the number at the bottom of the exponent is called a power, true or false

Answer:

15%

Step-by-step explanation:

3÷20=0.15

0.15×100=15

The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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Market classes and grades are used to describe the quality and characteristics of agricultural products, including meat, poultry, fruits, and vegetables.  True

They provide a common language for buyers and sellers to communicate about the characteristics, such as the age, sex, fat content, and muscling, of the product. Market classes and grades help ensure that buyers receive products that meet their quality standards and help sellers receive a fair price for their products. For example, beef is graded based on marbling, maturity, and lean color, with the highest grade being USDA Prime, followed by USDA Choice and USDA Select.

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Full Question: market classes and grades encompass descriptive terminology of carcasses and products for the understanding of different groups or buyers. T/F

This standardized system of classification allows for easier communication and understanding between buyers and sellers, and ensures consistency and fairness in the marketplace.

Market classes and grades refer to the categorization and labeling of carcasses and products based on their quality and characteristics. These classifications use descriptive terminology that is understood by different groups of buyers, such as meat packers, wholesalers, retailers, and consumers. Market classes typically group animals based on their intended use, such as beef cattle for slaughter, while grades are assigned based on factors such as maturity, marbling, and fat content. This standardized system of classification allows for easier communication and understanding between buyers and sellers, and ensures consistency and fairness in the marketplace.

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Answer:

25x+10=47.50

Step-by-step explanation:

x represents the ticket amount and if he buys 25 tickets then that will be 25 times x. Plus the $10 entrance fee.

The question is: Alex expects to graduate in 3.5 years and hopes to buy a new car then. He will need a 20% down payment, which amounts to $3600 for the car he wants.

How much should he save now to have $3600 when he graduates if he can invest it at 6% compounded monthly?To determine the value of Alex's savings when he graduates, use the future value formula:  $$FV=P\cdot{\left(1+\frac{r}{n}\right)}^{nt}$$where FV is the future value, P is the principal (the amount Alex saves), r is the annual interest rate (6%), n is the number of times interest is compounded per year (12, since the interest is compounded monthly), and t is the time in years.

Therefore, using the formula, $$FV=P\ cdot{\left(1+\frac{r}{n}\right)}^{nt}$$$$3600=P\cdot{\left(1+\frac{0.06}{12}\right)}^{12(3.5)}$$$$3600=P\cdot{\left(1+0.005\right)}^{42}$$$$3600=P\cdot{1.270096}$$Divide both sides of the equation by 1.270096 to solve for P, $$\frac{3600}{1.270096}=P$$$$2833.41=P$$Therefore, Alex should save $2833.41 to have $3600 when he graduates if he can invest it at 6% compounded monthly.

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Answer:

Answer is 11. You have to add the 4 and 7.

In rectangles all sides are either perpendicular or parallel, so you know that the missing side is equal to the bottom 2 horizontal sides added up.

4 + 7 = 11.

The missing side is 11cm.

Using trigonometric identities and algebraic manipulations, we derive an expression for sin x and cos x in terms of cos y. The value of (sin x + cos x)(sin y + cos y) is 2.49.


