Math 285 Quiz One Name: ________________ 1. The product of these two matrices 5 2 2 −1  4 −2 1 3  is (Please show your work for full credit.) 2. For what value of a is this determinant equal to 0? 0 5 2 0 1 −8 −4 2 (please justify your answer.) 3. What is the product of these matrices? 3 2 6 −2 1 0 4 1 0   2346  (Please justify your answer.) 4. What is the largest possible number of pivots a 7 × 5 matrix can have? (Please justify your answer.) Homework 1 5. Find the standard matrix of the linear transformation : →  which rotates a point about the origin through an angle of   radians (counterclockwise). True or False (Simply enter T or F, no need to justify the answer) If matrices  and  are row equivalent, they have the same reduced echelon form. In general,  +  ≠  +  (assume  and  are  x  matrices). If a matrix  is symmetric, then so is  + “#. A matrix  must be a square matrix to be invertible. If $%&’( ≠ 0, then columns of  are linearly independent. If an  x  matrix  is equivalent to “#, then )* is also equivalent to “#. If an + x  matrix  has a pivot position in every row, then the equation , = . has a unique solution for each . in /0. If  = “, then  is invertible.

Math 285 Quiz One Name: ________________ 1. The product of these two matrices 5 2 2 −1  4 −2 1 3  is (Please show your work for full credit.) 2. For what value of a is this determinant equal to 0? 0 5 2 0 1 −8 −4 2 (please justify your answer.) 3. What is the product of these matrices? 3 2 6 −2 1 0 4 1 0   2346  (Please justify your answer.) 4. What is the largest possible number of pivots a 7 × 5 matrix can have? (Please justify your answer.) Homework 1 5. Find the standard matrix of the linear transformation : →  which rotates a point about the origin through an angle of   radians (counterclockwise). True or False (Simply enter T or F, no need to justify the answer) If matrices  and  are row equivalent, they have the same reduced echelon form. In general,  +  ≠  +  (assume  and  are  x  matrices). If a matrix  is symmetric, then so is  + “#. A matrix  must be a square matrix to be invertible. If $%&’( ≠ 0, then columns of  are linearly independent. If an  x  matrix  is equivalent to “#, then )* is also equivalent to “#. If an + x  matrix  has a pivot position in every row, then the equation , = . has a unique solution for each . in /0. If  = “, then  is invertible.

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Lab on Confidence Intervals The story: Studies have shown that the random variable X, the processing time required to do a multiplication on a new 3-D computer, is normally distributed with mean and standard deviation 2 microseconds. A random sample of 16 observations is to be taken (i.e. 16 random multiplications will be performed and the time that it takes to perform each one of them will be annotated). The sample mean will be calculated. Part 1- The very basics 1. Before we collect the random sample, what can we say about the sampling distribution of ? 2. Before we collect the random sample, what is the probability that the sample mean will have a value that is greater than or equal to , and less than or equal to In other words, what is the probability that the sample mean is within 0.98 microseconds ( ) of the true (unknown) mean time? 3. A random sample was taken (i.e.16 multiplications were done) and the processing times were as follows: 42.65 45.15 39.32 44.44 41.63 41.54 41.59 45.68 46.50 41.35 44.37 40.27 43.87 43.79 43.28 40.70 Round the times to the nearest tenth (e.g. 42.65 ~ 42.6) and do the stem-and-leave display Do the stem and leaf display. Calculate the sample mean 39 40 41 42 43 44 45 46 4. Now we will use our knowledge of the value of the sample mean for this particular sample and the relationship between sample means (in general) and population mean (see questions 1 and 2 of this lab) to make an intelligent guess (estimation) of the population mean. Use the formula to calculate a 95 % confidence interval for the population mean (Show your work) ( , ) From the Minitab menu, use STAT>BASIC STATISTIC>ONE SAMPLE Z to check your calculations. Calculate the width of the confidence interval _______________ 5. Interpret the confidence interval you just found: We are 95% confident that the true mean processing time required to do a multiplication on a new 3-D computer lies between __________ and __________ microseconds. (The meaning of this is the following: Think of all the possible samples (all the possible sets of 16 multiplications) that we could have been done with this type of computer; 95% of those samples would have produced confidence intervals that contain the true mean, the other 5% would have been off)

Lab on Confidence Intervals The story: Studies have shown that the random variable X, the processing time required to do a multiplication on a new 3-D computer, is normally distributed with mean and standard deviation 2 microseconds. A random sample of 16 observations is to be taken (i.e. 16 random multiplications will be performed and the time that it takes to perform each one of them will be annotated). The sample mean will be calculated. Part 1- The very basics 1. Before we collect the random sample, what can we say about the sampling distribution of ? 2. Before we collect the random sample, what is the probability that the sample mean will have a value that is greater than or equal to , and less than or equal to In other words, what is the probability that the sample mean is within 0.98 microseconds ( ) of the true (unknown) mean time? 3. A random sample was taken (i.e.16 multiplications were done) and the processing times were as follows: 42.65 45.15 39.32 44.44 41.63 41.54 41.59 45.68 46.50 41.35 44.37 40.27 43.87 43.79 43.28 40.70 Round the times to the nearest tenth (e.g. 42.65 ~ 42.6) and do the stem-and-leave display Do the stem and leaf display. Calculate the sample mean 39 40 41 42 43 44 45 46 4. Now we will use our knowledge of the value of the sample mean for this particular sample and the relationship between sample means (in general) and population mean (see questions 1 and 2 of this lab) to make an intelligent guess (estimation) of the population mean. Use the formula to calculate a 95 % confidence interval for the population mean (Show your work) ( , ) From the Minitab menu, use STAT>BASIC STATISTIC>ONE SAMPLE Z to check your calculations. Calculate the width of the confidence interval _______________ 5. Interpret the confidence interval you just found: We are 95% confident that the true mean processing time required to do a multiplication on a new 3-D computer lies between __________ and __________ microseconds. (The meaning of this is the following: Think of all the possible samples (all the possible sets of 16 multiplications) that we could have been done with this type of computer; 95% of those samples would have produced confidence intervals that contain the true mean, the other 5% would have been off)

