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mathematics
a survey of mathematics with applications

Questions and Answers of A Survey of Mathematics with Applications

Consider the set of whole numbers under the operation of addition.a) Is the system closed? Explain.b) Is there an identity element? If so, what is it?c) Does each element in the set have an inverse?
In Exercise, determine A × B. A B = 4 3 -3 5
Determine what number the sum, difference, or product is congruent to in modulo 5.4 + 1
Determine the modulo class to which the number belongs for the indicated modulo system.54, mod 14
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
Fill in the blank with an appropriate word, phrase, or symbol(s).The set of all 2 × 3 matrices under the operation of matrix addition forms a commutative ________.
In Exercise fill in the blanks with an appropriate word, phrase, or symbol(s).In a finite mathematical system, if every element does not appear in every row and every column of the table, you need to
In Exercise, fill in the blanks with an appropriate word, phrase, or symbol(s).If a mathematical system possesses the following properties—closure, identity element, inverses, and the associative
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
Fill in the blank with an appropriate word, phrase, or symbol(s).Multiplication of matrices is possible only when the number of ________ of the first matrix is the same as the number of ________ of
Consider the mathematical systema) What is the binary operation?b) Is this system closed? Explain.c) Is there an identity element for this system under the given operation? Explain.d) What is the
In Exercise fill in the blanks with an appropriate word, phrase, or symbol(s).In clock 12 arithmetic under the operation of addition, since the system is closed, there is an identity element, each
In Exercise, fill in the blanks with an appropriate word, phrase, or symbol(s).When a binary operation is performed on two elements in a set and the result is the identity element for the binary
Determine the sum or difference in clock 12 arithmetic.8 - 10
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
Fill in the blank with an appropriate word, phrase, or symbol(s).When multiplying a matrix by a real number, the real number is called a(n) ________.
In Exercise fill in the blanks with an appropriate word, phrase, or symbol(s).In clock 12 arithmetic, for any elements a and b, a + b = b + a ; therefore, the ________ property holds under the
In Exercise, fill in the blanks with an appropriate word, phrase, or symbol(s).Since the product of 1 and any integer is the given integer, we say that 1 is the ________ identity element for the set
Determine the sum or difference in clock 12 arithmetic.10 + 8
Fill in the blanks with an appropriate word, phrase, or symbol(s).To determine the value that 45 is congruent to in modulo 7, we ________ 45 by 7 and determine the remainder.
Fill in the blank with an appropriate word, phrase, or symbol(s).To add or subtract two matrices, the matrices must have the same ________.
In Exercise fill in the blanks with an appropriate word, phrase, or symbol(s).In clock 12 arithmetic, for any elements a, b, and c, (a + b) + c = a + (b + c); therefore, the ________ property holds
In Exercise, fill in the blanks with an appropriate word, phrase, or symbol(s).Since the sum of 0 and any integer is the given integer, we say that 0 is the additive ________ element for the set of
Determine the sum or difference in clock 12 arithmetic.9 + 8
Fill in the blanks with an appropriate word, phrase, or symbol(s).If a and b have the same remainder when divided by m, we say that a is ________ to b modulo m.
Fill in the blank with an appropriate word, phrase, or symbol(s).The number of rows in a 4 × 3 matrix is ________.
In Exercise fill in the blanks with an appropriate word, phrase, or symbol(s).In clock 12 arithmetic, since 1 + 11 = 11 + 1 = 12, we say that 1 and 11 are additive ________.
In Exercise, fill in the blanks with an appropriate word, phrase, or symbol(s).A specific example illustrating that a property is not true is called a(n) ________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In a modulo m system, the number m is called the ________ of the system.
In Exercises 1–8, fill in the blank with an appropriate word, phrase, or symbol(s).The number of columns in a 3 * 2 matrix is ________.
In Exercises 1–8, fill in the blank with an appropriate word, phrase, or symbol(s).The number of columns in a 3 × 2 matrix is ________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).If a binary operation is performed on any two elements of a set and the result is an element of the set, then that set is ________
Fill in the blanks with an appropriate word, phrase, or symbol(s).In any modulo m system, we can develop a set of modulo classes by dividing the numbers by m and placing all numbers with the same
In Exercises 1–6, fill in the blanks with an appropriate word, phrase, or symbol(s).In a modulo m system, in addition to the m elements, there is also a(n) ________ operation.
In Exercises 1–8, fill in the blank with an appropriate word, phrase, or symbol(s).A rectangular array of real numbers, symbols, or expressions is called a(n) ________.
In Exercise fill in the blanks with an appropriate word, phrase, or symbol(s).Since clock 12 arithmetic, under the operation of addition, contains only the elements {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
∡ABC and ∡CBD are complementary and m∡CBD is twice the m∡ABC. ∡ABD and ∡DBE are supplementary angles.a) Draw a sketch illustrating ∡ABC, ∡CBD, and ∡DBE.b) Determine m∡ABC.c)
In Exercise, fill in the blanks with an appropriate word, phrase, or symbol(s).A mathematical system consists of a set of elements and at least one ________ operation.
In Exercise fill in the blanks with an appropriate word, phrase, or = symbol(s).In the mathematical system of clock 12 arithmetic, under the operation of addition, the set of elements is ________.
