Hi there!
Answer:
1/6
Explanation:
The first probability of getting blue is 4 out of the total marbles so 4/9.
The second time there are only 3 blue marbles out of 8 now so 3/8.
So the answer is 4/9X3/8
which equals 12/72 or 1/6
Hope this helps!
125 goes to 5^3, 5^2 goes to (3+2) x 5, and 50 stays the same.
(a) With a unit rate of 8, repeated (iterated) 72 times, we can simply multiply 8 by 72 to get the net change: 8 × 72 = 576 fish.
(b) For the unit rate (i.e. rate of change per time - minutes in this case) we can simply divide the total water pumped out by the total time it took to perform this. So: 48 ÷ 8 = 6 gallons/min.
Hope I could help you! :)
Answer:
We have been given a unit circle which is cut at k different points to produce k different arcs. Now we can see firstly that the sum of lengths of all k arks is equal to the circumference:

Now consider the largest arc to have length \small l . And we represent all the other arcs to be some constant times this length.
we get :

where C(i) is a constant coefficient obviously between 0 and 1.

All that I want to say by using this step is that after we choose the largest length (or any length for that matter) the other fractions appear according to the above summation constraint. [This step may even be avoided depending on how much precaution you wanna take when deriving a relation.]
So since there is no bias, and \small l may come out to be any value from [0 , 2π] with equal probability, the expected value is then defined as just the average value of all the samples.
We already know the sum so it is easy to compute the average :