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MAE 384: Advanced Mathematical Methods for Engineers Spring 2015 Homework #8 Due: Wednesday, April 8, in or before class. Note: Problems 2 (extra credit) and 3 have to be solved by hand. Problems 1 and 5 require MATLAB. The item 1(a) must be shown by hand. Problem 4 can be done either in Matlab or by hand. 1. Consider the following ODE: d y d x = ?8 y with y(0) = 3 on 0 < x < 5, (a) Calculate the largest step size required to maintain stability of the numerical solution to this equation using explicit Euler method. (b) Choose a step size two times smaller than this value. Solve the ODE with explicit Euler method using this step size. (c) Choose a step size two times larger than this value. Solve the ODE with explicit Euler method using this step size. (d) Now repeat parts (b) and (c) with implicit Euler method. (e) Plot all the solutions, including the analytical solution to this problem, on the same plot. Discuss your results. 2. Extra credit. Investigate the stability of the following numerical schemes on the example of an ODE d y d x = ? y with > 0. Show whether the scheme is conditionally or unconditionally stable. Derive the stability threshold if the scheme is conditionally stable. (a) The semi-implicit trapezoidal method: yi+1 = yi + 1 2 (f(xi; yi) + f(xi+1; yi+1)) h (b) The explicit midpoint method: yi+1 = yi + f  xi+1=2; yi + f(xi; yi) h 2  h 3. Solve Problem 25.1 from the textbook with third-order Runge-Kutta (page 734) and fourth-order Runge Kutta (page 735) methods with h = 0:5. Plot your results on the same plot. Also, include results from (a),(b),(c) from the two previous homeworks, on the same plot. 4. Solve Problem 25.2 from the textbook with third-order Runge-Kutta (page 734) and fourth-order Runge Kutta (page 735) methods with h = 0:25. Plot your results on the same plot. Also, include results from (a),(b),(c) from the two previous homeworks, on the same plot. There is a typo in this problem. The interval should be from t=0 to 1, not x=0 to 1. 5. For the following rst-order ODE d y d t = t2 ? 2 y t with y(1) = 2, the purpose will be to write MATLAB functions that solve this equation from t = 1 to t = 4 with 1 of 2 MAE 384: Advanced Mathematical Methods for Engineers Spring 2015 (a) Third-order Runge-Kutta (page 734) (b) Fourth-order Runge-Kutta (page 735) For each method, (a) Write the MATLAB function that solves the ODE by using the number of intervals N as an input argument. (b) Solve the ODE using your MATLAB function for N equal to 8, 16, 32, 64. Calculate the step size h inside the function. (c) Calculate the EL2 errors between the true solution and the numerical solution for each N (consult HW6 for the true solution). The following plots should be presented: 1. Plot your solutions for the methods (a), (b), along with the analytical solution, explicit Euler solution from HW6, and solutions to problem 5 (a) – (c) from HW7, on the same plot for N = 8. Do not print out the values at your grid points. 2. Plot your solutions for the methods (a), (b), along with the analytical solution, explicit Euler solution from HW6, and solutions to problem 5 (a) – (c) from HW7, on the same plot for N = 32. Do not print out the values at your grid points. 3. Plot the values of EL2 errors for the methods (a), (b), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of h, on the same plot. What do you observe? 4. Plot the values of EL2 errors for all the methods (a)-(c), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of h, on the same plot, but in log-log scale. Discuss how you can estimate the order of convergence for each method from this plot. Estimate the order of convergence for each method. 5. Plot the values of EL2 errors for all the methods (a)-(c), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of N, on the same plot, but in log-log scale. Discuss how you can estimate the order of convergence for each method from this plot. Estimate the order of convergence for each method. 6. Discuss whether your convergence results for each method correspond to the known order of accuracy for each method. Explain why or why not. 2 of 2

MAE 384: Advanced Mathematical Methods for Engineers Spring 2015 Homework #8 Due: Wednesday, April 8, in or before class. Note: Problems 2 (extra credit) and 3 have to be solved by hand. Problems 1 and 5 require MATLAB. The item 1(a) must be shown by hand. Problem 4 can be done either in Matlab or by hand. 1. Consider the following ODE: d y d x = ?8 y with y(0) = 3 on 0 < x < 5, (a) Calculate the largest step size required to maintain stability of the numerical solution to this equation using explicit Euler method. (b) Choose a step size two times smaller than this value. Solve the ODE with explicit Euler method using this step size. (c) Choose a step size two times larger than this value. Solve the ODE with explicit Euler method using this step size. (d) Now repeat parts (b) and (c) with implicit Euler method. (e) Plot all the solutions, including the analytical solution to this problem, on the same plot. Discuss your results. 2. Extra credit. Investigate the stability of the following numerical schemes on the example of an ODE d y d x = ? y with > 0. Show whether the scheme is conditionally or unconditionally stable. Derive the stability threshold if the scheme is conditionally stable. (a) The semi-implicit trapezoidal method: yi+1 = yi + 1 2 (f(xi; yi) + f(xi+1; yi+1)) h (b) The explicit midpoint method: yi+1 = yi + f  xi+1=2; yi + f(xi; yi) h 2  h 3. Solve Problem 25.1 from the textbook with third-order Runge-Kutta (page 734) and fourth-order Runge Kutta (page 735) methods with h = 0:5. Plot your results on the same plot. Also, include results from (a),(b),(c) from the two previous homeworks, on the same plot. 4. Solve Problem 25.2 from the textbook with third-order Runge-Kutta (page 734) and fourth-order Runge Kutta (page 735) methods with h = 0:25. Plot your results on the same plot. Also, include results from (a),(b),(c) from the two previous homeworks, on the same plot. There is a typo in this problem. The interval should be from t=0 to 1, not x=0 to 1. 5. For the following rst-order ODE d y d t = t2 ? 2 y t with y(1) = 2, the purpose will be to write MATLAB functions that solve this equation from t = 1 to t = 4 with 1 of 2 MAE 384: Advanced Mathematical Methods for Engineers Spring 2015 (a) Third-order Runge-Kutta (page 734) (b) Fourth-order Runge-Kutta (page 735) For each method, (a) Write the MATLAB function that solves the ODE by using the number of intervals N as an input argument. (b) Solve the ODE using your MATLAB function for N equal to 8, 16, 32, 64. Calculate the step size h inside the function. (c) Calculate the EL2 errors between the true solution and the numerical solution for each N (consult HW6 for the true solution). The following plots should be presented: 1. Plot your solutions for the methods (a), (b), along with the analytical solution, explicit Euler solution from HW6, and solutions to problem 5 (a) – (c) from HW7, on the same plot for N = 8. Do not print out the values at your grid points. 2. Plot your solutions for the methods (a), (b), along with the analytical solution, explicit Euler solution from HW6, and solutions to problem 5 (a) – (c) from HW7, on the same plot for N = 32. Do not print out the values at your grid points. 3. Plot the values of EL2 errors for the methods (a), (b), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of h, on the same plot. What do you observe? 4. Plot the values of EL2 errors for all the methods (a)-(c), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of h, on the same plot, but in log-log scale. Discuss how you can estimate the order of convergence for each method from this plot. Estimate the order of convergence for each method. 5. Plot the values of EL2 errors for all the methods (a)-(c), as well as for the explicit Euler method from HW6, and solutions to problem 5 (a) – (c) from HW7, as a function of N, on the same plot, but in log-log scale. Discuss how you can estimate the order of convergence for each method from this plot. Estimate the order of convergence for each method. 6. Discuss whether your convergence results for each method correspond to the known order of accuracy for each method. Explain why or why not. 2 of 2

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Chapter 07 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 7 Reading Quiz Question 17 Part A A lake is currently at high pool, with the same amount of water flowing into the lake as is flowing over the spillway. Which of the following temporary changes would increase the resident time of water in this lake? ANSWER: Chapter 7 Reading Quiz Question 16 Part A A large reservoir behind a dam is rapidly rising, as rain and melting snow add more water than is being released out of the dam’s spillway. In this situation, _____. ANSWER: Chapter 7 Reading Quiz Question 1 Part A Which one of the following statements is correct? ANSWER: Double the rate of water flow into the lake and double the rate of water flow out of the lake, while keeping the lake at the same level. Keep the inflow into the lake the same, but release twice as much water from the lake, resulting in a lowering of the lake level. Decrease the inflow into the lake by half, and decrease the outflow of the lake by half. None of the choices would increase the resident time in the lake. the net flux is positive and the capital of water within the reservoir is decreasing the net flux is positive and the capital of water within the reservoir is increasing the net flux is negative and the capital of water within the reservoir is increasing the net flux is negative and the capital of water within the reservoir is decreasing Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 18 Part A A raging river cascades down a granite mountain and eventually reaches the ocean. At the mouth of the river is a beautiful sandy beach composed of fine grains of granite particles from the river. The entire process of producing this sand is a result of _____. ANSWER: Chapter 7 Reading Quiz Question 4 Part A The physical and chemical properties of soils are primarily determined by _____. ANSWER: Chapter 7 Reading Quiz Question 19 Part A Several inches of rain fall over a field of tall corn, soaking into the soil and draining into ditches. Within an hour, there is no standing water and the humidity over the field rises quickly. At a nearby shopping mall, the rainwater fell onto blacktop and drained to sewer pipes, which carried the water directly into a stream. Which of the following occurred in The cycling time of an element or molecule in an ecosystem is equal to the sum of all the flux times. The cycling time is how long it takes an element or molecule to pass through a biogeochemical cycle. The cycling time of water moving through an ecosystem is typically shorter than the resident time in any pool in this system. The amount of time that water spends in an ocean is the cycling time. mineral evaporation erosion, weathering, transport, and then deposition erosion, dissolution, and precipitation organisms consuming and eroding granite the properties of rock from which the soils develop the amount of precipitation that the soil experiences the range of temperatures that the soil experiences the types of animals that live and move through the soils Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 8 5/21/2014 8:01 PM the cornfield but not in the parking lot? ANSWER: Chapter 7 Reading Quiz Question 6 Part A Most of the water on Earth is found in _____. ANSWER: Chapter 7 Reading Quiz Question 5 Part A Which one of the following primarily results from the effects of solar energy? ANSWER: Chapter 7 Reading Quiz Question 20 Part A A rural Minnesota farmer grows a variety of vegetables to feed her family. In addition, she cuts down some of her dead trees for firewood to heat her home in the winter. This farmer is adding to the flux of the carbon cycle in her region by _____. precipitation evaporation runoff transpiration the polar ice caps lakes and streams aquifers the oceans evaporation of water from a lake the formation of ice on the top of a pond movement of ocean tides the movement of water over a waterfall Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 8 5/21/2014 8:01 PM ANSWER: Chapter 7 Reading Quiz Question 8 Part A In a terrestrial ecosystem, most carbon is stored in the biomass of _____. ANSWER: Chapter 7 Reading Quiz Question 7 Part A In which of the following countries would we expect that the terrestrial ecosystems have the highest net primary production and biomass? ANSWER: Chapter 7 Reading Quiz Question 22 Part A Some farmers in the Midwest of the United States rotate their crops from year to year, switching from soybeans to corn on the same fields. What is one of the advantages of doing this? encouraging photosynthesis as she raises crops burning carbon-based fuels by consuming vegetables grown on her farm All of the choices are correct. the animals living there air the top layers of soil containing dead organisms living plants China Australia Brazil United States Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 8 5/21/2014 8:01 PM ANSWER: Chapter 7 Reading Quiz Question 10 Part A Most nitrogen enters the biosphere through the process of _____ ANSWER: Chapter 7 Reading Quiz Question 9 Part A Where do we expect to find the least amount of nitrogen? ANSWER: Chapter 7 Reading Quiz Question 12 Part A Along the west coast of the United States, upwellings bring deep ocean waters to the surface, carrying with them _____, which greatly increases NPP. ANSWER: The corn crop benefits from reactive nitrogen added to the soil by the soybean crop. Both crops require the same fertilizing supplies, so farmers save by buying fertilizer in bulk. Soybeans add large amounts of carbon dioxide to the soil, which helps the corn crop. Corn adds large amounts of phosphorus to the soil, which helps the soybean crop. nitrogen fixation in which bacteria convert N2 to NH3 cellular respiration, in which animals convert N2 to NH4 fermentation in which bacteria convert N2 to HNO3 photosynthesis, in which plants convert N2 to NO2 in Earth’s crust in plants in animals in the atmosphere Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 11 Part A Which one of the following statements about the carbon, phosphorus, and nitrogen cycles is true? ANSWER: Chapter 7 Reading Quiz Question 24 Part A A large coal-burning power plant is about 50 miles upwind from a lake that used to be popular for fishing. But now, just five years after the plant was constructed, the fish populations are decreasing dramatically. Which one of the following impacts of this coal-burning power plant is most likely hurting the fish populations in this downwind lake? ANSWER: Chapter 7 Reading Quiz Question 14 Part A Which one of the following statements about sulfur is correct? ANSWER: oxygen phosphate carbon sulfur Phosphorus is virtually absent in the atmosphere. The major source of carbon used by plants is the soil. Bacteria drive the phosphorus cycle. The major source of nitrogen used by plants is the air. insufficient sunlight reaching the lake low oxygen levels from burning fossil fuels eutrophication of the lake acidification of the lake Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 13 Part A Nitrogen and sulfur are important to all organisms because they are important constituents of _____. ANSWER: Chapter 7 Reading Quiz Question 25 Part A In Iowa, a small, deep lake in the summer becomes stratified with warmer, less-dense water at the surface and colder, denser water near the bottom. As fall air temperatures decrease, the surface water cools and then drops toward the bottom, mixing the lake levels together. As a result of this mixing, _____. ANSWER: Chapter 7 Reading Quiz Question 15 Part A A fire spreads across hundreds of acres of prairie, burning most of the plant parts above the ground. Compared to before the fire, right after this fire the pool of nutrients in the prairie plants _____. The main pool of sulfur is in the atmosphere where the flux is high and the residence time is long. The main pool of sulfur is in rocks. The flux of sulfur through the atmosphere is high and the residence is short. The main pool of sulfur is in the atmosphere where the flux is low and the residence time is long. The main pool of sulfur is in rocks. The flux of sulfur through the atmosphere is low and the residence is short. nucleic acids glucose phosphates some amino acids nitrogen and phosphorus are added to the lake nitrogen and phosphorus decrease near the surface of the lake nitrogen and phosphorus increase near the surface of the lake None of the choices is correct. Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 8 5/21/2014 8:01 PM ANSWER: Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 21 points. and the soil decreases increases and the pool of nutrients in the soil decreases and the soil increases decreases and the pool of nutrients in the soil increases Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 8 5/21/2014 8:01 PM

Chapter 07 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 7 Reading Quiz Question 17 Part A A lake is currently at high pool, with the same amount of water flowing into the lake as is flowing over the spillway. Which of the following temporary changes would increase the resident time of water in this lake? ANSWER: Chapter 7 Reading Quiz Question 16 Part A A large reservoir behind a dam is rapidly rising, as rain and melting snow add more water than is being released out of the dam’s spillway. In this situation, _____. ANSWER: Chapter 7 Reading Quiz Question 1 Part A Which one of the following statements is correct? ANSWER: Double the rate of water flow into the lake and double the rate of water flow out of the lake, while keeping the lake at the same level. Keep the inflow into the lake the same, but release twice as much water from the lake, resulting in a lowering of the lake level. Decrease the inflow into the lake by half, and decrease the outflow of the lake by half. None of the choices would increase the resident time in the lake. the net flux is positive and the capital of water within the reservoir is decreasing the net flux is positive and the capital of water within the reservoir is increasing the net flux is negative and the capital of water within the reservoir is increasing the net flux is negative and the capital of water within the reservoir is decreasing Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 18 Part A A raging river cascades down a granite mountain and eventually reaches the ocean. At the mouth of the river is a beautiful sandy beach composed of fine grains of granite particles from the river. The entire process of producing this sand is a result of _____. ANSWER: Chapter 7 Reading Quiz Question 4 Part A The physical and chemical properties of soils are primarily determined by _____. ANSWER: Chapter 7 Reading Quiz Question 19 Part A Several inches of rain fall over a field of tall corn, soaking into the soil and draining into ditches. Within an hour, there is no standing water and the humidity over the field rises quickly. At a nearby shopping mall, the rainwater fell onto blacktop and drained to sewer pipes, which carried the water directly into a stream. Which of the following occurred in The cycling time of an element or molecule in an ecosystem is equal to the sum of all the flux times. The cycling time is how long it takes an element or molecule to pass through a biogeochemical cycle. The cycling time of water moving through an ecosystem is typically shorter than the resident time in any pool in this system. The amount of time that water spends in an ocean is the cycling time. mineral evaporation erosion, weathering, transport, and then deposition erosion, dissolution, and precipitation organisms consuming and eroding granite the properties of rock from which the soils develop the amount of precipitation that the soil experiences the range of temperatures that the soil experiences the types of animals that live and move through the soils Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 8 5/21/2014 8:01 PM the cornfield but not in the parking lot? ANSWER: Chapter 7 Reading Quiz Question 6 Part A Most of the water on Earth is found in _____. ANSWER: Chapter 7 Reading Quiz Question 5 Part A Which one of the following primarily results from the effects of solar energy? ANSWER: Chapter 7 Reading Quiz Question 20 Part A A rural Minnesota farmer grows a variety of vegetables to feed her family. In addition, she cuts down some of her dead trees for firewood to heat her home in the winter. This farmer is adding to the flux of the carbon cycle in her region by _____. precipitation evaporation runoff transpiration the polar ice caps lakes and streams aquifers the oceans evaporation of water from a lake the formation of ice on the top of a pond movement of ocean tides the movement of water over a waterfall Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 8 5/21/2014 8:01 PM ANSWER: Chapter 7 Reading Quiz Question 8 Part A In a terrestrial ecosystem, most carbon is stored in the biomass of _____. ANSWER: Chapter 7 Reading Quiz Question 7 Part A In which of the following countries would we expect that the terrestrial ecosystems have the highest net primary production and biomass? ANSWER: Chapter 7 Reading Quiz Question 22 Part A Some farmers in the Midwest of the United States rotate their crops from year to year, switching from soybeans to corn on the same fields. What is one of the advantages of doing this? encouraging photosynthesis as she raises crops burning carbon-based fuels by consuming vegetables grown on her farm All of the choices are correct. the animals living there air the top layers of soil containing dead organisms living plants China Australia Brazil United States Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 8 5/21/2014 8:01 PM ANSWER: Chapter 7 Reading Quiz Question 10 Part A Most nitrogen enters the biosphere through the process of _____ ANSWER: Chapter 7 Reading Quiz Question 9 Part A Where do we expect to find the least amount of nitrogen? ANSWER: Chapter 7 Reading Quiz Question 12 Part A Along the west coast of the United States, upwellings bring deep ocean waters to the surface, carrying with them _____, which greatly increases NPP. ANSWER: The corn crop benefits from reactive nitrogen added to the soil by the soybean crop. Both crops require the same fertilizing supplies, so farmers save by buying fertilizer in bulk. Soybeans add large amounts of carbon dioxide to the soil, which helps the corn crop. Corn adds large amounts of phosphorus to the soil, which helps the soybean crop. nitrogen fixation in which bacteria convert N2 to NH3 cellular respiration, in which animals convert N2 to NH4 fermentation in which bacteria convert N2 to HNO3 photosynthesis, in which plants convert N2 to NO2 in Earth’s crust in plants in animals in the atmosphere Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 11 Part A Which one of the following statements about the carbon, phosphorus, and nitrogen cycles is true? ANSWER: Chapter 7 Reading Quiz Question 24 Part A A large coal-burning power plant is about 50 miles upwind from a lake that used to be popular for fishing. But now, just five years after the plant was constructed, the fish populations are decreasing dramatically. Which one of the following impacts of this coal-burning power plant is most likely hurting the fish populations in this downwind lake? ANSWER: Chapter 7 Reading Quiz Question 14 Part A Which one of the following statements about sulfur is correct? ANSWER: oxygen phosphate carbon sulfur Phosphorus is virtually absent in the atmosphere. The major source of carbon used by plants is the soil. Bacteria drive the phosphorus cycle. The major source of nitrogen used by plants is the air. insufficient sunlight reaching the lake low oxygen levels from burning fossil fuels eutrophication of the lake acidification of the lake Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 13 Part A Nitrogen and sulfur are important to all organisms because they are important constituents of _____. ANSWER: Chapter 7 Reading Quiz Question 25 Part A In Iowa, a small, deep lake in the summer becomes stratified with warmer, less-dense water at the surface and colder, denser water near the bottom. As fall air temperatures decrease, the surface water cools and then drops toward the bottom, mixing the lake levels together. As a result of this mixing, _____. ANSWER: Chapter 7 Reading Quiz Question 15 Part A A fire spreads across hundreds of acres of prairie, burning most of the plant parts above the ground. Compared to before the fire, right after this fire the pool of nutrients in the prairie plants _____. The main pool of sulfur is in the atmosphere where the flux is high and the residence time is long. The main pool of sulfur is in rocks. The flux of sulfur through the atmosphere is high and the residence is short. The main pool of sulfur is in the atmosphere where the flux is low and the residence time is long. The main pool of sulfur is in rocks. The flux of sulfur through the atmosphere is low and the residence is short. nucleic acids glucose phosphates some amino acids nitrogen and phosphorus are added to the lake nitrogen and phosphorus decrease near the surface of the lake nitrogen and phosphorus increase near the surface of the lake None of the choices is correct. Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 8 5/21/2014 8:01 PM ANSWER: Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 21 points. and the soil decreases increases and the pool of nutrients in the soil decreases and the soil increases decreases and the pool of nutrients in the soil increases Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 8 5/21/2014 8:01 PM

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Normal time for a stopwatch study is equal to which of the following? Answer Average observed time × Performance rating factor Average observed time + Performance rating factor Average observed time / Performance rating factor Average observed time – Performance rating factor

Normal time for a stopwatch study is equal to which of the following? Answer Average observed time × Performance rating factor Average observed time + Performance rating factor Average observed time / Performance rating factor Average observed time – Performance rating factor

Normal time for a stopwatch study is equal to which … Read More...
8) A heavy steel ball is attached to a light rod to make a pendulum. The pendulum begins at rest at instant A, as shown. The ball is then pulled to one side and held at rest. At instant B, the pendulum is released from rest. It swings down and passes its original height at instant C, as shown. The total mechanical energy of the pendulum is greatest at: a) Point B b) Point C c) Equal at both instants d) Since the mass of the ball and the height it is raised to before it is released is not given it is impossible to determine.

8) A heavy steel ball is attached to a light rod to make a pendulum. The pendulum begins at rest at instant A, as shown. The ball is then pulled to one side and held at rest. At instant B, the pendulum is released from rest. It swings down and passes its original height at instant C, as shown. The total mechanical energy of the pendulum is greatest at: a) Point B b) Point C c) Equal at both instants d) Since the mass of the ball and the height it is raised to before it is released is not given it is impossible to determine.

