## A 2000 N force is applied mid chord of member BC as shown in the figure. 1) Determine the support reaction at A exerted on member AB. (15 pt) 2) Determine the support reaction at C exerted on member BC. (15 pt)

## A coutainor of weight W is suspended from ring A . cable BAC passes through the ring and is attached to fixed support knowing that w=376N, determine P and Q (hint The tension is the same in both postions of cables BAC.

## MAE 241 – Homework 2 Page 1 of 2 MAE 241 – Spring 2019 – Homework 2 Administered 1/18/2019 – Due 11PM, Sunday 1/27/2019 to Gradescope Problem 1 The average water head (vertical height of water column) maintained in Hoover dam reservoir is about 500 ft. Assume water density of 62.43 lb/ft3. a. Determine the maximum pressure at the bottom of reservoir. b. Find the power generation potential of the water at that pressure if the discharge rate is 500×103 ft3/s. Problem 2 The Vestas V164 is one of the largest wind turbines in the world, with diameter of 164 m. If the theoretical limit on the capacity of a wind turbine is 1/3rd of its power generation potential, determine the capacity of the turbine when it is placed in a location where the average wind speed is 10 m/s. Assume air density as 1.25 kg/m3. Problem 3 An automobile has a mass of 1200 kg. What is its kinetic energy, in kJ, relative to the road when traveling at a velocity of 50 km/h? If the vehicle accelerates to 100 km/h, what is the change in kinetic energy, in kJ? Problem 4 A 5 kg brick is dropped from a height of 12 m onto a spring with a spring constant 8 kN/m. If the spring has a unstretched length of 0.5m, find (a) the shortest length the spring will be compressed before recoil, and (b) the final length of spring once the whole system becomes static. Problem 5 A piping installation is used to transport 20 L/s of water from a reservoir (location 1) to a point of use (location 2) 20 meters above. The absolute pressure of water at the inlet of the installation is 110 kPa; the gauge pressure measured right before the point of use is 552 kPa. Determine the power input required, in kW. Assume that because the piping at locations (1) and (2) have the same diameter the average velocities of water are equal and the density of water is 1000 kg/m3. Problem 6 A system receives 10 MJ in the form of heat in a process and it produced 4 MJ of work. The system velocity changes from 10 m/s to 25 m/s. For a 50 kg mass of the system, determine the change in internal energy of the system. MAE 241 – Homework 2 Page 2 of 2 Problem 7 On a recent energy assessment performed to an industrial facility in Tempe by a team of ASU’s Industrial Assessment Center, the team evaluated a boiler whose rated input was 6 MBTUH (6 million BTU per hour). After measuring the composition of flue gases it was apparent that the boiler was not be operating at its best operating point; this suspicion was validated by determining that the combustion efficiency was equal to 0.65. As corrective measure the boiler received a tune up that increased the combustion efficiency to 0.8. The boiler operates 48 weeks per year continuously while the plant is in production. Taking the cost of energy to be $13 per MBTU, determine: a. The annual energy cost. b. The annual cost savings as a result of tuning up the boiler. c. List the assumptions used in your computations. Problem 8 Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force, which can be expressed as 𝐹𝑏 = 𝜌𝑎𝑖𝑟𝑔𝑉𝑏𝑎𝑙, will push the balloon upward. (a) If the balloon has a diameter of 15 m and carries eight people, 75 kg each, determine the acceleration of the balloon when it is first released. (b) The change in air density with altitude can be approximated up to 10km using a linear function 𝜌𝑎𝑖𝑟 = 1.173 − 8 × 10−5ℎ where ℎ is the altitude in m. At what theoretical altitude the balloon will stop climbing upwards? Assume the density of air is 1.173 kg/m3 at ground level, and neglect the weight of the ropes and the cage. Problem 9 A differential manometer is used to measure pressure difference between two fluid systems. Two parallel pipes carrying freshwater and seawater are connected to each other by a double U-tube differential manometer, as shown in Figure. (a) Determine the pressure difference between the two pipelines if ℎ = 10 cm. (b) If the pressure difference between the pipes is doubled, what will be the difference in heights (ℎ) of mercury? Take the density of seawater at that location to be 1035 kg/m3, and the specific gravity of the oil is 0.72. Assume all fluids are incompressible.

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## ) A steel rod of radius 0.01 m and length 2. M is pulled on with a tensile force of 200,000 N, and the bar stretches to a length of 2.08 m. The radius of the bar is reduced to 0.0099 m. Determine the stress, strain, Young’ modulus (E), and Poisson’s ratio () from this test. Use the Young’s modulus and Poisson’s ratio to determine the Bulk Modulus and Shear Modulus, using the equations given in class.

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## Identify legislative and regulative requirements relative to information security for a bank

A number of federal laws directly control the collection and … Read More...

## 2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm on Saturday, February 28, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? You did not open hints for this part. ANSWER: Part B Which two vectors, when added, will have the largest (positive) y component? You did not open hints for this part. ANSWER: C and E E and F A and F C and D B and D 2/24/2015 Assignment 2 =3484333 2/22 Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? You did not open hints for this part. ANSWER: Components of Vectors Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from 5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. Part A C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F _._ _._ ._ 2/24/2015 Assignment 2 =3484333 3/22 What is the x component of ? Express your answer to two significant figures. You did not open hints for this part. ANSWER: Part B What is the y component of ? Express your answer to the nearest integer. ANSWER: Part C What is the y component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: Part D What is the component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: _._ _4 = _._ _5 = _._ _5 = 4 _._ _4 = 2/24/2015 Assignment 2 =3484333 4/22 The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation. The answers below are all integers, so estimate the components to the nearest whole number. Part E In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part F In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part G What is true about and ? Choose from the pulldown list below. ANSWER: Finding the Cross Product The figure shows two vectors and separated by an angle . You are given that , , and . _._ _._ _4, _5 = _._ _4 , _5 = _._ _._ They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors. _ ._ _._ J56 _ .__ _ _ _ _.__ _ _ _ _ ._g_.__ _ ._ 2/24/2015 Assignment 2 =3484333 5/22 Part A Express as an ordered triplet of values, separated by commas. ANSWER: Part B Find the magnitude of . ANSWER: Part C Find the sine of the angle between and . ANSWER: Significant Figures Conceptual Question In the parts that follow select whether the number presented in statement A is greater than, less than, or equal to the number presented in statement B. Be sure to follow all of the rules concerning significant figures. _ ._ _ ._= _ ._ ]_ ]._ = _ ._ _._ TJO J__ = 2/24/2015 Assignment 2 =3484333 6/22 Part A Statement A: 2.567 , to two significant figures. Statement B: 2.567 , to three significant figures. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: Part B Statement A: (2.567 + 3.146 ), to two significant figures. Statement B: (2.567 , to two significant figures) + (3.146 , to two significant figures). Determine the correct relationship between the statements. ANSWER: Part C Statement A: Area of a rectangle with measured length = 2.536 and width = 1.4 . Statement B: Area of a rectangle with measured length = 2.536 and width = 1.41 . Since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying numbers while respecting significant figures. If you need a reminder, consult the hint. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: LN LN Statement A is greater than less than equal to Statement B. LN LN LN LN Statement A is greater than less than equal to Statement B. N N N N 2/24/2015 Assignment 2 =3484333 7/22 ± Vector Dot Product Let vectors , , and . Calculate the following: Part A You did not open hints for this part. ANSWER: Part B What is the angle between and ? Express your answer using one significant figure. You did not open hints for this part. ANSWER: Part C ANSWER: Part D ANSWER: Statement A is greater than less than equal to Statement B. _.__ _ _Ã_ _.__ Ã_ _ _ _.__ Ã_Ã_ _ _._ø _._ = J”# _._ _._ J”# = SBEJBOT __._ø __._ = 2/24/2015 Assignment 2 =3484333 8/22 Part E Which of the following can be computed? You did not open hints for this part. ANSWER: and are different vectors with lengths and respectively. Find the following: Part F Express your answer in terms of You did not open hints for this part. ANSWER: Part G If and are perpendicular, You did not open hints for this part. ANSWER: _ _._ø __._ = _._ø _._ø _._ _._ø _._ø _._ _._ø _.___._ _ ø _._ _ .__ _ .__ __ __ __ = ø _ .__ _ .__ _ .__ _ .__ = ø _ .__ _ .__ 2/24/2015 Assignment 2 =3484333 9/22 Part H If and are parallel, Express your answer in terms of and . You did not open hints for this part. ANSWER: ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Part A Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part B _ .__ _ .__ __ __ = ø _ .__ _ .__ _ ._ _ È _._ _ C È _._ = ._ 2/24/2015 Assignment 2 =3484333 10/22 Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part C Find the components of the vector with length = 1.00 and angle 30.0 as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Exercise 1.28 Part A How many dollar bills would you have to stack to reach the moon? (Depending on age, dollar bills can be stacked with about 23 per millimeter.) Express your answer using one significant figure. ANSWER: Problem 1.80 A boulder of weight rests on a hillside that rises at a constant angle above the horizontal, as shown in the figure . Its weight is a force on the boulder that has direction vertically downward. _._ _ D È _._ = _._ _ ] _ È _._ = dollar bills 3 C 2/24/2015 Assignment 2 =3484333 11/22 Part A In terms of and , what is the component of the weight of the boulder in the direction parallel to the surface of the hill? Express your answer in terms of and . ANSWER: Part B What is the component of the weight in the direction perpendicular to the surface of the hill? Express your answer in terms of and . ANSWER: Part C An air conditioner unit is fastened to a roof that slopes upward at an angle of . In order that the unit not slide down the roof, the component of the unit’s weight parallel to the roof cannot exceed 550 N. What is the maximum allowed weight of the unit? ANSWER: Problem 1.84 You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 23.5 from yours, in the direction 19.0 north of east. Karl’s tent is 40.0 from yours, in the direction 36.0 south of east. C 3 C 3 ]3,_. ] = C 3 ]3,!., ] = ____È 3 = / N È N È 2/24/2015 Assignment 2 =3484333 12/22 Part A What is the distance between Karl’s tent and Joe’s tent? ANSWER: Multiple Choice Question 1.8 Part A The components of vectors and are given as follows: Ax = +5.7 Bx = 9.8 Ay = 3.6 By = 6.5 The magnitude of the vector difference , is closest to: ANSWER: OneDimensional Kinematics with Constant Acceleration Learning Goal: To understand the meaning of the variables that appear in the equations for onedimensional kinematics with constant acceleration. Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of motion most frequently involved in introductory kinematics problems. The kinematic equations for such motion can be written as , , where the symbols are defined as follows: is the position of the particle; _ = N _ ¥ _ ¥ Ã _ ¥ _ ¥ 5.0 11 5.0 16 250 4 0_ 4J_2J0_ _ __ 0_ 2 0 _ 2J __0 4 0 2/24/2015 Assignment 2 =3484333 13/22 is the initial position of the particle; is the velocity of the particle; is the initial velocity of the particle; is the acceleration of the particle. In anwering the following questions, assume that the acceleration is constant and nonzero: . Part A The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part B The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part C The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part D The quantity represented by is a function of time (i.e., is not constant). ANSWER: 4J 2 0 2J _ _ Ü _ 4 true false 4J true false 2J true false 2 true false 2/24/2015 Assignment 2 =3484333 14/22 Part E Which of the given equations is not an explicit function of and is therefore useful when you don’t know or don’t need the time? ANSWER: Part F A particle moves with constant acceleration . The expression represents the particle’s velocity at what instant in time? ANSWER: More generally, the equations of motion can be written as and . Here is the time that has elapsed since the beginning of the particle’s motion, that is, , where is the current time and is the time at which we start measuring the particle’s motion. The terms and are, respectively, the position and velocity at . As you can now see, the equations given at the beginning of this problem correspond to the case , which is a convenient choice if there is only one particle of interest. To illustrate the use of these more general equations, consider the motion of two particles, A and B. The