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Words 707

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Words 707

Pages 3

Mensuration

Surface area of sphere = 4πr 2

Area of curved surface of cone = πr × slant height

Arithmetic series

S n a l n[ a n d] u a n d n n

( ) 2 ( 1)

= ( 1)

2

1

2

= 1 + = + −

+ −

Geometric series

1 for 1

1

(1 )

1

= − <

−

= −

=

∞

−

r r

S a r S a r u ar n n n n

Summations

( )1 2

1

1

+ = Σ= r n n n r

( 1)(2 1) 6

1

1

2 + + = Σ= r n n n n r

2 2

4

1

1

3 ) 1 ( + = Σ= r n n n r

Trigonometry – the Cosine rule a2 = b2 + c2 − 2bc cos A

Binomial Series

∈ + + ⎟

⎟⎠

⎞

⎜ ⎜⎝

⎛

+ + ⎟

⎟⎠

⎞

⎜ ⎜⎝

⎛

+ ⎟

⎟⎠

⎞

⎜ ⎜⎝

⎛

+ = + − − a − b b n r n a b n a b n a b n an n n n r r n (

2

1

( ) 1 2 2 … … ) where !( )!

C ! r n r n r n r n −

= = ⎟

⎟⎠

⎞

⎜ ⎜⎝

⎛

+ = + + − + + − − + x + x < n∈ r x n nx n n x n n n r r ( 1,

1.2

( 1) ( 1)

1.2

(1 ) 1 ( 1) 2 …

…

… … )

Logarithms and exponentials ax = exln a

Complex numbers

{r(cosθ + i sinθ )}n = r n (cos nθ + i sin nθ ) eiθ = cosθ + i sinθ

The roots of z n = 1 are given by n k z

2π i

= e , for k = 0, 1, 2, … , n −1

N

R klj 5

Maclaurin’s series f( ) f(0) f (0) 2! f (0) … ! f ( ) (0) …

2

= + ′ + ′′ + + r + r r x x x x r x x x x x x r e exp( ) 1 2! ! for all

2

= = + + +…+ +… r x x x x x x r + = − + − + (−1)r+ + (−1 < ln(1 ) 2 3 2 3 1

… … 1) x r x x x x x r r for all

(2 1)!

( 1)

3! 5! sin 3 5 2 1

… +…

+

= − + − + −

+

x r x x x x r r for all

(2 )!

( 1)

2! 4! cos 1

2 4 2

= − + −…+ − +…

Hyperbolic functions cosh2 x − sinh2 x = 1 sinh 2x = 2sinh x cosh x cosh 2x = cosh2 x + sinh 2 x cosh−1 x = ln{x + x2 −1} (x 1) sinh−1 x = ln{x + x2 +1}

( 1)

1

tanh ln 1 2

1 1 < ⎟⎠

⎞

⎜⎝

⎛

−

− = + x x x x

Conics

Ellipse Parabola Hyperbola Rectangular hyperbola Standard form 1 2

2

2

2

+ = b y a x ax y 2 = 4 1 2

2

2

2

− = b y a x 2 xy = c

Asymptotes none none b y

a…...

...• o Question o Answer o Side 3 • o Budgeted At Completion (BAC) o How much was originally planned for this project to cost. No one formula exists. Is derived by looking at the total budgeted cost for the project. o No one formula exists. Is derived by looking at the total budgeted cost for the project. • o Planned Value (aka Budgeted Cost of Work Scheduled) (PV or BCWS) o How much work should have been completed at a point in time based on the plan. Derived by measuring planned work completed at a point in time. Planned % Complete x BAC o Planned % Complete x BAC • o Earned Value (aka Budgeted Cost of Work Performed) (EV or BCWP) o How much work was actually completed during a given period of time. Derived by measuring actual work completed at a point in the schedule. EV = Actual % Complete x BAC o EV = Actual % Complete x BAC • o Actual Cost (aka Actual Cost of Work Performed) (AC or ACWP) o The money spent during a given period of time. Sum of the costs for the given period of time. o Sum of the costs for the given period of time. • o Cost Variance (CV) o The difference between what we expected to spend and what was actually spent. CV = EV-AC o CV = EV-AC • o Schedule Variance (SV) o The difference between where we planned to be in the schedule and where we are in the schedule SV = EV-PV o SV = EV-PV • o Cost Performance Index (CPI) o The rate at which the project performance is meeting cost expectations during a......

