Determining Objects of Observation for the Accuracy of the Singing Assessment Instrument
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Probability and Counting Rules
blu03683_ch04.qxd 09/12/2005 12:45 PM Page 171 C HAPTER 44 Probability and Counting Rules Objectives Outline After completing this chapter, you should be able to 4–1 Introduction 1 Determine sample spaces and find the probability of an event, using classical 4–2 Sample Spaces and Probability probability or empirical probability. 4–3 The Addition Rules for Probability 2 Find the probability of compound events, using the addition rules. 4–4 The Multiplication Rules and Conditional 3 Find the probability of compound events, Probability using the multiplication rules. 4–5 Counting Rules 4 Find the conditional probability of an event. 5 Find the total number of outcomes in a 4–6 Probability and Counting Rules sequence of events, using the fundamental counting rule. 4–7 Summary 6 Find the number of ways that r objects can be selected from n objects, using the permutation rule. 7 Find the number of ways that r objects can be selected from n objects without regard to order, using the combination rule. 8 Find the probability of an event, using the counting rules. 4–1 blu03683_ch04.qxd 09/12/2005 12:45 PM Page 172 172 Chapter 4 Probability and Counting Rules Statistics Would You Bet Your Life? Today Humans not only bet money when they gamble, but also bet their lives by engaging in unhealthy activities such as smoking, drinking, using drugs, and exceeding the speed limit when driving. Many people don’t care about the risks involved in these activities since they do not understand the concepts of probability. -
A FIRST COURSE in PROBABILITY This Page Intentionally Left Blank a FIRST COURSE in PROBABILITY
A FIRST COURSE IN PROBABILITY This page intentionally left blank A FIRST COURSE IN PROBABILITY Eighth Edition Sheldon Ross University of Southern California Upper Saddle River, New Jersey 07458 Library of Congress Cataloging-in-Publication Data Ross, Sheldon M. A first course in probability / Sheldon Ross. — 8th ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-13-603313-4 ISBN-10: 0-13-603313-X 1. Probabilities—Textbooks. I. Title. QA273.R83 2010 519.2—dc22 2008033720 Editor in Chief, Mathematics and Statistics: Deirdre Lynch Senior Project Editor: Rachel S. Reeve Assistant Editor: Christina Lepre Editorial Assistant: Dana Jones Project Manager: Robert S. Merenoff Associate Managing Editor: Bayani Mendoza de Leon Senior Managing Editor: Linda Mihatov Behrens Senior Operations Supervisor: Diane Peirano Marketing Assistant: Kathleen DeChavez Creative Director: Jayne Conte Art Director/Designer: Bruce Kenselaar AV Project Manager: Thomas Benfatti Compositor: Integra Software Services Pvt. Ltd, Pondicherry, India Cover Image Credit: Getty Images, Inc. © 2010, 2006, 2002, 1998, 1994, 1988, 1984, 1976 by Pearson Education, Inc., Pearson Prentice Hall Pearson Education, Inc. Upper Saddle River, NJ 07458 All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Pearson Prentice Hall™ is a trademark of Pearson Education, Inc. Printed in the United States of America 10987654321 ISBN-13: 978-0-13-603313-4 ISBN-10: 0-13-603313-X Pearson Education, Ltd., London Pearson Education Australia PTY. Limited, Sydney Pearson Education Singapore, Pte. Ltd Pearson Education North Asia Ltd, Hong Kong Pearson Education Canada, Ltd., Toronto Pearson Educacion´ de Mexico, S.A. -
Solving Words Problems (+ - ÷ ×) Name: Use Addition, Subtraction, Multiplication Or Division to Solve Each Problem
Solving Words Problems (+ - ÷ ×) Name: Use addition, subtraction, multiplication or division to solve each problem. Answers 1) Robin had 17 math problems for homework. If she finished 8 of them on the bus ride home, how many more did she have to do? 1. 9 2) Carol needs to buy 16 apples for apple bobbing. If each bag contains 4 apples, how many 2. 4 bags will she need? 3) Tom bought 4 boxes of candy. Later he bought 2 more boxes. How many boxes did he 3. 6 have total? 4. 4 4) For a potluck lunch Katie brought 6 bottles of soda. If everyone only drank 2 of the sodas, how many did she have to take back home? 5. 16 5) Victor played 8 games of basketball with his friends. If Victor scored 2 points each game, 5 how many points did he score total? 6. 6) While playing basketball Team A scored 35 points. If each person scored 7 points, how 7. 36 many people were playing? 8. 9 7) A pet store had 4 cages of snakes with 9 snakes in each cage. How many snakes did the pet store have total? 9. 12 8) Ned bought 17 books at the book fair. If he gave 8 of them to his brother, how many books 3 did he have left? 10. 9) Edward was drawing super heroes on a sheet of scrap paper. He drew 4 heroes on the front 11. 6 and 8 heroes on the back. How many heroes did he draw total? 12. -
