by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia"

Transcription

1 Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs as ithr fixd or variabl and to stimat th fixd and variabl componnts of mixd costs, is important bcaus it nabls th us of dcision making tchniqus lik cost volum profit analysis (CVP analysis). This is ssntially a short-trm (or tactical) dcision tool which shows th ffct on profit of changs in costs, prics and sals volum in units. W cannot stimat accuratly th impact of ths changs unlss w know which costs ar fixd and which ar variabl. A managr may want th answrs to qustions such as what would b th impact on monthly profit of an incras in production and sals of 100 units pr month, what incras in sals volum is rquird to covr th additional fixd costs of our nw advrtising campaign or how many units of product X do w nd to mak and sll in ordr for it to b profitabl? Ths and othr qustions can b answrd using CVP analysis. CVP analysis is somtims calld brak-vn analysis bcaus it allows th usr to calculat a brak-vn point. This is th lvl of production and sals at which a product or srvic stops losing mony and bcoms profitabl. At th brak-vn point profit quals zro. Onc w know th brak-vn point w can assss th financial viability of a nw product or analys our currnt oprating prformanc. Assumptions Undrlying CVP Analysis A numbr of basic assumptions undrli CVP analysis and ths nd to b kpt in mind whn assssing its usfulnss in a particular dcision making situation. Th assumptions ar: 1. Th bhaviour of sals rvnu and costs is linar throughout th rlvant rang of activity. In othr words, w assum that slling pric pr unit, variabl cost pr unit and th total amount of fixd costs will rmain constant during th tim priod undr considration. 2. Th numbr of units sold is qual to th numbr of units producd during ach priod i.. all th units producd ar sold. 3. Variabl costs chang in total in dirct proportion to th lvl of activity. 4. All costs can b dividd into fixd and variabl lmnts. 5. Labour productivity, production tchnology and markt conditions do not chang. 6. In multiproduct firms, th sals mix rmains constant i.. th numbr of units of ach product sold will rmain a constant prcntag of th total numbr of all th units sold in ach priod (for all products). continud pag 11 10

2 N TARGET CVP analysis is a simplifid modl of rality, howvr, in many cass th stimats that it producs ar accurat nough to b quit usful. Th main dangr is using it whn a larg chang in th lvl of activity will tak oprations outsid th usual or rlvant rang, so that th CVP assumptions may no longr b valid. Contribution Incom Statmnt Th starting point for a CVP analysis is th prparation of a contribution format incom statmnt. This groups togthr all th variabl costs and all th fixd costs for a crtain priod. Most importantly, it shows th amount of contribution margin as an intrmdiat figur instad of th gross profit amount shown on a convntional incom statmnt. Contribution margin is th amount of rvnu rmaining aftr dducting all variabl costs. It can b statd both as a total amount and on a pr unit basis as shown in Illustration 1. blow. [ CVP analysis is a simplifid modl of rality, howvr th stimats that it producs ar accurat nough to b quit usful Illustration 1. A contribution incom statmnt continud pag 12 Run a Bttr Businss 11

3 Studnt Nots [ Using th CMR nabls managrs to quickly dtrmin th ffct on profit from any plannd chang in sals Th incom statmnt for th Widmark Clock Company shows that contribution margin pr unit ($200) is qual to th slling pric pr unit ($500) lss th variabl cost pr unit ($300). W will assum that th trm cost includs all costs and xpnss prtaining to th production and sal of th product. Hnc variabl costs includ variabl manufacturing costs plus variabl slling and administrativ xpnss. W can s that for vry clock that Widmark maks and slls it will hav $200 to covr fixd costs and contribut towards profit. Bcaus total fixd costs ar $80, 000 pr month, Widmark must gnrat at last $80, 000 of contribution margin ach month bfor it starts arning any profit. Its monthly sals must xcd 400 clocks ($ $200). This is Widmark s brak-vn point as shown in Illustration 2. blow. If Widmark sold 401 clocks in a month its profit bfor tax for that month would b $200. Onc th sals volum of a product passs th brakvn point, contribution margin pr unit is qual to profit bfor tax pr unit. Contribution Margin pr Unit Illustration 2. A contribution incom statmnt at th brak-vn point Contribution Margin Ratio Th contribution margin ratio (CMR) is th proportion of th slling pric pr unit rprsntd by contribution margin pr unit. For xampl, if th slling pric is $10 pr unit and this yilds $8.50 in contribution margin, th CMR is 85 pr cnt or Altrnativly, th CMR is th proportion of total sals rvnu rprsntd by th total contribution margin amount. For th Widmark Clock Company th CMR is $200 $500 or 40 pr cnt. Out of ach sals dollar 40 cnts is availabl to apply to fixd costs and to contribut to profit. If Widmark s sals rvnu incrasd by $20, 000 from $200, 000 in August to $220, 000 in Sptmbr its profit bfor tax would incras from zro to $8 000 ($ x 40 pr cnt). Using th CMR nabls managrs to quickly dtrmin th ffct on profit from any plannd chang in sals providd that th chang dos not tak th lvl of activity outsid th rlvant rang. If this occurs, total fixd costs and/or variabl cost pr unit may chang. Th rlvant rang is an important limitation on CVP analysis. If w wr considring an infinitly larg rang of output and sals, starting from zro, all costs would tnd to b variabl. Th assumptions that total fixd costs will rmain constant and that variabl cost pr unit dos not chang ar only valid within th normal or rlvant rang. Not that th contribution margin ratio plus th variabl cost ratio (total variabl costs sals rvnu) quals 100 pr cnt i.. CMR + VCR = 100 pr cnt (or 1.0) continud pag 13 12

4 N TARGET Calculating th Brak-Evn Point Th brak-vn point can b calculatd in thr ways: 1. Th graphical mthod 2. Th quation mthod 3. Th contribution margin mthod 1. Th Graphical Mthod A CVP graph nabls us to visualis th rlationships btwn sals rvnu, total cost, th numbr of units sold and profit. Illustration 3. blow shows a CVP graph basd on th rvnu and cost information for th Widmark Clock Company. Sals volum is rcordd along th horizontal axis whil sals rvnu and total costs ar shown on th vrtical axis. Th sals rvnu (SR) lin starts at th origin (whr th two axs intrsct) and passs through th brak-vn point which, as w saw in Illustration 2., is 400 units or $200, 000 of sals rvnu. For vry clock that Widmark slls, rvnu incrass by th slling pric pr unit of $500 which w assum rmains constant. This is th gradint or slop of th sals rvnu lin. Sa ls R SR v nu Profit Ara TCC an d Co sts Brak- Evn $ Point Loss Ara $$ TFC $$ R R v nu Units Sold $R Illustration 3. Th CVP graph for th Widmark Clock Company v Th amount of total nfixd costs is dpictd by a horizontal lin (TFC) which starts at a point u on th vrtical axis R rprsnting $80, 000. W assum that th rlvant rang xtnds from zro to at last 800 vunits so fixd costs rmain unchangd in total. Th total cost (TC) lin starts at th sam nu point as th TFC lin and has a uniform gradint qual to variabl cost pr unit ($300). On th graph, th amount of total variabl cost is rprsntd by th vrtical distanc btwn th total cost lin and th total fixd cost lin. Profit at any lvl of activity is th diffrnc btwn sals rvnu and total costs, and whr th SR lin crosss th TC lin profit quals zro. This is th brak-vn point. 2. Th Equation Mthod This mthod is basd on th following quation: Sals rvnu = Variabl costs + Fixd costs + Profit Bcaus at th brak-vn point profit is zro, brak-vn occurs whn sals rvnu is xactly qual to variabl costs plus fixd costs. Th brak-vn point in units can b calculatd by insrting in th quation th amounts for slling pric pr unit, variabl cost pr unit and total fixd costs. So for th Widmark Clock Company: continud pag 14 [ A CVP graph nabls us to visualis th rlationships btwn sals rvnu, total cost, th numbr of units sold and profit Run a Bttr Businss 13

5 Studnt Nots Sals rvnu = Variabl costs + Fixd costs + Profit $500Q = $300Q + $80,000 + $0 Whr: Q = Numbr of clocks sold $500 = Slling pric pr unit $300 = Variabl cost pr unit $80,000 = Total fixd costs Now solv for th valu of Q: $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 $200 Q = 400 clocks This is th brak-vn point in trms of units sold. To find th sals rvnu ndd to brak-vn, w multiply th numbr of units sold at th brak-vn point by th slling pric pr unit: 400 x $500 = $200, 000 (brak-vn sals rvnu) 3. Th Contribution Margin Mthod Th third mthod of calculating th brak-vn point is drivd from th quation mthod dscribd abov. Whn w solvd for th valu of Q, th last stp involvd dividing total fixd costs by th contribution margin of $200 pr unit to giv brakvn units (Q = 400). This simpl calculation can b xprssd thus: Brak-vn point in units sold = Total fixd costs Contribution margin pr unit 400 = $80,000 $200 To calculat th amount of brak-vn sals rvnu w us th contribution margin ratio instad of contribution margin pr unit: Brak-vn point in dollars of sals rvnu = Total fixd costs Contribution margin ratio $200, 000 = $80, Th contribution margin mthod can b xtndd to giv th numbr of sals units or sals dollars rquird to rach a crtain targt profit figur simply by adding th targt profit to th total fixd cost amount in th brak-vn formula. Not that th targt profit figur w must us is th profit rquird bfor tax has bn dductd. If you ar givn a targt profit figur aftr tax, dividing it by (1 th tax rat) will convrt it into th largr bfor tax amount: Targt profit bfor tax = (targt profit aftr tax) (1 t) whr t dnots th incom tax rat. CVP Analysis with Multipl Products So far w hav considrd situations involving singl products. Howvr, th rality is that thr ar vry fw singl product organisations. CVP analysis can b adaptd for situations whr thr is mor than on product bing mad and sold. For xampl, assum that th Contx Calculator Company producs two typs of calculator: Modl A and Modl B. Thir dtails ar as follows: Modl A Modl B Slling Pric Pr Unit $30 $50 Variabl Cost pr Unit Contribution Margin Pr Unit $15 $30 Sals Mix 2 1 Contx typically slls two Modl A calculators for ach Modl B that is sold. Th sals mix is, thrfor, two to on. Assum that Contx s total fixd costs ar $100, 000. W can now calculat th wightd avrag contribution margin (WACM) pr unit using th sals mix numbrs as wights. Sinc two Modl As ar sold for ach Modl B, th contribution margin of A is multiplid by 2, and th contribution margin of B is multiplid by 1. Th sum of th answrs is thn dividd by 3 (th sum of th wights) to giv th wightd avrag contribution margin pr unit of $20. WACM pr unit = ($15 x 2) + ($30 x 1) 3 = $20 Th wightd avrag contribution margin pr unit can now b usd to calculat th brak-vn point in units: Brak-vn sals in units = Total fixd costs WACM pr unit = $100, 000 $20 = 5, 000 Ths 5, 000 units would consist of 3, 333 units of Modl A (two-thirds of 5, 000) and 1, 667 units of Modl B (on-third of 5, 000). Chck: TCM = (3, 333 x $15) + (1, 667 x $30) = $100, 005 = TFC ($5 rounding rror) Although th mthod w hav just usd is appropriat for situations whr th sals mix is constant, in rality a constant sals mix is vry rar. If a firm s sals mix dos vary ovr tim, on of th main assumptions undrlying CVP analysis bcoms invalid and th rsults it producs bcom lss rliabl. 14

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13)

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13) con 37: Answr Ky for Problm St (Chaptr 2-3) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc

More information

Question 3: How do you find the relative extrema of a function?

Question 3: How do you find the relative extrema of a function? ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating

More information

QUANTITATIVE METHODS CLASSES WEEK SEVEN

QUANTITATIVE METHODS CLASSES WEEK SEVEN QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.

More information

14.3 Area Between Curves

14.3 Area Between Curves 14. Ara Btwn Curvs Qustion 1: How is th ara btwn two functions calculatd? Qustion : What ar consumrs and producrs surplus? Earlir in this chaptr, w usd dfinit intgrals to find th ara undr a function and

More information

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix Non-Homognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous first-ordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach

More information

Genetic Drift and Gene Flow Illustration

Genetic Drift and Gene Flow Illustration Gntic Drift and Gn Flow Illustration This is a mor dtaild dscription of Activity Ida 4, Chaptr 3, If Not Rac, How do W Explain Biological Diffrncs? in: How Ral is Rac? A Sourcbook on Rac, Cultur, and Biology.

More information

New Basis Functions. Section 8. Complex Fourier Series

New Basis Functions. Section 8. Complex Fourier Series Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ral-valud Fourir sris is xplaind and formula ar givn for convrting

More information

Improving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost

Improving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 50-54 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin

More information

Foreign Exchange Markets and Exchange Rates

Foreign Exchange Markets and Exchange Rates Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls

More information

Category 7: Employee Commuting

Category 7: Employee Commuting 7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil

More information

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book.

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book. Rsourc Allocation Abstract This is a small toy xampl which is wll-suitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of C-nts. Hnc, it can b rad by popl

More information

Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis ch03.qxd 9/7/04 4:06 PM Pag 86 CHAPTER Cost-Volum-Profit Analysis In Brif Managrs nd to stimat futur rvnus, costs, and profits to hlp thm plan and monitor oprations. Thy us cost-volum-profit (CVP) analysis

More information

AP Calculus AB 2008 Scoring Guidelines

AP Calculus AB 2008 Scoring Guidelines AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos mission is to connct studnts to collg succss and opportunity.

More information

Lecture 20: Emitter Follower and Differential Amplifiers

Lecture 20: Emitter Follower and Differential Amplifiers Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.

More information

Adverse Selection and Moral Hazard in a Model With 2 States of the World

Adverse Selection and Moral Hazard in a Model With 2 States of the World Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,

More information

7 Timetable test 1 The Combing Chart

7 Timetable test 1 The Combing Chart 7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing

More information

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim

More information

Modelling and Solving Two-Step Equations: ax + b = c

Modelling and Solving Two-Step Equations: ax + b = c Modlling and Solving To-Stp Equations: a + b c Focus on Aftr this lsson, you ill b abl to φ modl problms φ ith to-stp linar quations solv to-stp linar quations and sho ho you ord out th ansr Cali borrod

More information

Lecture 3: Diffusion: Fick s first law

Lecture 3: Diffusion: Fick s first law Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th

More information

e = C / electron Q = Ne

e = C / electron Q = Ne Physics 0 Modul 01 Homwork 1. A glass rod that has bn chargd to +15.0 nc touchs a mtal sphr. Aftrword, th rod's charg is +8.00 nc. What kind of chargd particl was transfrrd btwn th rod and th sphr, and

More information

Financial Mathematics

Financial Mathematics Financial Mathatics A ractical Guid for Actuaris and othr Businss rofssionals B Chris Ruckan, FSA & Jo Francis, FSA, CFA ublishd b B rofssional Education Solutions to practic qustions Chaptr 7 Solution

More information

Statistical Machine Translation

Statistical Machine Translation Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm

More information

http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force

http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd

More information

Long run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange

Long run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) 92.222 - Linar Algbra II - Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial

More information

Solutions to Homework 8 chem 344 Sp 2014

Solutions to Homework 8 chem 344 Sp 2014 1. Solutions to Homwork 8 chm 44 Sp 14 .. 4. All diffrnt orbitals mans thy could all b paralll spins 5. Sinc lctrons ar in diffrnt orbitals any combination is possibl paird or unpaird spins 6. Equivalnt

More information

Deer: Predation or Starvation

Deer: Predation or Starvation : Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,

More information

Modern Portfolio Theory (MPT) Statistics

Modern Portfolio Theory (MPT) Statistics Modrn Portfolio Thory (MPT) Statistics Morningstar Mthodology Papr May 9, 009 009 Morningstar, Inc. All rights rsrvd. Th information in this documnt is th proprty of Morningstar, Inc. Rproduction or transcription

More information

Factorials! Stirling s formula

Factorials! Stirling s formula Author s not: This articl may us idas you havn t larnd yt, and might sm ovrly complicatd. It is not. Undrstanding Stirling s formula is not for th faint of hart, and rquirs concntrating on a sustaind mathmatical

More information

SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY

SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY 1 SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY ALEXA Vasil ABSTRACT Th prsnt papr has as targt to crat a programm in th Matlab ara, in ordr to solv, didactically

More information

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000 hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails

More information

Basis risk. When speaking about forward or futures contracts, basis risk is the market

Basis risk. When speaking about forward or futures contracts, basis risk is the market Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also

More information

Free ACA SOLUTION (IRS 1094&1095 Reporting)

Free ACA SOLUTION (IRS 1094&1095 Reporting) Fr ACA SOLUTION (IRS 1094&1095 Rporting) Th Insuranc Exchang (301) 279-1062 ACA Srvics Transmit IRS Form 1094 -C for mployrs Print & mail IRS Form 1095-C to mploys HR Assist 360 will gnrat th 1095 s for

More information

A Derivation of Bill James Pythagorean Won-Loss Formula

A Derivation of Bill James Pythagorean Won-Loss Formula A Drivation of Bill Jams Pythagoran Won-Loss Formula Ths nots wr compild by John Paul Cook from a papr by Dr. Stphn J. Millr, an Assistant Profssor of Mathmatics at Williams Collg, for a talk givn to th

More information

Gas Radiation. MEL 725 Power-Plant Steam Generators (3-0-0) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi

Gas Radiation. MEL 725 Power-Plant Steam Generators (3-0-0) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi Gas Radiation ME 725 Powr-Plant Stam Gnrators (3-0-0) Dr. Prabal Talukdar Assistant Profssor Dpartmnt of Mchanical Enginring T Dlhi Radiation in absorbing-mitting mdia Whn a mdium is transparnt to radiation,

More information

Section 7.4: Exponential Growth and Decay

Section 7.4: Exponential Growth and Decay 1 Sction 7.4: Exponntial Growth and Dcay Practic HW from Stwart Txtbook (not to hand in) p. 532 # 1-17 odd In th nxt two ction, w xamin how population growth can b modld uing diffrntial quation. W tart

