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Draw a probability tree diagram. For this question, only two branches are required (orange and orange). At the start, there are n sweets in total, 6 are orange, so p(O) = 6/n. On our second pick, there ar...

We are given that Karen got 38% in her English test, so all that's left to do is work out the percentage she achieved in her maths test and then compare it with 38%: We calculate the percentage by taking ...

Define the original cost as 100%.

So £16=85% (100-15) of the original cost.

Find 1% of the original cost by dividing both sides by 85. 

16/85=85/85%

To find the orginal cost, 1...

So we know that 3/5 teachers in the school are female, and we also know that 36 teachers are male. 

The first thing to note is that if 3/5 are female, that leaves 2/5 to be male. This is because al...

let sin(x)=u , let cos(x)=v

du/dx = cos(x),   dv/dx = -sin(x)

d[sin(x)cos(x)]/dx = v.du/dx + u.dv/dx

= cos^2(x) - sin^2(x)