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Answer:

Equal volumes

Step-by-step explanation:

Given

[tex]h \to[/tex] height of cone

[tex]d \to[/tex] diameter of cone

[tex]H \to[/tex] height of cylinder

[tex]D \to[/tex] diameter of cylinder

Such that:

[tex]d = 2D[/tex]

[tex]h =\frac{3}{4}H[/tex]

Required

The relationship between the volumes

The volume of a cylinder is:

[tex]V_1 = \pi R^2H[/tex]

Where

[tex]R = 0.5D[/tex]

So:

[tex]V_1 = \pi (0.5D)^2H[/tex]

[tex]V_1 = \pi *0.25*D^2H[/tex]

[tex]V_1 = 0.25\pi D^2H[/tex]

The volume of the cone is:

[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]

Where

[tex]r =0.5d[/tex]

[tex]r = 0.5 * 2D[/tex]

[tex]r = D[/tex]

and

[tex]h =\frac{3}{4}H[/tex]

So, we have:

[tex]V_2 = \frac{1}{3}\pi * D^2 * \frac{3}{4}H[/tex]

[tex]V_2 = \frac{1}{4}\pi * D^2H[/tex]

[tex]V_2 = 0.25\pi * D^2H[/tex]

[tex]V_2 = 0.25\pi D^2H[/tex]

So, we have:

[tex]V_1 = 0.25\pi D^2H[/tex]

[tex]V_2 = 0.25\pi * D^2H[/tex]

[tex]V_1 = V_2[/tex]

Answer: : When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

Step-by-step explanation:

Answer:

(1,0) and (3,0)

Step-by-step explanation:

The roots are always shown where the parabola crosses the x-axis.

In this particular graph, the parabola crosses at (1, 0) and (3, 0). Which means the roots are:

x = 1 and x = 3

Answer:

4,500

Step-by-step explanation:

150,000x.03=4500

The commission of the real estate agent is 4500 which is 3% of 150,000.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A real estate agent earns a 3% commission on each house she sells and she sells a 150,000 house.

So, His commission is 3% of 150,000.

Therefore,

Commission = (3/100)×150000.

Commission = 4500.

So, The commission of the real estate agent is 4500.

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Answer:

216 cubic centimeters

Step-by-step explanation:

I divided the shape as two separate rectangular prisms.

4 times 6 times 6 = 144

3 times 4 times 6 = 72

144 + 72 = 216

I hope this helps! :-)

Answer:

The percentage is 1/2 * 2/5 = 1/5 = 20%.

Answer:

The correct answer is 20%

Step-by-step explanation:

If you were to pick two marbles from the pile, there would be 30 different possible combinations. Out of the 30 possible combinations, 6 of them meet the requirement of green marble on the first pick and red marble on the second pick. The fraction that represents the situation would be [tex]\frac{6}{30}[/tex] or [tex]\frac{1}{5}[/tex], which would be equal to 20%, so that is the correct answer.

Answer:

24 miles

Step-by-step explanation:

Given that the cost of the company consist of two elements; a fixed cost equivalent to $4 and a variable cost element which depends on the miles driven. If the car travels x miles then the cost will be

= 4 + 1*x

= 4 + x

If the total cost is $28 then

4 + x = 28

Subtract 4 from both sides

x = 28 - 4

= 24  

The car ride is

24/1 = 24 miles

Answer:

D

Step-by-step explanation:

The cost of a t-shirt is £3 and the cost of a hat is £2.

What is a linear equation?

When an equation contains one or more variables with exponents as 1 then such equations are linear equations.

For example, 3x+2y=9 and 4y=6. The first equation is a linear equation with two variables and the second equation is with the linear equation in one variable.

Let the cost of a t-shirt is £m and the cost of a hat is £n.

Formulate two linear equations using the given statements in the question.

[tex]2m+3n=12\,\,\, ...(1)\\5m+4n=23\,\,\, ...(2)[/tex]

Obtain the value of m from equation (1).

[tex]2m=12-3n\\m=\frac{12-3n}{2}[/tex]

Substitute the obtained value of m into equation (1) and find n.

[tex]5 \times(\frac{12-3n}{2})+4n=23\\ 60-15n+8n=46\\14=7n\\n=2[/tex]

Substitute the value of n into [tex]m=\frac{12-3n}{2}[/tex]and obtain the value of m.

[tex]m=\frac{12-3(2)}{2}\\=\frac{12-6}{2}\\ =\frac{6}{2}\\ =3[/tex]

Thus, the cost of a t-shirt is £3 and the cost of a hat is £2.

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Answer:

a⁸=112 is the answer.

Step-by-step explanation:

a⁸=32(1/2)⁷

a⁸=32(7/2)

a⁸=112

Answer:

1884.96 cm squared

Answer: 1306.5 m^3

Step-by-step explanation:

1. The formula for the volume of a cylinder is: V=[tex]\pi[/tex]r^2h

2. If you substitute the values into the equation, you get

V = pi * 5.7^2 * 12.8 = 1306.5

3. 1306.5 is already to the nearest tenth, so that is the answer.

