Answer:
$102,677.20
Step-by-step explanation:
The present value of an annuity due is determined by the following expression:

Where 'P' is the amount of each payment received, 'r' is the interest rate on the investment and 'n' is the number of yearly payments.
With 20 annual payments of $10,000 at a rate of 8.5%, the present value is:

The present value of your winnings is $102,677.20.
The radius of the new sphere is 9
The new SA should be 1017.36 in
New volume should be 3052.08in^3
I have an expression

floating around in my head; let's see if it makes sense.
The variance of binary valued random variable b that comes up 1 with probability p (so has mean p) is

That's for an individual sample. For the observed average we divide by n, and for the standard deviation we take the square root:

Plugging in the numbers,

One standard deviation of the average is almost 2% so a 27% outcome was 3/1.9 = 1.6 standard deviations from the mean, corresponding to a two sided probability of a bit bigger than 10% of happening by chance.
So this is borderline suspect; most surveys will include a two sigma margin of error, say plus or minus 4 percent here, and the results were within those bounds.
There are 20 books in each box.
If each box has 20 books, then the number of books is 20 times the number of boxes. (20 books: 1 box, 40 books: 2 boxes...)
So, using mathematical terms, the number of books is equal to the number of boxes x 20.
Here, it says James packs x boxes of books. This means that we call the number of boxes, x. X could be 1,2,3, or any other number.
So, since there are 20 times as many books as boxes, the number of books is 20 times x.
In math terms, this is written like 20x.
So the answer is 20x.