EBK THINKING MATHEMATICALLY
6th Edition
ISBN: 9780100802728
Author: Blitzer
Publisher: YUZU
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Textbook Question
Chapter 4.4, Problem 12CVC
Fill in the blank so that the resulting statement is true. = ____
Like the system in Exercises 10-11, the Greek Ionic system requires that new symbols be added to represent higher numbers. ____
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Chapter 4 Solutions
EBK THINKING MATHEMATICALLY
Ch. 4.1 - CHECK POINT 1 Write each of the following in...Ch. 4.1 - CHECK POINT 2 Express each expanded form as a...Ch. 4.1 - CHECK POINT 3 Write each Babylonian numeral as a...Ch. 4.1 - CHECK POINT 4 Write each Mayan numeral as a...Ch. 4.1 - Q.1. A number addresses the question “how many?” A...Ch. 4.1 - Q.2. Our number system is called the __________...Ch. 4.1 - Prob. 3CVCCh. 4.1 - Q.4. When we write 547 as, , we are using an...Ch. 4.1 - Prob. 5CVCCh. 4.1 - The Hindu Arabic numeration system uses power of...
Ch. 4.1 - Prob. 7CVCCh. 4.1 - Using ∨ for 1 and < for 10, the expanded from < ...Ch. 4.1 - Q.9. The place value in the Mayan numeration...Ch. 4.1 - Q.10.
= = .
...Ch. 4.1 - In Exercises 1-8, evaluate the expression.
1.
Ch. 4.1 - In Exercises 1-8, evaluate the expression.
2.
Ch. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - In Exercises 1-8, evaluate the expression. 3 4Ch. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - In Exercises 23-32, express each expanded form as...Ch. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - In Exercises 34-46, use Table 4.1 on page 215 to...Ch. 4.1 - In Exercises 34-46, use Table 4.1 on page 215 to...Ch. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - In Exercises 34-46, use Table 4.1 on page 215 to...Ch. 4.1 - Prob. 46ECh. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Prob. 73ECh. 4.1 - Prob. 74ECh. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - Prob. 77ECh. 4.1 - Prob. 78ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.1 - Prob. 81ECh. 4.1 - Explain how to write a Hindu-Arabic numeral in...Ch. 4.1 - 83. Describe one way that the Babylonian system is...Ch. 4.1 - 84. Describe one way that the Mayan system is...Ch. 4.1 - Research activity Write a report on the history of...Ch. 4.1 - Prob. 86ECh. 4.1 - Prob. 87ECh. 4.1 - Prob. 88ECh. 4.1 - Make Sense? In Exercises 86-89, determine whether...Ch. 4.1 - Prob. 90ECh. 4.1 - Prob. 91ECh. 4.1 - Use Babylonian numerals to write the numeral that...Ch. 4.2 - CHECK POINT 1 Convert to base ten.
Ch. 4.2 - CHECK POINT 2 Convert to base ten.
Ch. 4.2 - CHECK POINT 3 Convert to base ten.
Ch. 4.2 - CHECK POINT 4 Convert the base ten numeral 6 to a...Ch. 4.2 - CHECK POINT 5 Convert the base ten numeral 365 to...Ch. 4.2 - CHECK POINT 6 Convert the base ten numeral 51 to a...Ch. 4.2 - CHECK POINT 7 Convert the base ten numeral 2763 to...Ch. 4.2 - In the numeral 324 five , the base is _____. In...Ch. 4.2 - 324 five = ( 3 × _ _ ) + ( 2 × _ _ ) + ( 4 × _ _ )Ch. 4.2 - Prob. 3CVCCh. 4.2 - Prob. 4CVCCh. 4.2 - Prob. 5CVCCh. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Prob. 7CVCCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - In Exercises 1-18, convert the numeral to a...Ch. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - In Exercises 19-32, mentally convert each base ten...Ch. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - In Exercises 33-48, convert each base ten numeral...Ch. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - In Exercises 49-52, use Table 4.1 on page 215 to...Ch. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - In Exercises 53-56, use Table 4.2 on page 216 to...Ch. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - 59. Convert to base eight.
