(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 by 7 and determine the remainder.
> 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?
> 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
> 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
> 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.
> 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.
> Identify the figure as a line, half line, ray, line segment, open line segment, or half open line segment. Denote the figure by its appropriate symbol.
> Distances in Illinois A triangle can be formed by drawing line segments on a map of Illinois connecting the cities of Rockford, Chicago, and Bloomington (see figure below). If the actual distance from Chicago to Rockford is approximately 85.5 miles, use
> Use your intuition to determine whether the variation between the indicated quantities is direct or inverse. The number of workers hired to install a fence and the time required to install the fence
> Identify the figure as a line, half line, ray, line segment, open line segment, or half open line segment. Denote the figure by its appropriate symbol.
> Angles on a Picnic Table The legs of a picnic table form an isosceles triangle as indicated in the /
> Identify the figure as a line, half line, ray, line segment, open line segment, or half open line segment. Denote the figure by its appropriate symbol.
> Determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A(B(C(D(. /
> Suppose you have three distinct lines, all lying in the same plane. Find all the possible ways in which the three lines can be related. There are four cases. Sketch each case.
> Determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A(B(C(D(.
> If lines l and m are parallel lines and if lines l and n are skew lines, is it true that lines m and n must also be skew? (Hint: Look at Fig. 8.5 on page 439.) Explain your answer and include a sketch to support your answer.
> Determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A(B(C(D(. The length of side
> (a) Will three noncollinear points A, B, and C always determine a plane? Explain. (b) Is it possible to determine more than one plane with three noncollinear points? Explain. (c) How many planes can be constructed through three collinear points? (d) Draw
> Find the length of the sides and the measures of the angles for the congruent triangles ABC and A(B(C(. m / A(C(B(
> Determine (a) the area and (b) the perimeter of the quadrilateral.
> What is the intersection of two distinct nonparallel planes?
> Find the length of the sides and the measures of the angles for the congruent triangles ABC and A(B(C(.
> Determine whether the statement is always true, sometimes true, or never true. Explain your answer. A triangle contains two obtuse angles.
> Find the length of the sides and the measures of the angles for the congruent triangles ABC and A(B(C(.
> Alternate exterior angles are supplementary angles. Determine whether the statement is always true, sometimes true, or never true. Explain your answer.
> Triangles ABC and DEC are similar figures. Determine the length of /
> A triangle contains exactly two acute angles. Determine whether the statement is always true, sometimes true, or never true. Explain your answer.
> Triangles ABC and DEC are similar figures. Determine the length of
> The figure below suggests a number of lines and planes. The lines may be described by naming two points, and the planes may be described by naming three points. Use the figure to name the following. Many answers are possible. A line and a plane whose int
> The figures are similar. Find the length of side x and side y.
> For each inequality, determine whether (-2, 4) is a solution to the inequality. (a) 4x - 2y < -10 (b) 4x - 2y (-10 (c) 4x - 2y >-10 (d) 4x - 2y ( -10
> The figure below suggests a number of lines and planes. The lines may be described by naming two points, and the planes may be described by naming three points. Use the figure to name the following. Many answers are possible. Three planes whose intersect
> The figures are similar. Find the length of side x and side y.
> The figure below suggests a number of lines and planes. The lines may be described by naming two points, and the planes may be described by naming three points. Use the figure to name the following. Many answers are possible. Two planes that intersect at
> The figures are similar. Find the length of side x and side y.
> The figure below suggests a number of lines and planes. The lines may be described by naming two points, and the planes may be described by naming three points. Use the figure to name the following. Many answers are possible. Two parallel lines
> (a) Determine the measure of an interior angle of the named regular polygon. (b) If a side of the polygon is extended, determine the supplementary angle of an interior angle. Dodecagon
> The angles are supplementary angles. Determine the measures of
