Ppt on rational and irrational numbers for class 9

11/7 Are there irrational numbers p and q such that p q is a rational number? Hint: Suppose p=q= Rational Irrational Why is the set that is the set of.

discussed a cute example of existential proof—is it possible for an irrational number power another irrational number to be a rational number—we proved it is possible, without actually giving an example). 11/9 The absence of evidence is not the evidence of /– a. Develop “tractable subclasses” of languages and require the expert to write all their knowlede in the procrustean beds of those sub-classes (so we can claim “complete and tractable inference” for that class) OR –Let users write their knowledge in the/


CPSC 121: Models of Computation Unit 7: Proof Techniques Based on slides by Patrice Belleville and Steve Wolfman.

Proof by Contradiction: Example 2 Theorem: For all real numbers x and y, if x is a rational number, and y is an irrational number, then x+y is irrational. Proof  Assume x is any rational number, y is any irrational number and that x+y is a rational number.  Then x+y = a / b for some a  Z and some b  Z +  Since x is rational, x = c /d for some c  Z and some d  Z +  Then (c /d/


Algebraic Expressions

2 1 In addition to level 3.0 and above and beyond what was taught in class,  the student may: ·         Make connection with other concepts in math ·         Make connection with other content areas. The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions on contextual situations. - justify the  sums and products of rational and irrational numbers -interpret expressions within the context of a problem/


Convert Decimals to Fractions. Focus 4 - Learning Goal #1: Students will know that there are numbers that are not rational, and approximate them with.

numbers that are not rational, and approximate them with rational numbers. - Convert a decimal expansion that repeats into a fraction. - Approximate the square root of a number to the hundredth & explain the process. - For all items listed as a 2, students can explain their process. Students will know the subset of real numbers. - Know that all numbers have a decimal expansion. - Compare the size of irrational number. - Locate approximately irrational numbers on a number/


TCAP REVIEW BEGINS Bring your TCAP foldable and your comp book each day to class.

notebook paper divided into 9 sections. You will turn in your work at the end of the class. In order for your team to /Numbers look for key words to determine the operation. how many times really means DIVIDE how many more really means SUBTRACT combined means to ADD Time to play: STATION 1  Each team is getting a board with two sections labeled Rational and Irrational.  Your team will get an envelope with several numbers in it. Your team must separate the numbers into two groups, Rational and Irrational/


Unit 1 Understanding Numeric Values, Variability, and Change 1.

following numbers as Irrational, Rational, Whole Natural, and/or Integers: 0909 0 Rational, integer, whole, natural 0 3.666666666 0 rational 0 -5 0 Rational, Integer 0 4.75 0 rational 0 7.154976352118568763215489736 0 irrational 7 Worksheet 0 Complete Worksheet in Groups 0 Complete Part I then stop 0 Complete Part II then stop 0 Complete Part III then stop 0 Review Time!! 0 Complete Page 1-12 for/


Section 1-3 Explore Real Numbers SPI 12A: Order a given set of rational numbers TPI 12F: Explore various representations of Absolute Value Objectives:

Section 1-3 Explore Real Numbers SPI 12A: Order a given set of rational numbers TPI 12F: Explore various representations of Absolute Value Objectives: Investigate the Real Number System Classify and Compare Numbers Natural Numbers Real Number System Whole Numbers Integers Rational Numbers Irrational Numbers X y Real number line Coordinate Plane Natural Numbers 1, 2, 3, … 1 2 3 4 5 6 7 8 9 10 11 Whole Numbers 0, 1, 2, 3, … 0 1 2 3/


Welcome, parents! 1. Write a “someone special” note to your child. (Pick up the note from the front table.) 2. Have a look around the room and then have.

