Runners in a 5k race were surveyed about their finishing times (f) and the number of previous races they had run (n). there was a negative linear relationship between f and n that is best modeled by the equation f=−1.2n+38.1 .

a the model predicts that the finishing time for a runner in a 5k race is about 38.1 minutes. b the model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 38.1 minutes. c the model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes. d the model predicts that the finishing time for a runner in a 5k race is about 38.1 minutes.

arithmetic sequence: a sequnce in which the diffrence between any two consecutive terms is the same

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