Let f be a function of two variables that has continuous partial derivatives and consider the points A(3, 5), B(7, 5), C(3, 7), and D(11, 20). The directional derivative of f at A in the direction of the vector $\vec{AB}$ is 4 and the directional derivative at A in the direction of $\vec{AC}$ is 22. Find the directional derivative of f at A in the direction of the vector $\vec{AD}$. (Round the answer to two decimal places.)

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).