Describe the transformation of f(x) = x² represented by g(x) = (x + 4)2 - 1. Transformation(s):

Vertex of F:
Vertex of g:

Notice that the function is of the form g(x) = a(x-h)+ k. Rewrite g(x) to identify h and k.

Describe in detail how you would construct a 95% confidence interval for a set of 30 data points whose mean is 20 and population standard deviation is 3. be sure to show that you know the formula and how to plug into it. also, clearly state the margin of error.

This is so hard and it’s for a test

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e. g. 98.76543).