8) A heavy steel ball is attached to a light … Read More...
Ch 2 Questions that might be on the test. If you cannot answer them, check your class notes or the textbook. 1. A mineral is a naturally occurring substance formed through geological processes that has: a) a characteristic chemical composition, b) a highly ordered atomic structure c) specific physical properties d) all of the above 2. There are currently more than ______ known minerals, according to the International Mineralogical Association, a) 40 b) 400 c) 4000 d) 40 000 3. Some minerals, like quartz, mica or feldspar are: a) rare b) common c) valuable d) priceless 4. Rocks from which minerals are mined for economic purposes are referred to as: a) gangue b) tailings c) ores d) granite 5. Electrons, which have a _____ charge, a size which is so small as to be currently unmeasurable, and which are the least massive of the three types of basic particles. a) positive b) negative c) neutral 6. Both protons and neutrons are themselves now thought to be composed of even more elementary particles called: a) quarks b) quakes c) parsons d) megans 7. In processes which change the number of protons in a nucleus, the atom becomes an atom of a different chemical: a) isotope b) compound c) element d) planet 8. Atoms which have either a deficit or a surplus of electrons are called: a) elements b) isotopes c) ions d) molecules 9. In the Bohr model of the atom, electrons can only orbit the nucleus in particular circular orbits with fixed angular momentum and energy, their distances from the nucleus being proportional to their respective energies. They can only make _____ leaps between the fixed energy levels. a) tiny b) quantum c) gradual 10. It is impossible to simultaneously derive precise values for both the position and momentum of a particle for any given point in time; this became known as the ______ principle. a) Bohr b) Einstein c) uncertainty d) quantum 11. The modern model of the atom describes the positions of electrons in an atom in terms of: a) quantum levels b) orbital paths c) probabilities d) GPS 12. Isotopes of an element have nuclei with the same number of protons (the same atomic number) but different numbers of: a) electrons b) neutrons c) ions d) photons 13. In helium-3 (or 3He), how many protons are present? a) 1 b) 2 c) 3 d) 4 14. In helium-3 (or 3He), how many neutrons are present? a) 1 b) 2 c) 3 d) 4 15. The relative abundance of an isotope is strongly correlated with its tendency toward nuclear _____, short-lived nuclides quickly go away, while their long-lived counterparts endure. a) fission b) fusion c) decay d) bombardment 16. The isotopic composition of elements is different on different planets. a) True b) False 17. As a general rule, the fewer electrons in an atom’s valence shell, the ____ reactive it is. Lithium, sodium, and potassium have one electron in their outer shells. a) more b) less 18. Every atom is much more stable, or less reactive, with a ____ valence shell. a) partly full b) completely full 19. A positively-charged ion, which has fewer electrons than protons, is known as a: a) anion b) cation c) fermion d) bation 20. Bonds vary widely in their strength. Generally covalent and ionic bonds are often described as “strong”, whereas ______ bonds are generally considered to be “weak”. a) van der Waals b) Faradays c) van Neumans 21. This bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared a) ionic b) covalent c) van der Waals d) metallic 22. This bond results from electrostatic attraction between atoms: a) ionic b) covalent c) van der Waals d) metallic 23. A sea of delocalized electrons causes this bonding: a) ionic b) covalent c) van der Waals d) metallic 24. The chemical composition of minerals may vary between end members of a mineral system. For example the ______ feldspars comprise a continuous series from sodiumrich albite to calcium-rich anorthite. a) plagioclase b) orthoclase c) alkaline d) acidic 25. Crystal structure is based on ____ internal atomic arrangement. a) irregular b) regular c) random d) curvilinear 26. Pyrite and marcasite are both _______, but their arrangement of atoms differs. a) iron sulfide b) lead sulfide c) copper silfide d) silver sulfide 27. The carbon atoms in ______ are arranged into sheets which can slide easily past each other, while the carbon atoms in diamond form a strong, interlocking three-dimensional network. a) sapphire b) graphite c) aluminum d) carbonate 28. TGCFAOQTCD a) Crystal habit b) Hardness scale c) Luster scale 29. Dull to metallic, submetallic, adamantine, vitreous, pearly, resinous, or silky. a) Crystal habit b) Hardness scale c) Luster scale d) Heft scale 30. The color of the powder a mineral leaves after rubbing it on unglazed porcelain. a) color b) streak c) lustre d) iridescense 31. Describes the way a mineral may split apart along various planes. a) fracture b) streak c) lustre d) cleavage 32. In modern physics, the position of electrons about a nucleus are defined in terms of: a) probabilities b) circles c) ellipses d) chromodomes 33. The symbol H+ suggests a: a) hydrogen atom b) hydrogen isotope c) hydrogen cation d) hydrogen anion 34. The tabulated atomic mass of natural carbon is not exactly 12 because carbon in nature always has multiple ________ present. a) electrons b) isotopes c) quarks d) protons 35. This type of bonding due to delocalized electrons leads to malleability, ductility, and high melting points: a) covalent b) ionic c) van der Waals d) metallic 36. The mineral ___________ is 3 on Mohs Scale whereas the mineral ___________ is 9. a) calcite, corundum b) corundum, calcite c) caliche, calcite d) chalcedony, quartz 37. In hand specimens, geologists identify most minerals based on: a) physical properties b) chemical analyses c) xray diffraction 38. This type of chemical bonding is the weakest but occurs in all substances. a) covalent b) ionic c) metallic d) none of the above 39. Quartz, feldspar, mica, chlorite, kaolin, calcite, epidote, olivine, augite, hornblende, magnetite, hematite, limonite: these minerals are: a) common in rocks b) occasionally found c) rare d) extremely rare 40. Characteristics of a mineral do NOT include: a) naturally occurring b) characteristic chemical formula c) crystalline d) organic e) all of the above 41. The chemical composition of a particular mineral may vary between end members. For example, the common mineral plagioclase feldspar varies from being _______-rich to being _________-rich. a) sodium, calcium b) potassium, sodium c) iron, magnesium d) carbon, oxygen 42. Sharing of electrons typifies the __________ bond whereas electrostatic attraction typifies the _______ bond. a) ionic, covalent b) ionic, triclinic c) covalent, ionic d) triclinic, covalent 43. If number of protons does not equal the number of electrons, the atom is a(n) : a) isotope b) ion c) quark d) simplex e) google 44. Atoms generally consist of: a) electrons b) protons c) neutrons d) all of the above 45. Not counting rare minerals, about how many mineral species are at least occasionally encountered in rocks? a) 20 b) 200 c) 2000 46. Carbon is atomic number 6. Carbon-13 has _______ protons and _______ neutrons. a) thirteen, six b) six, seven c) twelve, twenty-five d) twelve, twelve 47. Which of these particles are not nucleons? a) electrons b) neutrons c) protons 48. A mineral with visibly recognizable crystals is said to have good crystal habit; otherwise the mineral is said to be: a) massive b) granular c) compact d) any of the above 49. In chemical bonding, two atoms become linked by moving or sharing __________. a) neutrons b) protons c) electrons 50. The name of an element is determined by the number of ______ present in the ______ of an atom. a) electrons, nucleus b) neutrons, nucleus c) protons, nucleus d) protons, electron cloud e) neutrons, electron cloud 51. Generally ________ and ____________ bonds are strong whereas the ______________ bond is weak. a) covalent, ionic, van der Waals b) van der Waals, covalent, ionic c) ionic, van der Waals, covalent 52. Which of the following are held together by chemical bonds? a) molecules b) crystals c) diatomic gases 53. An ion with fewer electrons than protons is called an ______ and it carries a _________ electric charge. a) cation, positive b) anion, negative c) cation, negative d) anion, positive 54. Two or more minerals may have the same _________ composition but different _______ structure. These are called polymorphs. a) crystal, chemical b) chemical, crystal 55. Industrial minerals are: a) gem quality b) commercially valuable c) tailings d) worthless 56. All minerals are crystalline. If the crystals are too small to see, they can be detected by: a) x-ray diffraction b) cosmic rays c) sound waves d) odor 57. If two atomes have the same number of protons but different numbers of neutrons, the atoms are _______ of the same _________. a) elements, mineral b) atoms, isotope c) elements, isotope d) isotopes, element 58. Modern physics recognizes that electrons show both particle and ______ behavior. a) wave b) emotional c) thermal d) revolting 59. Sodium and potassium have one ______ electron in their outer shells and are extremely ________. a) valence, stable b) inverted, reactive c) valence, reactive d) contaminated, inactive 60. The luster of _______ would be described as ________. a) glass, vitreous b) diamond, dull c) pyrite, silky d) graphite, resinous 61. The minerals ________ and __________ are polymorphs of carbon. a) diamond, graphite b) calcite, silicate c) bonite, bronzite 62. In the ______ atom based on _______ physics, electrons were restricted to circular orbits of fixed energy levels. a) Bohr , quantum b) Rutherford, classical c) Bohr, classical d) Rutherford, quantum 63. Virtually all elements other than ______ and _______ were formed in stars and supernovae long after the Big Bang. a) hydrogen, helium b) carbon, phosphorus c) carbon, oxygen d) silica, carbon 64. Physicist Werner _________ developed the ___________ principle which means that it is impossible to know exactly the position and momentum of a particle. a) Heisenberg, certainty b) Heisenberg, uncertainty c) Bohr, uncertainty d) Bohr, certainty

