Computer Code The ASCII code used by most computers uses the last seven positions of an eight-bit byte to represent all the characters on a standard keyboard. How many different orderings of 0’s and 1’s (or how many different characters) can be made by using the last seven positions of an eight-bit byte?
> In Exercises 13–20, use lattice multiplication to determine the product. 47 ( 259
> Answer true or false. If false, give the reason. {cheesecake, pie} ( {pie, cookie, cheesecake, brownie}
> The set of Academy Awards winners in 2014
> In Exercises 13–20, use lattice multiplication to determine the product. 75 ( 12
> Determine whether the number used is a cardinal number or an ordinal number. Emily paid $35 for her new blouse.
> In Exercises 13–20, use lattice multiplication to determine the product. 9 ( 509
> Determine whether the number used is a cardinal number or an ordinal number. Lincoln was the sixteenth president of the United States.
> In Exercises 13–20, use lattice multiplication to determine the product. 8 ( 567
> Determine whether the number used is a cardinal number or an ordinal number. Study the chart on page 25 in the book.
> In Exercises 13–20, use lattice multiplication to determine the product. 5 ( 417
> Determine whether the number used is a cardinal number or an ordinal number J. K. Rowling has written 7 Harry Potter books.
> In Exercises 13–20, use lattice multiplication to determine the product. 4 ( 327
> Housing Market The following table shows the five cities where the average U.S. house prices have increased the most from 2012 to 2013. The table also shows the percent change from 2006 to 2013 for those cities. (a) If a house in Las Vegas, NV, cost $200
> Consider sets A and B below A = { x | 2 < x ≤ 5 and x ( N } and B = { x | 2 < x ≤ 5 } (a) Write a description of set A and set B. (b) Explain the difference between set A and set B. (c) Write set A in roster form. (d) Can set B be written in roster
> In Exercises 5–12, multiply using duplation and mediation. 49 ( 124
> Set-builder notation is often more versatile and efficient than listing a set in roster form. This versatility is illustrated with the following two sets. A = {x | x ( N and x > 2 } B = {x | x > 2 } a) Write a description of set A and set B. b) Explain
> In Exercises 5–12, multiply using duplation and mediation. 93 ( 93
> Determine whether the pairs of sets are equal, equivalent, both, or neither. A is the set of states. B is the set of state capitals.
> In Exercises 5–12, multiply using duplation and mediation. 96 ( 53
> Determine whether the pairs of sets are equal, equivalent, both, or neither. A is the set of letters in the word bank. B is the set of letters in the word post.
> In Exercises 5–12, multiply using duplation and mediation. 35 ( 236
> Determine whether the pairs of sets are equal, equivalent, both, or neither. A is the set of Siamese cats. B is the set of cats.
> In Exercises 5–12, multiply using duplation and mediation. 138 ( 41
> Answer true or false. If false, give the reason. {book, magazine} ( {book, newspaper, journal}
> Determine whether the pairs of sets are equal, equivalent, both, or neither. A = { grapes, apples, oranges }, B = { grapes, peaches, apples, oranges }
> Convert the given numeral to a numeral in base 10. 234
> Determine whether the pairs of sets are equal, equivalent, both, or neither. A = { purple, green, yellow } , B = { q, r, s }
> Convert the given numeral to a numeral in base 10. 213
> Determine whether the pairs of sets are equal, equivalent, both, or neither. A = { lion, tiger, monkey } , B = { tiger, monkey, lion }
> Convert the given numeral to a numeral in base 10. 123
> Use the sets A = {2, 4, 6, 8}, B ={1, 3, 7, 9, 13, 21 }, C = { }, and D = {#, &, %, (,*} . Determine n(D) .
> Convert the given numeral to a numeral inbase 10. 57316
> Use the sets A = {2, 4, 6, 8}, B ={1, 3, 7, 9, 13, 21 }, C = { }, and D = {#, &, %, ,*} . Determine n(C) .
> Convert the given numeral to a numeral inbase 10. 100512
> Bachelor’s Degrees The circle graph below shows the percent of bachelor’s degrees awarded in 2012 in Business, Social Sciences and History, Health Professions, Psychology, Education, and other fields. In 2012, the numb
> Use the sets A = {2, 4, 6, 8}, B ={1, 3, 7, 9, 13, 21 }, C = { }, and D = {#, &, %, ,*} . Determine n(B) .
