ElectricPavlov

Re - write as

x^2 + 12x + 9 = 0        in the QUadratic formula   a =1    b = 12   c = 9

\(x = {-12 \pm \sqrt{12^2-4(1)(9)} \over 2(1)a}\)     You can finish I'm sure !     (Ignore the 'a' on the bottom....I forgot to delete it) 

20 even numbers    20 odd numbers

20 P 3             +         20 P 3 = 13680 combos

Re- arange to

x^2 + 6x - 233      Again...Quadratic Formula results in x =  -3 +- 11 sqrt 2   

                                            the smallest would be   - 3- 11 sqrt 2

Ugh....and YIKES !    again !  

100x^2 + 20x + 1 = x^2 + 8x + 16.     Gather everything to the left side

99x^2 + 12x -15 = 0       Now you can use the Quadratic Formula to find x = 66/198  and  - 90/198     (simplify if needed)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)      a = 99   b = 12   c = -15

x  -7     +   (x+7)      +  x/7     = 60

 15/7 x = 60

 = 28           so the numbers are     21    35   and   4       and  N = 28

I know it sums to 0.75    but I do not know how to compute that result ....  anyone?

I am stuck on this one.....here is a diagram I started:

40 % of 200 hit the board = 80 darts

1/4 will hit in the upper R quadrant  (20 darts)

^{**** edited ***}

   the area of the shaded region   is   1/4  pi (2r)^2   - 1/4 pi r^2

                                                         4r^2 - r^2  = 3 r^2      out of   total quadrant   1/4 pi (2r^2 )

                                                                                       3r^2 / 4r^2     

                                 3/4 of the 20 darts will hit the shaded area    3/4 x 20 = 15 darts ( as Cphil found below)

I saw Chris' answer and realized a mistake in my calcs....Thanx Chris !

{3/4 * 2   +  1/4 * (-1) ] / 2 = .625      62.5 cents      ( not positive of this answer)     Anyone else?    ~EP