Ch 2 Questions that might be on the test. If you cannot answer them, check your class notes or the textbook. 1. A mineral is a naturally occurring substance formed through geological processes that has: a) a characteristic chemical composition, b) a highly ordered atomic structure c) specific physical properties d) all of the above 2. There are currently more than ______ known minerals, according to the International Mineralogical Association, a) 40 b) 400 c) 4000 d) 40 000 3. Some minerals, like quartz, mica or feldspar are: a) rare b) common c) valuable d) priceless 4. Rocks from which minerals are mined for economic purposes are referred to as: a) gangue b) tailings c) ores d) granite 5. Electrons, which have a _____ charge, a size which is so small as to be currently unmeasurable, and which are the least massive of the three types of basic particles. a) positive b) negative c) neutral 6. Both protons and neutrons are themselves now thought to be composed of even more elementary particles called: a) quarks b) quakes c) parsons d) megans 7. In processes which change the number of protons in a nucleus, the atom becomes an atom of a different chemical: a) isotope b) compound c) element d) planet 8. Atoms which have either a deficit or a surplus of electrons are called: a) elements b) isotopes c) ions d) molecules 9. In the Bohr model of the atom, electrons can only orbit the nucleus in particular circular orbits with fixed angular momentum and energy, their distances from the nucleus being proportional to their respective energies. They can only make _____ leaps between the fixed energy levels. a) tiny b) quantum c) gradual 10. It is impossible to simultaneously derive precise values for both the position and momentum of a particle for any given point in time; this became known as the ______ principle. a) Bohr b) Einstein c) uncertainty d) quantum 11. The modern model of the atom describes the positions of electrons in an atom in terms of: a) quantum levels b) orbital paths c) probabilities d) GPS 12. Isotopes of an element have nuclei with the same number of protons (the same atomic number) but different numbers of: a) electrons b) neutrons c) ions d) photons 13. In helium-3 (or 3He), how many protons are present? a) 1 b) 2 c) 3 d) 4 14. In helium-3 (or 3He), how many neutrons are present? a) 1 b) 2 c) 3 d) 4 15. The relative abundance of an isotope is strongly correlated with its tendency toward nuclear _____, short-lived nuclides quickly go away, while their long-lived counterparts endure. a) fission b) fusion c) decay d) bombardment 16. The isotopic composition of elements is different on different planets. a) True b) False 17. As a general rule, the fewer electrons in an atom’s valence shell, the ____ reactive it is. Lithium, sodium, and potassium have one electron in their outer shells. a) more b) less 18. Every atom is much more stable, or less reactive, with a ____ valence shell. a) partly full b) completely full 19. A positively-charged ion, which has fewer electrons than protons, is known as a: a) anion b) cation c) fermion d) bation 20. Bonds vary widely in their strength. Generally covalent and ionic bonds are often described as “strong”, whereas ______ bonds are generally considered to be “weak”. a) van der Waals b) Faradays c) van Neumans 21. This bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared a) ionic b) covalent c) van der Waals d) metallic 22. This bond results from electrostatic attraction between atoms: a) ionic b) covalent c) van der Waals d) metallic 23. A sea of delocalized electrons causes this bonding: a) ionic b) covalent c) van der Waals d) metallic 24. The chemical composition of minerals may vary between end members of a mineral system. For example the ______ feldspars comprise a continuous series from sodiumrich albite to calcium-rich anorthite. a) plagioclase b) orthoclase c) alkaline d) acidic 25. Crystal structure is based on ____ internal atomic arrangement. a) irregular b) regular c) random d) curvilinear 26. Pyrite and marcasite are both _______, but their arrangement of atoms differs. a) iron sulfide b) lead sulfide c) copper silfide d) silver sulfide 27. The carbon atoms in ______ are arranged into sheets which can slide easily past each other, while the carbon atoms in diamond form a strong, interlocking three-dimensional network. a) sapphire b) graphite c) aluminum d) carbonate 28. TGCFAOQTCD a) Crystal habit b) Hardness scale c) Luster scale 29. Dull to metallic, submetallic, adamantine, vitreous, pearly, resinous, or silky. a) Crystal habit b) Hardness scale c) Luster scale d) Heft scale 30. The color of the powder a mineral leaves after rubbing it on unglazed porcelain. a) color b) streak c) lustre d) iridescense 31. Describes the way a mineral may split apart along various planes. a) fracture b) streak c) lustre d) cleavage 32. In modern physics, the position of electrons about a nucleus are defined in terms of: a) probabilities b) circles c) ellipses d) chromodomes 33. The symbol H+ suggests a: a) hydrogen atom b) hydrogen isotope c) hydrogen cation d) hydrogen anion 34. The tabulated atomic mass of natural carbon is not exactly 12 because carbon in nature always has multiple ________ present. a) electrons b) isotopes c) quarks d) protons 35. This type of bonding due to delocalized electrons leads to malleability, ductility, and high melting points: a) covalent b) ionic c) van der Waals d) metallic 36. The mineral ___________ is 3 on Mohs Scale whereas the mineral ___________ is 9. a) calcite, corundum b) corundum, calcite c) caliche, calcite d) chalcedony, quartz 37. In hand specimens, geologists identify most minerals based on: a) physical properties b) chemical analyses c) xray diffraction 38. This type of chemical bonding is the weakest but occurs in all substances. a) covalent b) ionic c) metallic d) none of the above 39. Quartz, feldspar, mica, chlorite, kaolin, calcite, epidote, olivine, augite, hornblende, magnetite, hematite, limonite: these minerals are: a) common in rocks b) occasionally found c) rare d) extremely rare 40. Characteristics of a mineral do NOT include: a) naturally occurring b) characteristic chemical formula c) crystalline d) organic e) all of the above 41. The chemical composition of a particular mineral may vary between end members. For example, the common mineral plagioclase feldspar varies from being _______-rich to being _________-rich. a) sodium, calcium b) potassium, sodium c) iron, magnesium d) carbon, oxygen 42. Sharing of electrons typifies the __________ bond whereas electrostatic attraction typifies the _______ bond. a) ionic, covalent b) ionic, triclinic c) covalent, ionic d) triclinic, covalent 43. If number of protons does not equal the number of electrons, the atom is a(n) : a) isotope b) ion c) quark d) simplex e) google 44. Atoms generally consist of: a) electrons b) protons c) neutrons d) all of the above 45. Not counting rare minerals, about how many mineral species are at least occasionally encountered in rocks? a) 20 b) 200 c) 2000 46. Carbon is atomic number 6. Carbon-13 has _______ protons and _______ neutrons. a) thirteen, six b) six, seven c) twelve, twenty-five d) twelve, twelve 47. Which of these particles are not nucleons? a) electrons b) neutrons c) protons 48. A mineral with visibly recognizable crystals is said to have good crystal habit; otherwise the mineral is said to be: a) massive b) granular c) compact d) any of the above 49. In chemical bonding, two atoms become linked by moving or sharing __________. a) neutrons b) protons c) electrons 50. The name of an element is determined by the number of ______ present in the ______ of an atom. a) electrons, nucleus b) neutrons, nucleus c) protons, nucleus d) protons, electron cloud e) neutrons, electron cloud 51. Generally ________ and ____________ bonds are strong whereas the ______________ bond is weak. a) covalent, ionic, van der Waals b) van der Waals, covalent, ionic c) ionic, van der Waals, covalent 52. Which of the following are held together by chemical bonds? a) molecules b) crystals c) diatomic gases 53. An ion with fewer electrons than protons is called an ______ and it carries a _________ electric charge. a) cation, positive b) anion, negative c) cation, negative d) anion, positive 54. Two or more minerals may have the same _________ composition but different _______ structure. These are called polymorphs. a) crystal, chemical b) chemical, crystal 55. Industrial minerals are: a) gem quality b) commercially valuable c) tailings d) worthless 56. All minerals are crystalline. If the crystals are too small to see, they can be detected by: a) x-ray diffraction b) cosmic rays c) sound waves d) odor 57. If two atomes have the same number of protons but different numbers of neutrons, the atoms are _______ of the same _________. a) elements, mineral b) atoms, isotope c) elements, isotope d) isotopes, element 58. Modern physics recognizes that electrons show both particle and ______ behavior. a) wave b) emotional c) thermal d) revolting 59. Sodium and potassium have one ______ electron in their outer shells and are extremely ________. a) valence, stable b) inverted, reactive c) valence, reactive d) contaminated, inactive 60. The luster of _______ would be described as ________. a) glass, vitreous b) diamond, dull c) pyrite, silky d) graphite, resinous 61. The minerals ________ and __________ are polymorphs of carbon. a) diamond, graphite b) calcite, silicate c) bonite, bronzite 62. In the ______ atom based on _______ physics, electrons were restricted to circular orbits of fixed energy levels. a) Bohr , quantum b) Rutherford, classical c) Bohr, classical d) Rutherford, quantum 63. Virtually all elements other than ______ and _______ were formed in stars and supernovae long after the Big Bang. a) hydrogen, helium b) carbon, phosphorus c) carbon, oxygen d) silica, carbon 64. Physicist Werner _________ developed the ___________ principle which means that it is impossible to know exactly the position and momentum of a particle. a) Heisenberg, certainty b) Heisenberg, uncertainty c) Bohr, uncertainty d) Bohr, certainty

