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Martin commutes to work. Each day he either drives his car, takes the bus, or takes a taxi. He never drives his car two days in a row. There is a 19% chance that he will drive if he did NOT drive the previous day. He is always twice as likely to take the bus as he is to take a taxi. (Example: If the probability that he takes a taxi is 1/4, then the probability that he takes a bus is twice that: 2(1/4) = 2/4 = 1/2.) This gives you enough information to set up the transition matrix. (Hint: When creating transition matrices it is important not to round any of the numbers because when you start multiplying matrices the round-off error will get compounded. To avoid this, use fractions instead of approximated decimals. For example, you would put a fraction such as 5/6 in your matrix as "5/6" instead of using the decimal approximation "0.83333333".) Use the matrix to answer the following questions. (Give your answers correct to three decimal places.) (a) If Martin drives on Monday, what is the probability he will take the bus on Wednesday? (b) If Martin drives on Monday, what is the probability he will take a taxi on Thursday? If Martin drives on Monday, what is the probability he will drive on Thursday? (c) In the long run, what fraction of the time does he drive? In the long run, what fraction of the time does he take the bus? In the long run, what fraction of the time does he take a taxi?
Let E be a metric space, S a subset of E, and let f:E-R be the function which takes the value 1 at each point of S and 0 at each point of the complement of S. Prove that the set of points of E at which f is not continuous is precisely the boundary..
The temperature u in a star of conductivity 2 is inversely proportional to the distance from the center: u=(2/sqrt(x^2+y^2+z^2)). If the star is a sphere of radius 1, find the rate of heat flow outward across the surface of the star.
Support your answer. Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate.
manufacturers use random samples to test whether or not their product is meeting specifications. these samples could be
Given that the y-intercept of a line is (0,-5) and the slope is 1/3, find the equation of the line in slope-intercept form. What is the x-intercept?
a college administrator wants to study the average age of students who drop out of college after only attending one
A survey was mailed to a total of 400 students; 100 were randomly selected from each of the freshman, sophomore, junior and senior classes last semester. What sampling method was used?
If this same card were issued 30 years ago, what would your interest rate be? In the event that there were multiple prime interest rates for a year, use the one that is 30 years from the day your class started. Use the Internet to determine what t..
Calculating the height of the statue - find out how high is the statue?
A particular company produces widgets. Each widget sells for $9, and the variable cost of producing each unit is 40% of the selling price. If the monthly fixed costs incurred by the company are $50,000, what is the break-even point?
U sing an equal number of participants, find how many subjects will you need in each group
An executive invests $28,000, some at 6% and some at 5% annual interest. If he receives an annual return of $1540, how much is invested at each rate.
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