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nature of mathematics

Questions and Answers of Nature Of Mathematics

Your test scores are \(78,95,87\), and 92. What score on the fifth exam will make your average score at least 80 ?
If the length of the semimajor axis of the orbit of Mars is \(1.4 \times 10^{8} \mathrm{mi}\) and the eccentricity is about 0.093 , determine the greatest and least distance of Mars from the sun.
For each number \(x\) in the domain, the corresponding range value \(y\) is found by adding 1 to the domain value and then dividing that result into 5 added to 5 times the domain value.
If the planet Mercury is 28 million miles from the sun at perihelion and the eccentricity of its orbit is about \(1 / 5\), how long is the major axis of Mercury's orbit?
"Look out! That old abandoned well is very dangerous, Huck. I think that it should be capped so that nobody could fall in and kill his self." "Ah, shucks, Tom, let's climb down and see how deep it
In archaeology, carbon-14 dating is a standard method of determining the age of certain artifacts. Decay rate can be measured by half-life, which is the time required for one-half of a substance to
The moon's orbit is elliptical, with the earth at one focus. The point at which the moon is farthest from the earth is called the apogee, and the point at which it is closest is called the perigee.
Rework Example 6 for an \(8 \%\) interest rate.Data from Example 6Suppose that you deposit \(\$ 100\) at \(10 \%\) interest. Graph the total amounts you will have if you invest your money at simple
You can rent a car for \(\$ 36 /\) day \(+65 \% /\) mile (option A) or a flat \(\$ 75 /\) day with unlimited miles (option B). For how many miles will option A be cheaper than option B?
It is estimated that \(t\) years from now, the population of a certain suburban community will be\[P(t)=20-\frac{6}{t+1}\]thousand people.a. What will the population of the community be 9 years from
The healing law for skin wounds states that\[A=\frac{A_{0}}{e^{0.1 t}}\]
Name and describe several different types of graphs.
Distinguish between a frequency distribution and a stem-and-leaf plot.
Write down what you think the following advertisement means:Nine out of ten dentists recommend Trident for their patients who chew gum.
Write down what you think the following advertisement means:Eight out of ten owners said their cats prefer Whiskas.
Consider the line graph shown in Figure 14.11.a. During which month did Herb incur the most expenses?b. During which month did Lisa incur the least expenses? Expenses ($) 400 300 200 100 J FMAM J
Consider the graph shown in Figure 14.12.Figure 14.12a. How many types of payments are tracked? Can you think of any other payments that might have been included? If so, why do you think they have
Consider the graph shown in Figure 14.13.Figure 14.13a. What is being illustrated in this graph?b. Did the United States have more imports or exports for the years 1990-2010? Billions of dollars 280
Consider the graph shown in Figure 14.14.Data from Figure 14.14a. What is being illustrated in this graph?b. Did the United States have more imports or exports for the years 1990-2010? Billions of
The amount of electricity used in a typical all-electric home is shown in the circle graph in Figure 14.15.If, in a certain month, a home used 1,100 kWh (kilowatt-hours), find the amounts of
At a well-known major university, the career choices of 1,500 graduates from an MS program are shown in Figure 14.16.Figure 14.16a. How many plan to get a job in a national laboratory?b. How many are
We will discuss scatter diagrams, which are used to study the relationship between two variables, such as the students' final exam score and final grade in Smith's Math 10 class (see Figure
we will discuss scatter diagrams, which are used to study the relationship between two variables, such as incomes from crops and livestock for selected states in the United States, as shown in Figure
Decide whether something is wrong with each of the graphs shown in Problems 13-17. Explain your reasoning.Consider the graph shown in Figure 14.19. Clearly, Anacin is better. ANACIN BUFFERED ASPIRIN
Decide whether something is wrong with each of the graphs shown in Problems 13-17. Explain your reasoning.Consider the graph shown in Figure 14.20. Chevy trucks are clearly better. 95% CHEVY FORD
Decide whether something is wrong with each of the graphs shown in Problems 13-17. Explain your reasoning.Consider the graph shown in Figure 14.21. The potential commercial forest growth, as compared
Decide whether something is wrong with each of the graphs shown in Problems 13-17. Explain your reasoning.Consider the graph shown in Figure 14.22. How much is "in the bank"? Conflicting estimates of
Decide whether something is wrong with each of the graphs shown in Problems 13-17. Explain your reasoning.The graph shown in Figure 14.23 was circulated throughout the mathematics department of a
When a person in California renews the registration for an automobile, the bar graph shown in Figure 14.24 is included with the bill.Use this bar graph to answer the questions in Problems 18-23. The
When a person in California renews the registration for an automobile, the bar graph shown in Figure 14.24 is included with the bill.Use this bar graph to answer the questions in Problems 18-23. The
When a person in California renews the registration for an automobile, the bar graph shown in Figure 14.24 is included with the bill.Use this bar graph to answer the questions in Problems 18-23. The
When a person in California renews the registration for an automobile, the bar graph shown in Figure 14.24 is included with the bill.Use this bar graph to answer the questions in Problems 18-23. The
When a person in California renews the registration for an automobile, the bar graph shown in Figure 14.24 is included with the bill.Use this bar graph to answer the questions in Problems 18-23. The
When a person in California renews the registration for an automobile, the bar graph shown in Figure 14.24 is included with the bill.Use this bar graph to answer the questions in Problems 18-23. The
Prepare a frequency distribution for each data set in Problems 24-27.Consider the following data sets:Data set A Data set A: The annual wages of employees at a small accounting firm are given in
Prepare a frequency distribution for each data set in Problems 24-27.Consider the following data sets:Data set B Data set A: The annual wages of employees at a small accounting firm are given in
Prepare a frequency distribution for each data set in Problems 24-27.Consider the following data sets:Data set \(C\) Data set A: The annual wages of employees at a small accounting firm are given in
Prepare a frequency distribution for each data set in Problems 24-27.Consider the following data sets:Data set D Data set A: The annual wages of employees at a small accounting firm are given in
Draw a stem-and-leaf plot for each data set in Problems 28-31.Data set A Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1 2 2 2
Draw a stem-and-leaf plot for each data set in Problems 28-31.Data set B Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1 2 2 2
Draw a stem-and-leaf plot for each data set in Problems 28-31.Data set C Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1 2 2 2
Draw a stem-and-leaf plot for each data set in Problems 28-31.Data set D Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1 2 2 2
Draw a bar graph for each data set in Problems 32-35.Data set \(\mathrm{A}\) Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1 2
Draw a bar graph for each data set in Problems 32-35.Data set B Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1 2 25 18 2 2
Draw a bar graph for each data set in Problems 32-35.Data set \(\mathrm{C}\) Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1 2
Draw a bar graph for each data set in Problems 32-35.Data set \(\mathrm{D}\) Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1 2
Draw a line graph for each data set in Problems 36-39.Data set A Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 25 16 25 25 14 18 1 2 2 2 Data
Draw a line graph for each data set in Problems 36-39.Data set B Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 25 16 25 25 14 18 1 2 2 2 Data
Draw a line graph for each data set in Problems 36-39.Data set \(\mathrm{C}\) Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 25 16 25 25 14 18
Draw a line graph for each data set in Problems 36-39.Data set D Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 25 16 25 25 14 18 1 2 2 2 Data
The amounts of time it takes for three leading pain relievers to reach a person's bloodstream are as follows: Brand A, 480 seconds; Brand B, 500 seconds; Brand C, 490 seconds.c. If you were an
The number of trucks from three automobile manufacturers that are still on the road 10 years after they are originally sold are Brand A, 98\%; Brand B, 97.5\%; Brand C, 96.4\%.c. If you were an
The financial report from a small college shows the following income:Draw a circle graph showing this income. Tuition Development Fund-raising Athletic Dept. Interest Tax subsidy TOTAL $1,388,000
The financial report from a small college shows the following expenses:Draw a circle graph showing this income. Salaries Academic Plant operations Student activities Athletic programs TOTAL
The national debt is of growing concern in the United States. It reached \$1 billion in 1916 during World War I and climbed to \(\$ 278\) billion by the end of World War II. It reached its first
Top Women on Wall Street Draw a pictograph to represent the following data on women in big Wall Street firms. In 1996, women comprised approximately \(11 \%\) of the top-tier executives. Regina
Using Figure 14.13 (Problem 7), what was the approximate balance of trade with Canada in 2010?Data from Problem 7Consider the graph shown in Figure 14.13.Figure 14.13a. What is being illustrated in
Using Figure 14.14 (Problem 8), what was the approximate balance of trade with Mexico in 2010?Data from Problem 8Consider the graph shown in Figure 14.14.Data from Figure 14.14a. What is being
Using Figure 14.12 (Problem 6), it looks like there is one time when the changes in payouts for three of the benefit programs are the same. What is that time? Data from Problem 6Consider the graph
Using Figure 14.12 (Problem 6), what is the total change in benefits at the time the recession ended, as compared with the previous year?Data from Problem 6Consider the graph shown in Figure
Using Figure 14.12 (Problem 6), what is the maximum difference in change in payout between benefit programs (as compared to a year ago)?Data from Problem 6Consider the graph shown in Figure
