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Carolyn Ellis is setting up an annuity for her retirement. She can set aside $2,000 at the end of each year for the next 20 years and it will earn 6% annual interest. What lump sum will she need to set aside today at 6% annual interest to have the same retirement fund available 20 years from now? How much more will Carolyn need to invest in periodic payments than she will if she makes a lump sum payment if she intends to accumulate the same retirement balance?
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Antonio is a simple minded carpenter. He bought a shipment of external drywall panels (12 ft x 4 ft) that he wants to use for building new houses in a new development.
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Let epsilon, gamma >0. If x is epsilon-close to y, and y is gamma-close to z, then x and z are (epsilon + gamma)-close. Let epsilon>0. If y and z are both epsilon close to x, and w is between y and z (i.e.. y
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