A cone has a volume of 108 pi and a base diameter of 12. What is the height of the cone?

Step-by-step explanation:

Step 1:  Find the angle a

All triangles add up to 180 degrees

81 + 62 + a = 180

143 + a = 180

a = 180 - 143

a = 37

Answer:  Option A, 37

Let x = cost of the dishwasher.

The amounts the children are paying are:

Mark =20% = 1/5, so  1/5x

Sorin = 75

Raymond = 1/4x

Stephanie = 75

Kristin = 1/3x

Add them together:

x = 1/5x + 1/4x + 1/3x + 75 + 75

x - ( 1/5x + 1/4x + 1/3x ) = 150

Rewrite fractions with common denominator:

x - ( 12/60x + 15/60x + 20/60x ) = 150

60/60x - 47/60x = 150

13/60x = 150

x = 150/1 • 60/13

x = 9000/13

x = 692.31

The total cost of the dishwasher is $692.31

Now calculate the amount each child pays:

Mark = 1/5 x = 692.31/ 5 = $138.46

Sorin = $75.00

Raymond = 1/4 x = 692.31 / 4 = $173.08

Stephanie = $75.00

Kristin =  1/3 x = 692.31 / 3 = $230.77

Answer:

sin 56 = 0.8290

cos 23 =0.9205

Step-by-step explanation:

you can literally find this by typing: sin 56 deg in google.

or use a calculator.

Answer:

11

Step-by-step explanation:

[tex] \sqrt{121} = \sqrt{11 \times 11} = 11 \\ [/tex]

Answer:

23 Girls

Step-by-step explanation:

23 plus 13 equals 36 and 23 is 10 more than 13.

Answer:

the number of girls in the class is 23

Step-by-step ex

23 +13=36

Answer:

Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume.

Step-by-step explanation:

Answer:

cylinder volume formula

v = (π * r²) * h

Step-by-step explanation:

To calculate the volume of a cylinder we have to multiply the height by the area of ​​the circle that is the base

The area of ​​a circle is calculated with this formula (a = π * r²)

Let's do an example where the radius is 5.5ft  and the height is 13ft  to see how to calculate the volume

To calculate the volume of a cylinder we have to use the following formula:

v = volume

h = height = 13ft

π = 3.14

r = radius = 5.5ft

v = (π * r²) * h

we replace the unknowns with the values we know

v = (3.14 * (5.5ft)²) * 13ft

v = (3.14 * 30.25ft²) * 13ft

v = 94.985ft² * 13ft

v = 1234.805ft³

The volume of the cylinder is 1234.805ft³

The pre-image of A' is (-4,-4), and the correct option is D.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

The image is shown and a scale factor of 1/2 to find the pre-image.

[tex]\rm Scale\ factor = \dfrac{Dimension\ of\ New \ Shape}{Dimension\ of \ Original \ Shape}\\\\Dimension\ of\ New \ Shape= Scale\ factor \times Dimension\ of \ Original \ Shape\\\\A' =\dfrac{1}{2}(-8, \ -8)\\\\A' =(-4,-4)[/tex]

Hence, the pre-image of A' is (-4,-4), and the correct option is D.

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To calculate the surface area of a regular pyramid, add the area of the base to the combined area of the triangular faces. The base area is known, but without the base perimeter or side lengths, the total surface area cannot be determined.

To find the surface area of a regular pyramid, we need to first know the surface area of the base, which is given as 84.3 cm². Then, we must calculate the surface area of the triangular faces. The student has provided the slant height (9 cm) and the base of the pyramid, but the length of the base side is not clear from the question. Typically, the formula for the surface area (SA) of a regular pyramid is SA = base area + 1/2 × perimeter of base × slant height. Since the area of the base is known, we only need the perimeter of the base to continue. If that perimeter or the number of sides and the length of each side were provided, we could use it to find the area of each triangle using the formula for the area of a triangle, which is 1/2 × base × height, and then multiply it by the number of triangles (sides) the pyramid has to get the total area of the triangular faces. This sum, along with the base area, would give us the total surface area of the pyramid. Without the individual side lengths or the perimeter, an exact surface area cannot be calculated.

Answer:

2

Step-by-step explanation:

Answer:

3077.2

Step-by-step explanation:

A circle's mass is found by

Pie times R^2

7^2 is 49, times 3.14 is 153.86

then you Multiply 153.86 by 20 which gives you 3077.2

Answer:

[tex]F(x)=\left \{ {{-\frac{1}{2}+1, x<0 } \atop {2x-2, x\geq0}} \right.[/tex]

Step-by-step explanation:

There are 2 linear equations, one with an open circle and one with a closed one. Depending on where the circle is, that will tell you your start. Both circles start at 0 on the graph. The open circle means that the first equation will be   x < 0. The second equation has a closed circle so it will be [tex]x\geq 0[/tex] because the linear equation is increasing positively.

Now you need to the start point of both equations.

[tex]x<0[/tex]   start point is 1 on the y-axis

[tex]x\geq 0[/tex]   start point is 2 on the y-axis

Now you have to find the slope for the two equations

[tex]x<0[/tex]  the equation goes up 1 and and over 2

[tex]x\geq 0[/tex]  the equation goes up 2 and over 1

Now put together the equations

[tex]x<0[/tex] [tex]\frac{-1}{2} + 1[/tex]

[tex]x\geq 0[/tex]  [tex]2x - 2[/tex]

Answer:

On my test i just took it was a total of 30.

Step-by-step explanation:

Answer:

$ 32.63

Step-by-step explanation:

$3200 -$ 2156 = $ 1044

Therefore $ 1044 divided by 32 equal $ 32.625.Round it to the nearest hundreth and you get $ 32.63.

Each student have to pay $32.625.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A group of 32 students have raised money to help pay for a field trip to the Outer Banks Research Park.

The trip will cost $3,200 and they have raised $2,156.

Now,

Since, The trip will cost $3,200 and they have raised $2,156.

Hence, The remaining cost to pay by students = $3,200 - $2,156

                                                                        = $1,044

So, The cost pay by each students = $1,044/32

                                                      = $32.625

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Answer:

Area = 31.5 (I think)

Step-by-step explanation:

Split into 3 parts:

Rectangle: 7 · 3 = 21

Triangle 1: 3 · 3.5= 10.5

10.5 ÷ 2 = 5.25

Triangles(they are the same): 5.25 · 2 = 10.5

Area: 10.5 + 21 = 31.5

Area = 31.5

Answer:

102

Step-by-step explanation:

Each triangle will have a perimeter of 3. When joined, the outside triangles will have 2 sides showing, or 2 inches. The middle 98 will only have one free side, or one inch. This means that 98*1 + 2*2 = 102

To calculate the perimeter of 100 equilateral triangles joined side to side, each with a side of one inch, use the formula P = 2s + (n - 1)s. With s = 1 inch and n = 100, the perimeter is 101 inches.

To find the perimeter of a train of 100 equilateral triangles, we start by acknowledging that each triangle contributes two sides to the perimeter since they are joined side to side. An individual equilateral triangle has three sides of equal length; however, when joined in a train, the shared side does not contribute to the perimeter. Therefore, the equation to determine the perimeter (P) of the triangle train with 100 triangles, each with a side length (s) of one inch, would be:

P = 2s + (n - 1)s

Where n is the number of triangles in the train. Plugging in the values, we get:

P = 2(1 inch) + (100 - 1)(1 inch) = 2 inches + 99 inches = 101 inches.

This calculation shows that the perimeter of a train of 100 equilateral triangles, each with sides of one inch, is 101 inches.

Answer:

what is the radius given?

Step-by-step explanation:

With a height of 16 feet and a base radius of 5 feet, the volume of the cone is approximately 418.67 cubic feet, rounded to the nearest tenth.

To find the volume  V  of a cone, we use the formula:

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

Where:

[tex]- \( \pi \)[/tex] is approximately 3.14

-  r is the radius of the base of the cone

-  h is the height of the cone

Given that the height h is 16 feet and the radius r is 5 feet, we substitute these values into the formula:

[tex]\[ V = \frac{1}{3} \times 3.14 \times (5)^2 \times 16 \]\[ V = \frac{1}{3} \times 3.14 \times 25 \times 16 \]\[ V = \frac{1}{3} \times 3.14 \times 400 \]\[ V = \frac{1256}{3} \]\[ V \approx 418.67 \][/tex]

So, the volume of the cone is approximately 418.67 cubic feet.

Complete question : Using 3.14 for pi, what is the volume, to the nearest tenth, of a cone that has a height of 16 feet and a base with radius of 5 feet.

Step-by-step explanation:

Step 1:  Subtract 18 from both sides

[tex]12 = 18 + 6b[/tex]

[tex]12 - 18 = 18 - 18 + 6b[/tex]

[tex]-6 = 6b[/tex]

Step 2:  Divide both sides by 6

[tex]-6 / 6 = 6b / 6[/tex]

[tex]-1 = b[/tex]

Answer: [tex]b = -1[/tex]

y = 1200(.80)^t  Plug in 5 for t (time).

y = 1200(.80)^5

.80^5= 0.33

0.33 x 1200 = 395

Therefore, the value of the computer after 5 years has deteriorated to $396.

The function represents the value of the computer will be y = $1200 × (0.80)ˣ. Then the value of the computer after 5 years will be $393.22.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a (1 - r)ˣ

The value of a computer is $1200. It loses 20% of its value every year. Then the equation is given as,

y = $1200 × (1 - 0.20)ˣ

y = $1200 × (0.80)ˣ

Where 'x' is the number of years and 'y' is the amount. Then the value of the computer after 5 years will be given as,

y = $1200 × (0.80)⁵

y = $1200 × 0.32768

y = $393.22

The function represents the value of the computer will be y = $1200 × (0.80)ˣ. Then the value of the computer after 5 years will be $393.22.

