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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Use the figure to determine the following: B Н °FE U FG
Use the figure to determine the following: B Н АВ П DC
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. A B
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. A B
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. A B
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. B A
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. A B
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. B
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. B
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. A B
Fill in the blanks with an appropriate word, phrase, or symbol(s).When two straight lines intersect, the nonadjacent angles formed are called _________ angles.
Fill in the blanks with an appropriate word, phrase, or symbol(s).An angle whose measure is less than 90° is called a(n) _________ angle.
Fill in the blanks with an appropriate word, phrase, or symbol(s).An angle whose measure is greater than 90° but less than 180° is called a(n) _________ angle.
Fill in the blanks with an appropriate word, phrase, or symbol(s).An angle whose measure is 90° is called a(n) _________ angle.
Fill in the blanks with an appropriate word, phrase, or symbol(s).An angle whose measure is 180° is called a(n) _________ angle.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Two angles, the sum of whose measures is 180°, are called _________ angles.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Two angles, the sum of whose measures is 90°, are called _________ angles.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The union of two rays with a common endpoint is called a(n) _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Two lines that do not lie in the same plane and do not intersect are called _________ lines.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Two lines in the same plane that do not intersect are called _________ lines.
Wacky Noodle Pool Toys 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
If the radius of a sphere is doubled, how is the volume of the sphere affected?
If the side of a cube is doubled, how is the volume of the cube affected?
(a) Explain how to demonstrate, using the cube shown below, that(a + b)3 = a3 + 3a2b + 3ab2 + b3 (b) What is the volume in terms of a and b of each numbered piece in the figure?(c) An eighth
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?
The diameter of Earth is approximately 12,756.3 km. The diameter of the moon is approximately 3474.8 km. Assume that both Earth and the moon are spheres.(a) Determine the surface area of
Find the missing value indicated by the question mark. Use the following formula.(Number of vertices) - (number of edges) + (number of faces) = 2Number of VerticesNumber of EdgesNumber of Faces18?20
Find the missing value indicated by the question mark. Use the following formula.(Number of vertices) - (number of edges) + (number of faces) = 2Number of VerticesNumber of EdgesNumber of Faces12?20
Find the missing value indicated by the question mark. Use the following formula.(Number of vertices) - (number of edges) + (number of faces) = 2Number of VerticesNumber of EdgesNumber of Faces?3012
Find the missing value indicated by the question mark. Use the following formula.(Number of vertices) - (number of edges) + (number of faces) = 2Number of VerticesNumber of EdgesNumber of Faces?128
Find the missing value indicated by the question mark. Use the following formula.(Number of vertices) - (number of edges) + (number of faces) = 2Number of VerticesNumber of EdgesNumber of Faces46?
Find the missing value indicated by the question mark. Use the following formula.(Number of vertices) - (number of edges) + (number of faces) = 2Number of VerticesNumber of EdgesNumber of Faces812?
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 trapezoid measure 12 in. and 8 in., respectively, and the height is 9 in. Find
The engine in a 1957 Chevrolet Corvette has eight cylinders. Each cylinder is a right cylinder with a bore (diameter) of 3.875 in. and a stroke (height) of 3 in. Determine the total displacement
A Wacky Noodle Pool Toy, frequently referred to as a “noodle,” is a cylindrical flotation device made from cell foam (see photo). One style of noodle is a cylinder that has a diameter of 2.5 in.
A bag used to apply icing to a cake is in the shape of a cone with a diameter of 3 in. and a height of 6 in. How much icing will this bag hold when full?Solve the given problem. When appropriate, use
The Louisburg Creamery pack-ages its homemade ice cream in tubs and in boxes. The tubs are in the shape of a right cylinder with a radius of 3 in. and height of 5 in. The boxes are in the shape of a
When baking a cake, you can choose between a circular pan with a 9-in. diameter and a 7 in. x 9 in. rectangular pan.(a) Determine the area of the base of each pan. (b) If both pans are 2 in.
The Everest model globe has a diameter of 20 in. Determine the surface area of this globe.Solve the given problem. When appropriate, use the π key on your calculator and round your answer to the
A baseball is displayed in a cube-shaped glass case. The diameter of the baseball and the length of each side of the cube are both 7.5 cm. What is the volume of the air outside the baseball that
The dimensions of the interior of an upright freezer are height 46 in., width 25 in., and depth 25 in. Determine the volume of the freezer(a) In cubic inches.(b) In cubic feet.Solve the given
(a) How many cubic centimeters of water will a fish tank in the shape of a rectangular solid hold if the tank is 80 cm long, 50 cm wide, and 30 cm high?(b) If 1 cm3 holds 1 mℓ of liquid, how many
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 rectangle. Marisa wishes to add a 4-in. layer of organic topsoil on top of the
Bob is building a backyard play-ground for his grandchildren and wishes to put down rubber mulch to provide safety from falls. Bob wishes to put the mulch in a pit in the shape of a rectangular solid
Use the fact that 1 m3 equals 1,000,000 cm3 to make the conversion.9,160,000 cm3 to cubic meters.
Use the fact that 1 m3 equals 1,000,000 cm3 to make the conversion.500,000 cm3 to cubic meters.
Use the fact that 1 m3 equals 1,000,000 cm3 to make the conversion.13.7 m3 to cubic centimeters.
Use the fact that 1 m3 equals 1,000,000 cm3 to make the conversion.0.25 m3 to cubic centimeters.
Use the fact that 1 yd3 equals 27 ft3 to make the conversion.278.1 ft3 to cubic yards
Use the fact that 1 yd3 equals 27 ft3 to make the conversion.453.6 ft3 to cubic yards
Use the fact that 1 yd3 equals 27 ft3 to make the conversion.15.75 yd3 to cubic feet
Use the fact that 1 yd3 equals 27 ft3 to make the conversion.6 yd3 to cubic feet
Determine the volume of the shaded region. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 11 in. 6 in. 3 in. K 4 in. 8 in.
Determine the volume of the shaded region. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 4 ft 3 ft 3 ft
Determine the volume of the shaded region. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. A m- -3 m –
Determine the volume of the shaded region. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. (6.9 cm 20.8 cm K-7 cm÷ 'cm-|
Determine the volume of the shaded region. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. +6 mm 6 mm 6 mm - 6 mm-
Determine the volume of the shaded region. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. -8 ft 7 ft 14 ft 7 ft K-4 ft-
Determine the volume of the shaded region. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. -5 in. -4 in.→ 4 in. 11 in.
Determine the volume of the shaded region. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 5 ft 5 ft 20 ft 10 ft F10 ft-
Determine the volume of the three-dimensional figure. When appropriate, round your answer to the nearest hundredth. 13 ft 15 ft 9 ft
Determine the volume of the three-dimensional figure. When appropriate, round your answer to the nearest hundredth. 15 cm 12 cm 12 cm
Determine the volume of the three-dimensional figure. When appropriate, round your answer to the nearest hundredth. 8 in. 10 in. 12 in. 24 in. 8 in. 10 in. 12 in.
Determine the volume of the three-dimensional figure. When appropriate, round your answer to the nearest hundredth. 12 m 18 m 12 m
Determine (a) The volume. (b) The surface area of the three-dimensional figure. When appropriate,use the π key on your calculator and round your answer to the nearest hundredth. - 9 cm
Determine (a) The volume. (b) The surface area of the three-dimensional figure. When appropriate,use the π key on your calculator and round your answer to the nearest hundredth. K7 mi
Determine (a) The volume. (b) The surface area of the three-dimensional figure. When appropriate,use the π key on your calculator and round your answer to the nearest hundredth. 24 ft
Determine (a) The volume. (b) The surface area of the three-dimensional figure. When appropriate,use the π key on your calculator and round your answer to the nearest hundredth. 3 cm
Determine (a) The volume. (b) The surface area of the three-dimensional figure. When appropriate,use the π key on your calculator and round your answer to the nearest hundredth. 24
Determine (a) The volume. (b) The surface area of the three-dimensional figure. When appropriate,use the π key on your calculator and round your answer to the nearest hundredth. 12
Determine (a) The volume. (b) The surface area of the three-dimensional figure. When appropriate,use the π key on your calculator and round your answer to the nearest hundredth. 5 yd
Determine (a) The volume. (b) The surface area of the three-dimensional figure. When appropriate,use the π key on your calculator and round your answer to the nearest hundredth. 6 ft
Fill in the blanks with an appropriate word, phrase, or symbol(s).Euler’s polyhedron formula states that, for any polyhedron, the number of vertices minus the number of edges plus the number of
Fill in the blanks with an appropriate word, phrase, or symbol(s).A prism whose sides are rectangles is called a(n) __________ prism.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A polyhedron whose bases are congruent polygons and whose sides are parallelograms is called a(n) _____________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A regular polyhedron, whose faces are all regular polygons of the same size and shape, is also called a(n) _____________ solid.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The sum of the areas of the surfaces of a three-dimensional figure is called the figure’s _____________ area.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A measure of the capacity of a three-dimensional figure is called the figure’s _____________.
In the figure, one side of the largest square has length a + b. Therefore, the area of the largest square is (a + b)2. Answer the following questions to find a formula for the expansion of (a +
A second formula for determining the area of a triangle (called Heron’s formula) isA = √[s(s -a)(s -b)(s -c)]where s = 1/2 (a + b + c) and a, b, and c are the lengths of the sides of the
The screen of a plasma television is in the shape of a rectangle with a diagonal of length 43 in. If the height of the screen is 21 in., determine the width of the screen. Round your answer to the
In Fenway Park, home of baseball’s Boston Red Sox, the left field wall is known as the Green Monster. The distance from home plate down the third baseline to the bottom of the wall is 310 feet (see
Brian is bringing his boat into a dock that is 9 ft above the water level (see figure). If a 41-ft rope is attached to the dock on one side and to the boat on the other side, determine the horizontal
Lorrie places a 29-ft ladder against the side of a building with the bottom of the ladder 20 ft away from the building (see figure). How high up on the wall does the ladder reach? 29 ft ladder 20 ft
Larry wishes to have three quartz countertops installed in his new kitchen. The counter-tops are rectangular and have the following dimensions: ft x 6 ft, ft x 8 ft, and 3 ft x ft.
A National Basketball Association (NBA) basketball court is a rectangle that is 94 ft long and 50 ft wide.(a) If you were to walk around the outside edge of a basketball court, how far would you
Jim and Wendy’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
Clarence and Rose’s home lot is illustrated here. Clarence and Rose wish to hire Picture Perfect Lawn Service to cut their lawn. How much will it cost Clarence and Rose to have their lawn cut if
The cost of Saxony carpeting is $7.49 per square foot. This price includes the cost of installation. Determine the cost for Nancy to have this carpeting installed in all three bedrooms.Nancy has just
The cost of Berber carpeting is $9.99 per square foot. This price includes the cost of installation. Determine the cost for Nancy to have this carpeting installed in all three bedrooms.Nancy has just
The cost of linoleum is $3.49 per square foot. This price includes the cost of installation. Determine the cost for Nancy to have linoleum installed in the kitchen and in both bathrooms.Nancy has
The cost of ceramic tile is $10.49 per square foot. This price includes the cost of installation. Determine the cost for Nancy to have ceramic tile installed in the kitchen and in both
The cost of oak laminate flooring is $9.75 per square foot if Nancy installs the flooring herself or $12.75 per square foot if she has the flooring installed by the flooring company. Determine the
(a) In the figure, m∡CED = m∡ABC. Explain why triangles ABC and DEC must be similar.(b) Determine the distance across the lake, DE. Lake|Joy 356.0 ft B 1404.0 ft 543.0 ft
You are asked to measure the height of an inside wall of a warehouse. No ladder tall enough to measure the height is available. You borrow a mirror from a salesclerk and place it on the floor. You
If the scaling factor of quadrilateral E'F'G'H' with respect to quadrilateral EFGH is 1/3, determine the length of the sides of quadrilateral E'F'G'H'.
If the scaling factor of ΔDEF with respect to ΔD'E'F' is 3, determine the length of the sides of triangle ΔD'E'F'.We use a scaling factor. Examine the similar triangles ABC and A'B'C' in the
Determine the measure of the angle. In the figure, ∡ABC makes an angle of 125° with the floor and l1 and l2 are parallel.m∡DEC B G
Determine the measure of the angle. In the figure, ∡ABC makes an angle of 125° with the floor and l1 and l2 are parallel.m∡DFE B G
Determine the measure of the angle. In the figure, ∡ABC makes an angle of 125° with the floor and l1 and l2 are parallel.m∡EDF B G

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