Question: Suppose there are n people in a group, each aware of a scandal no one else in the group knows about. These people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. For example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals. The gossip problem asks for G(n), the minimum number of telephone calls that are needed for all n people to learn about all the scandals. a). Find G(1), G(2), G(3), and G(4). b). Use mathematical induction to prove that G(n) 4. [Hint: In the inductive step, have a new person call a particular person at the start and at the end.] c). Prove that G(n)= 2n – 4 for n> 4.

Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X B

Al Watan supermarket has hire-purchases scheme for locals and expats. The customers will get the credit facility if they satisfy any of the following conditions: The customer must hold the present job for more than 5 years and reside in the same place at least for 3 years. In this case, the customer will get credit upto rupees 300 omr. The monthly salary of the customer must exceed 1000 omr and must hold the present job for more than 5 years. In this case credit will be given upto rupees 500 omr. The monthly salary must exceed 1000 omr and reside at the same place at least for 3 years. In this case credit will be given upto 500 omr. In the case, the customer’s monthly salary exceeds 1000 omr, holds the present job for more than 5 years and also reside in the same place at least for the 3 years, the credit facility will be upto 1000 omr The credit facility is rejected for all other customers. Prepare a Decision Table for this hire- purchase scheme

This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".

Suppose that the grading of x University courses is as follows:• Each student can get grades between 0 and 100.• If the student's grade is less than 40, the student is informed that the course failed (Unsuccessful).• If the student's grade is higher than 40,o The difference between the student's current grade and the number that is a multiple of 5 higher than the closest to his / her grade is less than 3.If it is lower, the student's grade is equal to the 5 fold higher than the closest one.o If the difference is 3 or more than 3, no change is made in the grade of the student.In this context, the updated grades of the students are calculated according to the entered student gradesWrite the Java code showing.Solve this question in c ++ language.ü Define the section to be calculated as Java object ("Question1").ü Question1; Take the note string as input.public Question1 (int [] input)ü Print out the updated notes as a series after the calculation is madeo public int [] gradingStudents…

Suppose that the grading of x University courses is as follows:• Each student can get grades between 0 and 100.• If the student's grade is less than 40, the student is informed that the course failed (Unsuccessful).• If the student's grade is higher than 40,o The difference between the student's current grade and the number that is a multiple of 5 higher than the closest to his / her grade is less than 3.If it is lower, the student's grade is equal to the 5 fold higher than the closest one.o If the difference is 3 or more than 3, no change is made in the grade of the student.In this context, the updated grades of the students are calculated according to the entered student gradesWrite the Java code showing.ü Define the section to be calculated as Java object ("Question1").ü Question1; Take the note string as input.public Question1 (int [] input)ü Print out the updated notes as a series after the calculation is madeo public int [] gradingStudents ()Code sample:public class Question1…

The Mayfree Appliance Company requires sheet metal for its appliances. The company can purchase long coils of sheet metal in two different widths: 65 inches and 40 inches. The company must purchase the coils by linear foot of length: $1.20 per foot for a 64-inch coil and $1.00 per foot for a 40-inch coil. (This implies that a square foot, say, of the wider coil is less expensive.) Up to 4000 feet of the 65-inch coil is available, and up to 6000 feet of the 40-inch coil is available. There are manufacturing requirements for six different widths: 50, 45, 40, 35, 20, and 10 inches. Mayfree’s requirements are expressed as lengths of the various widths. The company requires 1000 feet of 50-inch width, 2500 feet of 45-inch width, 3000 feet of 40-inch width, 2300 feet of 35-inch width, 1300 feet of 20-inch width, and 2000 feet of 10-inch width. Determine how much of each width coil Mayfree should purchase and how it should cut the coils into various widths to meet its requirements at minimal…

The public utilities commission has decided that the electric company overcharged its customers for two months last year. To make up the difference to the customers, the commission orders the company to decrease each of the next month’s bills by 10%. The city also levies a 3%utility tax, which is to be applied to the bill before it is discounted. Also, the10% discount does not apply to the utility tax. Assume electricity costs $0.16per kilowatt-hour. Write a program to compute the next month’s electricity bill given the number of kilowatt-hours consumed as input

A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below. Bulldozer/ A B C D Site Students 1 90 75 75 80 solve it 2 35 85 55 65 yourself 3 125 95 90 105 4 45 110 95 115 How should the bulldozers be moved to the construction sites in order to minimize the total distance traveled?