Question: (a) Explain why the generating function for the number of ways to have n cents in pennies and nickels is (1 + x + x2

(a) Explain why the generating function for the number of ways to have n cents in pennies and nickels is
(1 + x + x2 + x3 +------)(1 + x5 + x10 + ......).
(b) Find the generating function for the number of ways to have n cents in pennies, nickels, and dimes.

Step by Step Solution

★★★★★

3.47 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The first factor counts ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

954-M-L-A-L-S (7988).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Determine the generating function for the number of ways to distribute 35 pennies (from an unlimited supply) among five children if (a) there are no restrictions; (b) each child gets at least 1; (c)...

(a) Find the generating function for the number of ways to select 10 candy bars from large supplies of six different kinds. (b) Find the generating function for the number of ways to select, with...

Determine the generating function for the number of partitions of n N where 1 occurs at most once, 2 occurs at most twice, 3 at most thrice, and, in general, k occurs at most k times, for every k ...

Verify that (1 - x - x2 - x3 - x4 - x5 - x6)-1 is the generating function for the number of ways the sum n, where n e N, can be obtained when a single die is rolled an arbitrary number of times.

We will use generating functions to determine how many ways there are to use pennies, nickels, dimes, quarters, and half-dollars to give n cents change. (a) Write the generating function P(x) for the...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

1. Consider the sensitivity report below for problems 1-5. The optimal solution to this linear program is x1 = 34, x2 = 40. x1 = 6, x2 = 11. x1 = 3, x2 = 6. x1 = 0, x2 = 0. x1 = 7.33, x2 = 6. 2....

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make...

A clever but ethically corrupted mathematics student used to sell assignment solutions to her lazy fellow students. The student, however, learned that she can make much more money by charging the...

Consider the sensitivity report below for problems 1-4. 1. Which of the following constraints are binding? Packing only Additive only Extrusion and Packaging Extrusion only All constraints are...

QRS Ltd has three main departments - casting, dressing and assembly - and for period 3 has prepared the following production overhead budgets for an output level of 110,000 units: Department Casting...

Explain why both business investments and purchases of new homes rise when interest rates decline.

(Appendix 3A) Separating Fixed and Variable Costs, Service Setting Louise McDermott, controller for the Galvin plant of Veromar Inc., wanted to determine the cost behavior of moving materials...

The more frequently bacteria are exposed to antibiotics, the more quickly the bacteria will develop resistance to the antibiotics. Health Canada states: There is an increasing concern around the...

In Exercises, find a sequence of elementary matrices E1, E2, . . , Ek such that Ek · · · E2E1A = I. Use this sequence to write both A and A-1 as products of elementary matrices....

(a) Prove that if A is invertible and AB = 0, then B = 0. (b) Give a counterexample to show that the result in part a may fail if A is not invertible.

(a) Prove that if A is invertible and BA = CA, then B = C. (b) Give a counterexample to show that the result in part a may fail if A is not invertible.

Please can you help with this problem? Thank you. Question 1 1.5 pts Which of the following is a necessary component for an experiment to potentially yield a cause-and- effect conclusion? 0 Subjects...

Question 1) Todays electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Phyllis Weinberger, who is responsible for...

CBD Computer Inc. is attempting to estimate its needs for funds during each of the months covering the third quarter of 20XX. Pertinent information is given below: a. Past and estimated future sales...