## Two friends, Tiffany and Ana, are planning a skiing vacation

Two friends, Tiffany and Ana, are planning a skiing vacation in the Rockies. They plan to purchase round-trip airline tickets from Atlanta, Georgia, to Denver, Colorado. They will fly into Denver on a Fri-day morning, rent a midsize car, and drive to Aspen that same day. They will stay at the Holiday Inn in Aspen. They will begin skiing at the Buttermilk Ski Area on Saturday, ski up to and including Wednesday, drive back to Denver on Thursday, and f ly out of Denver Thursday evening.

(a) Estimate the total cost of the vacation for the two friends. Do not forget items such as food, tips, gas, and other incidentals.

(b) Using informational sources, including the Internet, determine the airfare cost, hotel cost, cost of ski tickets, cost of a car rental, and so forth. You will need to make
an estimate for food and other incidentals.Answers will vary.

(c) How close was your estimate in part (a) to the amount you found in part (b)? Was your estimate in part (a) lower or higher than the amount obtained in part (b)?

## A topic generally associated with sequences is series.(a) Research series

A topic generally associated with sequences is series.

(a) Research series and explain what a series is and how it differs from a sequence. Also write a formal definition of series. Give examples of different kinds of series.

(b) Write the arithmetic series associated with the arithmetic sequence 1, 4, 7, 10, 13, . . .

(c) Write the geometric series associated with the geometric sequence 3, 6, 12, 24, 48, . . .

(d) What is an infinite geometric series?

(e) Determine the sum of the terms of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + 1/16 + . . .

## When two panes of glass are placed face to face,

When two panes of glass are placed face to face, four interior reflective surfaces exist, labeled 1, 2, 3, and 4. If light is not reflected, it has just one path through the glass (see the figure below). If it has one reflection, it can be reflected in two ways. If it has two reflections, it can be reflected in three ways. Use this information to answer parts (a) through (c).

(a) If a ray is reflected three times, there are five paths it can follow. Show the paths.

(b) If a ray is reflected four times, there are eight paths it can follow. Show the paths.

(c) How many paths can a ray follow if it is reflected five times? Explain how you determined your answer.

(a) About how much water does your household use per day? Use the following data to estimate your house-hold’s daily water usage.

(b) Determine from your water department (or company) your household’s average daily usage by obtaining the total number of gallons used per year and dividing that amount by 365. How close was your estimate in part (a)?

(c) Current records indicate that the average household uses about 300 gal of water per day (the average daily usage is 110 gal per person). Based on the number of people in your household, do you believe your household uses more or less than the average amount of water? Explain your answer.

## Suppose you purchase a new wardrobe for \$1000 with a

Suppose you purchase a new wardrobe for \$1000 with a credit card. You decide to pay for your new wardrobe by making the minimum monthly payment each month. You do not charge anything else to this credit card until you have the wardrobe paid off. Your credit card company determines your minimum monthly payment by adding all new interest to 1% of the outstanding principal. The credit card company charges an annual percentage rate of 18%. Go to an Internet credit card payment calculator web site such as www.bankrate.com to answer the following questions.

(a) How long will it take you to pay off the entire credit card debt if you make the minimum monthly payments?

(b) How much interest will you pay?

(c) Adding the interest paid to the cash price, determine the total cost of your wardrobe.

## Use a straightedge and a compass to construct a triangle

Use a straightedge and a compass to construct a triangle with sides of equal length (an equilateral triangle) by doing the following:

(a) Use the straightedge to draw a line segment of any length and label the end points A and B (Fig. a).

(b) Place one end of the compass at point A and the other end at point Band draw an arc as shown (Fig. b).

(c) Now turn the compass around and draw another arc as shown. Label the point of intersection of the two arcs C (Fig. c).

(d) Draw line segments AC and BC. This completes the construction of equilateral triangle ABC (Fig. d).

Figure a:

Figure b:

Figure c:

Figure d:

## Using paper, scissors, and tape, perform the construction described in

Using paper, scissors, and tape, perform the construction described in the Recreational Mathematics box. Once you have completed the construction, cut along the dashed line as instructed. Set the result aside.

In this exercise we will construct another interesting surface. We begin by constructing a “cross” shape from two strips of paper, as shown below, using scissors and tape. Note the red dashed line and the green dashed line and the ends of the strips labeled A or B.

Next, using tape connect the two ends labeled A without twisting the ends. Then, connect the two ends labeled B by giving one end a half twist. The strip that connects the B ends should resemble a Möbius strip. Finally, cut the object first along the green dashed line and then along the red dashed line. Compare the result with that from the construction. What do you notice?

## Obtain a set of test scores from your instructor.(a) Determine

Obtain a set of test scores from your instructor.

(a) Determine the mean, median, mode, and midrange of the test scores.

(b) Determine the range and standard deviation of the set of scores. (You may round the mean to the nearest tenth when finding the standard deviation.)

(c) Construct a frequency of the set of scores. Select your first class so that there will be between 5 and 12 classes.

(d) Construct a histogram and frequency polygon of the frequency in part (c).

(e) Does the histogram in part (d) appear to represent a normal Explain.

(f) Use the procedure explained in Exercise 84 to deter-mine whether the set of scores approximates a normal Explain.

## (a) Select a category of bivariate data that you think

(a) Select a category of bivariate data that you think has a strong positive correlation. Designate the independent variable and the dependent variable. Explain why you believe that the bivariate data have a strong positive correlation.

(b) Collect at least 10 pieces of bivariate data that can be used to determine the correlation coefficient. Explain how you chose these data.

(c) Plot a scatter diagram.

(d) Calculate the correlation coefficient.

(e) Does there appear to be a strong positive correlation? Explain your answer.

(f)  Calculate the equation of the line of best fit.

(g) Explain how the equation in part (f) may be used.

## Come up with a list of five cities you would

Come up with a list of five cities you would like to visit. Use the Internet to search for airline prices between these five cities. Make sure to include the city with the airport nearest your home from which you would start and end your trip.

(a) Draw a complete, weighted graph that represents these cities and the costs associated with flying between each pair of cities.

(b) Use the brute force method to determine the optimal solution to visiting each city and returning home.

(c) Use the nearest neighbor method to approximate the optimal solution.

(d) How much money does the optimal solution, obtained in part (b), save you over the approximation obtained in part (c)?