how to solve triangle prisms

Answer:

The height of small can need to be 12.8 cm to hold all the paint

Step-by-step explanation:

- Jamil had a 1/4 can of paint left

- The radius of the can is 8 cm and its height is 20 cm

- He wants to put the remaining paint into a smaller can with a

 radius of 5 cm

- We need to find the height of the smaller can

- The volume of the paint in the larger can is the same volume of paint

  will put in the smaller can

- Lets find the volume of the paint in the larger can

∵ The volume of the paint in the larger can = 1/4 its volume

∵ The can is shaped a cylinder

∵ Volume the cylinder = πr²h, where r is the radius of it and h its height

∵ r = 8 cm and h = 20 cm

∴ The volume of the paint = [tex]\frac{1}{4}\pi (8)^{2}(20)=320\pi[/tex] cm³

- Same amount of paint will put in the smaller can

∵ r = 5 cm and V = 320π cm³

∴ 320π = π(5)²h

- Divide both sides by π

∴ 320 = 25 h

- divide both sides by 25

∴ h = 12.8 cm

* The height of small can need to be 12.8 cm to hold all the paint

The height of the smaller can need to be to hold all the paint will be 12.8 cm.The term height is frequently used to describe someone's or something's height.

Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.

From the given conditions;

The volume of the paint in the larger can is,[tex]\rm V_L[/tex]

The volume of the paint in the smaller can is,[tex]\rm V_S[/tex]

The volume of the cylinder is, V

The radius of the can is,r= 8 cm

The height is,h=20 cm

The volume of the paint in the larger can is found as;

[tex]\rm V_L = \frac{1}{4} V \\\\ V=\pi r^2 h \\\\ V_L= \frac{1}{4} \pi (8)^2 (20) \\\\ V_L = 320 \pi \ cm^3[/tex]

The volume of the larger can is equal to the volume of the smaller can;

[tex]\rm V_S = V_L \\\\ 320 \ \pi \ cm^3=\pi r^2 h \\\\ \pi \ cm^3=\pi (5)^2 h \\\\ 320=25h \\\\ h =12.8 \ cm[/tex]

Hence the height of the smaller can need to be to hold all the paint will be 12.8 cm.

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The actual distance between the two towns, considering that they are 7cm apart on a map with a scale of 1:500000, is 35 kilometers.

In the given scenario, you're being asked to find the actual distance between two towns based on their distance on a map, using the map's scale, which is 1:500000. This means 1 cm on the map is equivalent to 500000 cm on the ground.

Since the towns are 7 cm apart on the map, the actual distance on the ground will be 7 (distance on the map) multiplied by 500000 (scale of the map), i.e., 3500000 cm. Since there is 100000 cm in 1 km, you convert the distance to kilometers by dividing by 100000. Hence, the actual distance is 3500000/100000 = 35 km.

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Answer: $2875

Step-by-step explanation:

The formula to calculate the simple interest is given by :-

[tex]S.I.=P\times r\times t[/tex], where P is the principal amount , r is the rate of interest and t is the time period.

Given: Principal amount = $2500

Rate of interest = 15%=0.15

Time period = 1 year

Now, the simple interest gained by Darrel after 1 year will be :-

[tex]S.I.=2500\times 0.15\times 1=\$375[/tex]

Now, the total amount his friend owed altogether= [tex]P+I=2500+375=\$2875[/tex]

Answer:

1.29 x 10^7 people

Step-by-step explanation:

1.29 x 10^7 people

If she made $192 at work. Then the amount of money she puts in her savings account will be $80.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Elena always puts 5/12 of the money she makes at work in her savings account. If she made $192 at work.

Then the amount of money she puts in her savings account will be

→ 5/12 x 192

→ 80

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Answer:

n=21

Step-by-step explanation:

Ik im late but hopefully it can help other people :)

The equation is :

4(9+n)=120

n+9=120/4

n+9=30

n+9-9=30-9

n=21

Please rate... Thankyou :)

All figures are in 3-D form. But the base of each polygonal prism is different.

One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.

A prism is a solid form that is enclosed by plane faces on all of its sides. A prism has two different kinds of faces. Bases refer to identical top and bottom faces. The name "prism" refers to the form of these bases.

All figures are in 3-D form. And all the figures are polygonal prism.

But the base of each polygonal prism is different.

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The value of Terrence's car after x years is

A = 20,000 ( [tex]1-0.15)^x[/tex]

Subtract the asset's salvage value (what you expect it to be worth at the end of its useful life) from its cost to calculate depreciation using the straight-line technique. The depreciable basis, or the amount that can be depreciated, is the result. Divide this figure by the number of years the asset will be useful.

Depreciation is the rate at which an object's value declines over time.

it is given by the formula,

A = P [tex](1-r)^t[/tex]

where A is the value of object after x period of time, P is the principal amount, r is the rate of depreciation, and t is the for the time period.

Given:

Terrence buys a new car for $20,000,

rate of depreciation = 15%,

We know the formula of the rate of depreciation,

A = P [tex](1-r)^t[/tex]

Here A= $20, 000

r = 15% = 0.15

So, the value of Terrence's car is A = 20,000 ( [tex]1-0.15)^x[/tex].

