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    Discrete Math

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    Proof : Differentiability

    Suppose f(b) = f'(b) = 0 and a < b. Show that if f''(x) ≥ 0 for x є [a,b], then f(x) ≥ 0 for x є [a,b].

    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

    Fractions in Binary

    There are fractions in binary (floating points). Please convert 1.1 subscript 2 to decimal. Kindly show the steps. Thanks.

    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

    Trace proof

    Suppose T in L(V). Prove that if trace(ST) = 0 for all S in L(V), then T = 0.

    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

    Trees and Graphs : Vertices and Edges

    1. True or False. It is possible to obtain a graph in which the number of vertices is 9, each with degree 5. 2. How many edges are there in a tree with 14 vertices? Choose one answer. (a) 10 (b) 13 (c) 14 (d) 15 (e) none of the above 3. If there 5 sections of Discrete Math with a total enrollment of 31 students, what is t

    Game theory/ determining value of a game

    Two DC senate candidates must decide what city to visit the day before the November election. The same four cities, Indianapolis, Evansville, Fort Wayne, and South Bend are available for both candidates. These cities are listed as strategies 1 to 4 for each candidate. Travel plans must be made in advance, so the candidates mu

    two-person, zero-sum game:Value of the game

    6. Consider the following two-person, zero-sum game. Identify the pure strategy. What is the value of the game? Player B ________b1_____b2_____b3 player A A1________8______5______7 A2________2______4____ _10

    Module Proof Exact Sequences

    If N and P are submodules of M that is an R-module and modules (N intersects P) and (N+P) are finitely generated then show that modules N and P are finitely generated.

    Proof of Splitting Field

    Let K1 and K2 be finite extensions of F contained in the field K, and assume both are splitting fields over F 1. Prove that their composite K1K2 is splitting field over F. 2. Prove that K1^K1 is a splitting field over F.

    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?

    Finite Math

    Two cards are drawn at random from an ordinary deck of playing cards. The first is not replaced before the second is drawn. What is the probability that: a. Both cards are aces? b. At least one card is black? Using the following sample: 28, 30, 24, 30, 32, 40, 22, 25, 26, 34 a. Find the mean. b. Find the median.

    Finite Math

    1. Find the present value of an ordinary annuity with annual payments of $1,000, for 6 years, at 10% interest compounded annually. 2. In a marketing survey, consumers are asked to give their first three choices, of 9 different drinks. In how many different ways can they indicate their choices? 3. A class consists of 15

    Compounding Interest and Value of Annuity

    1. What is the ending balance from an initial deposit of $4,250 at 12% compounded quarterly for 6 years? 2. Find the present value of $5,000 in 5 years at 10% compounded annually. 3. Find the value of an annuity in which $1,100 is deposited at the end of each year for 5 years, at an interest rate of 11.5% compounded ann

    Point Set Theory and Sequences

    1.) Let 'S" be the set of points on the curve y = Sin (1/x) (X #0) in the XY -Plane. (a) Find a sequence of point Pn on the X - axis and in "S" such that Pn converges to (0, 0). (b) Find a sequence of pints Pn on the line Y = 1 and in "S" such that Pn coverges to (0, 1). (c) What points must be adjoined to "S" in order to ge

    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

    Binary Bits

    Part A: Use 2's complement to represent - 1910 (using 6 binary bits)? Part B: Use 2's complement representation to calculate 510 - 1910 (using 6 binary bits)? See attached file for full problem description.