Explore Graphs of Linear Relations. 1. a) Use a method of your choice to determine how much water will be needed each day of a sevenday cruise.


 Blaze Mason
 1 years ago
 Views:
Transcription
1 . Graphing Linear Relaions Focus on Aer his lesson, ou will be able o graph linear relaions mach equaions o linear relaions wih graphs solve problems b graphing a linear relaion and analsing he graph Tina is in charge o ordering waer supplies or a cruise ship. She knows he amoun o waer required per da or each passenger and crew member as well as he amoun o waer reserves ha he ship carries. She decides o use her knowledge o linear relaions o draw a graph represening he relaionship beween he amoun o waer needed and he lengh o a cruise. I Tina were o develop an equaion, how could she deermine i he graph and he equaion represen he same relaionship? Maerials grid paper ruler Wha values will ou plo along he horizonal ais? along he verical ais? Eplore Graphs o Linear Relaions On a cruise, he average person requires a minimum o L o waer per da. The cruise ship has capaci or passengers and crew. The ship also carries a reserve o L o waer in case o emergenc.. a) Use a mehod o our choice o deermine how much waer will be needed each da o a sevenda cruise. b) On grid paper, plo he daa and label our graph. Compare our graph wih ha o a classmae.. a) Predic how much waer is needed or a enda cruise. b) Wha linear equaion represens he lires o waer needed per da? c) How could ou veri our answer or par a)? Tr ou our sraeg. Relec and Check. Do our graph and he equaion represen he same relaionship? Eplain.. Discuss wih a parner i i would be appropriae o inerpolae or erapolae values using a racion o a da. Eplain wh or wh no.. a) I he cruise ship used L o waer, approimael how long did he rip las? Compare he mehod ou used wih a classmae s. b) Is here more han one wa o answer par a)? Eplain. Which mehod seems more eicien?. Graphing Linear Relaions MHR
2 Link he Ideas Eample : Graph a Linear Equaion The world s larges cruise ship, Freedom o he Seas, uses uel a a rae o kg/h. The uel consumpion,, in kilograms, can be modelled using he equaion =, where is he number o hours ravelled. a) Creae a graph o represen he linear relaion or he irs h. b) Approimael how much uel is used in h? Veri our soluion. c) How long can he ship ravel i i has approimael kg o uel? Veri our soluion. Describe he connecion beween he equaion and he graph. Soluion Mehod : Use Paper and Pencil a) Creae a able o values. Graph he coordinae pairs. Time, (h) Fuel Consumpion, (kg) Fuel Consumpion (kg) Cruise Ship Fuel Consumpion Time (h) Wha dieren mehods migh ou use o represen and hen solve he problem? b) Draw a sraigh line o connec he daa poins. Eend he line pas he las daa poin. Approimael kg o uel are used in h. Fuel Consumpion (kg) Cruise Ship Fuel Consumpion MHR Chaper Time (h)
3 Check: Subsiue he value = ino he equaion =. = () = The approimae soluion is correc. c) The uel will las approimael. h. Check: Subsiue = ino he equaion and solve or. = =. The approimae soluion is correc. Mehod : Use a Spreadshee a) In he spreadshee, cell A has been labelled Time,. Cell B has been labelled Fuel Consumpion,. Ener he irs eigh values or in cells A o A. Then, ener he ormula or he equaion ino cell B. Use an = sign in he ormula and * or muliplicaion. The value or comes rom cell A. Use he cursor o selec cells B down o B. Then, use he Fill Down command o ener he ormula in hese cells. The appropriae cell or will auomaicall be insered. For eample, =*A will be insered ino cell B. Use he spreadshee s graphing command o graph he able o values. Noe ha dieren spreadshees have dieren graphing commands. Use our spreadshee s insrucions o ind he correc command. Tech Link You could use a graphing calculaor o graph his linear relaion. To learn abou how o do his go o and ollow he links. A B C D E F G H I Fuel Consumpion (kg) Cruise Ship Fuel Consumpion Time (h). Graphing Linear Relaions MHR
4 b) and c) From he menu, selec Add Trendline o draw a sraigh line rom he irs daa poin o he las one. Eend he line pas he las daa poin. A B C D E F G H I J Fuel Consumpion (kg) Cruise Ship Fuel Consumpion Time (h) For par b), approimael kg o uel are used in h. For par c), he uel will las approimael. h. Did You Know? Fish inders operae using sonar, which uses sound waves o see objecs underwaer. The ish inder produces a sound wave and sends i hrough he waer. When he sound wave mees an objec wihin is range, i bounces back o he ish inder. The ish inder deermines he deph o he objec b measuring he ime beween when he sound wave was sen and when i reurns. The ish inder hen skeches he objec on he screen. Show You Know a) Graph he linear relaion = . b) Use he graph o esimae he value o i =. c) Use he graph o esimae he value o i = . Eample : Deermine a Linear Equaion From a Graph Grea Slave Lake, which is locaed in he Norhwes Terriories, is he deepes lake in Norh America. I has a maimum deph o m. Sam decided o check he deph using his ish inder. He colleced he ollowing daa up o a deph o m, which was he maimum deph ha his ish inder could read. Disance From Shore, d (m) Waer Deph, w (m) Lierac Link A deph, such as m, is epressed in dieren was. In a able and a graph, use he negaive value, . In a senence, sa m below surace. MHR Chaper
5 Sam used a spreadshee o graph he daa. A B C D E F G H I J Waer Deph (m) Grea Slave Lake Deph Recordings Disance From Shore (m) a) Wha linear equaion does his graph represen? How do ou know he equaion maches he graph? b) I his paern coninues, how ar rom shore would Sam be when he waer is m deep? c) A wha rae is he deph o he waer decreasing? d) Is i appropriae o inerpolae or erapolae values on his graph? Eplain. Soluion a) Add a column o he able o help deermine he paern. Disance From Shore, d (m) Waer Deph, w (m) Paern: Mulipl d b The waer deph, w, decreases b. m or each m increase in he disance rom shore, d. The equaion is w = .d. Check b subsiuing a known coordinae pair, such as (, ), ino he equaion. Le Side =  Righ Side = .() =  Le Side = Righ Side The equaion is correc. Wha is he connecion beween he graph and he equaion?. Graphing Linear Relaions MHR
