Answer The problem is to be formulated as two integer programming problems, one for the first year and the other for the second... year. I Year Problem Total fund available = $10,000 For convenience rename the brand Petite Sirah as Brand I and brand Sauvignon Blanc as Brand II For Brand I the cost for grape is $0.80 per bottle and for Brand II the cost for grape is $0.70 per bottle. It is given that one dollar spent for promoting Brand I produce a demand for 5 bottles and one dollar spent...
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Integer Programming 9 The linear-programming models that have been discussed thus far all have been continuous,... in the sense that decision variables are allowed to be fractional. Often this is a realistic assumption. For instance, we might 3 easily produce 102 4 gallons of a divisible good such as wine. It also might be reasonable to accept a solution 1 giving an hourly production of automobiles at 58 2 if the model were based upon average hourly production, and the production had the interpretation...
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Exercises (p. 386), numbers 2-3 2. 7 cells of memory, integers, 0,7 3.int sqrt[11] int pow(x,3)[11] Hanly, Chapter 8, Self-Check Exercises... (p. 394), number 1 1.int sqrt[11] Int pow (x,3)[11] Int index =0,I; For (i=0,i<index,i++ Hanly, Chapter 8, Self-Check Exercises (p. 396), numbers 1-2 1.sqrt (xi+1-xi)pow(x,2) + (yi+1-yi)pow(y,2) 2.int LIST_SIZE[6]; Int odd; Int sum, I; For(i=0,i<=LIST_SIZE,++i) Sum=i+ odd; Hanly, Chapter 8, Programming (pp. 396-397), number 1 1. #include<stdio.h> Int main...
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Addition and Subtraction of Integers Addition of Positive Integers Consider the addition of 2 + 3. The plus sign, +,... tells us to face the positive direction. So, to evaluate 2 + 3, start at 2, face the positive direction and move 3 units forwards. This suggests that: Positive integers can be added like natural numbers. Addition of Negative Integers Consider the addition of (–2) + (–3). The plus sign, +, tells us to face the positive direction. So, to evaluate...
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iterations. 4. A loop that iterates a specific number of times. 5. Initialization, test, and increment A.W. 1. Declare Integer num... Declare Integer product = 0 While product < 100 Display “Enter a number to be multiplied by 10” Input num Set product = num * 10 Display product End While 2. Declare Integer num1 Declare Integer num2 Declare Integer sum 3. Declare String condition Do Display “Enter first number to be added” Input num1 Display “Enter second number...
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Operational Research 153 (2004) 117–135 www.elsevier.com/locate/dsw An integer programming formulation for a case study in... university timetabling S. Daskalaki b a,* , T. Birbas b, E. Housos b a Department of Engineering Sciences, University of Patras, GR-26500 Rio Patras, Greece Department of Electrical and Computer Engineering, University of Patras, GR-26500 Rio Patras, Greece Abstract A novel 0–1 integer programming formulation of the university timetabling problem is presented. The...
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2013 MTAP-DepEd Program of Excellence Mathematics Grade 1 Session 1 I. Read the following numbers. 1. 89 2. 106 3. 736... 4. 245 5. 899 6. 302 7. 720 8. 1200 9. 5075 10. 7001 II. What is the place value of each underlined digit? Give the value of each underlined digit. Give the answers orally. A B C D E F 1. 601 215 520 1,364 5,...
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Riphah International University, Faisalabad Visual Programming – Assignment 2 Functions and Control Sructures Instructions for Submission... Submission Guidelines: • Your code must be properly commented and your code should be neat and nested format. • All the steps involved in solution of each question should be written. Just Answers are not required • Try NOT to copy paste data from your friends etc. • This is an individual assignment. PLAGIARISM IS NOT ACCEPTABLE! In case of plagiarism...
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ADAMSON UNIVERSITY Bachelor of Science in Information Technology 900 San Marceline Street, Eremite, Manila 1000 Philippines Topic: 2 GUI... (Graphical User Interface) Programming Language and their Graphics Functions Title: Contrast of the Graphic Functions: GUI’s Programming Languages C++ and C Apuyan, Herchel Mae Fernandez, Neil Gabriel Gimoto, Christine Ann Santos, Allen Royce Mrs. Imelda Galo Professor Technical English Introduction The computer is most likely...