position of particle A depends on time as . That is, particle A starts moving at time with velocity , from . At time , particle B has twice the acceleration, half the velocity, and the same position that particle A had at time . Part G What is the equation describing the position of particle B? You did not open hints for this part. ANSWER: 0 4_ 4J_2J0_ _ __ 0_ 2 _ 2J __0 _ ___ 4Ã 2_ 2_J 4J _ 2J __0 only at time only at the “initial” time when a time has passed since the particle’s velocity was 0 _ _ 0 2J 4 0_ 4J_2J 0_ _ 0 __ _ 2 0 _ 2J __ 0 0 0 _ 0Ã0J 0 0J 4J 2J 0 _ 0J 0J _ _ 4″ 0 _ 4J _2J0_ ____0_ 0 _ 0J” _ _ 2J” _ 2J 4J” _ 4J 0 _ 0_ 0 _ _ 2/24/2015 Assignment 2 =3484333 15/22 Part H At what time does the velocity of particle B equal that of particle A? You did not open hints for this part. ANSWER: Given Positions, Find Velocity and Acceleration Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordinate of a moving object. The position is tabulated at 1s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes. time (s) 0 1 2 3 4 5 6 7 8 9 x (m) 0 1 4 9 16 24 32 40 46 48 Part A Which graph best represents the function , describing the object’s position vs. time? 4# 0_ 4J__2J0_ _ __ 0_ 4# 0 _ 4J ____2J0__0_ 4# 0_ 4J__2J 0_0__ _ 0_ __ 0__ 4# 0 _ 4J ____2J 0_0_ __ 0_0_ _ 4# 0_ 4J__2J 0Ã0__ _ 0Ã __ 0__ 4# 0 _ 4J ____2J 0Ã0_ __ 0Ã0_ _ The two particles never have the same velocity. 0_ 0__ 2J __ 0__0__ 2J __ 0__0__ 2J __ 4 0 2/24/2015 Assignment 2 =3484333 16/22 You did not open hints for this part. ANSWER: Part B Which of the following graphs best represents the function , describing the object’s velocity as a function of time? You did not open hints for this part. ANSWER: 1 2 3 4 2 0 2/24/2015 Assignment 2 =3484333 17/22 Part C Which of the following graphs best represents the function , describing the acceleration of this object? You did not open hints for this part. ANSWER: A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. 1 2 3 4 _ 0 1 2 3 4 _ 0 _ _ _ _ 4 _ _ 2/24/2015 Assignment 2 =3484333 18/22 Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . You did not open hints for this part. ANSWER: Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . You did not open hints for this part. ANSWER: Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . You did not open hints for this part. 4NBO 0 _ _ 0 4NBO 0 = 4CVT 0 _ 0 4CVT = 0DBUDI 2/24/2015 Assignment 2 =3484333 19/22 ANSWER: Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Stopping on Snow Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about twofifths as much as that of stopping on wet snow. Part A For a given initial velocity, how does the time it takes to stop on dry snow differ from the time it takes to stop on wet snow? You did not open hints for this part. ANSWER: Part B For a given initial velocity, how does the stopping distance on dry snow differ from the stopping distance on wet snow? 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI _ _ _ Ç 0DBUDI 0E 0X 0E _ ___0X 0E _ 0X 0E _ ___0X 4E 4X 2/24/2015 Assignment 2 =3484333 20/22 You did not open hints for this part. ANSWER: Exercise 2.34 A subway train starts from rest at a station and accelerates at a rate of for 14.0 . It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station. Part A Find the total distance covered. ANSWER: Problem 2.57 Dan gets on Interstate Highway I280 at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88.0 . After traveling 76 km, he reaches the Aurora exit . Realizing he has gone too far, he turns around and drives due east 34 back to the York exit at an average velocity of magnitude 75.0 . Part A For his whole trip from Seward to the York exit, what is his average speed? 4E _ ___4X 4E _ 4X 4E _ ___4X ____ N_T_ T T ____ N_T_ = LN LN_I LN LN_I 2/24/2015 Assignment 2 =3484333 21/22 ANSWER: Part B For his whole trip from Seward to the York exit, what is the magnitude of his average velocity? ANSWER: Multiple Choice Question 2.1 Part A A train starts from rest and accelerates uniformly, until it has traveled 5.9 km and acquired a velocity of 35 m/s. The train then moves at a constant velocity of 35 m/s for 400 s. The train then decelerates uniformly at 0.065 m/s2, until it is brought to a halt. The acceleration during the first 5.9 km of travel is closest to: ANSWER: Multiple Choice Question 2.8 Part A A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision? ANSWER: 2 = LN_I 2 = LN_I 0.13 m/s2 0.11 m/s2 0.12 m/s2 0.10 m/s2 0.093 m/s2 2/24/2015 Assignment 2 Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 18 points. zero 200 m/s2 1500 m/s2 1300 m/s2 2800 m/s2

