1. 6.25 x 10^0
2. 8.07 x 10^-1
Answer:RPS is 90 degrees...
I hope this helps you
a1=2
a2= -4
a3= -4-6= -10
a4= -10-6= -16
a5= -16-6= -22
a6= -22-6= -28
Answer:
Step-by-step explanation:
From the given information:
There are 30 collections of gems, of which 8 are worthless;
Thus, the number of the genuine diamonds = 30 - 8 = 22.
Let X = random variable;
X consider the value as 0 (for 2 worthless stone selection),
X = 1200(1 worthless stone & 1 genuine stone)
X = 2400 (2 genuine stones selected)
However, the numbers of ways of selecting and chosen Gems can be estimated as:
![(^n_r) = (^{30}_2) \\ \\ \implies \dfrac{30!}{2!(30-2)!} \\ \\ \implies \dfrac{30!}{2!(28)!} \\ \\ \implies \dfrac{30*29*28!}{2!(28)!} \\ \\ \implies \dfrac{30*29}{2*1} \\ \\ \implies 435](https://tex.z-dn.net/?f=%28%5En_r%29%20%3D%20%28%5E%7B30%7D_2%29%20%5C%5C%20%5C%5C%20%5Cimplies%20%5Cdfrac%7B30%21%7D%7B2%21%2830-2%29%21%7D%20%5C%5C%20%5C%5C%20%5Cimplies%20%5Cdfrac%7B30%21%7D%7B2%21%2828%29%21%7D%20%20%5C%5C%20%5C%5C%20%20%5Cimplies%20%5Cdfrac%7B30%2A29%2A28%21%7D%7B2%21%2828%29%21%7D%20%5C%5C%20%5C%5C%20%20%5Cimplies%20%20%5Cdfrac%7B30%2A29%7D%7B2%2A1%7D%20%5C%5C%20%5C%5C%20%5Cimplies%20435)
Thus;
![Pr (X = 0) = \dfrac{(^8_2)}{435}](https://tex.z-dn.net/?f=Pr%20%28X%20%3D%200%29%20%3D%20%5Cdfrac%7B%28%5E8_2%29%7D%7B435%7D)
![Pr (X = 0) = \dfrac{\dfrac{8!}{2!(8-2)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7*6!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7}{2*1}}{435} \\ \\ Pr (X = 0) = 0.0644](https://tex.z-dn.net/?f=Pr%20%28X%20%3D%200%29%20%3D%20%5Cdfrac%7B%5Cdfrac%7B8%21%7D%7B2%21%288-2%29%21%7D%7D%7B435%7D%20%5C%5C%20%5C%5C%20Pr%20%28X%20%3D%200%29%20%3D%20%5Cdfrac%7B%5Cdfrac%7B8%21%7D%7B2%21%286%29%21%7D%7D%7B435%7D%20%20%5C%5C%20%5C%5C%20Pr%20%28X%20%3D%200%29%20%3D%20%5Cdfrac%7B%5Cdfrac%7B8%2A7%2A6%21%7D%7B2%21%286%29%21%7D%7D%7B435%7D%20%5C%5C%20%5C%5C%20%20Pr%20%28X%20%3D%200%29%20%3D%20%5Cdfrac%7B%5Cdfrac%7B8%2A7%7D%7B2%2A1%7D%7D%7B435%7D%20%5C%5C%20%5C%5C%20%20%20Pr%20%28X%20%3D%200%29%20%3D%200.0644)
![P(X =1200) = \dfrac{(^{8}_{1})(^{22}_{1})}{435}](https://tex.z-dn.net/?f=P%28X%20%3D1200%29%20%3D%20%5Cdfrac%7B%28%5E%7B8%7D_%7B1%7D%29%28%5E%7B22%7D_%7B1%7D%29%7D%7B435%7D)
![P(X =1200) = \dfrac{ \dfrac{8!}{1!(8-1)!}) ( \dfrac{22!}{1!(22-1)!}) }{435}](https://tex.z-dn.net/?f=P%28X%20%3D1200%29%20%3D%20%5Cdfrac%7B%20%5Cdfrac%7B8%21%7D%7B1%21%288-1%29%21%7D%29%20%28%20%5Cdfrac%7B22%21%7D%7B1%21%2822-1%29%21%7D%29%20%7D%7B435%7D)
![P(X =1200) = \dfrac{ (8) ( 22) }{435}](https://tex.z-dn.net/?f=P%28X%20%3D1200%29%20%3D%20%5Cdfrac%7B%20%288%29%20%28%2022%29%20%7D%7B435%7D)
![P(X =1200) =0.4046](https://tex.z-dn.net/?f=P%28X%20%3D1200%29%20%3D0.4046)
![Pr (X = 2400) = \dfrac{(^{22}_2)}{435}](https://tex.z-dn.net/?f=Pr%20%28X%20%3D%202400%29%20%3D%20%5Cdfrac%7B%28%5E%7B22%7D_2%29%7D%7B435%7D)
![Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(22-2)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(20)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22*21*20!}{2!(20)!}}{435} \\ \\ Pr (X =2400) = \dfrac{\dfrac{22*21}{2*1}}{435} \\ \\ Pr (X = 2400) = 0.5310](https://tex.z-dn.net/?f=Pr%20%28X%20%3D%202400%29%20%3D%20%5Cdfrac%7B%5Cdfrac%7B22%21%7D%7B2%21%2822-2%29%21%7D%7D%7B435%7D%20%5C%5C%20%5C%5C%20Pr%20%28X%20%3D%202400%29%20%3D%20%5Cdfrac%7B%5Cdfrac%7B22%21%7D%7B2%21%2820%29%21%7D%7D%7B435%7D%20%20%5C%5C%20%5C%5C%20Pr%20%28X%20%3D%202400%29%20%3D%20%5Cdfrac%7B%5Cdfrac%7B22%2A21%2A20%21%7D%7B2%21%2820%29%21%7D%7D%7B435%7D%20%5C%5C%20%5C%5C%20%20Pr%20%28X%20%3D2400%29%20%3D%20%5Cdfrac%7B%5Cdfrac%7B22%2A21%7D%7B2%2A1%7D%7D%7B435%7D%20%5C%5C%20%5C%5C%20%20%20Pr%20%28X%20%3D%202400%29%20%3D%200.5310)
To find E(X):
E(X) = (0 × 0.0644) + (1200 × 0.4046) + (2400 × 0.5310)
E(X) = 0 + 485.52 + 1274.4
E(X) = 1759.92