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Question
What happens when 1 cm worms are sent through these hook-ups?

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Solution
If 1 cm worms are sent through (× 2–1) and (× 2)–2 hooked machine, the result comes with `1 xx 1/2 xx 1/(2 xx 2)`
= `1/(2 xx 4)`
= `1/8`
= 0.125 cm
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An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop. So, she will be at `1/2` after one hop, `3/4` after two hops, and so on.

- Make a table showing the insect’s location for the first 10 hops.
- Where will the insect be after n hops?
- Will the insect ever get to 1? Explain.
For hook-up, determine whether there is a single repeater machine that will do the same work. If so, describe or draw it.

If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use (× 1) machines.

The left column of the chart lists the lengths of input chains of gold. Repeater machines are listed across the top. The other entries are the outputs you get when you send the input chain from that row through the repeater machine from that column. Copy and complete the chart.
| Input Length | Repeater Machine | ||
| × 23 | |||
| 40 | 125 | ||
| 2 | |||
| 162 | |||
Simplify:
`[(4/3)^-2 - (3/4)^2]^((-2))`
