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

Food and Nutrition

Food is the act of providing sustenance to the human body, while nutrition encompasses the physiological processes by which the body receives, transforms, and utilizes the chemical components in food.

Inherited Diseases

• Hemophilia
• Huntington's disease
• Cystic fibrosis
• Color blindness
• Phenylketonuria

Measures of Dispersion

Measures of dispersion indicate how close the data are to the average.

Vaccines

Vaccines are preparations containing killed or attenuated microorganisms. They are introduced into our bodies to produce antibodies that kill the organism, providing immunity.

Common Pathogens

Pathogens such as bacteria and fungi are the most common causes of infectious diseases.

Health and Disease

Health is a state of complete physical, mental,... Continue reading "Key Concepts in Health, Nutrition, and Statistics" »

IT Project Management and Departmental Structure

Resource Management in IT Projects

Resource management projects often involve:

• IT professionals (informaticians).
• SAP systems, often developed in Germany.
• Project integrity, focusing on achieving target costs and timelines.

Evolving Role of the IT Department

The aim is for the Information Technology (IT) department to become more self-sufficient, reducing its reliance on other functions like accounting or human resources.

Within the IT department, there are project managers, analysts, and programmers. Each functional area typically has a manager, and similarly, the IT department should also have its own manager.

IT Department as a Cost Center

While most functions within an organization generate revenue,... Continue reading "Optimizing IT Operations: Systems, Costs, and Users" »

The Colonnade of St. Peter's Basilica

A masterpiece of Baroque urban design by Gian Lorenzo Bernini.

Historical Context and Style

• Timeline: De Lany 1656–1667.
• Style: High Baroque (Distillation Baroque).
• Architect: Gian Lorenzo Bernini.
• Building System: Architrave.
• Location: Vatican City (Rome).

Architectural Elements and Structure

The colonnade supports an entablature surmounted by a balustrade and a large collection of statues. The structure is composed of four rows of Doric columns, which are more slender than usual, topped with an Ionic entablature. The 296 columns form a seemingly endless forest, wisely separating the square from the exterior without a harsh break.

The colonnade is crowned with a balustrade housing 140 statues of saints.

Spatial

Topic 11: Polyhedra and Their Geometric Shapes
Polyhedra are geometric shapes with polygonal faces. Euler's Formula: c + v = a + 2. Regular Polyhedra: When all the faces are regular, equal polygons, and moreover, each vertex converges at the same number of faces. Convex: In a convex polyhedron, none of its faces are cut. Concave: These are polyhedra in which at least one of the faces extends inward. Prism: A polyhedron with two parallel faces called bases, and the other faces are parallelograms. The classes of prisms are: straight, regular, irregular, oblique, and parallelepipeds. Area: P_b * h + P_b + apothem / 2 = A_l + 2 * A_b.

Pyramid: A pyramid is a polyhedron with a polygonal base and all other faces are triangles that converge at a point.... Continue reading "Understanding Polyhedra and Cartesian Coordinates" »

Gantt Charts and Project Status

Gantt charts are bar graphs that immediately show the status of implementation within a project, identifying any delays or advances. They attempt to represent the duration of each of the activities into which the project is divided. A drawback to their use is that they do not permit cross-connections showing directly how one activity depends on or influences another.

CPM / PERT Terminology Definitions

Activity

Each element of the project or program represented by an arc in CPM. This arc sometimes represents a time duration or a connection between two events of the graph. An activity cannot begin while the preceding event has not occurred.

Event

An event in the project or CPM that marks the beginning or end of an activity.... Continue reading "Understanding Gantt Charts and CPM/PERT Terminology" »

Exercise 01: Call Center Call Time

Suppose that the time needed for customer service calls in a telephone call center follows a Normal distribution with a mean of 8 minutes and a standard deviation of 2 minutes.

1. What is the probability that a call lasts less than five minutes?
2. What is the probability that a call lasts more than 9.5 minutes?
3. What is the probability that a call lasts between 7 and 10 minutes?
4. 75% of calls require at least how long for service?

Exercise 02: Rabbit Weight Classification

The distribution of the weights of rabbits raised on a farm may well be represented by a Normal distribution with a mean of 5 kg and a standard deviation of 0.9 kg. An abattoir buys 5000 rabbits and intends to classify them according to weight as follows:... Continue reading "Statistics Exercises: Normal Distribution" »

Core Concepts in Probability Distributions

Random Variables Defined

Random variables are those variables that assume different values as a result of a random experiment. They are classified into two main types:

• Discrete Random Variables: These support only integer values (countable outcomes).
• Continuous Random Variables: These support all types of values, including integers and fractions (measurable outcomes).

What is a Discrete Probability Distribution?

It is a theoretical frequency distribution, similar to relative frequencies. It maps the values of variables to the probability of occurrence of that value, representing what would be expected if the experiment were carried out repeatedly.

Key Discrete Probability Distributions

Binomial Distribution

Working Papers

These are the documents in which the auditor records the data and information obtained during their review, as well as the results of the tests performed.

Summary Warrant

A sample of major accounts that are an item.

Worksheet

This is the card that shows the groups or items that comprise the financial statements.

Decree of Detail

The items that comprise an account balance of a major account or any other account.

Certificates of Verification

The work performed to verify the correctness of an item or transaction.

Situations for Audit Work Plan

• Ensure that the service is clearly controlled.
• Be fully aware of what is being offered.

Conditions to Perform the Audit

• Maintain independence of mind regarding the specific client.
• Possess the ability to

Sampling Process and Principles

To ensure a sample accurately represents the population under investigation, its size and the methodology used must adhere to specific principles.

Core Sampling Concepts

Population (Universe)

The population, or universe, is defined as the complete set of elements existing within a specific space and time, all of which are affected by the same problem under study, and from which information is desired.

Sample

A sample is a representative fraction of the population. From the sample, we can infer or estimate the characteristics of the entire population.

Sampling

Sampling is the procedure for selecting a subset of elements (the sample) from a larger group (the population) in order to make inferences about the population.... Continue reading "Statistical Sampling: Core Concepts and Essential Elements" »

Balance Sheet: The second column in this column should note the value amount of each account. The third column space in this column records the total amount for each group. The fourth column in this column should write down the total amounts of the assets, liabilities, and stockholders' equity. Comparative balance sheet reporting shows that assets less liabilities equals capital employed. The first column should write down the amount of each of the accounts involved in the final. The second column is used to note the amount of each of the accounts up to the initial balance. The third column is used to assemble the alteration or difference of each account. The fourth column is used to denote the signs of plus or minus. Output states location... Continue reading "Understanding Balance Sheets and Income Statements" »