Introduction to simulation

pptx

School

Concordia University *

*We aren’t endorsed by this school

Course

311

Subject

Industrial Engineering

Date

Oct 30, 2023

Type

pptx

Pages

65

Uploaded by ElderBookAlpaca11

Report
Dr. Ali Akgunduz EV04-157 ali.akgunduz@concordia.ca You can access to course materials from Moodle. You will access to the course resources using your ENCS account INDU 311 Simulation of Industrial Systems
Simulation Is … Simulation (very broad term) methods and applications to imitate or mimic real systems, usually via computer Applies in many fields and industries Very popular and powerful method Book covers simulation in general and the Arena simulation software in particular This chapter – general ideas, terminology, examples of applications, good/bad things, kinds of simulation, software options, how/when simulation is used
learn? System to be studied Bank; School; Factory; Airline etc. Learn about the system: Collect data Learn about the system: Analyze data Estimate distributions that best represent your data Normal; Exponential ; Model the system Arena Simulation Randomness How to introduce randomness Verify model with actual system Design Alternatives using Simulation Run Model Compare Alternative s Your Expectations: Define objective Select the best alternative Implement
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Systems • System – facility or process, actual or planned – Examples abound … • Manufacturing facility • Bank operation • Airport operations (passengers, security, planes, crews, baggage) • Transportation/logistics/distribution operation • Hospital facilities (emergency room, operating room, admissions) • Computer network • Freeway system • Business process (insurance office) • Criminal justice system • Chemical plant • Fast-food restaurant • Supermarket • Theme park • Emergency-response system
Would you assign two or three cashiers at a bank during 8 am until 4 pm shift? In order to produce 500 part in one week: how many employees do I need? how long over time is required Is it better to have two slow machines or purchasing a new faster, more efficient machineries? Can Dorval airport handle new jumbo Airbuses when they start flying? What was the best way to evacuate New Orleans
What do we do with a system? Study the system – measure, improve, design, control Maybe just play with the actual system Advantage — unquestionably looking at the right thing But it’s often impossible to do so with the actual system System doesn’t exist Would be disruptive, expensive, or dangerous
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
System Models: Model – set of assumptions/approximations about how the system works Study the model instead of the real system … usually much easier, faster, cheaper, safer Can try wide-ranging ideas with the model Make your mistakes on the computer where they don’t count, rather than for real where they do count Often, just building the model is instructive – regardless of results Model validity (any kind of model … not just simulation) Care in building to mimic reality faithfully Level of detail Get same conclusions from the model as you would from system
Types of Models Physical ( iconic ) models Tabletop material-handling models Mock-ups of fast-food restaurants Flight simulators Logical ( mathematical ) models Approximations and assumptions about a system’s operation Often represented via computer program in appropriate software Exercise the program to try things, get results, learn about model behavior
Studying Logical Models If model is simple enough, use traditional mathematical analysis … get exact results, lots of insight into model Queueing theory Differential equations Linear programming But complex systems can seldom be validly represented by a simple analytic model Danger of over-simplifying assumptions … model validity? Type III error – working on the wrong problem Often, a complex system requires a complex model, and analytical methods don’t apply … what to do?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Computer Simulation Broadly interpreted, computer simulation refers to methods for studying a wide variety of models of systems Numerically evaluate on a computer Use software to imitate the system’s operations and characteristics, often over time Can be used to study simple models but should not use it if an analytical solution is available Real power of simulation is in studying complex models Simulation can tolerate complex models since we don’t even aspire to an analytical solution
Advantages of Simulation (cont’d.) • Advances in computing/cost ratios – Estimated that 75% of computing power is used for various kinds of simulations – Dedicated machines (e.g., real-time shop-floor control) • Advances in simulation software – Far easier to use (GUIs) – No longer as restrictive in modeling constructs (hierarchical, down to C) – Statistical design & analysis capabilities
Disadvantages of Simulation • Don’t get exact answers, only approximations, estimates – Also true of many other modern methods – Can bound errors by machine roundoff • Get random output ( RIRO ) from stochastic simulations – Statistical design, analysis of simulation experiments – Exploit: noise control, replicability, sequential sampling, variance- reduction techniques – Catch: “standard” statistical methods seldom work
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Different Kinds of Systems • Static vs. Dynamic – Does time have a role in the model? • Continuous-change vs. Discrete-change – Can the “state” change continuously or only at discrete points in time? • Deterministic vs. Stochastic – Is everything for sure or is there uncertainty? • Most operational models: – Dynamic , Discrete-change , Stochastic
Using Computers to Simulate • General-purpose languages (FORTRAN) – Tedious, low-level, error-prone – But, almost complete flexibility • Support packages – Subroutines for list processing, bookkeeping, time advance – Widely distributed, widely modified • Spreadsheets – Usually static models – Financial scenarios, distribution sampling, SQC
Using Computers to Simulate (cont’d.) • Simulation languages – GPSS, SIMSCRIPT, SLAM, SIMAN (on which Arena is based, and is included in Arena) – Popular, still in use – Learning curve for features, effective use, syntax • High-level simulators – Very easy, graphical interface – Domain-restricted (manufacturing, communications) – Limited flexibility — model validity?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Where Arena Fits In • Hierarchical structure – Multiple levels of modeling – Can mix different modeling levels together in the same model – Often, start high then go lower as needed • Get ease-of-use advantage of simulators without sacrificing modeling flexibility
How to analyze a system?
B >2 hour s EXPO(0.3 hours) TBA<0.0 5 hours 20% 200 patients for 40 of them TBA<0.05 hour 30 of them 0.05<TBA<0.1 hour 15% TBA<0. 1 TBA Probabilit y $52 If 60 people have less than $10, can we still have the average 52$?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
a b P(x) = p a<x<b UNIF(0.1, 0.2) p=1/(b-a) If x is a continuous variable, P(x = value) =0 P(l<x<u) =
a b c TRIA(a, c, b) == TRIA(0.8, 1.2, 1.6)
Patient Arrival s ? Nurse / Assess ment ? BEDS Doctors Waiting Area How do we predict arrivals? How is decided who goes where? Who gets the bed first? Leave the system
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
What kind of data do you need to collect for modeling this system? Number of resources Capacity =={Nurse capacity, Doctor Capacity, Bed capacity} Capacity = {1, 2, 3} one nurse will not be available for 24/7 Because Nurse is a human with needs, doctors are human with needs Also, I might have 1 doctor evening time, 2 doctors day time???? On the other hand 3 beds will provide 3 capacities for all 24/7 Processing times {Performance of each doctor may vary} Time between arrivals Frequency of patient groups Understanding of the information and material flow (Process flow)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
I don’t need to collect number of people waiting And how long they are waiting To model my system in mathematical or simulation format Your model will create these outcomes? In order to validate your model with the actual system, you expect to have similar waiting times and number of people waiting. :Average, maximum …
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Goals of the simulation study Collect data and analyze it What kinds of data? Total number of outputs Average waiting time in the queue Maximum waiting time in the queue Time-average number of parts waiting in the queue Maximum number of objects waiting in the queue Average time objects stay in the system Maximum time objects stay in the system Utilization of resources
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
What are the parameters of simulations Entities: Anything we process Attributes: Characteristics of entities Variables: System wide values, visible in all parts of the system Resources Processing units Queues Where entities wait to be processed Statistical accumulators Collecting statistics for certain purpose Events: The moment something happens– Arrive, Departure, end of the simulation Simulation clock: It increments by the event. Different from the traditional timers Starting and stopping criteria: Simulate by the time, or by the number etc.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
The System: A Simple Processing System Arriving Blank Parts Departing Finished Parts Machine (Server) Queue (FIFO) Part in Service 4 5 6 7 • General intent: Estimate expected production Waiting time in queue, queue length, proportion of time machine is busy • Time units Can use different units in different places … must declare Be careful to check the units when specifying inputs Declare base time units for internal calculations, outputs Be reasonable (interpretation, roundoff error)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Queuing Theory 1. Single Server, single queue systems M/M/1 systems: First M states that arrival process is Markovian: The inter arrival times are independent and identically distributed (IID), draws from the same distribution. Second M states that processing time is IID Finally 1 states that this is a single server system MM/2 ? Queuing theory enables us to predict the behavior of the system by equations Average Waiting Time in Queue Where μ s is the average service time and μ a is the average time between arrivals
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Queuing Theory Where μ s is the average service time μ A is the average time between arrivals ω is the service rate λ is the arrival rate ρ is the expected utilization at the steady state
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Example In an M/M/1 queuing system, the average time between arrivals is 10 minutes and the expected service time is 8 minutes What is the expected utilization in this system?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Solution ρ = μ s / μ A = 8/10 = 80%
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Queuing Theory Can we calculate the expected number of people in the queue (L q ) (L, number of people in the system is Lq+1 L q = ρ 2 /(1- ρ) = 0.8 2 /0.2 = 3.2 people is expected to be in the Queue
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
L ρ 1 20 60 100 0.80
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Pieces of a Simulation Model Statistical accumulators for the simple processing system Number of parts produced so far Total of the waiting times spent in queue so far No. of parts that have gone through the queue Max time in queue we’ve seen so far Total of times spent in system Max time in system we’ve seen so far Area so far under queue-length curve Q ( t ) Max of Q ( t ) so far Area so far under server-busy curve B ( t ) Where Q(t) is the number of customers in the queue at time t. And B(t) is the utilization of the resource at time t.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation Dynamics: The Event-Scheduling “World View” Identify characteristic events Decide on logic for each type of event to Effect state changes for each event type Observe statistics Update times of future events (maybe of this type, other types) Keep a simulation clock , future event calendar Jump from one event to the next, process, observe statistics, update event calendar Must specify an appropriate stopping rule Usually done with general-purpose programming language (C, FORTRAN, etc.)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Events for the Simple Processing System Arrival of a new part to the system Update time-persistent statistical accumulators (from last event to now) Area under Q ( t ) Max of Q ( t ) Area under B ( t ) “ Mark” arriving part with current time (use later) If machine is idle: Start processing (schedule departure), Make machine busy, Tally waiting time in queue (0) Else (machine is busy): Put part at end of queue, increase queue-length variable Schedule the next arrival event