8-Polynomials and Rational Expressions Dividing polynomials; Simplifying rational expressions; Exponent rules; Adding, subtracting, multiplying, and dividing rational expressions; Complex fractions Chapter 9- Rational Expressions in Open Sentences Percent problems; Fractional equations; Word problems: Work, motion; Ratio and proportion; Direct, inverse, joint, combined variation Chapter 10-Irrational Numbers and Radicals Rational numbers; Decimals and fractions; Rational square roots; Irrational square/


Quasi-Periodicity & Chaos 1.QP & Poincare Sections 2.QP Route to Chaos 3.Universality in QP Route to Chaos 4.Frequency Locking 5.Winding Numbers 6.Circle.

for any Θ and integer n (modulus action suspended) i.e. ∴ Adjust Ω’’ to get f is monotonic with Ω → Ω’’  [Ω, Ω’] Analytic Approach Continued Fraction n th order approximation: Approximation of irrational number by rational fractions for i = 1,2,3,… Golden Ratio → Fibonacci numbers/ increasing K pass 1 → Chaos Ω= 0.606661 Ω= 0.5 Universality Classes of Circle maps Criteria: functional form near inflection point (Θ = 0, /0 Fractal dim of q.p. regions: see chap 9. Breaking up of the torus in a Benard experiment/


1 Math/CSE 1019C: Discrete Mathematics for Computer Science Fall 2011 Suprakash Datta Office: CSEB 3043 Phone: 416-736-2100 ext 77875.

Manipulating propositions –not, and, or, implication, biconditional Truth tables Propositional equivalences Table 6 (page 27) 3 Last class: quick recap – contd/x  y  z (x  y)  (x < z < y)  (y < z < x) Is it true? 9 Nested Quantifiers - 2  x  y (x + y = 0) is true over the integers Proof: Assume an arbitrary integer x./irrational Suppose  2 is rational. Then  2 = p/q, such that p, q have no common factors. Squaring and transposing, p 2 = 2q 2 (even number) So, p is even (previous slide) Or p = 2x for/


Welcome to The Wonderful World of College Algebra Unit 1 Seminar To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right.

in our class This means /RATIONAL NUMBERS: Definition 1 – A rational number is a number that can be expressed as the quotient of two integers Examples: Definition # 2 – a rational number is a number that can be written as either a terminating or repeating decimal. Examples:.8, -1.85, IRRATIONAL NUMBERS: Definition # 1 – An irrational number is a number that cannot be written as the quotient of two integers Definition # 2 – An irrational number is a number that is a nonterminating and/ and then come back for /


Foundations of Research 1 Introduction to research in psychology. 12 / 18 / 14  No screens in class (including phones) : turn it off and put it away!

to science, 2  Foundations of Research 42 Are we rational? Are people “rational”? Are our beliefs generally scientific? Irrational beliefs have increased in the U.S. in the 21 /9/15 EXAMPLE Foundations of Research 49 3 rd variables in spurious correlations Spurious correlations …often a 3 rd variable actually causes both terms in the correlation. Shoe size and reading performance for elementary school children Age: Older children have larger shoe sizes and read better. Number of police officers and number/


Proof Techniques Chuck Cusack These notes are loosely based on material from section 3.1 of Discrete Structures and its Applications, 4 th Edition.

they will get an A in this class (q). What can you say about a student / write x = y + 3, for some y  1. Thus, x 2 = (y+3) 2 = y 2 + 6y + 9 > 6y + 9  6 + 9 = 15. Indirect Proof Since p/rational number and an irrational number is irrational. Proof: Assume that the product of a rational and an irrational number is rational (the negation of what we want to prove.) Then we can express this as xw=y, where x and y are rational, and w is irrational. Thus, we can write x=a/b and y=c/d, for some integers a, b, c, and/


BBA4 Semester 1, 2003 Advanced Company Finance.

number/ 29 (9) 28 (11) 3 /Class discussion paper: Masulis (1980)- Highly significant Announcement effects: +7.6% for leverage increasing exchange offers. -5.4% for leverage decreasing exchange offers. Practical Methods employed by Companies. Trade off models: PV of debt and equity. Pecking order. Benchmarking. Life Cycle. Increasing Debt? time Introduction to Behavioural Finance. Standard Finance assumes that agents are rational and self-interested. Behavioural finance: agents irrational. Irrational/


