Authority (LCRA) has been studying congestion at the boat-launching ramp near Mansfield Dam. On weekends‚ the arrival rate averages 5 boaters per hour‚ Poisson distributed. The average time to launch or retrieve a boat is 10 minutes‚ with negative exponential distribution. Assume that only one boat can be launched or retrieved at a time. a.) The LCRA plans to add another ramp when the average turnaround time exceeds 90 minutes. At what average arrival rate per hour should the LCRA begin to consider
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The Koch Snowflake Math Mock Exploration Shaishir Divatia Math SL 1 The Koch Snowflake The Koch Snowflake is a fractal identified by Helge Von Koch‚ that looks similar to a snowflake. Here are the diagrams of the first four stages of the fractal - 1. At any stage (n) the values are denoted by the following – Nn - number of sides Ln - length of each side Pn - length of perimeter An - Area of snowflake Mentioned below are the values of these above variables‚ for the first 4 stages
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ST421 Exercise 1 — Solutions 1. Note that P (uj ≤ Xj ≤ vj ) = e−λuj − e−λvj ‚ and fXj (x|uj ≤ Xj ≤ vj ) = λe−λx /{e−λuj − e−λvj }. Hence‚ Xj (λ) ≡ Eλ (Xj |Xj ∈ [uj ‚ vj ]) = 1 uj exp(−λuj ) − vj exp(−λvj ) + . λ exp(−λuj ) − exp(−λvj ) The log-likelihood function based on the full sample is n ∑ l(θ) ≡ l(θ; X1 ‚ · · · ‚ Xn ) = n log λ − λ Xj ‚ j=1 which yields the MLE based on full sample θ(X1 ‚ · · · ‚ Xn ) = n/ ∑ 1≤j≤n Xj . Now the E-step is Q(λ) = Eλ0 {l(θ)
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As mentioned above‚ bacterial growth rates during the phase of exponential growth‚ under standard nutritional conditions (culture medium‚ temperature‚ pH‚ etc.)‚ define the bacterium’s generation time. Generation times for bacteria vary from about 12 minutes to 24 hours or more. The generation time for E. coli in the laboratory is 15-20 minutes‚ but in the intestinal tract‚ the coliform’s generation time is estimated to be 12-24 hours. For most known bacteria that can be cultured‚ generation times
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management “how to” book in the search for answers * Buying external consultants in the search for the silver bullet Richard Pascale‚ a leading US business school professor‚ has compiled an “influence index” of business fads that shows an exponential increase in management ideas in the 1980s and 1990s‚ from zero-based budgeting to MBWA‚ from benchmarking to business process re-engineering. Most academics criticise most of the ideas as simplistic and deterministic‚ although the authors themselves
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Corporation retains a service crew to repair machine breakdowns that occur on an average of 3 per day (approximately Poisson in nature). The crew can service an average of 8 machines per day‚ with a repair time distribution that resembles the exponential distribution. a. What is the utilization rate for this service? b. What is the average downtime for a machine that is broken? c. How many machines are waiting to be serviced at any given time? d. What is the probability that more than one
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quantified as the change in the number of individuals in a population using "per unit time" for measurement (Wikipedia.com). A population can grow in an exponential or logistic growth pattern. Exponential population growth is the geometric increase of a population as it grows in an ideal‚ unlimited environment. For a continuously reproducing population‚ exponential growth is an excellent first-approximation of population growth. When resources are not limiting‚ and interspecific competition is at a minimum
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One of the most common models of population growth is the exponential model. These models use functions of the torm p(t) : po€rt‚ wherep6 is the initial population and r > 0 is the rate constant. Because exponential models describe unbounded growth‚ they are unrealistic over long periods of time. Due to shortages of space and resources‚ all populations must eventually have decreasing grovtrth rates. Logistic growth models allow for exponential growth when the population is small. However‚ as the population
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following policy: if a customer has to wait‚ the price is $3.50 per gallon; if they don’t have to wait‚ the price is $4.00 per gallon. Customers arrive according to a Poisson process with a mean rate of 20 per hour. Service times at the pump have an exponential distribution with a mean of 2 minutes. Arriving customers always wait until they can by gasoline. Determine the expected price of gasoline per gallon. Problem 3 The Old Colony theme park has a new ride‚ the Double-Disgusting Cyclonic Twister
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A Review of The Limits to Growth The Limits to Growth: a Report for the Club of Rome ’s Project on the Predicament of Mankind was published in 1972 predicting the future of exponential growth of economy and population in a finite world. Since 1972‚ more than 10 million copies in 37 languages have been sold by now (Gambino‚ 2011). This ambitious book is written by MIT researchers for Club of Rome which is an international think tank. The authors created a global computer model‚ Wolrd3‚ to simulate
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