AIP Logic Chapter 4 Notes

Save this PDF as:

Size: px
Start display at page:

Download "AIP Logic Chapter 4 Notes"

Transcription

1 AIP Lgic Chapter 4 Ntes Sectin 4.1 Sectin 4.2 Sectin 4.3 Sectin 4.4 Sectin 4.5 Sectin 4.6 Sectin The Cmpnents f Categrical Prpsitins There are fur types f categrical prpsitins. Prpsitin Letter Name Prpsitin What is the assertin? A All S are P. The whle subject class [S] is included in the predicate class [P]. E N S are P. The whle subject class [S] is excluded frm the predicate class [P]. I Sme S are P. Part f the subject class [S] is included in the predicate class [P]. O Sme S are nt P. Part f the subject class [S] is excluded frm the predicate class [P]. 5 parts f a categrical prpsitin 1. Statement letter name (A, E, I r O). 2. Quantifier: "all", "n" r "sme" 3. Subject term 4. Cpula: either "are" r "are nt"; links/cuples the subject term with the predicate term. 5. Predicate term Things t remember: Standard-frm prpsitins have fur distinct cmpnents. Yu cannt cmbine the varius parts in lgic. The terms "subject" and "predicate" "d nte mean the same thing in lgic" that they mean in grammar. The frm "All S are nt P", is nt a standard frm. Tw ways f translating it are: 1. N S are P. r 2. Sme S are nt P. In this text there are nly three frms f quantifiers and tw types f cpulas (see abve). Other texts allw fr variatins, but fr simplicity s sake, we ll nly deal with this limited set.

2 2 Hurley Chapter 4 Lgic Ntes 4.2 Quality Quantity & Distributin Universal Prpsitins: assert smething abut every member f the S class A: All S are P. E: N S are P. Particular Prpsitins: assert smething abut ne r mre members f the S class I: Sme S are P O: Sme S are nt P. Affirmative Prpsitins: affirm class membership r put members int grups A: All S are P. I: Sme S are P. Negative Prpsitins: deny class membership r remve members frm grups. E: N S are P. O:: Sme S are nt P.

3 3 Hurley Chapter 4 Lgic Ntes 4.3 Venn Diagrams & the Mdern Square f Oppsitin 2 Ways t Interpret Categrical Prpsitins 1. Aristtelian: things actually exist in all prpsitins 2. Blean: n assumptins abut existence Aristtelian and Blean differ nly in regard t A and E prpsitins. Fr I and O prpsitins, there is a psitive claim abut existence (things actually exist). Jhn Venn (19th century): created Venn Diagram system. A E I O Cntradictries: A & O; E & I Review the mdern square f ppsitin. Cntradictry relatin = ppsite truth value

4 4 Hurley Chapter 4 Lgic Ntes Hw t test arguments fr validity using the Mdern Square f Oppsitin: a step-by-step guide. 1. Symblize the argument. 2. Draw a small square. 3. Plt the truth values given fr the premise and cnclusin nt the square. 4. Ask yurself if a) the statements are diagnally ppsed, and b) have ppsite truth values (i.e., ne is true and the ther is false). 5. If the answer t either questin is "n," then the argument is invalid. 6. If yu answer "yes" t bth questins, then the argument is valid. immediate inferences = arguments that have nly ne premise See prcess in actin Prcess fr testing arguments fr validity with Venn diagrams: a step-by-step guide. 1. Determine the letter names fr bth the premise and cnclusin statements. 2. Draw a Venn diagram fr the premise. 3. Draw a Venn diagram fr the cnclusin. 4. What t d when yu have a false statement: When yu have a statement that begins with the phrase "it is false that..." draw the diagram fr the cntradictry prpsitin f that statement. Fr example, if yu have an A statement, "Is is false that all S are P." [A statement false], draw the Venn diagram fr the statement, "Sme S are nt P." [O statement True] GIVEN STATEMENT False A False E False I False O DIAGRAM TO DRAW O I E A 5. If the tw diagrams express the same infrmatin (i.e., are identical), the argument is valid, therwise the argument is invalid.

5 5 Hurley Chapter 4 Lgic Ntes 4.4 Cnversin, Obversin & Cntrapsitin (three mves t alter subjects and predicates) General Ntes: 1. We are adding a new truth value fr prpsitins in Sectin 4.4. It is called undetermined. 2. Each mve belw can nly be perfrmed n the statements indicated within the explanatin. When a mve is applied t a statement accrding t the rules belw, it is called a legal mve. 3. When yu make a legal mve, statements keep/retain their riginally truth values. Thus, if a statement is true and yu make a legal mve, the statement stays true. When a statement is false and yu make a legal mve, the statement stays false. 4. When a mve is applied t a statement and vilates ne f the rules belw, it is called an illegal/illicit mve and the truth value fr the resulting statement will be undetermined. 5. When yu make a legal mve, the beginning statement and the statement generated after making the mve are said t be lgically equivalent (i.e., this indicates bth statements mean the same thing). Cnversin: switch subject and predicate Review the diagrams t be sure yu understand the relatin being expressed. What is it? Cnversin is a mve that allws us t switch subjects and predicates fr E & I statements nly. When is it a legal mve? Cnversin can nly be used n E & I statements. Hw d I cnvert E & I statements? Switch the subject and predicate terms. Examples: T cnvert the statement: N cats are fish, we switch the subject and predicate terms t N fish are cats. Since these tw statements mean the same thing, we state that they are lgically equivalent. Cntrapsitin: tw steps Review the diagrams t be sure yu understand the relatin being expressed. What is it? Cntrapsitin is a mve that allws us t switch the subject and predicate terms fr A & O statements while als changing each term t its cmplement. When is it a legal mve? Cntrapsitin can be used n A & O statements nly. Hw d I cntrapse statements? this is a tw-step prcess 1. Switch subject and predicate terms. 2. Change bth the subject and predicate term t its cmplement (i.e., ppsite). Examples: T cntrapse the statement: All cats are fish, we first switch the subject & predicate terms t the A statement yielding "All fish are cats. Next we change each term t its cmplement and the final statement is All nn-fish are nn-cats. Obversin: tw steps Yu d nt have t shw each step, just the riginal and final statements. Since these tw statements mean the same thing, we state that they are lgically equivalent. Review the diagrams t be sure yu understand the relatin being expressed. What is it? Obversin is a mve that allws us t switch the quality and predicate terms fr all fur statements: A, E, I & O. When is it a legal mve? Obversin can be used n A, E I & O statements.

6 6 Hurley Chapter 4 Lgic Ntes Hw d I bvert statements? this is a tw-step prcess 1. Change the quality f the statement (i.e., mve hrizntally acrss the square frm the current statement letter) and, 2. Change the predicate term t its cmplement (i.e., ppsite). Examples: T bvert the statement: N cats are fish, we first mve hrizntally t the A statement yielding "All cats are. Next we change the predicate term t its cmplement and the final statement is All cats are nn-fish.. Yu d nt have t shw each step, just the riginal and final statements. Since these tw statements mean the same thing, we state that they are lgically equivalent. Testing arguments fr validity. Three Steps: 1. Symblize the argument. 2. Determine which f the three new mves: cnversin, cntrapsitin r bversin has taken place between the premise and cnclusin f the argument. 3. If the mve is a legal mve, then the argument is valid. If the mve is illegal/illicit, the argument is invalid. Nte: it is critical that yu memrize legal versus illegal mves (r learn which statements are nt lgically equivalent) t d well n the quiz and subsequent tests n this material. 4.5 The Traditinal Square f Oppsitin (mves t determine truth relatinships fr statements with the same subject & predicate) This square is ften called the Aristtelian Square f Oppsitin. 1. All f the general rules intrduced at the beginning f sectin 4.4 still apply here. 2. Thus when we add the three new mves belw, there will be legal versus illegal mves. 3. It is pssible t have an illegal cntrary statement, illegal subcntrary statement and illegal subalternatin. The truth value f the resulting statements (after an illegal mve) is undetermined. 4. T understand the cncepts belw, yu must understand the cncept f a minimum cnditin. The minimum cnditin is met when the criteria fr meeting a rule are fulfilled: e.g. each credit card has a minimum mnthly payment fr peple wh carry balances mnth t mnth. When yu make the minimum payment, yu are fulfilling the minimum cnditin t keep the accunt in gd standing. Anther example is that requirement that yu have a minimum amunt f credits t graduate alng with a passing prtfli. When bth requirements are fulfilled, yu have met the minimum cnditins fr graduatin. Remember: 1. Aristtelian: things actually exist in all prpsitins 2. Blean: n assumptins abut existence Here are the three new mves (i.e., relatinships) we are adding t the square:

7 7 Hurley Chapter 4 Lgic Ntes Pints t nte: Cntrary relatin (A & E statements nly): at least ne is false S, if we already knw that either the A r the E prpsitin is false, the truth value f the remaining prpsitin is undetermined. Subcntrary relatin (I & O statements nly): at least ne is true S, if we already knw that either the I r the O prpsitin is true, the truth value f the remaining prpsitin is undetermined. Subalternatin relatin (relatin between A & I statements and E & O statements): truth flws dwnward and falsity flws upward If we are given an A r an E prpsitin that is false, the truth value f the crrespnding I r O prpsitin is undetermined. Als, if we are given an I r an O prpsitin that is true, the truth value f the crrespnding A r E prpsitin is undetermined. Testing Immediate Inferences There are tw kinds f immediate inferences: thse yu can use the square f ppsitin t test, (i.e., subjects and predicates remain the same) and thse in which yu will have t reduce the number f terms thrugh cnversin, bversin and cntrapsitin befre using the square t test. Testing Immediate Inferences using the traditinal square f ppsitin nly Three Steps: 1. Symblize the argument 2. Assume the premise and cnclusin are true unless yu see the phrase: "It is false that..." 3. Determine the type f relatin (i.e., the mve that has ccurred) that exists between the premise and cnclusin.

8 8 Hurley Chapter 4 Lgic Ntes 4. Using the basic relatins frm the traditinal square f ppsitin, deduce the truth value f the cnclusin. 5. If the mve is a legal mve, then the argument is valid. If the mve is illegal/illicit (i.e., the cnclusin is undetermined), the argument is invalid. Three Fallacies:these fallacies ccur when arguments ask us t vilate the relatinal rules in the traditinal square. Any time the prblem generates an undetermined truth value fr the cnclusin, the argument is invalid and ne f the fallacies belw has been cmmitted. 1. Illicit cntrary (An A r E premise is false and the cnclusin is undetermined): argument tries t use an invalid applicatin f the cntrary relatin. 2. Illicit subcntrary (An I r O premise is true and the cnclusin is undetermined): argument tries t use an invalid applicatin f the subcntrary relatin. 3. Illicit subalternatin (Truth is flwing upwards r falsity is flwing dwnwards between A & I statements r E & O statements): argument tries t use an invalid applicatin f the subalternatin relatin. The Prfs: Sectin 4.5 Part V (Testing Immediate Inferences using cnversin, bversin and cntrapsitin plus the traditinal square f ppsitin) Please understand that yu will nt be able t cmplete these prblems unless yu thrughly understand the mves presented in sectins 4.4 & 4.5. If yu d nt learn thse mves, yu will nt understand hw t chse yur mves in step 4 belw. Hence, if yu have prblems with the prfs, my advice is always the same, g back and learn the mves again. A Step-by-step prcess fr ding these prblems: 1. Symblize the argument. 2. The bject f the game is t transfrm the premise statement int the cnclusin statement using nly legal mves. 3. Determine which terms (subject and predicate) may have t be switched and/r transfrmed int their cmplements. This determinatin will help yu chse the mves that yu will use. 4. Sme hints fr chsing yur mves: 1. If nly ne term is t be changed t its cmplement, then it is likely that yu will use bversin alng the way. 2. If the terms have t be switched, it is likely yu will need t use cnversin. 3. If bth terms must be switched and changed t their cmplements, then cntrapsitin will be used. 4. Mving arund the square des nt change subjects and predicates, it changes letter names and truth values nly. 5. Keep track f letter names and truth values fr each statement because they will influence yur next mve in the prf.

9 9 Hurley Chapter 4 Lgic Ntes Make a chart fr each prblem that lks like this: (This example is frm the exercises: Part V, #9.) Letter Name Truth Value Prpsitin Inference Name O F Sme nn-l are nt S. given E F N nn-l are S. subalternatin E F N S are nn-l. cnversin A F All S are L. bversin O T Sme S are nt L. cntradictry 4.6 Venn Diagrams and the Traditinal Standpint 1. Nte hw the cncept f existence changes the diagramming f relatinships. 2. The diagrams have been mdified t shw that the subalternatin mve can prduce valid arguments. 3. Tw diagrams change fr the purpse f prving arguments valid r invalid by subalternatin: The A diagram:yu will use this diagram fr premise statements in tw cases: 1) a true A statement r 2) a false O statement The E diagram: yu will use this diagram fr premise statements in tw cases: 1) a true E statement r 2) a false I statement 4. Nte the changes in prving validity when we add the existence symbl t the A and E prpsitins. There are nw direct inferences that can be made frm the universal prpsitins

10 10 Hurley Chapter 4 Lgic Ntes t their respective particular prpsitins (I and O) via subalternatin and vice versa ging upward frm the particulars t the universals. 5. When d I use the new diagrams? Use the new diagrams when yu have t draw an A r E diagram fr a premise statement nly. When yu are drawing an A r E diagram fr a cnclusin statement, cntinue t draw the ld diagram. 6. Hw des this change ur view f an argument's validity? By using this technique yu are shwing that arguments can als be valid under the rule f subalternatin: when A is true, I is als true and when E is true, O is als true. 4.7 Translating Ordinary Language Statements int Categrical Frm Tw Benefits 1. Can manipulate using square f ppsitin and new argument evaluatin techniques learned in this chapter. 2. Renders statements "cmpletely clear and unambiguus." Types f Transfrmatins: 1. Terms Withut Nuns Review the sentence beginning "Nuns and prnuns." 2. Nn-standard Verbs We are wrking with the frm f the verb "t be." Varius tenses (i.e., will, will nt, has, has nt). This invlves translating all ther cpulas int statements that cntain the phrases "are" r "are nt." 3. Singular Prpsitins Watch fr plural frms f nuns as they shuld nt be translated in this matter. 4. Adverbs and Prnuns Wrds t lk ut fr - the ht list: Spatial Adverbs where wherever anywhere Tempral Adverbs when whenever anytime

11 11 Hurley Chapter 4 Lgic Ntes Spatial Adverbs everywhere nwhere Tempral Adverbs always never NOTE: There is a "switching the rder" trick that must ccur if ne f the abve wrds ccurs in the middle f a statement. 5. Unexpressed Quantifiers Here, "quantifiers are implied but nt expressed." The trick is figuring ut if we are talking abut "all" r "sme" f the nun in questin. Nte the last tw examples in this sectin use tw different uses f the wrd children. 6. Nnstandard Quantifiers The frm "All S are nt P" is nt standard frm. Translatin determines meaning: e.g., All athletes are nt superstars. The previus statement is nt a universal prpsitin, but rather a particular claim. Read "At least ne athlete is nt a superstar." 7. Cnditinal Statements Cnditinal statements are always rendered as universals! NOTE: When a cnditinal statement appears in the middle f a sentence, "the statement must be restructured s that it the beginning." Transpsitin: applies t cnditinal statements where bth terms are negated. Nte/reread the middle paragraphs n p.246 and g ver the examples again. The wrd "unless" means "if nt"again, the transpsitin rule applies here. Carefully g ver the examples. 8. Exclusive Prpsitins Wrds t lk fr: nly, nne but, nne except Tw step Prcess t render statement int standard frm: 1. First phrase as a cnditinal statement. 2. Transfrm int a categrical statement. (Remember all cnditinal statements are translated as universals as nted abve in #7.) Nte als hw individual references wrk. Basically, these references generate tw categrical prpsitins. Our curse ignres these special cases. When nly and nne but are in the middle f a sentence, they are transpsed. Only can be rendered in many ways. Thus, it is ambiguus.

