Question: Consider the multiplication / a) Multiply the

> 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 u

> 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.

> Perform the indicated operation

> Perform the indicated operation

> Write the Hindu–Arabic numerals in the numeration system discussed in Exercises 45–48 23

> Answer true or false. If false, give the reason. {circle} ( {square, circle, triangle}

> Reading a Map the scale on a map is 1 inch = 12 miles. How long a distance is a route on the map if it measures 4.25 in.?

> Use the rectangles in each graph to approximate the area of the region bounded by y = 5/x, y = 0, x = 1, and x = 5. Describe how you could continue this process to obtain a more accurate approximation of the area.

> Consider the function f(x) = 6x – x2 and the point P(2, 8) on the graph of f. a. Graph f and the secant lines passing through P(2, 8) and Q(x, f(x)) for x-values of 3, 2.5, and 1.5. b. Find the slope of each secant line. c. Use the results of part (b) to

> Consider the function f(x) = √x and the point P(4, 2) on the graph of f. a. Graph f and the secant lines passing through P(4, 2) and Q(x, f (x)) for x-values of 1, 3, and 5. b. Find the slope of each secant line. c. Use the results of part (b) to estimat

> A bicyclist is riding on a path modeled by the function f(x) = 0.08x, where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at x = 2.

> A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x − x2), where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at x = 2.

> Decide whether the problem can be solved using pre-calculus or whether calculus is required. If the problem can be solved using pre-calculus, solve it. If the problem seems to require calculus, explain your reasoning and use a graphical or numerical appr

> Decide whether the problem can be solved using pre-calculus or whether calculus is required. If the problem can be solved using pre-calculus, solve it. If the problem seems to require calculus, explain your reasoning and use a graphical or numerical appr

> Discuss the relationship between secant lines through a fixed point and a corresponding tangent line at that fixed point.

> Describe the relationship between pre-calculus and calculus. List three pre-calculus concepts and their corresponding calculus counterparts.

> Use a graphing utility to graph the two functions f(x) = x2 + 1 and g(x) = │x│ + 1 in the same viewing window. Use the zoom and trace features to analyze the graphs near the point (0, 1). What do you observe? Which function is differentiable at this poin

> Find the slope of the tangent line to the graph of the function at the given point. f(t) = 3t − t2, (0, 0)

> Let and Show that f is continuous, but not differentiable, at x = 0. Show that g is differentiable at 0 and find g′(0).

> If a function is differentiable at a point, then it is continuous at that point.

> If a function has derivatives from both the right and the left at a point, then it is differentiable at that point.

> If a function is continuous at a point, then it is differentiable at that point.

> If it is false, explain why or give an example that shows it is false. The slope of the tangent line to the differentiable function f at the point (2, f(2)) is f(2 + ∆x) - f (2) / ∆x.

> Consider the functions f(x) = x2 and g(x) = x3. a. Graph f and f′ on the same set of axes. b. Graph g and g′ on the same set of axes. c. Identify a pattern between f and g and their respective derivatives. Use the pattern to make a conjecture about h′(x)

> A line with slope m passes through the point (0, 4) and has the equation y = mx + 4. a. Write the distance d between the line and the point (3, 1) as a function of m. b. Use a graphing utility to graph the function d in part (a). Based on the graph, is t

> Determine whether the function is differentiable at x = 2.

> Determine whether the function is differentiable at x = 2.

> Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function differentiable at x = 1? f(x) = (1 − x)2/3

> Find the slope of the tangent line to the graph of the function at the given point. f(x) = 5 − x2 , (3, −4)

> Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function differentiable at x = 1?

> Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function differentiable at x = 1? f(x) = √1 – x2

> Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function differentiable at x = 1? f(x) = │x − 1│

> Describe the x-values at which f is differentiable.

> Describe the x-values at which f is differentiable. f(x) = √x+1

> Describe the x-values at which f is differentiable.

> Describe the x-values at which f is differentiable. f(x) = (x + 4)2/3

> Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = │x - 6│, c = 6

> Use the alternative form of the derivative to find the derivative at x = c, if it exists. h(x) = │x + 7│, c = −7

> Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = (x + 3)1/3 , c = −3

> Find the slope of the tangent line to the graph of the function at the given point. f(x) = 2x2 − 3, (2, 5)

> Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = (x − 6)2-3 , c = 6

> Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = 3/x, c = 4

> Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = √│x│, c = 0

> Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = x2 − x, c = 1

> Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = x3 + 2x2 + 1, c = −2

> Evaluate f (2) and f (2.1) and use the results to approximate f′(2). f(x) = 1/4x3

> Evaluate f (2) and f (2.1) and use the results to approximate f′(2). f(x) = x(4 − x)

> Consider the function f(x) = 1/3 x3. a. Use a graphing utility to graph the function and estimate the values of f′(0), f′( 1/2), f′(1), f′(2) and f′(3). b. Use your results from part (a) to determine the values of f′(−1/2), f′(−1), f′(−2) and f′(−3). c

> Consider the function f(x) = 1/2 x2. a. Use a graphing utility to graph the function and estimate the values of f′(0), f′( 1/2), f′(1), and f′(2). b. Use your results from part (a) to determine the values of f′(−1/2), f′(−1), and f′(−2). c. Sketch a po

> The figure shows the graph of g′. a. g’(0) = b. g’(3) = c. What can you conclude about the graph of g knowing that g′(1) = - 8/3? d. What can you conclude about the graph of g kn

> Find the slope of the tangent line to the graph of the function at the given point. g(x) = 3/2 x + 1, (-2, -2)

> Use a graphing utility to graph each function and its tangent lines at x = −1, x = 0, and x = 1. Based on the results, determine whether the slopes of tangent lines to the graph of a function at different values of x are always distinct. a. f(x) = x2 b.

> Find equations of the two tangent lines to the graph of f that pass through the indicated point. f(x) = x2