Business math problems

Complete the vertical and horizontal analysis of the comperative balance sheet for Miller's Model Ships. (See attached file for full problem description)

What are the math rules for the problem: K = R + [ (1.25 X (14 - R)]?

I am working on corporate finance and figuring out interest rates. The problem has some of the givens, I need to find the value of the unidentified given. Other examples: 15% = R + [1.25 x (14% - R )] 16% = 9% + [1.10 x (k - 9%)] 15% = 10% + [b x (12.5% - 10%)]

Solve these problems using inclusion-exclusion approach.

(See attached file for full problem description with equations) --- Solve these problems using inclusion-exclusion approach. 1- Given 2n letters, two of each of n types, how many arrangements are there with no pair of consecutive letters the same? 2- How many integers solution of are there with: a. b. -10 3- How many secret codes can be made by assigning each letter of the alphabet a (unique) different letter? Give an approximate answer using Euler's number e. 4- How many arrangement of 1, 2, 3…n are there in which only the odd integers must be deranged (even integers may be in their awn positions) ---

Combinatorial mathematics

I am majoring in mathematics, so I really need to understand this problem. Please show all work so that I can learn how to solve similar problems. 5. Four numbers are selected from the set: {-5,-4,-3,-2,-1,1,2,3,4} . In how many ways can the selections be made so that the product of the numbers is positive and: a) The numbers are distinct. b) Each number may be selected as many as four times. c) Each number may be selected at most three times.

Recurrence relations, partition, generating functions,etc

4. In noncommutative algebra, the term monomial refers to any arrangement of a sequence of variables from a set. For example, in a noncommutative algebraic structure on a set of four variables, {x,y,z,w} , examples of monomials of length 3 are xxx,xyx,xxy,zwy,wzx…….. a) Write a generating function for the number of monomials of length, n, in a noncommutative algebraic structure on a set of four variables. b) Find the number of monomials of length, n, in a noncommutative algebraic structure on a set of four variables.