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Why Qorvo? Screencastify - Screen Video Recorder. Both of his vice presidents, George Clinton and Elbridge Gerry, died in office. Your plan should include certain elements, like mission, values, and vision statements, and avoid common pitfalls, like neglecting the specific needs of your organization, so it Since most of my students are 13 or older, this similarity to Facebook is a big plus. PhET is supported by and educators like you.
Find and fix missing skills with personalized learning, pinpoint assessments, and motivating rewards. Standard features like password protection and meeting locks ensure meeting hosts can hold secure video conferences. For example Microsoft word is a processing software.
Practice: Divide by taking out factors of Step by step instructions are included to help you understand the overall process and the specifics on working with moveable pieces. Bypassing proxy, for testing, did not help. Sources created later by someone who did not participate in the event. This Instructable will hopefully demystify the basics of electronics so that anyone with an interest in building circuits can hit the ground running.
The interest return on capital is a predetermined rent of the lending. FFA, which stands for Future Farmers of America, is a national, student-led organization dedicated to educating high school students in different fields of agriculture. Original materials. With online maps, you can help plan evacuation strategies and share your findings with the people who make decisions.
Click on the moth to eat it. Customize your videos. Lunch Menus. You're probably already a member of one, especially considering that But UDL actually takes the opposite approach. Enjoy low prices and great deals on the largest selection of everyday essentials and other products, including fashion, home, beauty, electronics, Alexa Devices, sporting goods, toys, automotive, pets, baby, books, video games, musical instruments, office supplies, and more.
Google Hangouts. It set a vital precedent for the negotiated winding up of Designed by Amazon to protect and perfectly fit your Fire HD 8 tablet compatible with 10th generation, release. May evaluate athletes' strengths and weaknesses as possible recruits or to improve the athletes' technique to prepare them for competition. The ANS is part of the peripheral nervous system and it also controls some of the muscles within the body.
The Soundtrap Capture App provides a simple and quick way to record and develop music ideas collaboratively on mobile. Well, we've got that too. Government Printing Office.
Buy now. How to Invite Friends. Create a free website or blog in minutes by using a simple drag and drop interface. One of Time's 50 best websites of the year. Schoology is the official grade book for Edina secondary schools. In our Instructor Guide, you will find everything you need to know to use Canvas as a teacher, from creating assignments to managing course settings.
Our study guide contains easy-to-read essential summaries that highlight the key areas of the Common Core High School: Geometry test. This is called lift. These videos are short, sweet and focused so you can pick and choose just the ones you need to get your eLearning content online with SoftChalk. Manage your classroom, create and submit assignments, participate in interactive discussions, perform assessments, collaborate with your peers, and more!
Have rich and engaging academic experiences anytime, anywhere with the Contact Us! Schoology For Students. Treaty of Kars. The guide will show you in detail how to accomplish basic tasks in Schoology. Since flipped teaching relies so heavily on technology to create and share videos of lectures, choosing the technology that can best help you film, edit, and share your videos is a crucial first step.
Availability determines whether or not content or features are accessible to users. Get free downloads and examples and connect with thousands of e-learning pros. If you want to create a Google Meet or Agenda slide like mine or something similar , you can keep the default page dimensions and move onto Step 2.
Schoology Login. Classic Quiz Sunset Timeline Subscribe! Well, the template here would be handy for you with its readymade IT strategy map that highlights on varied parameters or attributes under different perspectives. Free Download. Strategy Map Template Free Download. Strategic Planning Process Map. Both Corel Quattro Pro and Microsoft Excel have built-in functions for multiplying matrices, although the procedures in the two programs differ somewhat.
In the pop-up window, enter the cell ranges for the two matrices you want to multiply and the cell where you want the resulting matrix to start. Note that you must list the 2 17 matrix rst. You can apply these techniques for matrix multiplication to the calculations for your tools for data management project.
Microsoft Excel: The MMULT matrix1,matrix2 function will calculate the product of the two matrices but displays only the rst entry of the resulting matrix. The identity matrix with dimensions n n is represented by In.