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...StaInstructor’s Manual CASE TEACHING NOTES The Formula One constructors Mark Jenkins 1. Introduction This case enables students to explore sources of competitive advantage using the context of Formula One (F1) motorsport. The case highlights the ways in which three particular F1 teams created four situations of competitive dominance for a sustained period. It allows the students to consider individual teams and the generic issues needed to succeed in this specialised context. The case is organised into five parts. The first is a brief overview designed to give those unfamiliar with F1 some understanding of its history and structure. This is followed by four detailed descriptions of particular periods of dominance by an F1 team. The introduction to the case describes the overall nature of Formula One motorsport and its origins in Europe after World War II. It identifies some of the central aspects of being an F1 constructor, such as the need to generate sponsor revenues through increasingly sophisticated marketing strategies, and also the need to design, develop, manufacture and race open-wheel single-seat racecars. Note: the term ‘constructor’ differentiates F1 from other racing series in which race teams compete with bought-in racecars. F1 constructors are effectively in the business of designing and constructing prototypes – each car being unique to each constructor but within a set of pre-defined rules that cover weight, dimensions and other basic parameters.......

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.....................................................................................52 Feeding low birthweight babies ........................................................................................56 Session 4.4: Formula Feeding ................................................................................................58 Overview of formula feeding ............................................................................................59 Conditions needed to safely formula feed.......................................................................60 Risks associated with formula feeding .............................................................................61 Minimising risks of formula feeding ................................................................................63 How often and how much.................................................................................................72 Avoid harm to infant feeding practices in the general population ..............................75 Stigma ...................................................................................................................................76 Common mistakes to avoid when formula feeding.......................................................76 Formula feeding: Q&A ......................................................................................................77 Session 4.5: Infant Feeding Counselling in the Context of HIV......................................80...

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...To Write a Chemical Formula in OWL Enclose subscripts with underscores _. Enclose superscripts with carats ^. The underscore key is next to the number zero on the keyboard. The carat key is the number six on the keyboard. H_2_O = H2O Cr^3+^ = Cr3+ Combined: SO_4_^2−^ = SO42− Ions Unit Charge Ions Write the number first and then the charge. Do not include the number one in unit charge ions. N^3−^ = N3− Ca^2+^ = Ca2+ Na^+^ = Na+ Cl^−^ = Cl− Using the Chemical Formula Input The chemical formula input box displays the superscripts and subscripts as you enter the formula. There are 3 ways to use the input box. • Keyboard: Use the keyboard to enter underscores and carats on your own. • Buttons after: Enter the formula without underscores or carats, then highlight each superscript and/or subscript, click the appropriate subscript or superscript button, and the underscores or carats will be filled in automatically. • Button during: Use the subscript or superscript buttons to enter the underscores and carats while you type the formula. To Write a Chemical Formula in OWL Enclose subscripts with underscores _. Enclose superscripts with carats ^. The underscore key is next to the number zero on the keyboard. The carat key is the number six on the keyboard. H_2_O = H2O Cr^3+^ = Cr3+ Combined: SO_4_^2−^ = SO42− Ions Unit Charge Ions Write the number first and then the charge. Do not include the number one in unit charge ions. N^3−^ = N3− Ca^2+^ =......

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...Microsoft Excel 2010 Formulas & Functions Table of Contents Excel 2010 Formulas & Functions ……………………………………………….….. o Formula Basics ……………………………………………….….. o Order of Operation ……………………………………………….….. Conditional Formatting ……………………………………………….….. Cell Styles ……………………………………………….….. Formulas & Functions ……………………………………………….….. Basic Formulas ……………………………………………….….. o Add the Values in Rows or Columns ……………………………………………….….. o Find the Average, Maximum, or Minimum ……………………………………………….….. Ranges & Individual Cells ……………………………………………….….. Copy a Formula ……………………………………………….….. o Using the Fill Handle ……………………………………………….….. o Using Traditional Copy & Paste ……………………………………………….….. Referencing Cells in Formulas ……………………………………………….….. o Relative References ……………………………………………….….. o Absolute References ……………………………………………….….. o Mixed References ……………………………………………….….. o References to Other Worksheets ……………………………………………….….. o Other Workbook References ……………………………………………….….. Quick Reference Guide ……………………………………………….….. o Add, Subtract, Multiple & Divide ……………………………………………….….. o Understanding Error Values ……………………………………………….….. Practical Purposes of Excel Formulas ……………………………………………….….. o Using Date & Time Formulas ……………………………………………….….. Commonly Used Functions & Formulas ……………………………………………….….. o Math & Trig Icon ……………………………………………….….. Logical Icon ……………………………………………….….. Lookup & Reference Icon ……………………………………………….….. Date & Time Icon ……………………………………………….….. AutoSum Icon ……………………………………………….…........

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...Rough Draft Formula Writing Have you ever had problems getting started on an essay? Most writers have. There is a technique that can help, and it’s called formula writing. Formula writing, like most essays, contains an introduction, body paragraphs, and a conclusion. These elements are the “formula” for writing. The first element of formula writing is the introduction. It is the first paragraph of the essay and introduces the main idea of the entire essay. In addition, this paragraph contains information to grab the reader’s attention. The first sentence can either present the thesis statement, which is not the preferred method, or it can hook the reader, as this essay does. The introduction also contains a listing of the main ideas that will be developed in the body paragraphs. If the thesis statement has not been expressed in the first sentence, it should be the last sentence of the introduction; this is the preferred placement of the thesis statement. If the thesis statement is the first sentence, the last sentence of the introductory paragraph should be a concluding sentence that either wraps-up the paragraph or leads into the first body paragraph. The body is the second element of formula writing. The body usually contains three paragraphs, although it can contain more or fewer. Each paragraph must have its own topic sentence, which is usually the first sentence of the paragraph. The remaining sentences develop the main idea, or topic sentence,......

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...Multiplication of Polynomial A. Multiplication of a Polynomial by a Monomial FORMULA 4a² (3a + 5) = (4a² • 5) + (4a² • 5) = 12a³ + 20a² Ex. 1. 4 4 2x (5x³ + x² - 4x – 2) = (2x • 5x³) + (2x • x²) - (2x • 4x) - (2x • 2) = 10x + 2x³ - 8x²- 4x 2. 5x²y (3x + 2y – 6) = (5x²y • 3x) + (5x²y • 2y) – (5x²y • 6) = 15x³y + 10x²y² - 30x²y 3. x (2x + 3y) = (x • 2x) + (x • 3y) = 2x³ + 3xy 4. -5x (3x – 2) = (-5x • 3x) - (-5x • 2) = -15x² + 10x 5. a (3a + 5) = (a • 3a) + (a • 5) = 3a² + 5a SPECIAL PRODUCTS B. Multiplication of a Binomial by Another Binomial FORMULA FOIL FOIL DISTRIBUTIVE DISTRIBUTIVE 4x – 4 2x + 5 8x²- 8x + 20x – 20 8x²+ 12x – 20 (x + 3) (x + 2) x²+ 2x + 3x + 6 x² + 5x + 6 (x + 3) (x + 2) x²+ 2x + 3x + 6 x² + 5x + 6 x + 3 x + 2 x²+ 3x 2x + 6 x²+ 5x + 6 x + 3 x + 2 x²+ 3x 2x + 6 x²+ 5x + 6 Ex. 1. (x + 3) ; (x + 2) (4x + 2) (2x + 3) 8x²+ 12x + 4x + 6 8x² + 16x + 6 (4x + 2) (2x + 3) 8x²+ 12x + 4x + 6 8x² + 16x + 6 4x + 2 2x + 3 8x²+ 4x 12x + 6 8x²+16x + 6 4x + 2 2x + 3 8x²+ 4x 12x + 6 8x²+16x + 6 2. (4x + 2) ; (2x + 3) (3x +4) (5x + 2) 15x²+ 6x + 20x + 8 15x² + 26x + 8 (3x +4) (5x +......

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...Formulas: 4 Total Cost 4 Contribution Margin 4 Unit Contribution 4 Total Contribution 4 Profit 4 Channel Margins 5 Margins (in %) – Based on Price 5 Mark-Ups (in %) – Based on Costs 5 Example: 5 Moving Up & Down the Value Chain 6 Move “Up” Chain 6 Move “Down” Chain 6 Breakeven Analysis 6 BE (units) 6 BE (dollars of sales) 7 Market Share 7 Dollar Share 7 Unit Share 7 BE MS (Dollars) 7 BE MS (Units) 7 Cannibalization 7 Total Contribution (NP) 7 Net Present Value: Today’s $ v. Next Year’s $ 8 Customer Lifetime Value (CLV) 8 Mkt Strat I: Strategy Formulation, Market Assessment Tools (Frameworks), Porter’s Generic Strategies 9 Dolan’s 5 Cs 9 Porter’s 5 Forces Model 10 BCG Matrix 10 Marketing Strategy II: Segmentation and Positioning 11 S-T-P 11 Consumer Segmentation Variables: 11 Business Segmentation Variables: 11 Characteristics of Effective Segmentation 11 Bases for Segmentation Evaluation 12 Targeting the Markets 12 Pricing 12 Top 3 of 5 Deadly Pricing Sins 12 8 Steps to Better Pricing Decisions 12 Value-Based Pricing 13 Marketing Research 14 Steps in Marketing Research 14 Reliability v. Validity 14 Marketing Channels 15 Value Adding Roles of Intermediaries 15 Channel Conflict and Efficiency 15 Salesforce Management 15 McMurry’s sales representative types: 16 Motivating the Salesforce 16 Simple Salesforce Structures 16 Salesforce Size 17 Brand Management 17 Brand......

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...Evaluation of Financial Policy GBA 546 Formula Sheet Prepared by P. Sarmas Cash Flow from Assets = Cash Flow to Creditors + Cash Flow to Stockholders Operating Cash Flow Interest Paid Dividend Paid - Net Working Capital - Net New Borrowing - Net New Equity - Net Capital Spending Cash Flow to Creditors Cash Flow to Stockholders Cash Flow from Assets EBIT Ending Net Fixed Assets + Depreciation - Beginning Net Fixed Assets - Taxes + Depreciation . Operating Cash Flow Net Capital Spending Ending Net Working Capital (CA – CL) - Beginning Net Working Capital (CA-CL) Change in Net Working Capital Ending L.T. Debt Ending Equity - Beginning L.T. Debt - Beginning Equity Net New Borrowing - Addition to Retained Earnings Net New Equity Dividend Payout Ratio = Dividends Net Income ROADuPont = Profit Margin * Total Assets t/o ROEDuPont = Profit Margin * Total Assets t/o * Equity Multiplier Earnings Retention Ratio = b = 1 – Dividend Payout Ratio = 1- DIV/NI (1+R) = (1+r)*(1+h) Operating Cycle = Inventory Period + Accounts Receivable Period Cash Cycle = Operating Cycle – Accounts Payable Period Operating Cash Flow = EBIT + Depreciation – Taxes Operating Cash Flow = (Sales – OC – Depreciation)*(1-T) + Depreciation......

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...Financial ratio formulas Prepared by Pamela Peterson Drake 1. Operating cycle Inventory Inventory = Average day's cost of goods sold Cost of goods sold / 365 Accounts receivable Accounts receivable = Average day's sales on credit Sales on credit / 365 Number of days of inventory = Number of days of receivables = Number of days of payables = Accounts payable Accounts payable = Average day's purchases Purchases / 365 Note: Purchases = Cost of Ending Beginning + + goods sold inventory inventory Operating cycle = Number of days Number of days + of inventory of receivables Number of days of inventory + Number of days Number of days − of receivables of purchases Net operating cycle = 2. Liquidity Current assets Current liabilitie s Current ratio = Quick ratio = Current assets - Inventory Current liabilitie s Current assets - Current liabilitie s Sales Net working capital to sales ratio = 3. Profitability Gross income Sales Operating income Sales Gross profit margin = Operating profit margin = Financial ratio formula sheet, prepared by Pamela Peterson-Drake 1 Net profit margin = Net income Sales 4. Activity Cost of goods sold Inventory Sales on credit Accounts receivable Inventory turnover = Accounts receivable turnover = Total asset turnover = Sales Total assets Sales Fixed assets Fixed asset turnover = 5. Financial leverage Total debt Total assets Long - term debt Total......

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...MAR 4231 = Financial Formulas Note: When calculating the financials, please round to four decimal places. For example: 1.7658643983 = 1.7659 (four decimal places) 0.4322222222 = 0.4322 (four decimal places) Asset turnover = Net sales Total assets Cost complement = is the relationship of cost to retail value of merchandise available for sale Total cost valuation Total retail valuation Cost of goods sold = Cost of merchandise available for sale – cost value of ending inventory Ending retail book value of inventory = on paper, how much is your inventory worth (at retail) = Merchandise available for sale – Sales – Deductions Financial Leverage = Total assets Net worth Gross Profit = Sales – Cost of Goods Sold Net Profit = Gross Profit – Operating Expenses Net Profit Margin = Net profit after taxes Net sales Profit & Loss Statement = Sales – less cost of goods sold = gross profit Return of Assets = Net profit margin x asset turnover Return on Net worth = Net profit margin x Asset turnover x Financial leverage Stock Shortages = how much inventory was stolen/lost? Ending retail book value of inventory – physical inventory at retail Total merchandise available (at cost) = Beginning monthly inventory + Net purchases + transportation charges Total merchandise available (at retail) = Beginning monthly inventory + Net purchases Adjusted ending retail book value of inventory = adjusted the value of the retail book value of......

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...Final Exam Formula Sheet PVIFn,i =[ ] 0 1 (1 i ) -n n (1 i) FVIFn,i (1 i ) n 1⁄ [ ] 0 = ln 1 + ) ( 1 FVIFA n,i (1 i ) n 1 i 1 FVIFA - Duen,i (1 i ) n 1 (1 i ) i t (1 k t ) ft 1 (1 k t-1 ) t-1 −1 1 1 - (1 i ) -n i 1 PVIFA - Duen,i 1 - (1 i ) -n (1 i ) i -in PV FVe PVIFA n,i m i EIR 1 1 m = [1 + ( i j 1 2 +− )] 365⁄ 2 m 1 −1 NAB≠Principalforfront-end fees, discount interest and compensating balance. FV - Price 365 kn = kr + + kr Bond Equivalen t Yield or Price Term (1 + ) = (1 + )(1 + ) YTM = kr + INF + MRP + LRP + DRP C C FV Pbond (1 k1 ) (1 k 2 ) 2 $FVn (1 in ) n Pzero Pbond $C Holding Period Return P t 1 P Holding Period Return D0 (1 g) t D0 (1 g) D P 1 t (1 k) k-g k-g t 1 k Payout Ratio k-g D1 g P0 Po Price BVPS Book value per share COV(k i , k j ) σi σ j n ~ ~ ~ ~ COV( k1 , k 2 ) Σ Pri k1i E( k1 ) k 2i E( k 2 ) i 1 Pt Pt 1 C t Pt 1 Pt 1 D D t (1 k) k TP0 (1 g) TP1 k-g k-g Po EPS1 ρ ij Pt Pt 1 D t Pt 1 Pt 1 1 $FV 1 - (1 k d ) -n kd (1 k d ) n σ n Pr k i 1 i E(k) 2 i Final......

