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A medical test will be positive for 0.05% of people and negative for everyone else. Suppose a hospital will test 4000 patients each day. Use an appropriate approximation to find the probability that 5 people test positive tomorrow. (5SF)

Note that we have a constant probability, fixed number of tests, independent patients and only two outcomes, so we can write a binomial distribution X~Bin(4000,0.0005) where X is the random variable represen...
JM
Answered by John M. • Maths tutor
3474 Views

Differentiate 2cos(x)sin(x) with respect to x

To solve this differential, firstly note that 2cos(x)sin(x) = sin(2x) (by the Double-Angle Sine Identity), this makes computing the differential a lot easier. To differentiate sin(2x) we need to use the chai...
RH
Answered by Ryan H. • Maths tutor
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Consider the function f(x) = 2/3 x^3 + bx^2 + 2x + 3, where b is some undetermined coefficient:

a) Find f ' (x) and f ''(x). f' = 2x 2 + 2bx + 2f'' = 4x + 2bb) You are given that f(x) has a stationary point at x = 2. Use this information to find b.2x 2 + 2bx + 2, x=2Stationary point is when f' = 02(2) ...
CP
Answered by Charlie P. • Maths tutor
4121 Views

Integrate 4/x^2

First of all, I would ask the tutee if they were familiar with the law of integration. i.e. that you increase the power of the variable (x) by 1, then divide by the new power, and if not then I would clarify...
AE
Answered by Ahmed E. • Maths tutor
5996 Views

integrate 1/((1-x^2)^0.5) between 0 and 1

I would require to demonstrate most of this working and explaining on a white, as a keyboard can not allow a lot of the mathematical notation required to solve this, but once I have a white board I can expla...
Answered by • Maths tutor
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