More information

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among

More information

Category 1: Purchased Goods and Services

Category 1: Purchased Goods and Services 1 Catgory 1: Purchasd Goods and Srvics Catgory dscription T his catgory includs all upstram (i.., cradl-to-gat) missions from th production of products purchasd or acquird by th rporting company in th

More information

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:

More information

Production Costing (Chapter 8 of W&W)

Production Costing (Chapter 8 of W&W) Production Costing (Chaptr 8 of W&W).0 Introduction Production costs rfr to th oprational costs associatd with producing lctric nrgy. Th most significant componnt of production costs ar th ful costs ncssary

More information

The Normal Distribution: A derivation from basic principles

The Normal Distribution: A derivation from basic principles Th Normal Distribution: A drivation from basic principls Introduction Dan Tagu Th North Carolina School of Scinc and Mathmatics Studnts in lmntary calculus, statistics, and finit mathmatics classs oftn

More information

Category 11: Use of Sold Products

Category 11: Use of Sold Products 11 Catgory 11: Us of Sold Products Catgory dscription T his catgory includs missions from th us of goods and srvics sold by th rporting company in th rporting yar. A rporting company s scop 3 missions

More information

(Analytic Formula for the European Normal Black Scholes Formula)

(Analytic Formula for the European Normal Black Scholes Formula) (Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually

More information

June 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8

June 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8 Jun 22 Enpris Rnt Author: Documnt Vrsion: Product: Product Vrsion: SAP Vrsion: Enpris Enpris Rnt 88 88 Enpris Rnt 22 Enpris Solutions All rights rsrvd No parts of this work may b rproducd in any form or

More information

Version Issue Date Reason / Description of Change Author Draft February, N/A 2009

Version Issue Date Reason / Description of Change Author Draft February, N/A 2009 Appndix A: CNS Managmnt Procss: OTRS POC Documnt Control Titl : CNS Managmnt Procss Documnt : (Location of Documnt and Documnt numbr) Author : Ettin Vrmuln (EV) Ownr : ICT Stratgic Srvics Vrsion : Draft

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13

Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13 Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions

More information

Simulated Radioactive Decay Using Dice Nuclei

Simulated Radioactive Decay Using Dice Nuclei Purpos: In a radioactiv sourc containing a vry larg numbr of radioactiv nucli, it is not possibl to prdict whn any on of th nucli will dcay. Although th dcay tim for any on particular nuclus cannot b prdictd,

More information

Optical Modulation Amplitude (OMA) and Extinction Ratio

Optical Modulation Amplitude (OMA) and Extinction Ratio Application Not: HFAN-.. Rv; 4/8 Optical Modulation Amplitud (OMA) and Extinction Ratio AVAILABLE Optical Modulation Amplitud (OMA) and Extinction Ratio Introduction Th optical modulation amplitud (OMA)

More information

3. Yes. You can put 20 of the 6-V lights in series, or you can put several of the 6-V lights in series with a large resistance.

3. Yes. You can put 20 of the 6-V lights in series, or you can put several of the 6-V lights in series with a large resistance. CHAPTE 6: DC Circuits sponss to Qustions. Evn though th bird s ft ar at high potntial with rspct to th ground, thr is vry littl potntial diffrnc btwn thm, bcaus thy ar clos togthr on th wir. Th rsistanc

More information

Parallel and Distributed Programming. Performance Metrics

Parallel and Distributed Programming. Performance Metrics Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:

More information

SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* Rostov-on-Don. Russia

SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* Rostov-on-Don. Russia SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT Eduard N. Klnov* Rostov-on-Don. Russia Th distribution law for th valus of pairs of th consrvd additiv quantum numbrs

More information

[ ] These are the motor parameters that are needed: Motor voltage constant. J total (lb-in-sec^2)

[ ] These are the motor parameters that are needed: Motor voltage constant. J total (lb-in-sec^2) MEASURING MOOR PARAMEERS Fil: Motor paramtrs hs ar th motor paramtrs that ar ndd: Motor voltag constant (volts-sc/rad Motor torqu constant (lb-in/amp Motor rsistanc R a (ohms Motor inductanc L a (Hnris

More information

CHAPTER 4c. ROOTS OF EQUATIONS

CHAPTER 4c. ROOTS OF EQUATIONS CHAPTER c. ROOTS OF EQUATIONS A. J. Clark School o Enginring Dpartmnt o Civil and Environmntal Enginring by Dr. Ibrahim A. Aakka Spring 00 ENCE 03 - Computation Mthod in Civil Enginring II Dpartmnt o Civil

More information

HSBC Bank International Expat Explorer Survey 08

HSBC Bank International Expat Explorer Survey 08 HSBC Bank Intrnational Expat Explorr Survy 08 Rport On: Expat Existnc Th Survy Th Expat Explorr survy qustiond 2,155 xpatriats across four continnts about th opportunitis and challngs thy fac. Th survy

