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Let X be a normally distributed random variable with mean 20 and standard deviation 6. Find: a) P(X < 27); and b) the value of x such that P(X < x) = 0.3015.

a) 27 is higher than the mean. So we can simply calculate the z value. z = (27 - 20)/6 ≈ 1.17. Using the table in the formula booklet, we find that P(Z &lt; 1.17) = 0.8790, so P(X &lt; 27) = 0.8790. b) Let's...
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Answered by Maximillian H. • Maths tutor
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How do I find the stationary points on the curve y = f(x) = x^3+6x^2-36x?

When trying to find stationary points, the first thing you should think about is differentiating. At a stationary point, the gradient of a curve or function is equal to zero. Therefore if we differentiate th...
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Answered by Luke S. • Maths tutor
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Given y=x^2(1+4x)^0.5, show that dy/dx=2x(5x+1)/((1+4x)^0.5)

You have to differentiate the equation y=x^2(1+4x)^0.5 with respect to x to get dy/dx and thereby prove the result in the question. An equation composed of the product of two x terms can be differentiated wi...
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Answered by Alistair G. • Maths tutor
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Differentiate 2e^(3x^2+6x)

Subsitute in u = 3x^2 + 6x and use chain rule to get dy/dx = dx/du x dy/dx to get dy/dx = 2(6x+6)e^(3x^2 +6)
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Answered by Nasser C. • Maths tutor
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Given that the binomial expansion of (1+kx)^n begins 1+8x+16x^2+... a) find k and n b) for what x is this expansion valid?

a) We compare the expansion given to the standard binomial expansion (remembering the powers of k).(1+kx) n =1+n(kx)+(n(n-1)/2)(kx) 2 +...As this is true for all x (for which the expansion holds), we can com...
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Answered by George C. • Maths tutor
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