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# Discrete Math

*1.In a multiple regression model, the value of the coefficient of multiple determination a. has to fall between -1 and +1. b. has to fall between 0 and +1. c. has to fall between -1 and 0. d. can fall between any pair of real numbers. *2.A medical doctor is involved in a \$1 million malpractice suit. He can either settl

### Business Statistic and Finite Math

1.If a categorical independent variable contains 2 categories, then _________ dummy variable(s) will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4 2. A dummy variable is used as an independent variable in a regression model when a. the variable involved is numerical. b. the variable involved is

### Jacobi and Legendre Symbols and Proofs

1. Prove that if b and c are odd, then (a/bc)=(a/b)(a/c) 2. Prove that if a==b (mod c), where c is odd, then (a/c)=(b/c)

### Finite math/business analysis- Multiple choice questions on statistics

1.A recent survey of frozen convenience meals found a correlation of r = 0.768 between calories and fat content in the sampled meals. Which of the following is the most appropriate conclusion from this survey about the relationship between calories and fat content? a. Higher fat content in the sampled meals resulted in a h

### Venn Diagram From a Table

The Wilcox fam is considering buying a dog. They have established several criteria for the family dog; It must be one of the breeds listed in the table, must not shed, must be less than 16 in tall, and must be good with children. a.) Using the information in the table, construct a Venn diagram in which the universal set is

### Game Theory Problem

Rose and Cathy decide to play a matrix game. Each has two options, conveniently called W and L. If both pick W, Cathy pays Rose \$4; if both pick L, Cathy pays Rose \$2; if Rose chooses L and Cathy chooses W, Cathy pays \$1 to Rose; and finally, if Rose chooses W and Cathy chooses L, Rose pays Cathy \$1. The payoff matrix for Rose

### Logic : Sets

Find A U B where A= {x | x is an even integer greater than 3} B = {x | x is an odd integer greater than 10}

### Proofs of least upper bounds

1. If supS=a and X={s-k l s element of S}. Prove that supX = a-k 2. If A and B have least upper bounds, prove sup(AUB) = max(supA, supB) 3. Prove for all x<supS there exists y that is an element of S such that x<y< or = supS.

### Detailed Explanation to truth table

Construct a truth table for the statement below: p^(~pVq) Is the statement a tautology?

### Use the Method Incorporating the Duality

Minimize C = 4x1 + 2x2 Subject to the constraints x1 + 2x2 >4 x1 + 4x2 >6 x1 >0, x2 >0 Use the method incorporating the duality.

### Logic Problem and Truth Value

Let p represent a statement having a truth value T, q represent a statement having a truth value F, and r represent a statement having a truth value T. Find the truth value for the following: p^(~q) p^q^r p^(qVr) ~(p^q) (~p)V(~q).

### Flow Augmenting Path Algorithm, Bipartite Graph and Cardinality

1. Find the maximum flow and the associated minimum capacity cut for the following network, by using flow augmenting path algorithm (in the order of "first labeled, first scannred"). *see attachment for diagram* 2. A maximum capacity flow augmenting path is an augmenting path such that we can increase the flow of the network

### Math Symbols, Logic, Predicate Logic and Simplification

Question 1. Translate each of the following statements into the notation of logic and predicate logic and simplify the negations of all. Which statements do you think are true? (i) Some questions are easy. (ii) Any integer with an even square is even. (iii) All students cannot correctly answer some questions in this assignme

### Finite Axiomatic Geometry

Geometry Finite Axiomatic Geometry Finite Axiomatic Geometry This abstract geometry confuses me and I just can't follow this logic. Here is a set up of the question. P

### Group Proofs : Properties of Groups

Let G be a group. x and y are elements of G. Prove that: a. The inverse of xy is y^-1x^-1 b. The identity element, e, is unique c. The inverse of any element x of G is unique d. If xy = xz then y = z e. If x^-1y^-1=y^-1x^-1 then xy = yx f. If every element x of G satisfies x x = e, then for any two elements, x, y,

### Continuous Map Limited Points

Let f: X --> Y be a continuous map. Let A (SYMBOL) C. Show that, if (FUNCTION1) is closed, then (FUNCTION2). *(For complete problem, including proper citation of functions and symbols, please see attachment)

### Proof : Absolute Values

Letting x,y be elements of the real numbers, prove that |xy|=|x||y|.

### Compound Interest Questions

A) Suppose I want to have \$60,682.50 in my account for my children's college education. I expect to earn an average return of 12%, compounding four times a year. If I deposit \$25,000.00 today in my account, how many years will it take me to meet my goal (\$60,682.50 in my account)? b) Now suppose my goal is to have \$100,000.00

### Drawing a Venn Diagram

Use the information provided: U={1,5,10,15,20,25,30} A={1,10,15} B={1,10,20,25} C={5,15,30} and use a venn diagram to determine wheather (A U B') U C= (A' U B) U C' for all sets A, B, and C. Show your work.

### Venn Diagram for People Watching Football

The Action Sports Network surveyed 265 of its viewers to determine which sports they watched most often. The results of the survey showed: 140 viewers watched football 130 viewers watched baseball 120 viewers watched hockey 60 viewers watched football and baseball 55 viewers watched baseball and hockey 50 viewers watche

### Finding the Greatest Common Divisor

Find the greatest common divisor of the following pairs: a)527, 765 (use technique like 527=341*1+186) b)361, 1178 (use technique like 527=341*1+186) c) -find the gcd (d) of 299, 481 (use technique like 31=186-155*1 --> 31=186-(341-186*1) -find integers such that 299x+481y=d -now replace 299 and 481 by 129 and 301.

### Principal Value Proof

Prove that if all of the powers invoved are principal values then... Please see the attached file for the fully formatted problems.

### Exponential Proof for a Function

Show that z^(1/n) = exp((1/n)log z) also holds when n is a negative integer.... Please see the attached file for the fully formatted problems.

### Finite Math for Normal Distributions

SHOW HOW TO SOLVE PROBLEM Consider the normal distributions drawn below (with different scales) AREA=.9 AREA=.9 ******--**** ******--****

### Binary Connections

Show that there are no complete single binary connectives other than NAND and NOR. Hint: Let f be the truth function for a complete binary connective. Show that f(true,true)=false and f(false,false)=true because the negation operation must be represented in terms of f. Then consider the remaining cases in the truth table for f

### Analyzing an Algorithm for Assignment Statements

For the following algorithm find the number of times the assignment statement (:=) is executed during the running of the program. Answer the question by giving a formula in terms of n: i := 1; while i < n + 1 do i := i + 2; for j := 1 to i do S od od

### Analyzing an Algorithm for Addition Operations

Trace the algorithm below and track the number of times that the addition operation (+) is executed over the course of the program's run time. Answer the question by giving a formula in terms of n: for i := 1 to n do for j := 1 to i do x := x + f(x) od; x := x + g(x) od

### Give an example of a binary relation R such that R is irreflexive but R^2 (R squared) is not irreflexive, and give an example of a binary relation R such that R is antisymmetric but R^2 is not antisymmetric.

For each of the following properties, find a binary relation R such that R has that property but R^2 (R squared) does not: (a) irreflexive (b) antisymmetric

### Chinese Remainder Theorem : Proof and Problems

I would appreciate it if someone could provide the solutions to QB5 of the attatched exam paper. Please see the attached file for the fully formatted problems. B5. (a) (1) State and prove the Chinese Remainder Theorem. (ii) Find the 2 smallest positive integer solutions of the simultaneous set of congruence equations: 2x

### What are random variables?

What are random variables?