A store manager wishes to investigate whether there is a relationship between the type of promotion offered and the number of customers who spend more than $30 on a purchase. Data will be gathered and placed into the two-way
table below.
Customer Spending by Promotion Run
Customers
Spending
More than $30
Customers
Spending
$30 or Less
$10 off $50
15% off
$5 off $25
Buy-1-Get-1 Half Off
Which statement best describes how the manager can check if there is an association between the two variables?
ОО
The manager must check relative frequencies by row because there are more than two different promotions.
The manager must check relative frequencies by column because there are more than two different promotions.

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

answer: 0.1,0.85

step-by-step explanation: