In: Other Topics

Submitted By fein1

Words 1898

Pages 8

Words 1898

Pages 8

Home>Math>Math symbols> Math symbols

Mathematical Symbols

List of all mathematical symbols and signs - meaning and examples.

Basic math symbols

Geometry symbols

Algebra symbols

Probability & statistics symbols

Set theory symbols

Logic symbols

Calculus & analysis symbols

Number symbols

Greek symbols

Roman numerals

Basic math symbols

Symbol Symbol Name Meaning / definition Example

= equals sign equality 5 = 2+3

≠ not equal sign inequality 5 ≠ 4

> strict inequality greater than 5 > 4

< strict inequality less than 4 < 5

≥ inequality greater than or equal to 5 ≥ 4

≤ inequality less than or equal to 4 ≤ 5

( ) parentheses calculate expression inside first 2 × (3+5) = 16

[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18

+ plus sign addition 1 + 1 = 2

− minus sign subtraction 2 − 1 = 1

± plus - minus both plus and minus operations 3 ± 5 = 8 and -2

∓ minus - plus both minus and plus operations 3 ∓ 5 = -2 and 8

* asterisk multiplication 2 * 3 = 6

× times sign multiplication 2 × 3 = 6

∙ multiplication dot multiplication 2 ∙ 3 = 6

÷ division sign / obelus division 6 ÷ 2 = 3

/ division slash division 6 / 2 = 3

– horizontal line division / fraction mod modulo remainder calculation 7 mod 2 = 1

. period decimal point, decimal separator 2.56 = 2+56/100 ab power exponent 23 = 8 a^b caret exponent 2 ^ 3 = 8

√a square root √a • √a = a √9 = ±3

3√a cube root 3√a • 3√a • 3√a = a 3√8 = 2

4√a fourth root 4√a • 4√a • 4√a • 4√a = a 4√16 = ±2 n√a n-th root (radical) for n=3, n√8 = 2

% percent

1% = 1/100 10% × 30 = 3

‰ per-mille

1‰ = 1/1000 = 0.1% 10‰ × 30 = 0.3 ppm per-million

1ppm = 1/1000000 10ppm × 30 = 0.0003 ppb per-billion 1ppb = 1/1000000000 10ppb × 30 = 3×10-7 ppt per-trillion 1ppt = 10-12 10ppt × 30 = 3×10-10

Geometry symbols

Symbol Symbol Name Meaning / definition Example

∠…...

...• 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......

Words: 394 - Pages: 2

...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+^ =......

Words: 264 - Pages: 2

...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 ……………………………………………….…........

Words: 478 - Pages: 2

...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 +......

Words: 1363 - Pages: 6

...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......

Words: 2241 - Pages: 9

...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......

Words: 311 - Pages: 2

...DeVry MATH 221 Week 3 quiz with Formulas - Latest IF You Want To Purcahse A+ Work then Click The Link Below For Instant Down Load http://www.acehomework.net/wp-admin/post.php?post=3352&action=edit IF You Face Any Problem Then E Mail Us At JOHNMATE1122@GMAIL.COM MATH 221 Week 3 Quiz - 2015 Use the Venn diagram to identify the population and the sample. Choose the correct description of the population. The number of home owners in the state The income of home owners in the state who own a car The income of home owners in the state The number of home owners in the state who own a car Choose the correct description of the sample The income of home owners in the state who own a car The income of home owners in the state The number of home owners in the state who own a car The number of home owners in the state Hint: Population is the entire group about which information is needed. A sample is a smaller group of members of a population selected to represent the population. Determine whether the variable is qualitative or quantitative. Favorite sport Is the variable qualitative or quantitative? Qualitative Quantitative Hint: Since the favorite sport cannot be expressed in numerical terms, it is qualitative. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below. 43 50 10 91 76 35 64 36 42 72 53 62 35 74 50 72 36 28 38 61 ......

Words: 2243 - Pages: 9

...DeVry MATH 221 Week 3 quiz with Formulas - Latest IF You Want To Purcahse A+ Work then Click The Link Below For Instant Down Load http://www.acehomework.net/?download=devry-math-221-week-3-quiz-with-formulas-latest IF You Face Any Problem Then E Mail Us At JOHNMATE1122@GMAIL.COM MATH 221 Week 3 Quiz - 2015 1. Use the Venn diagram to identify the population and the sample. Choose the correct description of the population. 1. The number of home owners in the state 2. The income of home owners in the state who own a car 3. The income of home owners in the state 4. The number of home owners in the state who own a car Choose the correct description of the sample 1. The income of home owners in the state who own a car 2. The income of home owners in the state 3. The number of home owners in the state who own a car 4. The number of home owners in the state Hint: Population is the entire group about which information is needed. A sample is a smaller group of members of a population selected to represent the population. 2. Determine whether the variable is qualitative or quantitative. Favorite sport Is the variable qualitative or quantitative? 1. Qualitative 2. Quantitative Hint: Since the favorite sport cannot be expressed in numerical terms, it is qualitative. 3. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below. 43 50 10 91 76 35 ...

Words: 2351 - Pages: 10

...DeVry MATH 221 Week 7 Quiz with Formulas – Latest IF You Want To Purcahse A+ Work then Click The Link Below For Instant Down Load http://www.acehomework.net/?download=devry-math-221-week-7-quiz-with-formulas-latest IF You Face Any Problem Then E Mail Us At JOHNMATE1122@GMAIL.COM 1. A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 35,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that don’t wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Tires that wear out by 31,412 miles will be replaced free of charge. Hint: Here we need a value of X say K such that P (X < K) = 0.10 We know P (Z < -1.282) = 0.10 Thus from Z score of K we have, Solving for K we have K = 31412 2. Find the indicated z-score shown in the graph to the right. The z-score is -1.18 Hint: From standard normal table, P (Z < -1.18) = 0.1190 Therefore, z = -1.18 3. A researcher wishes to estimate, with 95% confidence, the amount of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion. a) find the minimum sample size needed, using a prior study that found that 32% of the respondents said they have high-speed internet access. 4. b) no preliminary estimate is available. Find the minimum sample size needed. a) = 523 b) = 601 Hint: (a) The sample size is...

Words: 813 - Pages: 4

...DeVry MATH 221 Week 7 Quiz with Formulas – Latest IF You Want To Purcahse A+ Work then Click The Link Below For Instant Down Load http://www.acehomework.net/?download=devry-math-221-week-7-quiz-with-formulas-latest IF You Face Any Problem Then E Mail Us At JOHNMATE1122@GMAIL.COM 1. A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 35,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that don’t wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Tires that wear out by 31,412 miles will be replaced free of charge. Hint: Here we need a value of X say K such that P (X < K) = 0.10 We know P (Z < -1.282) = 0.10 Thus from Z score of K we have, Solving for K we have K = 31412 2. Find the indicated z-score shown in the graph to the right. The z-score is -1.18 Hint: From standard normal table, P (Z < -1.18) = 0.1190 Therefore, z = -1.18 3. A researcher wishes to estimate, with 95% confidence, the amount of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion. a) find the minimum sample size needed, using a prior study that found that 32% of the respondents said they have high-speed internet access. 4. b) no preliminary estimate is available. Find the minimum sample size needed. a) = 523 b) = 601 Hint: (a) The sample size is...

Words: 813 - Pages: 4

...DeVry MATH 221 Week 3 quiz with Formulas - Latest IF You Want To Purcahse A+ Work then Click The Link Below For Instant Down Load http://www.acehomework.net/?download=devry-math-221-week-3-quiz-with-formulas-latest IF You Face Any Problem Then E Mail Us At JOHNMATE1122@GMAIL.COM MATH 221 Week 3 Quiz - 2015 1. Use the Venn diagram to identify the population and the sample. Choose the correct description of the population. 1. The number of home owners in the state 2. The income of home owners in the state who own a car 3. The income of home owners in the state 4. The number of home owners in the state who own a car Choose the correct description of the sample 1. The income of home owners in the state who own a car 2. The income of home owners in the state 3. The number of home owners in the state who own a car 4. The number of home owners in the state Hint: Population is the entire group about which information is needed. A sample is a smaller group of members of a population selected to represent the population. 2. Determine whether the variable is qualitative or quantitative. Favorite sport Is the variable qualitative or quantitative? 1. Qualitative 2. Quantitative Hint: Since the favorite sport cannot be expressed in numerical terms, it is qualitative. 3. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below. 43 50 10 91 76 35 ...

Words: 2351 - Pages: 10

...DeVry MATH 221 Week 7 Quiz with Formulas – Latest IF You Want To Purcahse A+ Work then Click The Link Below For Instant Down Load http://www.acehomework.net/?download=devry-math-221-week-7-quiz-with-formulas-latest IF You Face Any Problem Then E Mail Us At JOHNMATE1122@GMAIL.COM 1. A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 35,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that don’t wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Tires that wear out by 31,412 miles will be replaced free of charge. Hint: Here we need a value of X say K such that P (X < K) = 0.10 We know P (Z < -1.282) = 0.10 Thus from Z score of K we have, Solving for K we have K = 31412 2. Find the indicated z-score shown in the graph to the right. The z-score is -1.18 Hint: From standard normal table, P (Z < -1.18) = 0.1190 Therefore, z = -1.18 3. A researcher wishes to estimate, with 95% confidence, the amount of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion. a) find the minimum sample size needed, using a prior study that found that 32% of the respondents said they have high-speed internet access. 4. b) no preliminary estimate is available. Find the minimum sample size needed. a) = 523 b) = 601 Hint: (a) The sample size is...

Words: 813 - Pages: 4

...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 ...

Words: 532 - Pages: 3

...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 ......

Words: 4665 - Pages: 19

...has hundreds of functions and nobody knows them all, but spend some time and learn to create more powerful formulas. Students will dive into decision making functions like if() and lookup() and make Excel work for them! Students will also explore efficient use of multiple sheets in a workbook, creating multi-sheet and multi-workbook formulas. Students will learn about: if() functions, lookup() functions, conditional formatting, and using multiple worksheets in a workbook. 1. Course objectives. a. To provide the class with an exploration of spreadsheet design. b. To develop computer and spreadsheet literacy. c. To address the class' questions. 2. Schedule a. 9:00 Registration b. 9:30 Morning session c. 12:00 Departure 3. Handouts available in Adobe Portable Document Format (PDF) for download at www.crowleycomputers.com/handouts.htm 1. 2. Formulas: All formulas begin with = or basic math function a. Simple operators Monthly weather (1) + averages.xls (2) (3) * multiply (4) / divide (5) ^ exponent (6) = < > comparison b. Order of operator precedence (or Algebraic Order of Operations, for those of you as old as me!) determines what order calculations occur. (1) Calculations do not occur from left to right. (2) 3+4*5 does not equal (3+4)*5 (3) When you’re not sure, use (parenthesis) to force order of calculation. c. Edit via double clicking on cell, clicking on formula bar or F2 Operators ( in order of......

Words: 1729 - Pages: 7