1) [2 points each] Simplify the following (= Write them with a single exponent.) 21) (P'3)(_13_1) b) P\" + P4 2) Solve for j. Round your answer to the nearest .001 17 j()_3=2 3) In Equal Temperament Tuning, what frequency ratio is associated with a minor sixth (8 half- steps)? Round your answer to the nearest 0.000001. 4) Calculate the frequency of B; in the following tuning systems. Round all answers, if necessary, to the nearest 0.00] Hz: a) Equal Temperament Tuning b) Harmonic Series in A c) Just Intonation in A\" 5) Calculate the frequency of E: in Pythagorean Tuning. Round, if necessary, to the nearest 0.00] Hz. 6) Divide the fundamental Frequency of F5 by the frequency of A4 in the following tuning systems. Round your answers (if necessary) to the nearest 0.000001: a) Equal Temperament Tuning b) Harmonic Series Tuning in E* Once you have an answer, calculate the difference in cents between this ratio and your answer to part (a). Round to the nearest cent. c) Pythagorean Tuning. Once you have an answer, calculate the difference in cents between this ratio and your answer to part (a). Round to the nearest cent. 7) [2 points each] The first three terms in an infinite geometric series are -42, 31.5, and -23.625.10) True fact: Ancient Roman contractors who built roads were paid half when the road was completed, and half 40 years after the road had been completed if the road was still in good working order. Assume the annual yield is 1.75%. A contractor receives a contract to build a small road and will be paid a total 12,000 denarii. It will take 3 years to complete the road, so the contractor will be paid 6,000 denarii in 3 years and another 6,000 denarii in 43 years. What (to the Ancient Roman contractor) is the present value of this contract? Round your answer to the nearest denarii. 11) After a weekend of lucrative gigs, a singer nds herself with an extra $1,500. She currently has 54,350 of credit card debt, on which she is charged an annual yield of 19%. Putting $1,500 toward this would cut that debt to 82,85 0. Calculate the annual rate of return if she does this. Round, if necessary, to the nearest 0.1%. 12) A homeowner spends S3,000 to insulate his home. His energy bills will drop by an average of S70 each month. What is the payback time of this investment? Round, if necessary, to the nearest 0.1 year. 13) A business is purchased for $400,000. It makes an annual prot of S40,000. Nine years later, it is sold for $1,120,000. Calculate the M (annual) rate of return for this investment. (Hint: there are two components of this, which will need to be added together.) Round, if necessary, to the nearest 0.1%