10 to the -21st power

Answer:

i'm pretty sure the answer is A

Step-by-step explanation:

The pmf of the sum when rolling these two dice is as follows:

Sum  | Probability
-----|------------
2    | 1/36
3    | 1/18
4    | 1/36
5    | 1/18
6    | 1/18
7    | 1/18
8    | 1/18
9    | 1/18
10   | 1/18
11   | 1/18
12   | 1/36

The pmf (probability mass function) of the sum when rolling two six-sided dice can be calculated by determining the probability of each possible sum.

To find the pmf, we need to consider all the possible outcomes when rolling the two dice. We will calculate the probability for each sum and then normalize the probabilities to add up to 1.

Let's list all the possible sums and their corresponding probabilities:

- The sum can be 2 when both dice show a 1. The probability of this is (1/6) * (1/6) = 1/36.
- The sum can be 3 when one die shows a 1 and the other die shows a 2. There are two possible combinations: (1, 2) and (2, 1). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 3 is 2 * (1/36) = 1/18.
- The sum can be 4 when one die shows a 2 and the other die shows a 2. The probability of this is (1/6) * (1/6) = 1/36.
- The sum can be 5 when one die shows a 2 and the other die shows a 3. There are two possible combinations: (2, 3) and (3, 2). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 5 is 2 * (1/36) = 1/18.
- The sum can be 6 when one die shows a 2 and the other die shows a 4. There are two possible combinations: (2, 4) and (4, 2). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 6 is 2 * (1/36) = 1/18.
- The sum can be 7 when one die shows a 3 and the other die shows a 4. There are two possible combinations: (3, 4) and (4, 3). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 7 is 2 * (1/36) = 1/18.
- The sum can be 8 when one die shows a 3 and the other die shows a 5. There are two possible combinations: (3, 5) and (5, 3). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 8 is 2 * (1/36) = 1/18.
- The sum can be 9 when one die shows a 3 and the other die shows an 8. There are two possible combinations: (3, 8) and (8, 3). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 9 is 2 * (1/36) = 1/18.
- The sum can be 10 when one die shows a 4 and the other die shows a 5. There are two possible combinations: (4, 5) and (5, 4). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 10 is 2 * (1/36) = 1/18.
- The sum can be 11 when one die shows a 4 and the other die shows an 8. There are two possible combinations: (4, 8) and (8, 4). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 11 is 2 * (1/36) = 1/18.
- The sum can be 12 when one die shows a 8 and the other die shows an 8. The probability of this is (1/6) * (1/6) = 1/36.

Now, let's add up all the probabilities:
(1/36) + (1/18) + (1/36) + (1/18) + (1/18) + (1/18) + (1/18) + (1/18) + (1/18) + (1/18) + (1/36) = 1/2

Therefore, the pmf of the sum when rolling these two dice is as follows:

Sum  | Probability
-----|------------
2    | 1/36
3    | 1/18
4    | 1/36
5    | 1/18
6    | 1/18
7    | 1/18
8    | 1/18
9    | 1/18
10   | 1/18
11   | 1/18
12   | 1/36

To know more about pmf refer here:

https://brainly.com/question/18688445

#SPJ11

The possible monthly high temperature is less than 25°.

It's important to note that temperature simply means the degree of hotness and the coldness that a particular medium has.

In this situation, the difference between the monthly high and low temperatures was less than 27° Fahrenheit and monthly low temperature

was -2° Fahrenheit. Therefore, the monthly high will be:

High - Low < 27

High - (-2) < 27

High + 2 < 27

High < 27 - 2

High < 25

The interpretation means that the temperature is less than 25°F.

Learn more about temperature on:

brainly.com/question/24746268

#SPJ1

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

To learn more about interest click here: https://brainly.com/question/31907854

#SPJ11

BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Triangle congruence: Two triangles are said to be congruent if their three corresponding sides and their three corresponding angles are of identical size.

You can move, flip, twist, and turn these triangles to produce the same effect. When relocated, they are parallel to one another.

Two triangles are congruent if they satisfy all five conditions for congruence.

They include the right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and angle-side-angle (SSS) (RHS).

So, in the given △DAB and △DCB:

AC = AC = Common

∠DAC = ∠BAC = AC is the angle bisector

∠DCA = ∠BCA = AC is the angle bisector

Then, △DAB ≅ △DCB under the ASA congruency rule,

Then, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Therefore, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Know more about triangle congruency here:

https://brainly.com/question/2938476

#SPJ1

Answer: D. 32/x

Step-by-step explanation: To find how many desks are in EACH row we need to DIVIDE 32 by x, so the correct equation is 32/x or the last answer choice.

Hope this helps!

Mark Brainliest if you want!

Answer:

32/x

Step-by-step explanation:

32 desks in x rows

like, for example, let's say x = 8 (8 rows)

32/8 = 4 so four desks per row

The breadth of each rectangle is 11 units.

Let's consider that each rectangle has a length of l and breadth of b. We have been given that the perimeter of the shape that is formed by putting together the 4 rectangles is 88 units. We know that, the perimeter of a rectangle is given by the formula 2(l + b).

Therefore, the perimeter of the shape is given by the formula: P = 2(l + b) + 2(l + b) = 4(l + b)

From the given information, we know that the perimeter of the shape is 88.

Therefore,4(l + b) = 88

Dividing both sides of the equation by 4, we get: l + b = 22

We have found the relationship between the length and breadth of each rectangle.

Now, we need to find the value of the breadth of each rectangle.

We know that there are 4 rectangles placed side by side to form the shape.

Therefore, the total breadth of all 4 rectangles put together is equal to the breadth of the shape.

Hence, we can find the breadth of each rectangle by dividing the total breadth by the number of rectangles.

Let's denote the breadth of each rectangle as b'.

Therefore, b' = Total breadth / Number of rectangles

b' = (l + b + l + b) / 4b' = (2l + 2b) / 4b' = (l + b) / 2

We have found that the sum of the length and breadth of each rectangle is equal to 22 units.

Therefore, the breadth of each rectangle is half the sum of the length and breadth of each rectangle.

Substituting this value in the above equation, we get:b' = (l + b) / 2b' = 22 / 2b' = 11

Therefore, the breadth of each rectangle is 11 units.

Learn more about: breadth

https://brainly.com/question/31078585

#SPJ11

The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.

The "center" of circle is called as midpoint of diameter.

The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and

The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.

So, center of circle is (4,3),

The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:

⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.

⇒ distance = √((4 - 4)² + (9 - (-3))²)

⇒ √(144) = 12.

So, radius is 6.

The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,

Substituting the values

We get,

⇒ (x - 4)² + (y - 3)² = 6²,

⇒ (x - 4)² + (y - 3)² = 36,

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.

Learn more about Circle here

https://brainly.com/question/29104982

#SPJ4

Mr. Garcia's classroom had 23 students.

Let's denote the number of students in Mr. Cooper's classroom as C and the number of students in Mr. Garcia's classroom as G.

Given that Mr. Cooper's classroom had 5 tables with 4 students at each table, we can write:

C = 5 * 4 = 20

It is also given that Mr. Garcia's classroom had 3 more students than Mr. Cooper's classroom, so we can write:

G = C + 3

Substituting the value of C from the first equation into the second equation, we get:

G = 20 + 3 = 23

Therefore, Mr. Garcia's classroom had 23 students.

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ4

3x-4y=16

add 4y to both sides

3x=4y+16

divide both sides by 3

x=(4y+16)/3

Answer:

Just find the coordinate at the point where the x-coordinate is 3

Step-by-step explanation:

F(x) is just another term for Y. The variable of X is the value that you input into the f(x), which just stands for a function. Since the value that they asked for was 3, you know that they inputted the value of 3 as x. Just look where the coordinate at the point where the x-coordinate is 3 to find the answer.

Answer:

Sample Response: For f(3), the input is 3 and you are looking for the output. To determine the function's value when x = 3, go to the value of 3 on the x-axis and then locate the graph for that value of x. Determine the value of y from the y-axis at that location on the graph.

Step-by-step explanation:

answer on edge2020

The series 9/10 - 9/12 + 9/14 - 9/16 + 9/18 - ... can be rewritten as the sum of an infinite series with the formula Σ[(-1)ⁿ-¹ * 9/(8+n*2)], where n starts from 1 and goes to infinity.

We can derive this formula by following these steps-
1. First, we can notice that the numerators are always 9 and the denominators are increasing by 2 each time (10, 12, 14, 16, ...).
2. We can rewrite the denominator as 8 + n*2, where n starts at 1 (8 + 1*2 = 10, 8 + 2*2 = 12, ...).
3. The signs alternate between positive and negative. This can be represented by (-1)^(n-1), where n starts at 1 (so the first term is positive).
4. Combine these elements into the formula: (-1)^(n-1) * 9/(8+n*2).
5. Write the series as the sum of an infinite series using the sigma notation:

Σ((-1)ⁿ-¹ * 9/(8+n*2)), where n starts from 1 and goes to infinity.

Learn more about the sum of the infinite series: https://brainly.com/question/11752555

#SPJ11

8 ounce of brown rice and 9 ounce quinoa sold.

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:

Brown rice: $2.00 per pound

Quinoa: $4.50 per pound

let the brown rice sold x ounces

and, let the Quinoa sold be y ounces

So, the equations are:

x + y= 17

2x+ 4.5y= 54

2( 17- y) + 4.5y= 54

34 - 2y + 4.5y= 54

2.5y= 20

y= 20/2.5

y= 8 ounce

and, x= 17-8= 9 ounce

Hence, 8 ounce of brown rice and 9 ounce quinoa sold.

Learn more about Equation here:

https://brainly.com/question/10413253

#SPJ1

Answer:

gooOoOood laCCccckK

Answer:

thats really cool

Step-by-step explanation:

good luck :)

please give brainly

A nurse should empty a Hemovac wound suction device when it is half full to ensure proper functioning and prevent discomfort or injury to the patient due to the device becoming too heavy.

The rationale for a nurse to empty a Hemovac wound suction device when it is half full is to ensure the device is functioning correctly and to prevent it from becoming too heavy and potentially causing discomfort or injury to the patient.

When a Hemovac wound suction device is half full, it may start to lose suction, which can result in less efficient drainage of fluid from the wound site. By emptying the device, the nurse can ensure that the device is functioning correctly and that the suction pressure is maintained.

Additionally, allowing the device to become too full can make it heavy and uncomfortable for the patient, potentially causing discomfort or injury to the wound site. Therefore, emptying the device when it is half full can help prevent these complications and ensure that the patient remains comfortable throughout the healing process.

Learn more about Hemovac wound here

brainly.com/question/30193125

#SPJ4

1. The word that describes a pattern in nature that is also exhibited in the external appearances of animals is "symmetry."

Symmetry refers to the balanced arrangement of parts or elements. In nature, many animals display symmetry in their body structure, such as butterflies with their symmetrical wings.

2. The word that describes a pattern exhibited by objects when their similar parts are regularly arranged around a central axis and the pattern looks the same after a certain amount of rotation is "rotational symmetry."

Rotational symmetry occurs when an object can be rotated and still maintain its original appearance. For example, a circle has rotational symmetry because it looks the same after any amount of rotation.

3. The word that describes curved patterns made by a series of circular shapes revolving around a central point is "spiral."

Spirals can be seen in various aspects of nature, like the arrangement of petals in a sunflower or the shape of a seashell.

4. The word that describes a pattern exhibited by objects that do not change their size and shape even if they are moved to another location is "translation symmetry."

Translation symmetry means that an object can be moved without altering its characteristics. For instance, a rectangle has translation symmetry because it remains the same even if it is shifted horizontally or vertically.

5. The word that describes an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a contour or an axis is "reflection symmetry" or "mirror symmetry."

Reflection symmetry means that an object can be divided into two equal halves, and each half is a mirror image of the other. For example, the letter "A" exhibits reflection symmetry when it is divided vertically down the middle.

Now, moving on to the second part of the question, which involves finding values in the Fibonacci sequence:

1. Fib(8) = 13
2. Fib(19) = 4181
3. Fib(23) = 28,657

1. To find Fib(8), we can use the Fibonacci sequence. Fib(1) = 1, Fib(2) = 1, and each subsequent term is the sum of the previous two terms. So, Fib(3) = Fib(1) + Fib(2) = 1 + 1 = 2.

Similarly, Fib(4) = 2 + 1 = 3, Fib(5) = 3 + 2 = 5, Fib(6) = 5 + 3 = 8, and Fib(7) = 8 + 5 = 13. Therefore, Fib(8) is 13.

2. To find Fib(19), we can continue using the Fibonacci sequence. By applying the same pattern of adding the previous two terms, we find that Fib(19) is 4181.

3. Given that Fib(22) = 17,711 and Fib(24) = 46,368, we can determine Fib(23) by subtracting the known terms

. Since Fib(23) = Fib(24) - Fib(22),

we have Fib(23) = 46,368 - 17,711 = 28,657.

