On January 1 you win $50,000,000 in the state lottery. The $50,000,000 prize will be paid in equal installments of $6,250,000 over eight years. The payments will be made on December 31 of each year, beginning on December 31 of this year. If the current interest rate is 5%, determine the present value of your winnings. Use the present value tables in Exhibit 7. Round to the nearest whole dollar.

Part a : solve -vp + 40 < 65 for v part b : solve 7w - 3r = 15 for r show your work .

Which is a reasonable estimate of the amount of water in a small, inflatable pool used by children?

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.