Essential Statistics for Public Managers and Policy Analysts / Edition 3 by Evan M Berman, Xiaohu Wang 1-Use the public perception dataset. Is the relationship between watching Orange TV (watch), the county’s cable television station, and trusting the government to do what is right most of the time (trust) statistically significant? Do you consider this a causal relationship or an association? Does the analysis satisfy the assumptions of the Chi-square test? If not, how might you address this problem? 2-Use the public perception dataset. Examine the relationship between residents who trust the county government to do what is right most of the time (trust) and their belief that county government works efficiently (works). What is the practical significant of this relationship? 3-Use the public perception dataset. In Chapter 10 of this workbook, you used Chi-square to examine the relationship between residents who trust the county government to do what is right most of the time (trust) and their belief that county government works efficiently (works). Reexamine this relationship using measures of gamma, Somer’s d, Kendall’s tau-c. What do you conclude? 4-Table W 12.1 is the printout of a t-test (independent samples). The continuous variable is an index variable of environmental concern. The dichotomous variable is a measure of education (college versus no college). Interpret and write up the results. What other information would you like to have about this relationship? 5-Table W 12.2 is the printout of a period-samples t-test. The data are before-and-after measurements of a public safety program. Interpret and write up the results. What other information would you like to have about this relationship? 6-Use the Public Perception dataset. An analyst wants to know whether incomes vary by age group. Treat the income variable as a continuous variable, and treat the age variable as an ordinal variable. Calculate the means for each of these groups, and then use ANOVA to determine whether any of these differences are statistically significant. For which group is the relationship linear?

Essential Statistics for Public Managers and Policy Analysts / Edition 3 by Evan M Berman, Xiaohu Wang 1-Use the public perception dataset. Is the relationship between watching Orange TV (watch), the county’s cable television station, and trusting the government to do what is right most of the time (trust) statistically significant? Do you consider this a causal relationship or an association? Does the analysis satisfy the assumptions of the Chi-square test? If not, how might you address this problem? 2-Use the public perception dataset. Examine the relationship between residents who trust the county government to do what is right most of the time (trust) and their belief that county government works efficiently (works). What is the practical significant of this relationship? 3-Use the public perception dataset. In Chapter 10 of this workbook, you used Chi-square to examine the relationship between residents who trust the county government to do what is right most of the time (trust) and their belief that county government works efficiently (works). Reexamine this relationship using measures of gamma, Somer’s d, Kendall’s tau-c. What do you conclude? 4-Table W 12.1 is the printout of a t-test (independent samples). The continuous variable is an index variable of environmental concern. The dichotomous variable is a measure of education (college versus no college). Interpret and write up the results. What other information would you like to have about this relationship? 5-Table W 12.2 is the printout of a period-samples t-test. The data are before-and-after measurements of a public safety program. Interpret and write up the results. What other information would you like to have about this relationship? 6-Use the Public Perception dataset. An analyst wants to know whether incomes vary by age group. Treat the income variable as a continuous variable, and treat the age variable as an ordinal variable. Calculate the means for each of these groups, and then use ANOVA to determine whether any of these differences are statistically significant. For which group is the relationship linear?

