Use your intuition to determine whether the variation between the indicated quantities is direct or inverse. On Earth, the weight and mass of an object
> Find the modulo class to which each number belongs for the indicated modulo system. 38, mod 9
> Consider the mathematical system defined by the following table. (a) Is the system closed? Explain. (b) Is there an identity element in the set? If so, what is it? c) For each element in the set, give the corresponding inverse element, if it exists. (d)
> Determine what number the sum, difference, or product is congruent to in modulo 5. (4 – 9) • 7
> Repeat parts (a)–(h) of Exercise 53 for the mathematical system defined by the given table. Assume that the associative property holds for the given operation.
> Determine what number the sum, difference, or product is congruent to in modulo 5. 2 - 4
> Determine (a) the area and (b) the circumference of the circle. Use the key on your calculator and round your answer to the nearest hundredth.
> Repeat parts (a)–(h) of Exercise 53 for the mathematical system defined by the given table. Assume that the associative property holds for the given operation.
> Determine what number the sum, difference, or product is congruent to in modulo 5. 8 . 7
> A mathematical system is defined by a three-element by three-element table where every element in the set appears in each row and each column. Must the mathematical system be a commutative group? Explain.
> Determine what number the sum, difference, or product is congruent to in modulo 5. 12 - 5
> Determine the sum or difference in clock 7 arithmetic. 3 – (2 – 6)
> Determine what number the sum, difference, or product is congruent to in modulo 5. 2 + 3
> Determine the sum or difference in clock 7 arithmetic. 2 – 3
> Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months. 5 years, 9 months
> Determine the sum or difference in clock 7 arithmetic. 6 + 7
> Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months. 7 years
> y < -2x + 2 Draw the graph of the inequality.
> Determine the sum or difference in clock 7 arithmetic. 2 + 6
> Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months. 4 years, 8 months
> Determine the sum or difference in clock 6 arithmetic. 2 + (1 – 3)
> Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume no leap years. 3 years, 25 days
> Determine the sum or difference in clock 6 arithmetic. 4 – 5
> Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume no leap years. 3 years, 34 days
> Determine the sum or difference in clock 6 arithmetic. 4 + 6
> Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume no leap years. 365 days
> Determine the sum or difference in clock 6 arithmetic. 4 + 4
> Give an example to show that the associative property does not hold for the set of integers under the operation of subtraction.
> Graph the solution set of the inequality, where x is a real number, on the number line.
> Determine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number. 12 – 12
> Give an example to show that the commutative property does not hold for the set of integers under the operation of division.
> Determine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number. 5 – 8
> Give the associative property of addition and illustrate the property with an example.
> Determine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number. 1 – 12
> Give the commutative property of multiplication and illustrate the property with an example.
> Determine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number. 11 – 8
> Is the set of irrational numbers a group under the operation of multiplication
> Use Table 9.1 on page 529 to determine the sum in clock 12 arithmetic. 18 + 72 + 6
> Is the set of rational numbers a group under the operation of subtraction?
> Solve the system of equations graphically. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. y = 3 y = x - 1
> Use Table 9.1 on page 529 to determine the sum in clock 12 arithmetic. 12 + 12
> Is the set of integers a group under the operation of multiplication
> Use Table 9.1 on page 529 to determine the sum in clock 12 arithmetic. 11 + 7
> Is the set of whole numbers a commutative group under the operation of multiplication?
> Use Table 9.1 on page 529 to determine the sum in clock 12 arithmetic. 10 + 3
> Is the set of negative integers a group under the operation of division?
> Determine if the system is commutative.Explain how you determined your answer.
> Is the set of positive rational numbers a commutative group under the operation of multiplication?
> Determine (a) the volume and (b) the surface area of the three-dimensional figure. When appropriate, use the key on your calculator and round your answer to the nearest hundredth.
> Is the set of whole numbers a commutative group under the operation of addition?
> More Pool Toys Wacky Noodle Pool Toys (see Exercise 44 on page 479) come in many different shapes and sizes. (a) Determine the volume, in cubic inches, of a noodle that is in the shape of a 5.5-ft-long solid octagonal prism whose base has an area of 5 in
> Is the set of real numbers a group under the operation of addition?
> If the side of a cube is doubled, how is the volume of the cube affected?
> State the theorem concerning the sum of the measures of the angles of a triangle in a) Euclidean geometry. b) Hyperbolic geometry. c) Elliptical geometry.
> Packing Orange Juice A box is packed with six cans of orange juice. The cans are touching each other and the sides of the box, as shown. What percent of the volume of the interior of the box is not occupied by the cans?
> List the three types of curvature of space and the types of geometry that correspond to them.
> In Exercises 47–52, find the missing value indicated by the question mark. Use the following formula.
> In forming the Koch snowflake in Figure 8.104 on page 510, the perimeter becomes greater at each step in the process. If each side of the original triangle is 1 unit, a general formula for the perimeter, L, of the snowflake at any step, n, may be found b
> In Exercises 47–52, find the missing value indicated by the question mark. Use the following formula.
> We show a fractal-like figure made using a recursive process with the letter “M.” In Exercises 9–12, use this fractal-like figure as a guide in constructing fractal-like figures with the letter given.
> Determine (a) the area and (b) the circumference of the circle. Use the key on your calculator and round your answer to the nearest hundredth.
> In Exercises 47–52, find the missing value indicated by the question mark. Use the following formula.
> We show a fractal-like figure made using a recursive process with the letter “M.” In Exercises 9–12, use this fractal-like figure as a guide in constructing fractal-like figures with the letter given.
> Solve the given problem. When appropriate, use the key on your calculator and round your answer to the nearest hundredth. Flower Box The flower box shown below is 4 ft long, and its ends are in the shape of a trapezoid. The upper and lower bases of the t
> Determine whether point B in Fig. 8.95(d) is inside or outside the Jordan curve.
> Solve the given problem. When appropriate, use the key on your calculator and round your answer to the nearest hundredth. Pool Toys A Wacky Noodle Pool Toy, frequently referred to as a “noodle,” is a cylindrical flotat
> Take a strip of paper, make one whole twist and another half twist, and then tape the ends together. Test by a method of your choice to determine whether this has the same properties as a Möbius strip.
> Solve the given problem. When appropriate, use the key on your calculator and round your answer to the nearest hundredth. Ice-Cream Comparison The Louisburg Creamery packages its homemade ice cream in tubs and in boxes. The tubs are in the shape of a rig
> Make a Möbius strip. Cut it one-third of the way from the edge, as in Experiment 4 on page 500. You should get two loops, one going through the other. Determine whether either (or both) of these loops is itself a Möbius strip.
> Solve the given problem. When appropriate, use the key on your calculator and round your answer to the nearest hundredth. Globe Surface Area The Everest model globe has a diameter of 20 in. Determine the surface area of this globe.
> How many separate strips are obtained in Experiment 3 on page 500?
> y
> Solve the given problem. When appropriate, use the key on your calculator and round your answer to the nearest hundredth. Volume of a Freezer The dimensions of the interior of an upright freezer are height 46 in., width 25 in., and depth 25 in. Determine
> Use the result of Experiment 1 on page 499 to find the number of edges on a Möbius strip.
> Solve the given problem. When appropriate, use the key on your calculator and round your answer to the nearest hundredth. Rose Garden Topsoil Marisa wishes to plant a rose garden in her backyard. The rose garden will be in the shape of a 9 ft by 18 ft re
> Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
> Use the fact that 1 m3 equals 1,000,000 cm3 to make the conversion. 9,160,000 cm3 to cubic meters
> Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
> Use the fact that 1 m3 equals 1,000,000 cm3 to make the conversion. 13.7 m3 to cubic centimeters
> Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
> Use the fact that 1yd3 equals 27 ft3 to make the conversion. 278.1 ft3 to cubic yards
> Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
> Graph the solution set of the inequality, where x is a real number, on the number line. -4x (12
> (2). In a modulo m system, in addition to the m elements, there is also a(n) ________ operation. (4). In a modulo m system, the number m is called the _______ of the system. (6). To determine the value that 45 is congruent to in modulo 7, we _______ 45 b
> Use the fact that 1yd3 equals 27 ft3 to make the conversion. 15.75 yd3 to cubic feet
> Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
> Determine the volume of the shaded region. When appropriate, use the key on your calculator and round your answer to the nearest hundredth.
> Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
> Determine the volume of the shaded region. When appropriate, use the key on your calculator and round your answer to the nearest hundredth.
> Determine if the point is inside or outside the curve. Point D
> Determine the volume of the shaded region. When appropriate, use the key on your calculator and round your answer to the nearest hundredth.
> Determine if the point is inside or outside the curve. Point B
> Determine the volume of the shaded region. When appropriate, use the key on your calculator and round your answer to the nearest hundredth.
> (a) Name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.
> Solve the system of equations graphically. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. x = 2 y = -1
> Determine the volume of the three dimensional figure. When appropriate, round your answer to the nearest hundredth.
> (a) Name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.
> Determine the volume of the three dimensional figure. When appropriate, round your answer to the nearest hundredth.
> We use a scaling factor. Examine the similar triangles ABC and A(B(C( in the figure below.
> Determine (a) the volume and (b) the surface area of the three-dimensional figure. When appropriate, use the key on your calculator and round your answer to the nearest hundredth.
> Determine the measure of the angle. In the figure and l1 and l2 are parallel.
