...Concept 1: (Functions) Functions can be taken as a relation of input against the output, so the function of x is dependent on the number included in the operation. Estimated time of arrival (ETA) can be a function. For example, riding a bicycle may consume 45 minutes; an equation can be formulated that will show that the person begins riding the bicycle at x-time. For instance 8:00 in the morning, that person will be able to arrive at their destination exactly at 8:00 plus 45 minutes. The following equation would be useful where x=time of departure f (x)= x+45 Concept 2: (Relations) Relations, in mathematics are defined as the set or group of ordered pairs. Lets say that there are 15 students in the room and a test containing 50 questions. Every student is given a particular number to acknowledge or distinguish each like 1,2,3, 4 and so on. The second set of number includes the test scores of each student. For example: 1 =40 The first number stands for the first student and the second number stands for the grade 4 = 30 Describes that the fourth student got 30 points from the test Concept 3: (Linear Equations) All of us can use the linear equations using various settings in every day life. For example, a date at the movies may consist of the following. Patron (A) consumed nachos and 2 bottles of water totaling $3.75; Patron (B) bought hotdogs and a Gatorade for three dollars. If another patron is watching the movie and is curious about the cost of food, then...
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...Practice Test: Ordered Pairs the Satisfy Equations in 2 Variables Decide whether or not the ordered pair is a solution to the equation. 1) x + y = 9; (4, 5) 2) x + y = 8; (4, 3) 3) x - y = 25; (5, 2) 4) 2x + y = 8; (2, 4) Complete the ordered pair so that each is a solution to the given equation. Give your answer as an ordered pair. 5) y = -x - 7 6) y = 2x - 5 (-6, ) (-6, ) 5) 6) 7) 8) 1) 2) 3) 4) 7) 2x + y = -9 ( , -1) 8) 4x + y = -19 ( , 5) Find the missing coordinate to complete the ordered pair. Give your answer as an ordered pair. 9) y = -x (16, ) (4, ) (-3, ) 1, 2 9) 10) 11) 12) 10) y = -x - 3 11) y = 3x - 6 12) 40x + 6y = 16 13) 6x + 1 y = 25 ( , 16) 2 13) 14) 4x + y = -13 ( , 7) 14) 1 15) 4x + y = -8 ( , 8) 16) 9x + y = -78 (0, ) Complete the ordered pairs so that each is a solution to the given equation. 17) x + y = 6 (2, ), (6, ), (0, ) 18) x + y = -6 Solve the problem. 19) If (a, 3) is a solution of the equation y = 2x - 5, what is a? 20) If (3, b) is a solution of the equation 3x - 2y = 17, what is b? 21) Suppose the sales of a particular brand of appliance satisfy the linear model y = 100x + 2300, where y represents the number of sales in year x, with x = 0 corresponding to 1982, with x = 1 corresponding to 1983, etc. Find the number of sales in 1999. 22) The linear model C = 600x + 30,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this, how much does it cost to produce 900 items...
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...Finals: Relations A relation is something that relates one set of values to another set of values. Sometimes the relationship that is specified between sets is meaningful, other times it is not. a relation is represented by a set of ordered pairs If A= {1,2,3}, then a relation R, from A to B might be, for example, R1={(a,2),(a,3),(b,2)}. The first element in each ordered pair comes from set A, and the second element in each ordered pair comes from set B. If we want to describe a relationship between elements of two sets A and B, we can use ordered pairs with their first element taken from A and their second taken from B. Since this is relation between two sets. A binary relation from A to B is a subset of A B. In other words, binary relation R we have RT A B. We use the notation aRb to denote that (a,b) TR and aRb to denote that (a,b)TR. When (a,b) belongs to R, a is said to be related to b by R. Example: Let P be set of people, C be a set of cars, and D be the relation describing which person drives which car(s). P = {Carl,Suzanne,Peter,Carla}, C = {Mercedes,BMW,tricycle} D = {(Carl,Mercedes),(Suzanne,Mercedes),(Suzanne,BMW),(Peter,tricycle)}, This means that Carl drives a Mercedes,Suzanne drives a Mercedes and BMW, Peter drives a tricycle, and Carla does not drive any of these vehicles. Let A and B be sets. A binary relation R is a subset of A X B. Example: Let A be the students in the CS major A={stud1,stud2,stud3} Let B be the courses the department offers B={CS101...
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...Lesson 22 Given below is a table of inputs, outputs, and ordered pairs for the function ( ) = 2 , as well as its graph. Inputs Outputs −2 −1 0 1 2 ( ) (−2) = 4 (−1) = 1 (0) = 0 (1) = 1 (2) = 4 Ordered Pairs (, ( )) (−2, 4) (−1, 1) (0, 0) (1, 1) (2, 4) I have plotted the ordered pairs above in the graph below. Function f 1 Example 1: Use the function on the previous page, its table, and its graph to answer the following: a. How can the function ( ) = 2 + 2 be written in terms of the function ? ( ) = ( ) + 2 b. Is the new function changing the inputs or the outputs of the original function ? It is changing the ‘outputs’. c. Make a table and graph the function . (Keep the same input values as function f on previous page.) Plot the points for function g from the table. The graph will be ‘shifted up’ 2 units from the graph of f g(x) as seen below. Inputs -2 -1 0 1 2 Outputs ( ) 6 3 2 3 6 How has function f been transformed to create function g? It has been shifted vertically upward 2 units. d. How can the function ℎ( ) = 2 − 2 be written in terms of the function ? ℎ( ) = ( ) − 2 e. Is the new function ℎ changing the inputs or the outputs of the original function ? It is changing the ‘outputs’. f. Make a table and graph the function ℎ. (Keep the same input values.) Plot these points on the graph at the right. The new graph will be ‘shifted down’ 2 units from the original...
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...assignment is to show the relation between the 2 sets of data, with the correspondences based on which players are or were a member of which teams. We are to show the relation in both a set of ordered pairs, and as a directional graph. Set D has the Jets, the Giants, the Cowboys, the 49ers, the Patriots, the Rams, and the Chiefs. Set Q has Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning. The first step is to assign a domain and range. For the first task D is the domain and Q is the range. The Set of ordered pairs of the domain and range would look like the following: {(Patriots, Tom Brady), (Jets, Joe Namath), (Cowboys, Troy Aikman), (49ers, Joe Montana), (Giants, Eli Manning), (Rams, Joe Namath), (Chiefs, Joe Montana)}. The graph of these sets is on the next page. The direction graph of this set would look like the following: Part two asks to explain if the relation is or is not a function. This relation would be identified as a function. It is a function because each x value, which is the domain, has only one y value, which is the range. In regards to the example/ at hand, each team only had the one player. Part three asks to swap the domain and range used earlier and to show it again in a set of ordered pairs, and as a directional graph. The Set of ordered pairs of the domain and range would look like the following: {(Tom Brady, Patriots), (Joe Namath, Jets), (Troy Aikman, Cowboys), (Joe Montana, 49ers), (Eli Manning, Giants), (Joe Namath, Rams), (Joe...
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...sets of data that list football teams and quarterbacks: D = {Jets, Giants, Cowboys, 49’ers, Patriots, Rams, Chiefs} Q = {Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning} 1. Using D as the domain and Q as the range, show the relation between the 2 sets, with the correspondences based on which players are (or were) a member of which team(s). (You can usehttp://www.pro-football-reference.com to find out this information). Show the relation in the following forms: * Set of ordered pairs (Jets, Namath) (Giants, Manning) (Cowboys, Aikman) (49ers, Montana) (Chiefs, Montana) (Patriots, Brady) 2. The relation is a function, no one element of the domain matches no more than one element of the range. * Directional graph Jets Namath Giants Manning Cowboys Aiken 49er’s Montana Chiefs Montana Patriot’s Brady 3. Now, use set Q as the domain, and set D as the range. Show the relation in the following forms: * Set of ordered pairs (Namath, Jets), (Manning, Giants), (Aiken, Cowboys), (Montana, 49er’s), (Montana, Chiefs), (Brady, Patriots) 4. The relation is not a function, one element of the domain matches with two elements of the range. ( Montana, Chief’s & 49er’s) * Directional graph Namath Jet’s Manning Giant’s Aiken Cowboy’s Montana 49er’s Montana Chief’s Brady Patriot’s Part 2 Mathematical sequences can be used to model real life applications. Suppose you want to construct a movie theater...
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...1) Create and justify a relation that represents a function with the given range. Write your answers as ordered pairs. a) { (0 , 11) , (1 , 20) , (2 , 34) , (3 , 41) } this is because no value is same for the order pairs in x values b)Create and justify a relation that does not represent a function with the given range. Write your answers as ordered pairs. { (0 , 11) , (0 , 20) , (2 , 34) , (3 , 41) } this is the case since the values of X in the first two cases are similar hence making it not be a function 2) Find the equation of the line in the graph, and mathematically model the scenario using function notation where cost is a function of number of minutes. We start by calculating the slope m = (40 - 20)/(400 - 0) m = 20/400 m = 2/40 m = 1/20 the form of the equation is given as; y = mx + b where m is the slope hence m = 1/20 , (0 , 20) y = (1/20)x + 20 3) A textbook company keeps track of its daily cost for printing whole textbooks to different schools, but can only print up to 500 books a day. The daily cost (C) to print x number of textbooks is given by C(x) = 3.50x + 1200. A. a) Using the function, determine one possible daily cost by evaluating the function for any input of your choice with four text books as x = 4, the cost is : C(4) = 3.50 * 4 + 1200 C(4) = 14 + 1200 C(4) = $ 1214 b) For what value of x does C(x) = 1900 C(x) = 3.50x + 1200 when C(x) = 1900 1900 = 3.50x + 1200 1900 - 1200 = 3.50x 700 = 3.50x 700/3.5 = x 200 books =...
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...Module-Four-Test-Part-1-GEM Click Link Below To Buy: http://hwcampus.com/shop/module-four-test-part-1-gem/ Question 1 (4 points) Simplify. (4 points) Question 1 options: 1) 2) 3) 4) 7 Save Question 2 (4 points) Evaluate. (4 points) Question 2 options: 1) 2) 3) 4) Save Question 3 (4 points) What is the exact value for the expression - + ? Simplify if possible. (4 points) Question 3 options: 1) 2) 3) 4) Save Question 4 (3 points) What is the product of 6 • 2 ? Simplify if possible. (3 points) Question 4 options: 1) 8 2) 12 3) 12 4) 84 Save Question 5 (3 points) The function f(x) = (1.008735)12x models the monthly interest that a bank offers to Dan after x years. Dan converts the function to have x isolated in the exponent. What is the approximate rate of growth? (3 points) Question 5 options: 1) 11% 2) 12% 3) 13% 4) 14% Save Question 6 (4 points) The function below shows the number of students of a school who enrolled for yoga classes. Let f(x) represent the total number of students who enrolled for the classes after x years: f(x) = 15(1.23)x The average rate of change in the number of students who enrolled for yoga classes from the third to the fifth year is ________students per year. Round your answer to the nearest whole number...
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...Assignments for Math 221, Discrete Structures J. Stanley Warford April 5, 2013 Assignment 1 1. 2. 3. 4. 5. Study Section 12.2. Do Exercises 12.4(b, e). Do Exercise 12.8. Math 221, Discrete Structures Do Exercise 12.9. In your induction case, you should start with (n + 1)2 and use the result from Exercise 12.8. Do Exercise 12.10. i is divisible by 3 means that i = 3k for some integer k. You may use the fact that the sum of two expressions, each one divisible by 3, is also divisible by 3. 1 Assignment 2 1. 2. 3. 4. Study Section 12.5. Do Exercise 12.5. Do Exercise 12.14. Math 221, Discrete Structures Prove (12.16.1). There are two base cases, one for n = 1 and one for n = 2. For the induction case, there are two inductive hypotheses–one with n − 1 and one with n. You can assume both of them to prove the case for n + 1. Start with the RHS, use (12.14), then the inductive hypotheses. Prove (12.35a). The base case is n = 1. Prove (12.35b). The base case is n = 1. 5. 6. 1 Assignment 3 1. 2. Study Section 10.1. Math 221, Discrete Structures Do Exercise 10.1(a, b, c, d, e, g). For 10.1(d), you will need an implication in the body of a universal quantification. For 10.1(g), it is easiest to translate “It is not the case that” as ¬. 1 Assignment 4 1. Do Exercise 10.1(h, i, j, k, l, m). For 10.1(h) and (l), you will need an implication with the ∈ symbol. For 10.1(m), you will need to quantify with Σ with a body of 1. Do Exercise 10.3. Math...
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...Chapter 5 Case Project Assignment for Chapter 5 In this assignment, use your problem-solving skills and information presented in this chapter to answer the following real-life scenario. Make sure to address all of the questions posed in the following Case Project. You have been asked to design the entire cabling system for a medical instrument manufacturer’s new warehouse. The company already has three buildings, each 1/2 a mile apart, and the warehouse, 2 miles away, will be its fourth building. Currently, the buildings run on separate networks, but the company wants to be able to exchange data among them. For example, the Quality Control Department in Building 1 would like to be able to access servers in the Research Department in Building 2. In addition, the Sales Department in Building 3 wants to conduct video training for its representatives in the field via the Internet. What kind of transmission media would you recommend for inside each different building and department of the medical instrument company and why? What type of media would you recommend using to connect the buildings together and why? Finally, what kind of media should the company use for connecting the corporate WAN to its ISP and ultimately, the Internet? NOTE: The above assignment needs to be turned in as a single Microsoft Word file containing only your answer to the Case Project for Chapter 5. This assignment is turned in using the Assignment Submission for this project found on the Moodle page...
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...Chapter 1: Introduction to Computer Networks and Data Communications TRUE/FALSE 1. Data is information that has been translated into a form that is more conducive to storage, transmission, and calculation. ANS: T 2. ANS: F PTS: 1 Some people call computer terminals thick-client workstations. PTS: 1 3. A type of microcomputer-to-local area network connection that is growing in popularity is the wireless connection. ANS: T PTS: 1 4. To communicate with the Internet using a dial-up modem, a user’s computer must connect to another computer that is already communicating with the Internet. ANS: T PTS: 1 5. It is not possible to connect two local area networks so that they can share peripherals as well as software. ANS: F PTS: 1 6. Metropolitan area networks can transfer data at fast, LAN speeds but over smaller geographic regions than typically associated with a local area network. ANS: F 7. ANS: T 8. networks. ANS: T 9. ANS: F PTS: 1 The Internet is not a single network but a collection of thousands of networks. PTS: 1 One of the most explosive areas of growth in recent years has been cellular phone PTS: 1 By the 1970s, telephone systems carried more computer data than voice. PTS: 1 10. Network architectures are cohesive layers of protocols defining a set of communication services. ANS: T PTS: 1 11. The OSI model tells us what kind of wire or what kind of connector to use to connect the pieces of a network...
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...Networking-Assignment 1-Outline Assignment 1: The Benefits of Twisted Pair Cable You are a recently hired consultant for a NCF, the Networking Consulting Firm, and your first consulting assignment is at Ocper, Inc. Upon arriving at the client, you learn from the president that there is no one dedicated to information technology or networking on the staff and there are 20 Windows peer-to-peer client computers all connected via coax cabling. The president also indicates that the company plans to double in size over the next two years, but she is weary of drastically changing the computing environment. Write a 2-3 page paper in which you: • Describe what changes you would suggest in terms of the current network type / structure and how you would lay out the benefits of the changes you recommend. • Describe why you would suggest connecting all current and new client computers using twisted pair cable instead of staying with the current coax wiring structure. • Discuss the possibility of using fiber optic cable instead of either twisted pair cable or staying with the existing coax wiring structure. • Research the costs involved with making these changes to the network (not including the cost for buying more computers) and determine whether or not there is a cost benefit. Your assignment must: Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; references must follow APA or school-specific format. Check with...
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...The Benefits of Twisted Pair Cable Introduction to Networking October 29, 2013 Ocper Inc. is a small company that has no one dedicated to information technology or networking on the staff, and there are 20 Windows peer-to-peer client computers all connected via coax cabling. The president has indicated that the company plans to double in size over the next two years, but she is weary of drastically changing the computing environment. This is my first assignment, but I feel that I have a very good plan to help give them a faster, more secure, and efficient network. The first change that I would recommend would be to move away from a peer-to-peer network to a client/server network. I would explain that there are many advantages to switching to a client/server network such as (Dean, 2009): * User logon accounts and passwords for anyone on a server-based network can be assigned in one place. * Access to multiple shared resources (such as data files or printers) can be centrally granted to a single user or groups of users. * Problems on the network can be monitored, diagnosed, and often fixed from one location. * Servers are optimized to handle heavy processing loads and dedicated to handling requests from clients, enabling faster response time. * Because of their efficient processing and larger disk storage, servers can connect more than a handful of computers on a network. The advantages of a client/server far outweigh any possible disadvantages. ...
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...select two backbone configurations and discuss which one you think is the better option for networks of today. Indicate why you think that planning an enterprise-level backbone can be such a challenging process. I think before going into details, we should understand what is backbone. After a lot of research, I came up this definition; a backbone is a means of connecting two or more LANs. It provides a transmission channel for packets being transmitted from one LAN to another. After connection to a backbone, a LAN may remain distinct or be merged with another. Backbone networks can be applied to a single building environment as well as to campus environments, where the backbone is used to connect LANs in different buildings. Parallel backbone: I think parallel back is the best worth it for any company. The additional cost of setting up a parallel backbone can be well worth the money. The design of this type of backbone consists of using two cables routed between the routers and switches. While there are additional initial costs of installing a parallel backbone, the benefits can quickly outweigh these costs. However if company wants to save some money, they can use distribute network. It consists of a number of connectivity devices connected to a series of central connectivity devices, such as hubs, switches, or routers, in a hierarchy. This kind of topology allows for simple expansion and limited capital outlay for growth, because more layers of devices can be added...
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...Product ) CAT5 / CAT5e Cables Add to Cart [pic] CAT5e CABLE ROLL 305M Solid conductor Category 5e is an independently verified 4 pair UTP cable which conforms to the e.. Add to Cart [pic] 305M CAT 5 Drum UV Protected Networking/CCTV Cable Security Genuine External Cable This reel comes on a drum. Cat 5 Cable for external use, comes with UV protected cable c.. Add to Cart [pic] CAT 5 UV Protected Networking/CCTV Cable Security Genuine External Cable Current lengths available: 5M, 10M, 15M, 20M, 25M, 30M, 40M, 50M. Cat 5 Cable for RG59 / Shotgun Cables Add to Cart [pic] RG59 50M Cable Video Only RG59 50M cables for CCTV installation. VIDEO ONLY .. Add to Cart [pic] RG59 100M Cable Video Only RG59 100M cables for CCTV installation. VIDEO ONLY .. Add to Cart [pic] 200M RG59 Shotgun Cable (Aluminium Core) 200m Heavy weight CCTV camera video and power cable shotgun(RG59+2). Cables are made up of Alumin.. Add to Cart [pic] 200M RG59 Shotgun Cable (Copper Core) 200M Heavy weight CCTV camera video and power cable shotgun(RG59+2). Cables are made up of Copper Sata Cables Add to Car [pic] Sata Hard Drive HDD Molex (IDE) To Sata Power Cable Connector Power cable for SATA Hard Drives for DVRs/Computers .. Add to Cart [pic] Sata Hard Drive HDD Data Cable Data Connection cable for SATA Hard Drives for DVRs/Computers Modem Router Lead [pic] 5M ADSL RJ11 Internet Extension Cable Broadband...
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