1) Describe the Pythagorean theorem. What is the equation you must know?

2) If you have a right triangle and one leg is 6 units in length and the other leg is 8 units in length what is the length of the hypotenuse?

3) If you have a right triangle and one leg is 9 units in length and the hypotenuse is 15 units in length what is the length of the other leg?

4) Please name the Platonic Solids and indicate which ones have duality.

5) You have twelve animals you are caring for in a veterinary hospital. A mixture of dogs and cats. You have 60 treats, and dogs eat 5 treats and cats eat 4 treats. You feed all the animals their allotted amount of treats and have two left over. How many dogs and cats are there?

6) What’s the big deal about the Golden Rectangle?

7) Reduce 228 to a series of prime numbers multiplied together.

8) Is 7.9756975697569 a rational number? Why or why not?

9) Express the square root of three as a decimal number. Is it rational? Why or why not?

10) My wife Marie and I have 3 children. Consider the set consisting of my wife, my kids, and I. How may elements are there? How many subsets in the Power Set. Now consider the set of just my three children. How many subsets are there? You need not show all the subsets for either part of this problem. I know this is a do over from last week but I think we should try it again.

11) Looking at problem ten above. I also have one son-in-law Tony, and Tony and my daughter Annie (who I have already counted as one of my kids) have four children. How many subsets are there in our whole family group: Me, Marie Tim, Annie, Steve, Tony and our four grand kids. I am not counting dogs or tropical fish. How many elements are in this group are there 6, 8, 10, or 12? How many subsets? You need not write them all down.

12) Does the Pythagorean theorem apply to all triangles or just a special kind?

13) Please state the Pythagorean theorem in words.

14) How many sides, edges, and vertices does a cube have? What other Platonic Solid does it have duality with?

15) Reduce these fat fractions to slimmer fractions:

6/48

12/84

52/128

53/167

16) What are the products when you multiply these fractions?

3/4X1/2 =

83/16 X 7/9 =

7/1X 15/48 =

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