Answer:
x=0
Step-by-step explanation:
0-0=0
Answer:
![(b)\ 2x - 9 = -1](https://tex.z-dn.net/?f=%28b%29%5C%202x%20-%209%20%3D%20-1)
![(c)\ -2x + 12 = 4](https://tex.z-dn.net/?f=%28c%29%5C%20-2x%20%2B%2012%20%3D%204)
![(e)\ 2(x - 10) = -12](https://tex.z-dn.net/?f=%28e%29%5C%202%28x%20-%2010%29%20%3D%20-12)
Step-by-step explanation:
Required
Which equals ![x = 4](https://tex.z-dn.net/?f=x%20%3D%204)
![(a)\ 2x + 6 = 2](https://tex.z-dn.net/?f=%28a%29%5C%202x%20%2B%206%20%3D%202)
Collect like terms
![2x = 2 - 6](https://tex.z-dn.net/?f=2x%20%20%3D%202%20-%206)
![2x = -4](https://tex.z-dn.net/?f=2x%20%20%3D%20-4)
Divide both sides by 2
![x = -2](https://tex.z-dn.net/?f=x%20%3D%20-2)
![(b)\ 2x - 9 = -1](https://tex.z-dn.net/?f=%28b%29%5C%202x%20-%209%20%3D%20-1)
Collect like terms
![2x = -1 + 9](https://tex.z-dn.net/?f=2x%20%3D%20-1%20%2B%209)
![2x = 8](https://tex.z-dn.net/?f=2x%20%3D%208)
Divide both sides by 2
![x = 4](https://tex.z-dn.net/?f=x%20%3D%204)
![(c)\ -2x + 12 = 4](https://tex.z-dn.net/?f=%28c%29%5C%20-2x%20%2B%2012%20%3D%204)
Collect like terms
![-2x =- 12 + 4](https://tex.z-dn.net/?f=-2x%20%3D-%2012%20%2B%204)
![-2x =-8](https://tex.z-dn.net/?f=-2x%20%3D-8)
Divide both sides by -2
![x = 4](https://tex.z-dn.net/?f=x%20%3D%204)
![(d)\ 2(x + 2) = 10](https://tex.z-dn.net/?f=%28d%29%5C%202%28x%20%2B%202%29%20%3D%2010)
Divide both sides by 2
![x + 2 =5](https://tex.z-dn.net/?f=x%20%2B%202%20%3D5)
Collect like terms
![x = 5-2](https://tex.z-dn.net/?f=x%20%3D%205-2)
![x = 3](https://tex.z-dn.net/?f=x%20%3D%203)
![(e)\ 2(x - 10) = -12](https://tex.z-dn.net/?f=%28e%29%5C%202%28x%20-%2010%29%20%3D%20-12)
Divide both sides by 2
![x - 10 = -6](https://tex.z-dn.net/?f=x%20-%2010%20%3D%20-6)
Collect like terms
![x = 10 - 6](https://tex.z-dn.net/?f=x%20%3D%2010%20-%206)
![x = 4](https://tex.z-dn.net/?f=x%20%3D%204)
Hence, the equations with the required solution are:
![(b)\ 2x - 9 = -1](https://tex.z-dn.net/?f=%28b%29%5C%202x%20-%209%20%3D%20-1)
![(c)\ -2x + 12 = 4](https://tex.z-dn.net/?f=%28c%29%5C%20-2x%20%2B%2012%20%3D%204)
![(e)\ 2(x - 10) = -12](https://tex.z-dn.net/?f=%28e%29%5C%202%28x%20-%2010%29%20%3D%20-12)
Answer: a) ![\dfrac{3}{874}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B874%7D)
b) ![\dfrac{30}{3059}](https://tex.z-dn.net/?f=%5Cdfrac%7B30%7D%7B3059%7D)
c) ![\dfrac{3575}{12236}](https://tex.z-dn.net/?f=%5Cdfrac%7B3575%7D%7B12236%7D)
Step-by-step explanation:
Given : Number of students : 11
Number of faculty members : 13
Total persons : ![11+13=24](https://tex.z-dn.net/?f=11%2B13%3D24)
Total number of ways to structure a jury of six people from a group of 24 people :-
![^{24}C_{6}=\dfrac{24!}{6!(24-6)!}=134596](https://tex.z-dn.net/?f=%5E%7B24%7DC_%7B6%7D%3D%5Cdfrac%7B24%21%7D%7B6%21%2824-6%29%21%7D%3D134596)
a) Number of ways of selecting a jury of all students :-
![^{11}C_{6}=\dfrac{11!}{6!(11-6)!}=462](https://tex.z-dn.net/?f=%5E%7B11%7DC_%7B6%7D%3D%5Cdfrac%7B11%21%7D%7B6%21%2811-6%29%21%7D%3D462)
Then , the probability of selecting a jury of all students :-
![\dfrac{462}{134596}=\dfrac{3}{874}](https://tex.z-dn.net/?f=%5Cdfrac%7B462%7D%7B134596%7D%3D%5Cdfrac%7B3%7D%7B874%7D)
b) Number of ways of selecting a jury of all faculty :-
![^{13}C_{6}=\dfrac{13!}{6!(13-6)!}=462](https://tex.z-dn.net/?f=%5E%7B13%7DC_%7B6%7D%3D%5Cdfrac%7B13%21%7D%7B6%21%2813-6%29%21%7D%3D462)
Then , the probability of selecting a jury of all students :-
![\dfrac{1716}{134596}=\dfrac{30}{3059}](https://tex.z-dn.net/?f=%5Cdfrac%7B1716%7D%7B134596%7D%3D%5Cdfrac%7B30%7D%7B3059%7D)
c) Number of ways of selecting a jury of two students and four faculty :-
![^{11}C_{2}\times^{13}C_{4}=\dfrac{11!}{2!(11-2)!}\times\dfrac{13!}{4!(13-4)!}=39325](https://tex.z-dn.net/?f=%5E%7B11%7DC_%7B2%7D%5Ctimes%5E%7B13%7DC_%7B4%7D%3D%5Cdfrac%7B11%21%7D%7B2%21%2811-2%29%21%7D%5Ctimes%5Cdfrac%7B13%21%7D%7B4%21%2813-4%29%21%7D%3D39325)
Then , the probability of selecting a jury of all students :-
![\dfrac{39325}{134596}=\dfrac{3575}{12236}](https://tex.z-dn.net/?f=%5Cdfrac%7B39325%7D%7B134596%7D%3D%5Cdfrac%7B3575%7D%7B12236%7D)