Given ad > bc, and we also know all the variables are positive (so when dividing/multiplying you don't have to switch the inequality), you can use the division property and divide both sides by d that still makes the inequality true: a > bc/d.
Then by the same property, you can keep the inequality true by dividing both sides by b, and you obtain a/b > c/d.
Same way to think of it as the example 5/19 > 6/23, because multiplying 23 to both sides won't change the fact that 5 * 23 / 19 > 6, logically speaking, if you fairly multiply each side by the same number, then it's obvious that the bigger side will be even bigger now. After you fiddle around with the division property, you can obtain a/b > c/d.
You can use complimentary counting, first let S = total number of possible subsets.
Let N = the number of subsets with no prime number, then the answer we are looking for is S - N.
S = 2^18 since there are 18 items.
N is any set with 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.
There are a total of 10 items.
So S - N = 2^18 - 2^10
2x + 3y = 15 can be written as 3y = -2x + 15 => y = -2x/3 + 5
The slope of this line is -2/3, and if a line is parallel to it, it must also have a slope of -2/3. So the new line is y = -2x/3 + b, where b is the y-intercept.
Plug in (-3, -5): -5 = -2(-3)/3 + b, b = -7
Equation of line: y = -2x/3 - 7 or in standard form: 2x + 3y = -21
PS: smarter solution is to know that new line would be 2x + 3y = c, and plug in -3, -5 to obtain -21. That's if you know the rule about parallel lines + slopes.
13 is prime, so we know we can write it as (13x _ _)(x _ _)
17 is also prime so we can guess put it into either one as (13x - 17)(x + 1) or (13x + 1)(x - 17) or (13x - 1)(x + 17) or (13x + 17)(x - 1).
FOILing it out:
(13x - 17)(x + 1) = 13x^2 - 4x - 17
(13x + 1)(x - 17) = 13x^2 - 220x - 17
(13x - 1)(x + 17) = 13x^2 + 220x - 17
(13x + 17)(x - 1) = 13x^2 + 4x - 17
Values of n: -220, -4, 4, 220