Alottery offers two options for the prize.

option a: $1000 a week for life.
option b: $1 000 000 in one lump sum.

if you choose option b, you have the opportunity to place the winnings into an investment that also makes regular payments, at a rate of 3%/a, compounded weekly. the annuity will pay out a specific amount weekly based on how long you want the annuity to last.

a. which option would the winner choose if you expect to live for another:
i. 20 years?
ii. 50 years?
b. use technology to determine the range of life expectancies when each option is preferred. show your work.

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )

X=-4 the correct answer