In this problem p and q are symmetric matrices. for each statement below, either give a proof or a specific counterexample. a) if p ≥ 0 then p + q ≥ q. b) if p ≥ q then −p ≤ −q. c) if p > 0 then p −1 > 0. d) if p ≥ q > 0 then p −1 ≤ q−1 . e) if p ≥ q then p 2 ≥ q2 . hint: you might find it useful for part (d) to prove z ≥ i implies z −1 ≤ i.

The length of a shadow of the building is 36m. the length of the pole, which is perpendicular to the ground, is 1.9m. the length of the pole's shadow is 1.52m. what is the height of the building?

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).

Bo is buying a board game that usually costs bb dollars. the game is on sale, and the price has been reduced by 18\%18%. what could you find the answer?