Lucky's Market wanted to see if they could increase the number of sales per day before they close their locations nation wide. To test this, they randomly chose half of their 80 locations and send 50% off coupons to their customers only at those locations, while the other half of locations did not receive the 50% off coupons. They also collected information the amount of money spend on these extra customers. Which of these answers would be the best way to randomization in this study?
a. allow location managers to volunteer
b. have an unbiased person just pick half of the locations for the coupons.
c. use a computer program to select the locations who get coupons and those that don't

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

pi or 3.14159265359 is an irratinal decimal