Complete the two column proof
Given angle to an angle five are supplementary
Prove: I || m

With this query, no effort is necessary. measure the tbsp. of all items.

A great source of both phosphorus and calcium, which are essential for the growth and upkeep of strong, strong teeth and bones, is milk. They lower the chance of developing osteoporosis and suffering broken bones later in life. Milk encourages strong bones.

1. Measure \(8\) tbsp. chocolate sauce and add \(2\frac{1}{2}\) cups of milk.

No work is required for this question. It is a simple instruction to measure out 8 tbsp. of chocolate sauce and add it to \(2\frac{1}{2}\) cups of milk.

2. Start with \(1\frac{3}{4}\) cups of milk and add \(2\frac{1}{2}\) tbsp. chocolate sauce.

No work is required for this question. It is a simple instruction to start with \(1\frac{3}{4}\) cups of milk and add \(2\frac{1}{2}\) tbsp. of chocolate sauce.

3. Add \(3\frac{1}{3}\) tbsp. chocolate sauce to \(1\frac{1}{4}\) cups milk.

No work is required for this question. It is a simple instruction to add  \(3\frac{1}{3}\)tbsp. of chocolate sauce to \(1\frac{1}{4}\) cups of milk.

4. For every 1 cup of milk add \(2\frac{1}{2}\) tbsp. of chocolate sauce.

No work is required for this question. It is a simple instruction to add \(2\frac{1}{2}\) tbsp. of chocolate sauce for every \(1\) cup of milk.

5. Stir \(1\) tbsp. chocolate sauce into \(\frac{2}{3}\) cup milk.

No work is required for this question. It is a simple instruction to stir 1 tbsp. of chocolate sauce into \(\frac{2}{3}\) cup of milk.

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Answer: \(x=\frac{15}{11}\)

Step-by-step explanation:

\(\frac{3}{5} x-\frac{1}{3}x=x-1\)

1. Find the common denominator, which is 15

2. Multiply each denominator to get 15

\(\frac{9}{15} x-\frac{5}{15}x=x-1\)

3. Combine like terms

\(\frac{4}{15} x=x-1\)

4. Subtract x from the right

\(\frac{4}{15} x-x=1\)

5. Combine the terms

\(-\frac{11}{15} x=-1\)

6. Multiply both sides by 15 to remove the fraction

\(-11x=-15\)

7. Divide both sides by -11

\(x=\frac{15}{11}\)

The probability that he will use both bus and the train among bus, cab, train is 0.11.

Given There are 3 choices to people each among bus, cab, train for his trip home.

Probability is the likeliness of happening an event among all the events possible. The value of probability lies between 0 and 1. The formula to calculate probability is as under:

Probability= number of things/ total things.

The value of probability cannot be negative.

Number of buses=3

Number of cab=3

Number of train=3

Probability that he will go through train and bus is 3/9*3/9

=9/81

=1/9

=0.11

Hence the probability that he will travel with bus and train is 0.11.

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Question is incomplete as it includes:

What is the probability that he will use both train and bus?

The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is 9980

The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is calculated by summing the area of each subinterval under the midpoint of the interval.

The formula for the midpoint Riemann sum is given by:

Sum = (width of interval) * (height of midpoint)

For this problem, since the width of each interval is 16/4 = 4, the midpoint Riemann sum is calculated by:

Sum = 4 * (1 + (16/4)^3 + (32/4)^3 + (48/4)^3)

Substituting the values for each midpoint, we get the following equation:

Sum = 4 * (1 + 4^3 + 8^3 + 12^3)

This simplifies to:

Sum = 4 * (1 + 64 + 512 + 1728)

Therefore, the midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is:

Sum = 4 * (2495)

Sum = 9980

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Answer:

no choise

Step-by-step explanation:

=54/8-73/8

=-19/8

so no choise

Answer:

3

Step-by-step explanation:

Explanation:

Start at a point like (0,2) which is on the blue f(x) line.

Move upward until you reach the red g(x) line. You should move up 3 units. Every point on f(x) follows the same pattern to land on a corresponding point on g(x). Therefore, this moves the entire blue line up 3 units.

This leads to k = 3

So g(x) = f(x) + 3

Answer:

0.390625 grams

Step-by-step explanation:

can i get a second opinion on this

Answer:

JMK

Step-by-step explanation:

Answer:

\(-\frac{1}{5}\) is the slope of the line.

Step-by-step explanation:

(7 , 1) = (x1 , y1)

(-3 , 3) = (x2 , y2)

slope = y2 - y1/x2 - x1

=3 - 1/-3 - 7

=2/-10

=1/-5

=\(-\frac{1}{5}\)

the third answer. x represents half of any even number. so half of any even number minus seven equals 1.5 is the answer.

Answer:

They won 17 games and drew 4 games

Step-by-step explanation:

The given parameters are;

The number of points the major league soccer team finished with = 55 points

The number of games the soccer team played = 28 games

The number of losses the soccer team had = 7 losses

The number of points awarded for each win = 3 points

The number of points awarded for each tie = 1 points

The number of points awarded for each loss = 0 points

Let x represent the number of wins, y represent the number of draws, and let z represent the number losses

Therefore;

z = 7

x + y + z = 28

3·x + y + 7×0 = 55

Therefore, we have the following system of equations;

x + y = 21...(1)

3·x + y = 55...(2)

Which gives;

\(\begin{bmatrix}1 & 1\\ 3 & 1\end{bmatrix} \begin{bmatrix}x \\ y\end{bmatrix} = \begin{bmatrix}21 \\ 55\end{bmatrix}\)

The inverse of the matrix is given as follows;

\(\dfrac{1}{1 - 3} \times \begin{bmatrix}1 & -3\\ -1 & 1\end{bmatrix} = \begin{bmatrix}-0.5 & 0.5\\ 1.5 & -0.5\end{bmatrix}\)

Therefore;

\(\begin{bmatrix}x \\ y\end{bmatrix} = \begin{bmatrix}-0.5 & 0.5\\ 1.5 & -0.5\end{bmatrix} \times \begin{bmatrix}21 \\ 55\end{bmatrix} = \begin{bmatrix}17 \\ 4\end{bmatrix}\)

x = 17, y = 4

Analysis of the data reveals that the age groups most affected by the situation can be determined by examining the prevalence rates across different age groups. It is important to note that without specific data, it is challenging to provide precise figures for prevalence rates or determine the exact age groups most and least affected.

However, based on general trends and observations, it is often observed that older age groups, such as individuals above the age of 60, tend to be more susceptible to certain health conditions or diseases. This could be due to a variety of factors, including weakened immune systems, underlying health conditions, or reduced access to healthcare. Therefore, it is likely that the older age groups may be more affected compared to younger age groups.

On the other hand, younger age groups, particularly children and adolescents, are often considered to be more resilient and less prone to severe health conditions. Their immune systems are generally stronger, and they may have fewer underlying health issues. However, it is important to note that this is a general trend, and there can still be cases where younger age groups are affected by specific health conditions or diseases. Additionally, the impact on age groups can vary depending on the specific situation being analyzed.

To provide a more accurate analysis and determine the prevalence rate per age group, it would be necessary to have access to specific data related to the situation being examined. This data would include the number of cases or individuals affected within each age group. By comparing the number of affected individuals within each age group to the total population within that age group, the prevalence rate can be calculated. This rate provides a measure of the proportion of individuals within a specific age group who are affected by the situation.

In conclusion, without specific data, it is challenging to provide a definitive answer regarding which age groups are most and least affected by the situation. However, based on general observations, older age groups may be more affected due to various factors, while younger age groups, particularly children and adolescents, tend to be more resilient. To determine the prevalence rate per age group accurately, specific data related to the situation under analysis is required, including the number of affected individuals within each age group and the total population of each age group.

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Answer

Distance = 4.1 km

Explanation

Let the distance between Jane's house from school be x

The distance can be calculated using pythagora's theorem

Therefore, the distance between Jane's house from school is 4.1 km

Answer:

Solving for m gives:

\(m=\frac{P-50}{5}\)

which is option C in the list of possible answers

Step-by-step explanation:

Starting with the given equation, we work on using distributive property, and then on isolating the term with the variable to express:

\(P=5\,(m+10)\\P=5m+50\\P-50=5m\\\frac{P-50}{5} = m\\m=\frac{P-50}{5}\)

Answer:

answer = 19.2

Step-by-step explanation:

48 = 24 + 1.25x

48 - 24 = 1.25x

24 = 1.25x

24/1.25 = x

19.2 = x

Answer: 130

Step-by-step explanation:

Answer: 130 (D)

What is the measure of angle TRV?

Double prime is called by different names as per the topics used in Mathematics :

Inches in length , second order derivative in differentiation, conjugate points, transformed coordinates etc.

As given in the question,

Therefore, the double prime is known by many names such as inches in length, second order derivative, conjugate points, transformed coordinates etc.

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Answer:

Blue: 2/8

Red or Yellow: 3/8

Not Brown: 8/8

Not Green: 5/8

Number Five: 20%

Step-by-step explanation:

First Four Questions: See how many parts the spinner is in then count the number of colors its asking or not asking for and put that number over the total amount of parts

Question Five: If it shows up on time 80 percent of the time then the other 20 percent of the time they were late so there is a 20 percent chance of that happening again.

The factored form of the considered polynomial is \((x+3)(x+8)\)

If the given quadratic expression is of the form

\(ax^2 + bx + c\)

then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

\(b = \alpha + \beta \\ ac =\alpha \times \beta\)

Then writing b in terms of alpha and beta would help us getting common factors out.

For the considered polynomial, we've got the quadratic expression as:

\(x^2 + 11x + 24\)

Comparing this with \(ax^2 + bx + c\), we get:

Therefore, we have : ac = c = 24

Two numbers whose multiplication gives 24 and and whose addition gives 11.

24 = \(2 \times 2 \times 2 \times 3\)

If we take first three 2s, and 3, then:

\(24 = 8 \times 3 = (2 \times 2 \times 2) \times 3\\11 = 8 + 3 = (2 \times 2 \times 2) + 3\)

Thus, we need to write 11 in the middle in terms of 8 and 3:

\(x^2 + 11x + 24 = x^2 + 8x + 3x + 24 = x(x+8) + 3(x+8) = (x+3)(x+8)\)

Thus, the factored form of the considered polynomial is \((x+3)(x+8)\)

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Answer:

(1) C. 24

(2) B. 11

(3) C. (x+3)(x+8)

Answer:

18

Step-by-step explanation:

Answer: I think it may be 18.

Step-by-step explanation: The reason is because, 118 plus 44 equals 162. 180-162=18

Given 2nd order Initial-Value ODE as, y" + 3y' – 4y + 12e-2x = 0Convert the 2nd order ODE into a system of 1st order ODE equations as follows:Let y'=zdy/dx = dz/dxSo, y" = d²y/dx² = d/dx(dz/dx) = dz²/dx².

Again, the equation becomes, dz²/dx² + 3z – 4y + 12e^(-2x) = 0The given Initial values for the problem is:y(0) = 2y'(0) = -4Therefore, using Euler's Method, over the interval from x = 0 to x = 0.4 and using 2 integration steps,We can say that the h = 0.2 (since we are taking 2 integration steps and the interval is from 0 to 0.4, which gives 0.4/2 = 0.2)So, the Main answer is:

Given y" + 3y' – 4y + 12e-2x = 0 Initial values:y(0) = 2, y'(0) = -4We know that, y'=zdy/dx = dz/dxSo, y" = d²y/dx² = d/dx(dz/dx) = dz²/dx²Now, dz²/dx² + 3z – 4y + 12e^(-2x) = 0.

We need to solve this system of first-order differential equations by applying Euler's method to find out the value of y at x=0.2 and x=0.4.

Substituting h = 0.2 in the above equations and using Euler's Method, we getThe first step is: x = 0, y = 2, z = -4 Therefore, z1 = z0 + h (-4).

Substituting the values we get, z1 = -4 – (0.2) (3) ( -4) – (0.2) (4) ( 2 + 12 e^(-2(0)) ) = -2.12So, the value of z at x=0.2 is -2.12. Similarly, we can get the value of y at x=0.2 using Euler's method.The second step is: x = 0.2, y = 1.56, z = -2.12Therefore, z2 = z1 + h ( -2.12 ).

Substituting the values we get,z2 = -2.12 - (0.2) (3) ( -2.12) - (0.2) (4) ( 1.56 + 12 e^(-2(0.2)) ) = -1.3148So, the value of z at x=0.4 is -1.3148.Similarly, we can get the value of y at x=0.4 using Euler's method.

Hence, the required answer is, y (0.4) = 0.2281

Solve the given initial value problem using Euler's method over the interval from x = 0 to x = 0.4 using 2 integration steps.

The given initial conditions for this problem is y(0) = 2, and y'(0) = -4. The 2nd order ODE is given as y" + 3y' – 4y + 12e-2x = 0.

We need to convert this 2nd order ODE into a system of 1st order ODE equations. Let y' = z. Therefore, dy/dx = dz/dx. So, y" = d²y/dx² = d/dx(dz/dx) = dz²/dx². Substituting these values in the given equation, we get dz²/dx² + 3z – 4y + 12e^(-2x) = 0.

To solve this system of first-order differential equations, we will apply Euler's method to find out the value of y at x=0.2 and x=0.4. Substituting h = 0.2 in the above equations and using Euler's Method, we get the values of y and z at x=0.2 and x=0.4.

Therefore, the required answer is y (0.4) = 0.2281. Hence, the solution to the given problem using Euler's method is y (0.4) = 0.2281.

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Step-by-step explanation:

To record the critical values for a chi-square test, we need to know the degrees of freedom in addition to the level of significance. Assuming the degrees of freedom are not given, I will provide the critical values for degrees of freedom (k-1) at each level of significance:

At 10% level of significance:

- df = 9, Chi-square critical value = 14.6846

- df = 15, Chi-square critical value = 23.6848

- df = 21, Chi-square critical value = 31.4104

At 16% level of significance:

- df = 9, Chi-square critical value = 16.9189

- df = 15, Chi-square critical value = 26.2962

- df = 21, Chi-square critical value = 34.1694

At 22% level of significance:

- df = 9, Chi-square critical value = 19.0228

- df = 15, Chi-square critical value = 29.1407

- df = 21, Chi-square critical value = 37.5662

The critical values for a chi-square test increase with increasing degrees of freedom and increasing level of significance.

Answer:

C. Full of

Step-by-step explanation:

Ous is defined as full of or possessing. An example of ous used as a suffix is in the word "contemptuous," which means full of contempt. Moreover, how does the suffix ous change a word? Adding the suffix -ous A suffix is a letter or a group of letters that can be added to a word to change its meaning.

I hope this helps :3

-ous means "full of".

When someone is courageous, they have a lot of courage

When someone is gracious, they have a lot of grace

Answer:

a) s × ($7.70 - $1.70) > $7,900

b) s > 1,306 sandwiches

c) 431 more sandwiches

Step-by-step explanation:

The question is

The given parameters are;

The constant total expenses (fixed cost), C = $7,900

The cost it takes to make each sandwich, \(p_s\) = $1.70

The price at which the food truck sells its sandwiches, \(c_s\) = $7.75

Where "s" represent the number of sandwiches sold, we have;

a) Therefore, the inequality that represent the number of sandwiches the food truck will have to sell each month to earn more money from selling sandwiches than it pays in expenses and sandwich costs is given as follows;

s × (\(c_s\) - \(p_s\)) > C

Substituting the known values, gives;

s × ($7.75 - $1.70) > $7,900.00

b) From the inequality, which we have;

s > $7,900/($7.75 - $1.70)

However, $7,900/($7.75 - $1.70) = 158,000/121 ≈ 1,305.79

We round up to the nearest whole number since we are counting sandwiches which are counted per each piece

Therefore;

s > 1,306 sandwiches

An explanation is that the food truck will have to sell more than 1,305 sandwiches to be earn more money than it pays in expenses and sandwich costs.

c) The amount in discount the food truck offers in a specific month = $1.50

Therefore, the amount the food truck sells the sandwich in the given month \(c_s\) = $7.75 - $1.50 = $6.25

Therefore the number of sandwich the food truck company will have to sell on that month to earn more money from selling sandwiches than it pays the in expenses and sandwich cost, "s" is given as follows;

s × (\(c_s\) - \(p_s\)) > C

s × ($6.25 - $1.70) > $7,900, which gives;

s > $7,900/($6.25 - $1.70)

$7,900/($6.25 - $1.70) ≈ 1,73.26

We round up to get, s > 1,737

We round up

Therefore, the number of more (extra) sandwiches the food truck have to sell to earn money from selling sandwiches than it pays in expenses and food costs is the difference in the number of sandwiches it has to sell at $7.75 and $6.25 to earn more money than it pays in fixed expenses (costs) and the sandwich cost which is given as follows;

