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Discrete Math

Find roots.

Note the cubic equation x3 - 6x2 + 11x - 6 = 0. I will claim that x = 1 constitutes a root of that equation ( replace x by 1 in the equation to verify ). Thus, the binomial (x - 1) will divide our cubic equation evenly, without remainder. Perform the division to obtain the quotient, which is a quadratic equation. Completely

Mathematics: Solving Systems of Equations

Solve system of two equations with x and y (use any technique): 1. 2x - y = 0 3x + 2y = 7 2. x + 2y = 4 2x - y = -7 3. 4x + y = 15 2x + 5y = 21 Assign x and y for unknown values, create system of two equations and find solution: 4. Investments. Michael Perez has a total of $2000 on deposit with two savings inst

correct set notation

1. Given the diagram below, find P ∩ Q. Write in correct set notation. 2. Write down all possible subsets of set P using correct set notation. 3. The cardinal number of the set {cat, dog, horse, fish, lizard, meerkat, rhinoceros, elephant, giraffe, platypus, hippopotamus, skunk, mouse} is _____ 4. Given the follow

Proof without using commutative axioms

How would the following proof be detailed if the commutative axioms did not exist? Explain your answer. Prove that for all real numbers r, s, t, and u: (r + s)(t + u) = rt + ru + st + su Commutative Axiom for Multiplication: For any two real numbers r and s, the following equation holds: rs = sr Commutative Axio

Properties of a group

@ H C S J H S J S H C H H J C S H J C S J H C S J Given the operation @ and the set {H,C,S,J} shown above, find and prove those properties of the table that are those of a group. For those properties that don't conform to a group, indicate and find a counterexample for each of those properties. (see attached)

Various Graph Theory Questions

Through the use of appropriate algorithms minimal spanning tree solutions and optimal networking routes are discovered and explained. The document contains detailed solutions and drawings to help understand how to use the included algorithms.

Finite Math

1.A safe can be unlocked by pressing the correct sequence of buttons. A display of five buttons on the door is shown below... 2.How many 3-letter code words are possible using the first 10 letters of the alphabet if a) no letter can repeat; b) letters can be repeated; c) adjacent letters cannot be the same? 3.Six people are

Discrete Mathematics and Induction

Use mathematiceal induction to prove expression... Construct a truth table to show that the expression ... (I require assistance with the attached questions)

Strong induction guidance

Suppose that a store offers gift certificates in denominations of25 dollars and 40 dollars. Determine the possible total amounts you can form using these gift certificates. Prove your answer using strong induction.

Properties of the closure of a set

See Attached If A is any subset of let denote the collection of all closed sets containing A. The set is called the closure of A.Note that is a closed set, prove that it is the smallest closed set containing A.Prove the following

PERT diagram and set operations

1. Given the following table, make a PERT diagram, and determine the project time and the critical path. Provide a justification on how you obtain your project time and critical path. Task Time Preceding Tasks A 1 None B 2 A C 3 A D 4 B E 5 B, C F 2 C G 2 D, E, F 2. Simplify expression: (B-A) UNION (B INTERSECTION

Finite Math Problem

A craft store sells small flags for $6 and large flags for $8. Recently, they sold a total of 70 flags in a single day. If flag receipts for the day totaled $520, how many of each type of flag were sold?

Steps to a Discrete Math Equation

Please help me solve this equation! Can you please also show me the steps as to how to solve this so I know in the future? Thank you I was unable to put lines between the #'s so it's supposed to be 2y over y - 1 = 4 over y + 9 - 7y over y squared - y. as written below. Thank you 2y/(y - 1) = (4/y) + (9 - 7y)/(y^2

Discrete Math: Binary Operation

Prove that any non empty set G with a binary operation satisfying the following requirements is a group: a) if x, y in G then x.y in G b) for all x,y,z in G, (x.y).z = x.(y.z) c) for all a,b in G, the equations x.a =b and a.y =b both have solutions. Hint: 1st show that if a in G then a has a right and left identity and be

Set Theory/Venn Diagrams

A recent survey of a group of students found that many participate in baseball, football and soccer. The Venn diagram below shows the results of the survey. a) How many students participated in the survey? b) How many of these students play both soccer and baseball? c) How many play only 1 sport? Given A = {a, b

Venn Diagram

Josh is conducting a telephone survey for a telecommunications company. Over the course of a 4 hour shift, he logged the following calls: 16 to single-family homes 21 to homes with more than one telephone line 17 to people who were satisfied with their current long-distance provider 11 to people who lived in single-fami

Set Theory/Venn Diagrams Multiple Choice Problems

If A and B are two sets, A â?© B represents: a) all elements in either A and B b) all elements in both A and B c) all elements that are in A but not B d) all sets that include A and B There are 8 students on the curling team and 12 students on the badminton team. What is the total number of students on the two

Venn Diagrams: Example Problem

There are 54 books in a book store: 28 are fiction, 21 are humour and 17 are children's books. If 12 of the books are humourous fiction, 8 are children's fiction, 3 are humourous fiction for children and 10 are serious non-fiction for adults, how many books are non-fiction humour for children. Illustrate your answer with a Ve

Statistics: Probability Distribution, Binomial Probability

Section 4.1 Probability Distribution 1. Decide whether the random variable is discrete or continuous. (References: example 1 page 195, end of section exercises 13 - 20 page 201) a. The number of bottles of water sold in Florida in August 2008 b. The weight of a wasp in the lab test nest c. The number of sopho

Mean of a set of data

When a student is taught how to find the mean of a set of data, why might the child have a difficult time accepting the answer? Please explain in details and give example.

Slope and the Equation of the Horizontal Line

1) find the slope and the equation of the horizontal line that passes through (-325, 185) 2) find the slope and the equation of the vertical line that passes through (-325, 185) 3) find the difference quotient of f(x) = 1/x^2 4)which of the following are true(select all that apply) x = 15 is a)a function b) constant function

11 Problems on Sets and Venn Diagrams

1. Given the venn diagram, find P ∩ Q. Write in correct set notation. [Please refer to the attachment for the Venn diagram] 2. 2. Write down all possible subsets of set P using correct set notation. [Please refer to the attachment for the Venn diagram] 3. The cardinal number of the set {triangle, rectangle, squ

Sets and Venn Diagrams explained in this answer

1. Given the following sets, select the statement below that is NOT true. A = {s, i, r}, B = {r, i, s, e}, C = {r, i, s, k, e, d} A ⊆ B A ⊂ B C ⊂ B A ⊂ C B ⊆ C 2. An electronics store surveyed every 9th customer who came onto the store for a week. Of the 185 peopl

The number of subsets

1. Given the following sets, select the statement below that is true. A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r} B ⊆ A and A ⊂ B C ⊂ A and B ⊂ C A ⊆ C and B ⊂ A C ⊆ B and B ⊆ A B ⊆ C and C ⊂ A 2. Without writing them all out, what is the number o

Finite math word problems

To pour a concrete sidewalk takes 2 hours of preparation and 3 hours of finishing. To pour a concrete patio takes 4 hours of preparation and 3 hours of finishing. ABC Concrete Company makes a profit of $450 on a sidewalks and $700 on a patio. How many sidewalks and patios should the company construct to maximize its profit? Set

Euler diagrams, logic statements, and truth tables.

1. Create an Euler diagram to determine whether the syllogism is valid or invalid. All grocery stores are open until 10 p.m. The store on the corner is open until 10 p.m. The store on the corner is a grocery store. 2. If the argument below is valid, name which of the four valid forms of argument is represented. If it

Determine whether the given statements are equivalent.

1. Write a truth table to determine whether the two statements are equivalent and explain your answer. ~(q-->P) v r , (p v q) --> ~r 2. Write a negation of the following statement and explain your answer. Some diet sodas contain saccharin. 3. Determine which, if any, of the three statements are equivalent. Give a reas

Constructing truth tables and interpreting logic statements.

I am asked to help set up a study group using sample study questions that gives some of us in the group the most trouble and I need help formulating these types of equations. 1. Determine the truth value of the following statement: The Leaning Tower of Pisa is located in England and all prime numbers divisible by 1. True o