The principal p is borrowed at simple interest rate r for a period of time t. find the loan's future value, a, or the total amount due at time t. round answer to the nearest cent. p = $160, r = 7%, t = 3 years

  $193.60

Step-by-step explanation:

The applicable formula is ...

  A = P(1 +rt)

Filling in the given numbers and doing the arithmetic, we find ...

  A = 160(1 + .07·3) = 160·1.21 = 193.60

The amount due is $193.60.

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

yes. we do proportions in probabilities.