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Assignment 2 Conditional Probability, Bayes Theorem, and Random Variables Conditional Probability and Bayes’ Theorem Problems 1-14 from Problem Set on Conditional Probability and Bayes’ Theorem I am including all the question here so that there is no confusion. Q1. Pair of six sided dices are rolled and the outcome is noted: What is the sample space? What is the size of the sample space? Suppose all we are interested in is the sum of the two outcomes. What is the probability that the sum of the two is 6? 7? 8? (Note: This can be solved using both enumeration and conditional probability method). Here, it makes more sense to use the enumeration approach than conditional probability. It is, however, listed here to set the stage for Q5. What is the probability that the sum of the two is above 5 and the two numbers are equal? Express this question in terms of events A, B, and set operators. What is the probability that the sum of the two is above 5 or the two numbers are equal? Express this question in terms of events A, B, and set operators. Q2. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.3 What is the value of (a) P(A|B) and (b) P(B|A) Q3. At a fair, a vendor has 25 helium balloons on strings: 10 balloons are yellow, 8 are red, and 7 are green. A balloon is selected at random and sold. Given that the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow? Q4. A bowl contains seven blue chips and three red chips. Two chips are to be drawn at random and without replacement. What is the probability that the fist chip is a red chip and the second a blue? Express this question in terms of events A, B, and set operators and use conditional probability. Q5. Three six sided dices are rolled and the outcome is noted: What is the size of the sample space? What is the probability that the sum of the three numbers is 6? 13? 18? Solve using conditional probability How does the concept of conditional probability help? Q6. A grade school boy has 5 blue and four white marbles in his left pocket and four blue and five white marbles in his right pocket. If he transfers one marble at random from his left pocket to his right pocket, what is the probability of his then drawing a blue marble from his right pocket? Q7. In a certain factory, machine I, II, and III are all producing springs of the same length. Of their production, machines I, II, and III produce 2%, 1%, and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, what is the probability that it is defective? Given that the selected spring is defective, what is the probability that it was produced on machine III? Q8. Bowl B1 contains 2 white chips, bowl B2 contains 2 red chips, bowl B3 contains 2 white and 2 red chips, and Bowl B4 contains 3 white chips and 1 red chip. The probabilities of selecting bowl B1, B2, B3, and B4 are 1/2, 1/4, 1/8, and 1/8 respectively. A bowl is selected using these probabilities, and a chip is then drawn at random. Find P(W), the probability of drawing a white chip P(B1|W): the probability that bowl B1 was selected, given that a white chip was drawn. Q9. A pap smear is a screening procedure used to detect cervical cancer. For women with this cancer, there are about 16% false negative. For women without cervical cancer, there are about 19% false positive. In the US, there are about 8 women in 100,000 who have this cancer. What is the probability that a woman who has been tested positive actually has cervical cancer? Q10. There is a new diagnostic test for a disease that occurs in about 0.05% of the population. The test is not perfect but will detect a person with the disease 99% of the time. It will, however, say that a person without the disease has the disease about 3% of the time. A person is selected at random from the population and the test indicates that this person has the disease. What are the conditional probabilities that The person has the disease The person does not have the disease Q11. Consider two urns: the first contains two white and seven black balls, and the second contains five white and six black balls. We flip a fair coin and then draw a ball from the first urn or the second urn depending on whether the outcome was a head or a tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? Q12. In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer. Assume that a student who guesses at the answer will be correct with probability 1/m where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer given that she answered it correctly? Q13. A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy persons tested (i.e., if a healthy person is tested, then, with probability 0.01, the test result will imply that he has the disease.). If 0.5% of the population actually have the disease, what is the probability a person has the disease given that his test results are positive? Q14. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn, c additional balls of the same color are put in it with it. Now suppose that we draw another ball. What is the probability that the first ball drawn was black given that the second ball drawn was red? Random Variables Q15. Suppose an experiment consists of tossing two six sided fair dice and observing the outcomes. What is the sample space? Let Y denote the sum of the two numbers that appear on the dice. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=7? What does it mean if I say that Y<7? Q16. Suppose an experiment consists of picking a sample of size n from a population of size N. Assume that n≪N. Also, assume that the population contains D defective parts and N-D non defective parts, where n<D≪N. What is the sample space? If we are interested in knowing the number (count) of defective parts in the sample space, describe how, the concept of a random variable could help. Define a random variable Y and describe what values the random variable Y can take? What does it mean if we say Y=5? Q17. Suppose an experiment consists of tossing two fair coins. Let Y denote the number of heads appearing. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=1? What are the probabilities associated with each outcome? What is the sum of the probabilities associated with all possible values that Y can take? Q18. A lot, consisting of 100 fuses, is inspected by the following procedure. Five fuses are chosen at random and tested: if all 5 fuses pass the inspection, the lot is accepted. Suppose that the lot contains 20 defective fuses. What is the probability of accepting the lot? Define the random variable, its purpose, and the formula/concept that you would use. Q19. In a small pond there are 50 fish, 10 of which have been tagged. If a fisherman’s catch consists of 7 fish, selected at random and without replacement. Give an example of a random variable that can be defined if we are interested in knowing the number of tagged fish that are caught? What is the probability that exactly 2 tagged fish are caught? Define the random variable, its purpose, and the formula/concept that you would use. Applied to Quality Control Q20. My manufacturing firm makes 100 cars every day out of which 10 are defective; the quality control inspector tests drives 5 different cars. Based on the sample, the quality control inspector will make a generalization about the whole batch of 100 cars that I have on that day. Let d denote the number of defective cars in the sample What are the values that d can take (given the information provided above)? What is the probability that the quality control inspector will conclude that: (a) 0% of the cars are defective- call this P(d=0); (b) 20% of the cars are defective- call this P(d=1); (c) 40% of the cars are defective- call this P(d=2); (d) 60% of the cars are defective- call this P(d=3),(e) 80% of the cars are defective- call this P(d=4), and (f) 100% of the cars are defective- call this P(d=5) What is P(d=0)+ P(d=1)+ P(d=2)+ P(d=3)+ P(d=4)+ P(d=5) Let’s assume that the quality control inspector has been doing the testing for a while (say for the past 1000 days). What is the average # of defective cars that he found? Q21. Assume that the quality control inspector is selecting 1 car at a time and the car that he tested is put back in the pool of possible cars that he can test (sample with replacement). Let d denote the number of defective cars in the sample (n) What are the values that d can take (given the information provided above)? What is the probability that the quality control inspector will conclude that: (a) 0% of the cars are defective, (b) 20% of the cars are defective, (c) 40% of the cars are defective, (d) 60% of the cars are defective, (e) 80% of the cars are defective, and (f) 100% of the cars are defective. Let’s call these P(d=0)….P(d=5) What is P(d=0)+ P(d=1)+ P(d=2)+ P(d=3)+ P(d=4)+ P(d=5) Let’s assume that the quality control inspector has been doing the testing for a while (say for the past 1000 days). What is the average # of defective cars that he found? Interesting Problems Q22. A closet contains n pairs of shoes. If 2r shoes are chosen at random (2r<n), what is the probability that there will be no matching pair in the sample? Q23. In a draft lottery containing the 366 days of the leap year, what is the probability that the first 180 days drawn (without replacement) are evenly distributed among the 12 months? What is the probability that the first 30 days drawn contain none from September? Q25. You and I play a coin-tossing game. If the coin falls heads I score one, if tails, you score one. In the beginning, the score is zero. What is the probability that after 2n throws our scores are equal? What is the probability that after 2n+1 throws my score is three more than yours?

