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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
A person's height is \(6 \mathrm{ft} 3 \mathrm{in}\). What is the approximate length from their belly button to the floor rounded to the nearest inch?
A person's length from their belly button to the floor is \(3 \mathrm{ft} 11 \mathrm{in}\). What is the person's approximate height rounded to the nearest inch?
A person's length from their belly button to the floor is \(58 \mathrm{in}\). What is the person's approximate height rounded to the nearest inch?
The spikes on a pineapple mirror the Fibonacci sequence. If a row on a pineapple contains five spikes, approximately how many spikes would be found on the next larger row of spikes?
The leaves on a plant mirror the Fibonacci sequence. If a set of leaves on the plant contains 5 leaves, how many leaves would be found on the previous smaller set of leaves?
The spines on a head of lettuce mirror the Fibonacci sequence. If a head of lettuce contains 13 spines, approximately how many spines would be found on the next inside layer?
The seeds on a sunflower mirror the Fibonacci sequence. If a circular layer on the sunflower contains 55 seeds, approximately how many seeds would be found on the next larger circular layer?
The segments on a palm frond mirror the Fibonacci sequence. If a palm frond contains 89 segments, approximately how many segments would be found on the next larger palm frond?
The 19th term of the Fibonacci sequence is 4,181 and the 20 th term is 6,765 . What is the 21 st term of the sequence?
The 23 rd term of the Fibonacci sequence is 28,657 and the 24 th term is 46,368 . What is the 22 nd term of the sequence?
The 18 th term of the Fibonacci sequence is 2,584 and the 20 th term is 6,765 . What is the 19 th term of the sequence?
The 25th term of the Fibonacci sequence is 75,025 and the 20 th term is 6,765 . What is the 24 th term of the sequence?
The 10 th Fibonacci number is 55 and the 11 th is 89 . Show that the ratio of the 11 th and 10 th Fibonacci numbers is approximately \(\phi\). Round your answer to the nearest thousandth.
The 23 rd Fibonacci number is 28,657 and the 24 th is 46,368 . Show that the ratio of the 24 th and 23 rd Fibonacci numbers is approximately \(\phi\). Round your answer to the nearest ten-thousandth.
The 22 nd Fibonacci number is 17,711 and the 21 st is 10,946 . Show that the ratio of the 22 nd and 21 st Fibonacci numbers is approximately \(\phi\). Round your answer to the nearest ten-thousandth.
The 16 th term of the Fibonacci sequence is 987 . Use the approximate value of \(\phi\) of 1.618 to estimate the 15 th term. Round your answer to the nearest whole number.
The 26 th term of the Fibonacci sequence is 121,393 . Use the approximate value of \(\phi\) of 1.618 to estimate the 25 th term. Round your answer to the nearest whole number.
A frame has dimensions of 20 in by \(24 \mathrm{in}\). Calculate the ratio of the sides rounded to the nearest tenth and determine if the size approximates a golden rectangle.
A fence has dimensions of \(75 \mathrm{in}\) by \(45 \mathrm{in}\). Calculate the ratio of the sides rounded to the nearest tenth and determine if the size approximates a golden rectangle.
A frame has a length of \(50 \mathrm{in}\). Calculate the width rounded to the nearest inch if the frame is to be a golden rectangle.
A typical showerhead uses 5 gal of water per minute. A water-saving showerhead uses approximately 2 gal of water per minute. How much water would one person save in a month if they take a 6-minute shower 4 times a week?
An average toilet uses \(5 \mathrm{gal}\) of water per flush. A high-efficiency toilet uses about 1.25 gal per flush. How much water would a household save in a week if the toilet was flushed 8 times a day?
When washing dishes, leaving the faucet running utilizes about 15 gal every 5 minutes, where filling the sink and turning the faucet off except to rinse the dishes uses about 5 gal for washing a dishpan-sized load of dishes. How much water is saved by not leaving the faucet running if it takes 10
Leaving the water running when washing your hands consumes about 4 gal of water, whereas turning the water off when lathering reduces the water used to 1 gal. How much water is saved in an apartment of 6 people in an academic term of 16 weeks if each person averages washing their hands 3 times a
How long would it take for an energy-saving light bulb to consume \(1 \mathrm{~kW}\) of power if the bulb is rated at \(7.5 \mathrm{~W}\) ? Round your answer to the nearest hour.
How long would it take for a \(120 \mathrm{~W}\) light bulb to consume \(1 \mathrm{~kW}\) of power? Round your answer to the nearest hour.
A portable television uses about \(80 \mathrm{~W}\) per hour. How many kilowatt-hours are needed to run the television during a 3-day trip if the television is run for an average of 5.5 hours a day?
