MATH 233 Unit 5 Individual ProjectNAME (Required): _____________________________In this IP assignment, you will have a choice between two different Unit 5 IP assignments. Complete only 1 of the following two assignment choices.Unit 5 IP Assignment Choice 1The Internet is defined as a worldwide interconnection of individual networks operated by governments, industries, academia, and private parties (Internet World Stats, 2015). As the Internet grows and becomes more accessible to many people in the world, there is an increasing interest in forecasting its number of users as it helps improve the technology and its security.In a recent study, researchers found that the rate of change of internet users in the world (in millions) is modeled by the functionwhere x is the number of years from 1994.For the questions that require calculations, be sure to show your work details and if applicable, round your final answers to the nearest hundredths (2 digits after the decimal point) to receive full credit. For critical thinking questions, explain in detail how the answers were determined.1.Using integration on, find the function P(x) that predicts the number of internet users in the world years after 1994. (Note: Since this is an indefinite integral, do not forget to add a constant of integration, C, in your final answer.) Show your work details.2.Based on the first letter of your last name, calculate the value of C from #1 by choosing an ordered pair (x, P(x)) from the table below. Show your work details. First letter of your last name x (years from 1994) P(x) (in millions) A–B 6 361 C–D 7 513 E–F 8 587 G–H 9 719 I–J 10 817 K–L 11 1,018 M–N 12 1,093 O–P 13 1,319 Q–R 14 1,574 S–T 15 1,802 U–V 16 2,267 W–X 17 2,497 Y–Z 18 2,802 3.From your answers in #1 and #2, state the mathematical model, P(x) (in millions), that will predict the number of internet users in the world. 4.Using P(x), complete the following table.Show the work details for full credit. Year x Predicted Number of Internet Users (in millions) 2016 2018 2020 5.Below is a graph of over the interval [6,22]. Set up the definite integral that will calculate the area of the shaded region on the graph.6.Calculate the area of the shaded region. Show your work details.7.What information does the area give in terms of number of Internet users in this scenario?Would you estimate that this is a reasonable growth of Internet users from 2000 to 2016? Explain and justify your answer with critical thinking. Unit 5 IP Assignment Choice 2:According to its Web site, “SpeedOf.Me is an HTML5 Internet speed test. The smartest and most accurate online bandwidth test; it works well on…mobile devices as well as desktop computers.” By using your browser to test the Internet connection, it returns download and upload speeds including maximum rates and latency time periods. “It reflects your actual browsing and download experience.”Be sure to show your work details for all calculations and explain in detail how the answers were determined for critical thinking questions. Round all value answers to three decimals.1.Go to this Web site, “stop all Internet activities, and click ‘Start Test’.” In the following order, record your device’s download, upload, latency, max download, and max upload values. Click “Share” and select the bottom right URL to copy and paste here below or or copy and paste your Speedof.me graph below.2.Below is an example of download Megabits per second (Mbps):Note, that the diagnostics give the graph repetitive spikes as for example:Let’s examine the first second of this activity, modeled by the polynomial function:Here, s(t) is the download speed Mbps with respect to t in seconds with the domain of [0,1]. Generate a graph of this function using Excel or another graphing utility. (There are free downloadable programs like Graph 4.4.2 or Mathematics 4.0; or, there are also online utilities such as this site and many others.) NOTE: Use axes scales -0.5 < x < 1.5 and -1 < y < 5.Insert the graph into the Word document containing your answers and work details. Be sure to label and number the axes appropriately.3.Evaluate: .Be sure to show the work details and include the constant of integration, .4.Based on the first letter of your last name, calculate the value of C from #3 by choosing an ordered pair (t, S(t)) from the table below. First letter of your last name t (seconds) S(t) (in megabits) A–B 6 361 C–D 7 513 E–F 8 587 G–H 9 719 I–J 10 817 K–L 11 1,018 M–N 12 1,093 O–P 13 1,319 Q–R 14 1,574 S–T 15 1,802 U–V 16 2,267 W–X 17 2,497 Y–Z 18 2,802 5.Evaluate the definite integral of this function over the interval [0,1].Be sure to show the intermediate work details.6.In terms of this scenario what is the meaning of the definite integral calculated in question #5. Make sure to include your unit label measurements.Does this result seem reasonable? Explain and justify your answer with critical thinking.References Desmos. (n.d.). Retrieved from https://www.desmos.com/ Graph 4.4.2. (n.d.). Retrieved from the Graph Web site: http://www.padowan.dk/ Internet World Stats. (2015). Internet growth statistics. Retrieved from http://www.internetworldstats.com/emarketing.htmMathematics 4.0. (n.d.). Retrieved from the Microsoft Web site: http://microsoft-mathematics.en.uptodown.com/SpeedOfMe. (n.d.). Retrieved from http:www.speedof.me/WolframAlpha. (n.d.). Retrieved from http://www.wolframalpha.com/

