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Discrete Math
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A deposit of \$100,000 is made to an investment fund at the beginning of a year. On the last day of each year, two dividends are awarded:
- 20% of the amount in the account during that year, and
- 45% of the amount in the account in the previous year.
No money is withdrawn. How much is in the account at the end of year 2?
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How many solutions are there to the equation , where and are nonnegative integers?
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How many strings with seven or more characters can be formed from the letters in EVERGREEN?
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The Fibonacci numbers satisfy the recurrence:
together with the initial conditions:
Find
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A committee is formed consisting of one representative from each of the 50 states in the United States, where the representative from a state is either the governor or one of the two senators from that state. How many ways are there to form this committee?
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A sequence satisfies a second-order linear recurrence relation whose characteristic equation has two roots and . Given the initial conditions:
what is the general formula for
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A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt are made?
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How many bit strings of length 10 contain either five consecutive 0s or five consecutive 1s?
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In the Tower of Hanoi puzzle, suppose our goal is to transfer all disks from peg 1 to peg 3, but we cannot move a disk directly between pegs 1 and 3. Each move of a disk must be a move involving peg 2. As usual, we cannot place a disk on top of a smaller disk. The number of moves required to solve the puzzle for 6 disks is:
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How many bit strings of length have more 0s than 1s?
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