6 Sraegies Solve an Equaion b) Subsiue w = ino he equaion and solve or d.  = .d  . = d d. How else could ou solve his problem? Sam would be approimael. m rom shore when he waer is m deep. c) The deph is decreasing a a rae o. m or each mere awa rom shore. The rae a which he waer deph is decreasing is he coeicien o d in he equaion. d) Yes, i is reasonable o inerpolae or erapolae values beween and beond he given daa poins since he values or disance and deph eis. However, i is unreasonable o erapolae values beond he maimum deph o m. Show You Know Ideni he linear equaion ha represens he graph. A B C D E F G H I Disance (m) d (, ) (, ) (, ) (, ) (, ) Time (s) MHR Chaper
7 Eample : Graph Horizonal and Verical lines For each able o values, answer he ollowing quesions: Table Table Time, (s) Disance, d (m) Disance, (m) Heigh, (m) a) Draw a graph o represen he able o values. b) Describe a siuaion ha he graph migh represen. c) Wrie he equaion. Eplain how ou know he graph represens he equaion. Soluion a) d Graph o Table. Graph o Table. Disance (m) Heigh (m) Time (s) Disance (m) b) Table : The graph could show he relaionship beween disance and ime when a pedesrian is waiing or a raic ligh o change. The disance rom he pedesrian o he opposie side o he road is consan. Table : The graph could show he relaionship beween he heigh o a ladder and is disance rom he wall where i is placed. The disance o he base o he ladder rom he wall is consan as he ladder is eended. Think o a dieren siuaion o represen each graph. c) Table : The disance, d, remains consan or each inerval o ime. The equaion is d =. For each value o in he able and he graph, he value o d is. Table : The disance,, remains consan or each inerval o heigh. The equaion is =.. For each value o in he able and he graph, he value o is... Graphing Linear Relaions MHR
8 Show You Know a) Wrie he linear equaion ha represens he graph. b) Eplain how ou know he graph maches he equaion. Disance (m) d Time (s) Ke Ideas You can graph a linear relaion represened b an equaion. Use he equaion o make a able o values. Graph using he coordinae pairs in he able. The graph o a linear relaion orms a sraigh line. k = j k  j k The graph o a linear relaion can orm a horizonal or a verical line. You can use graphs o solve problems b inerpolaing or erapolaing values. j Check Your Undersanding Communicae he Ideas. You are given a linear equaion. Describe he process ou would ollow o represen he equaion on a graph. Use an eample o suppor our answer.. Use eamples and diagrams o help eplain how horizonal and verical lines and heir equaions are similar and how he are dieren. MHR Chaper
9 . a) Describe a reallie siuaion o represen he daa on his graph. A B C D E F G H I (,.) (,.) (,.) (,.) (, ) b) Eplain how ou would deermine he equaion ha represens he graph. Give our eplanaion o a classmae. c) Can ou inerpolae or erapolae values on his graph? Eplain our hinking. Web Link For pracice maching graphs and linear equaions, go o www. mahlinks.ca and ollow he links. Pracise For help wih # o #, reer o Eample on pages.. Ian works parime a a movie heare. He earns $./h. The relaionship beween his pa, p, and he ime he works,, can be modelled wih he equaion p =.. a) Show he relaionship on a graph. b) Eplain how ou know he graph represens he equaion. c) Ian works h in one week. Use wo mehods o deermine his pa. A B. Andrea is ravelling b bus a an average speed o km/h. The equaion relaing disance, d, and ime,, is d =. a) Show he relaionship on a graph. b) How long does i ake Andrea o ravel km? C. Choose he leer represening he graph ha maches each linear equaion. a) = b) = + c) = +. Graphing Linear Relaions MHR
10 . Creae a able o values and a graph or each linear equaion. a) = b) r = s +. c) m = k + For help wih # o #, reer o Eample on pages.. The graph shows he relaionship beween he cos, C, in dollars and he mass, m, in kilograms o pears. C Cos o Pears Cos ($) Mass (kg) a) Wha is he linear equaion? b) How much could ou bu or $? c) Is i appropriae o inerpolae or erapolae values on his graph? Eplain.. The graph represens he relaionship beween he heigh o waer in a child s pool, h, and he ime,, in hours as he pool ills. Heigh (cm) A B C D E F G Waer Heigh in Pool Time (h) a) Deermine he linear equaion. b) Wha is he heigh o he waer aer h? c) Is i appropriae o inerpolae or erapolae values on his graph? Eplain. MHR Chaper m. Deermine he linear equaion ha models each graph. a) A B C D E F G b) A B C D E F. Wha linear equaion does each graph represen? a) b) A B C D E F A B C D E F
11 . Creae a graph and a linear equaion o represen each able o values. a) b) r Appl c) z d) h n The graph represens he aliude o a hoair balloon he irs min aer i was released. Aliude (m) A B C D E F G Balloon Aliude Over Time (, ) (, ) (, ) (, ) Time (min) (, ) (, ) (, ) a) Wha was he approimae aliude o he balloon aer min? b) Esimae how long i ook or he balloon o rise o an aliude o km. c) Wha linear equaion models he graph? d) How as is he balloon rising?. Sanja conduced an eperimen o deermine how long i akes o hea waer rom C o is boiling poin a C. He ploed his daa on a graph. Temperaure (ºC) w Waer Temperaure Over Time Time (min) a) Approimael how long did i ake or he waer o reach boiling poin? Eplain our reasoning. b) Wha was he emperaure o he waer aer min? c) A wha rae did he waer emperaure increase? Eplain our reasoning.. Paul drives rom Time, Disance, Edmonon o Calgar. (h) d (km) He uses a able o record.. he daa... a) Graph he linear.. relaion... b) How ar did Paul.. drive in he irs h?.. c) How long did i ake Paul o drive km? d) Wrie he equaion ha relaes ime and disance. e) Wha was Paul s average driving speed? Wha assumpions did ou make? Web Link To learn abou using a graphing calculaor o ener daa on a able and plo he daa on a graph, go o and ollow he links.. Graphing Linear Relaions MHR
12 . The relaionship beween degrees Celsius ( C) and degrees Fahrenhei ( F) is modelled b he equaion F = C +. a) Graph he relaionship or values beween  C and C. b) Waer boils a C. Wha is his emperaure in degrees Fahrenhei? c) Waer reezes a C. How did ou represen his on our graph? d) A wha emperaure are he values or C and F he same?. Scuba divers eperience an increase in pressure as he descend. The relaionship beween pressure and deph can be modelled wih he equaion P =.d +., where P is he pressure, in kilopascals, and d is he deph below he waer surace, in meres. a) Graph he relaionship or he irs m o diving deph. b) Wha is he approimae pressure a a deph o m? Veri our answer. c) The maimum pressure a scuba diver should eperience is abou kpa. A wha deph does his occur? Veri our answer. d) Wha does +. represen in he equaion? How is i represened on he graph? Did You Know? Aer deep or long dives, scuba divers need o undergo decompression. The do his b ascending o he surace slowl in order o avoid decompression sickness, also known as he bends. Eend. The graph shows he normal range o lengh or girls rom birh o age monhs. Lengh (cm) l Growh Char or Girls a Age (monhs) a) For wha age range does girls growh appear o represen a linear relaion? b) For wha age range, does girls growh appear o represen a nonlinear relaion?. Janice le he school a noon riding her bike a km/h. Flora le school a : riding her bike a km/h. a) Draw a disance ime graph o plo he daa or boh ccliss during he irs our hours. Use a dieren colour or each cclis. b) How can ou ell rom he graph ha Flora has caugh up o Janice? c) Abou wha ime did Flora cach up o Janice? d) I Janice and Flora coninued o ride a heir respecive speeds, a wha ime would he again be apar b a disance o km?. An online music download sie oers wo monhl plans. Plan A oers $ plus $ per download and Plan B oers $. per download. a) Graph boh linear relaions on he same grid. b) Eplain he condiions under which each deal is beer. MHR Chaper
13 . Simple ineres is paid according o he ormula I = p r, where p is he principal, r is he rae o ineres per ear, and is he ime in ears. The ineres is no added o he principal unil he end o he ime period. Canada Savings Bonds oer a simple ineres bond paable a.% per ear up o a maimum o en ears. a) Creae a able o values o show he ineres earned on a $ bond or he enear period. b) Use a graph o show he ineres earned over en ears. c) How man ears would i ake o earn $ ineres? $ ineres? d) I ou could leave he principal beond he enear period, esimae he number o ears i would ake o earn $ ineres. The world s ases submarines can reach speeds o km/h in s, saring rom res. I a submarine is alread moving, hen he ime o reach is op speed will dier. a) Choose our dieren saring speeds up o a maimum o km/h. For each speed, assume ha he acceleraion is he same. For each speed include: a able o values a linear equaion and a graph o represen he relaionship beween speed and ime Did You Know? A suden eam rom he Universi o Québec se a new world speed record or he ases oneperson, nonpropeller submarine. In, he submarine, OMER, reached a speed o. knos (. km/h) in he Inernaional Submarine Races. b) Describe each graph. Ideni an similariies and dierences ou observe beween he graphs and he equaions.. Graphing Linear Relaions MHR
Using Rates of Change to Create a Graphical Model. LEARN ABOUT the Math. Create a speed versus time graph for Steve s walk to work.
2.4 Using Raes of Change o Creae a Graphical Model YOU WILL NEED graphing calculaor or graphing sofware GOAL Represen verbal descripions of raes of change using graphs. LEARN ABOUT he Mah Today Seve walked
More informationInterpreting Sinusoidal Functions
6.3 Inerpreing Sinusoidal Funcions GOAL Relae deails of sinusoidal phenomena o heir graphs. LEARN ABOUT he Mah Two sudens are riding heir bikes. A pebble is suck in he ire of each bike. The wo graphs show
More informationAP Physics 1 Per. Unit 2 Homework. s av
Name: Dae: AP Physics Per. Uni Homework. A car is driven km wes in hour and hen 7 km eas in hour. Eas is he posiive direcion. a) Wha is he average velociy and average speed of he car in km/hr? x km 3.3km/
More informationProportional Reasoning
Proporional Reasoning Focus on Afer his lesson, you will be able o... solve problems using proporional reasoning use more han one mehod o solve proporional reasoning problems When you go snowboarding or
More informationKINEMATICS IN ONE DIMENSION
chaper KINEMATICS IN ONE DIMENSION Secion 2.1 Displacemen Secion 2.2 Speed and Velociy 1. A paricle ravels along a curved pah beween wo poins P and Q as shown. The displacemen of he paricle does no depend
More information3. The amount to which $1,000 will grow in 5 years at a 6 percent annual interest rate compounded annually is
8 h Grade Eam  00. Which one of he following saemens is rue? a) There is a larges negaive raional number. b) There is a larges negaive ineger. c) There is a smalles ineger. d) There is a smalles negaive
More information3.00 m. 8. At La Ronde, the freefall ride called the Orbit" causes a 60.0 kg person to accelerate at a rate of 9.81 m/s 2 down.
Physics Prees: Torque 1. Newon s 2 nd Law 2. Kinemaics (Free fall, graphs, and combined wih F R = ma) Pracice Quesions/Problems 1. Wha is Newon s 2 nd Law? Name and explain i. 2. Prove ha acceleraion for
More informationTime & Distance SAKSHI If an object travels the same distance (D) with two different speeds S 1 taking different times t 1
www.sakshieducaion.com Time & isance The raio beween disance () ravelled by an objec and he ime () aken by ha o ravel he disance is called he speed (S) of he objec. S = = S = Generally if he disance ()
More informationChapter : Linear Motion 1
Te: Chaper 2.12.4 Think and Eplain: 13 Think and Sole:  Chaper 2.12.4: Linear Moion 1 NAME: Vocabulary: disance, displacemen, ime, consan speed, consan elociy, aerage, insananeous, magniude, ecor,
More informationCHAPTER TEST REVIEW, LESSONS 41 TO 45
IB PHYSICS Name: DEVIL PHYSICS Perio: Dae: BADDEST CLASS ON CAMPUS CHAPTER TEST REVIEW, LESSONS 4 TO 45 S. Waer waves a he surface of a pon pass a floaing log of lengh L. The log is a res relaive o he
More informationWhat the Puck? an exploration of TwoDimensional collisions
Wha he Puck? an exploraion of TwoDimensional collisions 1) Have you ever played 8Ball pool and los he game because you scrached while aemping o sink he 8Ball in a corner pocke? Skech he sho below: Each
More information8/31/11. the distance it travelled. The slope of the tangent to a curve in the position vs time graph for a particles motion gives:
Physics 101 Tuesday Class 2 Chaper 2 Secions 2.12.4 Displacemen and disance Velociy and speed acceleraion Reading Quiz The slope of he angen o a curve in he posiion vs ime graph for a paricles moion gives:
More informationName Class Date. Step 2: Rearrange the acceleration equation to solve for final speed. a v final v initial v. final v initial v.
Skills Workshee Mah Skills Acceleraion Afer you sudy each sample problem and soluion, work ou he pracice problems on a separae shee of paper. Wrie your answers in he spaces provided. In 1970, Don Big Daddy
More information1. The value of the digit 4 in the number 42,780 is 10 times the value of the digit 4 in which number?
Mahemaics. he value of he digi in he number 70 is 0 imes he value of he digi in which number?. Mike is years old. Joe is imes as old as Mike. Which equaion shows how o find Joe s age? 70 000 = = = + =
More informationINSTRUCTIONS FOR USE. This file can only be used to produce a handout master:
INSTRUCTIONS OR USE This file can only be used o produce a handou maser: Use Prin from he ile menu o make a prinou of he es. You may no modify he conens of his file. IMPORTNT NOTICE: You may prin his es
More informationCALCULATORS: Casio: ClassPad 300 ClassPad 300 Plus ClassPad Manager TI: TI89, TI89 Titanium Voyage 200. The Casio ClassPad 300
The Casio ClassPad 300 CC Edwards 1950 1955 1960 1965 1970 23.0 23.8 24.4 24.5 24.2 1975 1980 1985 1990 1995 24.7 25.2 25.5 25.9 26.3 The able shows how he average age of he firs marriage of Japanese women
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper March 3, 2009 2009 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion by
More informationI t ' 4 ti. t ti. IQ:::: mass x heat of fusion (or heat of vaporization) I HEAT AND ITS MEASUREMENT. t t. t f I I I. Name
HEAT AND TS MEASUREMENT Name a (or energy) can be measured in unis of calories or joules. When here is a,,,,,,nperaure change (AT), hea (Q) can be calculaed using his formula: During a phase change, we
More informationSemester Review Session
Semeser Review Session We will have a semeser review session on Wednesda, 1/10 a 4pm, here in room MPHY 03. If ou have a quesion(s ha ou would like me o go over, please drop me an email wih he problem
More informationCMA DiRECtions for ADMinistRAtion GRADE 6. California Modified Assessment. test Examiner and Proctor Responsibilities
CMA 2012 California Modified Assessmen GRADE 6 DiRECions for ADMinisRAion es Examiner and Procor Responsibiliies Compleing all of he following seps will help ensure ha no esing irregulariies occur, ha
More informationPaul M. Sommers David U. Cha And Daniel P. Glatt. March 2010 MIDDLEBURY COLLEGE ECONOMICS DISCUSSION PAPER NO
AN EMPIRICAL TEST OF BILL JAMES S PYTHAGOREAN FORMULA by Paul M. Sommers David U. Cha And Daniel P. Gla March 2010 MIDDLEBURY COLLEGE ECONOMICS DISCUSSION PAPER NO. 1006 DEPARTMENT OF ECONOMICS MIDDLEBURY
More informationPRESSURE SENSOR TECHNICAL GUIDE INTRODUCTION FEATURES OF ELECTRIC PRESSURE SENSOR. Photoelectric. Sensor. Proximity Sensor. Inductive. Sensor.
Proximiy INTRDUCTIN Pressur sensor The sensor convers of gases or liquid ino elecrical magniude wih he sensing elemen, and generaes he analog oupu proporional o applied level or he swiching oupu oggled
More informationMaking Sense of Genetics Problems
Bio 101 Ms. Bledsoe Making Sense of Geneics roblems Monohbrid crosses Le s sar wih somehing simle: crossing wo organisms and waching how one single rai comes ou in he offsring. Le s use eas, as Mendel
More informationAutomatic airmain charging and pressure control system for compressed air supplies
Auomaic airmain charging and pressure conrol sysem for compressed air supplies Type PCS A module from he sysem vacorol Swiching onoff a compressed air uni in a compressed air supply generally akes place
More informationInstruction Manual. Rugged PCB type. 1 Terminal Block. 2 Function. 3 Series Operation and Parallel Operation. 4 Assembling and Installation Method
Rugged PCB ype Insrucion Manual 1 Terminal Block Funcion.1...4.5.6.7 Inpu volage range Inrush curren limiing Overcurren proecion Overvolage proecion Oupu volage adjusmen range Isolaion Remoe ON/OFF E9
More informationType Control action Setpoint range Air Weight Volume flow % capacity I n /h kg. Pressure diff. 1) Pa
7.0/ RL 0 & 0: neumaic volumeflow conroller Used in conjuncion wih an orifice plae or a dnamic pressure sensor and a pneumaic damper drive for conrolling he air volume in aircondiioning ssems. For fixed,
More informationKEY CONCEPTS AND PROCESS SKILLS. 1. An allele is one of the two or more forms of a gene present in a population. MATERIALS AND ADVANCE PREPARATION
Gene Squares 61 40 o 2 3 50minue sessions ACIVIY OVERVIEW P R O B L E M S O LV I N G SUMMARY Sudens use Punne squares o predic he approximae frequencies of rais among he offspring of specific crier crosses.
