Notes, summaries, assignments, exams, and problems for Mathematics

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The Golden Circle: Driving Innovation and Quality Management

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Golden circle:

This relates to the innovation. If a company is able to attract those who share its beliefs, it is also able to connect easier with innovators.

This is a graph made up of three circles, each inside the other. Each circle has a meaning and a way to apply it to our business efficiently.

We can explain the operation of the Golden Circle in such a way that while most companies ask themselves the answers to the question 'what' as their starting point, they are fully aware of the 'how', but very few companies are clear about the 'why'.

The 'what' responds to what we do and what we want to do. The 'how' responds to the processes through which we carry out our actions, and the 'why' would respond to the reason why we develop our business.... Continue reading "The Golden Circle: Driving Innovation and Quality Management" »

Algebra I: Equations, Inequalities, and Functions

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Algebra I Review

Inequalities

What happens to the inequality sign if you multiply or divide by a negative number?

Flip the inequality symbol

Which part of the inequality sign determines when you have a closed circle on a graph?

The line under the symbol. (Equal to line)

Domain is the _______ value of an ordered pair, which is also known as the _________ value.

x, independent

Range is the ______ value of an ordered pair, which is also known as the _______ value.

y, dependent

Linear Equations

What is the formula to find the slope of a line?

m = (y2 - y1) / (x2 - x1)

Write the equation of the point-slope form of a line.

y - y1 = m(x - x1)

Write the equation of the slope-intercept form of a line.

y = mx + b

Write the equation of the standard form of a line.

Ax +
... Continue reading "Algebra I: Equations, Inequalities, and Functions" »

Analyzing Corporate Liquidity and Financial Health

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Essential Aspects of Corporate Liquidity Analysis

There are two essential aspects in the analysis of the liquidity of a company. On one hand, there is the quality of the coverage of current debts with the most liquid assets; on the other hand, there is the temporal aspect—that is, the agility of current assets to become cash, as well as the agility of current debts to expire.

Evaluating Debt Coverage and Working Capital

In order to analyze the quality of the coverage of current debts, we start by calculating the working capital and its complementary ratios. The positive value of the working capital serves as an indicator (though never definitive evidence) of a good liquidity situation.

Liquidity Ratios: Acid Test and Cash Ratio

Due to the limitations... Continue reading "Analyzing Corporate Liquidity and Financial Health" »

Advanced English Exam Preparation: Grammar and Vocabulary

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Get Ready for Your Exam

Use of English

Vocabulary Check: Correct Spelling

  • 1. Inclusion
  • 2. Impressive
  • 3. Unprofessional
  • 4. Glamorous
  • 5. Repeatedly
  • 6. Unintentionally

Unreal Past and Had Better Structures

Incomplete Sentences/Corrections:
  • 1. I'd sooner we travel by boat.
  • 2. You'd better say sorry for...
  • 3. He acts as though he owns...
  • 4. I'd rather you came... (Correction: 'to come' changed to 'came' for correct structure)
  • 5. It's time to buy a new car....
  • 6. The party's over, so we might as well stay home. (Correction: 'staying' changed to 'stay')

Language Review

Grammar Practice: Conditionals and Wishes

Conditional Sentences (Corrections Needed)

  1. We wouldn't have been lost if you had remembered to bring the map. (Corrections: 'been' to 'have been', 'remember' to
... Continue reading "Advanced English Exam Preparation: Grammar and Vocabulary" »

Financial Ratio Analysis: Performance, Efficiency, and Growth

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Market Value Performance Measures

  • Market Value Added (MVA): Market Capitalization (Number of shares × Price per share) - Equity.
  • Market-to-Book Ratio: Measures value added per dollar invested by shareholders. Calculated as: Market Value of Equity / Book Value of Equity (Total Shareholders' Equity).