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## Determine the resulant of the three force of problem 2.22 determine 2.22 the x and Y componants of each of the force shown.

## 1 Lab Assignment Q1) The PIC16F1937 Memory Banks i) The Special Function Registers within the PIC16F1937 microcontroller are held within a number of memory banks. How many memory banks are there within the PIC16F1937 microcontroller? ii) Explain two methods to show how a special function register within a particular memory bank can be selected. Q1) The TRIS Registers The PIC16F61937 microcontroller has five TRIS registers, TRISA, TRISB, TRISC, TRISD, and TRISE situated in bank 1 in the special function register memory map. i) What is the function of the TRIS registers? ii) How can the TRIS registers in bank 1 be accessed? Write a short program to configure PORTA of the microcontroller as inputs and PORTB of the microcontroller as outputs. For the remaining exercises assume that PORTA is connected to switches and PORTB is connected to LEDs in common cathode configuration (i.e. output a 1 to illuminate). Q2) Key Press Accumulator It is required to produce a system incorporating a microcontroller that keeps count (in binary) of the number of times that a key has been pressed. The key is connected to bit RA0 of PORTA and when pressed should increment the binary value displayed on LEDs connected to PORTB. Write a program to meet the above specification, simulate the program to ensure correct operation, program a microcontroller and test. (Marks allocated for correct program demonstration). 2 Q3) Software Delays The PIC16F1937 assembly language program listed below is a software time delay incorporating two nested loops. value1 equ 0x20 value2 equ 0x21 org 0x00 delay movlw .65 movwf value1 outer movlw .255 movwf value2 inner decfsz value2 goto inner decfsz value1 goto outer wait goto wait By incorporating breakpoints and using the stopwatch determine the amount of time elapsed in the software delay assuming the microcontroller is operating from a 4 MHz crystal oscillator. Compare the value obtained above with that obtained by calculation. Are the time values equal? Q4) Travelling LED program It is required to produce a system incorporating a PIC16F1937 to produce the following sequence on LEDs (travelling LED). And repeat The LEDs are connected to PORTB and the sequence should only start after the key connected to RA0 has been asserted. Should key RA1 be pressed then all of the LEDs should be switched off. The sequence can be set off again by reasserting key RA0. Incorporate a 100ms delay between changes of state of the sequence. Write a program to carry out the above specification, simulate, program a microcontroller and test. (Marks allocated for correct program demonstration). 3 Lab Assignment Checklist Marks allocation: Q1) The PIC16F1937 memory banks Qi) 2% Qii) 2% Q1) TRIS Registers Qi) 2% Qii) 2% Configuration program 4% Q2) Key Press Accumulator Program Flowchart 8% Program 20% Explanation 5% Demonstration 5% Q3) Software Delays By stopwatch 6% By calculation 6% Q4) Travelling LED program Flowchart 8% Program 20% Explanation 5% Demonstration 5% TOTAL 100%

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## 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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