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Answer:

A

Step-by-step explanation:

Answer:

D) 18

Step-by-step explanation:

Answer:

8 hours

Step-by-step explanation:

In this case, the speed would be given by the garbage collection / hour, therefore the two together, that is to say from the sum of both, would be 1/6 the speed and for the small truck it would be 1/24

So to calculate the speed of the big truck it would be:

1/24 + 1 / x = 1/6

1 / x = 1/6 - 1/24

1 / x = 0.125

x = 1 / 0.125

x = 8

Which means that only the big truck would take only 8 hours

The large garbage truck, when working alone, can collect all the garbage in 8 hours. This is found by setting up equations for the combined rate of work of both trucks and the rate of work of the small truck alone, then solving for the large truck's rate of work.

The problem describes a work rate scenario where two garbage trucks work together and individually to complete a task. To solve for the amount of time the large truck would take to collect all the garbage by itself, we can use the rate of work formula which is Work = Rate * Time. When both trucks work together, their combined rate multiplied by 6 hours results in the work being completed. When the small truck works alone, its rate times 24 hours completes the work. We can set up equations to represent these scenarios.

Let, 1 represent the total work (collecting all the garbage), S be the small truck's rate of work, and L be the large truck's rate of work.

From the provided information, we have:

Substituting S from the second equation into the first equation, we get:

L + 1/24 = 1/6

Therefore, L = 1/6 - 1/24

After finding a common denominator and subtracting, we find:

L = 4/24 - 1/24

L = 3/24

L = 1/8

So, the large truck's rate of work is 1/8, meaning the large truck can collect all the garbage in 8 hours working alone.

The solution of given equation 6−by=19 is [tex]y = \frac{-13}{b}[/tex].

To find the value of y in the equation 6−by=19, subtract 6 from both sides, then divide by -b to isolate y as -13/b.

The variable y in the equation 6−by=19 can be solved for as follows:

6 -by =  19

Subtract 6 from both sides:

-by = 19 - 6

-by = 13

Divide by -b to isolate y is

[tex]y = \frac{13}{-b} = -\frac{13}{b}[/tex]

Therefore, y equals -13 divided by b.

Answer:

74

Step-by-step explanation:

74

Answer:

45

Step-by-step explanation:

The surface area of the square pyramid, square prism, and total surface area will be 103 square mm, 429 square mm, and 532 square mm, respectively.

The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The surface area of the square pyramid is calculated as,

SA of pyramid = 4 x 1/2 x 5 x 10.3

SA of pyramid = 103 square mm

The surface area of the rectangular prism is calculated as,

SA of prism = 4(13 x 5) + 13 x 13

SA of prism = 429 square mm

The total surface area of the composite figure is calculated as,

TSA = 103 + 429

TSA = 532 square mm

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Answer:

-2

Step-by-step explanation:

[tex]2 (\sqrt{\frac{80}{5} }-5)[/tex]

[tex]2(\sqrt{16}-5)[/tex]

[tex]2(4 - 5)[/tex]

[tex]2(-1)[/tex]

[tex]-2[/tex]

Answer:

Since AB || QR and PR is a transversal.

∠QRP=∠ABP=100 o

       [Corresponding angles]

Step-by-step explanation:

Answer:

The answer is option 2.

Step-by-step explanation:

It is given that she work for 7.5 hours at a rate of $15.75 per hours. In order to calculate how much she earned, you have to multiply it :

$15.75 = 1 hour

$ x = 7.5 hours

x = 7.5×$15.75

x = $118.13 (2d.p)

Answer:

A: The median weight for shelter A is greater than that for shelter B.

D: The data for shelter B are a symmetric data set.

E: The interquartile range of shelter A is greater than the interquartile range of shelter B.

Step-by-step explanation:

edg2020

From the box plots, we can conclude three things: (1) the median weight for Shelter A is greater than that for Shelter B, (2) neither Shelter A's nor Shelter B's data is symmetric, and (3) Shelter A has a greater interquartile range than Shelter B.

The box plots given provide valuable information about the weights of the dogs in two shelters. The line dividing the box represents the median weight of the dogs. For Shelter A, the median weight is 21 and for Shelter B, the median weight is 18. Therefore, the statement that the median weight for Shelter A is greater than that for Shelter B is correct.

Next, it's crucial to understand the concept of symmetry in the data set. If a data set is symmetric, the whiskers (that represent the variation or spread of the data) of the box plots would be roughly of equal lengths, indicating uniform spread around the median. Given the information, neither Shelter A nor Shelter B display symmetric whisker lengths, so the data for neither shelter A nor B is a symmetric data set.

Finally, the Interquartile Range (IQR) represents the range within which the central half of the weights lies — it is the difference between the third quartile (the right end of the box) and the first quartile (the left end of the box). For Shelter A, the IQR is 28 - 17 = 11, and for Shelter B, the IQR is 20 - 16 = 4. Therefore, the interquartile range of shelter A is indeed greater than the interquartile range of shelter B.

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Answer: There are 27 votes for Florida.

Step-by-step explanation:

Hi, to answer this question we have to write an equation:

The number of votes of North Carolina (15) must be equal to the number of votes of Florida (x) minus 12.

Mathematically speaking:

15 = x -12

Solving for x:

15+12 = x

27 = x

There are 27 votes for Florida.

Feel free to ask for more if needed or if you did not understand something.