In Shen's cooler there are bottles of soda and bottles of water. Shen is going to choose bottles at random from the cooler to give to his friends. What is the probability that he will choose sodas and waters? Round your answer to three decimal places.

In Trey's cooler there are 8 bottles of soda and 10 bottles of water. Trey is going to choose 12 bottles at random from the cooler to give to his friends. What is the probability that he will choose 5 sodas and 7 waters? Round your answer to three decimal places.

Step-by-step explanation:

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the bottom of the spinner is not flat.

step-by-step 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