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Chapter 1: Problem 76
If you spend \(\$ 1000\) each day, estimate how long it will take to spend a billion dollars.
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Use Polya's four-step method in problem solving to solve. You throw three darts at the board shown. Each dart hits the board and scores a 1,5 , or 10 . How many different total scores can you make?
Use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. $$ \begin{aligned} 1 \times 8+1 &=9 \\ 12 \times 8+2 &=98 \\ 123 \times 8+3 &=987 \\ 1234 \times 8+4 &=9876 \\ 12,345 \times 8+5 &=98,765 \end{aligned} $$
The Republic of Margaritaville is composed of four states: A, B, C, and D. According to the country's constitution, the congress will have 30 seats, divided among the four states according to their respective populations. The table shows each state's population. $$ \begin{aligned} &\text { POPULATION OF MARGARITAVILLE BY STATE }\\\ &\begin{array}{|l|l|l|l|l|l|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\ \hline \begin{array}{l} \text { Population } \\ \text { (in thousands) } \end{array} & 275 & 383 & 465 & 767 & 1890 \\ \hline \end{array} \end{aligned} $$ Allocate the 30 congressional seats among the four states in a fair manner.
Exercises 43-46 describe procedures that are to be applied to numbers. In each exercise, a. Repeat the procedure for four numbers of your choice. Write a conjecture that relates the result of the process to the original number selected. b. Use the variable \(n\) to represent the original number and use deductive reasoning to prove the conjecture in part (a). Select a number. Multiply the number by 4 . Add 8 to the product. Divide this sum by 2 . Subtract 4 from the quotient.
Describe procedures that are to be applied to numbers. In each exercise, a. Repeat the procedure for four numbers of your choice. Write a conjecture that relates the result of the process to the original number selected. b. Use the variable \(n\) to represent the original number and use deductive reasoning to prove the conjecture in part (a). Select a number. Add 3. Double the result. Add 4. Divide by 2 . Subtract the original selected number.
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