CPhill

10(.80) in  by 7(.80)in  =   8 in   by  5.6 in

Let x be the number of purple ones to be added.......and we have....

40 / [60 +  x]   = 5/12    cross multiply

40 [ 12]  = [60 + x] 5     simplify

480  = 300 + 5x         

180  =  5x

36   = x

Proof :

40 / [60+36]   =  40/ 96  = 5/12

|-2 (-5)-38|+2  =

l 10 - 38| + 2  =

l - 28  l   + 2  =

28  +   2   =

30

Thanks, Melody.....I never noticed that.....I'll give it a try.....!!!

Mountains Out Of Mole Hills.........indeed.......LOL!!!!!!!

Thanks, Melody......

I think we have

[(√8) x ] / [(³√16 ) x² ] =

[ √8 / ³√16 ] *  [   x  / x²  ]  =

 [ 2√2 / 2 ³√2 ] *  [  1/x ] =

[√2 /  ³√2 ]  * [ 1 / x ]  =

2^(1/2  − 1/3) / x  =

2^ (1/6)  / x   =

⁶√2 / x

I'll give his one a try

We have 6  ways to choose a consonant for the first position and 5 remaining ways to choose a consonant for the last position

And the other letters can be arranged in  7! ways

However........we must divide this by  [2! *2!]   to count only  the "identifiable" words  since we have repeated "O's"  and "S's"

So we have

[ 6 * 5  * 7! ] / [2! * 2!]   = 37800  arrangements

[ Can some other mathematician (Melody??)  check this  ??? ]

The form is   :

4p(x – h) = (y – k)^2

Where  p = 3  , h  =  – 5   and k  =  4    

And we have

4(3)(x + 5)  =  (y – 4)^2

12 (x + 5)  = (y – 4)^2

x + 5  =   (1/12) (y – 4)^2

x   = (1/12) (y – 4)^2  – 5

Here's a graph  :  https://www.desmos.com/calculator/7kcjwmhnxh

Rauhan.....See the approximate pentagon area formula I used here :

https://en.wikipedia.org/wiki/Pentagon

10.95/69.95x100

10.95      x  100    =

69.95

 219      x    100     =

1399

21900      ≈      15.65

1399