A tennis pro has 12 can of tennis balls. There are 3 balls in each can. He gives an equal number of balls to each of the 4 players. After the lesson, he realizes that each player lost 3 balls. How many tennis balls are left? Show your work and explain (in complete sentences) how you found your answer.

24 Tennis balls

Step-by-step explanation:

Calculation for How many tennis balls are left

First step

Since we have 12 can with 3 balls each Let the number of balls that the tennis pro has at the beginning be x

x=(12 can ×3 balls each)

x=36

Second step

Since we have 4 players who lost 3 ball each Let the total number of balls that was lost be y

y=(4 players×3 balls each)

y=12

Third step is to calculate How many tennis balls are left

Since x represent the number of balls at the beginning and y represent the number of balls that was lost , then let the number of tennis balls that was left after the session represent z

z=36−12

z=24 Tennis balls

Therefore the numbers of tennis balls that are left will be 24 Tennis balls

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

36

step-by-step explanation: