Question 4 (1 point) Find the theoretical probability of rolling two cubes and getting a sum of 3.

The theoretical probability is 1/18

Step-by-step explanation:

Firstly, we need to know the total number of possible results

By rolling two cubes, there are a total of 36 possible results

Now, the sum of 3 can be gotten by the addition of 1 to 2 or 2 to 1

If we have 1 on the first cube and 2 on the second, we have the correct sum

we can also have 2 on the first cube and 1 on the second

This gives a total of 2 possible ways of getting 3

The probability can be calculated by dividing the number of ways to get 3 by the total number of possible results

we have this simply as 2/36 = 1/18

step-by-step explanation:

just plug in each number for x and see which ones work and don't

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12