Answer:
![\frac{(2+5x)(2-5x)}{2x(5x-6)}](https://tex.z-dn.net/?f=%5Cfrac%7B%282%2B5x%29%282-5x%29%7D%7B2x%285x-6%29%7D)
Step-by-step explanation:
Simplify the numerator:
Rewrite 4 as ![2^{2}](https://tex.z-dn.net/?f=2%5E%7B2%7D)
![\frac{2^{2}-25x^{2} }{10x^{2}-11x-x }](https://tex.z-dn.net/?f=%5Cfrac%7B2%5E%7B2%7D-25x%5E%7B2%7D%20%20%7D%7B10x%5E%7B2%7D-11x-x%20%7D)
Rewrite
as ![(5x)^{2}](https://tex.z-dn.net/?f=%285x%29%5E%7B2%7D)
![\frac{2^{2}-(5x)^{2} }{10x^{2} -11x-x}](https://tex.z-dn.net/?f=%5Cfrac%7B2%5E%7B2%7D-%285x%29%5E%7B2%7D%20%20%7D%7B10x%5E%7B2%7D%20-11x-x%7D)
Since both terms are perfect squares, factor using the difference of squares formula,
and b = 5x.
![\frac{(2+5x)(2-(5x))}{10x^{2}-11x-x }](https://tex.z-dn.net/?f=%5Cfrac%7B%282%2B5x%29%282-%285x%29%29%7D%7B10x%5E%7B2%7D-11x-x%20%7D)
Multiply 5 by -1.
![\frac{(2+5x)(2-5x)}{10x^{2}-11x-x }](https://tex.z-dn.net/?f=%5Cfrac%7B%282%2B5x%29%282-5x%29%7D%7B10x%5E%7B2%7D-11x-x%20%7D)
Simplify the denominator:
Subtract x from -11x
![\frac{(2+5x)(2-5x)}{10x^{2}-12x }](https://tex.z-dn.net/?f=%5Cfrac%7B%282%2B5x%29%282-5x%29%7D%7B10x%5E%7B2%7D-12x%20%7D)
Factor 2x out of ![10x^{2} -12x](https://tex.z-dn.net/?f=10x%5E%7B2%7D%20-12x)
![\frac{(2+5x)(2-5x)}{2x(5x-6)}](https://tex.z-dn.net/?f=%5Cfrac%7B%282%2B5x%29%282-5x%29%7D%7B2x%285x-6%29%7D)
Answer:
6.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
We would apply the formula for binomial distribution which is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = (1 - r) represents the probability of failure.
n represents the number of trials or sample.
From the information given,
p = 18% = 18/100 = 0.18
q = 1 - p = 1 - 0.18
q = 0.82
n = 5
Therefore,
P(x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x = 0) = 5C0 × 0.18^0 × 0.82^(5 - 0)
P(x = 0) = 0.37
P(x = 1) = 5C1 × 0.18^1 × 0.82^(5 - 1)
P(x = 1) = 0.41
P(x = 2) = 5C2 × 0.18^2 × 0.82^(5 - 2)
P(x = 2) = 0.18
Therefore,
P(x ≤ 2) = 0.37 + 0.41 + 0.18 = 0.96