Mat205 Quantitative Explorations In Everyday Life In Your Wo

Mat205 Quantitative Explorations In Everyday Life In Your World Week

Assume you are visiting Canada, and driving along the highway. You need to maintain the speed limit on the road. Answer the following questions: • What units are used to express Canadian speed limits? • Convert the Canadian speed limit of 60 to American units. Then, find at least two Canadian news articles that involve numerical data and units different from speed limit units. What are the equivalent American units? Convert any of the Canadian units that you found in the news to the equivalent American unit. Number 2 Complete problem 84 on page 88 of your course textbook. Number 3 Read the following news article: OMG, the Water’s Warm! NASA Study Solves Glacier Puzzle. The article uses all sorts of metric and non-metric units. Use your mathematical abilities to show the following equivalencies: • 2.5 miles is equivalent to 4 km • 2000 feet is equivalent to 610 meters • 33 degrees Fahrenheit is 0.5 degrees Celsius. Then answer the following questions: • How did the news article affect you? • What will be the consequences, globally and locally on human lives, of the event mentioned in the article? Number 4 Complete problem 101 on page 107 of your course textbook. Number 5 Suppose you decide to drive across the country which is roughly a distance of 3000 miles. Compute the answer to the following questions: • How much energy will be required to drive the distance using an electric powered car? • How much money will you spend on energy for the electric-powered car? • How much energy will be required by a gasoline-powered car? • How much money will you spend on energy for the gasoline-powered one? Then, identify the cheaper option and describe the advantages and disadvantages of gasoline-powered and electric-powered cars. Number 6 Complete problem 103 on page 107 of your course textbook. MAT205: Quantitative Explorations in Everyday Life Number 7 Read the Scientists Agree: Global Warming is Happening and Humans are the Primary Cause post. The article identifies the following percent-values on human caused global warming. Convert these values into fractions. • Oreskes 2004 – 100% • Doran 2009 – 97% • Anderegg – 2010 – 97% • Cook 2013 – 97% • Verheggen 2014 – 91% • Stenhouse 2014 – 93% • Carlton 2015 – 97% Identify how these various percent-values (above) are used: either as a fraction to describe change or for comparison. Explain your claim. Calculate the percentage change of Americans who “worry a great deal” based on the Gallup Poll from 2017. Number 8 Complete problem 77 on page 155 of your course textbook. Number 9 Read the article: These are the Biggest Numbers in the Universe. Then, make a list of all the large numbers mentioned in the article, and write down those numbers mathematically. For example, if ten thousand is mentioned in the article, then you will write down: Ten thousand and in mathematical notation it is 10,000 Number 10 What is the law of large numbers? How is that law used in the article Confronting a Law of Limits? Number 11 Complete problem 79 on page 155 of your course textbook. Number 12 Complete problem 80 on page 155 of your course textbook. Number 13 Assume that the US Government has projected that it will have a deficit of $438 billion. But, in reality, the actual deficit is $587 billion. Describe the size of the error in terms of both absolute error and relative error. Describe any uncertainty that might be associated with these numbers. Number 14 The United Nations Development Program regularly releases its Human Development Report. A closely watched finding of this report is the Human Development Index (HDI) which measures the overall achievements of a country in three basic dimensions of human development: life expectancy, educational attainment, and adjusted income. Go to the Human Development Index (HDI) website to find all the report data and understand all the indices and answer the following questions: • How is HDI defined and computed? (b). What is the percent change in the United States’ indices from 1990 to 2015? • Locate the US indices for Education, Gender, Sustainability, and Health. Compare the indices to a country whose indices are better than those of the US and to a country whose indices are worse than those of the US. All your answers should be in percentages. Number 15 Complete problem 30 on page 188 of your course textbook.

Paper For Above instruction

Introduction

Quantitative explorations play a vital role in understanding and interpreting various aspects of daily life, from travel and environment to global statistics and economic data. This paper addresses multiple real-world scenarios that involve measurement units, data conversion, mathematical equivalencies, errors, and statistical interpretations, emphasizing the importance of quantitative literacy in making informed decisions and understanding the world better.

Speed Limits and Unit Conversions in Canada and the USA

Canadian speed limits are primarily expressed in kilometers per hour (km/h). To convert the Canadian speed limit of 60 km/h into American units, we use the conversion factor: 1 mile = 1.60934 kilometers. Thus, 60 km/h is approximately equivalent to 37.28 miles per hour (mph). This conversion highlights the difference in measurement systems used in Canada and the United States. Additionally, recent Canadian news articles involving numerical data in units such as meters, kilometers, or temperature may also require conversion to American units (for example, miles, feet, Fahrenheit). For example, a Canadian article mentioning a temperature of -10°C could be converted to approximately 14°F, indicating the importance of understanding different units for interpretation of data across regions.

Mathematical Equivalencies in Climate Data

Examining climate data and reports often involves conversions between metric and imperial units. For instance, 2.5 miles is equivalent to 4 km, 2000 feet to approximately 610 meters, and 33°F to about 0.5°C. These equivalencies demonstrate how temperature and distance are related across measurement systems. The article about NASA's glacier study highlighted the impact of warming temperatures, making these conversions crucial for understanding the severity of climate change effects. The global and local consequences include rising sea levels, loss of habitats, and increased frequency of extreme weather events, directly affecting human lives and ecosystems (Hansen et al., 2016).

Energy, Cost Calculations, and Vehicle Comparison

Driving across the country covering roughly 3000 miles involves significant energy consumption. Electric vehicles (EVs) and gasoline-powered cars differ substantially in energy requirements and costs. Assuming an electric car consumes about 0.3 kWh per mile, the total energy needed would be approximately 900 kWh. If the average electricity cost is $0.13 per kWh, the total cost would be around $117. For a gasoline vehicle averaging 25 miles per gallon, the total fuel consumption would be 120 gallons, costing approximately $360 at an average price of $3 per gallon. The electric car is more economical and environmentally friendly, but it depends on available charging infrastructure and battery technology, while gasoline vehicles offer longer range and established fueling networks (Faria et al., 2013).

Global Warming and Percentage Data

The reports on human impact on global warming provide percentage values such as 100% (Oreskes, 2004), 97% (Doran, 2009; Anderegg, 2010; Cook, 2013; Carlton, 2015), 91% (Verheggen, 2014), and 93% (Stenhouse, 2014). Converting these percentages into fractions entails dividing by 100, e.g., 97% to 97/100. These fractions are used in scientific discussions to evaluate consensus, express change, or compare proportions. For instance, the high consensus percentages reinforce the notion that human activities significantly contribute to global warming. The percentage change in Americans who worry "a great deal" from 2017 could be computed using survey data, which typically indicates shifts in public concern over climate change or other issues (Gallup, 2017).

Large Numbers and the Law of Large Numbers

The article "Biggest Numbers in the Universe" mentions large numbers such as a googol (10^100) and a googolplex (10^(10^100)). These are expressed in exponential notation, illustrating incredibly large quantities beyond everyday comprehension. The law of large numbers, a fundamental principle in probability theory, states that as the number of trials increases, the average of the results tends to converge to the expected value. In the context of the article, this law suggests that with enough observations, scientific measurements and theoretical predictions become more accurate and reliable (Ross, 2010).

Error Analysis in Economic Projections

The projected US deficit of $438 billion compared to an actual deficit of $587 billion involves an absolute error of $149 billion and a relative error of approximately 34%. Absolute error is calculated as the absolute difference: |587 - 438| = 149 billion, while relative error is (|actual - projected| / projected) 100% = (149 / 438) 100% ≈ 34%. Such discrepancies highlight uncertainties in economic forecasting due to unforeseen factors, policy changes, or economic shocks (Reifschneider & Tetlow, 2020).

Human Development Index (HDI) and Its Significance

The Human Development Index (HDI) measures a country's progress in health, education, and income. It is computed by aggregating normalized indicators of life expectancy, mean years of schooling, expected years of schooling, and gross national income per capita, usually combined into a geometric mean. From 1990 to 2015, the US experienced percentage improvements across these indices. When comparing the US to other countries with higher or lower indices, such as Norway (higher) or Niger (lower), differences in percentages highlight disparities in development (United Nations Development Programme, 2016). These metrics provide insight into global inequalities and development priorities.

Conclusion

Quantitative explorations are essential for interpreting data, understanding global issues, and making informed decisions. From converting measurement units to analyzing errors and studying international development metrics, mathematical literacy enhances our comprehension of the complex world we live in. Developing competence in these areas equips individuals and policymakers to address environmental, economic, and social challenges effectively.

References

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• United Nations Development Programme. (2016). Human Development Report 2016. UNDP. Retrieved from http://hdr.undp.org
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