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a) Write an application that reads a non-negative integer from an input dialogue and computes and prints its factorial static void... Main(string[] args) { int i, n, fac = 1; string s; Console.WriteLine("Please enter any number to find its factorial(0 to 19):\n"); s = Console.ReadLine(); n = Int32.Parse(s); for (i = 1; i <= n; i++) { fac = fac * i; } Console...
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written as 3 separate constraints in an integer program. Answer Selected Answer: False Correct Answer: False . Question 2... 2 out of 2 points Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Answer Selected Answer: False Correct Answer: False . Question 3 2 out of 2 points If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a...
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_______ integer model, some solution values for decision variables are integer and others can be non-integer.... a. total b. 0 – 1 c. mixed d. all of the above 2. In a total integer model, some solution values for decision variables are integer and others can be non-integer. TRUE/FALSE 3. In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. TRUE/FALSE 4. If a maximization linear programming problem...
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Quantitative Methods in Business – Linear Programming 1- Statement of the Problem: Middle East for investment offers a bundle of investment... options in many types of securities. Mr. Brown, an investor, would like to invest $ 5 million in various securities. He wishes to maximize his yearly profit over the next year. The investment company offered him a portfolio including Bonds, Stocks, Gold and Land. The expected return is 6% for Bonds, 14% for Stocks, 10% for Gold and 5% for Land. For diversification...
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Declare hours as integer Declare number as integer Declare response as character Repeat Set hour = 0 Write “This... program can calculate your total hours worked” Write “Enter the number of hours worked on Monday:” Write “Enter 0 when you are done” Input number While number != 0 Set hours = hours + number Write “Enter your hours for the next day or 0 if you are done:” Input number End While Write “Your total hours worked are” + hours ...
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Febuary 11, 2013 AT&T U-verse On Demand Terrebonne Parish 6:00 p.m. In the episode of Pawn-stars 01-14 “Herd that” a lady came in with a... Manhattan Project Souvenir from 1945. The Manhattan Project was a top secret plan to develop the atomic bomb. The project required 30,000 people to complete and cost two billion dollars, or about twenty-five billion dollars in today’s money. This project was so top secret the newly elected president, who was previously vice-president, didn’t even know...
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Declare a counter variable. Declare Integer // Constant for the maximum value Constant Integer MAX_VALUE = 100 //Display the... multiples of 10 from 0 through 100 For counter = 0 to MAX_VALUE Display counter End while 4. //Declare Integer number Declare an accumulator variable Declare Integer total = 0 Declare Integer counter For counter = 1 to 10 Display “Enter a number.” Input number Set total = total + number End While Display “The total is”, total 9. Declare Integer count For count < 50 Display “The...
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Declare a counter variable. Declare Integer // Constant for the maximum value Constant Integer MAX_VALUE = 1000 //Display... the multiples of 10 from 0 through 1000 For counter = 0 to MAX_VALUE Display counter End For 4. Design a loop that asks the user to enter a number. The loop should iterate 10 times and keep a running total of the numbers entered. //Declare Integer number Declare an accumulator variable Declare Integer total = 0 Declare Integer counter For counter = 1 to 10 Display...
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Workbench 1. Design a module named timesTen. The module should accept an Integer argument. When the module is called, it should display the... product of its argument multiplied times 10. Module Main () Call timesTen Module timesTen (Integer Value) Declare integerValue Set result = value*10 Display result End Module 5. Design a module named getNumber, which uses a reference parameter variable to accept an Integer argument. The module should prompt the user to enter a number and then...
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Unit 7 Assignment 1 Steven Rogusta ITT Technical Institute PT1420 Intro to Programming Misty Kitzul November 1, 2014 Unit 1 Assignment... 1 Short Answer Why should you indent the statements in the body of a loop? It visually set them apart from the surrounding code, this makes your program easier to read and debug. Describe the difference between pretest loops and posttest loops? Pretest loop or do while loop tests its condition before performing iteration whereas a posttest loop or do until...
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Question Number 1 Points: 5.00/5.00 Question Text What event marks the line between the Old English and Middle English periods? Your Answer B. the... Norman invasion Question Number 2 Points: 0.00/5.00 Question Text What was the effect of the Norman conquest on the language of Britain? Your Answer . The upper class spoke French Question Number 3 Points: 0.00/5.00 Question Text Why is Beowulf an epic poem? Your Answer It is about a hero who represents cultural values. ...
