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# Discrete Math

### Game Theory: Perspective and Transformational Matrices

See attached. 1. in the diagram below, an arrow object is located at point C; P is an arbitrary point in space. a) How would you generate a transformation matrix that would point the arrow object at point P? The arrow object is defined in a Left Handed System with the following

### Word Problemson basic statistics and finite math

1. A large aquarium at an exhibit is 20 ft long, 10 ft wide, and 6 ft high. What is its volume of the aquarium? 2. Evaluate the following : 33 lb/ft x 6.5 ft 3. One side of an equilateral triangle is 5/8 in. What is the perimeter of the triangle? 4. What is the perimeter of a semi-circle (half of a circle) wit

### Logic - Truth Tables, DeMorgan's Laws.

1) Construct a truth table and determine the truth value of the statement ~ q = { ~r ^ ( p v q) }, when p is false, q is true and r is true. 2) Use De Morgan's Laws to determine whether the two statements are equivalent. ~( p ^ q), ~(q v ~p) 3) Determine which, if any of the three statements are equivalent.

### Venn Diagram Post Survey

Creating a venn diagram post survey. Construct a Venn diagram, label your diagram clearly. Use your diagram to answer the following questions A survey asked participants many questions. Among the questions were these two: Do you own an Ipod? Are you over the age of 45? 33 did own an Ipod 57 were over the age of 45

### Rigid Body Dynamics

(Please refer attachment for detailed problem description) Problem 1 : The 40 kg disc is released from rest with the spring compressed. At the instant shown (see attachment) it has a speed of 4 m/s and the spring is unstretched. From this poinr determine the distance d that the disc moves down the 30 degree ramp before moment

### Finite mathematics six questions

1.Simplify the expression 3&#8730; (-1000) 2.Total profit is defined as total revenue minus total cost. R(x) and C(x) are the revenue and cost from the sale of x televisions. If R(x)= 240x - 0.9x^2 and C(x) - 4000 + 0.6x^2, find the profit from the sale of 100 televisions. 3.Simplify the complex fraction X/x+1 9/ x^2

### A student thinks of a polynomial p(x) of arbitrary degree, and non-negative integer coefficients.

A student thinks of a polynomial p(x) of arbitrary degree, and non-negative integer coefficients. How can you determine the student's polynomial by asking for two values of her polynomial, say p(a) and p(b), where a and b are positive integers? Hint: A positive integer n can be written uniquely in base k, where k is a positive

### Logic: Diplomat Row Example

Please see the attached file for the fully formatted problems. On Diplomat Row, an area of Washington, DC. there are five houses. Each owner is a different nationality, each has a different pet, each has a favorite food, each has a different drink, and each house is painted a different colour. All Statements: (1) Green H

### Dynamics and Kinematics

For detailed description with figs. please refer the attachment. Prob. 1 : A box slides down a ramp with two straight segments and on leaving the ramp it slides on a rough horizontal surface and then impacting a spring. To determine kinetic energy, velocity at different points and the compression of the spring. Prob. 2 : A

### Goal Programming (Lindo) - First West Chemical

First West Chemical First West Chemical Company produces two chemical ingredients for pharmaceutical firms; formula X and formula Y. Production of each ingredient requires two processes. A unit of Formula X requires 4 hours in process 1 and 3 hours in process 2. A unit in formula Y requires 2 hours in process 1 an

### Propositional logics

Problem: If Cleopatra was powerful, then she was venerated, but if she was not powerful, then she was not venerated and she was feared. If Cleopatra was either venerated or feared, then she was a queen. Cleopatra was a leader if she was a queen. Can you prove that Cleopatra was powerful? a leader? a queen? Do not use

### Finding a Recursive Algorithm

23. Give a recursive algorithm for computing n * a using only addition, where n is a positive integer and a is a real number (add a to itself n times).

### Logic : Determine whether each of the following is a tautology, a contradiction or neither.

13. Determine whether each of the following is a tautology, a contradiction, or neither. * (a) [( P fa] P. (b) Pe=>PA(PvQ). (c) P=.Q.=›PA—Q. * (d) P=IP (P (e) P A (Q v .1=› P (f) IQ A (P P. (g) ( P <=). Q) <=> (—Pv Q)v(—P AQ). (h) [P(Qv R)] [(Q R)v (R (i) P A(P Q) A —Q. (j) (PvQ).Q P. (k) [P (Q A R)] [R = (P Q)].

### Finite Math : Linear Equations, Optimization, Probability and Basic Statistics

Week 5 ________________________________________ 1.) ________________________________________ 2.) Find the solution of the following system of linear equations: x + 2y - 7z = -1 3x + 7y - 24z = 6 x + 4y - 12z = 26 ________________________________________ 3.) A cookie company makes three kinds of co

### Algorithm Timing

How much time does an algorithm take to solve a problem of size n if this algorithm uses 2n^2 + 2^n bit operations, each requiring 10^-9 second, with these values of n? i) 10 ii) 20 iii) 50 iv) 100 I need help with a question, the attachment contains the question as well as what I think is the answer. Could someone ple

### List the first 10 terms of each of these sequences

Please see the attached file for the fully formatted problems. Practice problem 20 List the first 10 terms of each of these sequences. a) The sequence whose nth term is the larges integer k such that k! <= n; b) The sequence whose nth term is 3^n - 2^n; c) The sequence whose nth term is sqrt(n) ; d) The sequence whos

### Proof methods & strategy

Problem: Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?

