The prizes at a carnival tossing game are different stuffed animals. there are 34 tigers, 27 bears, 12 hippopotamuses, 16 giraffes, and 22 monkeys. the carnival manager randomly selects a prize when a player wins the game. determine the probability that the prize selected is not a bear.

Step-by-step explanation:

Number of tigers in carnival tossing game = 34

Number of bears in carnival tossing game = 27

Number of hippopotamuses in carnival tossing game = 12

Number of giraffes in carnival tossing game = 16

Number of monkeys in carnival tossing game = 22

Total number of animals in the carnival tossing game = 34 + 27 + 12 + 16 + 22

                                                                                          = 111

Probability that the prize selected is not a bear = 1 - Probability that the prize selected is a bear

2

step-by-2step explanation:

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