B. Prove: For all integers n > 1, if n is not prime, then there exists a prime number p such that p ≤√n and n is divisible by p.(Hints: Use the result of part (a) and Theorems 4.3.1, 4.3.3, and 4.3.4.)

Which of the following is true about the graph of f(x)=7^x. select all that apply. a= it intercepts the x axis b=it intercepts both axis c=it intercepts neither d=it intercepts the y axis

Your client has saved $1,860 for a down payment on a house. a government loan program requires a down payment equal to 3% of the loan amount. what is the largest loan amount that your client could receive with this program

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.