Fill in the blank with an appropriate word, phrase, or symbol(s).A rectangular array of real numbers, symbols, or expressions is called a(n) ________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The elements in a modulo m system consist of the m numbers, 0 through ________.
In Exercise, fill in the blanks with an appropriate word, phrase, or symbol(s).A binary operation is an operation or rule that can be performed on exactly two elements of a set, with the result being
Explain your answer and include a sketch to support your answer.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?
The figure below suggests several 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
a) In the figure on the right, m∡ CED = m∡ ABC. Explain why triangles ABC and DEC must be similar.b) Determine the distance across the lake, DE. D Lake Joy 356.0 ft В 1404.0 ft A E 543.0 ft
Parallel lines are cut by the transversal shown. Determine the measures of ∡1 through ∡7. 3 2 20°-
A triangle can be formed by drawing line segments on a map of Missouri connecting the cities of Kansas City, Springfield, and St. Louis. If the actual distance from Kansas City to St. Louis is
A triangle can be formed by drawing line segments on a map of Texas connecting the cities of Austin, Houston, and San Antonio. If the actual distance from Austin to Houston is approximately 160
The difference between the measures of two complementary angles is 8°. Determine the measures of the two angles.
Determine the supplementary angle of the given angle.167°
Determine the supplementary angle of the given angle.29°
Determine the complementary angle of the given angle.62°
Determine the complementary angle of the given angle.13°
Chloe and Zion’s home lot is illustrated here. They wish to hire a lawn service to cut their lawn. M&M Lawn Service charges $0.03 per square yard of lawn. How much will it cost them to have
Use the figure to determine the following: B C E H FC U FI
In Exercise, determine the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. F10 in. 20 in. 30 in.
In Exercise, identify the quadrilateral.
In Exercise, determine(a) The volume(b) The surface area of the figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 5 yd
Use the figure to determine the following: B C D E H ВC U BA
In Exercise, determine the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 9 yd 10 yd 11 yd -18 yd-
In Exercise, identify the quadrilateral.
In Exercise, determine the volume of the figure. 12 m 9 m 8 m -15 m-
Use the figure to determine the following: B D H BC U CF U FB
In Exercise, use the fact that 1yd3 equals 27 ft3 to make the conversion.7 yd3 to cubic feet.
In Exercise, determine the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. CO 4 cm 16 ст
In Exercise, identify the quadrilateral.
In Exercise, determine the volume of the figure. 5 ft 7 ft 5 ft 6 ft
Use the figure to determine the following: B C D H BC U CF UFB
In Exercise, determine the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 2 ft 10 ft
In Exercise, determine the measure of ∡x. 132° 37°
Use the figure to determine the following: B C D E H BGN
In Exercise, determine the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 8 m 6 m 10 m
In Exercise, determine the measure of ∡x. 57° 27°
Use the figure to determine the following: B D E {C}N°CH
In Exercise, determine the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 12 mm
In Exercise, determine the measure of ∡x. 105° 133°
Use the figure to determine the following. C XABD N XDBG
In Exercise, determine the measure of ∡x. 35° 30°
Use the figure to determine the following. D C A E BC U BD
In Exercise, one square yard equals 9 ft2. Use this information to convert the following.63 ft2 to square yards
Use the figure to determine the following. C B. A 'F XGBC N 4CBE
In Exercise, one square yard equals 9 ft2. Use this information to convert the following.112.5 ft2 to square yards
Use the figure to determine the following. B А 'F XABG N X CBD
Davidson is building a backyard playground for his grandchildren and wishes to put down rubber mulch to provide safety from falls. Davidson wishes to put the mulch in a pit in the shape of a
In Exercise, one square meter equals 10,000 cm2. Use this information to convert the following.7 m2 to square centimeters
Use the figure to determine the following. A 'F XDBF N FG
Make a Möbius strip. Cut it one-third of the way from the edge, as in Experiment 4. You should get two loops, one going through the other. Determine whether either (or both) of these loops is itself
Use the figure to determine the following. C 'F BC U BG
In Exercise, use the fact that 1 m3 equals 1,000,000 cm3 to make the conversion.1.5 m3 to cubic centimeters.
In Exercise, determine the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 24 mm
Use the figure to determine the following. D C E XEBF N ED
In Exercise, one square meter equals 10,000 cm2. Use this information to convert the following.4072 cm2 to square meters
Use the figure to determine the following. G. B 'F XABE U AB
Use the figure to determine the following. D A 'F XCBF U BC
A softball is displayed in a cube-shaped glass case. See Exercise 39 for a similar description involving a baseball. The diameter of the softball and the length of each side of the cube are both
In Exercise, solve the given problem. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth.A regulation WNBA basketball has a diameter of 9.15 inches.a)
Use the figure to determine the following. D B A 'F XCBG U BG
In Exercise, solve the given problem. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth.A regulation NBA basketball has a diameter of 9.47 inches.a)
Use the figure to determine the following. D C B. A BF U BE
In Exercise,(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.Octagon

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