What do you assume in a direct proof?

G(x) = 2 sin(2x - π) + 4. using complete sentences, explain how to find the minimum value for the function.

This stem-and-leaf plot represents the heights of the students on ralph's basketball team. one student's height is missing from the plot. if the mean height of all the students on the team is 61 inches, what is the missing height? a. 55 in. b. 59 in. c. 61 in. d. 65 in.

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).