More information

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers) Intrmdiat Macroconomic Thory / Macroconomic Analysis (ECON 3560/5040) Final Exam (Answrs) Part A (5 points) Stat whthr you think ach of th following qustions is tru (T), fals (F), or uncrtain (U) and brifly

More information

Section A This ONE question is compulsory and MUST be attempted

Section A This ONE question is compulsory and MUST be attempted Profssional Lvl Options Modul Advancd Financial Managmnt Tusday 2 Dcmbr 2014 Tim allowd Rading and planning: Writing: 15 minuts 3 hours This papr is dividd into two sctions: Sction A This ONE qustion is

More information

Systems of Equations and Inequalities

Systems of Equations and Inequalities CHAPTER CONNECTIONS Systms of Equations and Inqualitis CHAPTER OUTLINE.1 Linar Systms in Two Variabls with Applications 04. Linar Systms in Thr Variabls with Applications 16.3 Nonlinar Systms of Equations

More information

Performance Evaluation

Performance Evaluation Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Bay-lik rputation systms: Analysis, charactrization and insuranc mchanism

More information

HOMEWORK FOR UNIT 5-1: FORCE AND MOTION

HOMEWORK FOR UNIT 5-1: FORCE AND MOTION Nam Dat Partnrs HOMEWORK FOR UNIT 51: FORCE AND MOTION 1. You ar givn tn idntial springs. Dsrib how you would dvlop a sal of for (i., a mans of produing rpatabl fors of a varity of sizs) using ths springs.

More information

SPECIAL VOWEL SOUNDS

SPECIAL VOWEL SOUNDS SPECIAL VOWEL SOUNDS Plas consult th appropriat supplmnt for th corrsponding computr softwar lsson. Rfr to th 42 Sounds Postr for ach of th Spcial Vowl Sounds. TEACHER INFORMATION: Spcial Vowl Sounds (SVS)

More information

Version 1.0. General Certificate of Education (A-level) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final.

Version 1.0. General Certificate of Education (A-level) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final. Vrsion.0 Gnral Crtificat of Education (A-lvl) January 0 Mathmatics MPC (Spcification 660) Pur Cor Final Mark Schm Mark schms ar prpard by th Principal Eaminr and considrd, togthr with th rlvant qustions,

More information

1 Walrasian Equilibria and Market E ciency

1 Walrasian Equilibria and Market E ciency 1 Walrasian Equilibria and Markt E cincy Rading in Txtbook: Chaptr 3 in Stiglitz. 1.1 Motivation Whn thinking about th rol of govrnmnt w hav to considr a numbr of rathr fundamntal qustions, such as: What

More information

ME 612 Metal Forming and Theory of Plasticity. 6. Strain

ME 612 Metal Forming and Theory of Plasticity. 6. Strain Mtal Forming and Thory of Plasticity -mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.

More information

CHAPTER EIGHT. Making use of the limit formula developed in Chapter 1, it can be shown that

CHAPTER EIGHT. Making use of the limit formula developed in Chapter 1, it can be shown that CONTINUOUS COMPOUNDING CHAPTER EIGHT In prvious stions, th as of m ompoundings pr yar was disussd In th as of ontinuous ompounding, m is allowd to tnd to infinity Th mathmatial rlationships ar fairly asy

More information

Northern Ireland Petrol and Diesel prices data analysis

Northern Ireland Petrol and Diesel prices data analysis Rsarch and Information Srvic Papr 163/12 04 Octobr 2012 NIAR 720-12 Aidan Stnntt and Barbara Lov Northrn Irland Ptrol and Disl prics data analysis 1 Background On th 5 Sptmbr 2012, th Offic of Fair Trading

More information

Remember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D

Remember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D 24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd

More information

Paper P4. Advanced Financial Management. March/June 2016 Sample Questions. Professional Level Options Module

Paper P4. Advanced Financial Management. March/June 2016 Sample Questions. Professional Level Options Module Profssional Lvl Options Modul Advancd Financial Managmnt March/Jun 2016 Sampl Qustions Tim allowd Rading and planning: Writing: 15 minuts 3 hours This qustion papr is dividd into two sctions: Sction A

More information

Development of Financial Management Reporting in MPLS

Development of Financial Management Reporting in MPLS 1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr

More information

Sigmoid Functions and Their Usage in Artificial Neural Networks

Sigmoid Functions and Their Usage in Artificial Neural Networks Sigmoid Functions and Thir Usag in Artificial Nural Ntworks Taskin Kocak School of Elctrical Enginring and Computr Scinc Applications of Calculus II: Invrs Functions Eampl problm Calculus Topic: Invrs

More information

Paper P4. Advanced Financial Management. Tuesday 4 June 2013. Professional Level Options Module. The Association of Chartered Certified Accountants

Paper P4. Advanced Financial Management. Tuesday 4 June 2013. Professional Level Options Module. The Association of Chartered Certified Accountants Profssional Lvl Options Modul Advancd Financial Managmnt Tusday 4 Jun 2013 Tim allowd Rading and planning: Writing: 15 minuts 3 hours This papr is dividd into two sctions: Sction A This ONE qustion is

More information

Traffic Flow Analysis (2)

Traffic Flow Analysis (2) Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. Gang-Ln Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,

More information

81-1-ISD Economic Considerations of Heat Transfer on Sheet Metal Duct

81-1-ISD Economic Considerations of Heat Transfer on Sheet Metal Duct Air Handling Systms Enginring & chnical Bulltin 81-1-ISD Economic Considrations of Hat ransfr on Sht Mtal Duct Othr bulltins hav dmonstratd th nd to add insulation to cooling/hating ducts in ordr to achiv

More information

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison Contnts Tchnology Nwly Dvlopd Cllo Tchnology Cllo Tchnology : Improvd Absorption of Light Doubl-sidd Cll Structur Cllo Tchnology : Lss Powr Gnration Loss Extrmly Low LID Clls 3 3 4 4 4 Advantag Installation

More information

Incomplete 2-Port Vector Network Analyzer Calibration Methods

Incomplete 2-Port Vector Network Analyzer Calibration Methods Incomplt -Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar

More information

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives.

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives. Volum 3, Issu 6, Jun 2013 ISSN: 2277 128X Intrnational Journal of Advancd Rsarch in Computr Scinc and Softwar Enginring Rsarch Papr Availabl onlin at: wwwijarcsscom Dynamic Ranking and Slction of Cloud

More information

Architecture of the proposed standard

Architecture of the proposed standard Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th

More information

Rural and Remote Broadband Access: Issues and Solutions in Australia

Rural and Remote Broadband Access: Issues and Solutions in Australia Rural and Rmot Broadband Accss: Issus and Solutions in Australia Dr Tony Warrn Group Managr Rgulatory Stratgy Tlstra Corp Pag 1 Tlstra in confidnc Ovrviw Australia s gographical siz and population dnsity

More information

Noble gas configuration. Atoms of other elements seek to attain a noble gas electron configuration. Electron configuration of ions

Noble gas configuration. Atoms of other elements seek to attain a noble gas electron configuration. Electron configuration of ions Valnc lctron configuration dtrmins th charactristics of lmnts in a group Nobl gas configuration Th nobl gass (last column in th priodic tabl) ar charactrizd by compltly filld s and p orbitals this is a

More information

Increasing Net Debt as a percentage of Average Equalized ValuaOon

Increasing Net Debt as a percentage of Average Equalized ValuaOon City of Orang Township Warning Trnd: Incrasing Nt Dbt as a prcntag of avrag qualizd valuation Nt Dbt 3 yr. Avg. qualizd Valuation Incrasing Nt Dbt as a prcntag of Avrag Equalizd ValuaOon rc 1.20% 1.00%

More information

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 08-16-85 WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 Summary of Dutis : Dtrmins City accptanc of workrs' compnsation cass for injurd mploys; authorizs appropriat tratmnt

More information

Electronic Commerce. and. Competitive First-Degree Price Discrimination

Electronic Commerce. and. Competitive First-Degree Price Discrimination Elctronic Commrc and Comptitiv First-Dgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg

More information

Analyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms

Analyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms A rsarch and ducation initiativ at th MIT Sloan School of Managmnt Analyzing th Economic Efficincy of Baylik Onlin Rputation Rporting Mchanisms Papr Chrysanthos Dllarocas July For mor information, plas

More information

E X C H A N G E R U L E S A N D C L E A R I N G R U L E S O F N A S D A Q O M X D E R I V A T I V E S M A R K E T S

E X C H A N G E R U L E S A N D C L E A R I N G R U L E S O F N A S D A Q O M X D E R I V A T I V E S M A R K E T S E X C H A N G E R U L E S A N D C L E A R I N G R U L E S O F N A S D A Q O M X D E R I V A T I V E S M A R K E T S Fair Valu 1 Valuation Variabls Tabl 1 blow shows th variabls us in th rspctiv valuation

More information

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs

More information

Differential Equations (MTH401) Lecture That a non-homogeneous linear differential equation of order n is an equation of the form n

Differential Equations (MTH401) Lecture That a non-homogeneous linear differential equation of order n is an equation of the form n Diffrntial Equations (MTH40) Ltur 7 Mthod of Undtrmind Coffiints-Surosition Aroah Rall. That a non-homognous linar diffrntial quation of ordr n is an quation of th form n n d d d an + a a a0 g( ) n n +

More information

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman Cloud and Big Data Summr Scool, Stockolm, Aug., 2015 Jffry D. Ullman Givn a st of points, wit a notion of distanc btwn points, group t points into som numbr of clustrs, so tat mmbrs of a clustr ar clos

More information

Paper P4. Advanced Financial Management. Tuesday 12 June Professional Level Options Module. The Association of Chartered Certified Accountants

Paper P4. Advanced Financial Management. Tuesday 12 June Professional Level Options Module. The Association of Chartered Certified Accountants Profssional Lvl Options Modul Advancd Financial Managmnt Tusday 12 Jun 2012 Tim allowd Rading and planning: Writing: 15 minuts 3 hours This papr is dividd into two sctions: Sction A BOTH qustions ar compulsory

More information

A Theoretical Model of Public Response to the Homeland Security Advisory System

A Theoretical Model of Public Response to the Homeland Security Advisory System A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial

More information

Cookie Policy- May 5, 2014

Cookie Policy- May 5, 2014 Cooki Policy- May 5, 2014 Us of Cookis on Sizmk Wbsits This Cooki Disclosur applis only to us of cookis on corporat wbsits (www.sizmk.com and rlatd rgional wbsits) publishd by Sizmk Inc. and its affiliats

More information

Theoretical aspects of investment demand for gold

Theoretical aspects of investment demand for gold Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is

More information

Making and Using the Hertzsprung - Russell Diagram

Making and Using the Hertzsprung - Russell Diagram Making and Using th Hrtzsprung - Russll Diagram Nam In astronomy th Hrtzsprung-Russll Diagram is on of th main ways that w organiz data dscribing how stars volv, ags of star clustrs, masss of stars tc.

More information

Analysis Of Injection Moulding Process Parameters

Analysis Of Injection Moulding Process Parameters Analysis Of Injction Moulding Procss Paramtrs Mr. M.G. Rathi Assistant Profssor, partmnt of Mchanical Enginring, Govrnmnt Collg of Enginring Aurangabad, (MS), India. Mr. Manoj amodar Salunk Studnt, partmnt

More information

Global Financial Management

Global Financial Management Global Financial Managmnt Valuation of Stocks Copyright 999 by Alon Brav, Stphn Gray, Campbll R Harvy and Ernst Maug. All rights rsrvd. No part of this lctur may b rproducd without th prmission of th authors.

More information

Entity-Relationship Model

Entity-Relationship Model Entity-Rlationship Modl Kuang-hua Chn Dpartmnt of Library and Information Scinc National Taiwan Univrsity A Company Databas Kps track of a company s mploys, dpartmnts and projcts Aftr th rquirmnts collction

More information

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List. Elmntary Rndring Elmntary rastr algorithms for fast rndring Gomtric Primitivs Lin procssing Polygon procssing Managing OpnGL Stat OpnGL uffrs OpnGL Gomtric Primitivs ll gomtric primitivs ar spcifid by

More information

Economic Analysis of Floating Exchange Rate Systems

Economic Analysis of Floating Exchange Rate Systems Economic Analysis of Floating Rat Systms Th businss sction of any nwspapr will hav a tabl of spot s. Ths ar th s at which a prson could hav bought othr currncis or forign, such as th English Pound, Frnch

More information

Continuity Cloud Virtual Firewall Guide

Continuity Cloud Virtual Firewall Guide Cloud Virtual Firwall Guid uh6 Vrsion 1.0 Octobr 2015 Foldr BDR Guid for Vam Pag 1 of 36 Cloud Virtual Firwall Guid CONTENTS INTRODUCTION... 3 ACCESSING THE VIRTUAL FIREWALL... 4 HYPER-V/VIRTUALBOX CONTINUITY

More information

TN Calculating Radiated Power and Field Strength for Conducted Power Measurements

TN Calculating Radiated Power and Field Strength for Conducted Power Measurements Calculating adiatd owr and Fild Strngth for Conductd owr Masurmnts TN100.04 Calculating adiatd owr and Fild Strngth for Conductd owr Masurmnts Copyright Smtch 007 1 of 9 www.smtch.com Calculating adiatd

More information

AP Calculus Multiple-Choice Question Collection 1969 1998. connect to college success www.collegeboard.com

AP Calculus Multiple-Choice Question Collection 1969 1998. connect to college success www.collegeboard.com AP Calculus Multipl-Choic Qustion Collction 969 998 connct to collg succss www.collgboard.com Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos

More information