# A basis for the non-crossing partition lattice top homology by Zoque E.

By Zoque E.

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B the tents? One morning a farmer notices that her hens, Gertrude, Gladys and Henrietta, have laid eggs in the ratio 2 : 3 : 4. a What fraction of the eggs did Gertrude lay? b What fraction of the eggs did Gladys lay? c How many more eggs did Henrietta lay than Gertrude? The recipe for a pudding is 125 g of sugar, 150 g of flour, 100 g of margarine and 175 g of fruit. What fraction of the pudding is each ingredient? Dividing amounts into given ratios To divide an amount into portions according to a given ratio, you first change the whole numbers in the ratio into fractions with the same common denominator.

How much did Kevin and John make last year? Gwen is making a drink from lemonade, orange and ginger in the ratio 40 : 9 : 1. 5 litres of orange, how much of the other two ingredients does she need to make the drink? When I harvested my apples I found some had been eaten by wasps, some were just rotten and some were good ones. These were in the ratio 6 : 5 : 25. Eighteen of my apples had been eaten by wasps. 50 a What percentage of my apples were just rotten? b How many good apples did I get? 2 09:34 Page 51 Speed, time and distance In this section you will learn how to: ● recognise the relationship between speed, distance and time ● calculate average speed from distance and time ● calculate distance travelled from the speed and the time ● calculate the time taken on a journey from the speed and the distance Key words distance speed time The relationship between speed, time and distance can be expressed in three ways: Speed = Distance Time Distance = Speed × Time Time = Distance Speed When we refer to speed, we usually mean average speed, as it is unusual to maintain one exact speed for the whole of a journey.

How much do they pay for the tumble dryer? Leila’s savings account earns 10% per year compound interest. Work out the value of –35 – –38 a She invests £1500 in the savings account. How much will she have in her account after 2 years? On Friday James drinks 1–34 pints of fruit punch. On Saturday he drinks 2–13 pints of fruit punch. Work out the total amount of punch that James drinks on Friday and Saturday. b Lewis has the same kind of account as his sister. After earning interest for one year, he has £858 in his account.