COMPREHENSIVE REVIEW FOR MIDDLE SCHOOL MATHEMATICS

it can be written as the ratio 1/3 Practice Irrational Numbers! Which of these is an irrational number? A    -2 B     √56 C     √64 D     3.14 Which of these is an irrational number? A    √3 B    -13.5 C     7 11 D     1 √9 Converting Rational Numbers! Fraction Decimal Percent Place number over its place value and reduce Divide by 100 Multiply by 100 75 = 3 100 4 0/


Chapter 3: Rational and Real Numbers

3/5 Example 3: Adding and Subtracting Fractions with Like Denominators Add or Subtract. 6/11 + 9/11 -3/8 – 5/8 Try these on your own… -2/9 – 5/9 -7/9 6/7 + (-3/7) 3/7 Example 4: Evaluating Expressions with Rational Numbers Try these on your own… 12.1 – x for x = -0.1 12.2 7/10 + m for m = 3 1/10 3/


GLOBAL PERSPECTIVES Rational Portfolios for Irrational Markets October 2010 for the period ending 9/30/10 Global Perspectives Market Overview Presented.

Rational Portfolios for Irrational Markets Global Strategic Allocation We believe a global approach to investing offers potential benefits for all investors, whether their primary objective is capital growth, income, capital preservation or a balance between them. Portfolio Construction We believe both active management and broad asset class/50 is expansionary. A number close to 60 is indicative of rapid economic growth. Economy The Global Purchasing Managers Index for manufacturing includes countries that /


1 Cultural Connection The Revolt of the Middle Class Student led discussion. The Eighteenth Century in Europe and America.

 7 §12-3 De Moivre Student Discussion. 8 §12-3 De Moivre’s Error Function 9 §12-3 Sterling’s Formula for n large. nActualSterlingAccuracy 13622702080061872394750.6% 202.432902008 10 18 2.422786847 10 18 0.4% 503./number! The five basic constants in mathematics in one neat formula. Hence, God must exist! 18 §12-5 Euler For any polyhedron the following holds: v + f = e + 2 19 §12 - 6 Clairaut, d’Alembert and Lambert Student Comment 20 §12 - 6  is irrational If x  0 is rational, then tan x is irrational/


Any questions on the Section 5. 8 homework

the two solutions will be rational numbers. If not, they’re both irrational.) b2 – 4ac > 0 Graph of y = ax2 + bx + c Kinds of solutions to ax2 + bx + c = 0 Discriminant b2 – 4ac Example Use the discriminant to determine the number and type of solutions for the following equation. 5 / formula instead (and you will find it to be easier and quicker than factoring.) Reminder: This homework assignment on Section 8.2 is due at the start of next class period. You may now OPEN your LAPTOPS and begin working on/


Snick  snack CPSC 121: Models of Computation 2010 Winter Term 2 Proof Techniques Steve Wolfman, based on notes by Patrice Belleville and others 1.

Equivalences –Proof by contradiction Strategies Summary Problems and Discussion Next Lecture Notes 2 Learning Goals: “Pre-Class” Be able for each proof strategy below to: –Identify /in my computer’s machine language. Problem: prove the theorem. 9 You pick: Java or Racket. WLOG Example: My Machine Speaks /Irrational Theorem: The  2 is an irrational number. Opening steps: (1) Assume for contradiction that  2 is rational. (2) Using our knowledge of rationals, we know  2 = a/b, where a  Z, b  Z+, and a and/


Snick  snack CPSC 121: Models of Computation 2011 Winter Term 1 Proof Techniques (Part B) Steve Wolfman, based on notes by Patrice Belleville and others.

Worked Problem:  2 is Irrational Theorem: The  2 is an irrational number. Opening steps: (1) Assume for contradiction that  2 is rational. (2) Using our knowledge of rationals, we know  2 = a/b, where a  Z, b  Z+, and a and b have no common factor except/the “Sequential Circuits” readings at the bottom of the “Textbook and References” area of the website.Textbook and References Complete the open-book, untimed quiz on Vista that was due before class. snick  snack More problems to solve... (on your own/


N4 Decimals and rounding

only looks neater but it is more accurate. Irrational numbers involving square roots are often written using surds. See N2.5 Surds. Examples of irrational numbers include: π √3 and sin 50° Rational or irrational? Decide whether the number shown is rational of irrational. N4.3 Calculating with decimals Contents N4 Decimals and rounding A N4.1 Decimals and place value A N4.2 Terminating and recurring decimals A N4.3 Calculating with decimals/


Honors Algebra 2 Spring 2012 Ms. Katz.

My e-mail address (for teacher purposes only) is: Day 2: January 31st Objective: Review expectations for class and homework. Work together to share mathematical ideas and to justify strategies as you//7, 22, and so on)   a number that can NOT be expressed as an integer fraction (π, √2, and so on) Irrational Numbers: NONE Symbols for Number Set Real Numbers: The set of all rational and irrational numbers   Rational Numbers Integers Irrational Numbers Real Number Venn Diagram: Natural Numbers less than or /


Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials. Today’s daily quiz will be given at the.

9)(3x + 8) = 0, which leads to the two solutions of 9/4 and -8/3. The Quadratic Formula The quadratic formula is another technique we can use for/and a perfect square, then you will get two real solutions that are real and rational numbers. If the discriminant is positive but not a perfect square, then you know for sure that your polynomial is prime (can’t be factored without using radicals), but there will be two irrational/ is due at the start of the next class session. Lab hours in 203: Mondays through /


1 Week 1 Given problems with signed real numbers, perform basic arithmetic operations, using a hand help calculator, including conversions of percentages,

; -77/3 9 The Irrational Numbers Real number that is not rational Can not be written as a ratio of two integers Example: √2, √3,π In Computation with irrational numbers we use rational approximation for them Example: √2≈1.4141; π≈3.14 : the ratio of the circumference and diameter of every circle Note: not all square roots are irrational Example: √9 = 3 10 The Number Line Every real number corresponds to one and only one/


Title: Functions, Limits and Continuity Prof. Dr. Nasima Akhter And Md. Masum Murshed Lecturer Department of Mathematics, R.U. 29 July, 2011, Friday Time:

Graphs 9 X Y f y = f (x) f : X → Y if for each x ∊ X ∃ a unique y ∊ Y such that y = f(x). Domain of f Range of f Co-domain of f f[X] = {f(x) : x ∊ X} Set function Class of sets Functions and its Graphs 10 X Y f y = f (x) If f : X → Y then ∃ two set/


Words for Production 1. introductory adj. 序論的,引導的; 入門的,初步的 This book includes an introductory chapter ( 章 ) that explains the goals of the research. For.

designers. 4)  The lecturer took up the class after a short break. Idioms and Phrases 8. for (so) long for a long time 很長一段時間 I haven’t seen Betty for so long that I doubt if she can still recognize me. 8. for (so) long 很長一段時間  I have been waiting here for my friend for so long that I fell asleep. Idioms and Phrases 9. catch up on something to do something/


RationalRational and Irrational Adventures in the Direct Loan Wonderland” Presented by Sherry Proper Director of Financial Aid & Enrollment Support.

RationalRational and Irrational Adventures in the Direct Loan Wonderland” Presented by Sherry Proper Director of Financial Aid & Enrollment Support Allegheny College 2 “Chapter 1 – Down the Uncertain Chasm” Liquidity injected into FFELP by Government purchasing of loans in 2008-09 & 2009-10 –Very unlikely to happen for 2010-11 July 1, 2010 not that far away Will FFELP $$$ be available? Will lenders remain in FFELP/


Words for Production 1. introductory adj. 序論的,引導的; 入門的,初步的 This book includes an introductory chapter ( 章 ) that explains the goals of the research. For.

designers. 4)  The lecturer took up the class after a short break. Idioms and Phrases 8. for (so) long for a long time 很長一段時間 I haven’t seen Betty for so long that I doubt if she can still recognize me. 8. for (so) long 很長一段時間  I have been waiting here for my friend for so long that I fell asleep. Idioms and Phrases 9. catch up on something to do something/


Test Item Test item Five girls in class 701 play a sport each week. Stephanie, Fiona and Juanita only play basketball. Sarah and Melanie only.

9 D. 15 7a A rational number can be written in the form: or a/b (where b can equal 1 or any other number except zero: b ≠ 0) The rational number is like a ratio of a to b, hence the term “rational.” Which of the following is not a rational number? 7b The square root of a non-perfect square is called an irrational/C.85 D.240 The table below records Lester’s results for 3 of his classes. 25c. Lester predicted that the average score for his ELA, Math and Science scores would be higher than 70%. How accurate was/


Copyright © 2011 Pearson Education, Inc. Foundations of Algebra CHAPTER 1.1Number Sets and the Structure of Algebra 1.2Fractions 1.3Adding and Subtracting.

repeats. This is the decimal equivalent of 1 over 3. Yes this is a rational number. Slide 1- 15 Copyright © 2011 Pearson Education, Inc. Irrational number: Any real number that is not rational. Examples: Real numbers: The union of the rational and irrational numbers. Slide 1- 16 Copyright © 2011 Pearson Education, Inc. Objective 3 Graph rational numbers on a number line. Slide 1- 17 Copyright © 2011 Pearson Education, Inc. Example 3 Graph on a/


REVIEW. Write down this problem on your COMMUNICATOR Be prepared to share your work with the class. Prepare for my Unit 5 Test By completing my practice.

COMMUNICATOR Be prepared to share your work with the class. Prepare for my Unit 5 Test By completing my practice test and making a 3x5 card of notes. Write down 5 Rational Numbers and 5 Irrational Numbers Defend your choices to your partner (justify your answers/ the pattern. Do you see a pattern? RATIONAL NUMBERS Decimals that terminate or repeat. Examples: 0.356 and 0.555… IRRATIONAL NUMBERS Real numbers that are NOT RATIONAL The CRAZY Ones! Perfect Squares MEMORIZE THEM 1 4 9 16 25 36 49 64 81 100 121/


COMPREHENSIVE REVIEW FOR MIDDLE SCHOOL MATHEMATICS Purpose: PSSA Review for 7th Grade (Can be used as enrichment or remediation for most middle school.

for. Example 1:4 kilometers = 4000 meters Example 2:36 millimeters = 3.6 centimeters COACH LESSON 11 65 Kilo - Hecto - Deka - Meter Liter Gram Deci - Centi- Milli - 66 PRACTICE UNIT CONVERSIONS! The students in a math class measured and/rational, because it can be written as the ratio 1/3 Practice Irrational Numbers! 73 Which of these is an irrational number? A -2 B √56 C √64 D 3.14 Which of these is an irrational number? A √3 B -13.5 C 7 11 D 1 √9 FractionDecimalPercent Place number over its place value and/


Tangram Legend and Project Objectives: 1.To simplify radical expressions 2.To complete the Tangram Project.

, 4, 9, 16, … Perfect Squares These numbers are called the Perfect Squares. Their square roots are integers. Real Numbers real numbers The real numbers (are there unreal numbers?) can be divided into two infinite sets: Rational and Irrational. rational numbersAll rational numbers can be written as a ratio of integers. (Ex: 4, 2/3, -6/25, etc.) Real Numbers real numbers The real numbers (are there unreal numbers?) can be divided into two infinite sets: Rational and Irrational. irrational numbersNo irrational/


Aswath Damodaran1 Smoke and Mirrors: Price patterns, charts and technical analysis Aswath Damodaran.

5.5%10.3%8,660-74.9% 2.0%0..2%10.3%/rational and irrational. The market continually and automatically weighs all these factors. (A random walker would have no qualms about this assumption either. He would point out that any irrational factors are just as likely to be one side of the market as on the other.) (3) Disregarding minor fluctuations in the market, stock prices tend to move in trends which persist for/market Measure: This is a measure of the number of stocks in the market which have advanced relative/


HATE GROUPS AMANDA, JAMAL, JOY, MARISSA. DEFINITION OF HATE: Hate, a complex subject, divides into two general categories: rational and irrational. Unjust.

rational and irrational. Unjust acts inspire rational hate. Hatred of a person based on race, religion, sexual orientation, ethnicity, or national origin constitutes irrational hate. Therefore: hate crimes=irrational hate Both irrational and rational/invitation, or any number of other actions to demean and isolate. The haters even may adopt a name for their group (Stage/9.5 percent) and anti-Islamic (9.0 percent) hate crimes. Disability: In 2007, 62 hate crimes against individuals with mental disabilities and/


Promoting Rational Use of Drugs

irrational use Discuss strategies and interventions to promote rational use of medicines Some questions to ponder Could there have been a better term than "Rational" ? The rational use of drugs requires that patients receive medications appropriate to their clinical needs, in doses that meet their own individual requirements for an adequate period of time, and/project. How many LMICs can provide this data? This provides antibiotics by class and total; how many of your countries can provide even the total? /


Wrapping up the first half: First-order logic for security analysis, First-order logic in Coq, Constructive logic, & Inductive proofs on paper/Coq Aquinas.

Logic – Model Checkers – Hoare Logic 9 Learning the tools is not easy… / implications (essentially how an attacker would break our policy) We have two basic classes of rules: – Network topology – Attack vulnerability Example rules (network topology): / 6.Flee country 17 Process for applying theory to practice 1./irrational. Now consider the number y = x x. By law of excluded middle, we know that either – y is rational: in this case a = b = x – y is irrational: in this case observe that y x = 2. Thus a = y and/


1 Math Review APEC 3001 Summer 2007. 2 Objectives Review basic algebraic skills required to successfully solve homework, quiz, and exam problems in this.

class of linear functions. –What is the slope? –What is the intercept? –Solutions to systems of linear equations. Review the basic differential calculus skills required to successfully solve homework, quiz, and exam problems. 3 Types of Numbers Integers –…,-3, -2, -1, 0, 1, 2, 3,… Rational Numbers –An Integer Divided By An Integer (e.g. ½ = 0.5 & -4/3 = -1.333…) –All Integers Are Rational Numbers Irrational Numbers –Not Rational/


10/29 Plan(s) for make-up Class 1.Extend four classes until 12:15pm 2.Have a separate make- up class on a Friday morning.

to a proposition 10/31  Midterm returned  Make-up class on Friday 11/9 (morning—usual class time) Herbrand Interpretations Herbrand Universe –All constants Rao,Pat –/entails every instantiation of it) –Existential instantiation (an existentially quantified statement holds for some term (not currently appearing in the KB). Can we combine these / and home once. so x is either home or office Existential proofs.. Are there irrational numbers p and q such that p q is rational? Rational Irrational This and the/


Myers’ Psychology for AP*

and effectiveness Psychological Disorders- Etiology Neurotic disorder (term seldom used now) *usually distressing but that allows one to think rationally and function socially *Freud saw the neurotic disorders as ways of dealing with anxiety Psychotic disorder *person loses contact with reality *experiences irrational ideas and/Continue reading below... For example, they develop/the number 13 (triskaidekaphobia) e) Fear of water (aquaphobia) 9) /j) Autism _____ A class of disorders including depersonalization /


Basics  We will meet Monday – Friday from 1 – 4pm  There is no class Tue., June 16  Last class is Thur., July 2  If the door is locked, you can call.

for the class, but …  You must master the material and pass the tests/quizzes to continue into Geometry in the fall.  Notes and /irrational numbers:Special numbers like Roots that are not whole numbers likeDecimals that don’t repeat the exact same thing like.34334433344433334444… Real NumbersALL numbers you know so farBoth rational and irrational numbers together Tell which numbers in this set are …NaturalWholeIntegersRational numbersIrrational numbersReal numbers Place, or = between each pair of numbers/


Promoting Rational Use of Drugs Krisantha Weerasuriya MD.

irrational use Discuss strategies and interventions to promote rational use of medicines Some questions to ponder Department of Essential Medicines and Health Products TBS 2012 The rational use of drugs requires that patients receive medications appropriate to their clinical needs, in doses that meet their own individual requirements for an adequate period of time, and/of Essential Medicines and Health Products TBS 2012 How many LMICs can provide this data? This provides antibiotics by class and total; how /


A very short history of Calculus presentation for MATH 1037 by Alex Karassev  Irrational numbers in Greek math  Theory of Proportion  The Method of.

