2.3 What is a ‘business’? The vast majority of companies are, indeed, set up and run with ‘commercial objects’ – in other words, they are business enterprises, or ‘undertakings’, set up to trade and make a profit. It is principally in the context of the company as a form of business organisation (or ‘business medium’) that we will be studying it. So, before we start to look in detail at what companies are, it is a good idea to have a grasp of what companies do, which will lead us on to consider why they
6.2 The supremacy of EU law Whenever there is a conflict between the provisions of EU law and the provisions of the domestic (national) law of a member state, then EU law will prevail. This is a principle which was developed by the ECJ as the relationship between domestic and EU law is not clarified by treaty provisions. This is an important principle, as it ensures the proper functioning of the EU. If an EU member state had the power to annul EU law by adopting new domestic (national) law which was in conflict with the
4.5 The European Parliament The European Parliament fulfils three main functions: it shares the power to legislate it exercises democratic supervision over all EC institutions it shares authority over the EC budget. The legislative and supervisory roles are based on the European Parliament's democratic legitimacy. Its members are directly elected every five years by the citizens of the EU member states. 4.4 The Council of the European Union The Council represents the interests of the individual member states and is seen as the legislative arm of the EU. It is composed of active representatives of the governments of the member states. Usually, these representatives are the departmental or junior ministers responsible for the matters under consideration at a specific Council meeting. This means that the Council itself, unlike the Commission, has no stable membership. Its membership varies depending upon the issues tabled for discu 4.2 The European Council The European Council brings together heads of state and government in order to decide on issues of common interest and overall EU policy and to review progress. In principle the European Council must meet at least twice a year but usually meets four times a year. The meetings are known as Summits. The European Council is the highest level policy-making body of the EU: The European Council shall provide the Union with t 4.1 Overview The institutions of the EU work towards objectives related to the three pillars and the creation of a body of Community law that applies uniformly in all member states. The institutions having legal rule-making powers include the European Council, the Council of the European Union, the European Parliament and the European Commission. Finally, there is the European Court of Justice (ECJ), which has the power to settle lega 2.4 The European Court of Human Rights Common law and the court hierarchy, statutory interpretation and judicial precedent are all peculiar to the domestic English law. The European Court of Human Rights operates in a different way. The rights in the European Convention on Human Rights are stated in general terms and are interpreted according to international legal principles. For example, Article 31(1) of the Vienna Convention on the Law of Treaties states: 2.2 The Convention itself The ECHR is essentially a charter of rights. Any charter of rights represents a consensus, a negotiated agreement between the drafters. Every state intending to adopt a charter will have its own vision and aims, and the drafters have to find a way of accommodating these visions and aims. This often results in the creation of provisions that are a compromise and are drafted in the widest possible terms. The ECHR is drafted in such a way. It is a vaguely worded aspirational charter inten 2.1 History The Council of Europe was set up in 1949. It is an intergovernmental organisation (based in Strasbourg, France) set up to protect human rights, promote cultural diversity and to combat social problems such as intolerance. Its creation was seen as a way of achieving a European approach to the protection of certain individual rights. Although presented now as historical events, the horrors of what had taken place in the Second World War were then fresh in the minds of the governments and Introduction to algebra Modelling and estimation Introduction to the calculus of variations 3.21 Division rules Lastly consider division. Dividing 8 by 2 means ‘How many times does 2 go into 8?’ or ‘What must you multiply 2 by to get 8?’. The answer is 4. So to find 8 ÷ −2, you need to ask ‘What do I have to multiply −2 by to get 8?’. The answer is −4, since −2 × −4 = 8. So 8 ÷ −2 = −4. Similarly, to find −8 ÷ −2 you need to ask ‘what do I have to mul 3.20 Multiplication rules The rules for multiplying positive and negative numbers can be illustrated by the table below. Multiplying a positive number by a positive number gives a positive answer. Multiplying a negative number by a positive number gives a negative answer. Multi 3.19 Multiplication with negative numbers Now that you have rules for addition and subtraction of negative numbers, think about multiplication and division. Describe each of the following in terms of the number line and the value of Thomas's piggy bank: (a) the mul 3.15.1 Subtraction on the number line Now what about subtraction? You can think of subtraction as undoing addition: adding 3 to 8 gets you 11, and so subtracting 3 from the answer, 11, gets you back to 8. Therefore, in terms of the number line, subtracting 3 from 11 means starting at 11 and moving 3 units to the left. 3.13.1 Try some yourself Evaluate each of the following. 3.13 More division with fractions How about other fractions? What is 6 ÷ 3.5.1 Try some yourself Carry out the following calculations, without your calculator. (a) 3 × (60 + 70). (b) (3 × 60) + 70. (c) (70 − 60) ÷ 5. 3.4.1 Try some yourself Look at the rules in the boxes above. Write in your own words the rules for multiplying and dividing, adding and subtracting two numbers, giving an example of each.
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This free course is an introduction to algebra which builds on the idea of using letters to represent numbers. Section 1 looks at finding, simplifying and using formulas and includes useful tips on learning algebra. Section 2 introduces some of the terminology used in algebra and techniques such as evaluating and checking equivalence of expressions, identifying terms in an expression and collecting like terms. Section 3 looks at how to simplify terms and introduces index notation and multiplying
This free course is concerned with modelling and estimation and looks in particular at the binomial distribution. Section 1 starts by defining probability, introduces relevant notation and briefly discusses basic properties of probabilities. The section concludes by considering some of the general features of and ideas about modelling discrete random variables. Section 2 looks at one particular probability model for discrete data, the binomial distribution. Section 3 investigates how data can be
This free course concerns the calculus of variations. Section 1 introduces some key ingredients by solving a seemingly simple problem – finding the shortest distance between two points in a plane. The section also introduces the notions of a functional and of a stationary path. Section 2 describes basic problems that can be formulated in terms of functionals. Section 3 looks at partial and total derivatives. Section 4 contains a derivation of the Euler-Lagrange equation. In Section 5 the Euler
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