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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
Does the Adams method result in an apportionment that satisfies or violates the quota rule in this scenario?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town Easter egg hunt. When they returned with their
Use the Webster method to apportion the Easter eggs. Determine whether it is necessary to modify the divisor. If so, indicate the value of the modified divisor.Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a
Does the Webster method result in an apportionment that satisfies or violates the quota rule in this scenario?Children from five families-the Chorro family, the Eswaran family, the Javernick family, the Lahde family, and the Stolly family-joined a town Easter egg hunt. When they returned with their
Hamilton's Method Use this information: Suppose that the State of Delaware received 2,000 packs of COVID-19 vaccines, with ten doses per pack. These (unopened) packs must be distributed to the three counties based on total population. Use the population information in the table below to determine
Jefferson's Method Use this information: Suppose that the State of Delaware received 2,000 packs of COVID-19 vaccines, with ten doses per pack. These (unopened) packs must be distributed to the three counties based on total population. Use the population information in the table below to determine
Adams's Method Use this information: Suppose that the State of Delaware received 2,000 packs of COVID-19 vaccines, with ten doses per pack. These (unopened) packs must be distributed to the three counties based on total population. Use the population information in the table below to determine how
Webster's Method Use this information: Suppose that the State of Delaware received 2,000 packs of COVID-19 vaccines, with ten doses per pack. These (unopened) packs must be distributed to the three counties based on total population. Use the population information in the table below to determine
Notice that the apportionments found in questions \(46,47,48\), and 49 all satisfy the quota rule. Does this contradict the statement, "The Jefferson, Adams, and Webster methods of apportionment all violate the quota rule"? Why or why not?Use this information: Suppose that the State of Delaware
Find \(\overleftrightarrow{A D} \cap \overrightarrow{C D}\)Use the given figure for the following exercise. A B C D
Find \(\overline{A B} \cup \overline{B C}\).Use the given figure for the following exercise. A B C D
Use the given figure to find the angle measurements. (8x+3) (28x+3) (9x-6)
Given that \(l_{1}\) and \(l_{2}\) are parallel lines, solve the angle measurements for all the angles in the given figure. 1/2 h 3/150 5/6 12 7/8
Find the angle measurements in the given figure. (6x+3) (3x+4) (7x+3)
The two triangles shown are congruent by what theorem?
Find the sum of the interior angles of a regular heptagon.
Determine the scaling factor between these two similar triangles. y cm 8 cm 3.5 cm 2.18 cm 5 cm 7 cm
Find the measure of the missing angles in the figure shown. X -25
Calculate the perimeter of a regular octagon with a side length of \(5 \mathrm{~cm}\).
Find the measurement of an interior angle of a regular heptagon.
Find the sum of the interior angles of a regular pentagon.
Find the measure of an exterior angle of a regular pentagon.
Find the circumference of the circle with a radius of \(3.5 \mathrm{~cm}\).
What are the four transformations that are used to produce tessellations?
Find the surface area of the triangular prism shown. 5.2 in 7.9 in 6 in 10 in
Find the volume of the right cylinder in the given figure. 2.5 cm 14 cm
Find the missing length in the given figure. 5 cm 6 cm X
Find the missing length in the given figure. 10 in 45
Find the length of side \(b\) in the given figure. b 14.8 in 24
Find the length of side \(a\) in the given figure. 10 cm 30
Find the measure of \(\theta\) in the given figure. 7.62 3
For the following exercises, use this line.1. Define \(\overrightarrow{B D}\)2. Define \(\overline{A B}\)3. \(\overleftarrow{B A}\)4. \(\overleftrightarrow{A D}\) A B C D
Using the street map in Figure 10.6, find two ways you would stop at the dry cleaners and the grocery store after school on your way home. H School A Grocery I E B Post Office F Dry Cleaners C G Home Library Figure 10.6 Street Map
Identify the sets of parallel and perpendicular lines in the given figure. R X U S V Y
For the following exercises, use the line shown to identify and draw the union or intersection of sets.1. \(\overline{A B} \cap \overline{B C}\)2. \(\overrightarrow{B C} \cup \overleftarrow{C A}\)3. \(\overline{B C} \cap \overline{A C}\) A B C
For the following exercises, refer to the given figure.1. Identify the location of points \(A, B, C, D, E\), and \(F\).2. Describe the line that includes point \(A\) and point \(B\).3. Describe the line from \(E\) to point \(F\).4. Describe the line from \(C\) to point \(D\).5. Does this figure
Name two pairs of intersecting planes on the shower enclosure shown. M. P N O R T S
Determine which angles are acute, obtuse, right, and straight in the graph. F LU E D C B A
Solve for the angle measurements in the figure shown. 5x 2x+5
Find the measure of each angle in the illustration. 6x 9x 7x+2
Given the two intersecting lines in the figure shown and \(m \measuredangle 2=67^{\circ}\), find the measure of the remaining angles. 67 1 4 3
Suppose you have a similar property to the one in Figure 10.53 , but the angle that corresponds to the garden corner is \(50^{\circ}\). What is the measure between the two cross streets? Figure 10.53
In the given figure if \(m \measuredangle 1=120^{\circ}\), find the \(m \measuredangle 5, m \measuredangle 4\), and \(m \measuredangle 8\). 3 1 2 4 9 5 7 8.
