Answer:
Step-by-step explanation:
![cos \theta=2 \\impossible~as~|cos~\theta|\leq 1\\no~solution.](https://tex.z-dn.net/?f=cos%20%5Ctheta%3D2%20%5C%5Cimpossible~as~%7Ccos~%5Ctheta%7C%5Cleq%201%5C%5Cno~solution.)
Answer:
umm people cry for a reason so it thy
Step-by-step explanation:
diadem is first
Answer:
Part 1: There are 4.7*10^21 ways to select 40 volunteers in subgroups of 10
Part 2: The research board can be chosen in 32760 ways
Step-by-step explanation:
Part 1:
The number of ways in which we can organized n elements into k groups with size n1, n2,...nk is calculate as:
![\frac{ n!}{ n1!*n2!*...*nk! }](https://tex.z-dn.net/?f=%5Cfrac%7B%20n%21%7D%7B%20n1%21%2An2%21%2A...%2Ank%21%20%7D)
So, in this case we can form 4 subgroups with 10 participants each one, replacing the values of:
- n by 40 participants
- k by 4 groups
- n1, n2, n3 and n4 by 10 participants of every subgroups
We get:
![\frac{ 40!}{10!*10!*10!*10!} = 4.7*10^{21}](https://tex.z-dn.net/?f=%5Cfrac%7B%2040%21%7D%7B10%21%2A10%21%2A10%21%2A10%21%7D%20%3D%204.7%2A10%5E%7B21%7D)
Part 2:
The number of ways in which we can choose k element for a group of n elements and the order in which they are chose matters is calculate with permutation as:
![nPk = \frac{ n!}{(n-k)!}](https://tex.z-dn.net/?f=nPk%20%3D%20%5Cfrac%7B%20n%21%7D%7B%28n-k%29%21%7D)
So in this case there are 4 offices in the research board, those are director, assistant director, quality control analyst and correspondent. Additionally this 4 offices are going to choose from a group of 5 doctors.
Therefore, replacing values of:
- n by 15 doctors
- k by 4 offices
We get:
![\frac{ 15!}{ (15-4)! } = 32760](https://tex.z-dn.net/?f=%5Cfrac%7B%2015%21%7D%7B%20%2815-4%29%21%20%7D%20%3D%2032760)
Answer:
y=-5/4x+4
Step-by-step explanation:
as long as the slope is the same and you have a different starting point the lines will be parallel.