A gelato shop tries to give consistent scoop sizes, but some flavors of gelato are denser than others. Here's the historical data for the mass per scoop of two flavors:
Flavor
Shape
Mean (g)
Standard deviation (g)
Hazelnut
Normal
83
9.3
Dulce de leche
Normal
67.5
7.8
Suppose they weigh a sample of 20 randomly selected scoops of hazelnut gelato and 15 scoops of dulce de
leche gelato. They will then look at the difference in their sample means (Tu – īp).
What do we know about the shape of the sampling distribution of CH
TD, and why?

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

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

what graph

step-by-step explanation: