To solve this problem, we make use of the z statistic.
The formula for the confidence interval can be calculated using the formula:
Confidence Interval = p ± MOE
where,
p is the portion of girls = 278 / 556 = 0.5
MOE is the margin of error
We calculate the margin of error using the formula:
MOE = z * sqrt[p (1 – p) / n]
From the standard distribution tables, the value of z at 99% confidence is:
z = 2.58
Therefore the MOE is:
MOE = 2.58 * sqrt[0.5 (0.5) / 556]
MOE = 0.055
Therefore the confidence interval is:
Confidence Interval = 0.5 ± 0.055
Confidence Interval = 0.445, 0.555
0.445<p<0.555
For this case, what you should keep in mind are the following considerations:
1) Rewrite the expressions correctly using the properties of the exponents: Addition, multiplication, division, subtraction and negative exponents.
2) Simplify the expression as much as possible.
Answer:
See attached image.
Answer for the first one - it's complicated, but that maths is correct
I kind of cheated and did it a different way than they'd expect. By doing 24 squared, that gives you 576.
since both angles are 45 degrees, then the sides are equal lengths. Therefore x squared times 2 = 576.
Because of this, x squared = 576 divided by 2, which equals 288.
Therefore the square root of 288 = 12 square root 2