Living Abroad Then the Fifth Tie (More Time in the UK Than in Any Other Country) Tie Can Be Ignored
TAX GUIDES Residence and Domicile Alliotts, Chartered Accountants & Business Advisors Imperial House, 15-19 Kingsway, London, WC2B 6UN T: +44 (0)20 7240 9971 F: +44 (0)20 7240 9692 E: [email protected] Friary Court, 13-21 High Street, Guildford, Surrey, GU1 3DL A Worldwide Alliance of Independent T: +44 (0)1483 533 119 F: +44 (0)1483 537 339 E: [email protected] www.alliotts.com RESIDENCE AND DOMICILE Planning to leave While the thought of going abroad to work or retire may be exciting, the months prior to departure are likely to be highly stressful. Finding somewhere to live in your chosen country, arranging the necessary visas and booking a suitable removal firm are just some of the issues you are likely to have to deal with. Nevertheless, during this mad rush, it is vital that you pay adequate attention to financial planning. In particular, the tax consequences of leaving the UK are quite complex so it is essential that you seek professional advice. Your residence status will be the main factor in determining your continuing liability to UK tax. Previously, it could be quite difficult to become non-UK resident for tax purposes, but since 6 April 2013 a set of statutory tests have made it much easier to establish your residence status. It is worth gaining a basic understanding of these concepts if you are thinking of leaving the UK to live abroad - or if you have been abroad and are now returning to the UK. For both situations you can minimise the amount of UK tax that you will have to pay if you plan well ahead. -
3Rd 9Wks Math Problems
PROBLEMS & TASKS 4 DISTANCE, RATE, & TIME Where am I? DISTANCE-1 (A-34): From the dock, Tommy paddled his canoe upstream against the current at 3 miles per hour for 40 minutes. Then Tommy paddled downstream for 36 minutes at 5 miles per hour. Where was he in relation to the dock? ============================================================== ==== DISTANCE-2 (A-41): The distance from Hillpoint to Plain is 148 miles. It is 115 miles from Jonestown to Plain. Smallville is 123 miles from Hillpoint. How far is it from Jonestown to Smallville? ============================================================== ==== DISTANCE-3 (C-33): A helicopter flies 16 miles from the airport to a downtown hotel in 10 minutes. At this rate, how far could the helicopter fly in 2 hours? =============================================================== === DISTANCE-4 (C-41): It is 85 miles from Kansas City to Camden. The distance from Camden to Bern is 40 miles. If Bern is on the road between Kansas City and Camden, how far is it from Kansas City to Bern? =============================================================== === DISTANCE-5 (D-32): Tony did 150 push-ups in 10 minutes. Eric can do push-ups at a rate of 2 every 10 seconds. How long, would it take Eric to do as many push-ups as Tony? =============================================================== === DISTANCE-6 (71-AA): A truck and a car are each traveling 60 miles per hour. About 5 how far apart will they be in 5 minutes? =============================================================== === DISTANCE-7 (88-BB): It takes Misty 12 minutes to walk the 0.7 of a mile from her house to the school. How long would it take Misty to walk a mile at the same speed? =============================================================== === DISTANCE-8 (148-BB): How long will it take a train 1 mile long traveling 60 miles per hour to go through a tunnel 1/2 mile long? =============================================================== === DISTANCE-9 (151-BB): When Mr. -
UK Tax Residence Rules March 2013 Welcome
UK tax residence rules March 2013 Welcome “My accountants have told me that I can have one foot in Jersey, my left elbow in the Isle of Man and my right foot in Zurich and pay little or no tax” Lord Alan Sugar PwC 2 Welcome Overview • Why are residence rules important? • Current rules • New rules • Potential issues • How can we help PwC 3 UK taxes Why are residence rules important? Impact on.... • Income tax • Capital gains • Inheritance tax • Corporate situations - Sole director of corporate? PwC 4 Residence for individuals Current rules Contentious and subjective Guidance in HMRC 6 • Resident • Breaking residence • “Ordinarily Resident” PwC 5 PwC 6 Residence for individuals - resident Current rules No statutory definition of residence Guidance in HMRC 6 • Day counts tests. • 183 days or more in UK in tax year. • 91 days or more in UK on average over a 4 year rolling period. • ‘Cinderella test’ and ‘transit rule’. • Year of departure and ‘split – year’ treatment (IT not CGT unless short term resident 4 of 7 rule). PwC 7 Residence for individuals - breaking residence Current rules Breaking UK residence 1. Working full-time abroad. 2. Evidence of a definite break. PwC 8 Residence for individuals Current rules Ordinarily resident Limited concept • “Your residence is typical of you, not casual”. • Settled purpose – business employment and family. • Regular and habitual mode of your life for time being, if come to UK with intention of staying 3 years or more. • Voluntarily (employment is voluntary). • Pattern of presence important factor. • Can be ordinarily resident in two jurisdictions. PwC 9 Residence for individuals New rules • Statutory test to come into force from 6 April 2013. -
Questionnaire Version 3.9.4 St001a CHECK IF PROXY IWER:Please
Sharelife: 50+ in Europe - Questionnaire version 3.9.4 ST001a CHECK IF PROXY IWER:Please check. Who answers the questionnaire? 1. Respondent only 2. Respondent and proxy 3. Proxy only IF ST001a (CHECK IF PROXY) = 3. Proxy only | | ST001b VALIDATE PROXY | | IWER:Are you sure that the respondent is not capable of answering the questionnaire? | 1. Yes | 5. No | ENDIF ST002 START OF INTERVIEW Welcome to the life history interview. I am going to ask you some questions about things that have happened during your life.Before we start, I'd like to check a few details you gave us last time we interviewed you. IWER:Press 1 and <ENTER> to continue. 1. Continue IF Preload.W3_CV005_Gender = EMPTY | | ST011 GENDER OF RESPONDENT | | IWER:Code respondents' sex (ask if unsure) | 1. Male | 2. Female | ENDIF IF Preload.W3_CV004_FirstName = EMPTY | | ST003 NAME OF RESPONDENT | What is your name? | | ___________ | | ELSE | | ST004 CHECK IF NAME IS CORRECTLY RECORDED | We have your name recorded as [{name of respondent}]. Is this correct? | | 1. Yes 1 | 5. No | | IF ST004 (CHECK IF NAME IS CORRECTLY RECORDED) = 5. No OR ST004 (CHECK IF NAME IS CORRECTLY RECORDED) = NONRESPONSE | | | | ST005 NAME OF RESPONDENT | | What is your name? | | | | ___________ | | | ENDIF | ENDIF IF Preload.W3_CV006_MoBirth = EMPTY OR Preload.W3_CV007_YrBirth = EMPTY | | ST006 MONTH OF BIRTH OF RESPONDENT | In which month were you born? | | 1. January | 2. February | 3. March | 4. April | 5. May | 6. June | 7. July | 8. August | 9. September | 10. October | 11. November | 12. December | | ST007 YEAR OF BIRTH OF RESPONDENT | In which year were you born? | | (1900..2009) | ELSE | | ST008 CHECK IF DATE OF BIRTH IS CORRECTLY RECORDED | We have recorded that you were born in [{month of birth}] of [{year of birth}]. -
Math 10 11-20 45 40 35 30 25 20 15 10 5 0
Multiplying Multiples of 10 Name: Solve each problem. Answers 1) 4 × 60 = 240 1. 240 2) 5,000 × 5,000 = 25,000,000 2. 25,000,000 3) 40 × 40 = 1,600 3. 1,600 4) 60 × 2,000 = 120,000 4. 120,000 5) 100 × 500 = 50,000 5. 50,000 6) 400 × 300 = 120,000 6. 120,000 7) 5 × 100 = 500 7. 500 8) 900 × 6,000 = 5,400,000 8. 5,400,000 9) 6,000 × 8 = 48,000 9. 48,000 10) 200 × 4,000 = 800,000 10. 800,000 11) 4 × 1,000 = 4,000 11. 4,000 12) 2,000 × 50 = 100,000 12. 100,000 13) 90 × 5,000 = 450,000 13. 450,000 14) 80 × 900 = 72,000 14. 72,000 15) 30 × 4,000 = 120,000 15. 120,000 16) 200 × 7,000 = 1,400,000 16. 1,400,000 17) 3,000 × 6 = 18,000 17. 18,000 18) 3,000 × 800 = 2,400,000 18. 2,400,000 19) 90 × 2,000 = 180,000 19. 180,000 20) 20 × 300 = 6,000 20. 6,000 1-10 95 90 85 80 75 70 65 60 55 50 Math www.CommonCoreSheets.com 10 11-20 45 40 35 30 25 20 15 10 5 0 Multiplying Multiples of 10 Name: Answer Key Solve each problem. Answers 1) 4 × 60 = 240 1. 240 2) 5,000 × 5,000 = 25,000,000 2. 25,000,000 3) 40 × 40 = 1,600 3. 1,600 4) 60 × 2,000 = 120,000 4.