What is the volume of a cylinder, in cubic centimeters, with a height of 8 centimeters
and a base diameter of 16 centimeters? Round to the nearest tenths place

The value of x and y in the right triangle are as follows:

x = 15√3 units

y = 30 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles of a right angle triangle is 180 degrees.

The side x and y can be found using trigonometric ratios,

tan 60° = opposite / adjacent

tan 60° = x / 15

cross multiply

x = 15 tan 60°

x = 15 × √3

x = 15√3 units

Let's find y as follows:

cos 60° = adjacent / hypotenuse

cos 60° = 15 / y

cross multiply

y = 15 / cos 60

y = 15 ÷ 1 / 2

y = 15(2)

y = 30 units

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Answer:

option 2

Step-by-step explanation:

Magnitude of `a` = `sqrt(15)`.

`cos(a) = 0.25` and `a` lies in the fourth quadrant, we can find the value of `sin(a)`, `tan(a)`, and the magnitude of `a`.

1. In the fourth quadrant, `cos(a)` is positive and `sin(a)` is negative.

2. Using the Pythagorean theorem, we can find the value of `sin(a)` as `sin(a) = -sqrt(1 - cos^2(a))`.

3. Substituting the value of `cos(a)` into the equation, we get `sin(a) = -sqrt(1 - 0.25^2) = -sqrt(15)/4`.

4. Therefore, the value of `sin(a)` is `-sqrt(15)/4`.

5. To find the value of `tan(a)`, we can use the formula `tan(a) = sin(a)/cos(a)`.

6. Substituting the values of `sin(a)` and `cos(a)`, we have `tan(a) = -sqrt(15)/(4 * 0.25) = -sqrt(15)/4`.

7. Hence, the value of `tan(a)` is `-sqrt(15)/4`.

8. Finally, to determine the magnitude of `a`, we consider the right triangle formed by `a` in the fourth quadrant.

9. Since `cos(a) = base/hypotenuse = 1/4`, we assume the hypotenuse to be `4` and the base to be `1`.

10. Applying the Pythagorean theorem, we find the height to be `sqrt(15)`.

Therefore, the magnitude of `a` is `sqrt(15)`.

The values are:

a) `sin(a) = -sqrt(15)/4`

b) `tan(a) = -sqrt(15)/4`

c) Magnitude of `a` = `sqrt(15)`.

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Answer:

Let F = Fran's income

Let W = Winston's income

Combined income is 80000  ==>  F + W = 80000

One quarter of Winston's income is the same as one-sixth of Fran's income  ==>  

(1/4)*W = (1/6)*F

Multiply the 2nd equation by 12 to clear the fractions  

3*W = 2*F

Solve this equation for F

F = (3/2)*W

Substitute this value for F into the 1st equation

(3/2)*W + W = 80000

(5/2)*W = 80000

W = (2/5)*80000 = 32000

So F = 80000 - 32000 = 48000

So Winston earns 32000 and Fran earns 48000

Check:  One quarter of Winston's income is 32000/4 = 8000

           One sixth of Fran'e income is 48000/6 = 8000

Step-by-step explanation: Hope this helps

172.16.0.0/20 is the required network address with a prefix if you need 16 subnets.

Given that,
If you require 16 subnets, your new network address with a prefix should be something different from the old one, which is 172.16.0.0/16. To determine the prefix corresponding to the 16 subnets.

Here,
Original network address with a prefix  = 172.16.0.0/16,
After 16 subnets the address would become,
New network address with the prefix with 16 subnets =  172.16.0.0/20.

172.16.0.0/20 is the required new address with prefix be if you need 16 subnets.

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6 feet 7 inches

1 feet = 12 inches

6 feet = 6(12) = 72 inches

6 feet 7 inches = 72 + 7 = 79 inches

Answer:

79 inches

The equation is given as follows:

d = 50t.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The bird can fly 400 kilometers in 8 hours, hence the velocity is given as follows:

v = 400/8

v = 50 km/h.

Then the equation is given as follows:

d = vt

d = 50t.

The complete problem is:

"An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Write an equation to represent the distance d, in kilometers, of each bird after t hours".

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Answer:

2. 3. possible answer: (14, 13) and (1, 4). 4a. 1. 4b. 8 __. 5 , or 1.6. 4c. 9 __. 4 ... 2)(x. 3). The areas of the inner rectangles are x 2, 2x, 3x, and 6. The sum of the areas of the ... 2. C. 3a. c 27. 3b. c 5.8. 3c. c 9. 4. B: x represents the number of dozens of calls ... 3d. IQR 548. 3e. Answers will vary. Possible answer: The three top.

Step-by-step explanation:

This power series represents the function h(x) in terms of its infinitely many terms, where each term involves the coefficients 6^n and the powers of x^n.

To find a power series representation for the function h(x) = 1 / (1 - 6x), centered at c = 0, we can use the geometric series formula.

The geometric series formula states that for a series of the form ∑(n=0 to infinity) ar^n, where |r| < 1, the sum can be expressed as a / (1 - r), where a is the first term.

In our case, we have h(x) = 1 / (1 - 6x), which can be written as h(x) = 1 * (1 - 6x)^(-1).

Now, we can use the geometric series formula with a = 1 and r = 6x:

h(x) = 1 * ∑(n=0 to infinity) (6x)^n

Expanding the power of (6x)^n, we have:

h(x) = ∑(n=0 to infinity) (6^n * x^n)

Therefore, the power series representation for h(x) = 1 / (1 - 6x), centered at c = 0, is:

h(x) = ∑(n=0 to infinity) (6^n * x^n)

This power series represents the function h(x) in terms of its infinitely many terms, where each term involves the coefficients 6^n and the powers of x^n.

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9514 1404 393

Answer:

  6.01 m

Step-by-step explanation:

Apparently, the washing line is the hypotenuse of a right triangle with sides (2.1-1.7) = 0.4 m and 6 m. The Pythagorean theorem can be used to find its length.

  ab = √(0.4² +6²) = √36.16 ≈ 6.0133

The distance ab is about 6.01 m.

\(a_{n}\) = 25 + 6(n - 1) best represents the formula for the sequence.

Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

How to determine this

The formula = \(a_{n}\) = a + (n - 1) d

Where a = First term

n = The nth term of the sequence

d = Common difference in the sequence

So,

a = 25

d = 31 - 25 = 6

So, to represent the value

\(a_{n}\) = 25 +(n - 1)6

Therefore, the option the represent the formula is C. 25 +6(n - 1)

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Answer:

Option h: 16h

Step-by-step explanation:

To get the answer to the question divide 480 by 30 to get the rate which is 16. So the answer would be H

When x does not have full rank, it means that the columns of x are not linearly independent. This means that there exists a non-zero vector b such that xb = 0. Let's see why px = x when this is the case.

First, let's recall what the projection matrix p is. The projection matrix p is defined as p = x(xTx)-1xT. This matrix projects any vector onto the column space of x.

Now, let's see what happens when we multiply px:
px = x(xTx)-1xTx
Since xTx is a scalar, we can write this as:
px = x(xTx)-1(xTx)
px = x

So we can see that px = x when x does not have full rank. This is because the projection matrix p projects any vector onto the column space of x, and when x does not have full rank, the column space of x is the same as the column space of px.

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Answer:

289

Step-by-step explanation:

6 sides to a cube, so the surface area would be the sum of all the sides. 1734/6 = 289

Answer:

17

Step-by-step explanation:

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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The value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

According to the given question.

The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

So, let the length of the quadrilateral be x, (x + 1), (x + 2), and (x + 3).

Also, it is given that the perimeter of the quadrilateral is 110 inches.

⇒ x + x+1 + x + 2 + x + 3 = 110

⇒ 4x + 6= 110

⇒ 4x = 110 -6

⇒ 4x = 104

⇒ x = 104/4

⇒ x = 26 inches

Thereofore, the length of the sides of the quadrilaterals is given by

x = 26 inches

x + 1 = 26 + 1 = 27 inches

x + 2 = 26 + 2 = 28 inches

x + 3 = 26 + 3 = 29 inches

Hence, the value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

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The the price of jacket before the sales tax was added was $50, if 6 percent of tax was added.

According to the given question.

The amount paid by a coustomer including the sale tax for a jacket is $53.00.

And 6 percent tax was added.

So,

Amount of tax paid by coustomer

= 6 percent of $53

= 6/100 × 53

= 318/100

= $3.18

Therefore, the price of jacket before the sales tax was added

= $53 - $3.18

= $49.82

≈ $50

Hence, the the price of jacket before the sales tax was added was $50, if 6 percent of tax was added.

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Answer:

The third one because its the only one that doesn't have the same (x) twice

Step-by-step explanation:

lmk if this helped

First, find the derivative of the function: f'(x) = 4x^3 - 3x^2.

Set f'(x) to 0 to find critical points:
4x^3 - 3x^2 = 0
x^2(4x - 3) = 0
x = 0, x = 3/4

Now, evaluate the function at the critical points and endpoints:
f(0) = 0^4 - 0^3 = 0
f(3/4) = (3/4)^4 - (3/4)^3 = 27/256
f(5) = 5^4 - 5^3 = 3125 - 625 = 2500

The absolute maximum is 2500 at x = 5, and the absolute minimum is 0 at x = 0.

To find the absolute maximum and minimum of the function f(x) = x^4 - x^3 on the interval [0,5], we first take the derivative of the function:

f'(x) = 4x^3 - 3x^2

Next, we set the derivative equal to zero to find critical points:

4x^3 - 3x^2 = 0

x^2(4x - 3) = 0

x = 0 or x = 3/4

We then check the values of the function at the critical points and the endpoints of the interval:

f(0) = 0

f(3/4) = 27/256 - 27/64 = -135/256

f(5) = 625 - 125 = 500

Therefore, the absolute maximum of f(x) on the interval [0,5] is f(5) = 500, and the absolute minimum is f(3/4) = -135/256.

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Answer:

-5

Step-by-step explanation:

\(gradient=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

              =\(=\frac{-8-2 }{3-1}\)

             =-5

Hope it helps:)

\(\textsf{The gradient of a line passing through two}\)\(\sf{given \: points \:(x_1,y_1) \:and \:(x_2,y_2) \: is \:given \: by - }\)

\(\green{ \underline { \boxed{ \sf{ Gradient =\frac{y_2-y_1}{x_2-x_1}}}}} \)

Here,

Putting Values:-

\(\begin{gathered}\begin{gathered}\\\implies\quad \bf Gradient =\frac{-8-2}{3-1} \\\end{gathered} \end{gathered} \)

\(\begin{gathered}\begin{gathered}\\\implies\quad \bf \frac{\cancel{-10}}{\cancel{2}} \\\end{gathered} \end{gathered} \)

\(\begin{gathered}\begin{gathered}\\\implies\quad \bf -5 \\\end{gathered} \end{gathered} \)

>>The gradient of the line segment is -5

The function h(x) = -0.046x provides a basic representation of the relationship between distance traveled and the resulting height of a long jumper, assuming a constant rate of decrease in height.

The given function h(x) = -0.046x represents the height, in meters, of a long jumper after jumping. In this model, x represents the distance traveled by the jumper on the horizontal axis, typically measured in meters.

The coefficient -0.046 indicates the rate of decrease in height per unit of distance traveled. This linear equation suggests that as the distance increases, the height of the long jumper decreases.

The negative sign in front of the coefficient indicates a downward slope, meaning the jumper's height decreases at a constant rate.

It is important to note that this model assumes a simplified scenario and neglects various factors such as air resistance, the athlete's technique, and other biomechanical aspects that can affect the actual height achieved by the long jumper.

The coefficient -0.046 implies that for every unit increase in distance traveled (x), the height (h) decreases by 0.046 units. This suggests that the long jumper's height decreases gradually but consistently as they cover more distance.

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The volume of the region within the cylinder and below the plane is πr² (h - (1/2)r).

The volume of the region within the cylinder and below the plane can be found using the equation for the volume of a cylinder and subtracting the volume of the triangular portion that lies above the plane.

The cylinder has volume V = πr²h, where h is the height of the cylinder.

The triangular portion above the plane can be considered as half of a cylinder with height r and base equal to the triangle. The volume of this half-cylinder can be found as V = (1/2)πr²h.

Since the plane is inclined at an angle of 45 degrees, the height of the triangular portion is r, and the base is r. Hence, the volume of the half-cylinder is (1/2)πr²r.

Subtracting this volume from the volume of the cylinder, we have:

V = πr²h - (1/2)πr²r

V = πr² (h - (1/2)r)

So, the volume of the region within the cylinder and below the plane is πr² (h - (1/2)r).

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Answer:

Angle X is congruent to angle F

I hope it helps.

Answer:

B and C IT CORRECTCORRECT

Step-by-step explanation:

Answer:

3/5, 67%, 0.7, 3/4  

Step-by-step explanation:

3/4= 75%

3/5= 60%

67%

0.7=  is equivelent to 70%  

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By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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The length of XZ is approximately 14.13 units. To find the length of XZ, we can use the trigonometric function sine.

This is because we have the opposite side, XY, and we want to find the length of the side opposite to the angle we have, angle Z.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the formula:

sin(Y) = XZ / XY

where Y is the measure of angle Y, XZ is the length of the side opposite angle Z, and XY is the length of the hypotenuse.

We can rearrange this formula to solve for XZ:

XZ = XY * sin(Y)

Substituting the given values, we get:

XZ = 29 * sin(29°)

Using a calculator, we can evaluate sin(29°) to be approximately 0.4877. Therefore:

XZ ≈ 29 * 0.4877 ≈ 14.13

So the length of XZ is approximately 14.13 units.

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It is constant because otherwise it wouldn't be proportional