Taylor Polynomial, Interval and Radius of Convergence and General Binomial Theorem

Please see the attached file for the fully formatted problems.

Bill owns a bike company, and wants to know how many bicycles and tricycles he should manufacture, with no leftovers, and how many boxes of seats he will order. (details given in actual problem)

Bill runs Bill's Big Bikes, a company that manufactures bicycles and specialty adult-sized tricycles. The bicycles and tricycles use the same-sized wheels and identical seats. Right now, Bill has 68 wheels in the shop and needs to order seats. Unfortunately, the company that supplies the seats will only ship seats in boxes of ...continues

An investor has $60,000 to invest in a CD and mutual fund. How much should be invested in CD's, and how much in the mutual fund to maximize return? This is a linear programming problem on investing

An investor has $60,000 to invest in a CD and mutual fund. How much should be invested in CD's, and how much in the mutual fund to maximize return? This is a linear programming problem on investing. For the following linear programing problem, define variables, write the objective function, and all constraints. Then solve t ...continues

Probability Question : Expected Value

Tom and Jim decided to play the following game for points. A single die is rolled. If it shows a non-prime number, Tom receives points equal to two times the number of dots showing. If it shows a prime number, Tom loses points equal to three times the number of dots showing. What is the expected value of the game?

Probability

In order to test a new car, an automobile manufacturer wants to select 4 employees to test drive the car for one year. If 12 management and 8 union employees volunteer to be test drivers and the selection is made at random, what is the probability that at least one union employee is selected?

Probability: Random Selection

Two balls are drawn in succession from a box containing 4 red and 2 white balls. a) What is the probability of drawing a red ball on the second draw if the first one is not put back in the box after it is drawn? b)What is the probability of drawing a red ball on the second draw if the first one is put back in the box after it ...continues

Probability : Dice and Payoff

Suppose you roll two fair dice a)what are the odds in favor of rolling a sum of 10? b) what are the odds against rolling a sum of 7 or 11? c) in part a, if you bet one dollar that a sum of 10 will turn up, what should the house pay (plus returning your one dollar bet) if a sum of 10 turns up for the game to be fair?

Word problem

You win the Zillion Dollar Lottery. Starting in 1 Year, you will receive$500,000 annually for 20 years. The states lottery commission has just enough in an account of 15% compounded annually to pay this annuity. How much money is in it today?] A treasury bill has a maturity value of $10,000 5 years from now. If I receive 5% ...continues

Finite math

Compare the yields (effective raters) of 10%compounded daily and 10.2% compounded semiannually. Which would you chooses and why?

Catalan Numbers

Prove recurrence relationship of Catalan Numbers. Question: Let n be a non-negative integer. The number, x[n], of topologically distinct binary trees with n nodes can be shown to satisfy the following recurrence (x[0] = 1): See attached file for full problem description.