I think it’s the last one sorry if I’m wrong
Answer:
x 4
Step-by-step explanation:
Answer:
Using sum and product method you can simplify the top as:
x^2-4x-5 = (x-5)(x+1) and x^2-5x+4 = (x-4)(x-1)
The x-4 and the x+1 cancel each other out and you will be left with
(x-5)/(x-1)
Step-by-step explanation:
Answer:
0.0157
Step-by-step explanation:
From the information given:
The sample size = 70
The expected no. of days of year that are birthday of exactly 4 people is:![P = \bigg [ \dfrac{1}{365} \bigg]^4](https://tex.z-dn.net/?f=P%20%3D%20%5Cbigg%20%5B%20%5Cdfrac%7B1%7D%7B365%7D%20%5Cbigg%5D%5E4)
The expected number of days with 4 birthdays = 
![\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ ^{70}C_{4} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{70-4} \bigg]](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7B365%7D_%7Bi%3D1%7D%20%20E%28x_i%29%20%3D%20365%20%5Ctimes%20%5Cbigg%5B%20%20%5C%20%5E%7B70%7DC_%7B4%7D%20%5Ctimes%20%28%20%5Cdfrac%7B1%7D%7B365%7D%29%5E4%20%28%201%20-%20%5Cdfrac%7B1%7D%7B365%7D%29%5E%7B70-4%7D%20%5Cbigg%5D)
![\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ \dfrac{70!}{4!(70-4)!} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{66} \bigg]](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7B365%7D_%7Bi%3D1%7D%20%20E%28x_i%29%20%3D%20365%20%5Ctimes%20%5Cbigg%5B%20%20%5C%20%5Cdfrac%7B70%21%7D%7B4%21%2870-4%29%21%7D%20%5Ctimes%20%28%20%5Cdfrac%7B1%7D%7B365%7D%29%5E4%20%28%201%20-%20%5Cdfrac%7B1%7D%7B365%7D%29%5E%7B66%7D%20%5Cbigg%5D)
![\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ 916895 \times 5.6342 \times 10^{-11} \times 0.8343768898 \bigg]](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7B365%7D_%7Bi%3D1%7D%20%20E%28x_i%29%20%3D%20365%20%5Ctimes%20%5Cbigg%5B%20%20%5C%20916895%20%5Ctimes%205.6342%20%5Ctimes%2010%5E%7B-11%7D%20%5Ctimes%200.8343768898%20%5Cbigg%5D)
= 0.0157
Therefore, the required probability = 0.0157
Answer:
n>-5
Step-by-step explanation:
We have to distribute the -7 first, so:
-105<-7(5-2n) becomes:
-105<-35+14n
To find n, we have to add 35, so:
-105<-35+14n
+35 +35
We get 14n>-70. Now, we have to divide each side by 14 to find n.
14n/14>-70/14.
So, the solution becomes n>-5.