Using Figure 14.12 (Problem 6), when, and for what, were there no changes when compared to the previous year?Data from Problem 6Consider the graph shown in Figure 14.12.Figure 14.12a. How many types
What is the difference between the amount of money collected from Social Security and Medicare taxes and the amount paid out in 1992?Figure 14.25 The crunch to come... Social Security taxes were
How many workers pay into Social Security for each person getting benefits in 2020 ?Figure 14.25 The crunch to come... Social Security taxes were raised to build a surplus... Money paid into the
What are "baby boomers"?Figure 14.25 The crunch to come... Social Security taxes were raised to build a surplus... Money paid into the system has been greatly exceeding benefits since 1983. Scale in
When will the baby boomers break the bank?Figure 14.25 The crunch to come... Social Security taxes were raised to build a surplus... Money paid into the system has been greatly exceeding benefits
How much money is projected for the Social Security system for the year 2012?Figure 14.25 The crunch to come... Social Security taxes were raised to build a surplus... Money paid into the system has
There seems to be an error in one of the three line graphs. What is it?Figure 14.25 The crunch to come... Social Security taxes were raised to build a surplus... Money paid into the system has been
There seems to be an error in the pictograph. What is it?Figure 14.25 The crunch to come... Social Security taxes were raised to build a surplus... Money paid into the system has been greatly
Find the error in the Saab advertisement. There are two cars built in Sweden. Before you buy theirs, drive ours. When people who know cars think about Swedish cars, they think of them as being strong
The following advertisements (adapted from "Caveat Emptor" by Robert Leighton, Games, January 1988, p. 38) show some vastly overpriced items. Read between the lines and identify the item each ad is
What do we mean by average?
What is a measure of central tendency?
What is a measure of dispersion?
Compare and contrast mean, median, and mode.
A professor gives five exams. Two students' scores have the same mean, although one student did better on all the tests except one. Give an example of such scores.
A professor gives six exams. Two students' scores have the same mean, although one student's scores have a small standard deviation and the other student's scores have a large standard deviation.
Comment on the following quotation, which was printed in the May 28, 1989, issue of The Community, Technical, and Junior College TIMES: "Half the American students are below average."
Comment on the following quotation: "I just received my SAT scores and I scored in the 78th percentile in English, and 50th percentile in math."
Is the standard deviation always smaller than the variance?
Suppose that a variance is zero. What can you say about the data? The data values are all the same.
In Problems 11-18, find the three measures of central tendency (the mean, median, and mode).1, 2, 3, 4, 5
In Problems 11-18, find the three measures of central tendency (the mean, median, and mode).\(17,18,19,20,21\)
In Problems 11-18, find the three measures of central tendency (the mean, median, and mode).\(103,104,105,106,107 \)
In Problems 11-18, find the three measures of central tendency (the mean, median, and mode).\(765,766,767,768,769\)
In Problems 11-18, find the three measures of central tendency (the mean, median, and mode).\(79,90,95,95,96 \)
In Problems 11-18, find the three measures of central tendency (the mean, median, and mode).\(70,81,95,79,85 \)
In Problems 11-18, find the three measures of central tendency (the mean, median, and mode).\(1,2,3,3,3,4,5\)
In Problems 11-18, find the three measures of central tendency (the mean, median, and mode).\(0,1,1,2,3,4,16,21 \)
Create a box plot for the data given in Problems 19-22.\(3,5,8,13,21\)
Create a box plot for the data given in Problems 19-22.\(1,4,9,16,25\)
Create a box plot for the data given in Problems 19-22.\(12,19,23,23,24,32,32,34,34,36,43,45,47\),
Create a box plot for the data given in Problems 19-22.\(18,27,34,52,54,59,61,68,78,82,85,87,91\),
In Problems 23-30, find the range and the standard deviation (correct to two decimal places). If you do not have a calculator, find the range and the variance.\(1,2,3,4,5 \)
In Problems 23-30, find the range and the standard deviation (correct to two decimal places). If you do not have a calculator, find the range and the variance.\(17,18,19,20,21 \)
In Problems 23-30, find the range and the standard deviation (correct to two decimal places). If you do not have a calculator, find the range and the variance.\(103,104,105,106,107 \)
In Problems 23-30, find the range and the standard deviation (correct to two decimal places). If you do not have a calculator, find the range and the variance.\(765,766,767,768,769 \)
In Problems 23-30, find the range and the standard deviation (correct to two decimal places). If you do not have a calculator, find the range and the variance.\(79,90,95,95,96 \)
In Problems 23-30, find the range and the standard deviation (correct to two decimal places). If you do not have a calculator, find the range and the variance.\(70,81,95,79,85 \)
In Problems 23-30, find the range and the standard deviation (correct to two decimal places). If you do not have a calculator, find the range and the variance.\(1,2,3,3,3,4,5 \)

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