CPhill

I live in Louisiana...so...no quake.....but.....how close are you to Los Angeles???

I was watching the Dodgers game and they felt the quake there!!!

We have   99 - 10 + 1  =  90 possible integers

The ones that contain at least one "7"   are

17, 27, 37, 47, 57, 67, 70 - 79, 87, 97   =  18 integers

So....the probability of selecting an integer with one with at least one "7"  is

18 / 90  =

1/5

P(rain on Sat or Sun)  =  

P(rain on Sat)  + P(rain on Sun)  -  P(rain on Sat and Sunday)  =

.40   +   .50  -  (.40)(.50)  =

.90  -  .20  =

.70  =

70%

The direction it travels  is given by   

arctan  (y/x)  =

arctan (-4/3) ≈  -53.13° ≈ 306.87°

This direction of travel  can also be described as  S 36.87° E

One question, Guest.....if each package contains one of each digit 0 - 9,   don't we need, at the most , only 52 packages???  [ since "1" is the most-used digit ]

4x^2 + 5x + 2     factor out the "4"

4(x^2 + (5/4)x + 2/4)

Take 1/2 of 5/4  =  (1/2)(5/4)  =   5/8 ....square this  = 25/64...add and subtract it within the parentheses

4( x^2 + (5/4)x + 25/64  + 2/4 - 25/64)        factor the first three terms, simplify the rest

4[ ( x+ (5/8))^2  +  32/64  25/64]

4 [ ( x + (5/8) )^2 +  7/64 ]    distribute the4 over the terms inside the parentheses

4(x + (5/8))^2  + 28/64

4 (x + (5/8))^2  +  7/16

Probability  of green marble on first draw  =  10/28  = 5/14

Probability of drawing a green marble on the second draw  =  9/27 =  1/3

So....probability that both marbles are green is     5/14 * 1/3   =  5 / 42

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%

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