In summary:
1. Fib(8) = 13
2. Fib(19) = 4181
3. Fib(23) = 28,657

To know more about Fibonacci sequence refer here:

https://brainly.com/question/29764204

#SPJ11

Answer:

Ya the other guys correct

Step-by-step explanation:

(only answering so u can give the other guy brainlyist)

The correct option regarding the scale factor and the statement in this problem is given as follows:

D. The statement is false. Because there are 3 feet in one​ yard, there are 9 square feet in one square yard.

The scale factor between the length dimensions of the yard are given as follows:

3 feet = 1 yard.

(as these length dimensions are given in yards).

Then for the square units, the correct scale factor is found applying the proportion as follows:

(3 feet)² = (1 yard)².

9 feet squared = 1 square yard.

Hence the statement given in this problem, that because there are 3 feet in one​ yard, there are also 3 square feet in one square yard, is false, and the correct option is given by option D.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

To find the eigenvalue of a matrix in R^2 which reflects a point across a line through the origin, we first need to construct the matrix.

Let the line through the origin be represented by the unit vector u = [cosθ, sinθ] where θ is the angle between the positive x-axis and the line. The matrix A which reflects a point across this line is given by:
A = 2(uu^T) - I
where uu^T is the outer product of u with itself and I is the identity matrix. Note that u^T is the transpose of u.
To find the eigenvalue λ of this matrix, we need to solve the characteristic equation:
det(A - λI) = 0
where I is the identity matrix of size 2. Substituting A into this equation and expanding the determinant, we get:
det(2(uu^T) - I - λI) = 0
det(2(uu^T - (1+λ)I)) = 0
Using the fact that det(cA) = c^n det(A) for any constant c and matrix A of size n, we can simplify this to:
det(uu^T - (1+λ)/2 I) = 0
Expanding the determinant, we get:
(λ+1/2)(λ-3/2) = 0
Therefore, the eigenvalues of A are λ = -1/2 and λ = 3/2.

To know more about matrix visit:

https://brainly.com/question/29132693

#SPJ11

Answer:

yes

Step-by-step explanation:

You have the correct intercepts

Answer:

8.21%

Step-by-step explanation:

r = (1/t)(A/P - 1)

t = 13

A = 6200

P = 3000

        1          6200

r = (-------) ((------------) - 1))

       13         3000

        1          31

r = (-------) ( ------ - 1)

       13         15

        1          16

r = (-------) ( ------ )

       13         15

       16

r = --------  =  0.0820512

       195

r = 0.0820512 x 100 = 8.20512

r ≈ 8.21%

I hope this helps!

Answer:

Step-by-step explanation:

Compounded Monthly:

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

A=6200

P=3000

t=13

n=12

​

Plug in and simplify:

1. Multiply 12 times 13

2. Divide out the 3000

3. Raise both sides to the 1/156 power to cancel out the exponent

4. Subtract 1 from both sides

5. Multiply by 12 on both sides

R should equal 0.0559716

That is about 5.60%

5.60%

e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

For more questions like P-value click the link below:

https://brainly.com/question/14790912

#SPJ4

The correct option for the past forecasts using the 2-period moving average method is:
A. F1 = 5582 F2 = 5352 F3 = 5438.5 F4 = 6037.5 F5 = 5736.5

Step-by-step explanation:
1. To calculate F2, take the average of Period 1 and Period 2 actual sales: (5582 + 5122) / 2 = 5352.
2. For F3, average Period 2 and Period 3 actual sales: (5122 + 5755) / 2 = 5438.5.
3. For F4, average Period 3 and Period 4 actual sales: (5755 + 6320) / 2 = 6037.5.
4. For F5, average Period 4 and Period 5 actual sales: (6320 + 5153) / 2 = 5736.5.

"Random variation" encompasses the irregular changes in a time series that are not caused by any other component. Some  common example of random variation is coin toss. It  is independent of the effects of systematic biases. In general, the larger the sample size is, the lower the random variation is of the estimate of a parameter. As random variation decreases, precision increases.

LEARN MORE ON FORECAST AT:https://brainly.com/question/31538767

#SPJ11

the standard matrix of the linear transformation T: ℝ² → ℝ², which first reflects points through the line x₂ = -x₁ and then reflects points through the origin, is:

[ -1  0 ]

[  0  1 ]

To find the standard matrix of the linear transformation T: ℝ² → ℝ², we can determine how the basis vectors of ℝ² transform under the given transformation.

The standard basis vectors of ℝ² are:

e₁ = (1, 0) (corresponding to the x-axis)

e₂ = (0, 1) (corresponding to the y-axis)

First, let's apply the reflection through the line x₂ = -x₁:

For e₁ = (1, 0), the reflection through the line x₂ = -x₁ maps it to (-1, 0).