12 12 Hurley Chapter 4 Lgic Ntes 9. "The Only" If the wrds "the nly" appear at the beginning f a phrase, they can be replaced by the wrd "all" an n transpsitin is necessary. But, if these wrds appear in the middle f a phrase, then the statement must be transpsed befre putting it int standard frm. "The nly" is like nly in that is ambiguus and has t be rendered using tw statements fr clarity. 10. Exceptive Prpsitins Tw frms: 1. All except S are P. 2. All but S are P. These statements generate tw standard frm prpsitins. Key Wrd Translatin Hint whever wherever always anyne never, etc. use all tgether with persns, places and times a few sme if.. then use "all" r "n" unless "if nt" nly nne but, nne except, and n.except. use "all" switch rder f terms the nly "all" all but, all except, few tw statements required

13 13 Hurley Chapter 4 Lgic Ntes "nt every" and nt all Key Wrd Translatin Hint "sme are nt" there is "sme"

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came. MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the

More information

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y ) (Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well

More information

Getting Involved O. Responsibilities of a Member. People Are Depending On You. Participation Is Important. Think It Through

Getting Involved O. Responsibilities of a Member. People Are Depending On You. Participation Is Important. Think It Through f Getting Invlved O Literature Circles can be fun. It is exciting t be part f a grup that shares smething. S get invlved, read, think, and talk abut bks! Respnsibilities f a Member Remember a Literature

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving. Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus

More information

37 Maxwell s Equations

37 Maxwell s Equations 37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut

More information

A proposition is a statement that can be either true (T) or false (F), (but not both).

A proposition is a statement that can be either true (T) or false (F), (but not both). 400 lecture nte #1 [Ch 2, 3] Lgic and Prfs 1.1 Prpsitins (Prpsitinal Lgic) A prpsitin is a statement that can be either true (T) r false (F), (but nt bth). "The earth is flat." -- F "March has 31 days."

More information

Lesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method.

Lesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method. Lessn Plan Reach: Ask the students if they ever ppped a bag f micrwave ppcrn and nticed hw many kernels were unppped at the bttm f the bag which made yu wnder if ther brands pp better than the ne yu are

More information

READING STATECHART DIAGRAMS

READING STATECHART DIAGRAMS READING STATECHART DIAGRAMS Figure 4.48 A Statechart diagram with events The diagram in Figure 4.48 shws all states that the bject plane can be in during the curse f its life. Furthermre, it shws the pssible

More information

Revisiting the Socrates Example

Revisiting the Socrates Example Sectin 1.6 Sectin Summary Valid Arguments Inference Rules fr Prpsitinal Lgic Using Rules f Inference t Build Arguments Rules f Inference fr Quantified Statements Building Arguments fr Quantified Statements

More information

SPH3U1 Lesson 06 Kinematics

SPH3U1 Lesson 06 Kinematics PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.

More information

Please Stop Laughing at Me and Pay it Forward Final Writing Assignment

Please Stop Laughing at Me and Pay it Forward Final Writing Assignment Kirk Please Stp Laughing at Me and Pay it Frward Final Writing Assignment Our fcus fr the past few mnths has been n bullying and hw we treat ther peple. We ve played sme games, read sme articles, read

More information

Lab 1 The Scientific Method

Lab 1 The Scientific Method INTRODUCTION The fllwing labratry exercise is designed t give yu, the student, an pprtunity t explre unknwn systems, r universes, and hypthesize pssible rules which may gvern the behavir within them. Scientific

More information

Lifting a Lion: Using Proportions

Lifting a Lion: Using Proportions Overview Students will wrk in cperative grups t slve a real-wrd prblem by using the bk Hw D yu Lift a Lin? Using a ty lin and a lever, students will discver hw much wrk is needed t raise the ty lin. They

More information

Pipetting 101 Developed by BSU CityLab

Pipetting 101 Developed by BSU CityLab Discver the Micrbes Within: The Wlbachia Prject Pipetting 101 Develped by BSU CityLab Clr Cmparisns Pipetting Exercise #1 STUDENT OBJECTIVES Students will be able t: Chse the crrect size micrpipette fr

More information

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

More information

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10] EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gate-level smetimes we just

More information

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018 Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

More information

ALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change?

ALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change? Name Chem 163 Sectin: Team Number: ALE 21. Gibbs Free Energy (Reference: 20.3 Silberberg 5 th editin) At what temperature des the spntaneity f a reactin change? The Mdel: The Definitin f Free Energy S

More information

BASD HIGH SCHOOL FORMAL LAB REPORT

BASD HIGH SCHOOL FORMAL LAB REPORT BASD HIGH SCHOOL FORMAL LAB REPORT *WARNING: After an explanatin f what t include in each sectin, there is an example f hw the sectin might lk using a sample experiment Keep in mind, the sample lab used

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

Trigonometric Ratios Unit 5 Tentative TEST date

Trigonometric Ratios Unit 5 Tentative TEST date 1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin

More information

Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law

Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law Sectin 5.8 Ntes Page 1 5.8 Expnential Grwth and Decay Mdels; Newtn s Law There are many applicatins t expnential functins that we will fcus n in this sectin. First let s lk at the expnential mdel. Expnential

More information

Introduction to Spacetime Geometry

Introduction to Spacetime Geometry Intrductin t Spacetime Gemetry Let s start with a review f a basic feature f Euclidean gemetry, the Pythagrean therem. In a twdimensinal crdinate system we can relate the length f a line segment t the

More information

Subject description processes

Subject description processes Subject representatin 6.1.2. Subject descriptin prcesses Overview Fur majr prcesses r areas f practice fr representing subjects are classificatin, subject catalging, indexing, and abstracting. The prcesses

More information

Five Whys How To Do It Better

Five Whys How To Do It Better Five Whys Definitin. As explained in the previus article, we define rt cause as simply the uncvering f hw the current prblem came int being. Fr a simple causal chain, it is the entire chain. Fr a cmplex

More information

CONSTRUCTING STATECHART DIAGRAMS

CONSTRUCTING STATECHART DIAGRAMS CONSTRUCTING STATECHART DIAGRAMS The fllwing checklist shws the necessary steps fr cnstructing the statechart diagrams f a class. Subsequently, we will explain the individual steps further. Checklist 4.6

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

Group Color: Subgroup Number: How Science Works. Grade 5. Module 2. Class Question: Scientist (Your Name): Teacher s Name: SciTrek Volunteer s Name:

Group Color: Subgroup Number: How Science Works. Grade 5. Module 2. Class Question: Scientist (Your Name): Teacher s Name: SciTrek Volunteer s Name: Grup Clr: Subgrup Number: Hw Science Wrks Grade 5 Mdule 2 Class Questin: Scientist (Yur Name): Teacher s Name: SciTrek Vlunteer s Name: VOCABULARY Science: The study f the material wrld using human reasn.

More information

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science Weathering Title: Chemical and Mechanical Weathering Grade Level: 9-12 Subject/Cntent: Earth and Space Science Summary f Lessn: Students will test hw chemical and mechanical weathering can affect a rck

More information

YEAR 5 TRINITY TERM EXAMINATIONS 2013

YEAR 5 TRINITY TERM EXAMINATIONS 2013 YEAR 5 TRINITY TERM EXAMINATIONS 2013 Maths 1 hur 1 hur nn calculatr paper. The main fcus f the exam will be. Term 3 Averages Understand the usefulness f expressing a set f data as ne number Can find the

More information

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards: MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use

More information

Aristotle I PHIL301 Prof. Oakes Winthrop University updated: 3/14/14 8:48 AM

Aristotle I PHIL301 Prof. Oakes Winthrop University updated: 3/14/14 8:48 AM Aristtle I PHIL301 Prf. Oakes Winthrp University updated: 3/14/14 8:48 AM The Categries - The Categries is ne f several imprtant wrks by Aristtle n metaphysics. His tpic here is the classificatin f beings

More information

Purpose: Use this reference guide to effectively communicate the new process customers will use for creating a TWC ID. Mobile Manager Call History

Purpose: Use this reference guide to effectively communicate the new process customers will use for creating a TWC ID. Mobile Manager Call History Purpse: Use this reference guide t effectively cmmunicate the new prcess custmers will use fr creating a TWC ID. Overview Beginning n January 28, 2014 (Refer t yur Knwledge Management System fr specific

More information

THE LIFE OF AN OBJECT IT SYSTEMS

THE LIFE OF AN OBJECT IT SYSTEMS THE LIFE OF AN OBJECT IT SYSTEMS Persns, bjects, r cncepts frm the real wrld, which we mdel as bjects in the IT system, have "lives". Actually, they have tw lives; the riginal in the real wrld has a life,

More information

Thermodynamics Partial Outline of Topics

Thermodynamics Partial Outline of Topics Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)

More information

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

More information

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax .7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical

More information

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical

More information

Activity Guide Loops and Random Numbers

Activity Guide Loops and Random Numbers Unit 3 Lessn 7 Name(s) Perid Date Activity Guide Lps and Randm Numbers CS Cntent Lps are a relatively straightfrward idea in prgramming - yu want a certain chunk f cde t run repeatedly - but it takes a

More information

Thermodynamics and Equilibrium

Thermodynamics and Equilibrium Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,

More information

Hypothesis Tests for One Population Mean

Hypothesis Tests for One Population Mean Hypthesis Tests fr One Ppulatin Mean Chapter 9 Ala Abdelbaki Objective Objective: T estimate the value f ne ppulatin mean Inferential statistics using statistics in rder t estimate parameters We will be

More information

Romeo and Juliet Essay

Romeo and Juliet Essay Rme and Juliet Essay Texts may be analyzed and interpreted in many ways. Shakespearean wrks are n different in that they have been subject t varius types f investigatin and analysis. Indeed, entire curses

