Amiddle school contains sixth, seventh, and eighth graders. each grade level contains approximately the same number of students. the principal wants to find the answer to a survey question affecting each student in the school. he asks a sample group “what time do you get up in the morning? ” which of these characteristics define the best sample?

one student chosen at random from each grade level
an equal number of students chosen at random from each grade level
the first 10 students from each grade level to arrive at school in the morning
all students arriving on one bus

"Sample in statistics is a small quantity that shows you what the rest is or should be like" .

The best sample would be:

an equal number of students chosen at random from each grade level.

Since by randomly selecting some students such that there are equal number of students from each grade we could easily get the information of all the students.

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

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

hope this !

~just a girl in love with shawn mendes