Answer:

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

So to do this, lets convert all of these fractions into decimals by dividing:

5/6 --> 0.833...

7/12 --> 0.583...

4/7 --> 0.571...

2/3 --> 0.66...

From this, it can be see that it is 5/6, since it is a larger decimal compared to the other choices.

Answer:

Mean

Step-by-step explanation:

I said mean because it would allow both Carl and Tamera to average their scores and compare one side by side rather than comparing 6 each which would just be time consuming and it seems like it wouldn't be any other choices.

Answer: A and D are the correct answers.

Step-by-step explanation:

Step-by-step explanation:

djifvodp09govovkvcicodsodoss

Answer:

Grey Hairs? Try some of our free Pi-Lights

Step-by-step explanation:

Answer:

A unit rate is the rate of change in a relationship where the rate is per 1.

The rate of change is the ratio between the x and y (or input and output) values in a relationship.  Another term for the rate of change for proportional relationships is the constant of proportionality.

If the rate of change is yx, then so is the constant of proportionality.  To simplify things, we set  yx=k, where k represents the constant of proportionality.  

If you solve a yx=k equation for y, (like this: y=kx), it is called a direct variation equation. In a direct variation equation, y varies directly with x. When x increases or decreases, y also increases or decreases by the same proportion.

To find y in a direct variation equation, multiply x by the constant of proportionality, k.

For example: Given the relationship y=7x, the constant of proportionality k=7,  so if x=3,  then y=3×7 or 21.

Given the same relationship, if x=7,  then y=7×7, or 49.  

Step-by-step explanation:

Answer:

Yes it is. Y=2.5x

Step-by-step explanation:

So, lets start with bthe first values of the table and work our way down:

2x=5y

Lets just divide both sides by the 2:

x=5/2y

This means that for every 1 x, there should be 5/2y's.

Or, for every 1 x, there should be 2.5ys.

Lets check the next few to see if thats correct:

3x=7.5y

Divide both sides by 3:

x=7.5/3

This means for every one x, there are again, 2.5ys.

Lets check one more just to be sure:

4x=10y

Divide both sides by 4:

x=10/4

This means for everyone one x, y equals 2.5ys, yet again,

So we can conclude that the poprotional relationship between x and y is:

When x equals 1, y=2.5

Or

Y=2.5x

Hope this helps!

The last name I am pretty sure of it.

Answer:

Zarathustra is the answer

Answer:

28.58 pounds, about 29 pounds

Step-by-step explanation:

Poultry meat with bones ; divide number to be served by 2.5

Meat with little or no bone ; divide number to be served by 3.5

If number of guests to be served = 100

Meat served = 100

The number of pounds of chicken required :

Number of guests to be served / meat served

Hence,

100 / 3.5

= 28.58 ; which is about 29 pounds

Answer:

43

Step-by-step explanation:

Answer:

Step-by-step explanation:

I need help

Answer:

It would be 4.

Step-by-step explanation:

Alright, this is a 30-60-90 special triangle. With special triangles, there is a formula that you can use to find unknown side lengths of a triangle if you know the angles of it.

With a 30-60-90 triangle, the sides opposite of these angles are:

30 degrees : x

60 degrees: x√3

90 degrees: 2x

With this, we can see that opposite of the 60 degrees is the length 2√3. From this, it can be found that the opposite of the 30 degrees would be 2, given the formula of the special triangle. Lastly, the unknown value would be 4, since it is two times this amount.

Answer:

x = 4

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{x}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] x = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

x = 4

Answer:

[tex]130cm^{2}[/tex]

Step-by-step explanation:

1) Calculate the entire rectangle and subtract the right triangle area

15 x 10 = 150 Entire rectangle area

(5 x 8) ÷ 2 = 20 Triangle area

150 - 20 = 130 Area of shaded region

Hence,

Hope it helps you. Please don't mind my rude handwriting. Just pretend it get bent due to a cyclone.

Answer:

uhhhh.....wut?

Step-by-step explanation:

The measure of the angle WSV is 38 degrees.

Complementary Angles Two angles are Complementary when they add up to 90 degrees.

The value of x is;

[tex]\rm 5x+17=9x-11\\\\ 5x-9x=-11-17\\\\-4x=-28\\\\x =\dfrac{-28}{-4}\\\\x=7[/tex]

The angle VST is equlas to;

[tex]\angle \rm VST=9x-11=9(7)-11=63-11=52 \ degrees[/tex]

The angle VST and angle WSV are the complementary angles;

[tex]\angle \rm WSV+\angle VST=90\\\\\angle \rm WSV+52=90\\\\ \angle \rm WSV=90-52\\\\\angle \rm WSV=38[/tex]

Hence, the measure of the angle WSV is 38 degrees.

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Answer: It’s 5%

Step-by-step explanation:45 divided by 9 is 5 so that the answer :)

Answer:

a b c and f

Step-by-step explanation:

rectangle parallelogram square and rhombus