After one month, devon finds that his 10 friends slept an average of 0.5 hour more each night when they drank milk before bed. based on this, devon concludes that drinking milk makes teenagers sleepy. what is one reason why devon's conclusion is most likely invalid?

He did not test it against anyone who did not drink milk before bed and he tested it on a relatively small number of people. In order to have more accurate results he should include more people in the study and should test it against the same number of people who haven't drank milk before bed. He should also take into account the amount of milk that they drank before going to bed.

it 2

step-by-step explanation:

8^1/3=2

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