From the distribution, it seems as though the digits at fairly even frequencies, though we can test our intuition by doing a few calculations.
The mean (or average) frequency can tell us quite a bit here, and we can calculate it by adding together all of the frequencies and then dividing by the number of frequencies (in this case, 10, since we have 10 digits)
Doing that, we find
(1 + 4 + 5 + 7 + 4 + 5 + 2 + 3 + 5 + 5)/10 = 41/10 = 4.1
When we divide the number of digits (40) by 4.1, we find it equals roughly 10, which means that, *on average*, each of the 10 digits appeared about 4 times. With this knowledge in hand, it wouldn’t be too out-there to suggest that this distribution is going to tend to even out more and more as we continue to add further decimal approximations of π
Given that Lorenzo ate 2/5 of his bag of almonds, the remaining amount was:
1-2/5=3/5
Given that 4 of his friend shared the remaining fraction equally, then the amount that each one ate was:
3/5÷4
that is:
3/5 divided by 4
this can be simplified to
=3/5×1/4
=3/20
The answer is: 3/5 divided by 4
Let S = Sum after 13 years
So = amount invested
t = time in years
i = annual interest rate = .0325
The S = So(1+i)t = $2,200(1.0325)13 = $3,334.21
The common factor is 4x^2
so factor that out:
4x^2 (1 + 7x) is the fully factored form