LuckyDucky

Yup! that's 100% correct

Also, next time I know how to do it because of your explanation

Well said!

Good!

We first compute for the surface area of the roller and the total area covered by the 5 gal paint
1gal = 20 ft2
5 gal = 20ft2 x 5
         = 100ft2
1 rev = surface area of the side of the cylinder
1 rev= 2pirh
where
radius= 1.5 in=0.125 ft
h= 8 in=0.67 ft
1 rev= 0.53 ft2
5 gal = 100ft2
total revolutions = 100ft2/0.53ft2
total revolutions = 188.68 revoluions
A 5 gal paint can take 188.68 revolutions of paint roller with 8in wide and diameter of 3 in.

1. 

a. 65:195

b. C 3/5

Nah you have the most thunder in this website while I just got on the leaderboard :D

Omg I'm so sorry your my idol in this website btw so I try to be more like you

so sorry 

We seat April first. She has 8 choices. We seat May next. She has 2 choices: two spots to the left of April or two spots to the right of April. Then, the remaining six members can sit in ways. This appears to give a total of 8*2*6!  seatings. However, because two seatings are considered the same if one is a rotation of the other, each distinct seating is counted 8 times in this product, once for each possible location of April. So, we must divide by 8 to give a total of 2*6! = 2*720 = 1440 seatings.

We might have instead started by noting that it doesn't matter where April sits. She starts by sitting anywhere, and we count the number of ways the members sit relative to April. May still has 2 choices: two spots to the left of April or two to the right of April. The remaining six participants then can be seated in 6! ways, for a total of 2*6! = 1440 seatings, as before.

I agree the only way I know how to do it is brute force, similarly I think CPhill answered this question with the same techqnie as you...

By the way everything below this is 100% CPhill's work even though I used the same methord

16 possible outcomes

P         N           D           Q                     Value  of Heads

H        H           H           H                        .41

T        H           H           H                        .40

T        T           H            H                        .35

T        T           T            H                        .25

T        T           T           T                            0

H       T            T           T                         .01

H       H           T            T                        .06

H      H            H            T                        .16

T       H           T            T                         .05

T      T            H            T                         .10

H      T            T            H                         .26

T      H           H             T                         .15

T      H           T             H                         .30

H     T            H            T                          .11

H     T            H            H                          .36

H     H           T             H                          .31

P ( 15 cents or more of heads)  = 10/16 =  5/8

We can also note that to form a sequence with two different letters in alphabetical order, we need first pick the letters we'll use, then put them in order. We can choose two letters to use in \($\binom{26}{2} = 325$\) ways, and there's only 1 way to put each pair in order.

Hence, there are 325 sequences that fit the problem.