> Convert the given numeral to a numeral in base 10. 30912
> Use the sets A = {2, 4, 6, 8}, B ={1, 3, 7, 9, 13, 21 }, C = { }, and D = {#, &, %, ,*} . Determine n(A).
> Convert the given numeral to a numeral in base 10. 7658
> 2 ( {x | x is an odd natural number}
> Convert the given numeral to a numeral in base 10. 2418
> 9 ( {1, 3, 5, 7, … }
> Suppose a base 4 place-value system has its digits represented by colors as follows: (a) Determine the value of /in base 10 (b) Write 177 in the base 4 system using only the four colors given in the exercise.
> Amazon ( {rivers in the United States}
> The Price Is Right Refer to the Recreational Mathematics on page 181. Determine the correct order in which to place the digits 0, 1, 2, 3, and 8 to match the price of the 2014 Chevrolet Impala LTZ Sedan
> Answer true or false. If false, give the reason. {potato, carrot} ( {carrot, squash, cucumber, celery}
> 3 ( {x | x (N and x is odd}
> Convert the given numeral to a numeral in base 10. 324
> Mickey Mouse Є {characters created by Walt Disney }
> Boxes of Fruit There are three boxes on a table, each with a label. Thomas knows that one box contains grapes, one box contains cherries, and the third box contains both grapes and cherries. He also knows that the three labels used—grapes, cherries, and
> (a) Use the numerals 0, 1, and 2 to write the first 20 numbers in the base 3 numeration system. (b) What is the next numeral after 2223?
> Spending Money Samantha went into a store and spent half her money and then spent $20 more. Samantha then went into a second store and spent half her remaining money and then spent $20 more. After spending money in the second store, Samantha had no money
> Find d if ddd5 = 124
> Finding the Area Rectangle ABCD is made up entirely of squares. The black square has a side of 1 unit. Find the area of rectangle ABCD.
> Find b if 111b = 43
> How Americans Spend Their Money The circle graph below shows the percent of Americans’ net monthly income spent on housing, transportation, food, insurance/ retirement, healthcare, and entertainment/miscellaneous. Sammy has a net monthl
> Counting Triangles How many triangles are in the figure? Answer: 16+16+4+4+4=44
> (a) What is 112 equal to in base 10? (b) What is 118 equal to in base 10? (c) What is 1116 equal to in base 10? (d) What is 1132 equal to in base 10? (e) In general, for any base b, what is 11b equal to in base10?
> Musicians Jaquan, Cindy, and Mark are musicians. One plays the guitar, one plays the saxophone, and one plays the drums. They live in three adjacent houses on Lake View Drive. From the following information, determine who plays the drums. (Hint: A table
> (a) What is 102 equal to in base 10? (b) What is 108 equal to in base 10? (c) What is 1016 equal to in base 10? (d) What is 1032 equal to in base 10? (e) In general, for any base b, what is l0b equal to in base 10?
> Insurance Policies Ray owns two cars (a Ford Mustang and a Ford Focus), a house, and a rental apartment. He has auto insurance for both cars, a homeowner’s policy, and a policy for the rental property. The costs of the policies are Mustang: $1648 per yea
> (a) What is 04 equal to in base 10? (b) What is 14 equal to in base 10? (c) What is 24 equal to in base 10? (d) What is 34 equal to in base 10? (e) In general, if n is a digit less than the base b, and the base b is less than or equal to 10, then d
> A Grid Place five 1’s, five 2’s, five 3’s, five 4’s, and five 5’s in a 5 × 5 grid so that each digit—that is, 1, 2, 3, 4, 5—appears exactly once in each row and exactly once in each column.
> Another Conversion Method There is an alternative method for changing a base 10 numeral to a different base. This method will be used to convert 328 to base 5. Dividing 328 by 5 gives a quotient of 65 and a remainder of 3. Write the quotient below the di
> A Digital Clock Digital clocks display numerals by lighting all or some of the seven parts of the pattern shown. If each digit 0 through 9 is displayed once, which of the seven parts is used least often? Which part is used most often?
