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4. (a) In your pocket you have some nickels, dimes, and quarters. There are 20 coins altogether and exactly twice as many dimes as nickels. The total value of the coins is $3.00. Find the number of coins of each type. (b) Find all possible combinations of 20 coins (nickels, dimes, and quarters) that will make exactly $3.00.
DVD Rentals Two new DVDs, a horror film and a comedy film, are released in the same week. The weekly number N of rentals decreases for the horror film and increases for the comedy film according to the models N=36024xHorrorfilmN=24+18xComedyfilm Where x represents the time (in weeks), with x=1 corresponding to the first week of release. (a) After how many weeks will the numbers of DVDs rented for the two films be equal? (b) Use a table to solve the system of equations numerically. Compare your result with that of part (a).
If Descartes’ Rule of Signs reveals a no changeof signs or one sign of changes, what specificconclusion can be drawn?
American Dollars and British Pounds Assume that at the current exchange rate, the British pound is worth 1.65 in American dollars. You have some dollars bills and several British pound coins. There are 17 items altogether, which have a total value of 20.25 in American dollars. How many American dollars and how many British pound coins do you have?
A forester is making a gasoline-oil mixture for a chainsaw engine. The forester has 2 gallons of a mixture that is 32 parts gasoline and 1 part oil. How many gallons of gasoline should the forester add to bring the mixture to 50 parts gasoline and 1 part oil?
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