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INDIAN INSTITUTE OF TECHNOLOGY ROORKEE EC101A: Computer Systems and Programming Spring Semester: 2010-2011 January 20, 2011... 1. Write a program program in C++ to find the square of the numbers from 1 to 10 using : (a) for loop (b) while loop (c) do-while loop The output of the program should be in the following format: Number Square ……… ……… 2. Write a program in C++ that calculates the value of π from the infinite series [pic] Print...
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whole numbers Tiny Integer [tinyint] - This field accepts integers or whole numbers with a fixed length of three (3) spaces.... Small Integer [smallint] - This field accepts integers or whole numbers with a fixed length of five (5) spaces. Integer [int] - This field accepts integers or whole numbers with a fixed length of ten (10) spaces. It also has an auto value feature that fills up the field with a value you set automatically. Big Integer [bigint] - This field accepts integers or whole numbers...
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accessing that variable. Most programs have many many modules. This makes global variables very time consuming to debug. Algorithm Workbench Review... Questions 1,5,6, and 7 from page 111 1. Design a module named timesTen. The module should accept an Integer argument. When this module is called, it should display the product of its argument multiplied by 10 1. Declare a variable called number and set the value of it 2. Call the module timesTen passing as an argument the variable number by reference...
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TECH - CSE C Programming Lab Program No: 1 Aim: To convert the temperature from Fahrenheit to Celsius. Algorithm:... www.jntuworld.com Page |1 www.jntuworld.com I.B.TECH - CSE C Programming Lab Source Code: #include main( ) { float c,f; printf(“ Enter the temperature in Fahrenheit: ”); scanf(“%f”, &f); c=(f-32)/1.8; printf(“\n The temperature in Celsius is: %f”, c); } www.jntuworld.com Page |2 www.jntuworld.com I.B.TECH - CSE C Programming Lab Page |3 ...
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and 7, page 111 (1) 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) Module main () Declare integer numBer Display “Please Enter a Number” Input numBer Call... timesTen (numBer) End Module Module timesTen (integer numXten) Declare integer answer Set answer = numXten * 10 Display , numXten ,”multiplied by 10 = “, answer End Module Unit 4 Assignment 1 Homework Jason Sims (5) 1) Module getNumber(Integer Ref value) 2) Declare integer value 3) Display “ Please Enter a Number “ 4) Input value 5) End Module (6) 1)...
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in Texas. All three items, the input, average, and printing family members from Texas will require the use of repetitive programming... statements/loops. Outputs: Average age of the family AverageAge (as a float variable) Name of family member Name (as a string variable array) Inputs: Name of family member Name (as a string variable array) Age of family member Age (as an integer variable array) State of family member State (as an string variable array) Derived Inputs: Number of family members will...
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9th element, for example, would therefore be accessed at index 8. The following program, ArrayDemo, creates an array of integers, puts some... values in it, and prints each value to standard output. class ArrayDemo { public static void main(String[] args) { // declares an array of integers int[] anArray; // allocates memory for 10 integers anArray = new int[10]; // initialize first element anArray[0] = 100; // initialize...
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In relation to computer programming explain in details the following: 1 Procedural Programming Languages A list of... instructions telling a computer, step-by-step, what to do, usually having a linear order of execution from the first statement to the second and so forth with occasional loops and branches. Procedural programming languages include C, C++, FORTRAN, Pascal, and Basic. The procedural programming language involves dividing a large program into a set of sub-procedures or subprograms...
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ENG1511Student no: 35765354 Assignment 01 Unique number: 286895 Section B: Language 1. The style of the story is informal (short direct... sentences) and detailed (explained everything to the point). 2. The tone of the sort is casual. The writer talks about his “homeboys” and back rooms. 3. “Dictionary” I. Tenant – renter, leaseholder, lessee, boarder, lodger, roomer, payer, remunerator II. Intrigue – machination, plot, secret plan, game, fascinate III....
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RESEARCH PAPER ON LINEAR PROGRAMMING Vikas Vasam ID: 100-11-5919 Faculty: Prof. Dr Goran Trajkovski CMP 561: Algorithm Analysis... VIRGINIA INTERNATIONAL UNIVERSITY Introduction: One of the section of mathematical programming is linear programming. Methods and linear programming models are widely used in the optimization of processes in all sectors of the economy: the development of the production program of the company...
