Answer:
<em><u>30 girls in the class</u></em>
Step-by-step explanation:
12 = 40%
12/40 = 1%
.3 = 1%
.3 * 100 = 100%
30 = 100%
30!
I hope this helps you
12(a-4)=12a-12.4=12a-48
Can you post a picture so I can help you
Step (1)
We know that the sum of all the terms in an infinite geometric sequence finding from following equation whenever |q| < 1 .
q = magnitude
![s( \infty ) = \frac{t(1)}{1 - q} \\](https://tex.z-dn.net/?f=s%28%20%5Cinfty%20%29%20%3D%20%20%5Cfrac%7Bt%281%29%7D%7B1%20-%20q%7D%20%5C%5C%20%20)
So :
![s( \infty ) = \frac{t(1)}{1 - q} \\](https://tex.z-dn.net/?f=s%28%20%5Cinfty%20%29%20%3D%20%20%5Cfrac%7Bt%281%29%7D%7B1%20-%20q%7D%20%5C%5C%20%20)
![81 = \frac{t(1)}{1 - q} \\](https://tex.z-dn.net/?f=81%20%3D%20%20%5Cfrac%7Bt%281%29%7D%7B1%20-%20q%7D%20%20%5C%5C%20)
![81(1 - q) = t(1)](https://tex.z-dn.net/?f=81%281%20-%20q%29%20%3D%20t%281%29)
Remember it I'll use it again.
_________________________________
Step (2)
We know that the sum of the n first terms of a geometric sequence finding from following equation.
![s(n) = \frac{t(1) \times (1 - {q})^{n} }{1 - q} \\](https://tex.z-dn.net/?f=s%28n%29%20%3D%20%20%5Cfrac%7Bt%281%29%20%5Ctimes%20%281%20-%20%20%7Bq%7D%29%5E%7Bn%7D%20%7D%7B1%20-%20q%7D%20%20%5C%5C%20)
_________________________________
Sum of all terms starting from the third is 9.
So :
![s(2) + s(3 - \infty ) = 81](https://tex.z-dn.net/?f=s%282%29%20%2B%20s%283%20-%20%20%5Cinfty%20%29%20%3D%2081)
![s(2) + 9 = 81](https://tex.z-dn.net/?f=s%282%29%20%2B%209%20%3D%2081)
Sides minus 9
![s(2) = 81 - 9](https://tex.z-dn.net/?f=s%282%29%20%3D%2081%20-%209)
![s(2) = 72](https://tex.z-dn.net/?f=s%282%29%20%3D%2072)
So :
![t(1) + t(2) = 72](https://tex.z-dn.net/?f=t%281%29%20%20%2B%20t%282%29%20%3D%2072)
![t(1) + t(1) \times q = 72](https://tex.z-dn.net/?f=t%281%29%20%2B%20t%281%29%20%5Ctimes%20q%20%3D%2072)
Factoring t(1)
![t(1) \times (1 + q) = 72](https://tex.z-dn.net/?f=t%281%29%20%5Ctimes%20%281%20%2B%20q%29%20%3D%2072)
We have found t(1) = 81 ( 1 - q ) in step (1).