At $7.75 the number of sandwiches the food truck has to sell s > 1,306

At $1.70 the number of sandwiches the food truck has to sell is s > 1,737

The more number of sandwiches it has to sell = 1,737 - 1,306 = 431 more sandwiches

The more number of sandwiches it has to sell = 431 more sandwiches

(From which we check to have; 1306 + 431 = 1737 which is correct)

The inequality represents how many sandwiches, the food truck is \(s \times ($7.75 - $1.70) > $7,900.00\)

The solution of the inequality is,1,305.79

The more number of sandwiches it has to sell is 1373 more sandwiches

Given that,

A local food truck specializes in gourmet grilled cheese sandwiches.

Each month, the owners of the truck have a constant total of $7,900 in expenses (salaries, truck loan, etc.) and it costs $1.70 per sandwich to make each sandwich.

The food truck sells its sandwiches for $7.75 each.

We have to determine,

Write an inequality to represent how many sandwiches, the food truck.

Solve the inequality.

To gain more sales, the food truck offers a discount one month of $1.50 off its sandwiches.

How many more sandwiches will it need to sell to earn more money from selling sandwiches than it pays in expenses and food costs

According to the question,

The constant total expenses (fixed cost), C = $7,900

The cost takes to make each sandwich,  = $1.70

The price at which the food truck sells its sandwiches,  = $7.75

Where "s" represents the number of sandwiches sold.

\(s \times (c_s-p_s)>c\)

Substituting the known value in the equation,

\(s \times ($7.75 - $1.70) > $7,900.00\)

       $7,900/($7.75 - $1.70)

       = 158,000/121

       ≈ 1,305.79

The nearest whole number since we are counting sandwiches which are counted per piece.

Therefore;

s > 1,306 sandwiches

An explanation is that the food truck will have to sell more than 1,305 sandwiches to earn more money than it pays in expenses and sandwich costs.

The number of sandwiches the food truck company will have to sell on that month to earn more money from selling sandwiches than it pays the in expenses and sandwich cost, "s" is given as follows;

\(s \times (c_s-p_s)>c\)

s × ($6.25 - $1.70) > $7,900, which gives;

s > $7,900/($6.25 - $1.70)

$7,900/($6.25 - $1.70) ≈ 1,73.26

s > 1,737

Therefore, the number of more (extra) sandwiches the food truck have to sell to earn money from selling sandwiches than it pays in expenses and food costs is the difference in the number of sandwiches it has to sell at $7.75 and $6.25 to earn more money than it pays in fixed expenses (costs) and the sandwich cost which is given as follows;

At $7.75 the number of sandwiches the food truck has to sell s > 1,306

At $1.70 the number of sandwiches the food truck has to sell is s > 1,737

The more number of sandwiches it has to sell = 1,737 - 1,306 = 431 more sandwiches

The more number of sandwiches it has to sell = 431 more sandwiches

= 1306 + 431 = 1737

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The revenue function of the tile factory in terms of tiles sold is y = 0.25x + 500 and the flat fee for delivery is $500.

The given equation relates the revenue of the tile factory to the number of tiles sold. To find the revenue function in terms of tiles sold, we can solve the given equation for y:

y - 3,000 = 0.25(x - 10,000)

y = 0.25x - 2,500 + 3,000

y = 0.25x + 500

So, the revenue function of the tile factory in terms of tiles sold is y = 0.25x + 500.

Now, we can use the given information to find the flat fee for delivery. We know that the customer paid a total of $3,000 for 10,000 tiles, so we can substitute these values into the revenue function and solve for the flat fee:

3,000 = 0.25(10,000) + flat fee

3,000 = 2,500 + flat fee

flat fee = 500

Therefore, the flat fee for delivery is $500.

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Answer:

miles is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

(x+1)(x+1)(2x−5)(x^2−4x+5)

Step-by-step explanation:

2x^5−9x^4+6x^3+22x^2−20x−25

2x^5−9x^4+6x^3+22x^2−20x−25

=(x+1)(x+1)(2x−5)(x2−4x+5)

Answer:

A. 75 in³

Step-by-step explanation:

\(volume = \frac{1}{3} \times \pi \: {r}^{2} \: h = \frac{1}{3} \times \pi \times { 3}^{2} \times 8 = 75.4\)