More informationCapacity Utilization Metrics Revisited: Delay Weighting vs Demand Weighting. Mark Hansen ChiehYu Hsiao University of California, Berkeley 01/29/04
Capaciy Uilizaion Merics Revisied: Delay Weighing vs Demand Weighing Mark Hansen ChiehYu Hsiao Universiy of California, Berkeley 01/29/04 1 Ouline Inroducion Exising merics examinaion Proposed merics
More informationZelio Control Measurement Relays RM4L Liquid Level Relays
Zelio Conrol Measuremen elays FNCTIONS These devices monior he levels of conducive liquids. They conrol he acuaion of pumps or valves o regulae levels; hey are also suiable for proecing submersible pumps
More informationExamining the limitations for visual anglecar following models
Examining he limiaions for visual anglecar following models Al Obaedi, JTS and Yousif, S Tile Auhors Type URL Published Dae 009 Examining he limiaions for visual angle car following models Al Obaedi, JTS
More informationHomework 2. is unbiased if. Y is consistent if. c. in real life you typically get to sample many times.
Econ526 Mulile Choice. Homework 2 Choose he one ha bes comlees he saemen or answers he quesion. (1) An esimaor ˆ µ of he oulaion value µ is unbiased if a. ˆ µ = µ. b. has he smalles variance of all esimaors.
More information1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z
o ffix uden abel ere uden ame chool ame isric ame/ ender emale ale onh ay ear ae of irh an eb ar pr ay un ul ug ep c ov ec as ame irs ame lace he uden abel ere ae uden denifier chool se nly rined in he
More informationTRACK PROCEDURES 2016 RACE DAY
TRACK PROCEDURES 2016 RACE DAY Pi gaes will officially open a 4:00pm for regular programs. Big shows will have earlier opening imes. Hauler parking may be available approximaely 1 hour prior o pi gaes
More informationA BETTER WAY THRU ROCKAWAY
A BETTER WAY THRU ROCKAWAY Projec Underway is a communiy redevelopmen iniiaive focused on convering a negleced and underuilized roadway ha spans five linear miles along he Rockaway Peninsula ino a safer
More informationOath. The. Lifechanging Impact TEACH HEAL DISCOVER. Going Into the Wild to Save Rhinos. Tracking Down Outbreaks page 2. Teaming Up for Nekot page 7
The Oah TEACH HEAL DISCOVER FALL/WINTER 2016 Tracking Down Oubreaks page 2 Teaming Up for Neko page 7 Turle Parnership Turns 20 page 9 Avian Fellowship Creaes Nes Egg page 10 Lifechanging Impac Going
More information67.301/1. RLP 10: Pneumatic volumeflow controller. Sauter Components
7.0/ RL 0: neumaic volumeflow conroller How energ efficienc is improved For demandled conrol of he air volume in office rooms. Areas of applicaion Conrol of he suppl and exhaus air of individual rooms
More informationReliability Design Technology for Power Semiconductor Modules
Reliabiliy Design Technology for Power Semiconducor Modules Akira Morozumi Kasumi Yamada Tadashi Miyasaka 1. Inroducion The marke for power semiconducor modules is spreading no only o generalpurpose inverers,
More informationChapter / rev/min Ans. C / in. C mm Ans teeth Ans. C / mm Ans.
Chaper 13 131 dp 17 / 8 15 in N 110 dg dp 15 4375 in N3 544 NG PdG 84375 35 eeh C 15 4375 / 35 in Ans Ans ng 1600 15 / 60 400 rev/min Ans p m 3 mm Ans C 3 15 60 115 mm Ans 13133 N G 16 4 64 eeh Ans
More informationTOPIC 7: MAPPING GENES
Page 1 OPIC 7: MAPPING GENES MAPPING GENES 7.1: uning Cossove Fequencies ino Maps Making a geneic map compises hee pocesses: 1. Couning he numbe of cossove evens beween wo genes 2. Conveing cossove evens
More information"Pecos Bill Rides a Tornado" Stages Written by: Striker
"Pecos Bill Rides a Tornado" Sages Wrien by: Sriker Now everyone in he Wes knows ha Pecos Bill could ride anyhing. No bronco could hrow hi, no sir! Fac is, I only heard of Bill geing' hrowed once in his
More informationCALCULATION OF EXPECTED SLIDING DISTANCE OF BREAKWATER CAISSON CONSIDERING VARIABILITY IN WAVE DIRECTION
CALCULATION OF EXPECTED SLIDING DISTANCE OF BREAKWATER CAISSON CONSIDERING VARIABILITY IN WAVE DIRECTION SU YOUNG HONG School of Civil, Urban, and Geosysem Engineering, Seoul Naional Universiy, San 561,
More informationANALYSIS OF RELIABILITY, MAINTENANCE AND RISK BASED INSPECTION OF PRESSURE SAFETY VALVES
ANALYSIS OF RELIABILITY, MAINTENANCE AND RISK BASED INSPECTION OF PRESSURE SAFETY VALVES Venilon Forunao Francisco Machado Mechanical Engineering Dep, Insiuo Superior Técnico, Av. Rovisco Pais, 04900,
More information2. JOMON WARE ROPE STYLES
Proceedings of he IIEEJ Image Elecronics and Visual Compuing Workshop 2012 Kuching, Malaysia, November 2124, 2012 A SIMULATION SYSTEM TO SYNTHESIZE ROPE ROLLING PATTERNS IN A VIRTUAL SPACE FOR RESEARCH
More informationEconomics 487. Homework #4 Solution Key Portfolio Calculations and the Markowitz Algorithm
Economics 87 Homework # Soluion Key Porfolio Calculaions and he Markowiz Algorihm A. Excel Exercises: (10 poins) 1. Download he Excel file hw.xls from he class websie. This file conains monhly closing
More informationEvaluation of a carfollowing model using systems dynamics
Evaluaion of a carfollowing model using sysems dynamics Arif Mehmood, rank Saccomanno and Bruce Hellinga Deparmen of Civil Engineering, Universiy of Waerloo Waerloo, Onario, Canada N2 3G1 Tel: 519 888
More information2017 MCM/ICM Merging Area Designing Model for A Highway Toll Plaza Summary Sheet
Team#55307 Page 1 of 25 For office use only T1 T2 T3 T4 Team Conrol Number 55307 Problem Chosen B For office use only F1 F2 F3 F4 2017 MCM/ICM Merging Area Designing Model for A Highway Toll Plaza Summary
More informationThe ttest. What We Will Cover in This Section. A Research Situation
The es 1//008 P331 ess 1 Wha We Will Cover in This Secion Inroducion Onesample es. Power and effec size. Independen samples es. Dependen samples es. Key learning poins. 1//008 P331 ess A Research
More informationBGWinstallation instruction for BGWanchor with data head
BGWinsallaion insrucion for BGWanchor wih daa head BGW lifing eye wih swivel for axial and diagonal lif. Grease he hread well. Lifing loop for diagonal lifing unil 45. Screw he loop unil he ground of
More information29 B ROUTE Bus Times Summer NOTES a = Time at Vicarage Way. * = On Schooldays bus operates up to 5 minutes later.
