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Discrete Math

Rate the importance of the following issues

In a survey conducted by a union, members were asked to rate the importance of the following issues: (1) job security, (2)increased fringe benefits, and (3) improved working conditions. Five different responses were allowed for each issue. Among completed surveys, how many different responses to this survey were possible? E

Finite Mathematics (Future Value - Present Value)

Can you help me with the following questions: - What is the difference between the accumulated amount (future value) and the present value of an investment? Please give examples of each. - Find the accumulated amount at the end of 8 mo on a $1200 bank deposit paying simple interest at a rate of 7%/year. - A bank depos

Absolute Convergence Test

Prove the absolute convergence test: Let the sum from n=m to infinity of a_n be a formal series of real numbers. If this series is absolutely convergent, then it is also conditionally convergent. Furthermore, in this case we have the triangle inequality - the absolute value of the sum from n=m to infinity of a_n <= the sum fr

Matlab Code

** Please see the attached file for the complete problem description ** Please prepare a simple and basic MATLAB code for the 2 attached problems. M-file and word documents with comments will help me understand the codes better. Thank you. 3) Write a recursive function computing the sum of cubes of all integers between 1 an

Loan Amortization Schedule Comparison Project

Develop a loan amortization project using Excel spreadsheets. This can be a car loan or a home mortgage. You will develop two alternative loan schedules using realistic rates and repayment schedules and write up a comparison of your two amortization schedules. This involves two tables and two line graphs displaying the decrease

Proof about union and cardinalities

Please help with the following problem. Provide a step by step explanation. Show that given finite sets A_1, A_2,...,A_n, that are pairwise-disjoint, that is A_i intersection A_ j = empty set for all i not equal to j, then their union is a finite set and the cardinality of their union is the sum of the cardinalities of the s

Proof showing the equality of integers

Please help with the following problem. Provide step by step. Show that equality of integers is an equivalence relation, that is show that equality of integers is reflexive, symmetric, and transitive. Recall two integers z=a--b, w=c--d, a, b, c, d belong to N (natural numbers) are equal if and only if a+d=b+c **where a--b

Various Problems in Discrete Mathematics

Prove Each Directly. 1. The product of any two even integers is even. Prove by cases, where n is an arbitrary integer and Ixl denotes the absolute value of x. 2. [-x]=[x] (*Brackets are the x's is the absolute value symbol) Give a counterexample to disprove each statement, where P(x) denotes an arbitrary p

Correcting Proofs in a False Statement

Not every error in a proof is a false statement. Sometimes every line is true, but the lines don't directly follow the previous lines. All that's needed to fix the error is more detail or explanation. Explain where the error is in the following proof and then fix it. Prove: If n^2 is not divisible by 3, then n is not di

Providing proof about Cardinality

Let A, B, C be sets. Show that the sets (A^B)^C and A^(BxC) have equal cardinality by constructing an explicit bijection between the two sets. Conclude that (a^b)^c=a^bc for any natural numbers a, b, c. Use a similar argument to also conclude a^b x a^c= a^b+c

Examining Proof about Cardinality

Let A and B be sets. Show that A x B and B x A have equal cardinality by constructing an explicit bijection between the two sets. Then use the following proposition to prove that multiplication is commutative. (Let n, m be natural numbers. Then nxm=mxn) Proposition: Cardinal arithmetic a) Let X be a finite set, and let x b

Counting Methods Roulette Wheel Diagrams

Part I: Set Theory Look up a roulette wheel diagram. The following sets are defined: A = the set of red numbers B = the set of black numbers C = the set of green numbers D = the set of even numbers E = the set of odd numbers F = {1,2,3,4,5,6,7,8,9,10,11,12} From these, determine each of the following: A?B A?D B?C

Mathematical Reasoning: The Sum of the Divisors Function

Prepare written answers to the following assignments: Preview Activity 3 (The Sum of the Divisors Function) Let s be the function that associates with each natural number the sum of its distinct natural number factors. For example, s (6) = 1 + 2 + 3 + 6 = 12. 1. Calculate s (k) for each natural number k from 1 thr

Discrete math Subsets Contained

Hello, I have another discrete problem I need help on. It says: How many subsets contain 1 or 2 or 3 in the set {1,2,...,20}? So my teacher told me that {1} is a subset, {1,3,4,5,19} would be a subset (i just chose that randomly), {2} would be a subset, {2,5,6,7,20} would be a subset (again, i just chose that at random

How many solutions do the equation have

Hello, I have a discrete math problem. It states how many solutions (X_1,...,X_6) in the Natural numbers have the equation X_1+ ... + X_6 = 10 So the way my teacher explained it was (10,0,0,0,0,0) would be one choice, (0,10,0,0,0,0) would be another, so basically it would look like this... (10,0,0,0,0,0) (0,10,0,0,0,0

Discrete Math: Proving a theorem

(a) Proof. Let f be onto. Consider any C is a subset of Y. Let y E f(f^-1(C)). Then y=f(x) for some x E F^-1(C). But the fact that x E f^-1(C) implies that f(x) E C. Moreover, f(x)=y. Therefore y E C. Thus we have proved that f(f^-1(C)) is a subset of C. For the converse, consider any c E C. Since f is onto, there exists a

SAT and ACT Scores

Bob compares his SAT Verbal score of 400 to Marge's ACT Verbal score of 20. "I whupped ya," he exclaims. "My score is 20 times your score!" Although Bob's multiplication is good, his logic is faulty. Exxplain why?

Analyses of Euclidean Algorithms

a) When we write a=mb+r in the Euclidean algorithm, call the number m a multiplier. How do the multipliers influence how long it takes the Euclidean algorithm to run? b) For which multipliers will the Euclidean algorithm take as long as possible to run? c) For two steps, three steps, and four steps, find the smallest pai

Bit String and Rule of Products

A bit string is a string of bits (0â??s and 1â??s). The length of a bit string is the number of bits in the string. An example, of a bit string of length four is 0010. An example, of a bit string of length five is 11010. Use the Rule of Products to determine the following: (a) How many bit strings are there of length eig

Find the value of x.

What is the value of x after each of the following statements are encountered in a computer program, if x = 1 before the statement is reached. Explain fully. (a) if 2 + 2 = 5 AND 3 + 4 = 7 then x:= x + 1 (b) if 2 + 3 = 5 XOR 3 + 4 = 8 then x:= x + 1

Probability is demonstrated.

PRACTICE PROBLEMS: 1. Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). A. rolling a sum of 11 on two fair six sided dice B. drawing a red ni

Explore statistics/probability

1. Light Switches A working light bulb is in a closed room with no windows. Outside the room, is a panel of three switches, one of which controls the light inside (up is on, down is off.) You may do anything you like to the three switches and then enter the room to inspect the light. After this, without any further experiment

Financial Management

Solve for the unknown number of years in each of the following (Round your answers to 2 decimal places. (e.g., 32.16)): Present Value Years Interest Rate Future Value $700 ? 10% $1,997 890 ? 6 3,400 17,400

Venn diagram is constructed.

1. List all the subsets of { 8, 16, 27, 31} 2. Determine the number of subsets of {mom, dad, son, daughter} 3. At MegaSalad, a salad can be ordered with some, all, or none of the following set of ingredients on top of the salad greens: {ham, turkey, chicken, tomato, feta cheese, cheddar cheese, cucumbers, onions, red pep

Binary variables

The Decision Sciences department head at a university will be scheduling faculty to teach courses during the coming fall semester. Three required courses need to be scheduled. The three courses are at the UG, MBA, and MS levels. Three professors will be assigned to the courses, with each professor receiving one of the courses. S

Set Theory Problems

Create two sets, set A and set B. Set A will be a list of five items you personally NEED to buy the most (essential items). Set B will be a list of five items that you WANT to buy the most (fun stuff). List the items in Set A and Set B, and also list or state the items in the union and in the intersection of Set A an

State Standards and DAP

Optain the academic standards for kindergarten for three states (available on state education websites). Compare the standards in a single category such as math or reading and describe how the standards are similar or different across the states. What are your thoughts regarding the developmental appropriates of these standards?