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

Quantitative Variables

1. Discrete: values of x have "gaps" between them (ex: test scores)

2. Continuous: no gaps between x values

Random Variable X

Assigns a number to outcomes of an experiment

Probability Distribution of a Discrete X

A table, graph, or forumla that shows the values of X and P(X) where:

Expected Value of Discrete X

1. The probability distribution of x represents a population (μ,σ^2,σ)

2. Mean of X = expected value of X

(1) Discrete in General

Variance of Discrete X

Standard Deviation of Discrete X

Ex:

(2) Binomial X

• Need n, P and q
• x = # of successes in n
• P(X) use binomial tables (if n < 5) or="" the="">

• mean --> μ = nP   variance --> σ^2 = nPq   standard deviation --> σ = √nPq
• NOTE: Formula gives

Investment Project Cash Flow Analysis

Southgate Inc. has identified an investment project with the following cash flows:

Present Value Calculations

a) If the discount rate is 8 percent, what is the total present value?
PV at 8% = $2,500/1.08 + $1,000/1.08² + $2,000/1.08³ + $3,000/1.08⁴ = $6,964.91

b) If the discount rate is 10 percent, what is the total present value?
PV at 10% = $2,500/1.10 + $1,000/1.10² + $2,000/1.10³ + $3,000/1.10⁴ = $6,650.84

c) If the discount rate is 9 percent, what is the total present value?
PV at 9% = $2,500/1.09 + $1,000/1.09² + $2,000/1.09³ + $3,000/1.09⁴ = $6,804.90

Financial Statements and Long-Term Planning

Given: Profit margin = 8.2%; Capital intensity ratio = 0.65; Debt-equity

Inheritance Tax Base Reductions

We highlight three primary types of base reductions:

Kinship-Based Reductions

The amount of reduction varies depending on the heir's kinship group. There are four standard groups:

• Group I: Descendants under 21 years old.
• Group II: Descendants aged 21 and older, ascendants, and the spouse.
• Group III: Second and third-degree collateral relatives by affinity.
• Group IV: Fourth-degree or more distant collateral relatives, and strangers.

Life Insurance Reductions

If the beneficiary is a spouse, ascendant, or descendant, a 100% reduction applies, up to a maximum limit.

Primary Residence Reductions

If the heir is a spouse, descendant, or ascendant and inherits the primary residence, a 95% reduction applies, up to a specific ceiling.... Continue reading "Understanding Inheritance Tax: Reductions, Rates, and Coefficients" »

The Financial Statement Audit Process

Financial statements represent several key assertions regarding the entity's financial position. These assertions ensure the reliability of the reported data:

• Existence and Occurrence: Reported assets and liabilities exist, and recorded transactions occurred during the particular accounting period.
• Completeness: The financial statements present all transactions and accounts.
• Rights and Obligations: Listed assets represent the enterprise's rights, and reported liabilities show the business's obligations.
• Valuation and Allocation: Financial statements record the enterprise's assets, liabilities, revenues, and expenses at appropriate amounts.
• Presentation and Disclosure: Proper classification, description, and disclosure

Fundamentals of Banking and Financial Instruments

Current Accounts: Features, Rights, and Duties

18. What is the attractive feature of a current account?

Answer: Operational agility and comfort, as collections and payments can be made by delivery of checks, substituting the use of cash.

19. Indicate two rights and two duties of the current account holder.

Answer:

• Rights:
  1. Dispose of the account balance.
  2. Realize transfers, payment orders, and payments.
• Duties:
  1. Do not issue operations that result in an overdraft.
  2. Communicate address changes to the bank.

Understanding Checks (Cheques)

20. If the amount written in numbers on a check does not match the amount written in characters, which one prevails?

Answer: The amount written in characters (the letter written)... Continue reading "Banking Fundamentals: Accounts, Checks, and Deposit Regulations" »

Points of Polar Coordinates

In the Cartesian plane, a point is located using its distances to the two axes x and y. Another way to represent a point is by specifying the distance from that point to a fixed point and the angle formed between the segment that joins the two points and a fixed line. The fixed point is called the pole and the fixed line is known as the polar axis. This point is represented as , known as a polar coordinate.

In the figure above, r represents the distance between the pole and point P. Angle is considered positive when measured counterclockwise and negative when measured clockwise.

Relation Between Rectangular and Polar Coordinates

If the polar plane is placed over a Cartesian plane so that the pole coincides with the... Continue reading "Polar and Rectangular Coordinates: Conversion and Distance Formulas" »

Measuring Instruments: Definition and Features

A measuring instrument is a device designed to be used to make measurements, either alone or in conjunction with ancillary equipment.

For proper use, the key features of a measuring instrument to be aware of are:

1. Graduated System

   This system will have its divisions. If the tenth division is a number, it indicates the metric system, where each division is 1 mm. Otherwise, it is the English system.

   Figure 1.2: Metric Ruler

2. Range

   The range of a measuring instrument is the field between the minimum and maximum values that can be measured.

   Figure 1.4: Range of a Ruler and a Micrometer

3. Degree of Accuracy or Reading

   This refers to the value of the minimum, exact subdivision that can be read on the instrument.

   Figure

Knowledge Concepts

Knowledge: How human beings interpret themselves and the world around them. This knowledge comes from experiences, the experience of being human.

Common Sense: It is the knowledge of day-to-day experience of life. It involves imprecise language, has certain sources, and lacks critical sense.

Scientific Knowledge: This possesses a well-developed critical sense. It is designed to discover, understand, and explain the world, and to solve problems definitively.

Research Methods

Methods:

• Induction: Observing the reality of facts and deriving general rules from them.
• Deductive: Starting from a general, generic situation to reach a particular conclusion (transforming complex ideas into simple and known ones).
• Intuition: Using thought and

Quality Control and Creative Graphic Techniques

Formats of Data Collection

• Array Type: A spreadsheet type of data collection. A data array allows us to have a relationship of orderly frequency for a specific data type.
• Concentration Diagram: This is another type of data collection template, which can be very useful when trying to see the most frequent location of any defect or failure.
• Counting or Sorting Data Template: Used for collecting data with the purpose of seeing how they are distributed and how many are in each class.

Graphic Techniques of Quality Management

• Management Graphics: Control charts that display the behavior of different processes.
• Line Charts: Allows us to represent the behavior and evolution over time of a feature, one or more

Description: An Explanation of an Observation

Measurement: A Way to Describe the World with Numbers

Estimation: Using Knowledge of Something Familiar to Guess the Size of a New Object

Precision: How Close Measurements Are to Each Other

Accuracy: Comparing the Measurement to the Actual, Accepted, or Real Value

S.I.: International System of Units

Meter: The S.I. Unit of Length

Volume: The Amount of Space an Object Occupies

Mass: The Amount of Matter in an Object (S.I. Uses Kilogram)

Kilogram: S.I. Unit for Mass

Weight: The Measurement for Force (S.I. Uses the Newton)

Kelvin: The SI Measurement of Temperature (Same as C but Starts at -273 C)

Rate: The Amount of Change in a Measurement in a Given Amount of Time

Table: Displays Information in a Row or Columns