The main idea is the number of marbles and the denominator of the probability. All you have to do is multiply the fraction by a fraction which is equal to 1 which makes the denominator equal to 63. We know 63 is a multiple of 9. 9 goes 7 times in 63 so we multiple the fraction with
which gives,
which when evaluated gives
and the numerator is the number of red marbles in the bag. So there are 14 red marbles in the bag :D
Set up your conversion using dimensional analysis. That's just a fancy way of saying set up your values so you cancel what you don't need and keep what you do. If we want to convert miles per hour to feet per second, we need to convert the miles to feet using the fact that there are 5280 feet in 1 mile, and then convert the hours to seconds using the fact that there are 3600 seconds in an hour. Your set up will look like this (it's all about setting up the fractions correctly): . If you look at that closely, you can see the there is a label of miles on the top in the first fraction and on the bottom in the second fraction. Those cancel each other out by reducing. Then in the bottom of the first fraction there is hours and in the top of the last fraction there is hours. Those cancel out. From top to bottom or bottom to top you can cancel like labels. This leaves us with feet in the top and seconds in the bottom. Now it's a matter of doing the math. You multiply straight across the top and straight across the bottom.
. Simplifying you get 46.933 feet per second.
From Left side:
NOTE: sin²θ + cos²θ = 1
Left side = Right side <em>so proof is complete</em>