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

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Understanding Corporate Bond Structures and Classifications

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Repayment: Long-term debt is typically repaid in regular amounts over the life of the debt. The payment of long-term debt by installments is called ​amortization(usually arranged by a sinking fund. Each year the corporation places money into a sinking fund, and the money is used to buy back the bonds).
Seniority: indicates preference in position over other lenders. Some debt is​subordinated.​In the event of default, holders of subordinated debt must give preference other specified creditors who are paid first.
Security​: it’s a form of attachment to property. It provides that the property can be sold in event of default to satisfy the debt for which the security is given. A mortgage is used for security in tangible property. Debentures

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Understanding Simple Random Sampling in Statistics

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Simple Random Sample

A sample designed in such a way as to ensure that (1) every member of a population has an equal chance of being included in the sample, and (2) every sample of size n has the same chance of occurring.

Selecting Elements

Subjects are selected at fixed sampling intervals by selecting every kth element thereafter. The interval between selections is determined by the ratio of the population size to the sample size (N/n). For example, if the population size is N=1,000 and a sample size of n=100 is desired, then the sampling interval is 1,000/100 = 10, so every 10th person is selected into the sample.

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Key Events in 19th Century Spain: Absolutism, Liberalism, and Democracy

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Different stages of Spain in the XIX

C) absolutism, liberalism, and democracy

Fernando VII accepted the Cortes de Cadiz

Falso

Who was Mariana Pineda?

B) A liberal fighter against absolutism

When did the War of Independence finish?

A) 1814

Why could Isabel II not govern in the first place?

B) Salic law

Who governed while Isabel II was a minor?

C) Both

Characteristics of moderates

Falso

The expropriations of Mendizabal

C) Broke large states belonging to the church and sold them to the wealthy bourgeoisie

In 1874 there was a coup d'état and Spain had again a king of the Bourbon dynasty, that was...

C) Alfonso XII

After the Convention of Vergara...

A and C are correct

Provisional government (1868-1870)

B) Amadeo of Savoy

Hidalgo, Bolivar, and San Martin led....

B) The
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Understanding Functions and Matrices in Mathematics

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1. f : A → R means that the codomain of f is A and its domain is R.

FALSE: Domain is A; codomain is R

2. Points of form (x, f(x)), x ∈ A, belong to the graph of function f : B → A, where A ̸= B are non-empty subsets of R.

3. A function f defined on R is called strictly increasing if f(x1) > f(x2) holds, whenever x1> x2.

FALSE: A function, is strictly increasing if f(x0) < f(x1) whenever x0 < x1.

4. The derivative fʹ(a) of f at a is the slope of the tangent line to the graph of f at (a,f(a)).

TRUE: y = f (x) at a point x = c on the curve if the line passes through the point (c, f (c)) on the curve and has slope f '(c) where f ' is the derivative of f.

5. If fʹ(a) ≥ 0, then f is strictly increasing in a neighbourhood of a.

FALSE:

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Global Packaging Aesthetics and Product Innovation

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Packaging Aesthetics and Local Preferences

Packaging aesthetics are particularly important to the Japanese. Packaging is an important consideration for products that are Japanese prefer plain soft colors on their packages. People have local tastes based on their perceptions and attitudes about a products.

Product Innovation and Branding

Prior to 2004, Nokia launched different cell phone product-communication adaptation. Procter & Gamble recently introduced Pampers Rash Guard, a continuous innovation. Product problems initially policymakers in many parts of the world supported Suzlon. Regulators in different countries have proposed various the use of terms "light" and "natural" are allowed on labels only in the United States. Scotland is a... Continue reading "Global Packaging Aesthetics and Product Innovation" »

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Key Concepts and Definitions in Statistics

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Key Concepts and Definitions in Statistics

Statistics - The science of collecting, organizing, analyzing, and interpreting data for the purpose of making more effective decisions.

Levels of Measurement - Nominal, ordinal, interval, and ratio levels of measurement.

Discrete Variables - Variables that can assume only certain values, and there are “gaps” between the values.

Inferential or Inductive Statistics - This facet of statistics deals with estimating a population parameter based on a sample statistic.

Statistic - A characteristic of a sample.

Parameter - A characteristic of a population.

Frequency Distribution - A grouping of data into classes showing the number of observations in each of the mutually exclusive and collectively exhaustive... Continue reading "Key Concepts and Definitions in Statistics" »

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Accounting Practice Problems: Assets, Liabilities, Cash Flow

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Financial Reporting & Transaction Analysis

This section presents accounting scenarios focusing on financial statement impact and transaction analysis for various companies.

Problem AP8-8A: Whiskey Industries & Holding Ltd.

Whiskey Industries Ltd. Financial Transactions

Whiskey Industries Ltd., a Nanaimo, British Columbia–based company, has a December 31 year-end. The company's comparative statement of financial position and its statement of income for the most recent fiscal year are presented here, along with some additional information:

  • During the year, Whiskey Industries sold, for $500 cash, equipment that had an original cost of $1,000 and a net carrying amount of $200.
  • Whiskey Industries borrowed an additional $8,000 by issuing notes
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Common English Mistakes and Corrections

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Grammar and Vocabulary

  1. I have lost my pen. Can I borrow yours?
  2. As soon as I have more information, I will call you.
  3. Did you know she was pregnant?
  4. We have had this can since last summer.
  5. When I lived in Hungary, I had to take a bus to go to work.
  6. Would you mind answering my questions?
  7. 80% of our electronic components are produced in the Far East.
  8. The manager and his staff usually meet once a week.
  9. What are you responsible for?
  10. When did you arrive at the hostel?
  11. The way of managing companies in this country is very different from ours.
  12. Has she answered your email yet?
  13. You will have to work hard if you really want to pass the exam.
  14. He never drinks any alcohol when he goes to parties.
  15. Have you got something to declare?
  16. The plane was four hours late.
  17. Driving too
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Math Terminology: Definitions and Examples

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Relatively Prime

When the greatest common factor of two numbers is 1

Rational Number

Any number that can be expressed as a ratio of two integers

Reciprocal

One of two numbers whose product is 1, also called multiplicative inverse

Relation

A set of ordered pairs

X Coordinate

The first number in an ordered pair; it tells the distance to move right or left from the origin (0,0)

Y Coordinate

The second number in an ordered pair; it tells the distance to move up or down from the origin (0,0)

X Axis

The horizontal axis on a coordinate plane

Y Axis

The vertical axis on a coordinate plane

Coordinate Plane

A plane formed by the intersection of a horizontal line (the x-axis) and a vertical line (the y-axis)

Vertical Line Test

A method for seeing if a graph represents a... Continue reading "Math Terminology: Definitions and Examples" »

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Understanding Analytics and Statistics: Key Concepts and Definitions

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Analytics and Statistics: Key Concepts

Analytics: the scientific process of transforming data into insight for making better decisions. Population: the set of all elements of interest in a particular study. Sample: a subset of the population. Data: the facts and figures collected, analyzed, and summarized for presentation and interpretation. Cross-sectional data: data collected at the same or approximately the same point in time. Statistics: the art and science of collecting, analyzing, presenting and interpreting data. Variable: a characteristic of interest for the elements. Data set: all the data collected in a particular study. Elements: the entities on which data are collected.

Data Summary

1. Cumulative Frequency Distribution: a tabular summary... Continue reading "Understanding Analytics and Statistics: Key Concepts and Definitions" »

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