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MA7077 Mathematics

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Consider the network defined in 2.1 above, but nowignoreorientation and regard theweights as distances between the nodes.(IFind the shortest paths fromOto all other nodes of the network(iiFind a minimal spanning tree of the network.(b)Queuing theory.2.4. A grocery store has one checkout stand with a full time cashier. Customers arrive atthe stand following the Poisson distribution with a mean rate of 30 per hour. When there isonly one customer at the stand, the average service time spent by the cashier is 1.5 min.Whenever two or more customers are at the stand, another staff joins to help the cashier bybagging. This reduces the average service time to 1 minute per customer. It is assumed thatthe service time is distributed exponentially.(i)]Sketch the rate diagram for this queueing system.(ii)Find the steady state distribution of the number of customers at the checkoutstand

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Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet.

Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

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The three MUIC maths teachers decided to run a marathon race which involved running along the beach (how far along along the beach was optional) and then swimming to the finish point on an island. See diagram.   There is a point (O) along the beach at right angles to both the start point ( ...

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Task: Questions 1.Mathematical issues  List and briefly describe five issues that you expect to resolve for Damian and Melissa using your mathematics skills. 2.Employing a junior Damian expects that a fulltime junior will work 35 hours during the week and 4 hours on Saturdays. Damian would ...

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Question: A reasonable attempt at answering Question (IV.4.) should be submitted on Canvas by 23:59 on Monday 25.10.2021 either as a text entry, a text file (txt), a pdf file, or a photo of the handwritten answer. This assignment makes up 1% of your final mark. We would like to encourage you to dis ...

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