What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%? Group of answer choices $18,367 $20,352 $16,576 $17,449 $19,334

The PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5% is $20,352.

Step-by-step explanation:

P = PMT [(1 - (1 / (1 + r))) / r]

= 2,700 [(1 - (1 / (1 + 0.055))) / 0.05]

= 2,700 [(1 - (1 / (1 + 0.055))) / 0.05]

= 2,700 [(1 - (1 / (1.708)) / 0.05]

= 2,700 [(1 - 0.58)) / 0.05]

= 2,700 [(0.41457) / 0.05]

= 2,700(7.53)

=$ 20,352

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

step-by-step explanation:

*calories burned = (weight)(calorie factor)*

calories burned = 180 (0.65)

calories burned = 117

the calories he used up is 117, which is 65% of his weight.