ElectricPavlov

Agree with tertre.....MAXIMUM t would be 69 tix at $ 61 each to clear $4200.....

...Note that Chris found the number of tix  which will maximize REVENUE @ 4225 (65 tix at $65 each)

You need  3:1  ts2  to m2r3 for a complete reaction.....

you have 50 ml of ts2   so you would need  16.67 ml of m2r3 for a complet reaction to occur.....you have 20-16.67 = 3.33 ml excess of m2r3 which will remain in solution         M and R  

You are correct in your assumption.....

instead of  2 r^3 + 8r^2 + 13 r + 6      I get

                  2 r^3 + 9r^2 + 13r + 6  .......     So when you were expanding, you got something a little befuzzled.....look at it again....G'Luck !

Is there any more info given for this question.......like the size or equation for the circle?  I think there are MANY circles that would fit the bill.....do you need an answer in terms of the circle size/equation?

A little web searching found this:

( https://sciencing.com/how-to-convert-mv-to-ppm-12618513.html)

one millivolt is equal to 11.000000e-03 PPM.

Converting would then be     5 ppm/.011 ppm/mv = 454.54 mv          ( Not positive about this answer...but I know there is one out there! )

R    Y    G    B

1     1     1    1          Person 1 gets all 4  R Y G B

1     1     1    2       Person 1 gets  R Y G and person 2 gets B  (& Peeps 3 &4 get 0: No Bracelet)

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4     4    4     4            where the numbers represent the person who gets the   R Y G B bracelet....

So there is   4 * 4 * 4 * 4  =256  combos 

                                   ( if a person is not reperesented by a number, it is zero: No Bracelet)

Rom answered this yesterday.......see your previous posting......

I get    2^9 / 10!       (a,b) = (9,10)

  Sometimes I just forget to take the trouble of 'signing in'....I have a password manager on my computer which I have to sign into first to then be able to sign into Web2.0 (the Web2.0 password is long and hard to remember....like all of my passwords on-line....so I use the password manager program).

Sample password:   u$@4VSt3gB

Wow, MB...I gave you the answer in paragraph form as your posted question asked!   

   Anyway  

              C2H6O ----> H2O + C2H4