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Question: Vehicles pass through a toll gate at a rate of 90 per hour. The average time to pass through the gate is 36 seconds. The arrival rate and service rate follow Poisson distribution. There is a complaint that the vehicles wait for a long duration. The authorities are willing to install one more gate to reduce the average time to pass through to 30 seconds, if the idle time of the toll gate is less than 10% and the present average queue length at the gate is more than five vehicles. Check whether the installation of the secood gate is justified.
Use the line of best fit to predict the number of mistakes for someone who goes 8 hours with no sleep. Does the result make sense? Why or Why not, explain.
explain how to solve a quadratic equation using the quadratic formula. Demonstrate the process with your own example. Provide a problem for your classmates to solve.
Maximize f = 2x + 6y subject tox + y ≤ 72x + y ≤ 12x + 3y ≤ 15
In the following figure, water is poured into an urn at a constant rate (in appropriate units), and the water level rises to a height of f(t) units at time t.
Show that the Petersen graph, shown here, does not have a Hamilton circuit, but that the subgraph obtained by deleting a vertex v.
Compare in terms of delay ( > ,
Linear Programming Case Study
What is the acceleration needed to travel the maximum distance when starting from a standstill? How is acceleration impacted by the distance error?
Math 104: Homework 6. In the lectures it was shown that a continuous map from [0, 1] to [0, 1] has a fixed point. Find an example of a continuous map from (0, 1) to (0, 1) that does not have a fixed point
To avoid creating a backlog, all cases must be handled by the end of December. Formulate a linear program that can be used to determine how many Judges the city needs.
the life of battery distributed with mean of 120 days and standard deviation of 5 days. What is the minimum number of days for the life time of randomly selected battery in order it can be top 10% of life time.
A large fire becomes a fire-storm when the nearby air acquires a circulatory motion. The associated updraft has the effect of bringing more air to the fire.
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