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Discrete Math

DeMorgan Law and converse statements

Write the negation of the conditional statement. 1. If I am in Seoul, then I am in Korea. 2. Write the nonequivalent converse and inverse of the statement. If you are getting a haircut , then you are not studying 3. Use the De Morgan law that states : ~( p ^ q) is equivalent to ~p v ~q 4. to write an eq

Mathematics - Binomial and Poisson probabilities

Objective: Calculate binomial and Poisson probabilities. 1) Chapter 5: Problem 5.5 (binomial) Solve the following problems by using the binomial formula. a. If n = 4 and p = .10 , find P(x = 3) . b. If n = 7 and p = .80 , find P(x = 4) . c. If n = 10 and p = .60 , find P(x ≥ 7) . d. If n = 12 and p = .45

Convert Compound Statement

Convert the symbolic compound statement into words. 1. p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: ~p 2. p represents the statement" Her name is Lisa" q represents the statement " She lives in Chicag

1. Mrs Bollo's second grade class of thirty student conducted a pet ownership survey . Results of the survey indicate that eight students own a cat, 15 students own a dog, and 5 students ...

1. Mrs Bollo's second grade class of thirty student conducted a pet ownership survey . Results of the survey indicate that eight students own a cat, 15 students own a dog, and 5 students own both a cat and a dog, How many of the students surveyed own only a cat? 2. Please use a venn diagram to answer the questions? At east

Finite Math

Attached is a study guide for my final exam in Finite Math. I need help with these questions. Thanks, Perform the indicated operations. Give the answer in lowest terms. 1) x/x^2 -16 - 6/x^2+5x+4 A )x^2-5x+24/(x-4)(x+4) B) x^2-5x+24/(x-4)(x+4)(x+1) C) x^2+5x+24/(x-4)(x+4)(x+1) D) x^2-5/(x-4)(x+4)(x+1) Perfor

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

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√ (-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

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

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?

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

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

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

Relations: reflexive, antisymmetric, transitive

For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R: ---------------------------------------- Row 1: 1 0 1 Row 2: 1 1 0 Row 3: 0 1 1 ----------------------------------------- Which of the properties (reflexive, antisymmetric, transitive) are satisfied by R?

In a street there are 5 houses, painted 5 different colors.

1. In a street there are 5 houses, painted 5 different colors. 2. In each house lives a person of different nationality. 3. These five homeowners each drink a different kind of beverage, smoke different brand of cigar and keep a different pet. THE QUESTION: WHO OWNS THE FISH? HINTS: 1. The Brit lives in a red house

Set Partitions : Coarseness and Fineness

The meet of the partitions f1,...,fI is the finest partition that is coarser then each fi. The join of the partitions f1,...,fI is the coarsest partition that is finer than each fi. The meet of partitions is denoted and the join of partitions is denoted I

Venn Diagrams, Probability and Combinations

1. In an experiment, a pair of dice is rolled and the total number of points observed. (a) List the elements of the sample space (b) If A = { 2, 3, 4, 7, 8, 9, 10} and B = {4, 5, 6, 7, 8} list the outcomes which comprise each of the following events and also express the events in words: A&#61602;, A &#61640; B, and A &#616