What is the probability of spinning these two spinners and having each one land
on a 3? write the probability as a decimal.

The probabilities are 0.4 and 0.6 respectively.

Step-by-step explanation:

We are given two spinning wheels with numbers on it and we have to find the probability of getting 3.

In the first wheel, there are 5 slots and the numbers are 3, 3, 2, 5 and 4.

So the probability of getting 3 =

                                            =

                                            = 0.4

In the second spinner there are three 3's and total of 5 slots.

So probability of getting 3 =

                                             =

                                             = 0.6

Hence the probabilities are 0.4 and 0.6 respectively.

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