Find an x such that x^443 =5 (mod 12) t 2. let a be an integer not divisible by some prime p, and let n be the smallest positive (nonzero) integer such that a" p- 1 1 (mod p) for some n. show that n divides integer hint; dividep-1 by n and write p - 1 as a quotient and a remainder.

Use the net as an aid to compute the surface area of the triangular prism. a) 550 m2 b) 614 m2 c) 670 m2 d) 790 m2

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)

Officer brimberry wrote 32 tickets for traffic violations last week, but only 4 tickets this week. what is the percent decrease? give your answer to the nearest tenth of a percent.