A statistics professor gives a survey to each of the 20 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use Excel to calculate the
population standard deviation and the population variance.
• Round your answers to one decimal place.
Texts sent yesterday
53
39
16
158
19
24
29
17
64 , 379, 62, 63, 6, 8,74, 14, 199,273,32,92 standard deviation: and variance:

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

i dony know

step-by-step explanation: