Is the mean of the squares of two numbers greater than, or less
than, the square of their means?
Can you use the diagram to prove the AM-GM inequality?
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
. . . like Samantha's here, from
I knew that to find the mean, you add up the numbers, and divide
by the quantity of numbers.
If the first two numbers had a mean of four, then they had to
add up to eight, because eight divided by two is four.
If the first three numbers had a mean of nine, they had to add
up to 27 because 27/3 is 9.
The third number then had to be 19, because 27 - 8 = 19
The sum of the four numbers had to be 60, since 60/4 = 15.
The third number had to be 33 because 60 - 27 = 33.
The answer to the problem is 2, 6, 19, 33.
Easy really! Well done Samantha.