A box is filled with 10 yellow cards, 3 green cards, and 2 brown cards. A card is chosen at random from the box. What is the probability that it is a yellow or a
brown card?
Write your answer as a fraction in simplest form.

4/5

Step-by-step explanation:

The total number of cards is 15. Pretend that the yellow and brown cards are one big group of blue cards. Now, the problem is asking for the number of blue cards over the total number of cards, which is (10+2)/15 = 12/15 = 4/5.

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

correct answer:

b.(19,-2)