20 pts ! randy has been awarded some money in a settlement. he has the option to take a lump sum payment of $300,000 or get paid an annuity of $2,000 per month for the next 20 years. which is the better deal for randy, and by how much, assuming the growth rate of the economy is 5.65% per year? (a) lump sum: by $23,606.12 (b) lump sum: by $16,726.56 (c) annuity: by $23,606.12 (d) annuity: by $16,726.56

Answer  - B

Formula to calculate present value of annuity:

PV = P( 1 - ( 1+r)^(-n) )/r

PV- present value,  P- payment,  r- periodic interest rate, n - number of periods

On putting the values,

PV = 2000( 1 - ( 1 + (5.65/1200)^(-240) ) / (5.65/1200)

PV = 283273.44

Lump sum - PV = 300000 - 283273.44 = 16726.56

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .