Style color regular light blue loose fit indigo boot cut washed slim fit black blue a. how many possible pairs of jeans are there if each pair has one style and one color? b. suppose you have one pair of jeans of each possible style and color in the table. what is the probability of choosing a pair of black jeans at random?

Answers: a) 20; b) 1/5

Explanation:

1) Start making clear the data in the table.

There are four different styles: regular, loose fit, boot cut, and slim fit.

There are five different colors: light blue, indigo,washed, black, and blue.

2) Question a:  How many possible pairs of jeans are there if each pair has one style and one color?

Since you can combine every style with every color, you can just use counting principle: the combinations of m and n equals m × n.

So, 4 × 5 = 20.

And the answer is that there are 20 possible pais.

3) Question b. Suppose you have one pair of jeans of each possible style and color in the table. What is the probability of choosing a pair of black jeans at random?

i) Probability = number of positive events / number of possible events

ii) Positive events: 4 (because there is one black jean of each style)

iii) Possible events: 20 (the 20 different pairs)

iv) Probability = 4 / 20 = 1 /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