Answer:
<em>159 feet of fabric</em>
Step-by-step explanation
We are told that 1 curtain is 36inches long
Since 1 foot = 12inches
x foot = 36inches
Cross multiply;
12 * x = 36
12x = 36
x = 36/12
x = 3
Hence 36inches is same as 3 feet
If Charlotte's curtain company wants to make 53 curtains, the length of 53 curtain is expressed as;
1 curtain = 3feet
53 curtain = y
y = 53 *3
<em>y = 159 feet</em>
<em>Hence she will need 159 feet of fabric</em>
<em> </em>
A³ b² 4ab³
Rearrange order:
4 a³ a b² b³
Now add up the exponents from same base:
4 a³⁺¹ b²⁺³
4 a⁴ b⁵
Final answer: 4 a⁴ b⁵
Answer:

Step-by-step explanation:
Given
Winning Percentage = 0.444 repeating
Required
Represent as a fraction
Represent the percentage with x

Convert to fraction

Next step, is to convert to fraction repeating
To do this, we simply subtract 1 from the denominator


Simplify to the lowest term: Divide numerator and denominator by 37


Simplify to the lowest term: Divide numerator and denominator by 3


Hence;
There winning fraction is 
Answer:
x= -4
Step-by-step explanation:
2x+4=6x+20
so 2x-6x=20-4
divide both sides by -4
-4x/-4 = 16/4
=-4
Answer:
Therefore, the volume of the cone is V=4π.
Step-by-step explanation:
From task we have a circular cone with radius 2 m and height 3 m. We use the disk method to find the volume of this cone.
We have the formula:

We know that r=2 and h=3, and we get:
![V=\int_0^3\pi \cdot \left(\frac{2}{3}x\right)^2\, dx\\\\V=\int_0^3 \pi \frac{4}{9}x^2\, dx\\\\V= \frac{4\pi}{9} \int_0^3 x^2\, dx\\\\V= \frac{4\pi}{9} \left[\frac{x^3}{3}\right]_0^3\, dx\\\\V= \frac{4\pi}{9}\cdot 9\\\\V=4\pi](https://tex.z-dn.net/?f=V%3D%5Cint_0%5E3%5Cpi%20%5Ccdot%20%5Cleft%28%5Cfrac%7B2%7D%7B3%7Dx%5Cright%29%5E2%5C%2C%20dx%5C%5C%5C%5CV%3D%5Cint_0%5E3%20%5Cpi%20%5Cfrac%7B4%7D%7B9%7Dx%5E2%5C%2C%20dx%5C%5C%5C%5CV%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%20%5Cint_0%5E3%20x%5E2%5C%2C%20dx%5C%5C%5C%5CV%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%20%5Cleft%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5Cright%5D_0%5E3%5C%2C%20dx%5C%5C%5C%5CV%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%5Ccdot%209%5C%5C%5C%5CV%3D4%5Cpi)
Therefore, the volume of the cone is V=4π.