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ILP Problem Formulation Ajay Kr. Dhamija (N-1/MBA PT 2006-09) Abstract Integer linear programming is a very important class... of problems, both algorithmically and combinatori- ally.Following are some of the problems in computer Science ,relevant to DRDO, where integer linear Pro- gramming can be e®ectively used to ¯nd optimum so- lutions. 1. Pattern Classi¯cation 2. Multi Class Data Classi¯cation 3. Image Contrast Enhancement Pattern Classi¯cation is being extensively used for automatic...
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Grade 12 Cluster Core Subject Mathematics Student Name Student Number Section Coverage SAT I, basic reasoning questions. 1. If 10 + x is 5 more than... 10, what is the value of 2x? (A) −5 (B) 5 (C) 10 (D) 25 (E) 50 2. If x and y are positive integers, what are all the solutions (x, y) of the equation 3x + 2y = 11? (A) (1,4) only (B) (3,1) only (C) (1,4) and (2,2) (D) (1,4) and (3,1) (E) (2,2) and (3,1) 3. When 70,000 is written as 7.0 × 10n, what is the value of n? (A) 1 (B) 2 (C) 3 (D) 4...
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previous lessons, the students had learned about positive and negative integers. Using concrete and realistic situations, the students were... able to understand the concept and were now ready to learn about adding and subtracting integers using algebra tiles. This would eventually allow the students to be able to solve simple equations, with and without the algebra tiles. However, the students were able to learn how to add integers conceptually while using the tiles first. This becomes even more important...
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Procedural programming It is technique that problem solving in “divide and conquer” method. It means program reach the complex problem step by... step and break it into separate subclasses. So, it is easy to solve the problem. Each sub classes have the connection with others. So this type of style can be active when it comes to the complex solutions. For example, if you want to calculate the month-end closing balance for a bank account, then the required steps would be as follows. First, you acquire...
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OBJECT ORIENTED PROGRAMMING CSC238 Lecture 3 – Common Algorithms Lecture 3 Objectives Common Algorithms Total T l Average Counting... Minimum value and maximum value Ranged value Unlimited l U li i d value 1 Mohd Hanapi Abdul Latif Total / Sum group of values The algorithm in this application may be used to solve sol e problem such as s ch To calculate the total of payment for N employees; To sum the amount that a customer has to pay; To calculate the total of salary that a...
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Java Problems SEQUENCE PROBLEMS: 1. Create a Java program that will print the sum of two integers. 2. Print the sum and product of three... integers. 3. Print the perimeter and area of a rectangle. 4. Given the number of a baseball team’s wins and losses, compute its winning percentage. Assume that there are no ties. 5. Input the number of a team’s wins, losses, and ties, and print its winning percentage. Assume that a tie game counts as a full game played and a half-game won. 6. Given the...
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valid: p false, q false, r true 9. Prove that the following is true for all positive integers n: n is even if and only if 3n2 8 is... even. Ans: If n is even, then n 2k. Therefore 3n2 8 3(2k)2 8 12k2 8 2(6k2 4), which is even. If n is odd, then n 2k 1. Therefore 3n2 8 3(2k 1)2 8 12k2 12k 11 2(6k2 6k 5) 1, which is odd. 10. Prove: if m and n are even integers, then mn is a multiple of 4. Ans: If m 2k and n 2l, then mn 4kl. Hence mn is a multiple...
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represented in the form p/q where p and q are integers and q is not zero. Example: 2/3, 1/10, 8/3 etc. They can be finite decimal numbers,... whole numbers, integers, fractions. Irrational numbers: A number that cannot be represented in the form p/q where p and q are integers and q is not zero. An infinite non recurring decimal is an irrational number. Example: √2, √5 , √7 and Π(pie)=3.1416. The rational numbers are classified into Integers and fractions Integers: The set of numbers on the number line...
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calculate and display a subtotal. 7. The program will calculate and display a final total for the items that are purchased. Input-Process-Output... Chart Complete the following input-process-output chart for the application using a structured programming approach. Input | Process | Output | ResponseItemNameOrNumberItemQuantityItemPrice | Get User Input | ItemTotalSubtotalItemQuantityItemPrice | ItemQuantityItemPrice | Calculate Discount Price | Subtotal | Subtotal | Calculate Sales Tax...
