Answer:
Step-by-step explanation:
Factorise the numerator and denominator
8a² - 2 ← factor out 2 from each term
= 2(4a² - 1) ← 4a² - 1 is a difference of squares
= 2(2a - 1)(2a + 1)
4a² + 4a + 1 ← is a perfect square
= (2a + 1)²
Thus
= ← cancel (2a + 1) on numerator/ denominator
=
=
The value of the P(A∩B) is equal to 0.04.
We have given that,
P(A)= 0.4 and P(B) = 0.85.
We have to determine the P(A and B)
<h3>What is the formula for Independent Events?</h3>For Independent Events,
P(A) × P(B) = P(A∩B)
so we have, P(A∩B) = 0.4×0.1
P(A∩B) = 0.04
P(A') = 1 - 0.4 = 0.6
This information can be represented on a Venn diagram as shown below
P(A'∪B) means the union of everything that is not A with everything that is B
P(A'∪B) = 0.06 + 0.54 + 0.04
P(A'∪B) = 0.64
To learn more about the events visit:
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Using the z-distribution, as we have the standard deviation for the population, it is found that the smallest sample size required to obtain the desired margin of error is of 77.
<h3>What is a z-distribution confidence interval?</h3>The confidence interval is:
In which:
The margin of error is given by:
In this problem, we have that the parameters are given as follows:
.
Hence, solving for n, we find the sample size.
Rounding up, the smallest sample size required to obtain the desired margin of error is of 77.
More can be learned about the z-distribution at brainly.com/question/25890103