10. Rappers use rhyme schemes to describe which lines of a rap rhyme. The rhyme at...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
10. Rappers use rhyme schemes to describe which lines of a rap rhyme. The rhyme at the end of each line is denoted by a letter of the alphabet, with the same letter given to two lines that rhyme. For example, to say that a rap has the rhyming scheme ABABCDED, indicates that the first and the third lines rhyme, the second and the fourth lines rhyme, and the sixth- and eighth-lines rhyme, but no others. More precisely, the first line of the rap is given the letter A. If a subsequent line rhymes with an earlier line, it is given the same letter; otherwise, it is given the first unused letter. (For the purposes of this question, you can assume that we have an infinite supply of "letters", not just the 26 letters of the alphabet.) (a) The purpose of this question is to investigate how many different rhyme schemes there are for raps of n lines. We write in for this number. There are five different rhyming schemes for raps of three lines, i.e. r3 = 5. List them. [1 marks] (b) Let Sn.k denote the number of rhyming schemes for raps with n lines that use exactly k different rhymes at the end of the line. For example, $3,2 = 3 because the three rhyming schemes that use 3 lines and 2 different rhymes at the end of the line are AAB, ABA and ABB. What is Sn, 1 for n > 1? What is Sn,n? Explain both answers. [2 marks] (c) Suppose that 1 < k < n. By considering the rhyme at the end of the final line of a rhyming scheme, explain why this is the case that Sn,k = Sn-1.k-1 + k Sn-1.k- [5 marks] (d) Explain how it is possible to calculate rn in terms of Sn,k. Hence calculate r4. [5 marks] (e) Give a formula for Sn,2 in terms of n (for n > 2). Justify your answer. [3 marks] 10. Rappers use rhyme schemes to describe which lines of a rap rhyme. The rhyme at the end of each line is denoted by a letter of the alphabet, with the same letter given to two lines that rhyme. For example, to say that a rap has the rhyming scheme ABABCDED, indicates that the first and the third lines rhyme, the second and the fourth lines rhyme, and the sixth- and eighth-lines rhyme, but no others. More precisely, the first line of the rap is given the letter A. If a subsequent line rhymes with an earlier line, it is given the same letter; otherwise, it is given the first unused letter. (For the purposes of this question, you can assume that we have an infinite supply of "letters", not just the 26 letters of the alphabet.) (a) The purpose of this question is to investigate how many different rhyme schemes there are for raps of n lines. We write in for this number. There are five different rhyming schemes for raps of three lines, i.e. r3 = 5. List them. [1 marks] (b) Let Sn.k denote the number of rhyming schemes for raps with n lines that use exactly k different rhymes at the end of the line. For example, $3,2 = 3 because the three rhyming schemes that use 3 lines and 2 different rhymes at the end of the line are AAB, ABA and ABB. What is Sn, 1 for n > 1? What is Sn,n? Explain both answers. [2 marks] (c) Suppose that 1 < k < n. By considering the rhyme at the end of the final line of a rhyming scheme, explain why this is the case that Sn,k = Sn-1.k-1 + k Sn-1.k- [5 marks] (d) Explain how it is possible to calculate rn in terms of Sn,k. Hence calculate r4. [5 marks] (e) Give a formula for Sn,2 in terms of n (for n > 2). Justify your answer. [3 marks]
Expert Answer:
Answer rating: 100% (QA)
a The five different rhyming schemes for raps of three lines r3 5 are 1 AAA 2 AAB 3 ABA 4 ABB 5 ABC b For Snk the number of rhyming schemes for raps w... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these statistics questions
-
can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...
-
In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...
-
You have recently been appointed as assistant to the financial controller of Chaffinch plc, a manufacturing company. He has asked you to help with the finalisation of the financial statements for the...
-
Direct foreign investment affects both the financial account and the current account over time. Agree? Disagree? Explain.
-
What is the difference between the component volume and the partial volume? When are these two equivalents?
-
Serum cholesterol levels (y) and age in years (x) were recorded for several men in a medical center. Cholesterol levels were measured in milligrams per deciliter. The following MINITAB output...
-
Hebert Company reported the following information for 2011: Repaid long-term debt ............. $50,000 Paid interest on note payable ............ 1,320 Issued common stock ............... 25,000...
-
As companies evolve, certain factors can drive sudden growth. This may lead to a period of nonconstant, or variable, growth. This would cause the expected growth rate to increase or decrease, thereby...
-
Max charley, an accountant, quit his $60,000-a-year job and bought an existing tattoo parlor from its previous owner, Sylvia Sidney. The lease has six years remaining and requires a monthly payment...
-
Do you feel that it is a coach's responsibility to teach sportsmanship? Then, identify at least one coach and one professional athlete you have observed demonstrating good or bad character and...
-
a) Derive or state the gate-voltage relationship of the MOS capacity. b) In inversion we find two charge types on the semiconductor side, describe their origin. Which ones are fixed, which ones are...
-
(a) Let f: R R+ be a a firm's differentiable production function satisfying the usual assumptions. Suppose that x ER is a vector of inputs and that we R are the factor prices. Let p E R+ denote the...
-
In a trend that scientists attribute, at least in part, to global warming, a certain floating cap of sea ice has been shrinking since 1980. The ice cap always shrinks in the summer and grows in...
-
Do you think Zara's supply chain strategy would work even in the post-pandemic, digital market environment? What is Zara's integrated store concept? In an omni channel retail environment, how would...
-
Make a presentation about Germany in detail, including an overview of the German culture and business practices
-
QUESTION 9 HC-O-C-R R-C-O-CH HC-O-P-O-CH-CH-NH3* O || O a. Phosphatidic acid, Serine O b. Lysophosphatidic acid, Serine, Free FA O c. Lysophosphatidylserine, Free FA O d. 2 Free FAs, Serine, Glycerol...
-
The rotor shown in Fig. 9.44 (a) is balanced temporarily in a balancing machine by adding the masses \(m_{1}=m_{2}=90 \mathrm{~g}\) in the plane \(A\) and \(m_{3}=m_{4}=90 \mathrm{~g}\) in the plane...
-
A turbine rotor is run at the natural frequency of the system. A stroboscope indicates that the maximum displacement of the rotor occurs at an angle \(229^{\circ}\) in the direction of rotation. At...
-
The reciprocating mass, crank radius, and connecting-rod length of each of the cylinders in a two-cylinder in-line engine are given by \(m, r\), and \(l\), respectively. The crank angles of the two...
Study smarter with the SolutionInn App