1. Start with the given equations sin(x+y) = 0.9 and sin(x-y) = 0.6.
2. Rewrite the equations using trigonometric identities. For sin(x+y) = 0.9, we have sin x cos y + cos x sin y = 0.9. For sin(x-y) = 0.6, we have sin x cos y - cos x sin y = 0.6.
3. Add the two equations together to eliminate the sin x cos y term: 2 sin x cos y = 1.5.
4. Divide both sides by 2 to solve for sin x cos y: sin x cos y = 0.75.
5. Square both sides of the equation to get (sin x cos y)^2 = 0.75^2. This gives us sin^2 x cos^2 y = 0.5625.
6. Use the trigonometric identity sin^2 x + cos^2 x = 1 to rewrite sin^2 x as 1 - cos^2 x: (1 - cos^2 x) cos^2 y = 0.5625.
7. Expand and rearrange the equation: cos^2 x cos^2 y - cos^4 x = 0.5625.
8. Use the identity cos^2 x = 1 - sin^2 x to substitute for cos^2 x: (1 - sin^2 x) cos^2 y - (1 - sin^2 x)^2 = 0.5625.
9. Expand and simplify: cos^2 y - sin^2 x cos^2 y - (1 - 2sin^2 x + sin^4 x) = 0.5625.
10. Combine like terms: cos^2 y - sin^2 x cos^2 y - 1 + 2sin^2 x - sin^4 x = 0.5625.
11. Rearrange the equation to isolate sin^2 x terms: sin^4 x - sin^2 x (cos^2 y + 2) + cos^2 y - 1 + 0.5625 = 0.
12. Combine like terms: sin^4 x - sin^2 x (cos^2 y + 2) + cos^2 y - 0.4375 = 0.
13. Solve the quadratic equation for sin^2 x: sin^2 x = [(cos^2 y + 2) ± √((cos^2 y + 2)^2 - 4(cos^2 y - 0.4375))] / 2.
14. Simplify the expression: sin^2 x = [(cos^2 y + 2) ± √(cos^4 y + 4cos^2 y + 4 - 4cos^2 y + 1.75)] / 2.
15. Further simplify: sin^2 x = [(cos^2 y + 2) ± √(cos^4 y + 5.75)] / 2.
16. Since 0 ≤ y ≤ x ≤ π/2, the value of cos y is positive. Therefore, cos^2 y + 2 is positive.
17. Thus, the equation simplifies to sin^2 x = (cos^2 y + 2 + √(cos^4 y + 5.75)) / 2.
18. Take the square root of both sides: sin x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2].
19. Since 0 ≤ y ≤ x ≤ π/2, the value of sin x is positive.
20. Therefore, sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √(1 - sin^2 x).
21. Substituting the values of sin x and cos x, we have sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √(1 - [(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2]).
22. Simplify the expression: sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √[(2 - cos^2 y - √(cos^4 y + 5.75)) / 2].
23. Multiply the two terms: (sin x + cos x)(sin y + cos y) = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] * √[(2 - cos^2 y - √(cos^4 y + 5.75)) / 2].
24. Simplify: (sin x + cos x)(sin y + cos y) = √[(cos^2 y + 2 + √(cos^4 y + 5.75))(2 - cos^2 y - √(cos^4 y + 5.75))] / 2.
25. Multiply the terms inside the square root: (sin x + cos x)(sin y + cos y) = √[4 - 2cos^2 y - 2√(cos^4 y + 5.75) + 4√(cos^2 y + 2) - 2cos^2 y + cos^4 y + 5.75] / 2.
26. Combine like terms: (sin x + cos x)(sin y + cos y) = √[5 + 2√(cos^2 y + 2) + 2cos^2 y - 2cos^2 y - 2√(cos^4 y + 5.75)] / 2.
27. Cancel out the common terms: (sin x + cos x)(sin y + cos y) = √[5 + 2√(cos^2 y + 2) - 2√(cos^4 y + 5.75)] / 2.
28. Simplify the expression: (sin x + cos x)(sin y + cos y) = √[5 - 2√(cos^4 y + 5.75) + 2√(cos^2 y + 2)] / 2.
29. The value of (sin x + cos x)(sin y + cos y) is 2.49.

Therefore, the value of (sin x + cos x)(sin y + cos y) is 2.49.

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In this problem, we use the product-to-sum trigonometric identities and the given information that sin(x+y) = 0.9 and sin(x-y) = 0.6 to find that the value of (sin x + cos x)(sin y + cos y) equals 1.5.

In this problem, you're asked to find the value of (sin x + cos x)(sin y + cos y). Before we solve it directly, let's take advantage of the given information: sin(x+y) = 0.9 and sin(x-y) = 0.6.

To solve this, we can use the product-to-sum trigonometric identities: sin(A)+cos(A)sin(B)+cos(B) = sin(A+B)+sin(A-B). According to the problem, sin(x+y) = 0.9 and sin(x-y)=0.6. Therefore, we have 0.9 + 0.6 which results in 1.5. Thus, the value of (sin x + cos x)(sin y + cos y) equals 1.5.

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(a) Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

(b) The difference equation and obtain an explicit formula for Pn,

Pₙ = (1 + 4Pₙ₋₁) / 6

Expressions that are equivalent serve the same purpose regardless of appearance. When we employ the same variable value, two algebraic expressions that are equivalent have the same value.

To prove the given difference equation for Pₙ , let's break it down into two parts: the case where the nth throw results in a six and the case where it does not.

(a) Case: The nth throw results in a six

In this case, we need to consider the previous (n-1) throws to determine the probability of having an even number of sixes. Since the (n-1)th throw cannot be a six, the probability of having an even number of sixes in (n-1) throws is Pₙ₋₁.

Now, for the nth throw to be a six, we have a probability of 1/6. Therefore, the probability of having an even number of sixes in n throws, given that the nth throw is a six, is (1/6) * (1 - Pₙ₋₁).

This is because (1 - Pₙ₋₁) represents the probability of having an odd number of sixes in (n-1) throws.

(b) Case: The nth throw does not result in a six

In this case, we still need to consider the previous (n-1) throws to determine the probability of having an even number of sixes.

Since the nth throw does not result in a six, the probability of having an even number of sixes in (n-1) throws remains the same, which is Pₙ₋₁.

Now, for the nth throw to not result in a six, we have a probability of 5/6. Therefore, the probability of having an even number of sixes in n throws, given that the nth throw does not result in a six, is (5/6) * Pₙ₋₁.

Combining the probabilities from both cases, we get:

Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

To solve the difference equation and obtain an explicit formula for Pn, we can rearrange the equation:

6Pₙ = 1 - Pₙ₋₁ + 5Pₙ₋₁

6Pₙ = 1 + 4Pₙ₋₁

Pₙ = (1 + 4Pₙ₋₁) / 6

Now, we can use this recursive formula to find explicit values for Pₙ. We start with P₀, which represents the probability of having an even number of sixes in 0 throws (which is 1):

P₀ = 1

Then, we can use the recursive formula to calculate P₁, P₂, P₃, and so on, until we reach the desired value of Pₙ.

Hence,

(a) Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

(b) the difference equation and obtain an explicit formula for Pn,

Pₙ = (1 + 4Pₙ₋₁) / 6

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Considering the images (a),(b),(c),(d),(e),(f) the oriented path is

(a) Negative

(b) Positive

(c) Positive

(d) Zero

(e) Zero

(f) Zero

calculating each quadrant's line integral and symmetry.

In calculus, a line integral is an integral where the function being evaluated is along a curve. A line integral is also known as a route integral, curve integral, or curvilinear integral.

What does a Line integral mean?

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Answer: y > -4 + x

Step-by-step explanation: graph the inequality by finding the boundary line

Answer:

y > -4 + x

***(see graph below)****

Step-by-step explanation:

Graph

x − y < 4

Solve for y

Subtract x from both sides of the inequality.

−y < 4 − x

Multiply each term in −y < 4 − x by −1

Multiply each term in −y < 4 − x by −1. When multiplying or dividing both sides of an

  inequality by a negative value, f lip the direction of the inequality sign.

  (−y) ⋅ −1 > 4 ⋅ −1 + (−x) ⋅ −1

     Multiply (−y) ⋅ −1.

     Multiply −1 by −1.

     1y > 4 ⋅ −1 + (−x) ⋅ −1

     Multiply y by 1.

     y > 4 ⋅ −1 + (−x) ⋅ −1

Simplify each term.

     Multiply 4 by −1.

      y > −4 + (−x) ⋅ −1

     Multiply (−x) ⋅ −1.

y > −4 + x

   Find the slope and the y-intercept for the boundary line.

Rewrite in s lope-intercept form.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Reorder −4 and x. y > x − 4

Use the slope-intercept form to find the slope and y-intercept.

Find the values of m and b using the form y = mx + b. m = 1

b = −4

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: 1

intercept: (0, −4)

Graph a dashed line, then shade the area above the boundary line since y is greater than −4 + x. y > −4 + x

There are 5x6=30 one-to-one functions from a set containing 5 elements to a set containing 6 elements.

A one-to-one (or injective) function is a type of mathematical function that maps each element of one set to one, and only one, element of another set. In other words, a one-to-one function is a function that has a unique output for each input. To calculate the number of one-to-one functions from a set containing 5 elements to a set containing 6 elements, we can use the formula f(x)=y, where x is the number of elements in the original set and y is the number of elements in the target set. In this case, x = 5 and y = 6, so f(x) = 6. Since each element in the original set must be mapped to a unique element in the target set, the total number of one-to-one functions is equal to the product of x and y, or 5 x 6 = 30.

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The linear function that models the cost of producing x chairs in one day is C(x) = 15x + 700.

To find a linear function that models the cost of producing x chairs in one day, we can use the slope-intercept form of a linear equation, which is:

C(x) = mx + b

Where C(x) represents the cost of producing x chairs, m is the slope of the line, and b is the y-intercept (the cost when no chairs are produced).

Given information:

Cost of producing 100 chairs = $2200

Cost of producing 300 chairs = $5200

Let's use these data points to find the slope (m) and the y-intercept (b).

We have two points: (100, 2200) and (300, 5200).

Slope (m):

The slope of a line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (100, 2200) and (300, 5200):

m = (5200 - 2200) / (300 - 100)

m = 3000 / 200

m = 15

Y-intercept (b):

To find the y-intercept, we can substitute one of the points into the equation and solve for b.

Using the point (100, 2200):

2200 = 15(100) + b

2200 = 1500 + b

b = 2200 - 1500

b = 700

Now that we have the slope (m = 15) and the y-intercept (b = 700), we can form the linear function that models the cost of producing x chairs:

C(x) = 15x + 700

Therefore, the linear function that models the cost of producing x chairs in one day is:

C(x) = 15x + 700

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We assume that the population standard deviation are known, the samples from each population are independent, the population is normally distributed if we use t test of two samples.

Given T test of significance has been used.

T test is a statistical test that is like z test. Z test is used when n>30 and t test is used when n<30. It is used in hypothesis testing.

We know that there are many test which can be used to test a hypothesis.

The requirements to perform a two sample t procedure are as follows:

1)The two samples have equal variance. Hence the variance should be known.

2) The samples for which the two sample t procedure is performed must be independent.

3) The data are in alignment with the normal distribution probability.

4) The sample are random samples taken from different respective population.

Hence when two sample t procedure is performed we have to assume population standard deviation is known and population is normally distributed.

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The required probability of spinning A is 25% as of the given conditions.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,

A circle is divided into 8 equal parts,
The percentage of each part is given as,
= 100/8
= 12.5%

Now,
Each section is named after A, B, and C
We have 2A, 3B and 3C

The probability of spinning A is given as,
= 2 / 8
= 1/4
= 0.25 or 25%

Thus, the required probability of spinning A is 25% as of the given conditions.

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Answer:

f(x) = -3x +2 to find f(4) you plug in the value of x=4 in the function

f(4) = -3(4) +2

= - 12 +2

=- 8

Hope it is helpful to you

The value of the linear function at x = 4 will be 14.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = 3x + 2

The degree of the function is one. Then the function is a linear function.

The value of the function at x = 4 will be given as,

f(4) = 3(4) + 2

f(4) = 12 + 2

f(4) = 14

The value of the linear function at x = 4 will be 14.

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A toy car moves by itself due to a type of motor called a self-propelled motor. This type of motor powers the movement of the toy car.

A self-propelled motor is a motor that does not require an external force to power it. It is powered by an internal mechanism that causes it to move. In a toy car, the self-propelled motor is usually a type of small electric motor.The motor is powered by a battery, and it generates rotational energy. This rotational energy is transferred to the wheels of the toy car, causing them to move. This movement allows the toy car to move forward or backward, depending on the direction of the motor's rotation.What makes the toy car move?The self-propelled motor is connected to the wheels of the toy car. The rotational energy generated by the motor is transferred to the wheels, causing them to rotate. As the wheels rotate, they come into contact with the ground, creating friction.

This friction causes the wheels to grip the surface of the ground and move the toy car forward or backward. The faster the motor rotates, the faster the wheels move, and the faster the toy car moves.

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The volume of the cylinder is approximately, 1,539.4 cubic meters.

Volume of a cylinder = πr²h

Given the following:

Diameter of cylinder = 14 m

Radius (r) = 14/2 = 7 m

Height of cylinder = 10 m

Volume of cylinder = πr²h = π(7²)(10)

Volume of cylinder ≈ 1,539.4 cubic meters.

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The transformation from the graph of f to the graph of g is a horizontal translation by 2 units to the left.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

On the other hand, the translation of a graph downward simply means subtracting a digit from the value on the negative y-coordinate of the pre-image; g(x) = f(x) - N.

By critically observing the functions, we can logically deduce that the parent function f(x) was shifted to the left by 2 units in order to produce g(x);

g(x) = f(x + 2)

g(x) = 1/2(x + 2) - 4

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Answer:

3

Step-by-step explanation:

Answer:

I hope this help you

Answer:

The equation is c = 250m

Cost of a 14-month is 3,500

Step-by-step explanation:

Each month, the value increase by 250

c = 250m

c = 250 x 14

c = 3,500

Answer:

The equation is (x=250)

A 14 month membership is 3500

Step-by-step explanation:

Answer: 6.5<6.55

Step-by-step explanation: Because you add the zero to the 6.50 but it’s still less than 6.55.

Answer:

−6.5<6.55

Step-by-step explanation:

I took the K12 test

Answer: -2; -1; 0; 1; 2

\(-8\leq 4n<12\\\\=> -2\leq n<3\)

because n is an integer => n ∈ {-2; -1; 0; 1; 2}

Step-by-step explanation:

Answer is : n ={-2; -1; 0; 1; 2}

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

given that,

-8 ≤ 4n < 12

=> -2≤ n <3

because, n is an integer => n ∈ {-2; -1; 0; 1; 2}

Hence, Answer is : n ={-2; -1; 0; 1; 2}.

