Teacher Scheduling Every semester the chairman of the CSSE department must assign faculty to teach the classes for the next quarter using the following information: • The list of courses and the number of sections that must be taught, along with their scheduled time slots. A course along with a time slot defines a possible section. Multiple sections of a course can be in the same time slot. E. g. 349-01 and 349-03 could both be MWF 10:00 a. m. or they might be in different time slots The list of faculty members along with each faculty member's time slot availability. That is, a faculty member may only be available for a certain subset of all the time slots. E. g. Mary may only be able to teach courses on MWF in the morning. Bill is only able to teach on TTH afternoons. • For each faculty member there is a list of courses that the faculty member is qualified to teach. In order for the schedule to be feasible there must find an assignment of faculty to sections subject to the following requirements: • Each faculty member is assigned to teach exactly two sections when the faculty member is available. The two sections assigned to a faculty member must be in different time slots • Each faculty member is assigned to teach only courses they are qualified to teach. Design a network flow model that will allow the department chairman to find a feasible schedule to this problem, or identify that no feasible schedule exists. Be sure to describe: • What each node, edges, and edge capacities represent in the network, • How to determine the assignment of faculty to sections that a given flow in your graph would represent. • How to know whether all the sections are covered - have a faculty member assigned to teach them.

George has seven boxes of five pencils. giulio three boxes of eight pencils. one of the boys arranges all his pencils equally into two groups. was this george or giulio how many are in each group explain

Complete the worksheet. use 3.14 for π and round all decimals to the nearest hundredth.find the volume of the composite three-dimensional figure above. important terms are written in bold.1. the pyramid has a square base that is inscribed in the circular base of the cone. draw an image of the composite shape of the base. 2. if the side length of the square base is 8 units long, what is the diameter of the circular base of the cone from the picture in number 1? 3. now that the diameter has been calculated, what is the circular area of the cone? ignore the square base of the pyramid.? 4. what is the formula for volume of a cone? 5.to calculate the volume of the cone, the height is still needed. if the cone has a lateral surface with a length of 13 units, what is the height of the cone? 6.now find the volume of the cone. do not include the empty space for the pyramid. 7.. the side length of the square base of the pyramid is 8 units long. what is the base area of the pyramid? 8.what is the formula for the volume of a pyramid9. since the cone and the pyramid share the same vertex, what is the volume of the pyramid10.using the volume of the cone and the pyramid, find the volume of the composite shape. remember, the pyramid is empty. 11,. referring to the picture in number 1, what is the area of the composite base knowing that the square is empty? 12what is the formula to find the lateral surface area of a cone? (13find the lateral surface area of the cone14what is the lateral surface area shape of the pyramid? what is the formula for its area? 15to find the lateral surface area of the pyramid the length is still needed. calculate the lateral surface length of the pyramid. 16 now that the lateral surface length is known, what is the lateral surface area of the pyramid17. using the lateral surface areas of the cone and pyramid, along with the area of the composite base, what is the total surface area?

Acollege student takes out a $7500 loan from a bank. what will the balance of the loan be after one year(assuming the student has not made any payments yet) a. if bank charges 3.8% interest each year ?