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EE118 FALL 2012 SAN JOSE STATE UNIVERSITY Department of Electrical Engineering TEST 2 — Digital Design I October 24, 2012 10:30 a.m. – 11:45 a.m. — Closed Book & Closed Notes — — No Crib Sheet Allowed — STUDENT NAME: (Last) Claussen , (First) Matthew STUDENT ID NUMBER (LAST 4 DIGITS): No interpretation of test problems will be given during the test. If you are not sure of what is intended, make appropriate assumptions and continue. Do not unstaple !!! Problems 1-14(4 points each) TOTAL Problems 15 – 17 (15 pts each) 1203 2 For the next 14 problems, circle the correct answer. No partial credit will be given. PROBLEM 1 (4 points) Which statement is not true? A. Any combinational circuit may be designed using multiplexers only. B. Any combinational circuit may be designed using decoders only. C. All Sequential circuits are based on cross-coupled NAND or NOR gates. D. A hazard in a digital system is an undesirable effect caused by either a deficiency in the system or external influences. E. None of the above PROBLEM 2 (4 points) For a 2-bit comparator comparing 2-bit numbers A = (a1 a0) and B = (b1 b0), what is the proper function for the f(A>B) output through logical reasoning? A. a1 b1’ + (a1 b1 + a1’b1’ ) a0 b0’ B. a1 b1’ + (a1 b1’+ a1’b1 ) a0 b0 C. a1 a0’ + (a1 a0 + b1’b0’ ) b1 b0’ D. a1 a0 + (a1 a0’+ b1’b0 ) b1 b0 PROBLEM 3 (4 points) What is the priority scheme of this encoder? Inputs Outputs I3 I2 I1 I0 O1 O 0 d d 1 d 0 1 d d 0 1 0 0 d 1 0 0 1 0 1 0 0 0 1 1 A. I3 > I2 > I1 >I0 B. I0 > I1 > I2 >I3 C. I1 > I0 > I2 >I3 D. I2 > I1 > I3 >I0 3 PROBLEM 4 (4 points) Which is the correct binary representation of the decimal number 46.625? A. 101101.001 B. 101000.01 C. 111001.001 D. 101110.101 PROBLEM 5 (4 points) Which is the decimal equivalent number of the sum of the two 8-bit 2’s complement numbers FB16 and 3748? A. 3 B. 5 C. 7 D. 9 PROBLEM 6 (4 points) For the MUX-based circuit shown below, f(X,Y,Z) = ? X Y Z f A. X’Y’ + Y’Z’ B. X’Y’Z’ + YZ’ C. XYZ’ + Y’Z D. X’Y’Z’ + YZ 1 0 MUX 4 PROBLEM 7 (4 points) Which is the correct output F of this circuit? E C B D F A A. (A’E+AB)(C’D) B. (AE+A’B)(C’+D) C. (A’E+AB)(C’D’+CD’+CD) D. (A’E+AB)(CD’)’ PROBLEM 8 (5 points) In order to correctly perform 2910  14510, how many bits are required to represent the numbers? A 8 B 9 C 10 D 11 PROBLEM 9 (4 points) Which is the negative 2’s complement equivalent of the 8-bit number 01001101? A. 11001101 B. 10111100 C. 10110000 D. 10110011 0 2-1 1 MUX 0 0 1 1 2-4 decoder 2 EN 3 5 PROBLEM 10 (4 points) Which is the correct statement describing the behavior of the following Verilog code? module whatisthis(hmm, X, Y); output [3:0] hmm; input [3:0] X, Y; assign hmm = (X < Y) ? X : Y; endmodule A. If X>Y, hmm becomes 1111. B. hmm assumes min(X,Y). C. If X<Y, hmm becomes 1111. D. hmm assumes max(X,Y). PROBLEM 11 (4 points) Which Boolean expression corresponds to the function g(W,X,Y,Z) implemented by the following “non-priority” encoder-based circuit? Assume that one and only one input is high at any time. f W X g Y Z A. Y + Z B. W + Y C. X + Y D. X + Z PROBLEM 12 (4 points) Which Boolean expression corresponds to the output of the following logic diagram? (/B = B’) A. Z = ( A(B’ + C)’ )’ + ( (B’ + C)’ + D )’ B. Z= A(B C’) + (B C’ + D) C. Z = (A(B’ + C)(B’ + C + D) )’ D. Z = A(B’ + C)’ + (B’ + C + D)’ 0 0 1 1 2 3 Encoder 6 PROBLEM 13 (4 points) Which is the correct gate-level circuit in minimal SOP form for the following circuit? A F = Y’X’ + W’ZY’X B F = YX’ + W’Z’Y’X C F = YX’ + W’ZY’X D F = Y’X + W’ZY’X’ PROBLEM 14 (4 points) For the following flow map of a certain cross-coupled gate