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(a) The derivative of r(t) is (2t + 6)i + (2t - 6)j. (b) The second derivative of r(t) is 2i + 2j. (c) The dot product of r'(t) and r''(t) is 8t.

(a) r'(t):

The derivative of r(t) can be found by differentiating each component separately.

r'(t) = (2t + 6)i + (2t - 6)j

(b) r''(t):

To find the second derivative of r(t), we differentiate each component of r'(t) with respect to t.

r''(t) = 2i + 2j

(c) r'(t) · r''(t):

To find the dot product of r'(t) and r''(t), we multiply the corresponding components and sum them.

r'(t) · r''(t) = (2t + 6)(2) + (2t - 6)(2)

= 4t + 12 + 4t - 12

= 8t

Therefore, r'(t) · r''(t) = 8t.

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Test the hypothesis step of the scientific method is he performing.

Making conjectures (hypothetical explanations) is a step in the scientific method. Predictions are then derived from the hypotheses as logical conclusions, and experiments or actual observations are conducted based on those predictions.

Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.

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Answer:

134 students at west middle school walk to school

Step-by-step explanation:

26% of students at West Middle School get to school by walking. The table shows 515 students in total. To find 26% of 515 we first divide 515 by 100 = 5.15 and then multiply 5.15 by 26% which is 134 students.

Answer: The correct answer to this problem would be C, or 32/3.

Step-by-step explanation:

The average rate of change in a function is the rate at which one value changes with respect to another value.

Given function: f(x) = 2x² + x + 5 on interval [-2, 2]

Therefore,

Average rate of change = f(2)-f(-2)/2-(-2)

f(2) = 2(2)² + 2 + 5

f(2) = 15

f(-2) = 2(-2)² - 2 + 5

f(2) = 11

Substitute the values,

Average rate = 5-11/2+2

Average rate = 4/4

Average rate = 1

So, the average rate of change is

Leading me to believe option C is correct.

Answer:

\(\textsf{1.} \quad 3x^2-4x+12\)

\(\textsf{2.} \quad 3x^2-8x+4\)

\(\textsf{3.} \quad 6x^3-8x+32\)

\(\textsf{4.} \quad \dfrac{3x^2-6x+8}{2x+4}\)

\(\textsf{5.} \quad 12x^2+36x+32\)

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x)=3x^2-6x+8\\g(x)=2x+4\end{cases}\)

Function composition is an operation that takes two functions and produces a third function.

The composite function (f + g)(x) means to add function f(x) and g(x):

\(\begin{aligned}\implies (f+g)(x) & = f(x)+g(x)\\&=(3x^2-6x+8)+(2x+4)\\ &=3x^2-6x+2x+8+4\\ &=3x^2-4x+12\end{aligned}\)

The composite function (f - g)(x) means to subtract function g(x) from function f(x):

\(\begin{aligned}\implies (f-g)(x) & = f(x)-g(x)\\&=(3x^2-6x+8)-(2x+4)\\&=3x^2-6x+8-2x-4\\ &=3x^2-6x-2x+8-4\\ &=3x^2-8x+4\end{aligned}\)

The composite function f(x) · g(x) means to multiply functions f(x) and g(x):

\(\begin{aligned}\implies f(x)\cdot g(x) & =(3x^2-6x+8)(2x+4)\\ &=3x^2(2x+4)-6x(2x+4)+8(2x+4)\\&=6x^3+12x^2-12x^2-24x+16x+32\\&=6x^3-8x+32\end{aligned}\)

The composite function f(x)/g(x) means to divide function f(x) by function g(x):

\(\begin{aligned}\implies \dfrac{f(x)}{g(x)} & = \dfrac{3x^2-6x+8}{2x+4}\\\end{aligned}\)

The composite function f(g(x)) means to substitute the function g(x) in place of the x in function f(x):

\(\begin{aligned}\implies f(g(x))&=3(g(x))^2-6(g(x))+8\\&=3(2x+4)^2-6(2x+4)+8\\&=3(2x+4)(2x+4)-12x-24+8\\&=3(4x^2+16x+16)-12x-16\\&=12x^2+48x+48-12x-16\\&=12x^2+48x-12x+48-16\\&=12x^2+36x+32\end{aligned}\)

Learn more about composite functions here:

https://brainly.com/question/24538829