Venn diagrams (1)
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This document defines and explains Venn diagrams and basic set operations including union, intersection, difference, symmetric difference, and complement. Venn diagrams use circles within a rectangle to visually represent sets and their relationships. The key operations are defined as the union being elements in A or B, intersection being elements in both A and B, difference being elements in A but not B, and symmetric difference being the exclusive elements of A and B.
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The document discusses key concepts in mathematics of finance including time value of money, compounding, and discounting. It explains that compound interest is calculated based on accumulated sums while simple interest is fixed. Various compound interest formulas are provided for different compounding periods such as annually, semiannually, quarterly, and monthly. Methods for calculating depreciation including fixed installment and diminishing balance are also summarized. Worked examples of simple interest calculations are listed.
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This document defines and describes several key concepts in set theory:
1. A set is a collection of well-defined objects that can be clearly distinguished from one another. Examples of sets include the set of natural numbers from 1 to 50.
2. Sets can be described using either the roster method, which lists the elements within curly brackets, or the set-builder method, which defines a property for the elements.
3. Types of sets include the empty set, singleton sets containing one element, finite sets that can be counted, infinite sets that cannot be counted, equivalent sets with the same number of elements, and subsets where all elements of one set are contained within another set.
Functions
The document defines what a function is as a relationship between two variables where each value of one variable corresponds to a unique value of the other. It provides examples of functions like supply and price or time and distance. It defines the domain as the set of inputs and range as the set of outputs. The document then discusses operations that can be performed on real-valued functions, including addition, subtraction, multiplication by a scalar, multiplication of two functions, and taking the quotient of two functions.
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The document defines and discusses various aspects of annuities. It defines an annuity as a fixed sum paid at regular intervals under certain conditions. It discusses the amount of an annuity as the total of unpaid installments plus compound interest. It also defines the annuitator as the person obliged to make payments, and the annuitant as the person entitled to receive payments. The document then discusses different types of annuities based on continuity and timing of payments. It provides characteristics of annuities and formulas used to calculate future amounts, accumulated amounts, and present values of annuities.
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This document defines and explains various types of annuities. It begins by defining an annuity as a fixed sum paid at regular intervals under certain conditions. It then discusses the amount of an annuity and defines relevant terms like annuitator and annuitant. The document goes on to explain different types of annuities based on continuity and payment timing, including annuity certain, annuity contingent, annuity perpetual, and others. It also provides formulas for calculating future amounts, accumulated amounts, and present values for different annuity types.
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The document discusses 5 concepts that guide marketing efforts: production, product, selling, marketing, and societal marketing. The production concept focuses on efficiency and availability, while the product concept emphasizes product improvements. The selling concept relies on promotion to drive sales. The marketing concept prioritizes customer needs and satisfaction over short-term sales. Finally, the societal marketing concept considers customer and societal well-being, not just wants. It questions if satisfying immediate wants benefits consumers and society long-term.
Introduction to marketing
This document provides an overview of key marketing concepts:
1. It defines marketing as satisfying customer needs through exchange and creating value.
2. It discusses how human needs give rise to wants and demands as they are shaped by culture. Products and services satisfy needs and wants.
3. Customer value, satisfaction, and quality are determined by a product's perceived performance relative to expectations. Satisfied customers purchase repeatedly and recommend the product.
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Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
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Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
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Venn diagrams (1)
- 2. Swiss mathematician Euler and British mathematician John-Venn gave idea of representing set through pictures. The diagrams drawn to represent sets are called Venn-Euler diagrams or simply Venn diagrams. In Venn diagrams the universal set U is represented by points within a rectangle and its subsets are represented by points closed (usually circles) within the rectangle .
- 3. Operation on Sets Union of Sets: Let A and B be two sets. The union of A and B is the set of all those elements which belong to A or to B or to both A and B. Thus AUB={x:x⊂A or x⊂B} Clearly x∈AUB⟺x∈A or x∈B And x∉AUB⟺x∉A or x∉ B. ⊂ ⊂⊂⊂⇒⇒
- 4. Intersection of Sets: Let A and B be two sets. The intersection of A and B is the set of all those elements that belong to both A and B The intersection of A and B is denoted by A⋂B A⋂B = {x:x∈A and x∈B} Clearly, x∈A⋂B⟺x∈A and x∈B. Disjoint Sets: Two sets A and B are said to be disjoint if A⋂B=Ø
- 5. Difference of Sets: Let A and B be two set. The difference of A and B, written as A-B, is the set of all those elements of A which do not belong to B. Thus A-B={x:x∈A and x∉B} Similarly the difference B-A is the set of all those elements of B that do not belong to A
- 6. Symmetric Difference of two sets: Let A and B be two sets. The symmetric difference of sets A and B is the set (A-B)U(B-A) and is denoted by A∆B. Thus A∆B=(A-B)U(B-A)={x:x∉A⋂B} Complement of a Set: Let U be the universal set and let A be a set such that A⊂U. Then, the complement of A with respect to U is denoted by Ac or A’ or U-A and is defined as the set of all those elements of U which are not in A
- 7. Thank You