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Discovering Advanced Algebra An Investigative Approach 1st edition Jerald Murdock, Ellen Kamischke, Eric Kamischke - Solutions

Answer the questions in Exercise 1a-e for the sequence generated by u0 = 500 and un = (1 + 0.04/4) un-1 -25 where n ≥ 1. Let n be measured in quarter-years. In Exercise 1 a. Is this a loan or an investment? Explain your reasoning. b. What is the principal? d. What is the deposit or payment
Find the first month's interest on a $32,000 loan at an annual interest rate of a. 4.9% b. 5.9% c. 6.9% d. 7.9%
Write a recursive formula for each financial situation. a. You borrow $10,000 at an annual interest rate of 10%, compounded monthly, and each payment is $300. b. You buy $7000 worth of furniture on a credit card with an annual interest rate of 18.75%, compounded monthly. You plan to pay $250 each
Find the balance after 5 years if $500 is deposited into an account with an annual interest rate of 3.25%, compounded monthly.
Consider a $1000 investment at an annual interest rate of 6.5%, compounded quarterly. Find the balance after a. 10 years b. 20 years c. 30 years
Find the balance of a $1000 investment, after 10 years, at an annual interest rate of 6.5% when compounded a. Annually b. Monthly c. Daily (In financial practice, daily means 360 times per year, not 365.) d. After the same length of time, how will the balances compare from investments that are
Beau and Shaleah each get a $1000 bonus at work and decide to invest it. Beau puts his money into an account that earns an annual interest rate of 6.5%, compounded yearly. He also decides to deposit $1200 each year. Shaleah finds an account that earns 6.5%, compounded monthly, and decides to
Regis deposits $5000 into an account for his 10-year-old child. The account has an annual interest rate of 8.5%, compounded monthly. a. What regular monthly deposit amount is needed to make the account worth $1 million by the time the child is 55 years old? b. Make a graph of the increasing
Consider this sequence: 256, 192, 144, 108, . . . a. Is this sequence arithmetic or geometric? b. Write a recursive formula that generates the sequence. Use u1 for the starting term. c. What is the 8th term? d. Which term is the first to have a value less than 20? e. Find u17
Oliver wants to buy a cabin and needs to borrow $80,000. What monthly payment is necessary to pay off the mortgage in 30 years if the annual interest rate is 8.9%, compounded monthly?
Consider this sequence: 3, 7, 11, 15, . . . a. Is this sequence arithmetic or geometric? b. Write a recursive formula that generates the sequence. Use u1 for the starting term. c. What is the 128th term? d. Which term has the value 159? e. Find u20.
List the first five terms of each sequence. For each set of terms, what minimum and maximum values of n and un would you use on the axes to make a good graph? a. u1 = - 3 un = un-1 + 1.5 where n ≥ 2 b. u1 = 2 un = 3un-1 - 2 where n ≥ 2
Atmospheric pressure is 14.7 pounds per square inch (lb/in.2) at sea level. An increase in altitude of 1 mi produces a 20% decrease in the atmospheric pressure. Mountain climbers use this relationship to determine whether or not they can safely climb a mountain and to periodically calculate their
Match each recursive formula with the graph of the same sequence. Give your reason for each choice.A. u0 = 5un = un-1 + 1 where n 1B. u0 = 1un = (1 + 0.5)un-1 where n 1C. u0 = 5un = (1 - 0.5)un-1 where n 1D. u0 = 5un = un-1 - 1 where n 1
The enrollment at a college is currently 5678. From now on, the board of administrators estimates that each year the school will graduate 24% of its students and admit 1250 new students. What will the enrollment be during the sixth year? What will the enrollment be in the long run? Sketch a graph
You deposit $500 into a bank account that has an annual interest rate of 5.5%, compounded quarterly. a. How much money will you have after 5 yr if you never deposit more money? b. How much money will you have after 5 yr if you deposit an additional $150 every 3 mo after the initial $500?
A, you saw an arithmetic sequence that generates from a geometric pattern: the number of seats around a linear arrangement of square tables is 4, 6, 8, . . . . Notice that the sequence comes from the increase in the perimeter of the arrangement. What sequence comes from the increase in area?Use
Here's a strategy an algebra student discovered for finding the monthly payment you would need to make to pay off a loan. First, specify the loan amount, the annual interest rate, and the term (length) of the loan. Choose trial monthly payment amounts that form a sequence, say, $0, $1, $2, $3.
Imagine a target for a dart game that consists of a bull's-eye and three additional circles. If it is certain that a dart will land within the target but is otherwise random, what sequence of radii gives a set of probabilities that form an arithmetic sequence? A geometric sequence? Sketch what the
Find the mean, median, and mode for each data set. a. Time for pizza delivery (min): {28, 31, 26, 35, 26} b. Yearly rainfall (cm): {11.5, 17.4, 20.3, 18.5, 17.4, 19.0} c. Cost of a small popcorn at movie theaters ($):{2.75, 3.00, 2.50, 1.50, 1.75, 2.00, 2.25, 3.25} d. Number of pets per household:
Invent a data set with seven distinct values and a mean of 12.
Invent a data set with seven values that creates this box plot.
Use the backpack data separated by grade level from Exercise 13. a. Create a box plot for each grade level. Put both box plots on the same axis. b. Based on the information in your box plots, write a brief statement analyzing these two groups. Use the vocabulary developed in this lesson in your
Lord Rayleigh was one of the early pioneers in studying the density of nitrogen. (Read the Science Connection below.) The following are data that he collected. Lord Rayleigh's measurements first appeared in Proceedings of the Royal Society of London (London, vol. 55, 1894). Each piece of data is
Find the next three terms in each sequence and write a recursive formula. a. 42, 45, 48 . . . b. 16, 40, 100, . . .
Evaluate each expression. Write your answers both in radical form and in decimal form rounded to one decimal place.a. ˆš 432/6b. ˆš(782+1354/24)c.
On credit, she will have paid for the drum set after 11 months. Her total cost will be $430.01. Use the recursive formula u0 = 400 andWhere n ‰¥ 1, and find when her balance would be 0. With savings, she could buy the drum set after 10 months. Sample advice: If it is worth it to Rebecca to
A data set has a mean of 12 days, the median is 14 days, and there are three values in the data set. a. What is the sum of all three data values? b. What is the one value you know? c. Create a data set that has the statistics given. Is there more than one data set that could have these statistics?
Match this data set to one of the four box plots. Licks to the center of a lollipop:{470, 510, 547, 558, 561, 574, 593}
Match this box plot to one of the data sets for the number of minutes on the phone spent by 13 customer service representatives in a given hour.A.{36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 48, 50, 52}B.{37, 40, 42, 50, 51, 51, 51, 51, 51, 51, 51, 51, 51}C.{36, 37, 40, 40, 40, 42, 42, 43, 44, 50, 50,
These box plots represent Connie's and Oscar's scores from Exercise 6.Write a paragraph describing the information pictured in the box plots. Use the box plots to help you draw some statistical conclusions. In your description, include answers to such questions as what does it mean that the second
Homer Mueller has played in the minor leagues for 11 years. His home run totals, in order, for those years are 56, 62, 49, 65, 58, 52, 68, 72, 25, 51, and 64. a. Construct a box plot showing Homer's data. b. Give the five-number summary. c. Find X. d. How many home runs would Homer need to hit next
The inter-quartile range (IQR) is the difference between the first and third quartiles, or the length of the box in a box plot. a. Look at the box plots in Exercise 7. What are the range and inter-quartile range for Connie? For Oscar? b. Find the range and inter-quartile range for your box plot
Given the data set {41, 55, 48, 44}: a. Find the mean. b. Find the deviation from the mean for each value. c. Find the standard deviation of the data set.
Students collected eight length measurements during a mathematics lab. The mean measurement was 46.3 cm, and the deviations of seven individual measurements were 0.8 cm, - 0.4 cm, 1.6 cm, 1.1 cm, -1.2 cm, -0.3 cm, and -1.0 cm. a. What were the original eight measurements collected? b. Find the
The students in four classes recorded their resting pulse rates in beats per minute. The class means and standard deviations are given at right.a. Which class has students with pulse rates most alike? How can you tell?b. Can you tell which class has the students with the fastest pulse rates? Why or
Here are the mean daily temperatures in degrees Fahrenheit for two cities.a. Find the mean and standard deviation for each city.b. Draw a box plot for each city. Find each median and inter-quartile range.c. Which city has the smaller spread of temperatures? Justify your conclusion.d. Does the
Members of the school mathematics club sold packages of hot chocolate mix to raise funds for their club activities. The numbers of packages sold by individual members are given at right.a. Find the median and inter-quartile range for this data set.b. Find the mean and standard deviation.c. Draw a
a. Suppose each package of hot chocolate yields a net profit of 28. Draw a box plot for the profit each club member generates. Find the median and inter-quartile range, and the mean and standard deviation for the profits. Compare your profit statistics with the original statistics describing the
Matt Decovsky wants to buy a 160W CD player for his car at an online auction site. Before bidding, he decides to do some research on the selling price of recently sold CD players. His search comes up with these 20 prices.a. Find the mean, median, and mode.b. Draw a box plot of the data. Describe
Solve the following question a. (x+5)/4 + 3 = 19 b. 3(y-4) + 6/6 -2 = 7
These data sets give the weights in pounds of the offensive and defensive teams of the 2002 Super Bowl Champion New England Patriots. (www.nfl.com) Offensive players' weights (lb): {190, 305, 310, 320, 315, 322, 255, 190, 220, 245, 230} Defensive players' weights (lb): {280, 305, 280, 270, 250,
The lengths in minutes of nine music CDs are 45, 63, 74, 69, 72, 53, 72, 73, and 50. a. Find the mean. b. Find the deviation from the mean for each value. c. Find the standard deviation of the data set. d. What are the units of the mean, the deviations from the mean, and the standard deviation?
Invent a data set with seven data values such that the mean and the median are both 84, the range is 23, and the inter-quartile range is 12.
Some statisticians identify outliers as data values that are more than two standard deviations, or 2s, from the mean. Use this method to identify any outliers in the student-to-teacher ratios from the example on page 89. How do the outliers found by standard deviation compare to the outliers found
Find the standard deviation and inter-quartile range of the backpack data from Example A in Lesson 2.1. Which of these two values is larger? Will this value always be larger? Explain your reasoning and find or create another data set that supports your answer.
Two data sets have the same range and inter-quartile range but the first is symmetric and the second is skewed left. a. Sketch two box plots that satisfy the conditions for the two sets. b. Would you guess that the standard deviation of the skewed data set is less than, more than, or the same as
The histogram at right shows a set of data of backpack weights. Weight of Students' Backpacks a. How many values are between 2 kg and 3 kg? b. How many values are in the data set? c. Make up a set of data measured to the nearest tenth of a kilogram that creates this histogram.
A road engineer studies a rural two-lane highway and presents this histogram to the County Department of Highways.a. For how many cars was data collected?b. What is the 85th percentile speed?c. What speed limit would you recommend for this highway?
Penny calculates that the deviations from the mean for a data set of eight values are 0, - 40, -78, -71, 33, 36, 42, and 91. a. How do you know that at least one of the deviations is incorrect? b. If it turns out that 33 is the only incorrect deviation, what should the correct deviation be? c. Use
At Piccolo Pizza Parlor, a large cheese pizza sells for $8.99. Each topping costs an additional $0.50. a. How much will a four-topping pizza cost? b. The Piccolo Extra Special has eight toppings and costs $12.47. How much do you save by ordering this special combination instead of ordering eight
Courtney can run 100 m in 12.3 s. Marissa can run 100 yd in 11.2 s. Who runs faster? (There are 2.54 centimeters per inch, 12 inches per foot, and 3 feet per yard.)
Carl and Bethany roll a pair of dice 1000 times and keep track of the sum on the two dice. The frequency of each sum is listed below and shown in the
Rita and Noah survey 95 farmers in their county to see how many acres of sweet corn each farmer has planted. They summarize their results in a histogram.a. The distribution is skewed right. Explain what this means in terms of the data set. b. Graph the histogram on your calculator. c. Describe what
Describe a situation and sketch a histogram to reflect each condition named below. a. Mound-shaped and symmetric b. Skewed left c. Skewed right d. Rectangular
Ignacio kept a log of the amount of time he spent doing homework and watching television during 20 school days.a. Draw two box plots, one showing the amount of time spent doing homework, and one showing the amount of time watching television. Which distribution has the greater spread? b. Make an
At a large university, 1500 students took a final exam in chemistry. a. Frank learns that his score of 76 (out of 100) places him at the 88th percentile. How many students scored lower than Frank? How many scored higher? b. Mary scored 82, which placed her at the 95th percentile. Describe how
Traffic studies have shown that the best speed limit to post on a given road is the 85th percentile speed.Assume a road engineer collects these data to determine the speed limit on a local street.a. Draw a histogram for these data.b. Find the 85th percentile speed.c. What speed limit would you
Consider these box plots. Group A conducted the rubber band launch experiment 30 times, and Group B conducted the experiment 25 times.a. How many data values are represented in each whisker of each box plot?b. Which data set has the greater standard deviation? Explain how you know.c. Draw two
The Los Angeles Lakers won the 2002 National Basketball Association Championship. This table gives the total points scored by each player during that season.a. Find the mean, median, and mode for this data set. b. Find the five-number summary. c. Draw a box plot of the data. Describe the shape of
Invent two data sets, each with seven values, such that Set A has the greater standard deviation and Set B has the greater inter-quartile range.
The table below contains the recorded extreme temperatures, in degrees Fahrenheit, for each of the seven continents.a. Find the mean and standard deviation of the high temperatures. b. Find the mean and standard deviation of the low temperatures. c. Which temperatures, if any, are outliers in each
Below is a list of Academy Award winners in the Best Actress and Best Actor categories and each person's age when he or she received the award.a. Find the mean age and the median age for the Best Actress winners. b. Find the mean age and the median age for the Best Actor winners. c. On the same
Following the 1998 Academy Awards ceremony, Best Actress nominee Fernanda Montenegro (age 70) said Gwyneth Paltrow (age 26) had won Best Actress for Shakespeare in Love because she was younger. This comment caused Pace University student Michael Gilberg and professor Terence Hines to test the
The 2000 U.S. passenger-car production totals are shown at right. a. Make a box plot of these data. b. Make a histogram using a bin width that provides meaningful information about the data. c. Suppose a different year has a similar distribution but the total number of cars produced is 400 thousand
The calculation of mean that you learned in this chapter the sum of all data values divided by the number of values-is more precisely called the arithmetic mean. Other means include the geometric mean, the harmonic mean, the quadratic mean, the trimean, and the midmean. Research one or more of
In Lesson 2.3, you learned how to find the median of a data set by looking at a histogram. How would you use the histogram to approximate the mean? The mode?
Another measure of spread, the mean deviation, MD, uses absolute value to eliminate the effect of the different signs of the individual deviations.Try using mean deviation for some of the exercises in which you calculated standard deviation. How do the values compare? When might standard deviation
Consider the sequenceu0 = 18un = un-1 -3 where n ≥ 1a. Graph the sequence.b. What is the slope of the line that contains the points? How is that related to the common difference of the sequence?c. What is the y-intercept of the line that contains these points? How is it related to the sequence?d.
A gardener planted a new variety of ornamental grass and kept a record of its height over the first two weeks of growth.a. How much does the grass grow each day? b. Write an explicit formula that gives the height of the grass after n days. c. How long will it take for the grass to be 28 cm
An arithmetic sequence of six numbers begins with 7 and ends with 27. Follow 11a-c to find the four missing terms. a. Name two points on the graph of this sequence: (?, 7) and (?, 27). b. Plot the two points you named in 11a and find the slope of the line connecting the points. c. Use the slope to
If an object is dropped, it will fall a distance of about 16 feet during the first second. In each second that follows, the object falls about 32 feet farther than in the previous second. a. Write a recursive formula for the distance fallen each second under free fall. b. Find an explicit formula
Suppose a company offers a new employee a starting salary of $18,150 with annual raises of $1,000, or a starting salary of $17,900 with a raise of $500 every six months. At what point is one choice better than the other? Explain.
Suppose that you add 300 mL of water to an evaporating dish at the start of each day, and each day 40% of the water in the dish evaporates. a. Write and solve an equation that computes the long-run water level in the dish. b. Will a 1 L dish do the job? Explain why or why not.
Five stores in Tulsa, Oklahoma, sell the same model of a graphing calculator for $89.95, $93.49, $109.39, $93.49, and $97.69. a. What are the median price, the mean price, and the standard deviation? b. If these stores are representative of all stores in the Tulsa area, of what importance is it to
Use statistics software to make a histogram of this data set: 44, 45, 51, 40, 28, 46, 34, 19. a. Based on the histogram, predict what a box plot of the data will look like. b. Use the software to create a box plot of the data. Were your predictions accurate?
Refer to the graph at right.a. Write a recursive formula for the sequence. What is the common difference? What is the value of u0?b. What is the slope of the line through the points? What is the y-intercept?c. Write the equation of the line that contains these points.
Write the equation of the line that passes through the points of an arithmetic sequence with u0 = 7 and a common difference of 3.
Write a recursive formula for a sequence whose points lie on the line y = 6 - 0.5x.
Find the slope of each line. a. y = 2 + 1.7x b. y = x + 5 c. y = 12 - 4.5x d. y = 12
An arithmetic sequence has a starting term, u0, of 6.3 and a common difference of 2.5. a. Write an explicit formula for the sequence. b. Use the formula to figure out which term is 78.8.
Suppose you drive through Macon, Georgia, (which is 82 mi from Atlanta) on your way to Savannah, Georgia, at a steady 54 mi/h.a. What is your distance from Atlanta two hours after you leave Macon? b. Write an equation that represents your distance, y, from Atlanta x hours after leaving Macon. c.
APPLICATION Melissa and Roy both sell cars at the same dealership and have to meet the same profit goal each week. Last week, Roy sold only three cars, and he was below his goal by $2050. Melissa sold seven cars, and she beat her goal by $1550. Assume that the profit is approximately the same for
The points on this graph represent the first five terms of an arithmetic sequence. The height of each point is its distance from the x-axis, or the value of the y-coordinate of the point.a. Find u0, the y-coordinate of the point preceding those given. b. How many common differences (d's) do you
Find the slope of the line containing each pair of points. a. (3, -4) and (7, 2) b. (5, 3) and (2, 5) c. (-0.02, 3.2) and (0.08, -2.3)
This table shows how long it took to lay tile for hallways of different lengths.a. What is the independent variable? Why? Make a graph of the data. b. Find the slope of the line through these data. What is the real-world meaning of this slope? c. Which points did you use and why? d. Find the
The manager of a concert hall keeps data on the total number of tickets sold and total sales income, or revenue, for each event. Two different ticket prices are offered.a. Find the slope of a line approximating these data. What is the real-world meaning of this slope? b. Which points did you use
How much does air weigh? The following table gives the weight of a cubic foot of dry air at the same pressure at various temperatures in degrees Fahrenheit.a. Make a scatter plot of the data. b. What is the approximate slope of the line through the data? c. Describe the real-world meaning of the
Rewrite each expression by eliminating parentheses and then combining like terms. a. 2 + 3(x - 4) b. (11 - 3x) - 2(4x + 5) c. 5.1 - 2.7(1 - (2x + 9.7))
Solve each equation. a. 12 = 6 + 2(x - 1) b. 27 = 12 - 2(x + 2)
Charlotte and Emily measured the pulse rates of everyone in their class in beats per minute and collected this set of data. {62, 68, 68, 70, 74, 66, 82, 74, 76, 72, 70, 68, 80, 60, 84, 72, 66, 78, 70, 68, 66, 82, 76, 66, 66, 80} a. What is the mean pulse rate for the class? b. What is the standard
Each of these two graphs was generated by a recursive formula in the form u0 = a and un = (1 + r)un-1 + p where n ‰¥ 1. Describe the parameters a, r, and p that produce each graph. (There are two answers to 16b.)(a)(b)
Each of these graphs was produced by a linear equation in the form y = a + bx. For each case, tell if a and b are greater than zero, equal to zero, or less than zero.a.b. c. d.
Find the slope of each line. a. y = 3x - 2 b. y = 4.2 - 2.8x c. y = 5(3x - 3) + 2 d. y - 2.4x = 5 e. 4.7x + 3.2y = 12.9 f. 2 / 3 y = 2 / 3 x + 1 / 2
Solve each equation. a. Solve y = 4.7 + 3.2x for y if x = 3. b. Solve y = - 2.5 + 1.6x for x if y = 8. c. Solve y = a - 0.2x for a if x = 1000 and y = - 224. d. Solve y = 250 + bx for b if x = 960 and y = 10.
Find the equations of both lines in each graph.a.b.
Consider the equations and graphs of Exercise 4. a. What do the equations in 4a have in common? What do you notice about their graphs? b. What do the equations in 4b have in common? What do you notice about their graphs?
Use this graph to determine the speed of a balloon rocket. The independent variable is time in seconds, and the dependent variable is distance from the sensor in meters.
Layton measures the voltage across different numbers of batteries placed end to end. He records his data in a table.a. Let x represent the number of batteries, and let y represent the voltage. Find the slope of a line approximating these data. Be sure to include units with your answer. b. Which
This graph shows the relationship between the height of some high-rise buildings and the number of stories in those buildings. A line is drawn to fit the data.a. Estimate the slope. What is the meaning of the slope? b. Estimate the y-intercept. What is the meaning of the y-intercept? c. Explain why

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