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Shower-cleaner liquid is sold in spray bottles. The volume of liquid in a bottle may be modelled by a normal distribution with mean 955 ml and a standard deviation of 5 ml. Determine the probability that the volume in a particular bottle is:

a) at most 960 ml Let X be the volume of liquid in a particular bottle, then we want to find P(X <= 960). We first need to transform from X to Z (to the standard normal distribution) so that we can use th...
SS
Answered by Sarah S. • Maths tutor
6893 Views

Use the product rule to differentiate y=2xsinx

The product rule states that y=uv and dy/dx=(u)dv/dx + (v)du/dx. As the equation is in this form we can let u=2x and v=sinx. Therefore du/dx=2 and dv/dx=cosx. Substituting for u and v we get dy/dx=(2x)(cosx)...
GK
Answered by Georgianna K. • Maths tutor
15795 Views

Show that the cubic function f(x) = x^3 - 7x - 6 has a root x = -1 and hence factorise it fully.

f(-1) = (-1)^3 - (-1)*7 - 6 = -1 + 7 - 6 = 0 Hence f(x) = (x+1)(x^2 + ax - 6) Expand this out f(x) = x^3 + ax^2 - 6x + x^2 + ax - 6 = x^3 + (a+1)x^2 + (a-6)x -6 By comparing co-efficients a + 1 = 0 a - 6 = -...
JB
Answered by James B. • Maths tutor
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What is Mathematical Induction?

Mathematical induction is a type of direct proof, where you can prove sequences or series. A good example of this is that we can prove 1 + 3 + 5 + .... + (2n-1) = n^2. There are 4 steps: 1. Prove the first c...
AH
Answered by Ayesha H. • Maths tutor
4471 Views

Find the value of x in (4^5⋅x+32^2)⋅2^5=2^16⋅x

Find the value of x in (4 5 ⋅ x +32 2 )⋅2 5 =2 16 ⋅ x First we transform everything into powers of 2 as all the numbers involved in this equation are multiples of 2. || 4 5 = (2 2 ) 5 = 2 2*5 = 2 10 || 32 2 ...
LC
Answered by Luis C. • Maths tutor
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