Find the volume of this cylinder. Give your answer to 1 decimal place 20 cm 9 cm​

The volume of the spherical segment above the plane is[tex](1/3) *\pi * (r^2 - (r-h)^2) * h[/tex] and the volume of the ring resulting from drilling a hole through the center of a sphere is [tex]\pi * (R^2 - r^2) * R.[/tex].

A sphere of radius "r" is cut by a plane "h" units above the equator. To find the volume of the solid (spherical segment) above the plane, we first need to find the height of the segment, which is (r - h). Then, we can use the formula for the volume of a spherical segment: [tex](1/3) * \pi * (r^2 - (r-h)^2) * h.[/tex]

A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. To find the volume of the resulting ring, we can use the formula for the volume of a cylindrical ring: [tex]\pi * (R^2 - r^2) * h[/tex], where h is the height of the ring. Since the hole goes all the way through the sphere, the height of the ring is equal to the radius of the sphere, R. So the volume of the ring is [tex]\pi * (R^2 - r^2) * R[/tex].

In the first problem, the volume of the solid (spherical segment) above the plane is [tex](1/3) * \pi * (r^2 - (r-h)^2) * h[/tex]. In the second problem, the volume of the resulting ring is [tex]\pi * (R^2 - r^2) * R.[/tex]

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The median salary in 2048 will be  2.853 million

A general linear equation is given by:

y=a × x + b

Where the slope is a and the y-intercept is b.

We shall discover that the linear equation for this scenario is

y = 0.033 ×  x + 1.269

And we may anticipate that in 2048, the median salary will be 2.853 million.

The slope can be expressed as if the line passes through the points (x1, y1) and (x2, y2).:

[tex]$a=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, we know that whereas the median player pay in 2007 (x = 7) was y = 1.5 million, it was y = 1.7 million in 2013 (x = 13).

The following two points can be written as follows:

(7,1.5)

(13,1.7)

Note that the y-value is in millions.

Then the slope of the linear equation will be:

[tex]$a=\frac{1.7-1.5}{13-7}=0.033[/tex]

So the linear equation is something like:

y=0.033 × x + b

Remember the point (7,1.5), which indicates that for x=7, we also get y=1.5, so we can substitute these in the equation above:

1.5=0.033 ×  7+b

1.5-0.033 ×  7 = b = 1.269

Then the linear equation is:

y=0.033 ×  x+1.269

b) Now we want to predict the median salary in 2048 . For 2048 the

x-value is x=48

So we just need to evaluate this in the linear equation:

y = 0.033 × 48 + 1.269 = 2.853

Then the median salary in 2048 will be  2.853 million

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A cube is a three-dimensional shape with all sides of equal length, width, and height. If the length of the packaging box is 4xy, then all the sides of the cube have the same length 4xy.

What is the straightforward meaning of volume?

The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.

To find the volume of a cube, we use the formula: volume = side x side x side = (side)^3

Therefore, the volume of the packaging box in terms of x and y is (4xy)^3 = (4xy)(4xy)(4xy) = (4xy)^3 = (4x)^3 * y^3 = 64x^3 * y^3

So the volume of the packaging box is 64x^3 * y^3 cubic units.

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Answer: mean would be d or 998.67 wouldn't it

Step-by-step explanation:

because mean 998.67 median 1100 and mode 1500

i think that is right but i am not 100% sure

Answer:

Q1 - 7910

Q2 - 9710

Q3 - 1097

Q4 - 7190

I don't know what these mean, but here you go..?

If s and t are integers greater than 1 and each is a factor of the integer n, then the product nst must be divisible by both s and t. This is because s and t are factors of n, which means that n is divisible by s and t.

The product of two integers is divisible by the factors of each of those integers. Therefore, since n is divisible by s and t, and nst is the product of n, s, and t, nst must also be divisible by s and t. This can be proven by the definition of divisibility: if a number, in this case n, is divisible by an integer, in this case s or t, then the product of that number and another integer, in this case t or s, is also divisible by the initial integer.

For example, if n = 24, s = 4, and t = 3, we can see that 4 and 3 are factors of 24, since 24 is divisible by 4 and 3. The product of 24, 4 and 3 is 2443 = 288. 288 is also divisible by 4 and 3.

In summary, if s and t are integers greater than 1 and each is a factor of the integer n, then s and t must be factors of nst.

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Answer:

Yes, Kazuko's reasoning is correct

Step-by-step explanation:

If u substitute 1 in place of x in both expressions, they both equal 5 when solved

We have used spherical coordinates to show that the triple integral from negative infinity to infinity of the [tex]\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$$[/tex]

Triple integrals, as their name suggests, are three sequential integrations that can be used to determine a volume or to integrate in a fourth dimension over three other independent dimensions.

The total amount of heat in the three-dimensional room can be calculated using this triple integral.

We understand that triple integrals have several uses if "dimension" can refer to something other than a spatial dimension. We could determine a 3-D object's overall inertia or the gravitational attraction on a basketball.

The sum of an infinite number of rectangular prisms across a bounded region in three-space is a double integral, which represents the volume beneath the surface above the xy-plane.

[tex]$$To show that $\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$, begin by converting the integral into spherical coordinates. Recall that $\rho^2=x^2+y^2+z^2$ and $d V=\rho^2 \sin \phi d \rho d \phi d \theta$. To convert the bounds, notice that as $x, y$, and $z$ expand infinitely in both directions, this can be modeled to a sphere of an infinite radius.\\$$[/tex]

[tex]$$This means that the new bounds become $0 \leq \rho \leq \infty, 0 \leq \phi \leq \pi$, and $0 \leq \theta \leq 2 \pi$. Because the integral is infinite, let the upper limit of $\rho$ be $R$ and take the limit as $R$ goes to infinity. To evaluate with respect to $\rho$, first use $u$ substitution by letting $u=\rho^2$ and then integrating by parts$$[/tex]

[tex]$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z$[/tex]

[tex]& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0 \int_0^R \sqrt{\rho^2} e^{-\left(\rho^2\right)} \rho^2 \sin \phi d \rho d \phi d \theta \\& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0^\pi \int_0^R e^{-\rho^2} \rho^3 \sin \phi d \rho d \phi d \theta \\[/tex]

[tex]& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0^2 \sin \phi\left[\frac{1}{2}\left(-e^{-\rho^2}\left(1+\rho^2\right)\right)\right]_{\rho=0}^{\rho-R} d \phi d \theta \\& =\frac{1}{2} \lim _{R \rightarrow \infty} \int_0^{2 \pi \pi} \int_0^\pi \sin \phi\left[-e^{-R^2}\left(1+R^2\right)+e^{-0^2}\left(1+0^2\right)\right] d \phi d \theta\end{aligned}$$[/tex]

[tex]$$\\\text{Use L' Hospital's Rule to simplify the limit}$$\begin{aligned}& \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z \\& =2 \pi(1)-2 \pi \lim _{R \rightarrow \infty}\left(\frac{2 R}{2 R e^{R^2}}\right) \\& =2 \pi-\lim _{R \rightarrow \infty} \frac{1}{e^{R^2}} \\& =2 \pi-0 \quad \text { As } \lim _{x \rightarrow \infty} \frac{1}{e^x}=0 . \\& =2 \pi\end{aligned}$$[/tex]

[tex]$$Therefore,$$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$$[/tex]

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Answered step-by-step

"Match the key aspect of a function's graph with its meaning. f(x) > 0 intervals of the domain where the graph is above the x-axis f(x) < 0 location on graph where input is zero x-intercept location on graph where output is zero y-intercept intervals of the domain where the graph is below the x-axis Common Core Algebra 'httpsinIscorekam edgenuftycomPlayer Common Core Algebra /- MAJIO9 / AcR 7haijliy Giapiij Instruction Active of a Graph the Meaning of Key Features Matching of a function $ graph with its meaning Match the key aspect intervals of Ihe domain where the graph. IS above the x-axis flx) > E Iocation on graph where input IS zero fix) < 0 Iocation on graph where output IS x-Intercepi zero Intervals Of the domain where the y-intercept graph Is below the x-axis Untto Done PrevousAaml Type here i0 search"

The shape of the sampling distribution of the sample mean is approximately normal because the sample size is greater than 3.

Given data :

a ) Approximately normal because the sample size is greater than 3.

b ) b )  ux  = 1.1 and Jx =  [tex]\frac{1.4}{\sqrt{40} }[/tex]= 0.198

c  ) c ) P ( ux ∠ 1 ) = normal cdf ( lower : 1000, upper : 1, u : 1.1 , J : 0.198 ) = 0.3068

d ) The principal could pick 50 students may times and find the median and repeat several times until he has every possible sampling distribution.

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The value of the voltage (E) is given as 33 + 48i

An equation is an expression showing the relationship between numbers and variables.

Given the equation:

E = IZ

Where E is the voltage, I is the current and Z is the impedance.

But I = 5 + 2i, Z = 9 + 6i, substituting the values gives:

E = IZ

E = (5 + 2i)(9 + 6i)

E = 45 + 30i + 18i - 12

E = 33 + 48i

The value of E is 33 + 48i

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The randomly number of the students who got selected  are 4,5,6,7,.......

Professor randomly select the fourth and every  student after that

Now  by using the next  term formula which is

=>a + d(n-1)

The next student is the 2nd student.

=>4 + 1*(2-1)

=>4 + (1)

=>4 + 1

=> 5

The 3rd student will be

=>4 + 1(3-1)

=>4 + 1(2)

=>4 + 2

=> 6

The 4th student will be

=>4 + 1(4-1)

=>4 + 1(3)

=> 4+ 3

=> 7

students numbers are 4,5,6,7......

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The equation of the line containing point  (7, -5) and having slope 4/5 is found as y = 4/5x - 3/5.

The given data:

Comparing eq with standard form:

5y = 4x - 2

y = 4/5 x - 2/5

slope m = 4/5

As both lines are parallel, the slope of both lines will be equal.

Thus, using slope intercept form

y - y1 = m(x - x1)

y + 5 = 4/5 (x - 7)

y + 5 = 4/5x - 28/5

y = 4/5x - 3/5

Thus, the equation of the line containing point  (7, -5) and having slope 4/5 is found as y = 4/5x - 3/5.

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Answer:

P/E = 125/9= 13.89:1

Step-by-step explanation:

2mm shares at $ 125/share

18mm earnings so earnings per share EPS = 18/2 =9

The P/E ratio is calculated by dividing the stock's current price by its latest earnings per share.

P/E = 125/9= 13.89:1

Answer:

Step-by-step explanation:

The earnings per share can be calculated as

Earnings per Share =Total EarningsTotal Shares=$18,000,0002,000,000=$9.

Therefore the PE ratio is

PE Ratio =$125$9≈13.89.

The amount of money which Jan's remodel would cost is equal to $624.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

Area of rectangle = 12 × 16

Area of rectangle = 192 square feet.

For the total cost, we have the following;

Total cost = Area of remodel × cost per square foot.

Total cost = 192 × 3.25.

Total cost = $624.

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Answer:

A=22 dots

B=51 squares

C=number of squares = the number of squares times 2, plus 2

Step-by-step explanation:

A-

10*2=20

20+2=22

B-

104-2=102

102/2=51

C-

there is only one row so that adds 2 dots and then you multiply the number of squares by 2 then add 2 to the product

Answer:

a) 22 dots

b) 51 squares

c) Number of dots = 4 + 2 x (number of squares - 1)

Step-by-step explanation:

Actually, in this question you are better off solving c) first for the formula and then using it to solve a) and b)

Let's look at the relationship between squares and dots:

Number of squares                 Number of dots
              1                                                 4

              2                                                6

              3                                                8

You can see that as the number of squares increases by 1, the number of dots increases by 2 with 4 dots as the starting point

We can easily come up with a formula by treating this as an arithmetic sequence.

The number of dots represents the term # and the number of dots the actual term value

The difference between consecutive terms is 2 and is called the common difference (d)

The nth term will be referred to using  aₙ

So we have

a₁ = 4

a₂ = 6

a₃ = 8

The nth term of any arithmetic sequence is

aₙ = a₁ + d(n-1) where d is the common difference

This is the answer to c). Translating to dots and squares we get

Number of dots = 4 +  2 x (number of squares - 1)

a) Use the formula

a₁₀ = 4 + 2(10-1) = 4 + 2 x9 = 4 + 18 = 22 dots

b) Here we are given the value of term = 104

Substituting we get

104 = 4 + 2(n-1)

104-4 = 2(n-1)

100 = 2(n-1)

n-1 = 100/2 = 50

n = 51

That means the there are 51 squares in the diagram which has 104 dots

Answer:

The answer is 1.04

Step-by-step explanation

For 1.04, 4 is in the hundredths place, and 0 is in the tenths place.

Answer:

I believe the answer may be 31.5cm.

Step-by-step explanation:

I first found the area of the total region which was 70cm. From there I found the area of the triangle to the left of the region by doing 6x7 which is 42, and multiplied by 1/2 because it is a triangle. I did the same to the triangle on the right, doing 5x7 which is 35, and multiplied by 1/2 since this is also a triangle. Finally, I subtracted both totals of 21, and 17.5 from the 70, getting a grand total of 31.5cm.

Answer:

31.5 cm²

Step-by-step explanation:

To find the area of the crossed region, subtract the areas of the two triangles from the area of the rectangle.

Formulae:

Area of the rectangle

⇒ A = (4 + 6) × 7

⇒ A = 10 × 7

⇒ A = 70 cm²

Area of triangle 1

⇒ A = ¹/₂ × 6 × 7

⇒ A = 3 × 7

⇒ A = 21 cm²

Area of triangle 2

⇒ A = ¹/₂ × 5 × 7

⇒ A = 2.5 × 7

⇒ A = 17.5 cm²

Area of the crossed region

⇒ A = 70 - 21 - 17.5

⇒ A = 49 - 17.5

⇒ A = 31.5 cm²

a) The expression D(225) represents the number of iced cappuccinos sold each week by a coffeehouse when the price is 225 cents.

b) Whether D(p) is an increasing or decreasing function depends on the relationship between the price of iced cappuccinos and the number sold. If the price of iced cappuccinos increases, the number sold may decrease (decreasing function) or if the price of iced cappuccinos decreases, the number sold may increase (increasing function) . It's possible that the coffeehouse has made a market research and they know what is the best price for their iced cappuccinos.

c) The equation D(p) = 180 tells you that the coffeehouse sells 180 iced cappuccinos each week when the price is p cents.

d) D(1.5t) represents the number of iced cappuccinos sold each week when the price is 1.5t (1.5 times the average price in the area). 1.5D(t) represents the number of iced cappuccinos sold each week when the price is the average price in the area multiplied by 1.5. D(t+50) represents the number of iced cappuccinos sold each week when the price is t+50 (50 cents more than the average price in the area). D(t)+50 represents the number of iced cappuccinos sold each week when the price is the average price in the area plus 50.

It's important to note that all these expressions doesn't give us any information about the relation between price and quantity sold, they just give us the value of the function for specific values of p.

4/3 is the value of k that makes the system of linear equations has no solutions .To determine the value(s) of k such that the system of linear equations has no solutions, we need to use the concept of consistency and consistency of a system of linear equations, which is the property that a system of equations has exactly one solution or no solution.

A system of linear equations is consistent if it has exactly one solution and inconsistent if it has no solution. We can use the concept of determinant of a matrix to check the consistency of the system of linear equations. The determinant of a matrix is a scalar value that can be calculated from the elements of a matrix and it tells us whether a matrix is invertible or not. An invertible matrix corresponds to a consistent system of linear equations and a non-invertible matrix corresponds to an inconsistent system of linear equations. To check the consistency of the system of linear equations, we can use Cramer's Rule, which states that the determinant of the coefficient matrix must be non-zero for the system to have a unique solution.

The coefficient matrix of the given system of equations is:

| 1 2 k |

| 3 6 8 |

The determinant of the coefficient matrix is:

|1 2 k|

|3 6 8| = (18) - (26) + (k*3) = 8 - 12 + 3k

If the determinant of the coefficient matrix is non-zero, the system of equations will have a unique solution, if the determinant of the coefficient matrix is zero, the system of equations will have no solution.

So for the system of linear equations to have no solution, the determinant of the coefficient matrix must be zero.

8 - 12 + 3k = 0

3k = 4

k = 4/3

So the value of k that makes the system of linear equations has no solutions is 4/3.

It is worth noting that if there are infinite solutions, the determinant of the matrix is zero but the rank of the matrix (the number of linearly independent rows or columns) is smaller than the number of variables

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The value of f(x) . g(x) is  3x² + 5x - 2 two linear functions multiplied together to form a quadratic function.

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, Are two function f(x)  3x - 1 and g(x) = x + 2.

Now, f(x) . g(x) is nothing but multiplication of f(x) and g(x).

Therefore,

f(x) . g(x) = (3x - 1)(x + 2).

f(x) . g(x) = 3x² + 6x - x - 2.

f(x) . g(x) = 3x² + 5x - 2.

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The firm's accounting profit earnings as required to be determined in the task content is; $0.

As evident in the task content, the firm produces 275,000 units a year and sells them all for $8 each.

Therefore, the total revenue generated from sales is; 275,000 × $8 = $2,200,000.

Hence, since the total cost is the sum of $1,800,000 and $400,000 which is; $400,000 + $1,800,000 = $2,200,000.

Ultimately, the total accounting profit earned is; Revenue generated - Expenses = $2,200,000 - $2,200,000 = $0.

Therefore, the total accounting profit earned is; $0.

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The equation 4x+8=4(x+4)−8 can be simplified by distributing the 4 on the right side of the equation:

4x+8=4x+16-8

Subtracting 4x from both sides:

8=16-8+8

Which simplifies to:

8=8

This is a true statement, so x could be any real number. The solution to the equation is x is any real number or x∈R.

Answer:52.8

Step-by-step explanation:

52.752

so it = 52.8

The scale factor of the dilated pentagon is the ratio of the side length of the original pentagon to the side length of the dilated pentagon.

In this case, the side length of the original pentagon is 5 and the side length of the dilated pentagon is 1. Therefore, the scale factor is 5:1 or 5/1. To calculate the scale factor, divide the side length of the original pentagon by the side length of the dilated pentagon. In this case, the calculation would be 5 / 1 = 5. The scale factor of the dilated pentagon is 5.

We can also use the formula for finding the scale factor of two figures: Scale Factor = Length of figure 1 / Length of figure 2. In this case, the length of figure 1 is 5 and the length of figure 2 is 1. So, the scale factor is 5.

Therefore, the scale factor of the first pentagon to the second pentagon is 5.

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The value of Q (1/4) as required to be determined in the task content is; 10 ½.

It follows from the task content that the value of the function instance Q (1/4) is to be determined based on the given function definition; Q(x)=8x^2+10.

Hence, since the given function is; Q (x) = 8x² + 10.

The function instance Q (1/4) can be evaluated as follows;

Q (1/4) = 8 ( 1/4 )² + 10

= 8 • 1/16 + 10

= 1/2 + 10

= 10 ½.

Ultimately, the value of the function instance Q (1/4) is; 10 ½.

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Answer: bottom right