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Question: a) Show that 1/(1 - x - x2 - x3 - x4 - x5 - x6) is the generating function for the number of ways that the sum n can be obtained when a die is rolled repeatedly and the order of the rolls matters.
b) Use part (a) to find the number of ways to roll a total of 8 when a die is rolled repeatedly, and the order of the rolls matters. (Use of a computer algebra package is advised.)
Let A(t) be the balance in a savings account after t years, and suppose that A(t) satisfies the differential equation - A'(t) = (ln 3)A(t)
A homeowner wants to enclose a 5,800 square feet rectangular garden by a fence in his backyard. If three sides of the fence cost $6.25 per foot and 4th side costs $10.25 per foot,
An investor buys 200 shares of GDT at a price of $63.90 per share, pays a 2 percent commission on the purchase, and sells the 200 shares a year later for $64.00 per share with a 2 percent commission on the sale. What is the total cost of the purch..
this assignment has question related to probabiltiy.questions given on probabiltiy.consider 52 card decherd lied out in
From the top of a building 70 meters high, the angles of depression of two objects that are directly east of the observation position are 38° and 25° respectively. find the distance between the objects.
A standard 1 kilogram weight is a cylinder 43.5 mm in height and 48.5 in diameter. What is the density of the material?
When constructing confidence intervals, there is always a trade-off between the confidence level and the precision of estimate. Which one do you think is more important and why? (Max 3 sentences).
One day you discover that there's an argument, Argument1, that Doofus can prove, but which you can show that Fitch cannot prove. What property does Fitch possess that justifies your answer to a)? Include a brief (one or two sentence) justification i..
Suppose six pairs of similar-looking boots are thrown together in a pile. How many individual boots must you pick to be sure of getting a matched pair? Why?
24. Business partners want to purchase a restaurant that costs $750,000. They have $300,000 for a down payment, and they can get a 25-year business loan for the remaining funds at 8% per year on the unpaid balance, with quarterly payments.
here is a context-free grammar that can be used to generate algebraic expressions via the arithmetic operators addition
Suppose that 100 people enter a contest and that different winners are selected at random for first, second, and third prizes.
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