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Miscellaneous algebra problems

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1. Allen, Bonita, Chloe and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the new subcommittee are there? There will be _____possible subcommittees.

2. Use induction to predict the next three numbers in the pattern. 25, 5, 1, 1/5, 1/25,...

3. Repeat the following procedure for the four given numbers.
Add 3. Double the result. Subtract 4. Divide by 2. Subtract the original selected number. The numbers are 1, 4, 8, 12. I get that the answer is 1 to all the numbers. The next part I am confused about. It says...
a) Write a conjecture that relates the result of the process to the original number selected. The result is___.

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This posting provides step by step solutions to miscellaneous algebra problems.

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See attached file; here is a cut & paste as well. Let me know if you have any questions.
Cheers, Alex.

1. Allen, Bonita, Chloe and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the new subcommittee are there? There will be _____possible subcommittees.
The answer to this problem is (4 0) + (4 1) + (4 2) + (4 3) + (4 4), where the numbers in the parentheses are supposed to be on top of each other: (4 choose 0 ...

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