Using the margin of error for the z-distribution, the sample sizes are given as follows:
a) 822.
b) 1068.
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:

The margin of error is given by:

In which:
is the sample proportion.
We have a 95% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
Item a:
The estimate is of
, hence we solve for n when M = 0.03.





n = 821.2
A sample of 822 is needed.
Item b:
No prior estimate, hence
.





n = 1067.11
A sample of 1068 is needed.
More can be learned about the z-distribution at brainly.com/question/25890103
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Answer:
b
Step-by-step explanation:
sin θ=√(1-cos²θ)=√(1-9/25)=√(16/25)=4/5
sin 2θ=2sin θ × cos θ=2×3/5×4/5=24/25
3/4*6 + 3/4*2x
18/4 + 6/4x
9/2 + 3/2x