Ch. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Read the Blitzer Bonus on page 222. Then use the...Ch. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Prob. 71ECh. 4.2 - Prob. 72ECh. 4.2 - Make Sense? In Exercises 73-76, determine whether...Ch. 4.2 - Prob. 74ECh. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - In Exercises 77-78, write, in the indicated base,...Ch. 4.2 - Prob. 78ECh. 4.2 - Prob. 79ECh. 4.2 - Prob. 80ECh. 4.2 - Prob. 81ECh. 4.2 - Prob. 82ECh. 4.2 - The following topics are appropriate for either...Ch. 4.2 - The following topics are appropriate for either...Ch. 4.3 - CHECK POINT 1 Add: 32 five + 44 five . _Ch. 4.3 - Prob. 2CPCh. 4.3 - Prob. 3CPCh. 4.3 - Prob. 4CPCh. 4.3 - Prob. 5CPCh. 4.3 - Prob. 6CPCh. 4.3 - Prob. 1CVCCh. 4.3 - Prob. 2CVCCh. 4.3 - Consider the following addition in base eight: ...Ch. 4.3 - Prob. 4CVCCh. 4.3 - Prob. 5CVCCh. 4.3 - 6. We can use products in base three to perform...Ch. 4.3 - 7. True or False: Computation in bases other than...Ch. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - 342 five + 413 five _Ch. 4.3 - Prob. 6ECh. 4.3 - In Exercises 1-12, add in the indicated base. 645...Ch. 4.3 - In Exercises 1-12, add in the indicated base. 632...Ch. 4.3 - In Exercises 1-12, add in the indicated base. 6784...Ch. 4.3 - In Exercises 1-12, add in the indicated base.
10....Ch. 4.3 - In Exercises 1-12, add in the indicated base....Ch. 4.3 - In Exercises 1-12, add in the indicated base. 53 B...Ch. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - 475 eight − 267 eight _ _ _ _ _ _ _ _ _ _ _ _ _ _...Ch. 4.3 - In Exercises 13-24, subtract in the indicated...Ch. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - Prob. 30ECh. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - In Exercises 35-38, use the multiplication tables...Ch. 4.3 - In Exercises 35-38, use the multiplication tables...Ch. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - In Exercises 39-46, perform the indicated...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Read the Blitzer Bonus on page 233. Then use the...Ch. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - 56. Describe two difficulties that youngsters...Ch. 4.3 - Make Sense? In Exercises 57-60, determine whether...Ch. 4.3 - Make Sense? In Exercises 57-60, determine whether...Ch. 4.3 - Make Sense? In Exercises 57-60, determine whether...Ch. 4.3 - Make Sense? In Exercises 57-60, determine whether...Ch. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Divide: 31 seven 2426 seven .Ch. 4.3 - 64. Use the Mayan numerals in Table 4.2 on page...Ch. 4.3 - Group members should research various methods that...Ch. 4.3 - 66. Organize a debate. One side represents people...Ch. 4.4 - CHECK POINT 1 Write the following numeral as a...Ch. 4.4 - CHECK POINT 2 Write 2563 as an Egyptian numeral.
