In 1876, Édouard Lucas proved, without the aid of a computer, that 2127 − 1 is a Mersenne prime. Use Euclid's procedure to write the perfect number associated with this prime. (Write your answer using exponents with a base of 2.)

The fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. round the answers to 4 decimal places. less-than-or-equal-to p less-than-or-equal-to (b) calculate a 95% upper confidence bound on the fraction of defective circuits. round the answer to 4 decimal places. p less-than-or-equal-to