More information

Standard Title: Frequency Response and Frequency Bias Setting. Andrew Dressel Holly Hawkins Maureen Long Scott Miller

Standard Title: Frequency Response and Frequency Bias Setting. Andrew Dressel Holly Hawkins Maureen Long Scott Miller Template fr Quality Review f NERC Reliability Standard BAL-003-1 Frequency Respnse and Frequency Bias Setting Basic Infrmatin: Prject number: 2007-12 Standard number: BAL-003-1 Prject title: Frequency

More information

Name: Block: Date: Science 10: The Great Geyser Experiment A controlled experiment

Name: Block: Date: Science 10: The Great Geyser Experiment A controlled experiment Science 10: The Great Geyser Experiment A cntrlled experiment Yu will prduce a GEYSER by drpping Ments int a bttle f diet pp Sme questins t think abut are: What are yu ging t test? What are yu ging t measure?

More information

How do scientists measure trees? What is DBH?

How do scientists measure trees? What is DBH? Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between

More information

AP Literature and Composition. Summer Reading Packet. Instructions and Guidelines

AP Literature and Composition. Summer Reading Packet. Instructions and Guidelines AP Literature and Cmpsitin Summer Reading Packet Instructins and Guidelines Accrding t the Cllege Bard Advanced Placement prgram: "The AP English curse in Literature and Cmpsitin shuld engage students

More information

Instructional Plan. Representational/Drawing Level

Instructional Plan. Representational/Drawing Level Instructinal Plan Representatinal/Drawing Level Name f Math Skill/Cncept: Divisin Prcess and Divisin with Remainders Prerequisite Skills Needed: 1.) Mastery f dividing cncrete bjects int equal grups. 2.)

More information

Writing Guidelines. (Updated: November 25, 2009) Forwards

Writing Guidelines. (Updated: November 25, 2009) Forwards Writing Guidelines (Updated: Nvember 25, 2009) Frwards I have fund in my review f the manuscripts frm ur students and research assciates, as well as thse submitted t varius jurnals by thers that the majr

More information

CHM112 Lab Graphing with Excel Grading Rubric

CHM112 Lab Graphing with Excel Grading Rubric Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline

More information

Experiment #3. Graphing with Excel

Experiment #3. Graphing with Excel Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-

More information

Supplementary Course Notes Adding and Subtracting AC Voltages and Currents

Supplementary Course Notes Adding and Subtracting AC Voltages and Currents Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the

More information

CHAPTER 2 Algebraic Expressions and Fundamental Operations

CHAPTER 2 Algebraic Expressions and Fundamental Operations CHAPTER Algebraic Expressins and Fundamental Operatins OBJECTIVES: 1. Algebraic Expressins. Terms. Degree. Gruping 5. Additin 6. Subtractin 7. Multiplicatin 8. Divisin Algebraic Expressin An algebraic

More information

Edexcel GCSE Physics

Edexcel GCSE Physics Edexcel GCSE Physics Tpic 10: Electricity and circuits Ntes (Cntent in bld is fr Higher Tier nly) www.pmt.educatin The Structure f the Atm Psitively charged nucleus surrunded by negatively charged electrns

More information

We can see from the graph above that the intersection is, i.e., [ ).

We can see from the graph above that the intersection is, i.e., [ ). MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with

More information

Who is the Holy Spirit?

Who is the Holy Spirit? ill at w w this h t h in SS est abut erence u O q L G ka iff hink : As m t t es a d K S k A the n ma. wn help rmati ur Jesus. y f t u inf e life ab h iple in t alk a disc f T : RE ce as ece t i A p SH

More information

Physics 2010 Motion with Constant Acceleration Experiment 1

Physics 2010 Motion with Constant Acceleration Experiment 1 . Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin

More information

Turing Machines. Human-aware Robotics. 2017/10/17 & 19 Chapter 3.2 & 3.3 in Sipser Ø Announcement:

Turing Machines. Human-aware Robotics. 2017/10/17 & 19 Chapter 3.2 & 3.3 in Sipser Ø Announcement: Turing Machines Human-aware Rbtics 2017/10/17 & 19 Chapter 3.2 & 3.3 in Sipser Ø Annuncement: q q q q Slides fr this lecture are here: http://www.public.asu.edu/~yzhan442/teaching/cse355/lectures/tm-ii.pdf

More information

Lab #3: Pendulum Period and Proportionalities

Lab #3: Pendulum Period and Proportionalities Physics 144 Chwdary Hw Things Wrk Spring 2006 Name: Partners Name(s): Intrductin Lab #3: Pendulum Perid and Prprtinalities Smetimes, it is useful t knw the dependence f ne quantity n anther, like hw the

More information

AP Physics Kinematic Wrap Up

AP Physics Kinematic Wrap Up AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x

More information

o o IMPORTANT REMINDERS Reports will be graded largely on their ability to clearly communicate results and important conclusions.

o o IMPORTANT REMINDERS Reports will be graded largely on their ability to clearly communicate results and important conclusions. BASD High Schl Frmal Lab Reprt GENERAL INFORMATION 12 pt Times New Rman fnt Duble-spaced, if required by yur teacher 1 inch margins n all sides (tp, bttm, left, and right) Always write in third persn (avid

