zMath 180  - Unit 33: Counting and Arrangements
1) Angeline will choose one sandwich and one drink for lunch from the menu choices shown below. List all the possible combinations of a sandwich and a drink that Angeline may choose.

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Use the tree diagram explained in the following scenario to answer the next two questions: Bob's Burgers sells combo meals in regular or super sized meals. Each size is available with a choice of a baked potato or French fries. There is also a choice of a soda or a milkshake to drink.

2) There are how many possible variations of combo meals at Bob's Burgers?

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3) If Bob's Burgers adds two new vegetable side dishes, curly fries or onion rings, how many variations would then be possible?

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4) Josh is purchasing a license plate made using three letters followed by two numbers. If Josh wants a license plate that does NOT have the letters “Q” or “S” or the numbers “0” or “2”, how many different possible license plates could Josh receive?

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5) Which factorial can be used to calculate the number of ways the word "MATH" can be arranged?

6) How many ways can a softball coach choose the first, the second, and the third batters for the batting order of a team of 9 players? There is more than one answer. State the LETTERS of the correct answers.

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7) How many ways can a volleyball coach choose 6 players from a team of 14 players? There is more than one answer. State the LETTERS of the correct answers.

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8) Six different vegetables are arranged on a shelf. How many different ways can the vegetables be arranged?

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9) How many ways can 6 people be arranged in 4 chairs seated in a row?

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10) How many different ways can the letters in the word RADAR be arranged?

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Review

Refer to the following scenario to answer the next four questions: Jana repairs bicycles for customers in her mother’s bike shop. She earns an average of $40.00 for each bike she fixes and is able to fix about 8 bikes per week. She needs to see how this will work for 8 to 12 weeks and how much money she can earn during that time period. Print out or copy the chart on paper and complete the chart. Once the chart is complete, use the chart to answer the questions about Jana’s possible earnings.

11) Refer to the completed chart and state the numbers in the chart by looking down the columns and listing the weeks of work, the number of bikes, and the total amount. For example, for 8 weeks of work report: 8 weeks: 64 bikes, $2560.

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12) What is the range of money that Jana can earn from working 8 weeks in comparison to 12 weeks?

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13) Write an algebraic equation that can be used to determine the amount of money (A) that Jana can earn in “w” weeks.

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14) Describe, in words, the number of repairs Jana will make in "w" weeks.

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15) Write an algebraic equation to determine the number of repairs (R) that Jana will make in “w” weeks.

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16) What type of correlation does the scatter plot display?

17) What type of correlation does the scatter plot display?

18) Solve the system of equations by graphing.

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19) Graph the system of equations to determine how many solutions the system has.

20) What is the missing ordered pair of a rectangle with the three given vertices?

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21) What is the missing ordered pair of a square with the three given vertices?

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22) Graph the equations and make a statement about the change in the graphs when the coefficient of “x” becomes more negative.

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23) Graph the equations and make a statement about the change in the graphs when the coefficient of “x” gets larger.

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24) Is the equation linear or nonlinear?

25) Is the equation linear or nonlinear?

26) What are the two roots of the quadratic equation?

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27) What are the two roots of the quadratic equation?

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28) Alissa was assigned the task of determining if the increase in new car prices for the year were reasonable to the customer. Describe one of the worst places to conduct a convenience sample about the increase in new car prices.

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29) Referring back to the previous problem, describe one of the best places to conduct a convenience sample about the increase in new car prices.

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30) What is the surface area of a square pyramid that has a base edge of 9 centimeters and a slant height of 12.8 centimeters?

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31) What is the surface area of a cylinder that has a radius of 4.2 centimeters and a height of 10 centimeters? Express the answer rounded to the nearest whole square centimeter and label the answer correctly.

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32) What is the volume of a cylinder that has a radius of 6 centimeters and a height of 10 centimeters? Express the answer rounded to the nearest tenth of a cubic centimeter and label the answer correctly.

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33) What is the volume of a cone with the same dimensions as the cylinder in the previous problem; that is, the cone has a radius of 6 centimeters and a height of 10 centimeters? Express the answer rounded to the nearest tenth of a cubic centimeter and label the answer correctly.

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34) Approximate the square root to the nearest tenth.

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35) Approximate the square root to the nearest tenth.

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36) Simplify the expression.

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37) Simplify the expression.

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38) Simplify.

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For the next two problems, consider the given data.

39) What is the mean of each data set?

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40) What is the median of each data set? What is the spread of each data set?

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The salaries of the employees of the Xylex company are listed in the table below. Refer to the information in the table to answer the next six questions. When making calculations, make sure to list each of the salaries as many times as there are persons filling the positions. For example, there are 6 foremen; thus, the salary of 35,000 must be listed 6 times.

Note: There is a link to a copy of the table in the content section that displays in a pop-up window. This link will make the table visible at all times while working through the problems. Some adjustments may need to be made to resize the browser window of the questions so that both the questions and the pop-up window are displayed on the screen at the same time.

41) What is the mean salary of the 47 people employed at Xylex?

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42) What is the median salary of the 47 people employed at Xylex?

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43) What is the mode of the salaries of the 47 people employed at Xylex?

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44) What is the lower quartile of the salaries of the 47 people employed at Xylex?

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45) What is the upper quartile of the salaries of the 47 people employed at Xylex?

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46) Find the interquartile range of the salaries of the 47 people employed at Xylex?

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47) To present the argument that the executives (vice-president and above) are overpaid, which of the measures of the “average” would be best to use? Why?

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48) To present the argument that the hourly employees (non-executives) need more pay, which of the measures would be best to use? Why?

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49) What percent of the total salaries of the Xylex Corporation is paid to the executives? Express the answer rounded to the nearest whole percent.

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