Let T be the three dimensional solid bounded from above by the half cylinder described by the equation z = √(9 - y) and from below the cy plane for 0 ≤ x ≤ 2 and -3 ≤ y ≤ 3. Let S be the closed surface that completely surrounds T. Let F➜ = (x,y,y+z). Use the Divergence Theorem to calculate ∫∫S F • n dS

The distance between X and B is 67.5 feet for the given triangle.

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

As per the given figure, we have two similar triangles, as below:

ΔXAB and ΔXCD are similar,

So AB/CD = BX/DX

45/63 = BX/(BX+BD)

45/63 = BX/(BX+27)

45(BX+27) = 63BX

63BX - 45BX = 1215

18BX = 1215

BX = 67.5

Thus, the distance between X and B is 67.5 feet.

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Answer:

... correct answer is 77 inches...

Answer:

A = 77 inches squared

Step-by-step explanation:

To find the area of a triangle, we use the formula

A = 1/2 bh where b is the base and h is the height

A = 1/2 (14) * 11

A = 77 inches squared

Answer:

1 to 7.99 miles

Step-by-step explanation:

According to the given histogram, Maria logged runs for 1 to 7.99 miles, and the number of runs for each mile range is also given. Therefore, the range of the number of miles Maria jogged is 1 to 7.99 miles.

Note that the histogram shows that there were no recorded runs for exactly 8 miles, so the range does not include 8.

If the car’s average tire pressure is on target, the probability that the TPMS will trigger a warning is 0.0000.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Given:

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.

Suppose the target tire pressure of a certain car is 31 psi (pounds per square inch.)

Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.

Target pressure = 31 psi

So, 26% of 31,

31 x 0.26 = 8.06

TPMS warns at below (31 - 8.06) = 22.94

Let X be tire pressure.

µ = 31, σ = 2

P(X < 22.94)

= P(x-µ / σ < (22.94 - 31) / 2)

= P(Z < -4.03)

= 0.0000 {from the z-score table}

Hence, the probability is zero.

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Answer:

Step-by-step explanation:

Total students = 275
Boy students = 150
So, girl students = (275-150) = 125

Percentage of boy students = (150/275)% = 54.55%

The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

a) P(Z < -1.35) =0.8708

b) P(Z > 1.48) =0.5714

c) P(-0.4 < Z < 1.5) =0.000

d) P(| Z | >2)=0.3830

Z-Score Table. A z-table, also known as the standard normal table, provides the area under the curve to the left of a z-score. This area represents the probability that z-values will fall within a region of the standard normal distribution.

Given:

The given condition is Z~N(μ = 0,σ = 1).

(a)

Find the value for .P(Z < -1.35)

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .P(Z < -1.35) =0.8708

(b)

Find the value for .P(Z > 1.48)

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of  .P(Z > 1.48) =0.5714

(c)

Find the value for .) P(-0.4 < Z < 1.5)

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .) P(-0.4 < Z < 1.5) =0.000

(d)

Find the value for .P(| Z | >2)

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .P(| Z | >2)=0.3830

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The probability distribution is calculated z-table.

Z-table is also known as standard normal table which is used to find the area under the curve to the left of a z-score.

(a)P(Z<-1.35)

Here Z value negative so it is lies left of the curve, using standard normal table , P(Z<-1.35) = 0.0885

(b)P(Z>1.48)

z value is positive it lies right of the curve, using standard normal table, area under the curve P(Z>1.48)= 0.9306

(c)P(-0.4 < Z < 1.5) = P(Z<1.5) - P(-0.4<Z)

                             = 0.9332 - 0.3446

                             = 0.5886

(d)P(| Z | >2), |Z| is both positive and negative we have,

  P(| Z | >2) = P(-2 < Z <2)

                  = P(Z<2) - P(-2<Z)

                  = 0.9772 - 0.0228

                 = 0.9544.

Hence, (a)P(Z<-1.35) = 0.0885

(b)P(Z>1.48) = 0.9306

(c)P(-0.4<Z<1.5) = 0.5886

(d)P(|Z|>2)  = 1.9544

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The exact values of two trigonometric functions are listed below:

- 2√2 / 3 and ± √6 / 3

In this problem we have the exact values of two trigonometric functions, and of which we need to determine the exact value of a set of trigonometric functions of more complexity, each of which can be found by understanding the nature of the trigonometric functions and trigonometric formulas.