circuit, the circuit is currently in the underlined state. If the inputs YZ change to 11, the circuit becomes meta-stable. Between which two states (WX) does the circuit oscillate ? A 00  11 B 01  10 C 11  10 D 10  00 YZ WX 00 01 11 10 00 00 11 00 10 01 10 10 10 01 11 00 00 11 01 10 10 01 01 10 G1 Y0 G2A Y1 G2B Y2 Y3 A Y4 B Y5 C Y6 Y7 G1 Y0 G2A Y1 G2B Y2 Y3 A Y4 B Y5 C Y6 Y7 OR W X Y Z X Y Z F + 5 V 7 For each of the next 3 problems, show all your work. Partial credits will be given. PROBLEM 15 (15 points) 1) Which logic variable causes the hazard for the circuit given by the K-map below? 2) Using the timing diagram, clearly show how the hazard occurs. 3) Find the best hazard-free logic function. YZ WX 00 01 11 10 00 0 0 1 1 01 0 0 0 0 11 1 0 0 0 10 1 0 1 1 8 PROBLEM 16(15 points) Analyze the following cross-coupled NAND gates by showing: (a) flow map with stable states circled and with meta-stability condition shown by arrows, (b) state table, and (c) completed timing diagram below. Note that d is the propagation delay of each gate. XY G1(t)G2(t) 00 01 11 10 00 01 11 10 Inputs  XY=00 XY=01 XY=11 XY=10 Present States  X Y G1(t) G2(t) 0 d 2d 3d 4d 5d 6d 7d 8d 9d X Y G1 G2 9 PROBLEM 17 (15 points) Using Quine-McCluskey algorithm, find the minimal SOP for the following minterm list. f(A, B, C) = (1,2,3,4,6,7) w(j) j Match I Match II 0 1 2 3 PI Covering Table

EE118 FALL 2012 SAN JOSE STATE UNIVERSITY Department of Electrical Engineering TEST 2 — Digital Design I October 24, 2012 10:30 a.m. – 11:45 a.m. — Closed Book & Closed Notes — — No Crib Sheet Allowed — STUDENT NAME: (Last) Claussen , (First) Matthew STUDENT ID NUMBER (LAST 4 DIGITS): No interpretation of test problems will be given during the test. If you are not sure of what is intended, make appropriate assumptions and continue. Do not unstaple !!! Problems 1-14(4 points each) TOTAL Problems 15 – 17 (15 pts each) 1203 2 For the next 14 problems, circle the correct answer. No partial credit will be given. PROBLEM 1 (4 points) Which statement is not true? A. Any combinational circuit may be designed using multiplexers only. B. Any combinational circuit may be designed using decoders only. C. All Sequential circuits are based on cross-coupled NAND or NOR gates. D. A hazard in a digital system is an undesirable effect caused by either a deficiency in the system or external influences. E. None of the above PROBLEM 2 (4 points) For a 2-bit comparator comparing 2-bit numbers A = (a1 a0) and B = (b1 b0), what is the proper function for the f(A>B) output through logical reasoning? A. a1 b1’ + (a1 b1 + a1’b1’ ) a0 b0’ B. a1 b1’ + (a1 b1’+ a1’b1 ) a0 b0 C. a1 a0’ + (a1 a0 + b1’b0’ ) b1 b0’ D. a1 a0 + (a1 a0’+ b1’b0 ) b1 b0 PROBLEM 3 (4 points) What is the priority scheme of this encoder? Inputs Outputs I3 I2 I1 I0 O1 O 0 d d 1 d 0 1 d d 0 1 0 0 d 1 0 0 1 0 1 0 0 0 1 1 A. I3 > I2 > I1 >I0 B. I0 > I1 > I2 >I3 C. I1 > I0 > I2 >I3 D. I2 > I1 > I3 >I0 3 PROBLEM 4 (4 points) Which is the correct binary representation of the decimal number 46.625? A. 101101.001 B. 101000.01 C. 111001.001 D. 101110.101 PROBLEM 5 (4 points) Which is the decimal equivalent number of the sum of the two 8-bit 2’s complement numbers FB16 and 3748? A. 3 B. 5 C. 7 D. 9 PROBLEM 6 (4 points) For the MUX-based circuit shown below, f(X,Y,Z) = ? X Y Z f A. X’Y’ + Y’Z’ B. X’Y’Z’ + YZ’ C. XYZ’ + Y’Z D. X’Y’Z’ + YZ 1 0 MUX 4 PROBLEM 7 (4 points) Which is the correct output F of this circuit? E C B D F A A. (A’E+AB)(C’D) B. (AE+A’B)(C’+D) C. (A’E+AB)(C’D’+CD’+CD) D. (A’E+AB)(CD’)’ PROBLEM 8 (5 points) In order to correctly perform 2910  14510, how many bits are required to represent the numbers? A 8 B 9 C 10 D 11 PROBLEM 9 (4 points) Which is the negative 2’s complement equivalent of the 8-bit number 01001101? A. 11001101 B. 10111100 C. 10110000 D. 10110011 0 2-1 1 MUX 0 0 1 1 2-4 decoder 2 EN 3 5 PROBLEM 10 (4 points) Which is the correct statement describing the behavior of the following Verilog code? module whatisthis(hmm, X, Y); output [3:0] hmm; input [3:0] X, Y; assign hmm = (X < Y) ? X : Y; endmodule A. If X>Y, hmm becomes 1111. B. hmm assumes min(X,Y). C. If X

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Distribution of the Sample Mean and Linear Combinations – Examples Example 1 Let X1;X2; : : : ;X100 denote the actual net weights of 100 randomly selected 50-pound bags of fertilizer. a. If the expected weight of each bag is 50 pounds and the standard deviation is 1 pound, approximate P(49:75 • ¹X • 50:25) using the CLT. b. If the expected weight is 49.8 pounds rather than 50 pounds, so that on average bags are under…lled, approximate P(49:75 • ¹X • 50:25). Example 2 The breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 500 psi. a. What is the approximate probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,900 psi and 10,200 psi? b. If the sample size had been 15 rivets rather than 40 rivets, could the probability requested in part a be approximated from the given information? Why or why not? Example 3 The lifetime of a certain type of battery is normally distributed with mean 8 hours and standard deviation 1 hour. There are four batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages? Example 4 Suppose your waiting time for a bus in the morning is uniformly distributed on [0; 5], while waiting time in the evening is uniformly distributed on [0; 10]. Assume that evening waiting time is independent of morning waiting time. a. If you take the bus each morning and evening for a week, what is your total expected waiting time. b. What is the variance of your total waiting time? expected value and variance of the di¤erence between morning and evening waiting time on a given day? d. What are the expected value and variance of the di¤erence between total morning waiting time and total evening waiting time for a particular week? 2 Example 5 Three di¤erent roads feed into a particular freeway entrance. Suppose that during a …xed time period, the number of cars coming from each road onto the freeway is a random variable, with expected value and standard deviation as given in the following table: Road 1 Road 2 Road 3 Expected Value 800 1000 600 Standard Deviation 16 25 18 : a. What is the expected total number of cars entering the freeway at this point during the period? b. What is the variance of the total number of entering cars? Have you made any assumptions about the relationship between the number of cars on the di¤erent roads? c. With Xi denoting the number of cars entering from road i during the period, suppose that Cov(X1;X2) = 80, Cov(X1;X3) = 90, and Cov(X2;X3) = 100 (so that the three streams of tra¢c are not independent). Compute the expected total number of entering cars and the standard deviation of the total. Example 6 In an area having sandy soil, 50 small trees of a certain type were planted, and another 50 trees were planted in an area having clay soil. Let X be the number of trees planted in sandy soil that survive one year and Y be the number of trees planted in clay soil that survive one year. If the probability that a tree planted in sandy soil will survive one year is 0.7 and the probability of one-year survival in clay soil is 0.6, compute an approximation to P(¡5 • X ¡ Y • 5). For the purposes of this exercise, ignore the continuity correction.

