Which of these observations is supported by the data in the table? note: a rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie. the majority of the audience in the 26-35 age group disliked the movie.
among those who liked the movie, the majority were in the oldest age group.
among those who disliked the movie, the majority were in the 26-35 age group.
the majority of the audience in the 16-25 age group liked the movie.
the majority of the audience from all the age groups disliked the movie.

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step-by-step explanation:

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