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e-lub [12.9K]
3 years ago
9

Maria want to make a footstool in the shape of a cylinder, as show below. She wants to fill the footstool with foam and cover it

with fabric. r=12in by h=18in
Mathematics
1 answer:
dexar [7]3 years ago
8 0

Answer:

She'll need 8143 cubic inches of foam and 1,809.6  square inches of fabric.

Step-by-step explanation:

Assuming you want to know how much foam and fabric she will need...

First the foam... so we need to determine the volume of that footstool.  The Volume of a cylinder is given by:

V = π * r² * h

So, we plug in the numbers:

V = π * 12² * 18 = π * 144 * 18

V = 2,592 π  = 8143 cubic inches.

Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.

The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool.  The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.

So the lateral surface of the cylinder is:

LS = 18 * 75.14 = 1,357.2 sq inches.

Then we need to calculate the area of the top... which is easy:

A = π * r²  = π * 12²  = 144 π = 452.4 sq inches

So, to cover the lateral side of the footstool and its top, she needs to use:

TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.

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There were 400 pieces of candy in all. If 60 pieces were chocolate, then what percent of the candy was chocolate.
Liono4ka [1.6K]
400 --- 100%
  60 ---  x%

x = 60/400 * 100 = 15%  <span>chocolate.</span>
5 0
3 years ago
You have $36,948.61 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until y
Luba_88 [7]
Current amount in account
P=36948.61

Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n

Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11

We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000

We can solve this by trial and error.


The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000.  It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.

So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.

So it takes 15.00 years to reach the goal of 280000 years.
8 0
3 years ago
What's the answer -5+ 8x - 9 = 3x+3)​
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We collect like terms
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This is bcos if a (-) sign crosses the equals sign it becomes a (+), and if a (+) sign crosses the equals sign it becomes (-)
We the have
5x = 17
Divide both sides by 5
x = 17/5
x = 3.4
5 0
2 years ago
Please help me out with this please
Natali [406]

Answer:

Step-by-step explanation:

We have 2 equations represented by the lines on the graph

5x + 4y = 20

2x - 6y = 12

To plot the first equation on the graph, we a assume different points

4y = 20 - 5x

y = (20-5x)/4

y = 5 - 5x/4

If x =0, y = 5

If x = 2, y = 2.5

If x = 4, y = 0,

These points corresponds to the first line that cuts the positive y axis.

The first line that cuts the positive y axis is represented by the equation,

5x + 4y = 20

Since the left region of the line representing equation is shaded, the unshaded side represents

5x + 4y lesser than 20

To plot the second equation on the graph, we a assume different points

-6y = 12-2x

y = (2x-12)/6 = x/3 - 2

if x= 0, y = -2

If x = 3,y = 1

These points corresponds to the second line that cuts the negative y axis.

The second line that cuts the negative y axis is represented by the equation,

2x -6y = 12

Since the downward region of the line representing the equation is shaded, the unshaded side represents

2x -6y greater than 12

8 0
2 years ago
Please help! <br> ThAnKs!
Helen [10]

Answer:

The angle is 135°

Step-by-step explanation:

7 0
2 years ago
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