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What about this? What do you want us to do with this?

P(rolling no 6's)  =  (5/6)^5

P(rolling one 6)  =  C(5,1) (1/6)(5/6)^4

P(rolling two 6's)  = C(5,2) (1/6)^2 (5/6)^3

So.....the probability is

(5/6)^5 + C(5,1)(1/6)(5/6)^4  + C(5,2) (1/6)^2 (5/6)^3  =  625/648 ≈  .964  ≈  96.4%

4) Sum of consecutive squares: 1/6*(2*1000 + 1) * 1000 * (1000 + 1) =333,833,500.

1)  sumfor(n, 1, 1000, n / 5^n) = 5 / 16

OK, man....!!!!

Call the number of people, N

So....the number of sodas  =  N / 8

The number of bags of chips  = N / 4

The number of cheesecakes  = N  / 6 

And the total of these = 78

So we have

N /8 + N /4 + N/6  = 78           the common denominator  = 24, so....

3N + 6N + 4N 

___________   =    78         multiply both sides by 24

       24

13N  =  78 * 24           divide both sides by 13

N  =   (78/13) * 24

N  =  6 * 24

N  =  144 people

Help, please?

Thank you so much, CPhill!

Sarah  could fill out  the entry forms issued at 8, 9, 10, 11, 12, 1, 2, 3, 4 =  9 forms

Davie  could fill out the forms issued at 9, 10, 11, 12, 1, 2 , 3  =  7 forms

Zeb could fill out the forms issued at  10, 11, 12, 1, 2, 3 , 4  = 7 forms

Alishe could fill out the forms issued at   12 , 1, 2, 3 , 4  =  5 forms

So the max entries are   9 + 7 + 7+ 5  =   28

Second one.....note that   

.11111....  =  1/9

.01111.... =  1/90

.00111.... =  1/900     etc.

So  we have the sum

1 + 1/9  + [  1/9 + 1/90 + 1/900 + 1/9000 +  1/90000 +  1/900000 +   ....... ]  =

1  + 1/9   +     [ (1/9)  / [ 1 - 1/10] ]  =

10/9    +   (1/9)  / [ 9/10 ]  =

10/9  +  (1/9) ( (10/9)  =

10/9 ( 1 + 1/9)    =

10/9 (10/9)  =

100/81

Here :   https://web2.0calc.com/questions/help_99177

Let the side of the square be, S

Let A  = (0,0)     B = (0, S)    C = (S, S)     D = (S,0)   E  = (S/2, S)    F = (S, S/2)

The slope of the line containing the segment AE  is   [S -0 ] / [S/2 - 0]  =   S/[S/2]  =  2

So the equation of the line containing this segment is  

y - 0  =  2(x - 0)

y = 2x        (1)

The slope of the line containing the segment BF   is   [ S - S/2] / [ 0 - S]  = [S/2] / [ -S]  = -1/2

So.....the equation of the line containing this segment is

y - S =  -(1/2)(x - 0)

y = -(1/2)x + S     (2)

Setting (1)  = (2)   we can find the x coordinate of G

2x = -(1/2)x + S

(5/2)x  = S

x =  (2/5)S

And the y coordinate of G  is  y = 2x  =  2(2/5)S  =  (4/5)S

So....by the distance formula,   DG  is

√[ (S - (2/5)S)^2 + ((4/5)S - 0)^2 ]  =

√[ [(3/5)S ]^2  +[ (4/5)S]^2 ]  =

√ [ (9/25)S^2 + (16/25)S^2 ]  =

√ [ (25/25)S^2 ]  =

√[ 1S^2 ]  =

S

Which is the same length as AB =  the side length of the square