CPhill

See my second answer, here : https://web2.0calc.com/questions/please-help-asap_86

[ It is based off my first answer ]

6.Dmitri has a pair of standard dice; one die is blue, and the other die is yellow. He rolls both of his dice. How many ways could the number on the blue die be larger than the number on the yellow die?

We have a total of  6 * 6  =  36 outcomes

6 outcomes will be the same   ....i.e., (1, 1) (2, 2)  , etc.

15 will have the number on the yellow die > the number on the blue die

And the same number of outcomes will have the number on the blue die > the number on the yellow die

b)  Similar to the first

[ x + x + 11] * 12  / 2  =

[2x + 11] * 12 / 2   =

[ 2x + 11] * 6  =

12x + 66  =

[12x + 12(5) ] + 6     

12 [ x + 5 ] + 6     which, when divided by 12,  will always leave a remainder of 6

Thanks, tertre......here's another approach

Let the first integer  = x

Let the 11th integer = x + 10

Sum  =  [ first integer + 11th integer] * number of terms   / 2     =

[ x + x + 10 ] *  11  /  2  =

[2x + 10 ] * 11 / 2   =

2 [ x + 5 ] * 11 /  2    =

[ x + 5 ] * 11       which is divisible by 11

Nice, tertre....!!!!

Thanks, tertre   !!!

(.45) (.45)  =  .2025

So....the last answer is correct

.

"D"   is correct....

sin 60  = sqrt (3) /2

tan 30  =  1 /sqrt 3

So

2 [ sqrt (3) / 2 ] * [ 1 /sqrt (3) ]   =

sqrt (3)  / sqrt (3)   =  

1  

Exp Value   = (0)(.35)  + (1)(.25) + (2)(.05) + (3)(.2) + (4)(.15)  = 1.55