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Polynomials: Basic Operations An algebraic expression involving only nonnegative-integer powers of one or more variable and containing no... variable in a denominator is called a polynomial. The degree of a polynomial is the same as the degree of the term with the highest degree in the polynomial. Ex. (degree 4) (degree 5) (degree 4) 5 (zero degree) 0 (no degree) Integer Exponents If n and m are positive integers and a and b are real numbers, then The Fundamental Theorem of Arithmetic. The...
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two (usually positive) integers, also known as the greatest common factor (GCF) or highest common factor (HCF). It is named after the Greek... mathematician Euclid, who described it in Books VII and X of his Elements. The GCD of two positive integers is the largest integer that divides both of them without leaving a remainder (the GCD of two integers in general is defined in a more subtle way). In its simplest form, Euclid's algorithm starts with a pair of positive integers, and forms a new pair that...
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correspondence between the set of positive integers and that set. a. The integers greater than 10. This is countably infinite.... Starting from the first integer greater than 10, which is 11, one can infinitely count upwards since there is no boundary on the right side of the number line for this instance. The equation ƒ(x) = x + 11 can be used to show a one-to-one correspondence. x: 1, 2, 3, 4, 5, 6, … ƒ(x): 11, 12, 13, 14, 15, 16 … b. The odd negative integers. This is countably infinite. Starting from...
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in the above equations -12+13=23 02+13=13 S = {2/3, 1/3, 5/3, 17/3, 50/3} 22+13=53 42+13=173... 72+13=503 “Q8: Construct a proof that a) If m is odd, then m^2 is odd b) for all integers m and n, if m is even and n is odd, the m+n is odd” a) If m is odd, then m=2k + 1 We have to prove that m^2 is odd, so squaring the above mentioned equation we get =(2k + 1)^2 = 4k2+1+2(2k)(1) =4k2+1+4k Put in any odd value in the above...
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a negative sign (-).These numbers are sometimes called directed numbers or signed numbers. e.g. 1.2 - FUNDAMENTAL OPERATIONS ON INTEGERS... 1.2.1 – ADDITION OF INTEGERS To add integers with the same sign ,add without regard to the signs.Then affix the common sign of the integers.To add two integers with different signs ,consider the distance of each integer from zero (that is, consider the absolute value of each addend).Subtract the shorter distance from the longer distance. In the answer...
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Tamara knows that the arithmetic mean of her five quiz scores 4. is 95%. However, she has misplaced one of these quizzes. The ones she can find have... scores of 100%, 100%, 99% and 98%. What is her score on the misplaced quiz? 5. How many integers between 100 and 300 have both 11 and 8 5. as factors? 6. One-half of a road construction 6. project was completed by 6 workers in 12 days. Working at the same rate, what is the smallest number of workers needed to finish...
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tblCustomer Field Name, Data Type CustID, Long Integer CustFirst, Text CustLast, Text Phone, Text DOB, Date/Time Gender, Text Balance,... Currency ChildCap, Yes/No PlanID, Text HouseID, Long Integer HeadHH, Yes/No Allergies, Memo tblEmployee Field Name-Data Type EmpID-Long Integer EmpFirst-Text EmpMI-Text EmpLast-Text SSN-Text DOB-Date/Time StartDate-Date/Time EndDate-Date/Time Address-Text City-Text State-Text ZIP-Text JobID-Long Integer Memo-Memo Phone-Text Cell-Text Salary-Currency ...
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that term, and the degree of the polynomial is defined as the greatest exponent of x in the polynomial We express a polynomial of degree n by A0Xn +... A1Xn-1 + A2Xn-2 + ….. + An-1X + An where A’s are real constants with A0≠0, and n is a positive integer Rules Addition and subtraction of monomials can be done only if the monomials to be added are similar Similar terms or like terms are those with the same factors or same literal parts Ex. 2x2y -5x2y 1/2 x2y Like...
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division algorithm to find the HCF of 135 and 225 8. Use Euclid’s division lemma to show that the square of any positive integer is... either of the form 3m or 3m + 1 for some integer m 9. Prove that √3 is irrational. 10. Show that 5 – √3 is irrational 11. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. 12. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march...
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question paper. Each question carries 5 marks. • Answer all questions. • Time allotted: 2 hours. QUESTIONS 1. What is the smallest positive... integer k such that k(33 + 43 + 53 ) = an for some positive integers a and n, with n > 1? n √ 2. Let Sn = k=0 1 √ . What is the value of k+1+ k 99 1 ? n=1 Sn + Sn−1 3. It is given that the equation x2 + ax + 20 = 0 has integer roots. What is the sum of all possible values of a? 4. Three points X, Y, Z are on a striaght line such that XY = 10 and XZ = 3. What...
