Alan

Try n = 120

If the two lines are separate and parallel there will be no solutions.  Rewrite 2y - 4 = ax as  y = (a/2)*x + 2

This is parallel to y = 11x + 14 if a/2 = 11 (so that the slopes are the same); i.e. if a = 22.

"Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both"

22% only like to cook,  36% only like to shop,  23% like to do both  (22+23 = 45; 36+23 = 59), so 19% don't like either. Hence probability of choosing one who likes one or the other or both is 1-0.19 or 0.81

The graph below should help:

Assuming that we exclude 1, I get that there are 25 quiteprimes less than 100.  Here's the list:

7    11    13    17    19    23    29    31    37    41    43    47    49    53    59    61    67    71    73    77    79    83    89    91    97

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I guess you are referring to combinations, and want 6 choose 4

₆C₄ = 6!/(4!*[6-4]!  = 6*5/2 = 15

This question was asked and answered here: https://web2.0calc.com/questions/i-m-stuck-on-this-problem#r1 

Use the following transformations:

\(x=\rho .\sin \theta. \cos \phi\\y=\rho .\sin \theta.\sin \phi\\z=\rho .\cos \theta\)

This reduces to 

(-5)*5*(-4)*4*(-3)*3*(-2)*2*(-1)*1

or - 5²*4²*3²*2² =  -14400

No! There are 4 possibilities out of a total of 15, so the probability is 4/15.