EXAM 1
366-504
Feb. 22

Name
SSN

Section I. For each of these problems circle the correct answer. You may support your reasons if you so desire. (3 pts each)

1. We say that the theoretical probability of an event is the number of outcomes in the event, divided by the number of outcomes in the sample space, no matter what kind of sample space we have.
   1. True
   2. False
2. In a regular n-sided polygon each interior angle has a measure of .
   1. True
   2. False
3. Every parallelogram is a rhombus.
   1. True
   2. False
4. An experiment consists of flipping a (fair) coin four times, recording head or tail each time. The sample space for this experiment has 12 equally likely outcomes.
   1. True
   2. False
5. Two lines which never intersect are called perpendicular.
   1. True
   2. False
6. Suppose a jar contains 12 red balls, 5 white balls and 5 green balls. If you draw a ball from this jar you are equally likely to get a white or green ball.
   1. True
   2. False
7. Two line segments are said to be congruent if they are parallel to one another.
   1. True
   2. False
8. A simple closed curve may divide a plane into as many as four different regions.
   1. True
   2. False
9. The set of numbers have a mean of
   1. 9.5
   2. 10
   3. 9
   4. 18
   5. none of the above
10. The set of numbers in problem 9 had a standard deviation of 5.148. Suppose I create a new set of numbers by adding 5 to each one of the previous numbers. Will the standard deviation of the new set
    1. increase by 5
    2. decrease by 5
    3. increase by
    4. decrease by
    5. none of the above

Section II. In each of the following problems you must support your answer. You need not write every detail, but you must show how you got your answer. (5 pts each)

1. Flip a penny and a nickel, recording head or tail for each coin, and if the penny comes up heads then roll a pair of four-sided dice and record their sum (if the penny comes up tails do nothing with the dice). Write down the sample space for this experiment.
2. I claim that if a person is shown a card with four colors on it, red, pink, blue and lavender, and told to choose one of those colors, there is about a .41 probability that the person will choose blue. What method might I have used to arrive at this conclusion?

3. You are working at a large school and have been assigned the job of designing an identification card for the students at this school. You decide that you will assign each student a card with a unique number on the card. The only restriction you want to put on this number is that the first digit should not be a 0. If the school has 973 students, how many digits should this ID number have so that each student will have a unique number?
4. Which of the following shapes are convex?
   

   

5. Assuming that the lines l and m are parallel find the angles r, s and t in the figure below.
   

   

6. Joe Human goes for a walk in the woods. From the time he left his house to the time he returned he followed the path described below. What total angle did Joe turn through?
   

   

Section III. In the following problems you need to describe your thought processes. Try to be concise.

1. Jane Jones, a state representative, wants to know how her constituents feel about a certain issue. She writes a questionnaire about the issue and hands this questionnaire to the first 1000 people that enter a certain Wal-Mart store on a Saturday morning. Will she get a good sample of her constituents using this method? Why or why not? What advice would you give Jane if you were here assistant?

2. Consider the following network.
   

   

   1. Is either of these a planar network?
      
      
      
      
   2. Is either of these networks traversable? If so are you allowed to start at an arbitrary vertex?
   3. If one of the networks is not traversable, can you make it traversable by adding or subtracting a single edge?
3. Find two triangles, one acute and one obtuse, whose interior angle measures are each an integer multiple of . Give a drawing of each.
4. Let V, E, F denote the number of vertices, edges, and faces of a polyhedron.
   1. Explain why (Hint: Every face has at least three sides, and every edge borders two faces.)
   2. Explain why . (Hint: Every vertex is the endpoint of at least three edges.)
   3. Show that every polyhedron has at least six edges. (Hint: Add the inequalities of parts (a) and (b), and use Euler's formula.)
   4. Use (a) and (b) to prove the no polyhedron can have seven edges.
   5. Show that there may be polyhedra with edges.

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