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of three consecutive integers is 126. x + (x + 1) + (x + 2) = 126 let x represent the first integer... x + 1 will represent the second integer, x + 2 will represent the third integer (The above can be thought of in the following way: an example of 3 consecutive integers would be 5,6,7. If 5 is the first integer, then what operation do you do to get to the next number - add one) 13) The sum of three consecutive odd integers is 123. x + (x +...
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for prime triplets * Continue till all Prime Triplets are printed Question 2: A unique digit integer is a positive... integer (without leading zeros) with no duplicate digits. For example 7, 135, 214 are all unique digit integers whereas 33, 3121, 300 are not. Given two positive integers m and n, where m<n, write a program to determine how many unique digit integers are there in the range between m and n (both inclusive) and output them. Algorithm: * Start * To input...
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primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. This theoremrequires... excluding 1 as a prime. ------------------------------------------------- Number theory Number theory is a branch of pure mathematics devoted primarily to the study of theintegers. Number theorists study prime numbers (which, when multiplied, give all the integers) as well as the properties of objects made out of integers (such as rational numbers) or...
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The second is a list of operations. For each class, select the operations that make sense for object in class. Discuss the behavior of each operation listed... for each class Classes variable length array-ordered collection of objects, indexed by integer , whose size can vary at run time Symbol Table- a table that maps text keywords into description Set-unordered collection of objects with no duplicates Operations Append---add an object to the end of collection Copy---make a copy of a...
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_____________. (Points : 6) Sizes Numbers Integers Subscripts None of the above | 4. Which is the... simplest search technique to use to find an item in an array? (Points : 7) Sequential Binary Bubble Select None of the above | 5. Which of the following arguments must be passed when passing an array as an argument? (Points : 6) The array itself An integer that specifies the number of elements in the array The...
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Number Theory Numbers have the ability to be grouped together in many different ways to form arithmetic. Arithmetic uses all types of numbers from... natural numbers, integers, rational numbers, and irrational numbers to form different types of equations. These equations and the numbers being used in them make up the number theory. The number theory goes back to the first discoveries of ancient number systems, and the beginnings of early mathematics. The number theory also deals with the number’s...
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include negative numbers; does not include fraction (such as 6/7 or 9/7); does not include decimals (such as 0.87 or 1.9) Whole numbers : The numbers {0,... 1, 2, 3, ...} There is no fractional or decimal part; and no negatives: 5, 49 and 980. Integers : Include the negative numbers AND the whole numbers. Example: {..., -3, -2, -1, 0, 1, 2, 3, ...} Rational numbers: It can be written as a fraction. For example: If a is 3 and b is 2, then: a/b = 3/2 = 1.5 is a rational number 2. Give examples...
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RATIONAL NUMBERS In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with... the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q it was thus named in 1895 byPeano after quoziente, Italian for "quotient". The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the...
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value assigned to an alphabet letter is 26. Therefore, using modular arithmetic is really helpful in this case. As the definition of modular arithmetic, for... a positive integer m, two integers a and b are said to be congruent modulo n, written as , if and only if their difference is an integer multiple of n. Therefore, for any integer , and the positive remainder of the division of by 26 are congruent modulo 26. For example, and . Applied the modular arithmetic, the matrix product can be rewritten...
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first line contains an integer T. The number of test cases.For each test case the first line contains the last page number N.The second line... contains the number of rooms R from which Bob collected the pages. The following R lines contains an integer P followed by P integers. Output The total number of pages missing.Print the answer for each test case in a seperate line. Constraints :1<=T<=100 1<=N<=500 1<=R<=10 0<=P<= (N/2) Each of the P integers will contain the page...
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Unit 2: Checklist Higher tier (43602H) recognise integers as positive or negative whole numbers, including zero work out the answer to a... calculation given the answer to a related calculation multiply and divide integers, limited to 3-digit by 2-digit calculations multiply and divide decimals, limited to multiplying by a single digit integer, for example 0.6 × 3 or 0.8 ÷ 2 or 0.32 × 5 or limited to multiplying or dividing by a decimal to one significant figure, for example 0.84 × 0.2 or 6.5 ÷ 0...
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