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Discrete Math

Exponential Functions ...

The expected future of Achworth, which presently has 2000 residents, can be approximated by the formula y=2000(e).02t , where t is the number of years in the future. A) Find the expected population of the town in years? B) How many years until the town will have doubled its population?

Continuity Proof Numbers

Let a < b, and f : ]a; b[ in R. Assume f is continuous at x0 in ]a; b[ and f(x0) > c for some number c in R. Prove that there is delta > 0 such that f(x) > c for all x in ]x0 - delta; x0 + delta[. Hint; what would happen if, for every delta>0 there were xdelta in ]x0 - delta; x0 + delta[ with f(xdelta)=< c?

One to one function proof

Let f:A->B where A and B are nonempty. Prove that f has the property f^-1(f(S))=S for every subset S of A if and only if f is one-to-one

Numerical Analysis Problem Using Matlab

With the definition that pi is the area of the unit circle, explain why pi equals 8 times the integral from 0 to 1/sqrt(2) of (sqrt(1 - x^2) - x) dx. use the Romberg algorithm to approximate the integral. Provide the codes used and all the results and work.

Finite Mathematics - Number System - Amicable Pair

In 1866, a sixteen-year-old Italian student, Nicolo Paganini, discovered the second smallest amicable pair: 1184 = 2^5 x 11^2. Confirm that this pair is indeed amicable, but is not found by Thabit's rule. The second smallest amicable pair is (1184, 1210).

Finite Math - Fibonacci Umbers - Sum of Consecutive Integers

Fibonacci proved that if the sum of two consecutive integers is a square (that is, if n + (n - 1) = u^2 for some u), then the square of the larger integer will equal the sum of two nonzero squares. Verify this result and furnish several numerical examples.

A Normal Subgroup Proof

If H is a subgroup of G, and K is a normal subgroup of G, prove that H intersection K is a normal subgroup of H

Outs in Baseball Games

Please see attachment How many outs are there in a baseball game that lasts nine innings?....

The Values of the Variables in the Formula

I was instructed to actually work the problem to show the formula, the value of the variables in the formula, and the results in the formula instead of using the finance calculators and just coming up with the answer. * What is the ending balance from an initial deposit of $5,000 at 14% compounded monthly for 4 years? *

Question about Relation - Ordered Pairs

See attached 5. Let A = {a, b, c} , and let R be the relation defined on A by the following matrix: MR = (a) Describe R by listing the ordered pairs in R and draw the digraph of this relation. (b) Which of the properties: reflexive, antisymmetric and transitive are true for the given relation? Begin your dis

Retraction Proof

Let A_0 be contained in A_1 contained in A_2 and so on be a nested sequence of subspaces of X such that the union of all A_n is X and such that An contained in the interior of A_(n+1). Suppose for each n, there is a retraction r_n:A_(n+1) to An. Prove there is a retraction r: X to A_0.

How Many Chickens was the Truck Originally Carrying

Pigeon Driver The red semi-truck driver was new in town and didn't realize the danger in having the little pigeon sit in the driver's seat while he went in to check on a few things. Finding the key still in the ignition, the pigeon's big round eyes lit up with joy! As the pigeon sped around the corner and over the curb, 6

Finance : Interest and Withdrawal Calculation

Hal deposited $100 a month in an account paying 9% per annum compounded monthly for 25 years. After 25 years, he stops making deposits. Over the next 35 years, Hal withdraws the same amount of money monthly. What amount does Hal withdraw monthly so his account has a $0 balance at the conclusion of the 35 year period? (Plea

Groups and proofs

I) Let A, B, and C be groups, let alpha, beta, and gamma be homomorphisms with gamma times alpha = beta alpha gamma beta A--------->B----------->C<---------A If alpha is surjective, prove that ker(gamma)= alpha((ker(beta)). ii) Prove that if K is a subgroup of a group G, and if every left coset of

Subgroups

Assume that G is a finite group, and let H be a nonempty subset of G; prove that H is closed iff H is a subgroup of G

Linear Functional Proof

On the attachment there is a mistake. It should be not continuous instead of not bounded. Prove that there exists a linear functional f:C([0,1])-->that is not continuous... See attached file.

Venn diagram and word problem

See attachment Use a Venn diagram to determine whether... 23. In a television game show, there are five questions to answer. Each question is worth twice as much as the previous question. If the last question was worth $6400, what was the first question worth?

Finite Problems

Please answer all the questions and give a detailed explanation for each. (see attached) 1. Use the echelon method to solve the system 2. Use the Gauss-Jordan method to solve the system of equations 3. A cable TV company charges $23 for the basic service plus $5 for each movie channel. Let C(x) be the total cost in

Finite Mathematics - Probability - Mean Unknotting Time

My question is as follows: Suppose that you are given a simple chain of length N beads, and in this chain you tie one knot in the centre. You perform an experiment 25 times in which each time you place the chain on a vibrating plate and measure how long it takes to unknot and you make a list of the un-knotting times as follow

Probability questions - Please help and show work. Thank you.1. In a small class of 10 students, 3 did not do their ...2. Suppose a card is drawn at random from an ordinary deck ...

Please help and show work. Provide step by step calculations for each. Thank you. 1. In a small class of 10 students, 3 did not do their homework. The professor selects half of the class to present solutions to homework problems on the board, and records how many of those selected did not do their homework. (a) give a probabi

Finite Mathematics for Commercial and Business Loans

A bank has set aside a maximum of $25 million for commercial and home loans. Every million dollars in commercial loans requires 2 lengthy application forms, while every million dollars in home loans requires 3 lengthy application forms. The bank cannot process more than 72 application forms at this time. The bank's policy is to

Binomial theorem proof

N + n + n + ..... = n + n + n + .... 0 2 4 1 3 5 (imagine the vertical sets of numbers are surrounded by a large parenthesis, as it is in a binomial expression) My problem: Prove the above expression for n = 2k. Thank you.

Mathematics - Finite Mathematics

An AAA bond yielding a 10% return and a BB bond yielding a 15% return. Invest as much in AAA bond as in the BB bond, at least $5000 in the AAA bond and no more than $8000 in the BB bond. How much should she invest in each to maximize her return.

Mathematics - Finite Mathematics for Carmels and Creams.

Sweet Delight Candies, Inc., sells boxes of candy consisting of creams and caramels. Each box sells for $4 and holds 50 pieces of candy (all pieces are the same size). If the caramels cost $0.05 to produce and the creams cost $0.10 to produce, how many caramels and creams should be in each box for no profit and no loss? Would