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sample of soil were prepared with varying amount of inorganic phosphorus. corn plant grown ineach soil were harvested after 8 days and analysed fir phosphorous contents. the objective was to see to what extent additional phosphorous in the soil increased the concentration of phosphorous in the plants. the data for 8 samples are as follows



Inorganic soil phosphorous (PPM) 1,4, 5, 9, 13, 11, 23. 23



Organic soil phosphorous (PPM) 64, 71, 54, 81, 93, 76, 77, 95

If a > 1, and  a | b , then 3b+1  mod a  =


The ratio of grey ties to black ties on display is 5 to 2. Use the ratio table to determine how many black ties will be on display if there are 35 gray ties



Ryan buys some jumpers to sell on a stall.

He spends £160 buying 60 jumpers.

He sells 80% of the jumpers for £12 each.

He then puts the rest of the jumpers on a Buy one get one half price offer.

He manages to sell half the remaining jumpers using this offer.

How much profit does Ryan make?


Three persons enter into car, where there are 5 seats. In how many ways can


they take up their seats?

There are four roads from city X to Y and five roads from city Y to Z, find


(i) how many ways is it possible to travel from city X to city Z via city Y.


(ii) how different round trip routes are there from city X to Y to Z to Y and back


to X.

Teams A and B play in a tournament. The first team to win three games wins the


tournament. Find the number n of possible ways the tournament can occur.

Mark and Erik are to play a tennis tournament. The first person to win two



games in a row or who wins a total of three games wins the tournament. Find



the number of ways the tournament can occur.

Two Balls are to be selected without replacement from a bag that contains one


red, one blue, one green and one orange ball. A) Use the counting principle to


determine the number of possible points in the sample space. Construct a tree


diagram and list the sample space.

Construct a tree diagram and list the sample space. find the number of possible


outcomes of these two “experiments” done in this specific order:


Experiment 1: a coin is tossed and the side that is face up is recorded


Experiment 2: a die is rolled and the number that is face up is recorded


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