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1) A rat runs in a 2 meter tube that has a number line below it marking off the lengths as shown on the number line. (Use the above number line) A student takes data of the rat's position every few seconds. She writes the following.
- The rat starts at 1/4 meter.
- Add 0.95m to get to its next point.
- To find its next point on the number line take this last value and multiply it by 150%.
- From this point subtract
the sum of 1/3 + 1/6 meter.
Where is the rat now located on the number line?
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2) A bank teller doesn't realize that on his computer screen the digit in the one's place is not printing. So he reads $12.00 when the actual number could be $126.00, he doesn't see the 6. A customer makes him aware of the problem when she doesn't get the right amount of cash. What's the most the teller could owe his customer if the number he saw on his screen looked like more than $10 but less than $100?
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3) PINs or personal identification numbers are needed everywhere once you start setting up accounts for just about anything. Eric decides he needs a plan for the PINs he will need. His first PIN will be 7862 for reasons known only to him. After that every new PIN will be obtained from 7862 by adding the next prime number , for example 7864 is his second pin (he added 2). All he needs to remember is where he is in the list of prime numbers, and he knows all his PINs. Where in the list is the first PIN that doesn't have an 8 in it?
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4) A small country prints only two kinds of stamps, 7 cent stamps and 13 cent stamps. One letter requires 64 cents postage. How many of each stamp should you ask for so that you can mail the letter and spend the least amount of money?
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5) Sonja swims in races. This season she notices that she drops in time for her butterfly at each race by 1/3 of the time she dropped at the previous race. She began the season at 1 minute and 25 seconds, the second race she did 1 minute and 7 seconds, an 18 second drop. What should her time be in the 5th race? Express you answer to the nearest one hundredth of a second.
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