Brighon Lewes Ringmer / Touris Aracions Lewes for Hisoric own wih Casle; Isfield for Lavender Line Railway; for Spa Valley Railway, Paniles CiySAVER ickes are only valid beween Brighon and Falmer. nework
More informationSan Francisco State University ECON 560 Fall Midterm Exam 2. Tuesday, October hour, 15 minutes
San Francisco Sae Universiy Micael Bar ECON 560 Fall 207 Miderm Exam 2 Tuesday, Ocober 3 our, 5 minues Name: Insrucions. Tis is closed book, closed noes exam. 2. No calculaors or elecronic devices of any
More informationLifecycle Funds. T. Rowe Price Target Retirement Fund. Lifecycle Asset Allocation
Lifecycle Funds Towards a Dynamic Asse Allocaion Framework for Targe Reiremen Funds: Geing Rid of he Dogma in Lifecycle Invesing Anup K. Basu Queensland Universiy of Technology The findings of he Mercer
More informationCombined air conditioning for heating rooms and improving of indoor climate
Agronomy Research 11 (2), 487 494, 2013 Combined air condiioning for heaing rooms and improving of indoor climae V. Viljasoo 1,*, J. Zadin 1, H. Jüris 2 and T. Pomerans 1 1 Insiue of Technology, Esonian
More information3 (R) 1 (P) N/en
3/ way failsafe safey valve, solenoid acuaed For mechanical presses and oher safey applicaions G /4... G, /4... NT Inherenly failsafe wihou residual pressure ynamic self monioring ouble valve conrol
More informationStrategic Decision Making in Portfolio Management with Goal Programming Model
American Journal of Operaions Managemen and Informaion Sysems 06; (): 3438 hp://www.sciencepublishinggroup.com//aomis doi: 0.648/.aomis.0600.4 Sraegic Decision Making in Porfolio Managemen wih Goal Programming
More information6.3 Using Slope LESSON EXPLORE ACTIVITY 1. rate of change =
v? LESSON 6.3 Using Slope ESSENTIL QUESTION Calculate and interpret the average rate of change of a function (presented smbolicall or as a table) over a specified interval. Estimate the rate of change
More informationXSz 8... XSz 50 Solenoid actuated failsafe safety valve
> > /way or size: G /4... G, /4... NT > > ouble valve conrol sysem, inherenly failsafe wihou residual pressure > > ynamic self monioring > > For use wih pneumaic cluch and brake sysems and oher way safey
More informationAn Alternative Mathematical Model for Oxygen Transfer Evaluation in Clean Water
An Alernaive Mahemaical Model for Oxygen Transfer Evaluaion in Clean Waer Yanjun (John) He 1, PE, BCEE 1 Kruger Inc., 41 Weson Parkway, Cary, NC 27513 Email: john.he@veolia.com ABSTRACT Energy consumpion
More informationBill Turnblad, Community Development Director City of Stillwater Leif Garnass, PE, PTOE, Senior Associate Joe DeVore, Traffic Engineer
Memorandum SRF No. 16 94 To: From: Bill Turnblad, Communiy Developmen Direcor Ciy of Sillwaer Leif Garnass, PE, PTOE, Senior Associae Joe DeVore, Traffic Engineer Dae: November 9, 16 Subjec: Downown Plan
More informationTHE DDL~c A~T\NO~KS RT!J BOX II!J HWYZ74 SEVEN POINTS, TX 7S143 TEL.!J0343Z!J426 FAX!J0343Z!JSOZ
PATTERN NUMBER 21.0verlap bib frons  aching dos pull up gahering hreads on fron bubble o fi bib frons hen pin and sew bib o bubble. Finish sea and bar ack sea allowances down a each side of he bib fron
More informationApplication of System Dynamics in Carfollowing Models
Applicaion of Sysem Dynamics in Carfollowing Models Arif Mehmood, rank Saccomanno and Bruce Hellinga Deparmen of Civil Engineering, Universiy of Waerloo Waerloo, Onario, Canada N2 3G1 Email: saccoman@uwaerloo.ca
More informationA Liability Tracking Portfolio for Pension Fund Management
Proceedings of he 46h ISCIE Inernaional Symposium on Sochasic Sysems Theory and Is Applicaions Kyoo, Nov. 12, 214 A Liabiliy Tracking Porfolio for Pension Fund Managemen Masashi Ieda, Takashi Yamashia
More informationPredicting Genotypes
Name: Preicing Genoypes ae: Perio: Preic he genoypes of each se of parens base on he phenoypes of he parens an offspring. Assume ha all possible phenoypes for he offspring are shown. Preic he mos likely
More informationA Probabilistic Approach to Worst Case Scenarios
A Probabilisic Approach o Wors Case Scenarios A Probabilisic Approach o Wors Case Scenarios By Giovanni BaroneAdesi Universiy of Albera, Canada and Ciy Universiy Business School, London Frederick Bourgoin
More informationMCW100A, B Time Proportional Rotary Position Controller
DESCRIPTION MCW100A, B Time Proporional Roary Posiion Conroller Issued: March 1992 The MCW100 Time Proporional Roary Posiion Conroller provides auomaic grade or seering conrol of paving, renching and curbing
More informationOverview. Do whitetailed tailed and mule deer compete? Ecological Definitions (Birch 1957): Mule and whitetailed tailed deer potentially compete.
COMPETITION BETWEEN MULE AND WHITE TAILED DEER METAPOPULATIONS IN NORTHCENTRAL WASHINGTON E. O. Garon, Kris Hennings : Fish and Wildlife Dep., Univ. of Idaho, Moscow, ID 83844 Maureen Murphy, and Seve
More informationThe Construction of a Bioeconomic Model of the Indonesian Flying Fish Fishery
Marine Resource Economics, Volume 0, pp. 357372 0738360/95 $3.00 +.00 Prined in he U.S.A. All righs reserved. Copyrigh 995 Marine Resources Foundaion The Consrucion of a Bioeconomic Model of he Indonesian
More informationThe safe ships trajectory in a restricted area
Scienific Journals Mariime Universiy of Szczecin Zeszyy Naukowe Akademia Morska w Szczecinie 214, 39(111) pp. 122 127 214, 39(111) s. 122 127 ISSN 1733867 The safe ships rajecory in a resriced area Zbigniew
More informationMVS. Electronic fan speed controller for DIN rail. Key features. Article codes Technical specifications. Area of use
MVS Elecronic fan speed conroller for DIN rail The MVS elecronic speed conrollers conrol he speed of singlephase volage conrollable elecric moors ( VAC / 5 6 z) according o a sandard inpu conrol signal.
More informationPatent NO: 8,430,895. Revision (3) OPERATION INSTRUCTIONS. Fully Automatic AirGun by AirOrdnance. HPA (High Pressure Compressed Air)
Paen NO: 8,430,895 Fully Auomaic AirGun by AirOrdnance Powered by: Co2 Nirogen HPA (High Pressure Compressed Air) OPERATION INSTRUCTIONS Revision (3) 62013 1. Please read his owner s manual compleely.
More informationWhat is a Practical (ASTM C 618) SAIStrength Activity Index for Fly Ashes that can be used to Proportion Concretes Containing Fly Ash?
2017 World of Coal Ash (WOCA) Conference in Lexingon, KY  May 911, 2017 hp://www.flyash.info/ Wha is a Pracical (ASTM C 618) SAISrengh Aciviy Index for Fly Ashes ha can be used o Proporion Concrees
More informationA Statistical, AgeStructured, LifeHistoryBased Stock Assessment Model for Anadromous Alosa
American Fisheries Sociey Symposium 35:275 283, 2003 2003 by he American Fisheries Sociey A Saisical, AgeSrucured, LifeHisoryBased Sock Assessmen Model for Anadromous Alosa A. JAMIE F. GIBSON 1 Acadia
More informationHood River Tributaries Instream Flow Study
Hood River Tribuaries Insream Flow Sudy Presened To: Hood River Couny 61 Sae Sree Hood River, OR 9731 Submied On: June 13, 214 Submied By: 89 L Sree Arcaa, CA 95521 www.normandeau.com Dra Hood River Tribuaries
More informationMarket Timing with GEYR in Emerging Stock Market: The Evidence from Stock Exchange of Thailand
Journal of Finance and Invesmen Analysis, vol. 1, no. 4, 2012, 5365 ISSN: 22410998 (prin version), 22410996(online) Scienpress Ld, 2012 Marke Timing wih GEYR in Emerging Sock Marke: The Evidence from
More informationSouthern Equestrian Challenge BIET IEA Horse Show Zone 4 Region 10 Host: BIET CoHost: Chelsea Equestrian
Souhern Equesrian Challenge BIET IEA Horse Show Zone 4 Region 10 Hos: BIET CoHos: Chelsea Equesrian Saurday ember 17, 2018 Show ID #: HB4032 Sunday ember 18, 2018 Show ID # HB4033 Clairmon Show Sables
More informationOutline. Objectives. Objectives. Objectives Progressive waves. Wave motion. Wave motion
Chaper. Liew Sau Poh Wave moion Ouline. Progressive Waves. Wave Inensi.3 Principle of Superposiion.4 Sanding Waves.5 Elecromagneic Waves Objecives a) inerpre and use he progressive wave equaion, = a sin
More informationMattaponi Sundowners
Maaponi Sundowner STAGES FOR SATURDAY, February 25, 2017 Sage Wrien by: Cody Maverick Sory Line: Sage Convenion SASS STAGE CONVENTIONS Fro Shooer Handbook v22.3 Sage Convenion, or andard range behavior,
More informationScienceDirect. Cycling Power Optimization System Using Link Models of Lower Limbs with CleatShaped Biaxial Load Cells
Available online a www.sciencedirec.com ScienceDirec Procedia Engineering 72 ( 20 ) 8 7 The 20 conference of he Inernaional Spors Engineering Associaion Cycling Power Opimizaion Sysem Using ink Models
More information2020 ClearTrace Inline Turbidity System
2020 ClearTrace Inline Turbidiy Sysem Code 5011324V Code 50113110V Preface This insrucion manual serves o explain he use of he LaMoe 2020 ClearTrace Inline Turbidiy Sysem and is wrien o cover as
More informationAs time goes by  Using time series based decision tree induction to analyze the behaviour of opponent players
As ime goes by  Using ime series based decision ree inducion o analyze he behaviour of opponen players Chrisian Drücker, Sebasian Hübner, Ubbo Visser, HansGeorg Weland TZI  Cener for Compuing Technologies
More informationAvoiding Component Failure in Industrial Refrigeration Systems
Avoiding Componen Failure in Indusrial Refrigeraion Sysems By Tim Kroeger, segmen markeing manager indusrial refrigeraion, Asia Pacific & India The aricle caegorises and gives examples of ypical componen
More informationIdiosyncratic Volatility, Stock Returns and Economy Conditions: The Role of Idiosyncratic Volatility in the Australian Stock Market
Idiosyncraic Volailiy, Sock Reurns and Economy Condiions: The Role of Idiosyncraic Volailiy in he Ausralian Sock Marke Bin Liu Amalia Di Iorio RMIT Universiy Melbourne Ausralia Absrac This sudy examines
More informationLesson 5.3 Interpreting and Sketching Graphs Exercises (pages )
Lesson 5.3 Interpreting and Sketching Graphs Exercises (pages 281 283) A 3. a) Bear F has the greatest mass because it is represented by the point on the graph farthest to the right and the horizontal
More informationMORTALITY ESTIMATES FOR JUVENILE DUSKY SHARKS CARCHARHINUS OBSCURUS IN SOUTH AFRICA USING MARKRECAPTURE DATA. A. GOVENDER* and S. L.