> Write the Hindu–Arabic numerals in the base 4 numeration system discussed in Exercises 53–56. You need to use the colors indicated above to write the answer. 56
> Answer true or false. If false, give the reason. {rain} ( {rain, snow, sleet, hail}
> Consecutive Digits Place the digits 1 through 8 in the eight boxes so that each digit is used exactly once and no two consecutive digits touch horizontally, vertically, or diagonally.
> Write the Hindu–Arabic numerals in the base 4 numeration system discussed in Exercises 53–56. You need to use the colors indicated above to write the answer. 60
> Handshakes All Around Five salespeople gather for a sales meeting. How many handshakes will each person make if each must shake hands with each of the four others?
> Write the Hindu–Arabic numerals in the base 4 numeration system discussed in Exercises 53–56. You need to use the colors indicated above to write the answer. 15
> Dominos Consider a domino with six dots as shown. Two ways of connecting the three dots on the left with the three dots on the right are illustrated. Using three lines, in how many ways can the three dots on the left be connected with the three dots on t
> Write the Hindu–Arabic numerals in the base 4 numeration system discussed in Exercises 53–56. You need to use the colors indicated above to write the answer. 10
> Stack of Cubes Identical cubes are stacked in the corner of a room as shown. How many of the cubes are not visible?
> Suppose colors as indicated below represent numerals in a base 4 numeration system. Write the Hindu–Arabic numerals equivalent to each of the following.
> Magic Square For a 3 by 3 magic square, how can you determine the sum of all the numbers in the square by using a key value in the magic square?
> Suppose colors as indicated below represent numerals in a base 4 numeration system. Write the Hindu–Arabic numerals equivalent to each of the following.
> Smartphone Price According to International Data Corporation, the average price of a smartphone decreased by 12.9% from 2012 to 2013. The average price of a smartphone in 2012 was $387. Determine the average price of a smartphone in 2013. Round your answ
> Magic Square For a 3 by 3 magic square, how can you determine the sum of the numbers in any particular row, column, or diagonal by using a key value in the magic square?
> Suppose colors as indicated below represent numerals in a base 4 numeration system. Write the Hindu–Arabic numerals equivalent to each of the following.
> Magic Square Examine the 3 by 3 magic squares and find the sum of the four corner entries of each magic square. How can you determine the sum by using a key number in the magic square?
> Suppose colors as indicated below represent numerals in a base 4 numeration system. Write the Hindu–Arabic numerals equivalent to each of the following.
> Magic Square Create a magic square by using the numbers 3, 4, 5, 6, 7, 8, 9, 10, and 11. The sum of the numbers in every column, row, and diagonal must be 21.
> Write the Hindu–Arabic numerals in the numeration system discussed in Exercises 45–48 85
> Magic Square Create a magic square by using the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 18. The sum of the numbers in every column, row, and diagonal must be 30.
> Write the Hindu–Arabic numerals in the numeration system discussed in Exercises 45–48 74
> Is it possible for an argument to be invalid if the conjunction of the premises is false in every case of the truth table? Explain your answer.
> Determine whether the argument is valid or invalid. If Lynn wins the contest or strikes oil, then she will be rich. ( If Lynn does not stop working, then she did not win the contest.
> Determine whether the argument is valid or invalid. b If Lynn wins the contest or strikes oil, then she will be rich. If Lynn is rich, then she will stop working. 6 If Lynn does not stop working, then she did not win the contest.
> Cuts in Cheese If you make the three complete cuts in the cheese as shown, how many pieces of cheese will you have?
> Is it possible for an argument to be invalid if the premises are all true? Explain your answer.
> In Exercises 35 and 36, (a) use lattice multiplication to perform the multiplication. (Hint: Be sure not to list any number greater than or equal to the base within the box.) Write the answer in the base in which the exercise is given. (b) Multiply the n
> Add in the indicated base.
> Add in the indicated base.
> Add in the indicated base.
> In a base 4 system, each of the four numerals is represented by one of the following colors: Determine the value of each color if the following addition is true in base 4.
> Determine b, by trial and error, if 1304b = 204.
> Consider the multiplication a) Multiply the numerals in base 8. b) Convert 4628 and 358 to base 10. c) Multiply the base 10 numerals determined in part (b). d) Convert the answer obtained in base 8 in part (a) to base 10. e) Are the answers obtai
> Perform the indicated operation
> Perform the indicated operation
