You have a realized income of $3,264.71/month. your housing and fixed expenses are 36% of your monthly realized income. you want to save 4 months of an emergency fund within 9 months. how much must you save each month?

$522.36

Step-by-step explanation:

First we need to find out how much money 4 months of an emergency fund is total.

36% of our monthly income is $1,175.30.

Our total emergency fund will be:

$1,175.30 x 4 months = $4,701.2

Now that we have a value for our total emergency fund, we then divide the total amount by 9.

$4,701.2/9 = $522.36

We would need to save $522.36 each month for 9 months.

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