The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 27 minutes, what is the probability that X is less than 32 minutes?

Find the image of a(4, -2) after it is reflected over the line y= 2, then reflected over the line x = 2. (-8,6) o (0.-2) o (0,6) (-8, -2)

If the dimensions of a rectangular prism are 5 ft x 3.5 ft x 2 ſt, what is the surface area?

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).