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Events for the Simple Processing System (cont’d.) Departure (when a service is completed) Increment number-produced stat accumulator Compute & tally time in system (now - time of arrival) Update time-persistent statistics (as in arrival event) If queue is non-empty: Take first part out of queue, compute & tally its waiting time in queue, begin service (schedule departure event) Else (queue is empty): Make the machine idle (Note: there will be no departure event scheduled on the future events calendar, which is as desired)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Events for the Simple Processing System (cont’d.) The End Update time-persistent statistics (to end of the simulation) Compute final output performance measures using current (= final) values of statistical accumulators After each event, the event calendar’s top record is removed to see what time it is, what to do Also must initialize everything
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand Manually track state variables, statistical accumulators Use “given” interarrival, service times Keep track of event calendar “Lurch” clock from one event to the next Will omit times in system, “max” computations here (see text for complete details)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand Assume a bank with single clerk who is serving all arriving customers (M/M/1 system: single queue, single service and arrivals and service times are random). Below is the arrival time of each customers and their service times.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
t : Simulation clock TBA : Time between arrivals t s : Service time t q : Queue waiting time t wq : Total queue waiting time t ws : Total service time t sys : Total stay in the system N : Number of customer arrive P : Number of customer processed and left B(t): Current state of the service: Busy/Idle Q(t): Number of customers in the queue Flow chart for the discrete system simulation
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
In order to simulate the banking system What kind of information do I need to know? Arriving Blank Parts Departing Finished Parts Machine (Server) Queue (FIFO) Part in Service 4 5 6 7
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Inter-arrival times 0, 1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ... Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ... All times in minutes. End of the simulation = 20 minutes Customer s 1 2 3 4 5 6 7 8 TBA 0 1.73 1.35 0.71 0.62 14.28 0.7 15.52 Arrival Time 0 1.73 3.08 3.79 4.41 18.69 19.39 34.91 Service Time 2.9 1.76 3.39 4.52 4.46 4.36 2.07 3.36
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: Setup
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 0.00, Initialize
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 0.00, Arrival of Part 1 1
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 1.73, Arrival of Part 2 1 2
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 2.90, Departure of Part 1 2
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 3.08, Arrival of Part 3 2 3
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 3.79, Arrival of Part 4 2 3 4
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 4.41, Arrival of Part 5 2 3 4 5
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 4.66, Departure of Part 2 3 4 5
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 8.05, Departure of Part 3 4 5
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 12.57, Departure of Part 4 5
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 17.03, Departure of Part 5
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 18.69, Arrival of Part 6 6
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 19.39, Arrival of Part 7 6 7
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: t = 20.00, The End 6 7
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
observation Value from each observation (Waiting time) 1 2
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Questions What is the average number of people waited in the queue? What is the average time each customer waited in the system? What is the average utilization of the teller? What is the average waiting time in the queue?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
5 6 7 4 Number of entities leave the system is increased by 1 Number of entities leave the Queue is increased by 1 Time enter the system = 4 Time leave the queue = 5 Time leaves the system = 6 Queue waiting time = 1 Time in system = 2 Time in service = 1 3 Time enter the system = 4.5 Time leave the queue = 6 Time leaves the system = ?? Queue waiting time = 1.5 Time in system = ??? Time in service = ??? Time enter the system = 6.2 Time leave the queue = ?? Time leaves the system = ?? Queue waiting time = ?? Time in system = ??? Time in service = ??? Time enter the system = 8.2 Time leave the queue = ?? Time leaves the system = ?? Queue waiting time = ?? Time in system = ??? Time in service = ??? Time enter the system = 11 Time leave the queue = ?? Time leaves the system = ?? Queue waiting time = ?? Time in system = ??? Time in service = ???
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Simulation by Hand: Finishing Up Average waiting time in queue: Time-average number in queue: Utilization of drill press: Total Waiting Times in Queue No . of items passed the qu ??? = 15.17 6 = 2.53 minutes per part
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Complete Record of the Hand Simulation Inter-arrival times 0, 1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ... Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Replication of simulations Why do we need to replicate our simulation many times? Due to randomness What we obtain in the first trial may not represent the behavior of the system in general Example (M/M/1 system) TBA = Exponential(2) Service Time = Normal (1.5, 0.5 2 ) Run length is 100 minutes Total 5 replications Replication Number 1 2 3 4 5 Average St. Dev. Total Output 44 54 56 54 54 52.4 4.77
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Why do computer generates different numbers each time? Computer starts with exactly the same random number each time simulation is started. From that point it will follow the same procedure to calculate the random numbers that are needed to obtain Service time Time between arrivals With the same parameters, computer generates exactly the same output all the time Since each replication start with a different random number (comparison to the
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help

Related Documents

Gantt chart.pdf
Lecture 60 - Mar8 - Preliminary Design (Prototyping).pdf
PITCH LOG IN PRACTICE.docx
edit (2).xlsx
6.pdf
Jeopardy Game Rules.docx
Assignments 3 and 4_2023.pdf
Kami Export - Week 1 Introduction Pre-Class Reading Guide.pdf
mkt241_natalyaLevelOfAttributesAssignment.docx
lect3.pdf
lect11.pdf
mkt241_document_4PsAssignment-1.docx

Browse Popular Homework Q&A

Q: 3x + y = 1 + 러 리 + 9 2 + x 9
Q: In this lesson, i want you to make the passive buzzer sing. I want you to write a code in C language…
Q: S Worksheet 2- Math 101 (USE A PENCIL) 1) Shown in the table below are the one-way airfares between…
Q: Convert 42,960 m/s to mi/s. 1 mile is 1.609 km. Round to 1 decimal place.
Q: How many molecules are there in (5.95*10^ ^ 2)gCCl 4
Q: A recent survey asked "What is your favorite vacation type or destination?" The responses from 24…
Q: How does Simplification Takes Place ?
Q: AA'B'C' is the image of AABC under a rotation about point P. C B A Po A' Determine the angles of…
Q: Problems and solutions of Austin's colony that he dealt with after returning from Mexico City. List…
Q: Discuss economic and policy factors that explain why racial discrimination is more likely in law…
Q: Assume a person has lungs that can hold V = 5.1 L of air (at 1 atm), and their body temperature is…
Q: Opcode 000 001 010 011 100 101 110 111 Operation O=B ALU inputs: A(7:0): 8 bit data to be operated…
Q: If after paying debts and expenses, the estate principal is not adequate to satisfy the various…
Q: You may need to use the appropriate technology to answer this question. We want to test whether or…
Q: Sketch the graph of each line. 1 y=x+4 √x+4 3 6 0 4
Q: Which of the following is not a legacy? a. a tract of land bequeathed to the local humane society…
Q: An online lending company is offering simple interest personal loans based on consumer credit…
Q: Why was the 1st Amendment written?
Q: Prepare journal entries to record the following transactions, assuming perpetual inventory updating…
Q: What does the contract curve in an Edgeworth production box signify? Why do competitive markets…
Q: def wear_tires(car): tire -=1 def use_gas(car): gas -=1 c = Car() # You need to make this part for i…
Q: 2.IS TA'AA'=A', then K=TA' is the Penrose inverse of A. Use this principle to find the Rearase…
Q: Let be an acute angle in a right triangle, where sin ( 0) = 2. Calculate: 13 1. cos(0)= 2. tan(0)=…
Q: ve an expression for f(x) using only Real-valued coefficients, having degree 4, passing through the…
Q: A piece of wood from an ancient Egyptian tomb is tested for its carbon-14 activity. It is found to…