ElectricPavlov

https://web2.0calc.com/questions/dice-roll_1#r1

sin x

amplitude 2

2 sinx

midline y = 10

2 sin x     + 10

period 4

2 sin pi/2 x   + 10

reflected

-2 sin (pi/2 x)   + 10

First round    Start 1024 people

                   512    games     512 people left

                   256     games     256 people left

                   128 games         128 people left                    

                    64 games           64 people left

                     32 games          32 people left  

                     16 games          16 people left                  

                      8 games             8 people left

                      4 games             4 people left

                      2 games             2 people left

                                 only one game left-----   last game for a winner !       A total of  1023 games played

(73400- 68000) / 1200    + 3   =   n

Thanx , Melody.....I assumed it DIDN'T care about gender as  'without restrictions' was part of the Q ...

    Have a good one !

Not sure how to solve this but  

-9³  + -7³  +  -5³  + -3³  = -1224

See all of the red circles?   The answer is the x coordiante of all of those circles....the y coordinate = -1

As the payments are made at the BEGINNING of the period....this is an ANNUITY DUE calculation...

Here is one form of this calc:

FV = PMT * [  (1+i)ⁿ  - 1 ] / i       * (1+i)       PMT = 1000    i = .08     n =10       plug and play!    

Possible first flip outcomes  (2³)

ttt

tth

tht

thh

htt

hth

hht

hhh                  Flipping any of th h's will result in a t or h combo already listed     so 8 possible outcomes I believe

6 + 8 = 14

14 c 6 = 3003 ways       = 14!/ (6! 8!)