So :
![81(1 - q)(1 + q) = 72](https://tex.z-dn.net/?f=81%281%20-%20q%29%281%20%2B%20q%29%20%3D%2072)
Divided sides by 81
![(1 - q)(1 + q) = \frac{72}{81} \\](https://tex.z-dn.net/?f=%281%20-%20q%29%281%20%2B%20q%29%20%3D%20%20%5Cfrac%7B72%7D%7B81%7D%20%20%5C%5C%20)
![(1 - q)( 1 + q) = \frac{8}{9} \\](https://tex.z-dn.net/?f=%281%20-%20q%29%28%201%20%2B%20q%29%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20%5C%5C%20%20)
![1 - {q}^{2} = \frac{8}{9} \\](https://tex.z-dn.net/?f=1%20-%20%20%7Bq%7D%5E%7B2%7D%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20%5C%5C%20%20%20)
Subtract sides minus -1
![- {q}^{2} = \frac{8}{9} - 1 \\](https://tex.z-dn.net/?f=%20-%20%20%7Bq%7D%5E%7B2%7D%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20-%201%20%5C%5C%20%20%20)
![- {q}^{2} = \frac{8}{9} - \frac{9}{9} \\](https://tex.z-dn.net/?f=%20-%20%20%7Bq%7D%5E%7B2%7D%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20-%20%20%5Cfrac%7B9%7D%7B9%7D%20%5C%5C%20%20%20%20)
![- {q}^{2} = - \frac{1}{9} \\](https://tex.z-dn.net/?f=%20-%20%20%7Bq%7D%5E%7B2%7D%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%5C%5C%20%20%20)
Negatives simplifies
![{q}^{2} = \frac{1}{9} \\](https://tex.z-dn.net/?f=%20%7Bq%7D%5E%7B2%7D%20%3D%20%20%5Cfrac%7B1%7D%7B9%7D%20%5C%5C%20%20%20)
Radical sides
![q = + \frac{1}{3} \\ q = - \frac{1}{3}](https://tex.z-dn.net/?f=q%20%3D%20%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%20q%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20)
_________________________________
Step (4)
If q = 1/3 :
![81(1 - q) = t(1)](https://tex.z-dn.net/?f=81%281%20-%20q%29%20%3D%20t%281%29)
![81(1 - \frac{1}{3}) = t(1) \\](https://tex.z-dn.net/?f=81%281%20-%20%20%5Cfrac%7B1%7D%7B3%7D%29%20%3D%20t%281%29%20%5C%5C%20%20)
![81( \frac{2}{3}) = t(1) \\](https://tex.z-dn.net/?f=81%28%20%5Cfrac%7B2%7D%7B3%7D%29%20%3D%20t%281%29%20%5C%5C%20%20)
![t(1) = 27 \times 2](https://tex.z-dn.net/?f=t%281%29%20%3D%2027%20%5Ctimes%202)
![t(1) = 54](https://tex.z-dn.net/?f=t%281%29%20%3D%2054)
So :
![t(2) = t(1) \times q](https://tex.z-dn.net/?f=t%282%29%20%3D%20t%281%29%20%5Ctimes%20q)
![t(2) = 54 \times \frac{1}{3} \\](https://tex.z-dn.net/?f=t%282%29%20%3D%2054%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%20%20)
![t(2) = 18](https://tex.z-dn.net/?f=t%282%29%20%3D%2018)
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
If q = - 1/3 :
![81(1 - q) = t(1)](https://tex.z-dn.net/?f=81%281%20-%20q%29%20%3D%20t%281%29)
![81(1 - ( - \frac{1}{3})) = t(1) \\](https://tex.z-dn.net/?f=81%281%20-%20%28%20-%20%20%5Cfrac%7B1%7D%7B3%7D%29%29%20%3D%20t%281%29%20%5C%5C%20%20)
![81(1 + \frac{1}{3}) = t(1) \\](https://tex.z-dn.net/?f=81%281%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%29%20%3D%20t%281%29%20%5C%5C%20)
![81( \frac{4}{3}) = t(1) \\](https://tex.z-dn.net/?f=81%28%20%5Cfrac%7B4%7D%7B3%7D%29%20%3D%20t%281%29%20%5C%5C%20%20)
![t(1) = 27 \times 4](https://tex.z-dn.net/?f=t%281%29%20%3D%2027%20%5Ctimes%204)
![t(1) = 108](https://tex.z-dn.net/?f=t%281%29%20%3D%20108)
So :
![t(2) = t(1) \times q](https://tex.z-dn.net/?f=t%282%29%20%3D%20t%281%29%20%5Ctimes%20q)
![t(2) = 108 \times - \frac{1}{3} \\](https://tex.z-dn.net/?f=t%282%29%20%3D%20108%20%5Ctimes%20%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%20%20)
![t(2) = - 36](https://tex.z-dn.net/?f=t%282%29%20%3D%20%20-%2036)
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️