Ch. 4.4 - Prob. 3CPCh. 4.4 - CHECK POINT 4 Write MCDXLVII as a Hindu-Arabic...Ch. 4.4 - Prob. 5CPCh. 4.4 - Prob. 6CPCh. 4.4 - Prob. 7CPCh. 4.4 - Prob. 1CVCCh. 4.4 - Prob. 2CVCCh. 4.4 - True or False: Like the system in Exercises 1-2,...Ch. 4.4 - Exercises 4-7 involve Roman numerals. Roman...Ch. 4.4 - Prob. 5CVCCh. 4.4 - Prob. 6CVCCh. 4.4 - Exercises 4-7 involve Roman numerals. Roman...Ch. 4.4 - Prob. 8CVCCh. 4.4 - Prob. 9CVCCh. 4.4 - Prob. 10CVCCh. 4.4 - Prob. 11CVCCh. 4.4 - Fill in the blank so that the resulting statement...Ch. 4.4 - Use Table 4.6 on page 236 to solve Exercises 1-12....Ch. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - In Exercises 13-28, write each Roman numeral as a...Ch. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - In Exercise 29-36, write each Hindu-Arabic numeral...Ch. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - In Exercises 43-48, write each Hindu-Arabic...Ch. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - In Exercises 49-52, write each Ionic Greek numeral...Ch. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Describe how a number is represented in the...Ch. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Make Sense? In Exercises 76-79, determine whether...Ch. 4.4 - Make Sense? In Exercises 76-79, determine whether...Ch. 4.4 - Prob. 80ECh. 4.4 - Prob. 81ECh. 4.4 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - 7. Explain why a symbol for zero is needed in a...Ch. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - Prob. 10TCh. 4 - Prob. 11TCh. 4 - Prob. 12TCh. 4 - In Exercises 13-15, convert each base ten numeral...Ch. 4 - Prob. 14TCh. 4 - Prob. 15TCh. 4 - Prob. 16TCh. 4 - Prob. 17TCh. 4 - Prob. 18TCh. 4 - Prob. 19TCh. 4 - Prob. 20TCh. 4 - Use the symbols in the table shown below to solve...Ch. 4 - Prob. 22TCh. 4 - Prob. 23TCh. 4 - Prob. 24TCh. 4 - In Exercises 1-2, evaluate the expression 11 2Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - In Exercises 13-18, convert the numeral to a...Ch. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - In Exercises 25-28, add in the indicated base.
25....Ch. 4 - In Exercises 25-28, add in the indicated base.
26....Ch. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - In Exercises 29-32, subtract in the indicated...Ch. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - 44. Describe how the Egyptian system or the system...Ch. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Use Table 4.8 on page 239 to solve Exercises...Ch. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Describe how the Chinese system or the system in...Ch. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - In Exercises 62-63, write each Hindu-Arabic...Ch. 4 - In Exercises 62-63, write each Hindu-Arabic...Ch. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RE
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- The following ordered data list shows the data speeds for cell phones used by a telephone company at an airport: A. Calculate the Measures of Central Tendency from the ungrouped data list. B. Group the data in an appropriate frequency table. C. Calculate the Measures of Central Tendency using the table in point B. D. Are there differences in the measurements obtained in A and C? Why (give at least one justified reason)? I leave the answers to A and B to resolve the remaining two. 0.8 1.4 1.8 1.9 3.2 3.6 4.5 4.5 4.6 6.2 6.5 7.7 7.9 9.9 10.2 10.3 10.9 11.1 11.1 11.6 11.8 12.0 13.1 13.5 13.7 14.1 14.2 14.7 15.0 15.1 15.5 15.8 16.0 17.5 18.2 20.2 21.1 21.5 22.2 22.4 23.1 24.5 25.7 28.5 34.6 38.5 43.0 55.6 71.3 77.8 A. Measures of Central Tendency We are to calculate: Mean, Median, Mode The data (already ordered) is: 0.8, 1.4, 1.8, 1.9, 3.2, 3.6, 4.5, 4.5, 4.6, 6.2, 6.5, 7.7, 7.9, 9.9, 10.2, 10.3, 10.9, 11.1, 11.1, 11.6, 11.8, 12.0, 13.1, 13.5, 13.7, 14.1, 14.2, 14.7, 15.0, 15.1, 15.5,…arrow_forwardA tournament is a complete directed graph, for each pair of vertices x, y either (x, y) is an arc or (y, x) is an arc. One can think of this as a round robin tournament, where the vertices represent teams, each pair plays exactly once, with the direction of the arc indicating which team wins. (a) Prove that every tournament