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Discrete Structures

Expected Value: Discrete Structures

See the attached file. 1. How many bit strings of length ten contain either at least five consecutive 0's or at least five consecutive 1's? explain 2. Which is more likely: rolling a total of 8 when two dice are rolled, or rolling a total of 8 when three dice are rolled? explain 3. Three fair dice are rolled.Let X be th

Euclidean algorithm .

1. Use the Euclidean algorithm to find a) gcd(100, 101) 2. gcd(123, 277) 3. gcd(1529, 14039) 2. consider congruence x^2 ≡ 16 (mod 105) for integer x a. Give one sample solution of the congruence in the range 0≤x≤104 that is different from 4 and also from 101 b. Find the number of solutions of ths congru

Grades

At a particular University students must receive one of the following grades: A, B, C, D and F. What is the minimum number of students required in a course to ensure that at least 8 will receive the same grade?

Discrete Mathematics: Graphs and Relations

Question for 8.1: Let G be a simple graph. Show that the relation R on the set of vertices of G such that uRv if and only if there is an edge associated to {u,v} is a symmetric, irreflexive relation on G. Question for 8.2: Show that a simple graph with at least two vertices there must be 2 vertices that have the same de

Mean, Median, Standard Deviation of Birth Rates

The National Center for Health Statistics maintains a website at: http://www.cdc.gov/nchs. Under the section labeled Tabulated State Data, click on Births. Go to that page and locate the table "Live Births by Race and Hispanic Origin of Mother: U.S., Each State, Puerto Rico, Virgin Islands, and Guam." Suppose you are interested

Statistics: 5 numbers summary

A psychologist interested in political behavior measured the square footage of the desks in the official office of four US governors and of four chief executive officers (CEOs) of major US corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, and 36 square feet

Calculating Normal and Standard Time

In a time supply study at a producer of LCD televisions, a worker assembled 20 units in 100 minutes. The time study analyst rated the worker a performance of 110 percent. An allowance for personnel time and fatigue is 15 percent. What are the normal time and standard time?

Calculating the Standard Quantity in Kilograms

Mayall Corporation is developing standards for its products. Each unit of output of the product requires 0.92 kilogram of a particular input. The allowance for waste and spoilage is 0.02 kilogram of this input for each unit of output. The allowance for rejects is 0.11 kilogram of this input for each unit of output. The standard

The standard price per kilogram of this input

Persechino Corporation is developing standards for its products. One product requires an input that is purchased for $82.00 per kilogram from the supplier. By paying cash, the company gets a discount of 2% off this purchase price. Shipping costs from the supplier's warehouse amount to $6.55 per kilogram. Receiving costs are $0.4

Mean Absolute Deviation..

See attachment I need help with b and c 6. The following table shows statistics for two college basketball teams. Central College Western College Mean points per game 89 89 Mean absolute deviation (MAD)

Setting standards: Preparing a Standard Cost Card

Svenska Pharmicia, a Swedish pharmaceutical company, makes an anticoagulant drug. The main ingredient in the drug is a raw material called Alpha SR40. Information concering the purchase and use of Alpha SR40 follows: Purchase of Alpha SR40: The raw material Alpha SR40 is purchased in 2-kilogram containers at a cost of 3,000 K

Matrices: Operation and Inverse

Perform the given operation for the following zero-one matrices: 1 0 1 1 1 1 0 0 = 0 1 0 1 1 1 1 Show that 2 3 -1 1 2 1 -1 -1 3 is the inverse of 7 -8 5 -4 5 -3 1 -1 1

Combinatories and Tree Diagram

5 coins are tossed a)in how many ways will the first coin turn up heads and the last coin turn up tails b)draw a tree diagram to illustrate the different possibilities c)in hoe many ways will the 2nd , 3rd, and 4th coins all turn heads d)would the same possibilities arise if one coin is tossed 5 times in succession. 2)Det

Discrete structures in mathematics and computer science

Q1) Use the standard logical equivalences to simplify the expression (ㄱp ^ q) v ㄱ(pVq) Q2) consider the following theorem "The square of every odd natural number is again an odd number" What is the hypothesis of the theorem? what is the conclusion? give a direct proof of the theorem. Q3) consider the follo

Standard deviation for height means

Men's height are normally distributed with mean 69.0 ins. and standard deviation 2.8 in women 's heights are normally distributed with mean 63.6 ins and standard deviation 2.5 ins. 1. the standard doorway height is 80 in. a. what percentage of men are too tall to fit through a doorway without bending , and what pe

Combinatorial Mathematics - Puzzle

In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants. No students shook hands with their own partners. After the fair, the students discussed the proje

Mean, Median, Mode and Standard Deviaton

1. Suppose you have administered a test of manual dexterity to two groups of 10 semi-skilled workers. one of these two groups of workers will be employed by you to work in a ware house with many fragile items. the higher the manual dexterity of a worker the less likelyhood that worker wil break significant inventory.Because of a

Data Distributions and Standard Deviation

In this Unit, you studied several measures of central tendency. By far the most frequently utilized of these measures is the mean of a population. Remember that the source of the data that you want to analyze always comes from what is called a population. If you are interested in the average high temperature in your area for the

Discrete Math : Logic (40 MC Problems)

1. Identify the rule of inference used in the following: If it rains today, the flood gates will open. The flood gates did not open today. Therefore, it did not rain. a. modus tollens b. hypothetical syllogism c. modus ponens d. disjunctive syllogism 2. Identify the rule of inference used in the following: If I work all

Discrete Structures Questions

1. By using the Pigeonhole Principle, we can show that if you take six classes in a term and classes do not meet on the weekend, then at least three of the classes must meet on the same day. True False 2. By using the Pigeonhole Principle, it can be shown that if you are paid bi-weekly (every two weeks) duri

mod-5 and Boolean Functions

1) If f is the mod-5 function, compute each of the following. a) f(17) b) f(48) c) f(169) 3) Convert (1011101)2 to base 16 (i.e., hex) 4) Find the sum of products expansion of this Boolean function F(x,y) that equals 1 if and only if x = 1. Note: one can write out the phrase "y complement" to represent the notation f

RSA encryptions

(See attached file for full problem description) --- Consider the RSA encryption system given by p=43,q=59, and e=13 i) Find d such that ed ≡ 1 (mod (p-1)(q-1)) ii) Decode the message : 1552 2069 1178 1637 1975 Using the convention A = 00, B = 01, ..., Z = 25 ---

Big O notation

I) Show that x^3 is O(x^4) but x^4 is not O(x^3) ii)Show that xlnx is O(x^2) but x^2 is not O(xlnx) iii)Show that a^x O(b^x) but b^x is not O(a^x) if 0 < a < b (0 = zero) iv)Show that 1^k + 2^k+...+n^k is O(n^(k+1)) for every positive integer k

Formula - Several Problems

(See attached file for full problem description with proper symbols) --- 2. Let f(x) = x2 +1 and g(x) = {x+1, x> =3; x-1, x<3 so both f and g map R into Find the formula for a. (f+g)(x) b. (f .g)(x) c. (f o g)(x) d. (g o f)(x) 3. Let A = {a,b,c,d} and B = {1,2,3} and let f : A &#61664; B be a function . Let g : Z

Discrete structures located

We worked on the attached problems today in class I am now trying to work through them again for understanding and I am not getting very far. My skills in discrete mathematics are not such that I can work through these on my own effectively. 3. Seven points are located in a plane. List the possible numbers of lines determi

Discrete Structures : Sequences, Subsequences and Remainders

1. How do I prove that in a group of n people there are two people with the same number of acquaintances within the group? 2. Prove that given a sequence of twelve integers, a1, a2, ...,a12, there is a subsequence aj, aj+1, ..., ak where 12 divides &#8721;kn= aa n. 3. A scrape of paper is found in an old desk that read: