6. In a math survey of 28 students, 9 have a Play Station and 17 have an X-Box. There are 6 students that don't have either a Play Station or X-Box. What is the
probability that a student chose at random has a Play Station and an X-Box?
7. A random survey of 25 students showed that 5 students ride bikes and 10 students 7.
ride skateboards. There were 12 students that rode neither a bike or skateboard.
What is the probability that a student chosen at random rode both a bike and skateboard?
8. A survey of 27 students at the mall showed that 11 students like to go to the park and 8.
13 students liked going to the beach. There were 5 students that didn't like going to
the park or the beach. What is the probability that a student chosen at random liked
going to the park or beach?

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

the anwser is d) 75°

step-by-step explanation:

need more information

step-by-step explanation:

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,