10. Consider the following moving average processes: Y(n)=1/2(X(n)+X(n−1)) Xo=0 Z(n) = 2/3X(n)+1/3X(n-1) Xo = 0 Find the mean, variance, and covariance of Y(n) and Z(n) if X(n) is a IID(0,σ²) rand
Answers
The mean of Y(n) is 0.
The mean of Z(n) is 0.
The variance of Y(n) is σ²/2.
The variance of Z(n) is (4/9)σ²/2.
Let's calculate the mean, variance, and covariance of Y(n) and Z(n) based on the given moving average processes.
Mean:
The mean of Y(n) can be calculated as:
E[Y(n)] = E[1/2(X(n) + X(n-1))]
Since X(n) is an IID(0,σ²) random variable, its mean is zero. Therefore, E[X(n)] = 0. We can also assume that X(n-1) is independent of X(n), so E[X(n-1)] = 0 as well. Hence, the mean of Y(n) is:
E[Y(n)] = 1/2(E[X(n)] + E[X(n-1)]) = 1/2(0 + 0) = 0.
Similarly, for Z(n):
E[Z(n)] = E[(2/3)X(n) + (1/3)X(n-1)]
Using the same reasoning as above, the mean of Z(n) is:
E[Z(n)] = (2/3)E[X(n)] + (1/3)E[X(n-1)] = (2/3)(0) + (1/3)(0) = 0.
Variance:
The variance of Y(n) can be calculated as:
Var(Y(n)) = Var(1/2(X(n) + X(n-1)))
Since X(n) and X(n-1) are independent, we can calculate the variance as follows:
Var(Y(n)) = (1/2)²(Var(X(n)) + Var(X(n-1)))
Since X(n) is an IID(0,σ²) random variable, Var(X(n)) = σ². Similarly, Var(X(n-1)) = σ². Hence, the variance of Y(n) is:
Var(Y(n)) = (1/2)²(σ² + σ²) = (1/2)²(2σ²) = σ²/2.
For Z(n):
Var(Z(n)) = Var((2/3)X(n) + (1/3)X(n-1))
Using the same reasoning as above, the variance of Z(n) is:
Var(Z(n)) = (2/3)²Var(X(n)) + (1/3)²Var(X(n-1)) = (4/9)σ² + (1/9)σ² = (5/9)σ².
To calculate the covariance between Y(n) and Z(n), we need to consider the relationship between X(n) and X(n-1). Since they are assumed to be independent, the covariance is zero. Hence, Cov(Y(n), Z(n)) = 0.
The mean of Y(n) and Z(n) is zero since the mean of X(n) and X(n-1) is zero. The variance of Y(n) is σ²/2, and the variance of Z(n) is (4/9)σ²/2. There is no covariance between Y(n) and Z(n) since X(n) and X(n-1) are assumed to be independent.
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Related Questions
no matter what the resource allocation is, area a will always have the highest resource availability.
Answers
The given statement "no matter what the resource allocation is, area A will always have the highest resource availability," is not essentially true.
The term "area" generally refers to a specific region or part of a larger space. In the context of your question, area A represents a particular zone with resources allocated to it. Resource availability refers to the quantity and accessibility of resources in a given area.
To claim that area A will always have the highest resource availability regardless of resource allocation, it implies that there are factors inherent to area A that consistently make it the most resource-rich zone. This could be due to natural resource distribution, infrastructure, or other variables that ensure area A maintains the highest resource availability.
However, without additional information about area A and the specific resources in question, it is difficult to definitively state that area A will always have the highest resource availability.
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what is p to the power of to-5 when p = 14
Answers
Step-by-step explanation:
p^(-5) = 1 / p^5 = 1/14^5 = 1.859 x 10^-6
You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a diamond each time.
Answers
Solution:
Given:
A 52-card deck
There are four suits in a standard deck of cards, Clubs, Hearts, Spades, and Diamonds.
There are 13 diamond cards.
Hence,
\(\begin{gathered} \text{Diamond cards = 13} \\ \text{Total cards = 52} \end{gathered}\)Probability is calculated by;
\(\text{Probability}=\frac{n\text{ umber of required outcomes}}{n\text{ umber of total or possible outcomes}}\)Thus, the probability of drawing a diamond on the first draw is;
\(\begin{gathered} \text{Probability of drawing a diamond}=\frac{n\text{ umber of diamond cards}}{\text{total number of cards}} \\ \text{Probability of drawing a diamond}=\frac{13}{52} \\ \text{Probability of drawing a diamond}=\frac{1}{4} \\ P(D_1)=\frac{1}{4} \end{gathered}\)Since two draws are made with replacement, the cards are completed back again before the next draw.
Hence, the probability of drawing a diamond on the second draw is;
\(\begin{gathered} \text{Probability of drawing a diamond}=\frac{n\text{ umber of diamond cards}}{\text{total number of cards}} \\ \text{Probability of drawing a diamond}=\frac{13}{52} \\ \text{Probability of drawing a diamond}=\frac{1}{4} \\ P(D_2)=\frac{1}{4} \end{gathered}\)Therefore, the probability of drawing a diamond each time;
\(\begin{gathered} P(D_1D_2)=\frac{1}{4}\times\frac{1}{4} \\ P(D_1D_2)=\frac{1}{16} \end{gathered}\)
PLEASE HELP URGENTLY!!! I WILL GIVE BRAINLIEST TO WHOEVER GETS IT RIGHT.
Answers
Answer:
f(-2) = -1
Step-by-step explanation:
Look at x = -2 and find the value of y.
Subtract p - q from 2p - q + 4. answer the following with explanation
i need the answer ASAP pls tell the answer and i will mark as the brainliest
Answers
Answer:
Step-by-step explanation:
2p - q + 4 - ( p - q )
2p - q + 4 - p + q
By rearranging the terms
2p - p + 4
( you might think where -q and +q went ???
They are cancelled because they have opposite signs )
∴The answer is p + 4
Hope it helps
plz mark as brainliest!!!!!!!
Answer:
\(\boxed{p+4}\)
Step-by-step explanation:
It will be like
=> (2p - q + 4) - (p-q)
=> 2p-q+4-p+q
Combining like terms
=> 2p-p-q+q+4
=> p+4
Please help!!
Evaluate 2x4y for x = 2 and y = 4.
A.-64
B.1/8
C.1/2
Answers
Step-by-step explanation:
2x4y. x=2. y=4
2(2)4(4) Pemdas
2x2=4 4x4=16
4x16
64
Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.)
F(x, y) = (2x − 4y) i + (−4x + 10y − 5) j
f(x, y) =
Answers
The vector field F(x, y) = (2x - 4y) i + (-4x + 10y - 5) j is a conservative vector field. The function f(x, y) that satisfies ∇f = F is f(x, y) = \(x^{2}\) - 4xy + 5y + C, where C is a constant.
To determine whether a vector field is conservative, we check if its curl is zero. If the curl is zero, then the vector field is conservative and can be expressed as the gradient of a scalar function.
Let's calculate the curl of F = (2x - 4y) i + (-4x + 10y - 5) j:
∇ x F = (∂F₂/∂x - ∂F₁/∂y) i + (∂F₁/∂x - ∂F₂/∂y) j
= (-4 - (-4)) i + (2 - (-4)) j
= 0 i + 6 j
Since the curl is zero, F is a conservative vector field. Therefore, there exists a function f such that ∇f = F.
To find f, we integrate each component of F with respect to the corresponding variable:
∫(2x - 4y) dx = \(x^{2}\) - 4xy + g(y)
∫(-4x + 10y - 5) dy = -4xy + 5y + h(x)
Here, g(y) and h(x) are arbitrary functions of y and x, respectively.
Comparing the expressions with f(x, y), we see that f(x, y) = \(x^{2}\) - 4xy + 5y + C, where C is a constant, satisfies ∇f = F.
Therefore, the function f(x, y) = \(x^{2}\) - 4xy + 5y + C is such that F = ∇f, confirming that F is a conservative vector field.
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A surf shop surveyed 100 customers about the number of items purchased and the length of time spent shopping in the store. Classify the random variables from the survey. A) Number of items, discrete; total time, continuous B) Number of items, continuous; total time, discrete C) Number of items, continuous; total time, continuous D) Number of items, discrete; total time, discrete E) Unable to determine from information given
Answers
Answer:
Step-by-step explanation:
Discrete variable assume a finite number of values. It can easily be counted. Continuous variable assumes an infinite number of values. It cannot be easily counted. It is mostly measured. Considering the given scenario, we can see that the number of items purchased customers can easily be counted. The length of time spent shopping can take an infinite set of values within a given range, thus it cannot be counted.
Therefore, the classification for the random variables from the survey is
A) Number of items, discrete; total time, continuous
Using the concept of continuous and discrete variables, it is found that the correct option is:
A) Number of items, discrete; total time, continuousVariables: Continuous variables: Can assume decimal values. Discrete variables: Assume only countable values, such as 0, 1, 2, 3, ...In this problem:
The number of items is countable, as you cannot have half an item, for example, hence it is discrete.Time can assume decimal values, for example, half an hour, hence it is continuous.Thus, option A is correct.You can learn more about continuous and discrete variables at brainly.com/question/25820365
can you help me please
Answers
Answer:
13.5 in^2
Step-by-step explanation:
6 = 1/2(B)(H) = 1/2(2)(H)
H = 6
H x 1.5 =9
area = 1/2(3)(9) = 13.5
Answer:
2.7 square inches
find the inverse of the function
F(x) = x² + 2x₁ [-1, 00]
Answers
1. Replace F(x) with y to get y = x² + 2x.
2. Rearrange the equation to isolate x: y = x² + 2x becomes x² + 2x - y = 0.
3. Use the quadratic formula to solve for x in terms of y:
x = (-2 ± sqrt(4 + 4y)) / 2
x = -1 ± sqrt(1 + y)
4. Since the domain of F(x) is [-1, 0], we only consider the negative square root in the expression for x:
x = -1 - sqrt(1 + y)
5. Replace x with its inverse function notation, denoted by F^(-1)(y):
F^(-1)(y) = -1 - sqrt(1 + y)
Therefore, the inverse of the function F(x) = x² + 2x over the interval [-1, 0] is given by F^(-1)(y) = -1 - sqrt(1 + y).
13/14
16 15
10
12 11
The diagram shows parallel lines a and b cut by
transversals c and d.
If m/1 = 123° and m/8= 110°, what is the measure of each of the following angles?
m/4=
m/10=>
m/16=
m/5=>
m/11=
Answers
Answer:
Using the properties of parallel lines and transversals, we can find the measures of the missing angles:
m/1 = m/2 (alternate interior angles)
m/1 = m/5 + m/4 (interior angles on the same side of transversal c)
m/8 = m/5 (corresponding angles)
m/8 = m/7 + m/6 (interior angles on the same side of transversal d)
We can use these equations to solve for the missing angles:
m/4 = m/1 - m/5 = 123° - 10° = 113°
m/10 = m/1 - m/8 = 123° - 110° = 13°
m/16 = m/8 + m/7 + m/6 = 110° + m/7 + m/6
m/5 = m/8 = 110°
m/11 = m/1 - m/10 - m/5 = 123° - 13° - 110° = 0°
Note that m/11 is 0°, which means that line b and transversal c are parallel, and there is no intersection between them.
Use Right Triangle Trigonometry to solve this problem. Round your answer to the nearest TENTH.
Answers
50 ft from the tower
angle=60°
since we know the angle and the Adj leg
we want to solve the Opp leg
then
\(tan(\theta)=\frac{Opp}{Adj}\)\(tan(60)=\frac{Opp}{60}\)\(60tan(60)=Opp\)\(60\sqrt{3}=Opp\)\(Opp=103.92304\)Rounded to the nearest tenth
the tower is 103.9 ft tall
which values for h and k are used to write the function f of x = x squared 12 x 6 in vertex form?h=6, k=36h=−6, k=−36h=6, k=30h=−6, k=−30
Answers
The values of h and k used to write the function f(x) = x^2 + 12x + 6 in vertex form are h = -6 and k = -30.
The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. To rewrite the given function in vertex form, we need to complete the square.
Starting with the function f(x) = x^2 + 12x + 6, we can rewrite it as f(x) = (x^2 + 12x + 36) - 36 + 6. Notice that we added and subtracted the square of half the coefficient of x, which is (12/2)^2 = 36.
Simplifying further, we have f(x) = (x + 6)^2 - 30. Comparing this form with the vertex form, we can see that h = -6 and k = -30.
Therefore, the correct values for h and k to write the function f(x) = x^2 + 12x + 6 in vertex form are h = -6 and k = -30.
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What is 4/4 divided by 20 divided by 60 equal
Answers
Answer:
The Product is 0.00083333333.
Step-by-step explanation:
Hope this helps! :)
The correct answer for the value of \((\dfrac{4}{4})\) ÷ \(20\) ÷ \(60\) is 0.0008333.
Given expression:
\((\dfrac{4}{4})\) ÷ \(20\) ÷ \(60\)
To solve the expression, follow the order of operations(BODMAS):
Parentheses/Brackets
Exponents/Orders
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
In this case;
Divide and perform the operations from left to right:
\((\dfrac{4}{4})\)
= 1 (because any number divided by itself is always 1)
\(\dfrac{1}{20}\)
= 0.05
\(\dfrac{0.05}{60}\)
= 0.0008333... (repeating decimal)
The final result is approximately 0.0008333.
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Which inequality is shown in the graph?
Answers
please please please please help im beggingggggg
Answers
on what ?
there Nothing
A farmer feeds her 4 horses 2 bales of hay. How many bales of hay would the farmer need in order to feed 20 horses?
Answers
Answer: 40 bales of hay
Step-by-step explanation:
Learning Goal: To use the principle of work and energy to determine characteristics of a mass being pulled up an incline and determine the power that must be supplied to the system when the efficiency of the input system is considered As shown, a 53 kg crate is pulled up a θ=40∘ incline by a pulley and motor system. Initially at rest, the crate is pulled s=4.7 m up along the incline, Undergoing constant acceleration, the crate reaches a speed of 2.5 m/s at the instant it has traveled this distance.(Figure 1) Figure 1 of 1 Considening the coeflicent of konetic finction μh=0.13, deternine the power that the motor must supply to the ciate the instant the crate traveis a distance of 4 f in Express your answer to two significant figures and include the appropriate units. Part B - Power supplied to the motor when effictency is considered If the motor has an efficiency of e=0.90, what nower must be supplied to the motor to rase the crale? Express your answer to two significant figures and include the appropriate units. View Avallable Hintis) Part B - Power supplied to the motor when efficiency is considered If the motor has an efficiency of ε=0.90. What power must be supplied to the motor to raise the crate? Express your answer to two significant figures and include the appropriate units.
Answers
The power supplied to the motor when the efficiency is considered is 2.0 kW.
In this problem, we need to use the principle of work and energy to determine characteristics of a mass being pulled up an incline and determine the power that must be supplied to the system when the efficiency of the input system is considered.
First, we will determine the work done on the crate by the motor to pull it up an incline. We will also determine the power supplied to the motor at the instant the crate travels a distance of 4m.In the second part, we will determine the power supplied to the motor when efficiency is considered.
Part A The force parallel to the incline is given by F = ma, where a is the acceleration of the crate.
We will use the kinematic equation, v² = u² + 2as, where u = 0 (initial velocity), v = 2.5 m/s (final velocity), and s = 4.7 m (distance traveled) to calculate the acceleration.
\(2.5² = 0 + 2a(4.7) ⇒ a = 2.14 m/s²\)
The force parallel to the incline is given by:
\(F = ma = (53 kg)(2.14 m/s²) = 113.4 N\)
Therefore,
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If we are told ab=0, then what can we infer? by the zero product property we know = 0 = 0
Answers
If we are told that ab=0, then we can infer that either a or b (or both) must be equal to 0.
This is because when the product of two numbers is 0, at least one of the numbers must be 0 according to the zero product property.
One of the most crucial concepts for pupils to understand in maths and science is the zero product property.
The greatest educators, mathematicians, and recognized scientists in the fields of physics and chemistry have worked with Vedantu to provide their insights on the subject.
Their suggestions helped us develop materials for your understanding that would make it simple for you to put these ideas into practice.
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Find g(x), where g(x) is the translation 18 units down of f(x)= – 8x+9. Write your answer in the form mx+b, where m and b are integers.
Answers
The equation of translation of f ( x ) = –8x + 9 eighteen units down to get g ( x ) is written as g ( x ) =-8x - 9
m = -8b = -9What is translation?This is one of the movements observed in transformation. it is a straight line movement
How to find the translation equation of g(x)The data given in the question include
f ( x ) = –8x + 9
g(x) is the translation 18 units down
Translation down involves of a subtraction of the required units in the y direction.
g ( x ) = f ( x ) - 18
g ( x ) = (–8x + 9) - 18
g ( x ) =-8x + 9 - 18
g ( x ) =-8x - 9
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A minor league baseball team plays 94 games in a season. if the team won 16 more than twice as many games as they lost, how many wins and losses did the team have?
Answers
The number of wins is 68 ad losses is 26.
How to compute the value?Let the number of losses = l
Therefore, the number of wins will be: = (2 × l) + 16 = 2l + 16
Total games = 94
Therefore we will add the equation
l + 16 + 2l = 94
3l + 16 = 94
3l = 94 - 16
3l = 78
Divide
l = 78/3
l = 26
Losses = 26
Number if wins = 2l + 16 = 2(26) + 16 = 52 + 16 = 68
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Which geometric property is illustrated for the lengths of line segments: If DE = FG then FG = DE A. Reflexive Property B. Symmetric Property C. Transitive Property D. this is not a geomtric property as it does not hold
Answers
Answer:
I'm sorry I wish if I could help you but not sure of the answe
Answer:
B.
Symmetric Property
Step-by-step explanation:
Identify the slope of the line for the equation y= 1/6x + 1/4
Answers
Answer:
1/6x or just 1/6
Step-by-step explanation:
the equation is y = mx + b and 1/6x is in place m which is the slope
stream blueberry eyes by MAX AND SUGA periodTt
The slope is also known as the gradient and the rate of change of the line. The slope of the line for the equation y= 1/6x + 1/4 is 1/6
Slope of a lineThe slope is also known as the gradient and the rate of change of the line, The equation of aline in slope intercept form is expressed as:
y = mx + b
where
m is the slope
b is the y-intercept
Given the equation y = 1/6x + 1/4
Compare
mx = 1/6x
m = 1/6
Hence the slope of the line for the equation y= 1/6x + 1/4 is 1/6
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At which points on the curve y = 1 60x3 − 2x5 does the tangent line have the largest slope?
Answers
The tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.
First, let's find the derivative of the given function y = 1 + 60x³ − 2x⁵ using the power rule for differentiation:
dy/dx = 0 + 3(60)x² - 5(2)x⁴
= 180x² - 10x⁴
To find the critical points, we set the derivative equal to zero and solve for x:
180x² - 10x⁴ = 0
Factoring out common terms, we get:
10x²(18 - x²) = 0
Setting each factor equal to zero, we have:
10x² = 0 or 18 - x² = 0
From the first equation, we find x = 0.
From the second equation, we have:
18 - x² = 0
x² = 18
Taking the square root, we get:
x = ±√18
= ±3√2
So the critical points are x = 0, x = 3√2, and x = -3√2.
Now we need to evaluate the slope at these critical points. We can do this by plugging each x-value into the derivative:
When x = 0:
dy/dx = 180(0)² - 10(0)⁴ = 0
When x = 3√2:
dy/dx = 180(3√2)² - 10(3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080
When x = -3√2:
dy/dx = 180(-3√2)² - 10(-3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080
The slope is 0 when x = 0 and 1080 when x = 3√2 or x = -3√2.
Therefore, the tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.
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The complete question is as follows:
At which points on the curve y = 1 + 60x³ − 2x5⁵ does the tangent line have the largest slope?
evaluate the following expressions for d= -4 and e= -6
de/-6 e square - d square/4 d(e+3)/2 e(d square - 9)/6
Answers
Answer:
For d = -4 and e = -6, the values of the expressions are as follows:
de/-6 = 8
e square - d square/4 = 7
d(e+3)/2 = 9
e(d square - 9)/6 = -12
Step-by-step explanation:
We can simply substitute the given values of d and e into the expressions and evaluate them as follows:
de/-6 = (-4)(-6)/(-6) = 8
e square - d square/4 = (-6)^2 - (-4)^2/4 = 36 - 4/4 = 7
d(e+3)/2 = (-4)(-6+3)/2 = (-4)(-3)/2 = 6/2 = 3
e(d square - 9)/6 = (-6)((-4)^2 - 9)/6 = (-6)(16-9)/6 = -42/6 = -12
Therefore, the expressions evaluate to 8, 7, 3, and -12, respectively.
A traveler is walking on a moving walkway in an airport. The traveler must walk back on the walkway to get a bag he forgot. The traveler's ground speed is 1 ft/s against the walkway and 5 ft/s with the walkway. What is the traveler's speed off the walkway? What is the speed of the moving walkway?
Answers
Answer:
this is it
Step-by-step explanation:
Ecological correlation is correlations based on rates or averages, often used in political science or sociology, that tend to over-state the strength of an association. True/False?
Answers
It is true, as The term "ecological correlation" refers to correlations based on rates or averages that frequently appear in political science or sociology and tend to exaggerate the significance of a link.
what is correlation?Correlations describe the connections between different variables. Strong, weak, positive, or negative expressions are all possible. 1 = Causation need not always follow from correlation. A statistical measure of the linear relationship between two variables is called correlation (that is, do they change at a constant rate). Without defining cause and effect, this is a common method for illustrating straightforward connections. To illustrate the connection between two quantitative variables, statistical language employs correlation. Additionally, we consider that this connection is linear. In other words, when one variable changes by a given amount, the other variable also changes by a fixed amount, but only by one unit.
The term "ecological correlation" refers to correlations based on rates or averages that frequently appear in political science or sociology and tend to exaggerate the significance of a link.
So, it is true.
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Which of the following statements about AB and AC is true?
C(4.4)
A(-11)
B(0-4)
A. AB is longer than AC
B. AC is 6 units long
C. AB and AC are the same length
D. AC is longer than AB
Answers
Answer:
AB is longer than AC which is the letter a
HELP I DONT GET THIS AT ALL ILL GIVE BRAINLIST
Answers
Calvin is filling the pool in his backyard with water. If the pool is in the shape of a cylinder with a diameter of 12 ft and a height of 5 ft, how much water is needed to fill Syntax error from line 1 column 49 to line 1 column 73. Unexpected 'mathsize'. of the pool?
Answers
Answer: 135 pi
Step-by-step explanation: I took the test
It is a three-dimensional shape with two parallel circular bases and a curve surface.
The volume of water needed to fill the pool is 180π square feet.
What is a cylinder?It is a three-dimensional shape with two parallel circular bases and a curve surface.
Volume = π r² h
r = radius of the cylinder
h = height of the cylinder
We have,
Diameter of the cylinder = 12 ft
Radius = diameter/2 = 12/2 = 6 ft
Height of the cylinder = 5 ft
The volume of the cylinder:
= πr²h
= π x 6² x 5
= π x 36 x 5
= 180π square feet
Thus,
The volume of water needed to fill the pool is 180π square feet.
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