CPhill

4.Two number cubes are rolled. Each number cube has sides numbered 1 through 6.

What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?

Outcomes        Frequency

   2                         1

   3                         2

   4                         3

   5                         4

   6                         5

   7                         6

   8                         5

   9                         4

  10                        3

  11                        2

  12                        1

P ( even or multiple of 3)  = P(even) + P(multiple of 3) - P(even and multiple of 3)  

                                         = 18 / 36  + 12 /36  - 6 /36    

                                            24 /36     

                                              2 / 3   ⇒  CORRECT!!!

1.

−6x^5+4x^3

Test for eveness.....replace x  with -x.....if we come back with what we started with....then even....so....

-6(-x)^5 + 4(-x)^3  =   6x^5 - 4x^3   not the same....so....not even

Test for oddness.....replace x with (-x)....if all the signs change, odd...

Note that this happened  in the first test.....so.....odd  !!!!!

2.  Correct   !!!!

3.     6 /15 =    2 / 5   =   40%

If I read this correctly, the numbers that belong to B are reals and satisfy √ [x^2 ]   =  - x

Note that    √[x^2]  is defined as   l x l

So.......

l x l  = - x        when    x  =   (- infinity, 0 ]

I think this is correct, AT.....

Note that triangle EAC is similar to triangle DBC

Therefore

EA / EC  =   DB / DC       so

80 / 10   = DB / 20

8 / 1  =  DB / 20

8 =  DB /20       multiply both sides by 20

160   =  DB   =   "x"

 (2x+sinx)(3x-cotx)

The derivative is

(derivative of first function ) ( second function ) + ( first function ) ( derivative of second function )  =

(2 + cos x) (3x - cot x)  + (2x + sin x) (3 + csc^2 x)

Don't know about (a), but here's the rest

(b)  P (x < 4)  =   [ 5 + 10 + 2 + 9 ] / 90  = 26 / 90  =   13 / 45

(c)  P (x = 6)  =   15 / 90   =   1 / 6

(d)  P  ( x ≥ 5 )  = [ 12 + 15 + 3 + 1 ] / 90   =   31 / 90