CPhill

I'm going to guess that this is:

-24 - 7x  = 18      add 24 to both sides

-7x  = 42       divide both sides by -7

x = - 6

Probability of all 3's   =  (1/6)^5  =  1 / 7776

P (black ace or red face card)  =

P(black ace)   +  P(red face card)   -  P(black ace and a red face card)  =

     2 / 52           +    6 / 52           -      0 / 52  =

                    8 / 52  =

                    2 / 13

It's a combination since the order of the flavors chosen doesn't  matter..

And the number of possibilities  is  

C(15,2)  = 105

Wow!!!....thanks to all these guests for their answers.....all were good....

This one - IMHO - was "tricky",,,,,

9 1/4 days = 9.25 days

3 weeks = 21 days

So

9.25 days  :  21 days =

37  :  84      [in terms of an integer ratio ]

Look at the graph, here : https://www.desmos.com/calculator/ksxxeals66

The corner points  appear to be

(4,4)   (.154, 6.308)  and ( 2,10)

P at (4,4) = 40

P at (2,10)  = 44

P  at (.154, 6.308)  = 20.002

So   (x, y)  =  (.154, 6.308)  minimizes P  =  20.002   and (2,10)  maximizes P  = 44

Very nice, both guests.....this was a "stumper"....!!!!

You would have to specify what "numbers" you are referring to....

(f/g)(x)   =  f(x)  / g(x)  =   [4x  - 5]  / [ 3x  ]