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...FORMULAS CHAPTERS 12, 14, 15 AND 16. CH 12 BREAK EVEN ANALYSIS Sales price EBIT = 0 = units X per unit Break-even level of units variable cost - units X sold per unit total fixed + sold cost total fixed cost = sales price variable cost per unit − per unit Total fixed cost S* = F/ [1 – (VC / S)] Break-even level of revenues = variable cost 1revenues Degree of operating leverage DOLs = Q (P – V) / [Q (P – V) – F] DOLs = revenue before fixed cost / EBIT = S – VC / [S - VC – F] Degree of financial leverage DFLEBIT = EBIT / (EBIT - I) Degree of combined leverage DCLS = (DOLS) X (DFLEBIT) EBIT – EPS indifference point: EPS: Stock plan (EBIT – I)(1 – t) – P / Ss = EPS: Bond plan (EBIT – I)(1 – t) – P / Sb EBIT = [Ib – Is (Sb / Ss ] / [ 1 - (Sb / Ss) ] 14 SHORT-TERM FINANCIAL PLANNING CURRENT ASSETS AS A PERCENTAGE OF SALES = Current assets / sales Projected current assets = projected sales X (current assets / sales) Projected addition net income cash dividends X 1 − = projected sales X to retained earnings sales net income Discretionary financing = projected total assets – projected liabilities – projected owner’s equity needed (DFN) predicted change predicted change − DFN = in total assets predicted change − in spontaneous liabilities in retained earnings External financing needs (EFN) EFN = predicted change in total assets – change in retained earnings ...

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...Roejohn Remzo P. Tiolengco 2 – 21 I. Introduction A. Brief facts about Formula One B. Formula One: The Pinnacle of Motor Sports II. The Formula A. The Chassis 1. Materials 2. Aerodynamics 3. Wheels 4. Maintenance B. The Power unit 1. Specifications 2. Development 3. Power 4. Loads C. The Driver 1. Talent 2. Fitness III. Conclusion A. Summary B. Recommendation The Elements of Formula One Formula One cars truly are a masterpiece of engineering, These cars are the most technologically advanced, most rapidly developed cars in the world and are unmatched at what they do. A product of the human mind that pushes technology and man to its absolute limits. Formula One is the pinnacle of motor sports racing. The heart of a Formula One car is the chassis – the part of the automobile onto which everything is bolted and attached. Like most modern cars and aircraft, Formula One race cars feature monocoque construction. Monocoque is a French word meaning “single shell” which refers to the process of making the entire body out of a single piece of material. This material is a strong composite that is made up of spun carbon fibre set in resin or carbon fibres layered over aluminium mesh. The end result, a car that weighs in at just three-quarters of a ton. This lightweight bodywork also enables the car to reach speeds in excess of 300 kilometres per hour. (How Stuff Works, 2007 ) When you move at such phenomenal speeds, you need a lot of......

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...per (it can fluctuate) Imputed costs Equity capital also has cost (investors expect a return) but these do not appear on the income statement⇒because there is no paper that says how much the company has to pay this cost must be estimated (imputed) The economist would subtract these cost but an accountant does not, the difference is important because many decisions are based on the numbers in the income statement: wages, bonuses, etc 4 Chapter 2. Evaluating financial performance Return on equity Most popular tool to evaluate financial performance ⇒ it is a measurement of efficiency⇒ earnings investedDOLLAR NETincome Is the basic formula but can be redefined as shareholdersEQUITY ROE = NETincome Sales Assets ⋅ ⋅ Sales Assets shareholdersEquity ROE = ROE = PROFITm argin ⋅ ASSETturnover ⋅ FINANCIALleverage Profit margin: earnings out of every dollar of sale NETincome ‐ Return on assets ROA = Assets GROSSprofits ‐ Gross margin: ⇒ used to find out the fixed and the variable costs Sales Asset turnover: sales generated for every dollar of assets employed Low: assets intensive industry cos tgoodssold Inventory ending Inventory turnover: Collection period: shows the company’s management of accounts receivable ⇒ average time ......

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