1.3.1 Who is affected by cardiovascular diseases?

Cardiovascular diseases are the main cause of premature death (before the age of 75) in the UK, across Europe and the USA â€“ indeed, across many parts of the world (Figures 3 and Author(s):

According to Equation 1, probability is defined as a fraction. However a fraction such as may also be expressed as a decimal number or as a percentage:

Â

You may have met complex numbers before, but not had experience in manipulating them. This course gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The course includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.

This OpenLearn course provides a sample of Level 3 study in Author(s):

Numbers

This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property. First published on Wed, 2

This course is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the *boxplot*. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. The other topic, is that of dealing with data presented in tabular form. You are, no doubt, familiar with such tables: they are common in the media and in reports an

This course is concerned with a special class of topological spaces called *surfaces*. Common examples of surfaces are the sphere and the cylinder; less common, though probably still familiar, are the torus and the MÃ¶bius band. Other surfaces, such as the projective plane and the Klein bottle, may be unfamiliar, but they crop up in many places in mathematics. Our aim is to *classify* surfaces â€“ that is, to produce criteria that allow us to determine whether two given surfaces are

Having discussed *n*th roots, we are now in a position to define the expression *a*^{x}, where *a* is positive and *x* is a rational power (or exponent).

## Definition

If *a*Â >Â 0, *m* Author(s):

This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognize mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the *Calculator Book*, *Tapping into Mathematics With the TI-83 Graphics Calculator*. The unit ends by asking you to reflect on the process of studying mathematics.

**In order to complete this unit you will need**

**All written material contained within this unit originated at the Open University.**

**Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence**

**1. Join the 200,000 students currently studyi**

**1** Use the method outlined in Example 9 to estimate each of the following, and then use yo

**1** Find the following powers by hand, as estimates for calculator work.

**(a) 10**^{7}**(b) 10**^{8}**(c) 3**^{4}**(d) (**^{âˆ’}2)^{2Author(s): The Open University}

**Here is a tale based on an ancient Eastern legend, which gives an idea of the impact of raising a number to a power.**

**Example 6**

**A long time ago there lived a very rich king whose son's life was saved by a poor old beggar woman. The king was naturally very grateful to the woman, so he offered to **

**Given any number, you now know how to find its square. But, given the squared number, how do you find the original number?**

**Example 3**

**If the gardener in Author(s): **

**By the end of this unit you should be able to:**

**evaluate the squares, cubes and other powers of positive and negative numbers with or without your calculator;****estimate square roots and calculate them using your calculator;****describe the power notation for expressing numbers;****use your calculator to find powers of numbers;****multiply and divide powers of the same number;****understand and apply negative powers, t**

**The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Once you have completed the workbook and exercises return to this page and watch the video below, â€˜The arch never sleepsâ€™, which discusses a practical application of some of the ideas in workbook.**

**Click 'View document' to open the workbook (PDF, 0.8 **

**2.2.2 Environmental economics and green consumerism **

**In economic terms, green consumerism is typically expressed using measures based on the willingness to pay (WTP) principle. As mentioned above, this takes two main forms: eco-taxation, in which environmental costs are estimated and added to the price of commodities (e.g. vehicles with high carbon emissions); and eco-labelling, in which products are labelled with relevant environmental information, such as is now required by the food industry and governments in many industrialised count**

**Evidence suggests that global temperature is beginning to rise. There are several factors that could cause this. Only one is affected by human activity.**

**Click on 'View document' to view a chart showing the rates of energy gain and loss by the Earth's surface and atmosphere **

**5.1 Pollution and loss of biodiversity **

**Unfortunately, halting the disappearance of species cannot be achieved simply by measures such as putting fences around special habitats and asking people not to pick the flowers or disturb the breeding birds. Many species are vanishing because of pollution. You probably have a good understanding of the meaning of this term, but it is variously defined. The Open University has a course on environmental control and public health, in which pollution is defined as the introduction into th**

**I would like to turn now to the possible consequences of our use of energy for global climate change. Our pattern of energy use relies heavily on burning carbon-based fossil fuels, releasing carbon dioxide which spreads evenly around the globe and builds up slowly in the atmosphere. Carbon dioxide is a greenhouse gas, which means that it has the potential both to warm the atmosphere and to change our global climate. It is not the only greenhouse gas but is the most important of those e**

**2.1 Environment and technology **

**A central concern of environmental studies is the relationship between technology and our environment: how people use technology to transform materials into forms which can meet our needs and wants. In the process of doing this we inevitably change the environment which provides these materials but which also supports all life.**

**A few moments ago I went to my fridge and took some milk out to add to a cup of coffee. I used this common example of a modern domestic appliance without a secon**

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