S. Afr. J. mar. Sci. 18: 1118 1997 11 MORTALITY ESTIMATES FOR JUVENILE DUSKY SHARKS CARCHARHINUS OBSCURUS IN SOUTH AFRICA USING MARKRECAPTURE DATA A. GOVENDER* and S. L. BIRNIE* A maximum likelihood
More informationCONNECTIONS. Key Words Splices, Bolted Splice, Bolted Column Splice, Minor Axis Splice
COECTIOS Boled Column Splice wih Minor Axi Bending Auhor: Zahid Hamid, Kevin Cowie Affiliaion: Seel Conrucion ew Zealand Inc. Dae: 19 h February 015 Ref: CO310 Key Word Splice, Boled Splice, Boled Column
More informationDo Competitive Advantages Lead to Higher Future Rates of Return?
Do Compeiive Advanages Lead o Higher Fuure Raes of Reurn? Vicki Dickinson Universiy of Florida Greg Sommers Souhern Mehodis Universiy 2010 CARE Conference Forecasing and Indusry Fundamenals April 9, 2010
More informationStock Return Expectations in the Credit Market
Sock Reurn Expecaions in he Credi Marke Hans Bysröm * Sepember 016 In his paper we compue longerm sock reurn expecaions (across he business cycle) for individual firms using informaion backed ou from
More informationINSTALLATION AND OPERATION MANUAL
Please read THE enire CONTENTS OF THIS MANUAL prior o insallaion AND OPERATION. BY PROCEEDING YOU AGREE THAT YOU FULLY UNDERSTAND AND COMPREHEND THE FULL CONTENTS OF THIS MANUAL. Forward his manual o all
More informationSection 4.2 Objectives
Section 4. Objectives Determine whether the slope of a graphed line is positive, negative, 0, or undefined. Determine the slope of a line given its graph. Calculate the slope of a line given the ordered
More informationLEWA intellidrive. The mechatronic AllinOne pump system. intelligent flexible dynamic high precision. Foto: ratiopharm
The mecharonic AllinOne pump sysem Foo: raiopharm inelligen flexible dynamic high precision For diverse applicaions: a limiless range of poenial uses Phoo: raiopharm Mixing wo media in one pump head:
More informationDevelopment of Urban Public Transit Network Structure Integrating MultiClass Public Transit Lines and Transfer Hubs
Developmen of Urban Public Transi Nework Srucure Inegraing MuliClass Public Transi Lines and Transfer Hubs Zhenbao Wang 1, Anyan Chen 2 1College of Civil Engineering, Hebei Universiy of Engineering Handan,
More informationEconomic Growth & Development: Part 3 Horizontal Innovation Models: Applications. By Kiminori Matsuyama. Updated on , 6:12:26 PM
iminori Masuyama Groh & Develomen Par3 Economic Groh & Develomen: Par 3 orizonal Innovaion Models: licaions By iminori Masuyama Udaed on 004 6::6 PM Page of 6 iminori Masuyama Groh & Develomen Par3
More informationUS 9,615,553 B2 Apr. 11,2017
111111111111111111111111111111111111111111111111111111111111111111111111111 US009615553B2 (12) Unied Saes Paen Coniglio e al. (10) Paen No.: (45) Dae of Paen: US 9,615,553 B2 Apr. 11,2017 (54) ARTIFICIAL
More informationModeling Exponential Growth and Decay
Lesson 74 Lesson 74 Modeling Eponential Growth and Deca Vocabular eponential regression BIG IDEA Situations of eponential growth and deca can be modeled b equations of the form = bg. As ou saw with the
More informationNozzle valve system for the variable atomization of very small liquid volumes
Nozzle valve sysem for he variable aomizaion of very small liquid volumes V E R Y S M A L L L I Q U I D V O L U M E S M A X I M U M B E N E F I T Innovaive spraying echnology opens up new applicaions The
More informationBackscattered Acoustic Energy by Monobubbles Experimental Approach and Statistical Study of the Attenuation
American J. of Engineering and Applied Sciences 2 (2): 399406, 2009 ISSN 19417020 2009 Science Publicaions Backscaered Acousic Energy by Monobubbles Experimenal Approach and Saisical Sudy of he Aenuaion
More informationDetection of activity cycles from capturerecapture data
See discussions, sas, and auhor profiles for his publicaion a: hps://www.researchgae.ne/publicaion/264644551 Deecion of aciviy cycles from capurerecapure daa Aricle in cological nomology February 1986
More informationCal. 7T85 INSTRUCTIONS (P. 3) BEDIENUNGSANLEITUNG (S. 27) INSTRUCTIONS (P. 51) ISTRUZIONI (P. 75) INSTRUCCIONES (P. 99) INSTRUÇÕES (P.
Cal. 7T85 INSTRUCTIONS (P. 3) BEDIENUNGSANLEITUNG (S. 27) INSTRUCTIONS (P. 51) ISTRUZIONI (P. 75) INSTRUCCIONES (P. 99) INSTRUÇÕES (P. 123) (147 ) You are now he proud owner of a SEIKO Analogue Quarz Wach
More informationCOVER S UNIVERSAL PORTFOLIO, STOCHASTIC PORTFOLIO THEORY AND THE NUMÉRAIRE PORTFOLIO
COVER S UNIVERSAL PORFOLIO, SOCHASIC PORFOLIO HEORY AND HE NUMÉRAIRE PORFOLIO CHRISA CUCHIERO, WALER SCHACHERMAYER AND INGKAM LEONARD WONG Absrac. Cover s celebraed heorem saes ha he long run yield of
More informationPerformance Attribution for Equity Portfolios
PERFORMACE ATTRIBUTIO FOR EQUITY PORTFOLIOS Performance Aribuion for Equiy Porfolios Yang Lu and David Kane Inroducion Many porfolio managers measure performance wih reference o a benchmark. The difference
More informationSPECIAL WIRE ROPES The Value Line
SPECIAL WIRE ROPES The Value Line INTRODUCTION Qualiy Producs, Ousanding Service and Comprehensive Technical Suppor I s wha oday s indusries expec from heir supplier parners. And ha s wha WireCo WorldGroup
More information