Note that A1. Multiplying the matrices gives four simultaneous equations for w, x, y, and z. The formulas for the inverses of larger matrices can be determined in the same way as for 2 2 matrices, but the calculations become much more involved.
However, it is relatively easy to nd the inverses of larger matrices with graphing calculators since they have the necessary formulas built in. The spreadsheet functions for inverse matrices are similar to those for matrix multiplication.
Use the Fraction feature to display the entries as fractions rather than decimal numbers. During the s, Lester Hill, an American mathematician, developed methods for using matrices to decode messages. The following example illustrates a simplied version of Hills technique. Example 4 Coding a Message Using Matrices a b. Determine the matrix key required to decode the message. Replace each letter with its corresponding number in the alphabet. Now, encode the message by multiplying with a coding matrix that only the sender and receiver know.
You can decode the message with the inverse matrix for the coding matrix. Thus, the decoding matrix, or key, is the inverse matrix of the coding matrix.
For the coding matrix used in part a , the key is 3 5 1 2 1. The decoded message is 16, 8, 15, 14, 5, 13, 5, 20, 15, 14, 9, 7, 8, 20, 26, Matrix multiplication and inverse matrices are the basis for many computerized encryption systems like those used for electronic transactions between banks and income tax returns led over the Internet.
Transportation and communication networks can be represented using matrices, called network matrices. Such matrices provide information on the number of direct links between two vertices or points such as people or places.
The advantage of depicting networks using matrices is that information on indirect routes can be found by performing calculations with the network matrix. To construct a network matrix, let each vertex point be represented as a row and as a column in the matrix. Use 1 to represent a direct link and 0 to represent no direct link.
A vertex may be linked to another vertex in one direction or in both directions. Assume that a vertex does not link with itself, so each entry in the main diagonal is 0. Note that the network matrix provides information only on direct links.
Matrixville Airlines offers ights between eight cities as shown on the right. Organize the matrix Vancouver so the cities are placed in alphabetical order. How many indirect routes with exactly one change of planes are there from London to Buenos Aires? What information does it contain? Calculate A3. Compare this calculation with the one for A2. Explain the signicance of any entry in matrix A3. The entries in A2 show the number of indirect routes with exactly one change of planes.
A2 does not contain any information on direct routes. London to Buenos Aires. A calculator or spreadsheet could be useful. Key Concepts To multiply two matrices, their inner dimensions must be the same. To nd the entry with row i and column j of matrix AB, multiply the entries of row i of matrix A with the corresponding entries of column j of matrix B, and then add the resulting products together.
Larger inverse matrices can be found using a graphing calculator or a spreadsheet. To represent a network as a matrix, use a 1 to indicate a direct link and a 0 to indicate no direct link. Calculations with the square of a network matrix and its higher powers give information on the various direct and indirect routings possible.
Explain how multiplying matrices is different from scalar multiplication of. Explain why a network matrix must be square. Describe how you would represent the following network A B. The downtown store sold 12 business calculators, 40 scientic calculators, and 30 graphing calculators during the past week.
The northern store sold 8 business calculators, 30 scientic calculators, and 21 graphing calculators during the same week, and the southern store sold 10 business calculators, 25 scientic calculators, and 23 graphing calculators. Application The manager at Sues Restaurant.
Employee Mon. In , about 11 males and 12 females in Canada were at least 15 years old. Determine how many males and how many females declared each of the above sports as their favourite. Describe how you used matrices to solve this problem.
Application A company manufacturing. Quality education at a school requires open. The material and labour needed to produce a box of shirts depends on the size of the shirts. List these links. Explain what. Solve both problems and compare your solutions with those of your classmate.
Can you suggest any improvements for either set of solutions? Show how you could use inverse matrices. Communication Research encryption. What is meant by bit encryption? How does the system of private and public code keys work? Use network matrices to answer the following questions. Honey Bridge to Connecting Bridge by crossing only one of the other bridges? List these routes. Describe how you could use a computer to break the code and decipher the message.
Blacksmith Bridge to Connecting Bridge without crossing more than one of the other bridges? Bridge to Green Bridge without crossing at least two other bridges? Use network matrices to nd the number C. Review of Key Concepts 1. List three types of software that can be used. Evaluate each spreadsheet expression. Describe how to reference cells A3 to A Use a spreadsheet to convert temperatures. Step 1: Construct a square. Step 2: Construct an isosceles right triangle with the hypotenuse on one side of the square.
Step 3: Construct a square on each of the other sides of the triangle. Repeat this process, with the newly drawn squares to a total of four iterations.
Describe how you would list temperatures at twodegree intervals in the Celsius column. Describe the characteristics of a well-.
List three commonly used simulations and B D. A chocolate bar manufacturer prints one of. Describe a manual simulation you could use to estimate the chances of getting two chocolate bars with the same brainteaser if you treat yourself to one of the bars every Friday for ve weeks.
Outline how you would use technology to. How many colours are needed to colour. Use graph theory to set up the shortest viewing schedule that has no conicts for any of these patrons. The vertices are adjacent if the children are friends. Sarah Mai. The manager orders and receives a shipment of 10 basketballs, 3 volleyballs, 15 footballs, 20 baseballs, 12 soccer balls, 5 packs of tennis balls, and 15 packs of golf balls.
During the next month, the store sells 17 basketballs, 13 volleyballs, 17 footballs, 12 baseballs, 12 soccer balls, 16 packs of tennis balls, and 23 packs of golf balls.
How many of each item will be left at the managers store? Outline the procedure you would use to. The rm did the following work for three of its clients: XYZ Limited, payrolls hours, tax returns 10 hours, auditing 10 hours YZX Limited, payrolls 60 hours, tax returns 8 hours, auditing 8 hours ZXY Limited, payrolls hours, tax returns 15 hours, auditing 20 hours a Use matrices to determine how much the.
Explain the meaning. Would your message be more secure if you then multiplied the resulting matrices by another coding matrix with the same dimensions as the rst one? If so, describe the pattern.
A fan-out calling system is frequently used. The rst person calls three people. Each of those people calls an additional three people; each of whom calls an additional three people, and so on. Describe how you would design a database.
Describe three different ways to generate. A local drama club staged a variety show for. Show that it is the shortest route. The following map. Use graph theory to determine if a continuous path could traverse all the bridges once each. On Wednesday, 52 adult tickets, student tickets, and child tickets were sold; on Thursday, 67 adult tickets, student tickets, and child tickets were sold; on Friday, 46 adult tickets, student tickets, and child tickets were sold; and on Saturday, 40 adult tickets, student tickets, and 89 child tickets were sold.
Use matrices to calculate how much money was collected from admissions. With your whole class or a small group, brainstorm criteria for ranking universities and community colleges. List the three universities or colleges that you think will most likely be the best choices for you. Have a class discussion on weighting 8. From your rankings, select the top ve.
Draw a diagram of the distances from each university or college to the four others and to your home. Then, use graph theory to determine the most efcient way to visit each of the ve universities or community colleges during a ve-day period, such as a March break vacation.
Based on your project, select your top three. Note the criteria that Macleans uses. Determine your own set of criteria. Choose the ten criteria you consider most. Research any data you need to rate universities and colleges with these criteria. Assign a weighting factor to each of the ten.
For example, living close to home may be worth a weighting of 5 and tuition cost may be worth a weighting of 7. Use a spreadsheet and matrix methods to. Suggested Resources Macleans magazine rankings of universities and community colleges Other publications ranking universities and community colleges University and community college calendars Guidance counsellors Map of Ontario Spreadsheets Refer to section 9.
Then, rank the universities or community colleges on the spreadsheet. Compare your rankings with those in Macleans magazine. Explain the similarities or differences. For details of the Macleans rankings of universities and colleges, visit the above web site and follow the links. Evaluating Your Project 1. Reect on your weighting formula and whether you believe it fairly ranks the universities and community colleges in Ontario.
Compare your rating system to that used. Can you suggest improvements to either system? If you were to do the project over again,. Presentation Prepare a written report on your ndings. Include the raw data a rationale for your choice of criteria a rationale for your weightings a printout of your spreadsheet a diagram showing the distances between your ve highest-ranked universities or community colleges and the route you would use to visit them a summary of your ndings.
