Answer:
The ratio of number of woman to the total number is 19 : 24.
Step-by-step explanation:
Total number of members in the club = 24
Number of men = 5
Number of women = 24 - 5 = 19
The ratio of number of women to the total number of members is
= ![\frac{19}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B19%7D%7B24%7D)
<span>(3x-4)+(x+3)^2
= 3x - 4 + x^2 + 6x + 9 .........(expand using (a+b)^2 = a^2 + 2ab + b^2)
= x^2 + 9x + 5 ..........(combine like terms and simplify)
hope that helps</span>
Answer:
.
Step-by-step explanation:
We have been given that a sphere has a radius of 8 centimeters. A second sphere has a radius of 2 centimeters. We are asked to find the difference of the volumes of the spheres.
We will use volume formula of sphere to solve our given problem.
, where r is radius of sphere.
The difference of volumes would be volume of larger sphere minus volume of smaller sphere.
![\text{Difference of volumes}=\frac{4}{3}\pi(\text{8 cm})^3-\frac{4}{3}\pi(\text{2 cm})^3](https://tex.z-dn.net/?f=%5Ctext%7BDifference%20of%20volumes%7D%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%28%5Ctext%7B8%20cm%7D%29%5E3-%5Cfrac%7B4%7D%7B3%7D%5Cpi%28%5Ctext%7B2%20cm%7D%29%5E3)
![\text{Difference of volumes}=\frac{4}{3}\pi(512)\text{ cm}^3-\frac{4}{3}\pi(8)\text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BDifference%20of%20volumes%7D%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%28512%29%5Ctext%7B%20cm%7D%5E3-%5Cfrac%7B4%7D%7B3%7D%5Cpi%288%29%5Ctext%7B%20cm%7D%5E3)
![\text{Difference of volumes}=\frac{4}{3}\pi(512-8)\text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BDifference%20of%20volumes%7D%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%28512-8%29%5Ctext%7B%20cm%7D%5E3)
![\text{Difference of volumes}=4\pi(168)\text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BDifference%20of%20volumes%7D%3D4%5Cpi%28168%29%5Ctext%7B%20cm%7D%5E3)
![\text{Difference of volumes}=672\pi\text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BDifference%20of%20volumes%7D%3D672%5Cpi%5Ctext%7B%20cm%7D%5E3)
Therefore, the difference between volumes of the spheres is
.
For this case we have the following statement:
<em>"You have 2 meters of fabric and you cut 85% to make curtains, 50% of the rest to make the strips that hold it. How many centimeters of fabric were left?"</em>
So, we have:
2 meters ---------> 100%
x ----------------------> 85%
Where "x" represents the amount of fabric meters equivalent to 85%.
![x = \frac {85 * 2} {100}\\x = 1.7](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B85%20%2A%202%7D%20%7B100%7D%5C%5Cx%20%3D%201.7)
Thus, 1.7 meters of fabric were used to make curtains.
There are 0.3 meters of fabric left, of which half (50%) is used to make the strips that hold the curtain. That is to say:
![\frac {0.3} {2} = 0.15m](https://tex.z-dn.net/?f=%5Cfrac%20%7B0.3%7D%20%7B2%7D%20%3D%200.15m)
Thus, 0.15 meters of fabric remain.
![0.15 m * \frac {100 cm} {1 m} = 15\ centimeters.](https://tex.z-dn.net/?f=0.15%20m%20%2A%20%5Cfrac%20%7B100%20cm%7D%20%7B1%20m%7D%20%3D%2015%5C%20centimeters.)
Thus, 15 cm of fabric remain
Answer;
15 cm