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1) Rudin, Ch. 1, Problem 1: If r is rational (r not equal to 0) and x is irrational, prove that r+x and rx are irrational.2) If (a_n), (b_n) are rational sequences, and lim a_n = a, lim b_n = b, show that: lim(a_n+b_n) = a+b, and lim(a_n b_n) = ab.3) Show: If a_n converges to a, any subsequence (a_(n_k)) of (a_n) converges to a.4) Let (b_n) be a Cauchy sequence of rational numbers such that b_n is not zero for any n. Show that if (b_n) does not converge to 0, then (b_n) has a multiplicative inverse in the set of Cauchy sequences.5) Show that between any two distinct real numbers there are infinitely many rational numbers.
Find the probability if the given information is known about the chosen card
A homeowner wants to enclose a 5,800 square feet rectangular garden by a fence in his backyard. If three sides of the fence cost $6.25 per foot and 4th side costs $10.25 per foot,
Consider two grocery stores at which the mean time in line is the same but the variation is different. at which store would you expect the customers to have more complaints about the waiting time?
Describe a queuing process in your work environment or community. b) Identify the model (M/M/1, M/M/m, M,D,1 etc.) used and c) its operating characteristics (arrival, waiting line, and service facility). d) Explain the assumptions that were made.
Use the method of undetermined coecients to fi nd the general solution of
Mr X has two children. One of them is a boy born on tuesday.What is the probability that the other one is also a boy?
The hypotenuse of a right triangle is 6 ft longer than the shortest side. If the sum of the lengths of the two legs is 21 ft, find the lengths of all three sides.
Inside a semicircular tunnel of diameter 24 feet, a vertical support beam is placed 5 feet from the side of the tunnel. How tall is the beam?
question consider quadrilateral abcd with a -34 b 26 c 2-1 and d -3-3. find the area and perimeter of abcd. please
Use the binomial distribution to find the probability that the company makes a profit from the 1300 policies. Compare this result to that from part b.
1. explain which of the two options below results in a lower balance after 6 months on a debt of 2500.annual simple
If the Gaussian elimination algorithm with scaled partial pivoting is used on the example shown, which row will be selected as the third pivot row
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