A bag of 30

tulip bulbs contains 11

red tulip bulbs, 11

yellow tulip bulbs, and 8

purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag.
(a) What is the probability that the two randomly selected tulip bulbs are both red?
(b) What is the probability that the first bulb selected is red and the second yellow?
(c) What is the probability that the first bulb selected is yellow and the second red?
(d) What is the probability that one bulb is red and the other yellow?
(a) The probability that both bulbs are red is nothing
.

the answer is 62

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 least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9