If the temperature is 20c what is it in Fahrenheit.

To estimate the proportion of junior executives leaving large manufacturing companies within three years within a 3% margin of error and a 95% confidence level, we can use the formula for sample size calculation

 Thus, the research firm should survey approximately 1,085 junior executives to update the study with a 3% margin of error and a 95% confidence level Where:n  = required sample sizeZ  = Z-value corresponding to the desired confidence level (in this case, 0.95)p  = estimated proportion from the previous study (30% or 0.3)

E = margin of error (3% or 0.03)P lugging in the values, we have:

n = (1.96^2 * 0.3 * (1 - 0.3)) / 0.03^2n  ≈ 1079.68 Rounding up to the nearest whole number, the required sample size is approximately 1080. Therefore, the answer closest to this value is 1,085.

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(a) To calculate the line integral ∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ over the circle C given by (x−8)²+(y−2)² = 16 oriented counterclockwise, we need to parametrize the curve C. The parametric equations for a circle of radius 4 centered at (8, 2) can be written as x = 8 + 4cos(t) and y = 2 + 4sin(t), where t ranges from 0 to 2π.

Substituting these expressions into the integrand and evaluating the dot product, we have:

∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ = ∫(4(8 + 4cos(t))² - (2 + 4sin(t)))dx + 5((2 + 4sin(t))² + (8 + 4cos(t)))dy.

Using the parametric equations and differentiating with respect to t, we can express dx and dy in terms of dt:

dx = -4sin(t)dt,

dy = 4cos(t)dt.

Substituting these expressions into the integral, we get:

∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ = ∫(4(8 + 4cos(t))² - (2 + 4sin(t)))(-4sin(t))dt + 5((2 + 4sin(t))² + (8 + 4cos(t)))(4cos(t))dt.

Integrating with respect to t over the range 0 to 2π, we can evaluate the integral to obtain the final answer.

(b) To calculate the line integral ∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ over the circle C given by (x−a)²+(y−b)² = r² in the xy-plane oriented counterclockwise, we need the specific values for a, b, and r. Please provide the values for a, b, and r in order to proceed with the calculation.

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The expression that represents the side length of the square is as follows:

A square is a quadrilateral with 4 sides equal to each other. The opposite sides are parallel to each other. The sum of angles in a square is 360 degrees. Each angle in the square is 90 degrees.

The sum of the whole side of a square is the perimeter of the square.

Therefore, the perimeter of the square is 80 minus 64 y units.

Let's use expression to find the side length as follows;

perimeter of a square = 4l

where

Therefore,

80 - 64y = 4l

divide both sides of the equation by 4

l = 80 / 4 - 64y / 4

l = 20 - 16y

Therefore,

side length =  20 - 16y

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Answer:

yo

Step-by-step explanation:

the answer is C

Answer:

Step-by-step explanation:

S = \(R^{2} *\pi\)

S = \(4^{2} * \pi\)

S = 16 * 3,14

S = 50,24

The value of the given equation is 12.

In order to solve this question, the BODMAS rule would be used. The BODMAS rule gives the order in which mathematical operations can be solved. The order is:

In the numerator:

the addition would be done first: 3² + 1 = 9 + 1 = 10

Then the subtraction would be done next = 14 - 10 = 4

Now determine the square of the term in the bracket : 4²= 16

In the denominator:

The multiplication would be solved first: 3 x 1/4 = 3/4

The next step is  to solve the division : 1 ÷ 3/4 = 1 x 4/3 = 4/3

The fraction becomes : 16 ÷ 4/3

16 x 3/4 = 12

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Answer:

The answer is 432

Step-by-step explanation:

I did the k 12 quiz and I got it right! good luck

Answer:

3 of the pyramids

Step-by-step explanation:

Given:

Hexagonal Prism

Hexagonal based pyramid

Required

How many of the pyramid will fill up the prism

To do this, we start by calculating the volumes of both shapes.

Let V1 be the volume of the hexagonal prism

\(V_1 = \frac{3\sqrt{3}}{2}a^2h\)

Where: a = base and h = height

Let V2 be the volume of the hexagonal based pyramid

\(V_2 = \frac{\sqrt{3}}{2}a^2h\)

Where: a = base and h = height

The number of the pyramid that can occupy the prism is calculated by dividing V1 by V2

\(Number = \frac{V_1}{V_2}\)

\(Number = \frac{3\sqrt{3}}{2}a^2h /\frac{\sqrt{3}}{2}a^2h\)

Convert division to multiplication

\(Number = \frac{3\sqrt{3}}{2}a^2h * \frac{2}{\sqrt{3}a^2h}\)

\(Number = \frac{3\sqrt{3}}{2} * \frac{2}{\sqrt{3}}\)

\(Number = \frac{3\sqrt{3}}{1} * \frac{1}{\sqrt{3}}\)

\(Number = \frac{3*1}{1} * \frac{1}{1}\)

\(Number = 3\)

The linear function for this problem is defined as follows:

y = x + 50.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph touches the y-axis at y = 50, hence the intercept b is given as follows:

b = 50.

When x increases by 10, y also increases by 10, hence the slope m is given as follows:

m = 10/10

m = 1.

Hence the function is given as follows:

y = x + 50.

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The value of Angle BXC is 70°

Corresponding angles are the angles which are formed in matching corners with the transversal when two parallel lines are intersected by any other line called the transversal.

The line which joins the two parallel lines is usually called a transversal.

Angle XBC is 55° because it is corresponding with Angle AXY

From triangle XBC, Angle XBC is equal to XCB( base angles of an isosceles triangle)

so XBC = XCB = 55°

Also,

XBC + XCB + BXC = 180( sum of angles in triangle XBC)

55 + 55 + BXC = 180

110 + BXC = 180

BXC = 180 - 110

BXC = 70°

In conclusion, Angle BXC is 70°

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Answer:

\(\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\)

\(x=-\frac{3}{8}+i\frac{\sqrt{31}}{8},\:x=-\frac{3}{8}-i\frac{\sqrt{31}}{8}\)

Step-by-step explanation:

\(8x^2+6x=-5\)

\(\mathrm{Add\:}5\mathrm{\:to\:both\:sides}\)

\(8x^2+6x+5=-5+5\)

\(8x^2+6x+5=0\)

\(\underline{\mathrm{Solve\: further\:using\:the\:quadratic\: formula}}\)

\(x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:8\cdot \:5}}{2\cdot \:8}\)

\(x_{1,\:2}=\frac{-6\pm \:2\sqrt{31}i}{2\cdot \:8}\)

\(\mathrm{Separate\:the\:solutions}\)

\(x_1=\frac{-6+2\sqrt{31}i}{2\cdot \:8},\:x_2=\frac{-6-2\sqrt{31}i}{2\cdot \:8}\)

\(\bold{\frac{-6+2\sqrt{31}i}{2\cdot \:8}=-\frac{3}{8}+\frac{\sqrt{31}}{8}i}\)

\(\bold{\frac{-6-2\sqrt{31}i}{2\cdot \:8}=-\frac{3}{8}-\frac{\sqrt{31}}{8}i}\)

More information

Quadratic equation formula:

\(\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\)

\(x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

Answer:

1. $97,265

2. $17,865

Step-by-step explanation:

Step one:

given data

cost of the house=  $397,000.

we are told that the commission is 4.5% real estate agency

and also the agent commission is 20%

Step two:

1.  How much did the agency make on the house?

this amount is 20% plus  4.5% together.

=20/100*397,000 +4.5/100*397,000

=0.2*397,000. +0.045*397,000.

=79400+17865

=97,265

The agent made a total of $97,265 on the house

2. How much did the agent earn in commission?

in commission, the rate is 4.5% which amounts to $17,865

The percentage that she spent on present for her sister is 26.67%

What does % example mean?

Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Given that :

She spent = 360 * 1/5 = $72 on presents for her parents

she spent = 360 - 72 = 288 * 2/3 = $192 on presents for her friends

She spent = 288 - 192 = $96 on presents for her sister

Percentage of the $360 that she spent on presents for her sisters is

96/360 * 100 = 26.67%

Hence the percentage that she spent on present for her sister is 26.67%

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\(\frac{12}{5}\)  or  \(2 \frac{2}{5\\}\)

Keep \(\frac{2}{5}\) the same

change the division sign to multiplication \(\frac{2}{5} \\\) × \(\frac{1}{6\\}\)

Flip  \(\frac{1}{6}\)  so that the denominator is on top and the numerator is on the bottom like this \(\frac{6}{1\\}\)

After doing those steps your new equation will look like this-  \(\frac{2}{5}\) × \(\frac{6}{1}\)

\(\frac{2}{5}\) × \(\frac{6}{1}\)        Now all you have to do is multiply

1st- multiply 2x6

2nd- multiply 5x1

\(\frac{2}{5}\) × \(\frac{6}{1\\\\}\) = \(\frac{12}{5}\)

So your answer is \(\frac{12}{5\\}\)  or \(2 \frac{2}{5}\)

Hope my explanation helps you out!

The decimal equivalent to the fraction of friends who vote for kiwi is 0.111.

In the given scenario, nine friends have voted on their favorite fruit, and only one person in the group voted for kiwi. We are tasked with finding the decimal equivalent of the fraction representing the friends who voted for kiwi.

To determine the decimal equivalent, we need to calculate the fraction and then convert it into decimal form. In this case, the fraction representing the friends who voted for kiwi is 1 out of 9, or 1/9.

To convert this fraction into a decimal, we divide the numerator (1) by the denominator (9):

1 ÷ 9 = 0.1111...

The decimal representation of 1/9 is 0.1111..., where the digit 1 repeats infinitely.

The decimal 0.1111... is an example of a recurring decimal, which means it repeats the same pattern of digits indefinitely. In this case, the digit 1 repeats endlessly. When we write it in decimal form, we typically use the ellipsis (...) to indicate the recurring pattern.

Therefore, the decimal equivalent to the fraction of friends who voted for kiwi is 0.1111..., where the digit 1 repeats indefinitely.

It is important to note that when working with decimals, we can approximate recurring decimals by rounding to a certain number of decimal places. However, in this case, since the pattern of 1s repeats indefinitely, it cannot be precisely represented in a finite number of decimal places.

In summary, the decimal equivalent of the fraction representing the friends who voted for kiwi is 0.1111..., where the digit 1 repeats indefinitely.

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The value of `csc 0.71` to three  decimal places is `1.534` which is option A.

The equation for the graph shown in the right is `y=x²(x-3)` which is option C.The graph of the function `y=x¹` is transformed to the graph of the function `y=

-[2(x + 3)]* + 1`

by a vertical stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up which is option A.

The equation of `f(x)` if `D = (x = Rx)` and the y-intercept is `(0,-2)` is `

f(x) = 2x + 1`

which is option B.

The value of `csc 0.71` to three decimal places is `1.534` which is option A.4. Given a graph, we can find the equation of the graph using its intercepts, turning points and point-slope formula of a straight line.

The graph shown on the right has the equation of `

y=x²(x-3)`

which is option C.5.

The graph of `y=x¹` is a straight line passing through the origin with a slope of `1`. The given function `

y=-[2(x + 3)]* + 1`

is a transformation of `y=x¹` by a vertical stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up.

So, the correct option is A as a vertical stretch is a stretch or shrink in the y-direction which multiplies all the y-values by a constant.

This transforms a horizontal line into a vertical line or a vertical line into a taller or shorter vertical line.6.

The function is given as `f(x)` where `D = (x = Rx)` and the y-intercept is `(0,-2)`. The y-intercept is a point on the y-axis, i.e., the value of x is `0` at this point. At this point, the value of `f(x)` is `-2`. Hence, the equation of `f(x)` is `y = mx + c` where `c = -2`.

To find the value of `m`, substitute the values of `(x, y)` from `(0,-2)` into the equation. We get `-2 = m(0) - 2`. Thus, `m = 2`.

Therefore, the equation of `f(x)` is `

f(x) = 2x + 1`

which is option B.7. `csc(0.71)` is equal to `1/sin(0.71)`. Using a calculator, we can find that `sin(0.71) = 0.649`.

Thus, `csc(0.71) = 1/sin(0.71) = 1/0.649 = 1.534` to three decimal places. Hence, the correct option is A.

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In the context of our theory of inductive proofs, P(n) represents the quantity about which we are proving something- False.

A proof by induction requires justification at every step, just like a regular proof. But, it uses a clever technique that enables you to demonstrate the truth of a proposition when n is 1, assume it is true for n=k, and then demonstrate that it is true for n=k+1.

