Twenty eighth graders were asked which color they liked best - red, green, or blue. Their responses appear below.

red, green, blue, blue, red, green, red, green, blue, red
red, blue, red, red, blue, red, blue, red, green, red

Which of the following represents the relative frequency table and the percent bar graph summarizing the survey results?

Frequency Table and Bar Graph showing relative frequency of 50% red, 30% blue, and 20% green.

Frequency Table and Bar Graph showing relative frequency of 40% red, 30% blue, and 30% green.

Frequency Table and Bar Graph showing relative frequency of 30% red, 20% blue, and 50% green.

Frequency Table and Bar Graph showing relative frequency of 25% red, 25% blue, and 50% green.

red = 10/20 * 100

5/10*100

=50%

blue= 6/20 *100

3/10*100

30

green= 4/20*100

1/5*100

20%

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