has a direct Hamiltonian path. That is a labeling of the teams V1, V2,..., Un so that vi beats Vi+1. That is a labeling so that team 1 beats team 2, team 2 beats team 3, etc. (b) A digraph is strongly connected if there is a directed path from any vertex to any other vertex. Equivalently, there is no partition of the teams into groups A, B so that every team in A beats every team in B. Prove that every strongly connected tournament has a directed Hamiltonian cycle. Use this to show that for any team there is an ordering as in part (a) for which the given team is first. (c) A king in a tournament is a vertex such that there is a direct path of length at most 2 to any…arrow_forwardUse a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.) y = 100e0.01x (x, y) = y = 11,250 ×arrow_forward
- how to construct the following same table?arrow_forwardThe following is known. The complete graph K2t on an even number of vertices has a 1- factorization (equivalently, its edges can be colored with 2t - 1 colors so that the edges incident to each vertex are distinct). This implies that the complete graph K2t+1 on an odd number of vertices has a factorization into copies of tK2 + K₁ (a matching plus an isolated vertex). A group of 10 people wants to set up a 45 week tennis schedule playing doubles, each week, the players will form 5 pairs. One of the pairs will not play, the other 4 pairs will each play one doubles match, two of the pairs playing each other and the other two pairs playing each other. Set up a schedule with the following constraints: Each pair of players is a doubles team exactly 4 times; during those 4 matches they see each other player exactly once; no two doubles teams play each other more than once. (a) Find a schedule. Hint - think about breaking the 45 weeks into 9 blocks of 5 weeks. Use factorizations of complete…arrow_forward. The two person game of slither is played on a graph. Players 1 and 2 take turns, building a path in the graph. To start, Player 1 picks a vertex. Player 2 then picks an edge incident to the vertex. Then, starting with Player 1, players alternate turns, picking a vertex not already selected that is adjacent to one of the ends of the path created so far. The first player who cannot select a vertex loses. (This happens when all neighbors of the end vertices of the path are on the path.) Prove that Player 2 has a winning strategy if the graph has a perfect matching and Player 1 has a winning strategy if the graph does not have a perfect matching. In each case describe a strategy for the winning player that guarantees that they will always be able to select a vertex. The strategy will be based on using a maximum matching to decide the next choice, and will, for one of the cases involve using the fact that maximality means no augmenting paths. Warning, the game slither is often described…arrow_forward
- Let D be a directed graph, with loops allowed, for which the indegree at each vertex is at most k and the outdegree at each vertex is at most k. Prove that the arcs of D can be colored so that the arcs entering each vertex must have distinct colors and the arcs leaving each vertex have distinct colors. An arc entering a vertex may have the same color as an arc leaving it. It is probably easiest to make use of a known result about edge coloring. Think about splitting each vertex into an ‘in’ and ‘out’ part and consider what type of graph you get.arrow_forward3:56 wust.instructure.com Page 0 Chapter 5 Test Form A of 2 - ZOOM + | Find any real numbers for which each expression is undefined. 2x 4 1. x Name: Date: 1. 3.x-5 2. 2. x²+x-12 4x-24 3. Evaluate when x=-3. 3. x Simplify each rational expression. x²-3x 4. 2x-6 5. x²+3x-18 x²-9 6. Write an equivalent rational expression with the given denominator. 2x-3 x²+2x+1(x+1)(x+2) Perform the indicated operation and simplify if possible. x²-16 x-3 7. 3x-9 x²+2x-8 x²+9x+20 5x+25 8. 4.x 2x² 9. x-5 x-5 3 5 10. 4x-3 8x-6 2 3 11. x-4 x+4 x 12. x-2x-8 x²-4 ← -> Copyright ©2020 Pearson Education, Inc. + 5 4. 5. 6. 7. 8. 9. 10. 11. 12. T-97arrow_forwardplease work out more details give the solution.arrow_forward
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