According to the theory, all that is required to demonstrate a person's ability to ascend to the nth floor of a fire escape is for them to demonstrate their ability to ascend the fire escape ladder (n=1) and their ability to ascend the stairs from any level of the fire escape (n=k) to the next level (n=k+1).

You could have been asked to assume the n-1 case and prove the n case if you've done proof by induction before, or to assume the n case and show the n+1 case. This is the same as what I'm describing here, but I'll use a different letter since I believe it helps people understand what each instance is for better.

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8.08 percent of babies are born prematurely .

We have following information,

lengths of pregnancy of humans are Normally distributed.

mean of distribution ( μ ) = 268 days

standard deviations of distribution = 15 days

We shall find out the pecent of babies are born. prematurely.

Using the Normal distribution formula ,

Z = ( X - μ ) /σ

where X---> sample mean

μ --> poplution mean

putting the possble values of variables we get,

if a baby born three weaks early then he is considered as premature.

X = 21 , μ = 268 , r =

Z = ( 21-268)/ 15 = - 247/15 = - 16.4

Now, p-value corresponding to Z-value= -16.4 is

8.08..

thus for z= -16.4 , p-value will be 8.08 .. So, 8.08 percent of babies are born prematurely.

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Step-by-step explanation:

That means the 96 is  75% of your grade

   96 (.75) + 75 (.25) = 90.75  final grade

The equation of the line perpendicular to y = 2x + 15 and passing through the point (12, -48) is y = -1/2x - 42.

To find the equation of the line passing through the point (12, -48) and perpendicular to y = 2x + 15, we need to first find the slope of the perpendicular line. The slope of the given line is 2. Since perpendicular lines have slopes that are negative reciprocals, the slope of the perpendicular line is -1/2.

Now, we use the point-slope form of the equation for a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Plug in the values: y - (-48) = -1/2 (x - 12)

Simplify the equation:

y + 48 = -1/2x + 6

Now, write the equation in the slope-intercept form (y = mx + b):

y = -1/2x + 6 - 48

y = -1/2x - 42

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Answer: u50=296

Step-by-step explanation:

30-10=20

50-30=20

u30-u10=

156-16=140

u50=u30+140

u50=156+140

u50=296

The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).

Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The radius of gyration Rg is defined as follows.

Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.

R(mean) is the mean position vector of all monomers.

Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).

Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).

The ratio R²/Rg² is given by R²/Rg² = L^(D-2).

When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.

This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.

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Answer:

48 degrees.

Step-by-step explanation:

The value of a triangle equals 180* in total, so, 47 + 85 = 132.

180-132=48*.

The value of x for the given angles will be  x= 50.

The study of the figures like square, rectangle circle and their angles is called as geometry.

We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:

∠CBE + ∠DBE + angle EBC = 180

Substituting the given expressions for angle CBE and angle DBE, we get:

(0.2x - 42) + (0.2x - 32) + angle EBC = 180

Simplifying the left side of the equation, we get:

0.4x - 74 + angle EBC = 180

Adding 74 to both sides, we get:

0.4x + angle EBC = 254

We know that angle EBC is supplementary to both angle CBE and angle DBE since they form a straight line. Therefore, we can write:

∠CBE + ∠EBC = 180

∠DBE + ∠EBC = 180

Substituting the expression (0.2x - 42) for angle CBE and the expression (0.2x - 32) for angle DBE, we get:

(0.2x - 42) + angle EBC = 180

(0.2x - 32) + angle EBC = 180

Simplifying each equation, we get:

∠EBC = 222 - 0.2x (1)

∠EBC = 212 - 0.2x (2)

Setting the right sides of equations (1) and (2) equal to each other, we get:

222 - 0.2x = 212 - 0.2x

Simplifying and solving for x, we get:

10 = 0.2x

x = 50

Therefore, the value of x is 50.

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Answer:

\(100^{t^{2}-0.5\cdot t}\) is not equivalent to \(\frac{10^{t^{2}}}{100^{t}}\).

\(100^{t^{2}-0.5\cdot t}\) is not equivalent to \(\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}\).

\(100^{t^{2}-0.5\cdot t}\) is not equivalent to \(\frac{50^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}\).