### M/M/1 Simulation

The fraction of the time that the server is busy (&#961;) = &#955;/ &#956; Without using &#955; (Lambda) and &#956; (Mu) in the equations and using only information from excel simulator output, can I use the IF Statement in excel to approximate the fraction of time that the server is busy(&#961;)? Why or why not? Please se

### Is the Set a Group?

Decide whether each of the given sets is a group with respect to the indicated operation. 1- For a fixed positive integer n, the set of all complex numbers x such that x^n=1(that is, the set of all nth roots of 1),with operation multiplication. 2-The set of all complex numbers x that have absolute value 1, with operation m

### Bijection is Homeomorphism

Let f : M -> N be a continuous bijection. M is compact. Show that f is a homeomorphism. Isn't a homeomorphism by definition a bijection? And since M is compact, will it not be true that N will be compact too?

### Unions and Intersections of Sets

Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set a) A ∩ B b) A ∩ C c) A U C d) B U C e) (A U B) ∩ C f) A U (B U C) g) (A ∩ B) ∩ C h) (A ∩ B) U C Given the diagram below, find a) A U B and b) A ∩ B

### Euclidean Algorithm Factorization

Please see attached file for full problem description. 1. Use the euclidean algorithm to find gcd(729,75), then rerun the algorithm to find integers m and n such that gcd(729,75) = 729m + 75n. 2. Find the prime factorizations of (482,1687). Thus find the gcd and the lcm of the pair. Also find the gcd by Euclid's algorith

### Finite Mathematics: Function and Linear Models

I am having trouble figuring out where to start on this word problem, can you help me figure it out? In 2006, Jenny began selling magazines. The company sold Jenny a beginning packet for \$250.00. Jenny's cost for each magazine is 10% of the sales price. 1. Find the linear model for Jenny's cost as a function of the doll

### Definitions and Formulas

Please help me with the #4, #8, #4 of pg60 p.95 #4 IN YOUR OWN WORDS What do we mean by negation? Include as part of your answer the definition. p.95 #8 According to the definition, which of the following examples are statements? a. Dan and Mary were married on August 3, 1979. b. c. Do not read this s

### Problem 52 : According to the National Institute of Standards and Technology, the preferred representation of 1,999 is MCMXCIX. Which of the following does not also represent 1,999? ? MCMXCXI ? MCMXCVIIII ? MDCCCCLXXXXVIIII ? MIM Problem 54: What year in the millennium from 1001 to 2000 is with the most Roman numerals? Problem 36: Using base systems ? Change 52 to base three ? Change 4,731 to base twelve *Use number bases to answer the following questions Problem 42: Change \$4.59 to quarters, nickels, and pennies. Problem 48: Change 54 months to years and months. Problem 14: Write the number given in the problem as a decimal numeral, 11111two Problem 22: Write the number given as a binary numeral. 46 Problem 42: Perform the indicated operation 1101two +1100two __________

If the text is available to who is working on the problem sets the page number and problem is all included below. If text is not available the complete problem question is also below. ? Prologue, p. P16, problem 58 ? Section 4.1, p.150, problems 52 and 54 ? Section 4.3, p. 160, problems 36, 42, and 48 ? Section 4.4,p. 164

### Projected Total Profit

Beaver's makes 3 products. Each requires work in a three different departments. Labor-hour Reqmts Dept Prod1 Prod2 Prod3 Tot avail A 1.50 3.00 2.00 450.00 B 2.00 1.00 2.50 350.00 C 0.25 0.25 0.25 50.00 Profit 25.00 28.00 30.00 Setup costs 400.00 550.00 600.00 Demand 175 150 140 What is the projected total profit a

### Sets and Venn Diagrams

9. In a survey of 75 consumers, 12 indicated that they were going to buy a new car, 18 said they were going to buy a new refrigerator, and 24 said they were going to buy a new washer. Of these, 6 were going to buy both a car and a refrigerator, 4 were going to buy a car and a washer, and 10 were going to buy a washer and a refr

### Statistics and Sampling

A survey of 100 students has the following results : 70 of the students stated they are pursuing at least one of the degrees: Mathematics, Computer Science, or Electrical Engineering. 40 were pursuing a Mathematics degree, 50 were pursuing a Computer Science degree, and 25 were pursuing an Electrical Engineering degree. 23 stu

### Sets and Binary Relations

2. Let A be the set { 1,2,3,4,5,6} and R be a binary relation on A defined as : {(1,1), (1,3), (1,5), (2,2), (2,6), (3,1), (3,3), (3,5), (4,4), (5,1), (5,3), (5,5), (6,2), (6,6)} (a) Show that R is reflexive. (b) Show that R is symmetric. (c)Show that R is transitive. 3. Let A be the set {1,2,3,4,5,6} and let F be t

### Newport manufactures coffee by blending 3 types of coffee

***Please see the attached file for details*** Newport manufactures coffee by blending 3 types of coffee beans. The cost per pound and the number of pounds used per hour are listed below. The coffees individually meet the following ratings: Bean Cost/lb 1 0.95 2 1.35 3 0.89 The Newport blend requires an aroma