THEOREM OBJECTIVES Recognize patterns in binomial expansions. Evaluate a binomial coefficient. Expand a binomial raised to a power. Find a particular term in a binomial expansion Understand the principle of mathematical induction. Prove statements using mathematical induction. Definition: BINOMIAL THEOREM Patterns in Binomial Expansions A number of patterns‚ as follows‚ begin to appear when we write the binomial expansion of a b n‚ where n is a positive integer. a
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1. Positioning- Positioning is the act of designing the company’s offering and image to occupy a distinctive place in the minds of the target market. The goal is to locate the brand in the minds of consumers to maximize the potential benefit to the firm. The result of positioning is the successful creation of a customer focussed value proposition. Examples- a) Mahindra & Mahindra positioned their SUV Scorpio to life style oriented consumers. b) Indica by Tata Motors for small car consumers
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Territorial Expansion Between 1800 and 1850‚ the United States was a nation extending in all possible ways. America experienced a amount change in national unity. Territorial expansion destroyed national unity. Between 1819 and 1824 is when the unified nation of America began to divide and depart from one another. Triggered by the concept of Manifest Destiny‚ people believed that America should extend from “sea to shining sea”. It was the issues of the expansion of slavery into the new territories
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desire to expand from the Atlantic to the Pacific Coast. This migration west benefited America in many ways. Through unity and technological advancements‚ westward expansion led to America’s success‚ thereby justifying that enterprise. A countless amount of people were brought together as one during and after the westward expansion of North America. Those who were involved in this treated it as a community project in which the U.S unites itself to work as a whole. For example‚ families and
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westward expansion was the key to the nation’s health: He believed that a republic depended on an independent‚ virtuous citizenry for its survival‚ and that independence and virtue went hand in hand with land ownership‚ especially the ownership of small farms. (“Those who labor in the earth‚” he wrote‚ “are the chosen people of God.”) In order to provide enough land to sustain this ideal population of virtuous yeomen‚ the United States would have to continue to expand.The westward expansion of the
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The United States serves as a giant puzzle. From coast to coast‚ each region of land is slowly being put together. This is very similar to westward expansion. From 1801 to1844‚ westward expansion spread rapidly and America experienced a serious change in national unity. During this period territorial expansion had a very large impact and overall brought Americans together. During the early 1800’s (1800-1823) the Louisiana Purchase and Treaty of 1818 increased national unity. The Louisiana Purchase
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What are the five steps required for effective product positioning? 1. Select key criteria that effectively differentiate products or services in the industry. 2. Diagram a two-dimensional product-positioning map with specified criteria on each axis. 3. Plot major competitors ’ products or services in the resultant four-quadrant matrix. 4. Identify areas in the positioning map where the company ’s products or services could be most competitive in the given target market. Look for
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COLONIAL EXPANSIONS AND RIVALRIES What is it? Colonialism expansion is where countries (such as Britain‚ France‚ Germany and Russia) settle on new land. They do this to expand their territories‚ and to use their resources for to benefit their empire. Rivalries between the empires are consequential. This is because many empires are involved in conflicts when attempting to regain new land. How did it contribute to the start of World War I? Imperialism was one of the causes of World War I.
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Principles of Marketing TARGET MARKETING: Market Segmentation‚ Targeting and Positioning Introduction 1. To succeed in today’s competitive marketplace‚ companies must be customer-centered‚ wining customers from competitors and keeping them by delivering greater value. a. Sound marketing requires a careful‚ deliberate analysis of consumers. b. Since companies cannot satisfy all consumers in a given market‚ they must divide up the total market (market segmentation)‚ choose the best
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Research Proposal # 1 Name of The Research Proposal: Brand Positioning & Repositioning Brand Positioning In marketing‚ Positioning has come to mean the process by which marketers try to create an image or identity in the minds of their target market for its product‚ brand‚ or organization. Generally‚ the Brand positioning process involves: 1. Defining the market in which the product or brand will compete (who the relevant buyers are) 2. Identifying the attributes
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