Of the 800 seventh grade students and 640 eighth grade students at Knox Middle School, 90 students will be chosen at random to attend an assembly.

Which of the following would be a representative sample of the number of seventh and eighth grade students at the school?

50 7th grade and 40 8th grade

Step-by-step explanation:

1. add to get total number of students, 1440

2. find percentage of total that are 7th grade students and 8th grade student:

640/1440 = ~45% (are 7th grade)

800/1440 = ~55% (are 8th grade)

3. 55% of 90 is 50, and 45% of 90 is 40

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

x=-7

step-by-step explanation:

x+3=-10

-10+3=-7

x=-7