QUESTION 1Solve the system of equations. If the system has no solution, say that it is inconsistent.x = -8, y = -4; (-8, -4)x = 0, y = -12; (0, -12)x = 0, y = 0; (0, 0)inconsistent0 points QUESTION 2Solve the system of equations by elimination.x = -10, y = 3; (-10, 3)x = 10, y = -3; (10, -3)x = 3, y = -10; (3, -10)x = -3, y = 10; (-3, 10)0 points QUESTION 3Solve the system of equations by substitution.x = 3, y = 7; (3, 7)x = 7, y = 12; (7, 12)x = 12, y = -2; (12, -2)x = -2, y = 3; (-2, 3)0 points QUESTION 4Solve the system of equations by elimination.x = -6, y = 5; (-6, 5)x = 11, y = -11; (11, -11)x = 5, y = -5; (5, -5)x = -5, y = 5; (-5, 5)0 points QUESTION 5Solve the system of equations by elimination.x = 3, y = 8; (3, 8)x = 3, y = 9; (3, 9)x = 2, y = 9; (2, 9)x = 2, y = 8; (2, 8)0 points QUESTION 6Solve the system of equations by substitution.x = 3, y = 9; (3, 9)x = 2, y = 9; (2, 9)x = 2, y = 8; (2, 8)x = 3, y = 8; (3, 8)0 points QUESTION 7Solve the system of equations. If the system has no solution, say that it is inconsistent.x = 4, y = 2; (4, 2)x = 2, y = 4; (2, 4)x = 2, y = 3; (2, 3)inconsistent0 points QUESTION 8Solve the system of equations by elimination.x = 8, y = 11; (8, 11)x = 8, y = -11; (8, -11)x = 3, y = 8; (3, 8)x = 3, y = -11; (3, -11)0 points QUESTION 9Verify that the values of the variables listed are solutions of the system of equations.x = -2, y = -3solutionnot a solution0 points QUESTION 10Solve the system of equations by substitution.x = 10, y = 0; (10, 0)x = 0, y = 10; (0, 10)x = 10, y = 10; (10, 10)x = 0, y = 0; (0, 10)0 points QUESTION 11Solve the problem.A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults?24 adults29 adults10 adults16 adults0 points QUESTION 12Solve the system of equations by elimination.x = 1, y = 1; (1, 1)x = 0, y = 0; (0, 0)x = 1, y = 0; (1, 0)x = 0, y = 1; (0, 1)0 points QUESTION 13Solve the system of equations by substitution.x = -3, y = 0; (-3, 0)x = 3, y = -3; (3, -3)x = -3, y = -3; (-3, -3)x = -3, y = 3; (-3, 3)0 points QUESTION 14Solve the problem.An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?147 mi132 mi168 mi153 mi0 points QUESTION 15Solve the problem.The Paperback Trader is a book store that takes in used paperbacks for 20% of their cover price and sells them for 50% of their cover price. Pat brings in a stack of 16 paperback books to trade and gets $17.50 credit. Some of the books had a cover price of $7.97, the rest $3.97. She wants to get some Tom Clancy books having a cover price of $7.97. How many $7.97 books did she bring in and how many Clancy books can she get without paying any additional cash?6 $7.97 books, 2 Clancy books6 $7.97 books, 4 Clancy books10 $7.97 books, 2 Clancy books6 $7.97 books, 5 Clancy books0 points QUESTION 16Solve the system of equations. If the system has no solution, say that it is inconsistent.x = -1, y = ; y = - x + 12, where x is any real numberor {(x, y) | y = - x + 12, where x is any real number}x = 0, y = 12; (0, 12)inconsistent0 points QUESTION 17Solve the system of equations by substitution.x = 2, y = 11; (2, 11)x = 2, y = -11; (2, -11)x = 9, y = -11; (9, -11)x = 9, y = 2; (9, 2)0 points QUESTION 18Solve the system of equations by elimination.x = -5, y = 18; (-5, 18)x = -18, y = 5; ( -18, 5)x = 18, y = -5; (18, -5)x = -18, y = 6; (-18, 6)0 points QUESTION 19Verify that the values of the variables listed are solutions of the system of equations.x = -3, y = 4solutionnot a solution0 points QUESTION 20Solve the problem.A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 7 slices of pizza and 4 soft drinks for $31.49. The second group bought 5 slices of pizza and 6 soft drinks for $26.61. How much does one slice of pizza cost?$3.75 per slice of pizza$3.25 per slice of pizza$1.31 per slice of pizza$1.81 per slice of pizza0 points QUESTION 21Solve the system of equations. If the system has no solution, say that it is inconsistent.x = -8, y = 0; (-8, 0)x = 0, y = 0; (0, 0)y =- - 4, where x is any real numberor {(x, y) | y =- - 4, where x is any real number}inconsistent0 points QUESTION 22Solve the system of equations. If the system has no solution, say that it is inconsistent.x = -4y + 5, where y is any real numberor {(x, y) |x = -4y + 5, where y is any real number}y = -4x + 5, where x is any real numberor {(x, y) | y = -4x + 5, where x is any real number}y = 4x + 5, where x is any real numberor {(x, y) | y = 4x + 5, where x is any real number}inconsistent0 points QUESTION 23Solve the system of equations. If the system has no solution, say that it is inconsistent.x = 9, y = 2; (9, 2)x = , y = ; x = -9, y = -8; (-9, -8)inconsistent0 points QUESTION 24Solve the system of equations by elimination.x = 0, y = 4; (0, 4)x = 0, y = -4; (0, -4)x = -4, y = 0; (-4, 0)x = 4, y = 0; (4, 0)0 points QUESTION 25Solve the system of equations by substitution.x = 1, y = 0; (1, 0)x = 0, y = 1; (0, 1)x = 1, y = 1; (1, 1)x = 0, y = 0; (0, 0)0 points Click Save and Submit to save and submit. Click Save All Answers to save all answers.

In this discussion, please answer the following question and post your response to the discussion board. Please keep in mind, in order to remain eligible for full credit in the discussion, you must, in addition to your initial reply, respond to at least two of your classmates’ or instructor’s posts.Matrices have several applications. This week, your task is to investigate and discuss an application of matrices that you find interesting. Your post must be substantive and informative.