60 people attend a game night. everyone chooses to play binx, a two player game, or zonks a four player game. all 60 people are playing either binx or zonks. there are 3 more games of zonks being played. how many of each game are being played?

8 binx games were played.

11 zonk games were played

Step-by-step explanation:

Let x represent the number of binx games that was played.

Let y represent the number of zonks games that was played.

60 people attend a game night and all 60 people are playing either binx or zonks. Everyone chooses to play binx, a two player game, or zonks a four player game. This means that

2x + 4y = 60 - - - - - - - - -1

There are 3 more games of zonks being played. This means that

x = y - 3

Substituting x = y + 3 into equation 1, it becomes

2(y - 3) + 4y = 60

2y - 6 + 4y = 60

2y + 4y = 60 + 6

6y = 66

y = 66/6 = 11

x = 11 - 3 = 8

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

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