Alan

Let the first digit be f and the second be s.

Then N = 10f + s  and M = 10s + f, so M+N = 11(f+s)

For this to be a perfect square we must have f + s = 11, so find all the digits, f and s that sum to 11.

The probability that you don't get the car is p = (39/40)*(38/39)*(37/38) = 37/40

Hence the probability that you do get the car is 1 - 37/40 = 3/40

Find the maximum/minimum value of the quadratic function x2 – 10x = y + 40 by completing the square method.

x² - 10x = y + 40

Add 25 to both sides:   

x² - 10x  + 25 = y + 65

Now the LHS can be written as:

(x - 5)² = y + 65

Subtract 65 from both sides:

y = (x - 5)² - 65

The minimum occurs when x = 5, at which point y = -65.

Possibly the questioner meant to ask for the number rounded to two significant figures, in which case the answer is 13.

Here's one way of doing this:

The numbers aren't consecutive, they increase by 2, so:

See https://web2.0calc.com/questions/functional-equation#r3 

How about  f(x) = x + 1

f(x).f(y) = x + y + x.y + 1

f(x+y) + x.y = x + y + x.y + 1

Looks to me like there are 36 up to and including a height of 150cm, so how many are above 150cm?

See https://web2.0calc.com/questions/please-help_90350#r3