Consider how the data management tools you used on this project could be applied to the culminating project in Chapter 9 to access resources carry out research carry out an action plan evaluate your project summarize your ndings in a written report. Now is a good time to draw up a schedule for your culminating project and to investigate methods for selecting a topic.
Refer to Chapter 9 for an overview of how to prepare a major project. Section 9. Also, consider how to nd the information you will need in order to choose your topic.
In this digital era, information is sent with blinding speed around the world. These transmissions need to be both secure and accurate. Although best known for their work on secret military codes, cryptographers also design and test computerized encryption systems that protect a huge range of sensitive data including telephone conversations among world leaders, business negotiations, data sent by credit-card readers in retail stores, and nancial transactions on the Internet.
Encrypted passwords protect hackers from reading or disrupting critical databases. Even many everyday devices, such as garage-door openers and TV remote controls, use codes. Cryptographers also develop error-correcting codes.
Adding these special codes to a signal allows a computer receiving it to detect and correct errors that have occurred during transmission. Such codes have numerous applications including CD players, automotive computers, cable TV networks, and pictures sent back to Earth by interplanetary spacecraft. Modern cryptography is a marriage of mathematics and computers.
A cryptographer must have a background in logic, matrices, combinatorics, and computer programming as well as fractal, chaos, number, and graph theory. Cryptographers work for a wide variety of organizations including banks, government ofces, the military, software developers, and universities.
Visit the above web site and follow the links for more information about a career as a cryptographer and about other careers related to mathematics. Life Expectancies Background Do women live longer than men?
Do people live longer in warmer climates? Are people living longer today than 50 years ago? Do factors such as education and income affect life expectancy? In this project, you will answer such questions by applying the statistical techniques described in the next two chapters. Your Task Research and analyse current data on life expectancies in Canada, and perhaps in other countries.
You will use statistical analysis to compare and contrast the data, detect trends, predict future life expectancies, and identify factors that may affect life expectancies. Developing an Action Plan You will need to nd sources of data on life expectancies and to choose the kinds of comparisons you want to make. You will also have to decide on a method for handling the data and appropriate techniques for analysing them.
Demonstrate an understanding of the purpose and the use of a variety of sampling techniques. Describe different types of bias that may arise in surveys. Illustrate sampling bias and variability by comparing the characteristics of a known population with the characteristics of samples taken repeatedly from that population, using different sampling techniques.
Organize and summarize data from secondary sources, using technology. Compute, using technology, measures of one-variable statistics i. Interpret one-variable statistics to describe characteristics of a data set. Describe the position of individual observations within a data set, using z-scores and percentiles. Explain examples of the use and misuse of statistics in the media.
Assess the validity of conclusions made on the basis of statistical studies, by analysing possible sources of bias in the studies and by calculating and interpreting additional statistics, where possible.
Explain the meaning and the use in the media of indices based on surveys. In earlier times they had no statistics, and so they had to fall back on lies.
Hence the huge exaggerations of primitive literaturegiants or miracles or wonders! They did it with lies and we do it with statistics; but it is all the same. Stephen Leacock His agent wants to bargain for a better salary based on Franois strong performance over his rst ve seasons with the team. Here are some of Franois statistics for the past ve seasons.
Season 1 2 3 4 5 Total Games 20 45 76 80 82 Goals 3 7 19 19 28 76 Assists 4 11 25 37 36 Points 7 18 44 56 64 Are there any trends in the data that the. As these questions suggest, statistics could be used to argue both for and against a large salary increase for Franois.
However, the statistics themselves are not wrong or contradictory. Franois agent and the teams manager will, understandably, each emphasize only the statistics that support their bargaining positions. Such selective use of statistics is one reason why they sometimes receive negative comments such as the quotations above. Also, even well-intentioned researchers sometimes inadvertently use biased methods and produce unreliable results. This chapter explores such sources of error and methods for avoiding them.
