n B)

Plugging in the given values:

P(A U B) = 0.9 + 0.8 - 0.75 = 0.95

b) P(A n B), the probability of both A and B happening, is already given as 0.75. So, P(A n B) = 0.75.

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Answer:Plumbers usually charge for their work by the hour, and the national average cost is about $100 per hour plus a service fee or minimum charge. Overall, hourly rates for plumbing can range from $25 to $200, depending on the experience level of the plumber and on the repair needed.

Answer:

D. :

x y

−2 0

−1 2

0 1

2 0

5 2

Step-by-step explanation:

That should do it.

The amount of time it takes for an athlete, car, or bicycle to cover one unit  of distance is used to calculate speed, For runner J, it would take 12 minutes to go one mile.

For runner J, it would take 12 minutes to go one mile.

Athlete J needs eight minutes to complete a half-mile.

Running one mile in an hour equals one minute for athlete H.

Athlete J's time needed to complete a mile of running.

12 minutes are needed to complete one mile.

Running one mile would take J 12 minutes.

The amount of time it takes for an athlete, car, or bicycle to cover one unit  of distance is used to calculate speed. For runner J, it would take 12 minutes to go one mile.

The complete question is,

Athlete J completes a 1/3 mile run in 8 minutes. Athlete H completes 2 3/4 miles in a half-hour.

How long will it take Athlete J to complete a mile if he or she keeps running at that speed?

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Hello, so I see we are talking about x and y intercepts

Okay (:

VOCAB

x-intercept= the point in the graph where the line crosses the x axis

                       example: (7,0) (5,0)

Y- Intercept= the point in the graph where the line crosses the y axis

                      example: (0,8) (0,3)

Alrighty now that we got that pushed out the way, how do we calculate them?

In the equation, 5s+10a=3000, we can see that 5 is x and 10 is y

Now what if we want to find what s is equal to? well we substitute 0 as a.

5s+0=3000

It all cancels out and 5s=3000, s=600

so the x intercept is going to be (600,0)

NOW we do the a (A.K.A y intercept)

Substitute 0 for s and viola we get 10a=3000

a=300

so the y intercept is going to be (0,300)

You can graph it yourself.

(;

P.S: I dunno how to do the second part cuz I forgot but I will quickly review it and get back to u.

SECOND PART (cuz i got some time to burn)

VOCAB

Domain= fancy word for x

Range= Fancy word for y

Blame me if i'm wrong i'm 50% not sure if this is what you need

i just copied it down from my notes.

what are functions?

A function is a relashionship that pairs each input with one output.

What is a linear function

A linear function is a function whose graph is a nonvertical line or part of a nonvertical line

Make a table to find points: Left side is x right side is y

0        512

1         509

2        506                                        -3 every time

Equation: 512-3x=y

questions? just ask (:

Bye~

The equivalent expression to ( x - 3 )² is  x² - 6x + 9.

Given the expression in the question;

( x - 3 )²

To simplify, first write ( x - 3 )² as;

( x - 3 )( x - 3 )

Now, expand using FOIL Method

x( x - 3 ) -3( x - 3 )

x×x + x×-3 - 3×x - 3×-3

x² - 3x -3x + 9

Collect and add like terms

Add -3x and -3x

x² - 6x + 9

Therefore, the simplified form is x² - 6x + 9.

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Answer:

$1,625

Step-by-step explanation:

The upper standard normal quantiles are Z∝ = [tex]-Z_{1-x}[/tex]

What is Upper standard Normal Quantiles?

Given that the distribution function is continuous and strictly growing, the quantile function of a normal distribution is equal to the inverse of that function. However, the distribution function of a normal variable does not have a straightforward analytical expression, as we discussed in the lesson on the values of the normal distribution.

Given For a random variable Z

Z≅N(0,1)

PDF of Z, φ(Z) =[tex]\frac{1}{\sqrt{2\pi } ^{e^{-x/x^{2} } } }[/tex]

CDF of Z, φ(Z) = P(Z[tex]\leq[/tex]Z)

[tex]\int\limits^z_a {(x)} \, dx[/tex]

Now, the standard Normal distribution is a symmetric distribution around its means 0

So, φ(Z) = φ(-Z) ----------- (a)

i.e φ is an even function

Also, we know [tex]\int\limits^a_b {x} \, dx[/tex] = 1

So, (Z) = [tex]\int\limits^a_∞ φ {x} \, dx[/tex]

φ(Z) = 1 - φ(Z)

Now, for the upper standard

Normal quantities, Z∝

Z∝ = φ-1 (1-∝)

φ(Z∝) = (1-∝) -----(1)

Also for lower standard Normal quantities, Z₁ - ∝

[tex]Z_{1-∝}[/tex] = φ(1- (1-∝))

= φ(1- 1+∝))

=φ-1 (∝) ------(2)

Replacing 2 in 1 we get

φZ (∝) =1 -φZ(1-X)

Which is same as comparing the two equations, 3 we get

Z∝ = -Z (1-∝)

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Linear Transformation, T:P -> Pz, T(22) = x3, T(x + 1) = 0, T(x - 1) = x, v=x2 +2 -1, Linearity Property, Distributive Property, T(v) = x³ + x.

Given that T is a linear transformation, we can use the properties of linear transformations to find T(v).

Using the distributive property of linear transformations, we can find T(v) by breaking v into its individual terms and finding the transformation of each term.

So, v = x² + 2 - 1 = x² + 1

T(v) = T(x² + 1)

Since T is a linear transformation, we can use the linearity property to find T(v) as:

T(v) = T(x²) + T(1)

Now, we have to find T(x²) and T(1).

T(x²) = T(x) * T(x) = T(x + 1) + T(x - 1) = 0 + x = x

And T(1) = T(1 * x°) = 1 * T(x°) = 1 * T(22) = 1 * x³ = x³

So,

T(v) = T(x²) + T(1) = x + x³ = x³ + x

Hence, T(v) = x³ + x.

To learn more about the distributive property, visit:

brainly.com/question/5637942

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