Distribution of the Sample Mean and Linear Combinations – Examples Example 1 Let X1;X2; : : : ;X100 denote the actual net weights of 100 randomly selected 50-pound bags of fertilizer. a. If the expected weight of each bag is 50 pounds and the standard deviation is 1 pound, approximate P(49:75 • ¹X • 50:25) using the CLT. b. If the expected weight is 49.8 pounds rather than 50 pounds, so that on average bags are under…lled, approximate P(49:75 • ¹X • 50:25). Example 2 The breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 500 psi. a. What is the approximate probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,900 psi and 10,200 psi? b. If the sample size had been 15 rivets rather than 40 rivets, could the probability requested in part a be approximated from the given information? Why or why not? Example 3 The lifetime of a certain type of battery is normally distributed with mean 8 hours and standard deviation 1 hour. There are four batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages? Example 4 Suppose your waiting time for a bus in the morning is uniformly distributed on [0; 5], while waiting time in the evening is uniformly distributed on [0; 10]. Assume that evening waiting time is independent of morning waiting time. a. If you take the bus each morning and evening for a week, what is your total expected waiting time. b. What is the variance of your total waiting time? expected value and variance of the di¤erence between morning and evening waiting time on a given day? d. What are the expected value and variance of the di¤erence between total morning waiting time and total evening waiting time for a particular week? 2 Example 5 Three di¤erent roads feed into a particular freeway entrance. Suppose that during a …xed time period, the number of cars coming from each road onto the freeway is a random variable, with expected value and standard deviation as given in the following table: Road 1 Road 2 Road 3 Expected Value 800 1000 600 Standard Deviation 16 25 18 : a. What is the expected total number of cars entering the freeway at this point during the period? b. What is the variance of the total number of entering cars? Have you made any assumptions about the relationship between the number of cars on the di¤erent roads? c. With Xi denoting the number of cars entering from road i during the period, suppose that Cov(X1;X2) = 80, Cov(X1;X3) = 90, and Cov(X2;X3) = 100 (so that the three streams of tra¢c are not independent). Compute the expected total number of entering cars and the standard deviation of the total. Example 6 In an area having sandy soil, 50 small trees of a certain type were planted, and another 50 trees were planted in an area having clay soil. Let X be the number of trees planted in sandy soil that survive one year and Y be the number of trees planted in clay soil that survive one year. If the probability that a tree planted in sandy soil will survive one year is 0.7 and the probability of one-year survival in clay soil is 0.6, compute an approximation to P(¡5 • X ¡ Y • 5). For the purposes of this exercise, ignore the continuity correction.

Materials Chemistry for Engineers 1. In the van der Waals corrections to the Ideal Gas Law: (P + a/V2)(V – b) = nRT (a) What do a and b correct for from the Ideal Gas Law? (b) How would one determine a and b experimentally? Describe a proposed experiment and data analysis method for your experiment. 2. (a) What are the assumptions of the Ideal Gas Law? How did van der Waal modify these assumptions to come up with his equation of state? (b) what is an equation of state, in general? Describe in your own words. 3. Given the following data: Material a b_____ (l2.atm/mole2) (l/mole) N2 1.39 0.03913 NH3 4.17 0.03107 Aniline 26.50 0.1369 Benzene 18.00 0.1154 (a) Plot P vs. T for each gas using the van der Waals equation of state. Assume that you have a 1 liter volume and 1 mole of gas and plot the temperature on the x-axis from room temperature to 1400 K (pressures should range from about 0 atm to about 120 atm, depending on the gas). Plot the Ideal Gas Law with the other data on one plot. Are the interactions between molecules attractive or repulsive at low temperature? How do you know? What is happening with the gases at high temperature? Is one of the gases different from the others at 1400 K? (b) Discuss the nature of the intermolecular interaction that creates the deviation from ideality for each material. Are there induced dipole-induced dipole interactions, iondipole interactions, etc. for each of the different gases? Draw their chemical structures. 4. Ethane (CH3CH3) and fluoromethane (CH3F) have the same number of electrons and are essentially the same size. However, ethane has a boiling point of 184.5 K and fluoromethane has a boiling point of 194.7 K. Explain this 10 degree difference in boiling point in terms of the van der Waals forces present. Bonus, what is the size of each molecule? Show your calculation/sources.

Materials Chemistry for Engineers 1. In the van der Waals corrections to the Ideal Gas Law: (P + a/V2)(V – b) = nRT (a) What do a and b correct for from the Ideal Gas Law? (b) How would one determine a and b experimentally? Describe a proposed experiment and data analysis method for your experiment. 2. (a) What are the assumptions of the Ideal Gas Law? How did van der Waal modify these assumptions to come up with his equation of state? (b) what is an equation of state, in general? Describe in your own words. 3. Given the following data: Material a b_____ (l2.atm/mole2) (l/mole) N2 1.39 0.03913 NH3 4.17 0.03107 Aniline 26.50 0.1369 Benzene 18.00 0.1154 (a) Plot P vs. T for each gas using the van der Waals equation of state. Assume that you have a 1 liter volume and 1 mole of gas and plot the temperature on the x-axis from room temperature to 1400 K (pressures should range from about 0 atm to about 120 atm, depending on the gas). Plot the Ideal Gas Law with the other data on one plot. Are the interactions between molecules attractive or repulsive at low temperature? How do you know? What is happening with the gases at high temperature? Is one of the gases different from the others at 1400 K? (b) Discuss the nature of the intermolecular interaction that creates the deviation from ideality for each material. Are there induced dipole-induced dipole interactions, iondipole interactions, etc. for each of the different gases? Draw their chemical structures. 4. Ethane (CH3CH3) and fluoromethane (CH3F) have the same number of electrons and are essentially the same size. However, ethane has a boiling point of 184.5 K and fluoromethane has a boiling point of 194.7 K. Explain this 10 degree difference in boiling point in terms of the van der Waals forces present. Bonus, what is the size of each molecule? Show your calculation/sources.

