Answer:
And rounded up we have that n=99
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by
and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that
and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We assume the value for
since we don't have previous info. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=99
Answer:

Step-by-step explanation:
Notice that you are given an isosceles right-angle triangle to solve, since each of its two acute angles measures
. Then such means that the sides opposite to these acute angles (the so called "legs" of this right angle triangle) must also be of the same length (x).
We can then use the Pythagorean theorem that relates the square of the hypotenuse to the addition of the squares of the triangles legs:

We use just the positive root, since we are looking for an actual length. then, the requested side is:

Multiply 65 and .4 which will give you the answer of 26.
Answer: 80%
Step-by-step explanation:
40/50 = 80/100 = .8 then move decimal over 2 places to the right for percent. .8 to 8.0 to 80.0