Math Answers

How many different outcomes can we expect if we flip the coin 5 times?

x² -10x + 33 ≡ (x - a)² + b

Work out the value of a and the value of b

What is the minimum value of x² - 10x + 33?

While in a newsagents the probability that Ed buys a newspaper is 0.8
In the same newsagents the probability that Ed independently buys a magazine is 0.3
Work out the probability that Ed buys at least a newspaper or a magazine in the same newsagents. Include diagram

Find the area of the parallelogram with sides a=i-2j+k and b=2i+j+k

Solve the differential equation (1 + yx) xdy + (1 − yx) ydx = 0

Suppose a biological cell contains 400 genes. When treated radioactively the probability that
a gene will change into mutant gene is 0.006 and is independent of the other genes. What is
the approximate probability that there are at most 4 mutant genes after the treatment?

Let V be the subspace of P3 spanned by the the following set
{1-x^2+x^3 , 2+x-x^2+x^3 , 1+2x+x^2-x^3}

(a) Show that f(x) = x + x^2 - x^3 ∈ V .
(b) Show that g(x) = 1 + x - x^2 +x^3 is not an element of V .
(c) Find a basis for V which contains f(x).
(d) Find a basis for P3 which contains g(x).

Given the square root of (x + 2) = 3a ..find x in terms of a

A plane flies between two cities.
The plane leaves London at 0850, flies to Glasgow and returns to London arriving at
1305
The time spent in Glasgow is 45 minutes.
The second flight is 10 minutes longer than the first flight.
What is the arrival time in Glasgow of the first flight?

A solid cone has a base radius of 4x and a height of 3x.
The total surface area of the cone is the same as the surface area of a sphere with a
radius of y.
Show that y = 3x.