In the provided figure given that the \(m \measuredangle 2=48^{\circ}\), find \(m \measuredangle 1\), and \(m \measuredangle 5\). 5 8 34 9. 12
Using Figure 10.58, find the measures of angles \(5,6,7,8\), and 9 . x 5 ft 57 ft Figure 10.58 7 ft
Find the measures of each angle in the triangle shown. (x-19) (x+1) to
Find the measure of angles 1,2 , and 3 in the figure shown. 35 145 60 1 3 2.
In the figure shown, is triangle \(A B C\) congruent to triangle \(D E F\) ? = A B F LLI D
Identify the congruence theorem being illustrated in the figure shown.
What congruence theorem is illustrated in Figure 10.54? Figure 10.54
Is triangle \(E F G\) similar to triangle \(J K L\) in the figure shown? G 5 3.7 E 3.4 F 4.9 6.6 4.5 K
Are these triangles similar? Find the lengths of sides \(x\) and \(y\) to prove your answer. y 30 m 18 m. 8 m 10 m X
A person who is 6 feet tall is standing 100 feet away from the base of a tree. The tree casts a shadow 107.5 -foot shadow. The person's shadow is 7.5 feet long. How tall is the tree? x 6 ft 107.5 ft 7.5 ft
A tree casts a shadow of 180 feet early in the morning. A 10 -foot high garage casts a shadow of 30 feet at the same time in the morning. What is the height of the tree?
Identify the shape. 1. 2. 3. 4.
What polygons make up the figure shown? 1 2 3 4 S 9
Find the perimeter of a square table that measures 30 inches across from one side to its opposite side.
Find the perimeter of a regular heptagon with a side length of 3.2 as shown in the figure. 3.2 in 3.2 in
Find the measure of each interior angle of a regular pentagon and then find the sum of the interior angles.
Find the sum of the measures of the interior angles and then find the measure of each interior angle in the figure shown. (5x+1) 151 (120+x) (-6x)
Find the sum of the measures of the exterior angles in the figure shown. B D E G A
Find the circumference of a circle with a radius of \(2.25 \mathrm{~cm}\).
Find the radius of a circle with a circumference of \(15.71 \mathrm{~cm}\).
To make a trim for the window in the figure shown, you need the perimeter. How many feet of trim do you need to buy? 2 ft 5.3 ft
Translate the hexagon with points \(A^{\prime}, B^{\prime}, C^{\prime}, D^{\prime}, E^{\prime}, F^{\prime} 6\) units down. B C D A F B' A' E C' D' E'
Starting with the triangle in the figure shown, explain how the pattern on the right was achieved. A A A A
Explain how this tessellation of equilateral triangles could be produced.
How does this tessellation of the squares come about? A1 A2 A A
Do regular pentagons tessellate the plane by themselves (Figure 10.94)? Figure 10.94
Do regular dodecagons (12-sided regular polygons) tessellate the plane by themselves?
Create a tessellation using polygons, regular or irregular.
Find the area of the triangle with a base equal to \(4 \mathrm{~cm}\) and the height equal to \(4 \mathrm{~cm}\).
Find the area of a rectangular region with a length of 18 feet and a width \(1 / 3\) of the length.
You remodel your kitchen and decide to change out the tile floor. The floor measures \(30 \mathrm{ft}\) by \(15 \mathrm{ft}\). One box of tile costs \(\$ 45\) and covers \(10 \mathrm{ft}^{2}\). How many boxes of tile should you buy, and what will it cost?
