Aresearch company is looking at the correlation between the years since 1970 and the average amount of years that couples stay married. use complete sentences to explain how the data below indicates a non-linear model.
time (in years) since 1970: 0, 10, 20, 30, 40
average age of a marriage (yrs.): 10, 11.2, 13.9, 17.2, 29

Answer and Step-by-step explanation:

Since we have given that

Time                Average age of a marriage

0                                  10

10                                 11.2

20                                13.9

30                                17.2

40                                29

We need to show that the above data indicated a non linear model.

For this it is enough to show that slope is different:

So, we consider the slope for first 2 points:

(0,10) and (10,11.2)

So, slope becomes

and similarly, (10,11.2) and (20,13.9)

so,

So, it becomes non linear model.

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

square pyramid

step-by-step explanation:

square prism looks like nothing like that

triangular prism has a rectangular base instead of a square base

tetrahedron has a triangular base