For e₂ = (0, 1), the reflection through the line x₂ = -x₁ maps it to (0, 1).

Next, let's apply the reflection through the origin:

For (-1, 0), the reflection through the origin keeps it the same (-1, 0).

For (0, 1), the reflection through the origin keeps it the same (0, 1).

Now, we have the transformed basis vectors:

T(e₁) = (-1, 0)

T(e₂) = (0, 1)

The standard matrix of the linear transformation T is constructed by placing the transformed basis vectors as columns:

[ -1  0 ]

[  0  1 ]

To know more about points visit:

brainly.com/question/30891638

#SPJ11

Answer:

c

Step-by-step explanation:

I did the test and got it correct

The correct for the new member's score will affect center and spread of the bowling team is,

⇒ The new member's score will increase the center and spread of the bowling team.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The members of a bowling team score from 159 to 221. Their average score is 172.

And, A new member with an outlying score of 279 joins the team.

We know that;

When we add new member with an outlying score of 279 joins the team, the value of average is increase.

Thus, The correct for the new member's score will affect center and spread of the bowling team is,

⇒ The new member's score will increase the center and spread of the bowling team.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

The efficient outcome in the market for milk portrayed in the figure would be where the marginal cost (MC) curve intersects with the demand (D) curve, which is at a price of $3 per gallon.

To determine which price yields an efficient outcome in the market for milk, we need to find the equilibrium price. The equilibrium price is where the supply and demand curves intersect, which represents the point at which the quantity demanded equals the quantity supplied.

                                At this price, the quantity of milk produced and consumed will be at the socially optimal level where the marginal benefit (MB) equals the MC, resulting in a Pareto efficient outcome. It is important to note that this assumes no externalities or market failures are present in the market for milk.

1. Identify the supply and demand curves in the figure. The demand curve typically slopes downward, while the supply curve slopes upward.
2. Locate the point where the supply and demand curves intersect.
3. Find the price corresponding to this point on the vertical axis (price axis).

The equilibrium price found in step 3 is the price that yields an efficient outcome in the market for milk.

Learn more about demand (D) curve

brainly.com/question/14333119

#SPJ11

Answer:

find out how many units higher g(x) is compared to f(x).

g(x) is 3 units higher than f(x)

Since the graph is 3 units higher, the value of k must be 3.

Step-by-step explanation:

ok i honestly hope i answerd this correctly because im terrible at reading math

According to the question The volume of the solid obtained by rotating the region about the \($y$\)-axis is \($0$\).

To find the volume of the solid obtained by rotating the region bounded by the curves \(x = 6 - 3y$, $x = 0$, and $y = 3$\) about the \($y$\)-axis, we can use the method of cylindrical shells.

The height of each cylindrical shell is the difference between the two curves, which is given by \($(6 - 3y) - 0 = 6 - 3y$\)

The radius of each cylindrical shell is the distance from the \($y$\)-axis, which is simply \($y$\).

The differential volume of each cylindrical shell is then given by \(dV = 2\pi y(6 - 3y) \, dy$.\)

To find the total volume, we integrate the differential volume from \(y = 0$ to $y = 3$:\)

\($V = \int_{0}^{3} 2\pi y(6 - 3y) \, dy$\)

To solve the integral, let's integrate the expression step by step:

\($V = \int_{0}^{3} 2\pi y(6 - 3y) \, dy$\)

Expanding the expression, we have:

\($V = \int_{0}^{3} 12\pi y - 6\pi y^2 \, dy$\)

Integrating term by term, we get:

\($V = \left[6\pi \left(\frac{1}{2}y^2\right) - 2\pi \left(\frac{1}{3}y^3\right)\right] \bigg|_{0}^{3}$\)

Simplifying further:

\($V = \left[3\pi y^2 - \frac{2}{3}\pi y^3\right] \bigg|_{0}^{3}$\)

Plugging in the limits of integration:

\($V = \left[3\pi \cdot 3^2 - \frac{2}{3}\pi \cdot 3^3\right] - \left[3\pi \cdot 0^2 - \frac{2}{3}\pi \cdot 0^3\right]$\)

Simplifying:

\($V = \left[27\pi - 27\pi\right] - \left[0 - 0\right]$\)

\($V = 0$\)

Therefore, the volume of the solid obtained by rotating the region about the \($y$\)-axis is \($0$\).

To know more about integration visit -

brainly.com/question/30543110

#SPJ11