Answer:
option A
![\frac{(x+2)(x+5)}{x^{3}-9x }](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B2%29%28x%2B5%29%7D%7Bx%5E%7B3%7D-9x%20%7D)
Step-by-step explanation:
Take LCM
![\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x^{2}-9)}+\frac{x+1}{(x+3)(x-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B5%7D%7Bx%28x-3%29%7D-%5Cfrac%7B3x%2B5%7D%7Bx%28x%5E%7B2%7D-9%29%7D%2B%5Cfrac%7Bx%2B1%7D%7B%28x%2B3%29%28x-3%29%7D)
![\frac{2x+5}{x(x-3)}-\frac{3x+5}{x((x+3)(x-3))}+\frac{x+1}{(x+3)(x-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B5%7D%7Bx%28x-3%29%7D-%5Cfrac%7B3x%2B5%7D%7Bx%28%28x%2B3%29%28x-3%29%29%7D%2B%5Cfrac%7Bx%2B1%7D%7B%28x%2B3%29%28x-3%29%7D)
![\frac{(2x+5)(x+3)}{x(x+3)(x-3)}-\frac{3x+5}{x((x+3)(x-3))}+\frac{(x+1)(x)}{x(x+3)(x-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B%282x%2B5%29%28x%2B3%29%7D%7Bx%28x%2B3%29%28x-3%29%7D-%5Cfrac%7B3x%2B5%7D%7Bx%28%28x%2B3%29%28x-3%29%29%7D%2B%5Cfrac%7B%28x%2B1%29%28x%29%7D%7Bx%28x%2B3%29%28x-3%29%7D)
Now the Denominator is same we can add the numerator
![\frac{(2x^{2}+11x+15)}{x(x+3)(x-3)}-\frac{3x+5}{x((x+3)(x-3))}+\frac{(x^{2}+x)}{x(x+3)(x-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B%282x%5E%7B2%7D%2B11x%2B15%29%7D%7Bx%28x%2B3%29%28x-3%29%7D-%5Cfrac%7B3x%2B5%7D%7Bx%28%28x%2B3%29%28x-3%29%29%7D%2B%5Cfrac%7B%28x%5E%7B2%7D%2Bx%29%7D%7Bx%28x%2B3%29%28x-3%29%7D)
![\frac{2x^{2}-x^{2}+11x-3x-x+15-5}{x(x+3)(x-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E%7B2%7D-x%5E%7B2%7D%2B11x-3x-x%2B15-5%7D%7Bx%28x%2B3%29%28x-3%29%7D)
![\frac{x^{2}+7x+10}{x(x+3)(x-3)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%2B7x%2B10%7D%7Bx%28x%2B3%29%28x-3%29%7D)
![\frac{(x+2)(x+5)}{x(x+3)(x-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B2%29%28x%2B5%29%7D%7Bx%28x%2B3%29%28x-3%29%7D)
![\frac{(x+2)(x+5)}{x^{3}-9x}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B2%29%28x%2B5%29%7D%7Bx%5E%7B3%7D-9x%7D)
Answer:
-4
Step-by-step explanation:
H(x) would be (x - 3)(x + 10)
= x^2 + 7x - 30
About 750 different permutations
Answer:
0.2264
0.1795
0.2264
Step-by-step explanation:
Given that:
p = 19% = 0.19
Sample size (n) = 12
Using binomial distribution formula :
p(x = x) = nCx * p^x * (1 - p)^(n-x)
1 - p = 1 - 0.19 = 0.81
Exactly 3:
p(x = 3) = 12C3 * 0.19^3 * 0.81^9
p(x = 3) = 220 * 0.001029499103502116970939
= 0.2264
B.) Atleast 4 :
P( x ≥ 4) = p(4) + p(5) + p(6) + p(7) + p(8) + p(9) + p(10) + p(11) + p(12)
To save time, we can use a binomial probability calculator :
P( x ≥ 4) = 0.1795
C.) Less than 8:
P( x < 8) = p(7) + p(6) + p(5) + p(4) + p(3) + p(2) + p(1) + p(0)
P(x < 8) = 0.9995