Measuring Profitability

  • Economic Value Added (EVA): Profit after deducting all costs, including the cost of capital. Formula: [After-tax operating income] - [Cost of Capital × Total Capitalization at start of year (Long-term debt + Total equity)].
  • Return on Equity (ROE): Net Income / Equity (start of year).
  • Return on Assets (ROA): [(1 - Tax Rate) × Interest Expense + Net Income] / Total Assets (start of year).
  • Return on Capital (ROC): [(1 - Tax Rate)
... Continue reading "Financial Ratio Analysis: Performance, Efficiency, and Growth" »

Spanish Tax Systems and VAT Regulations

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Fundamental Tax Concepts

Taxes: Tax is government revenue created by law and enforceable by taxpayers covered by the same. A tax liability always arises caused by a specific taxable event.

Taxable Event and Residence

Taxable Event: This is the reason or the cause that has been made to pay the tax. It determines what is taxed, whether or not these are linked to an imposition or subject. Exempt tax: No tax is paid because there may be a deficiency.

Taxable Person: This refers to a natural (Physical) or legal person who must pay the tax.

Tax Residence: This is where you reside for Hacienda (taxable purposes). Hacienda is where you live; for legal entities, it is where the act of constitution is performed or where the company is registered. You can... Continue reading "Spanish Tax Systems and VAT Regulations" »

Year-End Accounting Adjustments and Profit Determination

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B. Changes in Inventories

The company must make an inventory of the stocks it has, doing a physical count of them and checking the result with the information recorded in the book balance. After verifying this data and correcting any differences, it is necessary to stabilize stock accounts; that is, to correct the accounting balance of these accounts to reflect reality.

C. Verification of Accounting Data

Before determining the result of the accounting fiscal year, the company must verify accounting data by checking, on the one hand, that there are no mistakes in arithmetic or transcription and, on the other, contrasting it with the economic reality. To do this, perform the following inventories and balances:

  • Trial Balance: Its purpose is to check
... Continue reading "Year-End Accounting Adjustments and Profit Determination" »

Study Notes: English Grammar, Writing and Economics

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Personal Description: My Friend July

July is a really good friend of mine. She is my friend from school. We're both in the same crowd and we all go out quite often.

July is short and very slim. She's got fair skin and beautiful green eyes. Charlie thinks she's quite attractive. Her hair is straight and shoulder-length. She's got a great sense of humor.

She can be a bit bossy, but I don't mind because she's such great company. She's generous and helpful, and I can always count on her to be there when I need her. In her free time, she goes out with her friends and she goes to parties. She is now studying in high school.

In my opinion, for me, she is the best person and the best friend.

Conceptos Básicos de Economía y Mercado Laboral

Las empresas... Continue reading "Study Notes: English Grammar, Writing and Economics" »

IAS 10: Events After the Balance Sheet Date - Key Accounting Standards

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International Accounting Standard No. 10

Events Occurring After the Balance Sheet Date

Objective

The objective of this Standard is to prescribe:

  1. when an entity shall adjust its financial statements for events after the balance sheet date and
  2. the disclosures that an entity should give about the date on which the financial statements were authorized for issue and about events after the balance sheet date.

The Standard also requires the entity that does not prepare its financial statements under the assumption of going concern, if the events after the balance sheet date indicate that this hypothesis of continuity is not appropriate.

Scope

This Standard is applicable in the accounting and disclosures related to events after the balance sheet date.

The events

... Continue reading "IAS 10: Events After the Balance Sheet Date - Key Accounting Standards" »

Understanding Statistical Concepts and Variables

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Statistical Concepts

Population

A population is the set of all elements that are subjected to a statistical study.

Individual

An individual or statistical unit is each of the elements of the population.

Sample

A sample is a representative subset of the reference population; the number of individuals in a sample is less than that of the population.

Sampling

Sampling is the collection of data to be studied, obtained from a small proportion that is representative of the population.

Value

A value is each of the different results that can be obtained in a statistical study. For example, if you toss a coin 5 times, you get two values: heads and tails.

Data

Data refers to each of the values obtained by performing a statistical study. If you toss a coin 5 times,

... Continue reading "Understanding Statistical Concepts and Variables" »