More information

General Chemistry II, Unit I: Study Guide (part I)

General Chemistry II, Unit I: Study Guide (part I) 1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the

More information

Preparation work for A2 Mathematics [2017]

Preparation work for A2 Mathematics [2017] Preparatin wrk fr A2 Mathematics [2017] The wrk studied in Y12 after the return frm study leave is frm the Cre 3 mdule f the A2 Mathematics curse. This wrk will nly be reviewed during Year 13, it will

More information

Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms

Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms Chapter 5 1 Chapter Summary Mathematical Inductin Strng Inductin Recursive Definitins Structural Inductin Recursive Algrithms Sectin 5.1 3 Sectin Summary Mathematical Inductin Examples f Prf by Mathematical

More information

Matter Content from State Frameworks and Other State Documents

Matter Content from State Frameworks and Other State Documents Atms and Mlecules Mlecules are made f smaller entities (atms) which are bnded tgether. Therefre mlecules are divisible. Miscnceptin: Element and atm are synnyms. Prper cnceptin: Elements are atms with

More information

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

More information

Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 2013 Physics 172 Recitation 3 Momentum and Springs Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

More information

20 Faraday s Law and Maxwell s Extension to Ampere s Law

20 Faraday s Law and Maxwell s Extension to Ampere s Law Chapter 20 Faraday s Law and Maxwell s Extensin t Ampere s Law 20 Faraday s Law and Maxwell s Extensin t Ampere s Law Cnsider the case f a charged particle that is ming in the icinity f a ming bar magnet

More information

The Law of Total Probability, Bayes Rule, and Random Variables (Oh My!)

The Law of Total Probability, Bayes Rule, and Random Variables (Oh My!) The Law f Ttal Prbability, Bayes Rule, and Randm Variables (Oh My!) Administrivia Hmewrk 2 is psted and is due tw Friday s frm nw If yu didn t start early last time, please d s this time. Gd Milestnes:

More information

Year 3 End of Year Expectations Reading, Writing and Maths

Year 3 End of Year Expectations Reading, Writing and Maths Year 3 End f Year Expectatins Reading, Writing and Maths Year 3 Reading Wrd reading Apply their grwing knwledge f rt wrds, prefixes and suffixes (etymlgy and mrphlgy) as listed in Appendix 1 f the Natinal

More information

SticiGui Chapter 4: Measures of Location and Spread Philip Stark (2013)

SticiGui Chapter 4: Measures of Location and Spread Philip Stark (2013) SticiGui Chapter 4: Measures f Lcatin and Spread Philip Stark (2013) Summarizing data can help us understand them, especially when the number f data is large. This chapter presents several ways t summarize

More information

CHAPTER Read Chapter 17, sections 1,2,3. End of Chapter problems: 25

CHAPTER Read Chapter 17, sections 1,2,3. End of Chapter problems: 25 CHAPTER 17 1. Read Chapter 17, sectins 1,2,3. End f Chapter prblems: 25 2. Suppse yu are playing a game that uses tw dice. If yu cunt the dts n the dice, yu culd have anywhere frm 2 t 12. The ways f prducing

More information

Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes

Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin

More information

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24

More information

Homology groups of disks with holes

Homology groups of disks with holes Hmlgy grups f disks with hles THEOREM. Let p 1,, p k } be a sequence f distinct pints in the interir unit disk D n where n 2, and suppse that fr all j the sets E j Int D n are clsed, pairwise disjint subdisks.

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

Unit 1: Introduction to Biology

Unit 1: Introduction to Biology Name: Unit 1: Intrductin t Bilgy Theme: Frm mlecules t rganisms Students will be able t: 1.1 Plan and cnduct an investigatin: Define the questin, develp a hypthesis, design an experiment and cllect infrmatin,

More information

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402

More information

ENG2410 Digital Design Sequential Circuits: Part B

ENG2410 Digital Design Sequential Circuits: Part B ENG24 Digital Design Sequential Circuits: Part B Fall 27 S. Areibi Schl f Engineering University f Guelph Analysis f Sequential Circuits Earlier we learned hw t analyze cmbinatinal circuits We will extend

More information

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.

More information

Department of Electrical Engineering, University of Waterloo. Introduction

Department of Electrical Engineering, University of Waterloo. Introduction Sectin 4: Sequential Circuits Majr Tpics Types f sequential circuits Flip-flps Analysis f clcked sequential circuits Mre and Mealy machines Design f clcked sequential circuits State transitin design methd

More information

LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers

LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the

More information

Kinetic Model Completeness

Kinetic Model Completeness 5.68J/10.652J Spring 2003 Lecture Ntes Tuesday April 15, 2003 Kinetic Mdel Cmpleteness We say a chemical kinetic mdel is cmplete fr a particular reactin cnditin when it cntains all the species and reactins

More information

AP Physics. Summer Assignment 2012 Date. Name. F m = = + What is due the first day of school? a. T. b. = ( )( ) =

AP Physics. Summer Assignment 2012 Date. Name. F m = = + What is due the first day of school? a. T. b. = ( )( ) = P Physics Name Summer ssignment 0 Date I. The P curriculum is extensive!! This means we have t wrk at a fast pace. This summer hmewrk will allw us t start n new Physics subject matter immediately when

More information

Our Lady Star of the Sea Religious Education CIRCLE OF GRACE LESSON PLAN - Grade 1

Our Lady Star of the Sea Religious Education CIRCLE OF GRACE LESSON PLAN - Grade 1 Our Lady Star f the Sea Religius Educatin CIRCLE OF GRACE LESSON PLAN - Grade 1 Opening Prayer: (ech prayer) Hly Spirit (ech) Shw us the way (ech) Be with us in all we think.. d and say (ech) Amen GETTING

More information

Unit 9: The Mole- Guided Notes What is a Mole?

Unit 9: The Mole- Guided Notes What is a Mole? Unit 9: The Mle- Guided Ntes What is a Mle? A mle is a name fr a specific f things Similar t a r a One mle is equal t 602 602,000,000,000,000,000,000,000 That s 602 with zers A mle is NOT an abbreviatin

More information

IB Sports, Exercise and Health Science Summer Assignment. Mrs. Christina Doyle Seneca Valley High School

IB Sports, Exercise and Health Science Summer Assignment. Mrs. Christina Doyle Seneca Valley High School IB Sprts, Exercise and Health Science Summer Assignment Mrs. Christina Dyle Seneca Valley High Schl Welcme t IB Sprts, Exercise and Health Science! This curse incrprates the traditinal disciplines f anatmy

More information

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0

More information

Chem 163 Section: Team Number: ALE 24. Voltaic Cells and Standard Cell Potentials. (Reference: 21.2 and 21.3 Silberberg 5 th edition)

Chem 163 Section: Team Number: ALE 24. Voltaic Cells and Standard Cell Potentials. (Reference: 21.2 and 21.3 Silberberg 5 th edition) Name Chem 163 Sectin: Team Number: ALE 24. Vltaic Cells and Standard Cell Ptentials (Reference: 21.2 and 21.3 Silberberg 5 th editin) What des a vltmeter reading tell us? The Mdel: Standard Reductin and

More information

CLASS. Fractions and Angles. Teacher Report. No. of test takers: 25. School Name: EI School. City: Ahmedabad CLASS 6 B 8709

CLASS. Fractions and Angles. Teacher Report. No. of test takers: 25. School Name: EI School. City: Ahmedabad CLASS 6 B 8709 SEPTEMBER 07 Math Fractins and Angles CLASS 6 Teacher Reprt Test Taken 4 5 6 7 8 Schl Name: EI Schl City: Ahmedabad CLASS SECTION EXAM CODE 6 B 8709 N. f test takers: 5 6.5 Average.5 9.0 Range (Scres are

More information

Internal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9.

Internal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9. Sectin 7 Mdel Assessment This sectin is based n Stck and Watsn s Chapter 9. Internal vs. external validity Internal validity refers t whether the analysis is valid fr the ppulatin and sample being studied.

More information

PHOTOSYNTHESIS THE PRACTICALS 16 APRIL 2014

PHOTOSYNTHESIS THE PRACTICALS 16 APRIL 2014 PHOTOSYNTHESIS THE PRACTICALS 16 APRIL 2014 Lessn Descriptin In this lessn, we will: Review the prcess f phtsynthesis Study the starch test in leaves Study the varius practicals testing phtsynthesis Lk

More information

PHYS 314 HOMEWORK #3

PHYS 314 HOMEWORK #3 PHYS 34 HOMEWORK #3 Due : 8 Feb. 07. A unifrm chain f mass M, lenth L and density λ (measured in k/m) hans s that its bttm link is just tuchin a scale. The chain is drpped frm rest nt the scale. What des

More information

Mission Action Planning in the diocese of St Albans

Mission Action Planning in the diocese of St Albans The Dicese f St Albans Missin Actin ning in the dicese f St Albans Intrductin Missin Actin ning is a central element in the new dicesan initiative. This initiative is an invitatin t the peple, parishes

More information

I. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is

I. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is Length L>>a,b,c Phys 232 Lab 4 Ch 17 Electric Ptential Difference Materials: whitebards & pens, cmputers with VPythn, pwer supply & cables, multimeter, crkbard, thumbtacks, individual prbes and jined prbes,

More information

COMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification

COMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification COMP 551 Applied Machine Learning Lecture 5: Generative mdels fr linear classificatin Instructr: Herke van Hf (herke.vanhf@mail.mcgill.ca) Slides mstly by: Jelle Pineau Class web page: www.cs.mcgill.ca/~hvanh2/cmp551

More information

Phys. 344 Ch 7 Lecture 8 Fri., April. 10 th,

Phys. 344 Ch 7 Lecture 8 Fri., April. 10 th, Phys. 344 Ch 7 Lecture 8 Fri., April. 0 th, 009 Fri. 4/0 8. Ising Mdel f Ferrmagnets HW30 66, 74 Mn. 4/3 Review Sat. 4/8 3pm Exam 3 HW Mnday: Review fr est 3. See n-line practice test lecture-prep is t

More information

Assessment Primer: Writing Instructional Objectives

Assessment Primer: Writing Instructional Objectives Assessment Primer: Writing Instructinal Objectives (Based n Preparing Instructinal Objectives by Mager 1962 and Preparing Instructinal Objectives: A critical tl in the develpment f effective instructin

More information