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• Section 1: Design Description (<2/3 page) o Describe your design, including a SCHEMATIC, a PHOTOGRAPH, and a description of materials/items used o Describe why you chose your design • Section 2: Analysis (only as much length as is necessary to clearly communicate your analysis). Note that scanning handwritten resistance networks may be faster/easier than creating digital figures. o Estimate the rate in Watts at which sunlight is absorbed by your design (assume a solar flux of 1000 W/m2) o Show a thermal resistance network for each heat transfer path for the heat loss from your design. Calculate/estimate all thermal resistances. For all convection correlations, list the assumed geometry, the equation being used, and the calculated ‘h’ value. o Identify the dominant mode of heat loss, and discuss why this is the case. o STATE AND JUSTIFY all assumptions and estimates in the analysis. And by “justify” I mean “PROVE to me that your assumption is reasonable” • Section 3: Reflection (<1/2 page) o Suggest TWO design modifications that would significantly reduce the heat loss from your design. One modification must be a low-­‐cost modification that would fit within your project budget, and the other modification must be a modification using commercially available materials/technologies that would be realistically used in industry (i.e. without an absurd cost constraint). Note that you will have to perform some independent research on available materials and technologies to complete this. • Section 4: Bill of Materials o List ALL materials in the design (automatic 20% grade reduction for any material I find in your design that is unaccounted for in your bill of materials) o Can treat scavenged items as zero cost only if anyone could reasonably attain them freely (for donated items you must count the full purchase cost) o For structural materials, you must use the minimum UNIT COST, not a portion cost (i.e. if you buy an item in its smallest available quantity and only use 10% of the item, you still must include the TOTAL item cost) o For fastening/assembly/filler materials, you may use portion costs (e.g. glue, nails, screws, etc). If in doubt, ask me. o You must include the cost of any specialty tools required for your assembly that are not available in the machine shop (even if they are your own)

• Section 1: Design Description (<2/3 page) o Describe your design, including a SCHEMATIC, a PHOTOGRAPH, and a description of materials/items used o Describe why you chose your design • Section 2: Analysis (only as much length as is necessary to clearly communicate your analysis). Note that scanning handwritten resistance networks may be faster/easier than creating digital figures. o Estimate the rate in Watts at which sunlight is absorbed by your design (assume a solar flux of 1000 W/m2) o Show a thermal resistance network for each heat transfer path for the heat loss from your design. Calculate/estimate all thermal resistances. For all convection correlations, list the assumed geometry, the equation being used, and the calculated ‘h’ value. o Identify the dominant mode of heat loss, and discuss why this is the case. o STATE AND JUSTIFY all assumptions and estimates in the analysis. And by “justify” I mean “PROVE to me that your assumption is reasonable” • Section 3: Reflection (<1/2 page) o Suggest TWO design modifications that would significantly reduce the heat loss from your design. One modification must be a low-­‐cost modification that would fit within your project budget, and the other modification must be a modification using commercially available materials/technologies that would be realistically used in industry (i.e. without an absurd cost constraint). Note that you will have to perform some independent research on available materials and technologies to complete this. • Section 4: Bill of Materials o List ALL materials in the design (automatic 20% grade reduction for any material I find in your design that is unaccounted for in your bill of materials) o Can treat scavenged items as zero cost only if anyone could reasonably attain them freely (for donated items you must count the full purchase cost) o For structural materials, you must use the minimum UNIT COST, not a portion cost (i.e. if you buy an item in its smallest available quantity and only use 10% of the item, you still must include the TOTAL item cost) o For fastening/assembly/filler materials, you may use portion costs (e.g. glue, nails, screws, etc). If in doubt, ask me. o You must include the cost of any specialty tools required for your assembly that are not available in the machine shop (even if they are your own)

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