Assignment 2 Conditional Probability, Bayes Theorem, and Random Variables Conditional Probability and Bayes’ Theorem Problems 1-14 from Problem Set on Conditional Probability and Bayes’ Theorem I am including all the question here so that there is no confusion. Q1. Pair of six sided dices are rolled and the outcome is noted: What is the sample space? What is the size of the sample space? Suppose all we are interested in is the sum of the two outcomes. What is the probability that the sum of the two is 6? 7? 8? (Note: This can be solved using both enumeration and conditional probability method). Here, it makes more sense to use the enumeration approach than conditional probability. It is, however, listed here to set the stage for Q5. What is the probability that the sum of the two is above 5 and the two numbers are equal? Express this question in terms of events A, B, and set operators. What is the probability that the sum of the two is above 5 or the two numbers are equal? Express this question in terms of events A, B, and set operators. Q2. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.3 What is the value of (a) P(A|B) and (b) P(B|A) Q3. At a fair, a vendor has 25 helium balloons on strings: 10 balloons are yellow, 8 are red, and 7 are green. A balloon is selected at random and sold. Given that the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow? Q4. A bowl contains seven blue chips and three red chips. Two chips are to be drawn at random and without replacement. What is the probability that the fist chip is a red chip and the second a blue? Express this question in terms of events A, B, and set operators and use conditional probability. Q5. Three six sided dices are rolled and the outcome is noted: What is the size of the sample space? What is the probability that the sum of the three numbers is 6? 13? 18? Solve using conditional probability How does the concept of conditional probability help? Q6. A grade school boy has 5 blue and four white marbles in his left pocket and four blue and five white marbles in his right pocket. If he transfers one marble at random from his left pocket to his right pocket, what is the probability of his then drawing a blue marble from his right pocket? Q7. In a certain factory, machine I, II, and III are all producing springs of the same length. Of their production, machines I, II, and III produce 2%, 1%, and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, what is the probability that it is defective? Given that the selected spring is defective, what is the probability that it was produced on machine III? Q8. Bowl B1 contains 2 white chips, bowl B2 contains 2 red chips, bowl B3 contains 2 white and 2 red chips, and Bowl B4 contains 3 white chips and 1 red chip. The probabilities of selecting bowl B1, B2, B3, and B4 are 1/2, 1/4, 1/8, and 1/8 respectively. A bowl is selected using these probabilities, and a chip is then drawn at random. Find P(W), the probability of drawing a white chip P(B1|W): the probability that bowl B1 was selected, given that a white chip was drawn. Q9. A pap smear is a screening procedure used to detect cervical cancer. For women with this cancer, there are about 16% false negative. For women without cervical cancer, there are about 19% false positive. In the US, there are about 8 women in 100,000 who have this cancer. What is the probability that a woman who has been tested positive actually has cervical cancer? Q10. There is a new diagnostic test for a disease that occurs in about 0.05% of the population. The test is not perfect but will detect a person with the disease 99% of the time. It will, however, say that a person without the disease has the disease about 3% of the time. A person is selected at random from the population and the test indicates that this person has the disease. What are the conditional probabilities that The person has the disease The person does not have the disease Q11. Consider two urns: the first contains two white and seven black balls, and the second contains five white and six black balls. We flip a fair coin and then draw a ball from the first urn or the second urn depending on whether the outcome was a head or a tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? Q12. In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer. Assume that a student who guesses at the answer will be correct with probability 1/m where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer given that she answered it correctly? Q13. A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy persons tested (i.e., if a healthy person is tested, then, with probability 0.01, the test result will imply that he has the disease.). If 0.5% of the population actually have the disease, what is the probability a person has the disease given that his test results are positive? Q14. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn, c additional balls of the same color are put in it with it. Now suppose that we draw another ball. What is the probability that the first ball drawn was black given that the second ball drawn was red? Random Variables Q15. Suppose an experiment consists of tossing two six sided fair dice and observing the outcomes. What is the sample space? Let Y denote the sum of the two numbers that appear on the dice. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=7? What does it mean if I say that Y<7? Q16. Suppose an experiment consists of picking a sample of size n from a population of size N. Assume that n≪N. Also, assume that the population contains D defective parts and N-D non defective parts, where n