Properly used, statistical analysis is a powerful tool for detecting trends and drawing conclusions, especially when you have to deal with large sets of data. Fractions, percents, decimals The following 6.
Graphing data Consider the following. Determine the price of each item. Fractions, percents, decimals a How much will Josh make if he receives. Fractions, percents, decimals What is the. Fractions, percents, decimals Determine. Graphing data The table below gives the. Mean, median, mode Calculate the mean,. Statistics is the gathering, organization, analysis, and presentation of numerical information. You can apply statistical methods to almost any kind of data.
Researchers, advertisers, professors, and sports announcers all make use of statistics. Often, researchers gather large quantities of data since larger samples usually give more accurate results. The rst step in the analysis of such data is to nd ways to organize, analyse, and present the information in an understandable form. Carry out your survey and record all the results in a table.
Consider how you could organize these results to look for any trends or. Would it make sense to change the order of the data or to divide them into groups? Prepare an organized table and see if you can detect any patterns in the data.
Compare your table to those of your classmates. Which methods work best? Can you suggest improvements to any of the tables? Make a graph that shows how often each value or group of values occurs in. Does your graph reveal any patterns in the data? Compare your graph to those drawn by your classmates. Which graph shows the data most clearly? Do any of the graphs have other advantages? Explain which graph you think is the best overall.
Design a graph showing the total of the frequencies of all values of the. Compare this cumulative-frequency graph to those drawn by your classmates. Again, decide which design works best and look for ways to improve your own graph and those of your classmates.
The unprocessed information collected for a study is called raw data. The quantity being measured is the variable. A continuous variable can have any value within a given range, while a discrete variable can have only certain separate values often integers. For example, the height of students in your school is a continuous variable, but the number in each class is a discrete variable. Often, it is useful to know how frequently the different values of a variable occur in a set of data.
Frequency tables and frequency diagrams can give a convenient overview of the distribution of values of the variable and reveal trends in the data. A histogram is a special form of bar graph in which the areas of the bars are proportional to the frequencies of the values of the variable. The bars in a histogram are connected and represent a continuous range of values. Histograms are used for variables whose values can be arranged in numerical order, especially continuous variables, such as weight, temperature, or travel time.
Bar graphs can represent all kinds of variables, including the frequencies of separate categories that have no set order, such as hair colour or citizenship.
A frequency polygon can illustrate the same information as a histogram or bar graph. To form a frequency polygon, plot frequencies versus variable values and then join the points with straight lines. A cumulative-frequency graph or ogive shows the running total of the frequencies from the lowest value up. Cumulative Frequency. To learn more about histograms, visit the above web site and follow the links.
Write a short description of how to construct a histogram. Here are the sums of the two numbers from 50 rolls of a pair of standard dice. Use a frequency table to organize these data. Are any trends or patterns apparent in this table? Use a graph to illustrate the information in the frequency table. Create a cumulative-frequency table and graph for the data. What proportion of the data has a value of 6 or less? Solution a Go through the data and tally the frequency of each value of Sum 2 3 4 5 6 7 8 9 10 11 12 Tally Frequency 4 2 3 9 8 5 6 5 4 3 1.
From the frequency column, notice that the middle values tend to be the most frequent while the high and low values are much less frequent. Graph these cumulative frequencies against the values of the variable. When the number of measured values is large, data are usually grouped into classes or intervals, which make tables and graphs easier to construct and interpret.
Generally, it is convenient to use from 5 to 20 equal intervals that cover the entire range from the smallest to the largest value of the variable. The interval width should be an even fraction or multiple of the measurement unit for the variable. Technology is particularly helpful when you are working with large sets of data. This table lists the daily high temperatures in July for a city in southern Ontario.
Day Temperature C Day Temperature C Day Temperature C a b 1 27 12 25 23 22 2 25 13 26 24 18 3 24 14 31 25 20 4 30 15 33 26 25 5 32 16 33 27 26 6 31 17 30 28 29 7 29 18 29 29 32 8 24 19 27 30 31 9 22 20 28 31 28 See Appendix B for more detailed information about technology functions and keystrokes.
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