Answer:
The number of words that can be formed from the word "LITERATURE" is 453600
Step-by-step explanation:
Given
Word: LITERATURE
Required: Number of 10 letter word that can be formed
The number of letters in the word "LITERATURE" is 10
But some letters are repeated; These letters are T, E and R.
Each of the letters are repeated twice (2 times)
i.e.
Number of T = 2
Number of E = 2
Number of R = 2
To calculate the number of words that can be formed, the total number of possible arrangements will be divided by arrangement of each repeated character. This is done as follows;
Number of words that can be formed = ![\frac{10!}{2!2!2!}](https://tex.z-dn.net/?f=%5Cfrac%7B10%21%7D%7B2%212%212%21%7D)
Number of words = ![\frac{10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1}{2 * 1 * 2 * 1 * 2 * 1}](https://tex.z-dn.net/?f=%5Cfrac%7B10%20%2A%209%20%2A%208%20%2A%207%20%2A%206%20%2A%205%20%2A%204%20%2A%203%20%2A%202%20%2A%201%7D%7B2%20%2A%201%20%2A%202%20%2A%201%20%2A%202%20%2A%201%7D)
Number of words = ![\frac{3628800}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B3628800%7D%7B8%7D)
Number of words = 453600
Hence, the number of words that can be formed from the word "LITERATURE" is 453600
Answer:
The degree of the given expression is 2
- the type of pair is vertical angle.
- to find x:
-- vertical angles are equal.
4x + 10 = 5x - 1
10 = x - 1
x = 11
Answer:
![x=12\\y=\frac{13}{3}](https://tex.z-dn.net/?f=x%3D12%5C%5Cy%3D%5Cfrac%7B13%7D%7B3%7D)
Step-by-step explanation:
For it to be a parallelogram, opposite sides have to be of same length.
Using the expressions given, we can make 2 equations:
<u>Equation 1:</u>
![OL=NM\\3y-6=x-5\\-x+3y=1](https://tex.z-dn.net/?f=OL%3DNM%5C%5C3y-6%3Dx-5%5C%5C-x%2B3y%3D1)
<u>Equation 2:</u>
![ON=LM\\8x-8=7x+4\\](https://tex.z-dn.net/?f=ON%3DLM%5C%5C8x-8%3D7x%2B4%5C%5C)
<em>Solving equation 2, we have x:</em>
![8x-8=7x+4\\8x-7x=4+8\\x=12](https://tex.z-dn.net/?f=8x-8%3D7x%2B4%5C%5C8x-7x%3D4%2B8%5C%5Cx%3D12)
<em>Plugging this value of x into equation 1, we can solve for y:</em>
![-x+3y=1\\-(12)+3y=1\\-12+3y=1\\3y=13\\y=\frac{13}{3}](https://tex.z-dn.net/?f=-x%2B3y%3D1%5C%5C-%2812%29%2B3y%3D1%5C%5C-12%2B3y%3D1%5C%5C3y%3D13%5C%5Cy%3D%5Cfrac%7B13%7D%7B3%7D)
So,
![x=12\\y=\frac{13}{3}](https://tex.z-dn.net/?f=x%3D12%5C%5Cy%3D%5Cfrac%7B13%7D%7B3%7D)
Answer:
A=13684.7776
Step-by-step explanation:
![= 4\pi {r}^{2}](https://tex.z-dn.net/?f=%20%20%3D%204%5Cpi%20%7Br%7D%5E%7B2%7D%20)
![4\pi {33 }^{2} = 13684.7776](https://tex.z-dn.net/?f=4%5Cpi%20%7B33%20%7D%5E%7B2%7D%20%20%3D%2013684.7776)