Find info not obvious from data and graph it in a line, pie and bar graph

I need to analyze data (portion of the retirement investment portfolio) and graph the not so obvious info (such as total value) in a bar, pie, and line graph. I need to do this in excel and come up with formulas, name for the graphs, Y' and X's. What information should I be looking for as an investor (that's meaningful a ...continues

Working with recursions.

The sequence of catalan numbers, for each integer n > or equal to 1. Show that the sequence satisfies the recurrence relation Csubk= 4k-2/k+1 for all integers k>or equal to 2.

Working with iteration to develop a formula.

A single line divides a plane into two regions. Two lines (by crossing) can divide a plane into four regions, three lines can divide it into seven regions. Let psubn be the max number of regions into which n lines divide a plane where n is a positive integer.

Working with second order linear homogeneous recurrence relations with constant coefficients. Attachments in Word.

Suppose a sequence satisfies the given recurrence relation and initial conditions. Find an explicit formula for the sequence s(subk)=-4s(subk-1)-4S(subk-2), for all integers k>or equal to 2 s(sub0)=0,S(sub1)=-1

Methods Of Proof for Mathematical Equations

Can you give a direct proof and an indirect proof of the following? If x is any odd integer and if y is any odd integer, then xy is an odd integer.

Discrete math problems needs a WHIZ

Prove or disprove that, for matrices A,B,C for which the following operations are defined: a. A*(B+C) = A*B + A*C b. A+(B*C) = (A+B)(A+C)

Determining whether a relation is reflexive, symmetric, antisymmetric, transitive, partial order and an equivalence relation.

Let R = {(1,1)(3,1)(2,2)(1,2)(3,3)(3,2)} on Z = {1,2,3} Is R reflexive? Why? Is R Symmetric? Why? Is R antisymmetric? Why? Is R transitive? Why? Is R a partial order? Why? Is R an equivalence relation?

Discrete Structures

1. Consider the sequence of triangles Ti, i >= 2: T2 is simply a triangle sitting upright, on its base. T3 is T2, except that an additional straight line is drawn from the upper vertex, down to somewhere on the base. For each Ti+1, one more line is added to triangle Ti (such that each line meets the base at a different point). ...continues

Discrete structures

6. A string that contains only 0s 1s and 2s is called a ternary string a) find a recurrence relation for the number of ternary strings that contain two consecutive 0s b) what are the initial conditions c) how many ternary strings of length six contain two consecutive 0s The next 3 problems deal with a variation of the ...continues

Discrete Structures

11) Use generating functions to determine the number of different ways 12 identical action figures can be given to five children so that each child receives at most three action figures. 12) Use generating functions to find the number of ways to select 10 balls from an urn containing red, white and blue balls if: a. The ...continues