Rewrite 1/2^-4 using a positive exponent and evaluate the result.​

What is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4

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).

Find the length of the normal and the angle it makes with the positive x-axis. (see pictured below)