6. In triangle ABC all the sides have integer lengths. What is the length of side AC? 1. AB = 3 and BC = 4 2. One of the angles of ABC is a right angle

7. Your goal as a researcher is to understand if there is a relationship between whether or adultsfelt they had a close (or not close) relationship with their family and their level of happiness. Thedata below represent this relationship in a random sample of 32 adults living in Montreal. Variable: Relationship with Family (Not Close or Close). Variable: Level of Happiness (Not Happy, Somewhat Happy, Happy) What is the unit of analysis? b) What is the level of measurement of each variable? c) Formulate an hypothesis d) Construct a properly labeled Crosstabulation table reporting frequencies and appropriate percentages (i.e. standardize percentages along the independent variable). e) Is your hypothesis supported? Explain the relationship (use percentages to support your answer). f) What percentage of the total are adults who feel close to members of their family and are also somewhat happy (show your work)? Interpret.

4. A university has 2,000 faculty members all of whom have a masters degree, and some ofwhom also have a doctorate. 35 percent of the faculty members are female. What fraction ofthe faculty members are female doctorate holders? 1. 20 percent of the male faculty members have a doctorate. 2. A total of 1140 faculty members have only a masters degree.

4. What is the ratio of AB to BC in the rectangular figure above? 1. The perimeter of ABCD is 32. 2. All the small rectangles have the same dimensions.

I. Given the following data set, provide the five-number summary: 8, 11, 7, 15, 2, 6, 7, 12, 1, 17, 3, 6, 17, 4, 20, 15, 2, 18, 7

1. What is the average of x, y, and z? 1. 2x + y + 4z = 23 2. 3x + 4y +z = 22

\text { 8. Does } x^{3}-x \text { give a whole number when divided by } 3 \text { ? } 1. x is a positive integer greater than 1. 2. x>0

1. Calculate the appropriate measures of central tendency for each variable.Region of birth; the amount of money spent each week for food and drink; number of movies watched in the last week; opinion of cafeteria food (10=excellent, 0=very bad).If applicable, treat ordinal variables as interval. For Ranking of cafeteria food - put in a frequency distribution.

3. A die is rolled randomly on to a circular board with a triangle inscribed in the circle. (Allthree vertices of the triangle are on the circumference of the circle.) What is the probabilitythat the die comes to rest outside the triangular region? 1. The hypotenuse of the triangle is a diameter of the circle. 2. The radius of the circle is 2 units, and the area of the triangle is 4 square units.

A. statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question B. statement 2 alone is sufficient, but statement 1 alone is not sufficient