Alan

There are 13 club cards and a jack in each of the other three suits, so the probability of picking a club or a jack is (13+3)/52 = 16/52

$${\frac{{\mathtt{16}}}{{\mathtt{52}}}} = {\frac{{\mathtt{4}}}{{\mathtt{13}}}} = {\mathtt{0.307\: \!692\: \!307\: \!692\: \!307\: \!7}}$$

(The above assumes it is ok to pick the jack of clubs.  If you want the probability of picking a club or a jack, but not both at the same time then the probability reduces to 15/52.)

If the masses are identical then yes, a = g/2.

I don't think standard calculators will give you 606 places of digits!  I used some computer software that has symbolic math capabilities.

You could do it by hand, in principle, just by starting with 2 and multiplying it by itself 2013 times.  Good luck with that!

I'm not clear what you are asking here, but it might possibly refer to something like the following:

A composite number can be expressed as the product of a number of primes.  This means the logarithm of that number is the sum of the logarithms of those primes.

For example;  12 = 2*2*3  so log(12) = log(2) + log(2) + log(3)

Picture a right-angled triangle with side lengths 3, 4 and 5 (a Pythagorean triple).  cot (adjacent over opposite = 1/tan) is 4/3, so csc (hypotenuse over opposite = 1/sin) is 5/3.

There are just over 131 7's in 922 (922/7 = 131.7...), so the sum of all the multiples is given by 7*(1+2+3+...+131).

This is 7*131*132/2 = 60522

There are just over 48 19's in 922 (922/19 = 48.5...), so the sum of all these multiples is 19*(1+2+...+48)

This is  19*48*49/2 = 22344

If you meant the sum of both, then 

(1) total is 60522+22344 = 82866 unless you don't want common multiples counted twice.

(2) Since there are 6 common multiples the sum of these is 7*19*(1+2+...+6) = 7*19*6*7/2 = 2793. This is counted twice, so we subtract this from 82866 to get 80073.

I'm with you Chris - By definition it takes 1 year to travel a distance of 1 light-year when you are travelling at the speed of light!

Perhaps the questioner intended to travel at a different speed, but, if so, he/she didn't say!

Not sure what you are asking, but the point (x = -6, y = -3) doesn't lie on the line y = (1/3)x - 4.

If you put x = -6 in this you get y = (1/3)*(-6) - 4 = -2 - 4 = -6 (not -3).