8 caps => 4 balls
6 caps => (6 x 4)/8 = 24/8 = 3 balls.
Seeing as you have not included the answer choices, I cannot give you the exact answer. However, I can tell you the pattern is that the number is the order that the letter comes in the alphabet. For example: C is the third letter, while H is the eighth.
Answer:288ft
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
20% * 40 = 20 / 100 * 40 = 800 / 100 = 8
1/4 * 40 = 40 / 4 = 10
So far we have use 8 + 10 = 18
There are 40 - 18 pages left
articles = 22
Answer:
![\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}](https://tex.z-dn.net/?f=%5Cdfrac%7B%28-5%293x%5E7%28yz%29%5E4%7D%7B%283%292x%5E2y%5E8z%5E2%7D%3D%5Cdfrac%7B-5x%5E5z%5E2%7D%7B2y%5E4%7D)
Step-by-step explanation:
Given:
The expression to simplify is given as:
![\frac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-5%293x%5E7%28yz%29%5E4%7D%7B%283%292x%5E2y%5E8z%5E2%7D)
In order to simplify this, we have to use the law of indices.
1. ![(ab)^m=a^mb^m](https://tex.z-dn.net/?f=%28ab%29%5Em%3Da%5Emb%5Em)
So, ![(yz)^4=y^4z^4](https://tex.z-dn.net/?f=%28yz%29%5E4%3Dy%5E4z%5E4)
Substitute this value in the above expression. This gives,
![=\dfrac{(-5)3x^7y^4z^4}{(3)2x^2y^8z^2}\\\\\\=\dfrac{-15x^7y^4z^4}{6x^2y^8z^2}......(-5\times 3=15\ and\ 3\times 2=6)](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%28-5%293x%5E7y%5E4z%5E4%7D%7B%283%292x%5E2y%5E8z%5E2%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B-15x%5E7y%5E4z%5E4%7D%7B6x%5E2y%5E8z%5E2%7D......%28-5%5Ctimes%203%3D15%5C%20and%5C%203%5Ctimes%202%3D6%29)
Now, we use another law of indices.
2. ![\frac{a^m}{a^n}=a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D)
So, ![\frac{x^7}{x^2}=x^{7-2}=x^5,\frac{y^4}{y^8}=y^{4-8}=y^{-4}, \frac{z^4}{z^2}=z^{4-2}=z^2](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E7%7D%7Bx%5E2%7D%3Dx%5E%7B7-2%7D%3Dx%5E5%2C%5Cfrac%7By%5E4%7D%7By%5E8%7D%3Dy%5E%7B4-8%7D%3Dy%5E%7B-4%7D%2C%20%5Cfrac%7Bz%5E4%7D%7Bz%5E2%7D%3Dz%5E%7B4-2%7D%3Dz%5E2)
Substitute these values in the above expression. This gives,
![=\frac{-15}{6}\times x^5\times y^{-4}\times z^2\\\\=\frac{-5x^5y^{-4}z^2}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-15%7D%7B6%7D%5Ctimes%20x%5E5%5Ctimes%20y%5E%7B-4%7D%5Ctimes%20z%5E2%5C%5C%5C%5C%3D%5Cfrac%7B-5x%5E5y%5E%7B-4%7Dz%5E2%7D%7B2%7D)
Finally, we further simplify it using the law ![a^{-m}=\frac{1}{a^m}](https://tex.z-dn.net/?f=a%5E%7B-m%7D%3D%5Cfrac%7B1%7D%7Ba%5Em%7D)
So, ![y^{-4}=\frac{1}{y^4}](https://tex.z-dn.net/?f=y%5E%7B-4%7D%3D%5Cfrac%7B1%7D%7By%5E4%7D)
Therefore, the given expression is simplified as:
![\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}](https://tex.z-dn.net/?f=%5Cdfrac%7B%28-5%293x%5E7%28yz%29%5E4%7D%7B%283%292x%5E2y%5E8z%5E2%7D%3D%5Cdfrac%7B-5x%5E5z%5E2%7D%7B2y%5E4%7D)