There are 12! ways to line 12 people up. That is 12 factorial (the name for the exclamation point
12! means 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Using a scientific calculator to compute 12!, we get 479,001,600 ways to line up 12 people. I know it sounds amazing but here is a chart.
People Ways
3 6
4 24 (Notice that if you multiply 6 x 4 you get 24)
5 120 (Notice that if you muliply 24 x 5 you get 120 etc.)
6 720
7 5040
8 40,320
9 362,880
10 3,628,880
11 39,916,800
12 479,001,600
Answer:
(#14 - supplementary) x = 10.5
(#15 - supplementary) x = 10
Explanation:
For these problems, we must know that a supplementary angle can be viewed as a sum of angles that add to 180 degrees. With this known, we can write our equations to find x.
(#14)
15x - 12 + 5x - 18 = 180
20x - 30 = 180
20x = 210
x = 10.5
(#15)
6x + 13 + 14x - 33 = 180
20x - 20 = 180
20x = 200
x = 10
Hope this helps.
Cheers.