Step-by-step explanation:

The expression to be evaluated is \(100^{t^{2}-0.5\cdot t}\), we find by algebraic means the equivalent expression:

Possibility 1:

\(100^{t^{2}-0.5\cdot t}\)

\(\frac{100^{t^{2}}}{100^{0.5\cdot t}}\)

\(\frac{100^{t^{2}}}{(100^{0.5})^{t}}\)

\(\frac{100^{t^{2}}}{10^{t}}\)

\(100^{t^{2}-0.5\cdot t}\) is not equivalent to \(\frac{10^{t^{2}}}{100^{t}}\).

Possibility 2:

\(100^{t^{2}-0.5\cdot t}\)

\(\frac{100^{t^{2}}}{100^{0.5\cdot t}}\)

\(\frac{(50\cdot 2)^{t^{2}}}{(25\cdot 4)^{0.5\cdot t}}\)

\(\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}\)

\(100^{t^{2}-0.5\cdot t}\) is not equivalent to \(\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}\).

Possibility 3:

\(100^{t^{2}-0.5\cdot t}\)

\(\left(\frac{500}{5} \right)^{t^{2}-0.5\cdot t}\)

\(\frac{500^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}\)

\(100^{t^{2}-0.5\cdot t}\) is not equivalent to \(\frac{50^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}\).

The expected return on the market must be 10.5 percent, according to the given values.

Expected return is a measure used in finance to calculate the average return an investment is expected to generate over a specific period. It is a weighted average of the possible returns, where each return is multiplied by its respective probability.

The expected return on a stock can be determined using the capital asset pricing model (CAPM), which relates the expected return of an asset to its beta and the expected return of the market. The formula for the CAPM is as follows:

Expected Return = Risk-Free Rate + Beta * (Market Expected Return - Risk-Free Rate). In this case, the stock has an expected return of 10.5 percent, a beta of 1.00, and the risk-free rate is 6.25 percent. Let's denote the market expected return as "M."

Plugging in the values into the CAPM formula: 10.5% = 6.25% + 1.00 * (M - 6.25%).

Simplifying the equation:

10.5% - 6.25% = M - 6.25%

4.25% = M - 6.25%

M = 4.25% + 6.25%

M = 10.5%

Therefore, the expected return on the market must be 10.5 percent in order to be consistent with the given information.

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Answer:

19. 1      do 4^5 which is 1024 then do 1024^0 which is 1

21. 0.000064      do 5^-2 which is 0.04 then do 0.04^3 which is 0.000064

23. 2.33              do 9^4 which is 6561 then do 6561^-2 which is 2.32305731 so you round it to 2.33

btw you should talk to me more

To find the trapezoidal rule, you must integrate the function with the trapezoidal rule formula.

The trapezoidal rule is a numerical integration method used to approximate the definite integral of a function. It is a simple and popular method of approximating definite integrals, especially when the function is not easy to integrate analytically.

The trapezoidal rule estimates the definite integral by dividing the area under the curve into a series of trapezoids, and then summing the areas of these trapezoids.

The formula for the trapezoidal rule is: (b-a) * (f(a) + f(b)) / 2

Where a and b are the limits of integration, f(a) and f(b) are the function evaluated at the limits of integration and (b-a) is the width of the trapezoid.

In practice, to find the trapezoidal rule, you must divide the definite integral into small subintervals and then evaluate the function at the endpoints of each subinterval.

Then you can use the trapezoidal rule formula to find the approximate area under the curve by summing the areas of all the trapezoids. It's important to note that the more subintervals you use, the more accurate the approximation will be.

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The composite function is \(f\circ g(x) = x^8+x^6+x^4\)

Given that \(f(x)=x^4+x^3+x^2\) and \(g(x)=x^2\).

We need to calculate \(f\circ g(x)\) which is a composite function.

If two functions are given and we create another function by using the given functions, then the new function is called composite function.

So to calculate the composite function, put the value of \(g(x) = x^2\) in the function \(f(x)\).

\(f\circ g(x) = (x^2)^4+(x^2)^3+(x^2)^2\)

\(f\circ g(x) = x^8+x^6+x^4\)

Hence the composite function is \(f\circ g(x) = x^8+x^6+x^4\).

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