The probabilities described in Section 2.3 and Section 2.4 related to the outcomes of a single process, such as repeatedly tossing one coin. Now suppose you were to toss three separate coins simultaneously. What is the prob
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Scientists are always trying to get better and more reliable data. One way of getting a more precise measurement might be to switch to an instrument with a more finely divided scale. Figure 4 shows parts of two thermometers placed side by side to record the air temperature in a room.

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## Exercise 29

In this exercise, take

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You are now going to use the four operation keys (on the bottom right-hand side of the TI-84 keyboard): , Author(s): The Open University

## Example 3

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Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood.

## Activity 1 Carl Jung's school days

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## SAQ 25

Find the distance between the numbers 2 âˆ’ i and 1Â +Â 3i.

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In this section we have seen that the complex number system is the set RÂ Ã—Â R together with the operationsÂ +Â andÂ Ã—Â defined by

From this, one can justify the performance of ordinary algebraic operations on expressions of the form aÂ +Â ib
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Scientific notation can be very useful when estimating the answers to calculations involving very large and/or small decimal numbers.

## Example 9

A lottery winner won Â£7851 000. He put the money straight into a deposit account which earns 7.5% interest per annum (i.e. each year). If he wanted to
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1 The new home owners from Example 4 above want to price grass seed, as well as the turf (transport only). The best buy seems to be loose seed, which says â€˜1 kilo covers 80 m2â€™. They wonder what length the side of an 80 m2
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1 Without using your calculator, find the following:

• (a) 102

• (b) 1002

• (c) 0.12

• (d) 0.012

• (e)
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1 Evaluate the following:

• (a) 62

• (b) 0.52

• (c) 1.52

## Answer<Author(s): The Open UniversityLicense informationRelated contentExcept for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Up to now only those points with positive or zero coordinates have been considered. But the system can be made to cope with points involving negative coordinates, such as (âˆ’2, 3) or (âˆ’2, âˆ’3). Just as a number line can be extended to deal with negative numbers, the x-axis and y-axis can be extended to deal with negative coordinates.

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1 The frequency diagram below shows the numbers of people in different age groups in a sample of the UK population.

• (a) What is the width of each age group?

• (b) Which age group conta
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This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.

This unit is an adapted extract from the course Mathematical methods and models (MST209
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## Exercise 1

A vector a has magnitude |a|Â =Â 7 and direction Î¸Â =Â âˆ’70Â°. Calculate the component form of a, giving the components correct to two decimal places.

<
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After studying this unit you should:

• be able to perform basic algebraic manipulation with complex numbers;

• understand the geometric interpretation of complex numbers;

• know methods of finding the nth roots of complex numbers and the solutions of simple polynomial equations.

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This unit is an adapted extract from the Open University course Complex analysis (M337)

This unit is devoted solely to complex numbers.

In Section 1, we define complex numbers and show you how to manipulate them, stressing the similarities with the manipulation of real numbers.

Section 2 is devoted to the geometric representation of complex numbers. You will find that
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Journals and articles written by academics or experts are an excellent source of information. Journals are usually published monthly or quarterly, and contain a selection of articles providing details of recent research. Often they will also contain reviews of relevant books. They are usually published more quickly than books, and so are often more up to date.

To access content of journals, most publishers require a subscription. There are, however, some journals which you can freely ac
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Keywords are significant words which define the subject you are looking for. The importance of keywords is illustrated by the fact that there is a whole industry around providing advice to companies on how to select keywords for their websites that are likely to make it to the top of results lists generated by search engines. We often choose keywords as part of an iterative process; usually if we don't hit on the right search terms straight off, most of us tweak them as we go along based on t
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