Find the area of the parallelogram. i 15 in 18 in
Suppose your city has a park just like the one in Example 10.45. The length of each street is \(49 \mathrm{yd}\), and the perpendicular distance between streets is \(31 \mathrm{yd}\). How much sod, sold by the square foot at \(\$ 0.45\) per square foot plus \(\$ 1.00\) per square foot for
Find the area of the trapezoid shown. 16 in 13 in 112 in 13 in 6 in
Find the measurement of the diagonal \(d_{1}\) if the area of the rhombus is \(240 \mathrm{~cm}^{2}\), and the measure of \(d_{2}=24 \mathrm{~cm}\).
You have a kite that measures \(500 \mathrm{in}^{2}\). If one of the diagonals measures \(25 \mathrm{in}\), what is the length of the other diagonal?
Find the area of the regular pentagon with the apothem equal to \(5.5 \mathrm{~cm}\) and the side length equal to \(7 \mathrm{~cm}\). 7 cm 15.5 cm L
You want to carpet your bedroom, which measures \(15 \mathrm{ft}\) wide by \(18 \mathrm{ft}\) long. Carpeting is sold by the square yard, so you must convert your measurements to yards. How much carpeting do you buy?
Find the area of the circle with a radius of \(3 \mathrm{~cm}\).
You can buy a 9 -inch diameter pizza for \(\$ 10.99\), or a 15 -inch diameter pizza for \(\$ 14.99\). Which pizza is the better value?
You decide to install a new front door with a semicircle top as shown in the figure. How much area will the new door occupy? 3.5 ft- 3.5 ft- 6.25 ft
Find the area of the shaded region in the given figure. 10 cm 10 cm
You want to install sod on one-half of your parallelogram-shaped backyard as shown. The patio covers the other half. Sod costs \(\$ 50\) a bag and covers \(25 \mathrm{ft}^{2}\). How much will it cost to buy the sod? ih = 12 ft 25 ft
A rectangular solid has a width of \(6 \mathrm{~cm}\), length of \(15 \mathrm{~cm}\), and height or depth of \(6 \mathrm{~cm}\). Find the surface area and the volume. 15 cm 6 cm 6 cm
Find the surface area of the triangular prism shown. h = 4 cm w = 6 cm h = 4 cm w = 5 cm 1 = 7 cm
Find the surface area and the volume of the octagonal figure shown. h = 10 cm a = 4 cm w=3 cm
Calculate the surface area of a greenhouse with a flat roof measuring \(12 \mathrm{ft}\) wide, \(25 \mathrm{ft}\) long, and \(8 \mathrm{ft}\) high.
Find the surface area and volume of the cylinder with a radius of \(7 \mathrm{~cm}\) and a height of \(5 \mathrm{~cm}\). 7 cm 5 cm
You are making a casserole that includes vegetable soup and pasta. The size of your cylindrical casserole dish has a diameter of 10 inches and is 4 inches high. The pasta will consume the bottom portion of the casserole dish about 1 inch high. The soup can has a diameter of 3 inches and is 4 inches
You have \(25 \mathrm{ft}\) of rope to section off a rectangular-shaped garden. What dimensions give the maximum area that can be roped off?
Suppose you want to a build a container to hold 2 cubic feet of fabric swatches. You want to cover the container in laminate costing \(\$ 10\) per square foot. What are the dimensions of the container that is the most economical? What is the cost?
Use the Pythagorean Theorem to find the missing side of the right triangle shown. 12 a 13
How far is it to your workplace (as the crow flies) if the blocks in the previous example measure \(100 \mathrm{ft}\) by \(100 \mathrm{ft}\) ?
If 10 in is the maximum possible vertical rise as shown in the figure, how long would the ramp have to be to pass the building code rule of 12 horizontal inches to 1 vertical inch? 10 in C 120 in
Find the lengths of the missing sides in the given figure. b C 15 60%
You want to repair a window on the second floor of your home. If you place the ladder at a \(30^{\circ}\) angle to the ground, the ladder just about reaches the window. How far from the wall should you place the ladder? How far up will the ladder reach? Make a sketch as an aid. 24 ft
Find the measures of the unknown sides in the given figure. C X 8 A x B
Find the lengths of the missing sides in the given figure. y 40 x 5
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