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Given is a sculpture that is built up of metal and wood, and the weight of this sculpture is 14.9 kilograms.

It says that three-fourth of the total weight is metal and says to find the weight of wooden part.

We can find the weight of metal part and then subtract it from the total weight to calculate the answer.

Total weight = 14.9 kilograms.

Metal part = three-fourth of total weight = [tex] \frac{3}{4} *14.9=\frac{44.7}{4} =11.175 \;kilograms [/tex]

Wooden part = 14.9 - 11.175 = 3.725 kilograms.

Hence, the wooden part is 3.725 kilograms.

3.725 kilograms or ¹/₄ part

Given:

An artist builds a sculpture out of metal and wood that weighs 14.9 kilograms.

Question:

How much does the wood part of the sculpture weighs?

The Process:

From the information above, we make a diagram that matches the composition of the sculpture material.

[tex]\boxed{metal}\boxed{metal}\boxed{metal}\boxed{wood} = 14.9 \ kilograms[/tex]

And now, let us calculate the wood part of the sculpture weighs.

[tex]\boxed{ \ = \frac{1}{4} \times 14.9 \ kilograms \ }[/tex]

Both 4 and 14.9 are multiplied by 10.

[tex]\boxed{ \ = \frac{1}{40} \times 149 \ kilograms \ }[/tex]

[tex]\boxed{ \ = \frac{149}{40}  \ kilograms \ }[/tex]

Both the numerator and denominator are divided by 4.

[tex]\boxed{ \ = \frac{37.25}{10}  \ kilograms \ }[/tex]

[tex]\boxed{ \ = \frac{3,725}{1,000}  \ kilograms \ }[/tex]

[tex]\boxed{\boxed{ \ 3.725 \ kilograms \ }}[/tex]

Thus, the wood part of the sculpture weighs is 3.725 kilograms or ¹/₄ part.

Keywords: an artist, builds a sculpture, out of metal and wood, that weighs 14.9 kilograms, 3/4, metal, the rest is wood, how much, the wood part, of the sculpture weighs

Answer:

Option E - Box plot E

Step-by-step explanation:

Given : Data,

67, 66, 64, 62, 60, 56, 54, 50, 46, 42, 41, 40, 40, 38, 35, 21, 19

To find : Which choice below is a boxplot for the following distribution?

Solution :

Step 1- Arranging the data from lowest to highest,

{19,21,35,38,40,40,41,42,46,50,54,56,60,62,64,66,67}  

Step 2 - Find the median of the data  

As the data is odd numbers so the median is [tex]\frac{n+1}{2}[/tex] th term.

[tex]\frac{n+1}{2}=\frac{17+1}{2}=9th[/tex] term.

9th term is 46

∴ [tex]Q_2=46[/tex]  

Step 3 - To find Upper quartile and lower quartile  

Lower quartile data set is the median of the upper terms from median

{19,21,35,38,40,40,41,42}

Median of the set is [tex]M=\frac{38+40}{2}=39[/tex]

∴ [tex]Q_1=39[/tex]  

Upper quartile data set is the median of the lower terms from median

{ 50,54,56,60,62,64,66,67}

Median of the set is [tex]M=\frac{60+62}{2}=61[/tex]

∴ [tex]Q_3=61[/tex]  

We have plot the box plot attached below.

Our box plot is matched with Box plot E.

Therefore, Option E is correct.

Answer: Box plot E

Step-by-step explanation:

A P E X

Answer:

65 meters off the ground.

Step-by-step explanation:

The height of the monument is 9.80 m

To find the height of the monument, we can use the Pythagorean theorem. The rectangle on the pedestal forms a right triangle with the longest side of the monument being the hypotenuse. Let's call the height of the monument 'h'. Using the Pythagorean theorem, we have:

[tex]h^2 = (11^2) - (5^2)[/tex]

[tex]h^2 = 121 - 25[/tex]

[tex]h^2 = 96[/tex]

[tex]h = \sqrt{96[/tex]

h ≈ 9.80 meters

The exact surface area of the cylinder with a radius of 30 ft and height of 19 ft is calculated using the formula 2πr(h + r), resulting in an area of 2940π ft², which matches option D.

To find the exact surface area of a cylinder, we use the formula that states the surface area (SA) is SA = 2πr(h + r), where r is the radius and h is the height of the cylinder. Given that the radius (r) is 30 ft and the height (h) is 19 ft, we plug these values into the formula:

SA = 2π(30)(19 + 30)

SA = 2π30(49)

SA = 60π(49)

SA = 2940π ft²

Therefore, the exact surface area of the cylinder is 2940π square feet, which corresponds to option D.

Answer:

the answer is 189

1,289,845 rounded to the nearest ten thousand is 1,290,000.

To round 1,289,845 to the nearest ten thousand, we need to look at the digit in the ten thousandth place, which is the 8 in this case. If the digit is 5 or greater, we round up, and if it is less than 5, we round down. Since the 8 is greater than 5, we round up. To do this, we keep the digit in the ten thousandth place as it is and change all the digits to the right of it to zeros. Therefore, 1,289,845 rounded to the nearest ten thousand is 1,290,000.

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