400 – 350 BCE) The theory was designed to deal with (irrational) lengths using only rational numbers Length λ is determined by rational lengths less than and greater than λ Then λ 1 = λ 2 if for any rational r λ 1 ) Note: the theory of proportions can be used to define irrational numbers: Dedekind (1872) defined √2 as the pair of two sets of positive rationals L √2 = {r: r 2 2} (Dedekind cut) The/


SE 477 Software and Systems Project Management Dennis Mumaugh, Instructor Office: CDM, Room 432 Office Hours: Monday, 4:00 – 5:30.

(aka source code) and need to rewrite code 1.Backups essential 2.Use RAID for critical disks; tape for all; off-site backups for disaster  The rest of the story: About a week after the last person left, there was a system crash that caused major problems. [See note page for details.] May 25, 2015SE 477: Lecture 9 3 of 93 SE 477 – Class 9 Topics:  Miscellaneous: »Agile/


Abnormal Psychology Chapter 10 The scientific study of mental disorders and their treatment Prepared by J. W. Taylor V.

fist date of two party goers DUE NEXT CLASS! Anxiety Disorders Disorders in which excessive anxiety leads to personal distress and atypical, maladaptive and irrational behavior Specific Phobia Social Phobia & Agoraphobia Panic Disorder Generalized Anxiety Disorder Obsessive-Compulsive Disorder Phobia: irrational fear A strong and persistent fear of specific objects/situations that is excessive or unreasonable (irrational) Specific Phobia For example, there was woman with a specific phobia/


QualPro Recommendations for

QualPro Appendix 2 ACT Math Concepts and Problems Math Vocabulary area of a circle chord circumference collinear complex number congruent consecutive diagonal directly proportional endpoints function y = R (x) hypotenuse integer intersect irrational number least common denominator logarithm matrix mean median obtuse perimeter perpendicular pi polygon prime number quadrant quadratic equation quadrilateral quotient radian radii radius rational number real number slope standard coordinate plane transversal/


The Psychological Basis of Rationality: Examples from Games and Paradoxes Richard M. Shiffrin.

does, A can give B 3. Similarly for 9, and all multiples of 3. Hence if A/STOP, and end the game with both players getting nothing. This may seem as irrational to /B knows people fall into two classes, those choosing ONE and those choosing BOTH. B would very/for the rationality of one or another decision are heavily weighted by problem framing, and by examples. The finite exchange paradox also reveals a difference that a number of researchers have noted between ‘uncertainty’ and ‘vagueness’. The highest number/


Snick  snack CPSC 121: Models of Computation 2008/9 Winter Term 2 Proof Techniques Steve Wolfman, based on notes by Patrice Belleville and others.

: The  2 is an irrational number. Opening steps: (1) Assume  2 is rational. (2) Using our knowledge of rationals, we know  2 = a/b, where a  Z, b  Z+, and a and b have no common factor except 1. [But, we know nothing more about a and b!] Next, play around with the formula  2 = a/b and see where it takes you! Strategies for Predicate Logic Proofs Have/


Bayesian models of human learning and inference Josh Tenenbaum MIT Department of Brain and Cognitive Sciences Computer Science and AI Lab (CSAIL) Thanks.

and taking the limit as. Does not require that we commit to a fixed – or even finite – number of classes. Effective number of classes can grow with number/3 Species 4 Species 5 Species 6 Species 7 Species 8 Species 9 Species 10 FeaturesNew property Structure S (85 features from Osherson et al., e.g., for Elephant: ‘gray’, ‘hairless’, ‘toughskin’, ‘big’, ‘bulbous’,/ Snow and the cause of cholera (1854) Rational analysis of cognition Often can show that apparently irrational behavior is actually rational. Which/


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