Answer:
n=97
Step-by-step explanation:
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".
Assuming the X follows a normal distribution

We know that the margin of error for a confidence interval is given by:
(1)
The next step would be find the value of
,
and 
Using the normal standard table, excel or a calculator we see that:

If we solve for n from formula (1) we got:


And we have everything to replace into the formula:

And if we round up the answer we see that the value of n to ensure the margin of error required
is n=97.
Answer:
77
Step-by-step explanation:
Let's let the unknown number be x.
Supplementary angles add up to a total of 180 degrees. Since we already know one angle is 103, this means that:

Subtract 103 from both sides:

So, the measure of its supplementary angle is 77 degrees.
And we are done!
Step-by-step explanation:
Geometric mean

sine and cosecant.
you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate