Winners of the Georgia Lotto drawing are given the choice of receiving the winning amount divided equally over 21 years or as a lump-sum cash option amount. The cash option amount is determined by discounting the annual winning payment at 5% over 21 years. This week the lottery is worth $24 million to a single winner. What would the cash option payout be?

Acompany manufactures x units of product a and y units of product b, on two machines, i and ii. it has been determined that the company will realize a profit of $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 min available on machine ii in each work shift. how many units of a product should be produced in each shift to maximize the company's profit p?

How much more output does the $18 trillion u.s. economy produce when gdp increases by 3.0 percen?

4. what inspired selfridge to ensure that customers in his store could browse at their leisure?