Since sin(π/3-a) if cos(a)=-0.6 and π < a < 3π/2

Then, by the fundamental formula:

cos α = - √(1 - sin² α)

cos α = - √[1 - (1 / 3)²]

cos α = - √(8 / 9)

cos α = - 2√2 / 3

sin (π/3-a):

sin (π/3-a) = ± √[(1 - cos a) / 2]

sin (π/3-a) = ± √[[1 - (0.6)] / 2]

sin (π/3-a) = ± √6 / 3

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Answer:

(3, -7)

Step-by-step explanation:

If you choose 3 as one of your x-coordinates, you simply need to solve for y to get -7 as your y-coordinate:

[tex]3x+y=2\\3(3)+y=2\\9+y=2\\y=-7[/tex]

The area of the lawn in the Wilson family's back yard is 4400 square feet.

The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet.

Let us assume that A₁ be the area of the reactangular plot.

Using the formula for the area of rectangle,

A₁ = 100 × 80

A₁ = 8000 sq. ft.

The family planted a garden with a length and width of 60 feet.

This means, the shape of the garden must be square.

Using the formula for the area of square,

A₂ = 60 × 60

A₂ = 3600 sq. ft.

The family planted a lawn in the remaining area of the back yard, as shown.

Let us assume that A represents the area of the lawn in the Wilson family's back yard.

A = A₁ - A₂

A = 8000 - 3600

A = 4400 sq. ft.

Therefore, the required area is: 4400 sq.ft.

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The largest possible value of [tex]$k$[/tex] is [tex]$k=3^{11}$[/tex].

Let [tex]$a_1, a_2, \ldots, a_k$[/tex] be the [tex]$k$[/tex] consecutive positive integers, such that [tex]$a_1 + a_2 + \ldots + a_k = 3^{11}$[/tex]. The average of these [tex]$k$[/tex] numbers is [tex]$\frac{a_1 + a_k}{2} = \frac{3^{11}}{k}$[/tex], which is an integer if and only if [tex]$k$[/tex] divides [tex]$3^{11}$[/tex].

The largest divisor of  [tex]$3^{11}$[/tex] is  [tex]$3^{11}$[/tex] itself, so the largest possible value of [tex]$k$[/tex] is [tex]$k=3^{11}$[/tex].

However, [tex]$k$[/tex] must also be an integer greater than 0, so the largest possible value of [tex]$k$[/tex] for which [tex]$3^{11}$[/tex] is expressible as the sum of [tex]$k$[/tex] consecutive positive integers is [tex]$3^{11} - 1 = 177147$[/tex].

This problem is about finding the largest number of consecutive positive integers whose sum is equal to a given number. In this case, the given number is [tex]$3^{11}$[/tex].

By using the formula for the sum of consecutive integers, the average of the numbers is calculated, and the requirement for this average to be an integer is used to find the largest possible value of [tex]$k$[/tex], which represents the number of consecutive positive integers. The solution shows that the largest possible value of [tex]$k$[/tex] is [tex]$177147$[/tex].

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Answer: The range rule of thumb is used to estimate the standard deviation by taking the range of the data and dividing it by 4:

s = (max - min) / 4

In this case, the range is 191.1 cm - 150.0 cm = 41.1 cm.

s = 41.1 cm / 4 = 10.275 cm

This estimate of the standard deviation is 10.275 cm, which is close to the actual standard deviation of 10.84 cm. Since the difference between the two is less than 1.4 cm, we can say that the estimate is accurate.

According to the information, the order of the numbers would be 1, 3, 5, 8, 12.

To organize the numbers from smallest to largest we must use a number line in which we organize the numbers according to their position with respect to zero.

According to the above, the numbers closest to zero go first and then those that are further away from this number. Therefore, the sequence would look like this:

Since none of the numbers is negative, it can be inferred that they all go to the right of zero and are located in ascending order.

Note: This question has incomplete and disorganized information. Here is the complete and organized information.

Question/Task: Arrange the numbers from least to greatest.

Options:

3

8

5

1

12

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The equation for the table is r = -3s + 15,

when s = 0, r = 15 and when s = 9, r = -12

the formula for Δr in terms of Δs is Δr = -3Δs.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given value of r is varying at a constant rate with respect to s,

given table for r and s

s(independent quantity)            r(dependent quantity)

1                                                           12

3                                                           6

9                                                           ?

12                                                          -21

since both quantities vary at a constant rate so it is the condition of a linear equation,

y = mx + c

where m is the slope or the rate of change,

let s₁ = 1, s₂ = 3 and r₁ =  12, r₂ = 6

coordinates for graphs (1, 12) and (3, 6)

the equation is a form of s and r is

r = ms + c (because s is independent and r is dependent)

A: formula for Δr in terms of Δs is

Δr = mΔs

m = Δr/Δs = (6 - 12)/(3 - 1)

m = -3

Δr = -3Δs

the equation will be,

r = -3s + c

when s = 1 r = 12

12  = -3(1) + c

c = 15

the formula for r in terms of s  is,

r = -6s + 15

B: the value of r when s = 0

r = -3(0) + 15

r = 15

and when s = 9

r = -3(9) + 15

r = -12

C: true and false;

i.  The graph that represents s in terms of r is linear: True

ii.  r is proportional to s: False, no r is not proportional to s because the relation between r and s has a constant

iii. Δr is proportional to Δs: True because the relation is Δr = -3Δs.

iv. The graph of r in terms of s is a straight line that passes through the origin (0, 0): False, because when s = 0 r = 15, so the graph does not pass from the origin.

Hence equation for r and s is: r = -3s + 15

when s = 9, r = -12 and when s = 0, r = 15

and Δr = -3Δs.

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In this type of puzzle, "knight" means that the speaker is telling the truth, and "knave" means that the speaker is lying.

Let's start by analyzing the first two statements:

U says: None of us is a knight.

V says: At least three of us are knights.

If U is a knight, then his statement is false, meaning that at least one of the six is a knight, which contradicts V's statement that at least three of them are knights. Therefore, U must be a knave.

Next, let's look at the statement of W:

W says: At most three of us are knights.

If W is a knight, then his statement is true, meaning that there are three or fewer knights among the six. Since U is a knave, this would mean that at most two of the remaining five are knights, which contradicts V's statement that at least three of them are knights. Therefore, W must be a knave.

Continuing in this way:

X says: Exactly five of us are knights.

If X is a knight, then his statement is false, meaning that exactly five of them are not knights. But since U is a knave, this means that U is a knight, which is a contradiction. Therefore, X must be a knave.

Y says: Exactly two of us are knights.

If Y is a knight, then his statement is true, meaning that exactly two of them are knights. Since U is a knave, this means that exactly two of the remaining five are knights, which means that W, X, Y, Z are knaves. This is consistent with all of the statements so far, so Y must be a knight.

Z says: Exactly one of us is a knight.

If Z is a knight, then his statement is true, meaning that exactly one of them is a knight. Since Y is a knight, this means that Y is the only knight, and U, V, W, X, Z are all knaves. This is consistent with all of the statements so far, so Z must be a knight.

Therefore, the knights are Y and Z, and the knaves are U, V, W, X.

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The number of pea is 6. By using formulas of mean, median and mode.

A dataset's mean (also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. It is frequently referred to as the "average" and is the most widely used measure of central tendency.

Taking pea counts into account,

A pod of peas contains 4, 5, 6, 7 or 8 peas.

Number of pods: 2, 10, 18, 6, and 14

The mode is the number that corresponds to the highest frequency.

The frequency of each number in the list is 1.

Mode is not possible with the information provided.

The middle value, after sorting the numbers in ascending or descending order, is the median if all of the numbers are odd.

The median of the given numbers is.

Replace the values in the formula to get the mean value.

Mean = 4+5+6+7+8/5 = 30/5 = 6

Consequently, based on the quantity of peas provided, the values of the following measure are as follows:

It is impossible to use Peas in a Pod mode.

The median number of peas in a pod is 6.

the typical quantity of peas is 6.

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Answer:

1/24

Explanation:

1                                                    1        8

-    ÷    8       This translates to:   -   ÷    -

3                                                   3        1

1                1

-         =     -

3x8          24

Hope this helps!

Step-by-step explanation:

a) Find the angular speed of the blade in radians per minute:

The formula for angular speed is given by:

ω = 2 * π * f

where f is the frequency of rotation in revolutions per minute, and π is approximately equal to 3.14159.

Plugging in the values, we get:

ω = 2 * 3.14159 * 4300 revolutions per minute

ω = 26,957.1 radians per minute

Rounding to three decimal places, the answer is:

ω = 26,957.1 radians per minute = 26,957.1 radians/minute

b) Find the linear speed of the saw teeth (in inches per minute) as they contact the wood being cut:

The formula for linear speed (v) is given by:

v = ω * r

where ω is the angular speed in radians per minute, and r is the radius of the blade (half of the diameter).

Plugging in the values, we get:

v = 26,957.1 radians/minute * 4.125 inches

v = 111,542.7 inches per minute

Rounding to one decimal place, the answer is:

v = 111,542.7 inches per minute = 111,543 inches/minute

The ordered pair (4, 1) is not a solution to the system,

- x + y = - 3 and x + 3y = 6.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Given, A system of linear equations - x + y = - 3 and x + 3y = 6.

An ordered pair must satisfy both equations simultaneously.

For, - x + y = - 3

- 4 + 1 = - 3.

- 3 = - 3 (satisfied).

For, x + 3y = 6.

4 + 3(1) = 6.

4 + 3 = 6.

But, 7 ≠ 6.

Therefore, the ordered pair is not a solution.

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Answer:

Step-by-step explanation:

Let, width = x

length = x+4

perimeter, 2(x+4+x) = 40

4x+8 = 40

4x = 32

x = 8

so, (x+4) = 8+4 = 12

so, the area would be,

= 12 * 8 = 96 in²

The solution is, the minute hand will be 87.7 degrees ahead of the hour hand.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

Let's call the current position of the hour hand H and the current position of the minute hand M.

At the start, we have H = 0 and M = -20 degrees.

After 18 minutes, the minute hand will have moved 18 * 6 = 108 degrees, while the hour hand will have moved 18 * (6/60) = 0.3 degrees.

So the new position of the minute hand is M + 108 = 88 degrees,

and the new position of the hour hand is H + 0.3 = 0.3 degrees.

Therefore, the minute hand will be 88 - 0.3 = 87.7 degrees ahead of the hour hand.

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Answer: 0.47, 4.07,  4.70, 7.40, 74

Step-by-step explanation:

0.47, 4.07,  4.70, 7.4, 74

Answer:

0.47,4.07, 4.70, 7.40, 74

Step-by-step explanation:

In order the numbers from smallest to biggest, you can compare them pair-wise. For example, 0.47 is smaller than 4.07, so 0.47 is the smallest number. You can continue comparing the remaining numbers pair-wise to find the next smallest number, and so on.

Here is a more detailed explanation of how to order the numbers from smallest to biggest:

1. Compare 0.47 and 4.07. 0.47 is smaller than 4.07, so 0.47 is the smallest number.

2. Compare 4.07 and 4.70. 4.07 is smaller than 4.70, so 0.47, 4.07, and 4.70 are the smallest three numbers.

3. Compare 4.70 and 7.40. 4.70 is smaller than 7.40, so 0.47, 4.07, 4.70, and 7.40 are the smallest four numbers.

4. Compare 7.40 and 74. 74 is larger than 7.40, so 0.47, 4.07, 4.70, 7.40, and 74 are the smallest five numbers.

The value of a and c in the right triangle are 38.28 and 66.89 respectively.

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.

From the diagram:

sin(55.0892) = 54.855/c

c = 66.89

Also:

tan(55.0892) = 54.855/a

a = 38.28

The value of a and c are 38.28 and 66.89 respectively.

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In each case, the response variable, the explanatory variables, and the probability distribution is specified.

Before answering this question, let's us understand the Generalized linear models

Generalized linear models (GLMs) are used to model a response variable that has a non-normal distribution by linking the mean of the response variable to a linear combination of explanatory variables through a link function.

The Identification of cases are given below:

a) Response variable: number of trips per week to the supermarket for a household

Explanatory variables: number of people in the household, household income, distance to the supermarket

Probability distribution: Poisson

Justification: The response variable "number of trips per week" is count data and can be modeled using a Poisson distribution.

Linear component: log(μ) = β0 + β1 * number of people in the household + β2 * household income + β3 * distance to the supermarket

b) Response variable: person's weight

Explanatory variables: age, sex, height, mean daily food intake, mean daily energy expenditure

Probability distribution: Gaussian (Normal)

Justification: The response variable "person's weight" is continuous and approximately normally distributed.

Linear component: μ = β0 + β1 * age + β2 * sex + β3 * height + β4 * mean daily food intake + β5 * mean daily energy expenditure

c) Response variable: proportion of mice infected after exposure to bacteria

Explanatory variables: exposure level

Probability distribution: Binomial

Justification: The response variable "proportion of mice infected" is binary (yes/no) and can be modeled using a binomial distribution.

Linear component: logit(p) = log(p/(1-p)) = β0 + β1 * exposure level

The linear component represents the relationship between the mean of the response variable and the explanatory variables.

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____ The given question is incomplete, the complete question is given below:-

The following associations can be described by generalized linear models. For each one, identify the response variable and the explanatory variables, select a probability distribution for the response (justifying your choice) and write down the linear component.

a. The association between the number of trips per week to the supermarket for a household and the number of people in the household, the household income and the distance to the supermarket.

b. The effect of age, sex, height, mean daily food intake and mean daily energy expenditure on a person’s weight.

c. The proportions of laboratory mice that became infected after exposure to bacteria when five different exposure levels are used and 20 mice are exposed at each level.

Answer:

a) The two variables in this table are "students" and "parents".

b) The observational unit in this study is a student-parent pair.

c) The total number of students who do not use drugs is 141.

d) The total number of student-parent pairs in this study is 445.

Step-by-step explanation:

a) The two variables in this table are "students and parents" who do not use drugs and those who use drugs.

b) The observational unit in this study is a student-parent pair.

c) The total number of students who do not use drugs is 141.

d) The total number of student-parent pairs in this study is 445.

An observational unit is described as an entity for which data is collected and analyzed and enables conclusions to be drawn about its characteristics.

An observational unit is assigned a value based on the collected data.

On the other hand, we define a variable as the piece of information being collected from each observational unit.

                Does not use    Uses    Total

Students          141               94        235

Parents            110              100        210

Total               251              194        445

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The marginal revenue when q = 29 is 510 dollars.

To find the marginal revenue we need to differentiate the revenue equation, here we know that:

R(q) = -5q² + 800q

Differentiating that, we will get:

R'(q) = MR(q) = 2*(-5)*q + 800

                     = -10q + 800

The marginal revenue when q = 29 is

MR(29) = -10*29 + 800 = 510

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Answer: -4,9 I AM PRETTY SURE FROM ALL OF MY RESEARCH SIORRY IF I AM WRONG I WISH YOU GOODLUCK

Step-by-step explanation:

In a unit rate, the denominator is always 1.

When two observers on opposing sides of a flagpole are 500 feet apart, the height of the flagpole is 48.077 feet.

In Geometry and trigonometry, an aspect is a shape made up of two rays, referred to as the angle's sides, that converge at a center point termed as the angle's vertex. Two rays can create an angle in the region where they are arranged. Additionally, when two planes collide, an angle is created. Dihedral angles are what they are called. An angle is a possible structure for two rays or lines with only a common end in planar geometry. The English term "angle" originated from the Latin word "angulus," which meaning "horn." The vertex is the common endpoint of the opposite rays, also known as the side of the angle.

given

distance between two observer = 300 ft

angle of elevation to top pole = 17° and 16°

height of the flagpole = ?

now,

Let x be the distance of the pole

tan17° = h /x

x = h / tan17°

now,

tan20° = h / 500 - x

500 - x = h / tan16°

again applying

500 - 3.49h = 2.75h

h = 48.077 ft

When two observers on opposing sides of a flagpole are 500 feet apart, the height of the flagpole is 48.077 feet.

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Answer: 4/3

Step-by-step explanation:

Look at the points (0,-4) (3,0)

Formula: y2-y1/x2-x1

Substitute: 0-(-4)/3-0 = 4/3

Please make me brainliest, I would also add you as friend if you make me brainliest!

Let's consider what the question asks for:

--> slope of line

The slope of the line is calculated by:

  [tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

  --> where:

      [tex](x_1,y_1)-- > \text{any one point on the line}\\\\(x_2,y_2)-- > \text{another point on the line}[/tex]

Let's find our points

  [tex](x_1,y_1)-- > (3,0)\\\\(x_2,y_2)-- > (0,-4)[/tex]

Let's plug these points into our equation:

 [tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-4-0}{0-3}=\dfrac{-4}{-3} =\dfrac{4}{3}[/tex]

Answer: 4/3

Answer:

5425.92

Step-by-step explanation:

radius(r)=d/2

=24/2

=12ft

So,

Volume=πr^3

=(3.14*12^3)cubic feet

=5425.92cubic feet

Answer:

V≈7238.23 [ft³].

Step-by-step explanation:

1. formula of the required volume is

[tex]V=\frac{4}{3} \pi R, \ where \ R-radius.[/tex]

2. if diameter is 24 ft., then R=12 [ft] and the required volume is:

[tex]V=\frac{4}{3} *3.1415*12^3=7238.2294[ft^3].[/tex]