A flat iron to straighten hair is rated at \(331 \mathrm{~W}\). If it is used for 15 minutes a day, 5 times a week, how much would it cost a user over the course of a month if the electric rate is 13 cents per kilowatt-hour? Round your answer to the nearest cent.
You purchase a window air conditioner for your apartment living room rated at \(1,000 \mathrm{~W}\). If you run the air conditioner for an average of 3 hours a day for a week, how much would it cost if the electric rate is 12 cents per kilowatt-hour?
A cabin uses approximately \(25 \mathrm{~kW}\) of electricity per day. What size solar system would be needed to fuel \(90 \%\) of the
How many grams of sodium bicarbonate are contained in a \(300 \mathrm{~mL}\) solution of \(1.35 \% \mathrm{w} / \mathrm{v}\) sodium bicarbonate?
How many grams of sodium bicarbonate are contained in a \(175 \mathrm{~mL}\) solution of \(1.85 \% \mathrm{w} / \mathrm{v}\) sodium bicarbonate?
Using a saline solution that is \(0.75 \% \mathrm{w} / \mathrm{v}\), how many milligrams of sodium chloride are in \(150 \mathrm{~mL}\) ?
Using a saline solution that is \(1.25 \% \mathrm{w} / \mathrm{v}\), how many milligrams of sodium chloride are in \(200 \mathrm{~mL}\) ?
A prescription calls for a patient to receive \(23 \mathrm{mg}\) daily of a drug to be taken in pill form for 5 days. If the pills are available in \(5.75 \mathrm{mg}\), how many pills will the patient need for the full prescription run?
A prescription calls for a patient to receive \(21 \mathrm{mg}\) daily of a drug to be taken in pill form daily. If the pills are available in \(3.5 \mathrm{mg}\), how many pills will the patient need each day?
A patient is prescribed \(4 \mathrm{mg} / \mathrm{kg}\) of a drug to be delivered daily intramuscularly, divided into 2 doses. If the patient weighs \(30 \mathrm{~kg}\), how many milligrams of the drug would be needed for each dose?
A patient is prescribed \(1.5 \mathrm{mg} / \mathrm{kg}\) of a drug to be delivered intramuscularly, divided into 3 doses per day. If the drug is available in \(12.5 \mathrm{mg} / \mathrm{mL}\) and the patient weighs \(50 \mathrm{~kg}\), how many milliliters of the drug would be given per dose?
A patient is prescribed \(0.5 \mathrm{mg} / \mathrm{kg}\) of a drug to be delivered intramuscularly, divided into 2 doses per day. If the drug is available in \(2.5 \mathrm{mg} / \mathrm{mL}\) and the patient weighs \(45 \mathrm{~kg}\), how many milliliters of the drug would be given per dose?
A patient is prescribed \(1.5 \mathrm{mg} / \mathrm{kg}\) of a drug to be delivered intramuscularly, divided into 3 doses per day. If the drug is available in \(30 \mathrm{mg} / \mathrm{mL}\) and the patient weighs \(54 \mathrm{~kg}\), how many milliliters of the drug would be given per dose?
List the people who have a length of 2 from Justin.Use the mathematical modeling graph showing contact tracing for students in a particular class. Hani Luka Javier Nimal Nara Loise Aili Kalina Pasha Justin Tai Emmet
Find 2 paths of with a length of 3 from Emmet.Use the mathematical modeling graph showing contact tracing for students in a particular class. Hani Luka Javier Nimal Nara Loise Aili Kalina Pasha Justin Tai Emmet
Find the shortest path from Aili to Kalina.Use the mathematical modeling graph showing contact tracing for students in a particular class. Hani Luka Javier Nimal Nara Loise Aili Kalina Pasha Justin Tai Emmet
Which people does the model show as directly in contact with Nara?Use the mathematical modeling graph showing contact tracing for students in a particular class. Hani Luka Javier Nimal Nara Loise Aili Kalina Pasha Justin Tai Emmet
Find the shortest path from Tai to Hani.Use the mathematical modeling graph showing contact tracing for students in a particular class. Hani Luka Javier Nimal Nara Loise Aili Kalina Pasha Justin Tai Emmet
Of the 12 people in the model, how many have a path of 2 or less from Justin?Use the mathematical modeling graph showing contact tracing for students in a particular class. Hani Luka Javier Nimal Nara Loise Aili Kalina Pasha Justin Tai Emmet
A simple graph has no loops.a. Trueb. False
It is not possible to have a vertex of degree 0 .a. Trueb. False
A graph with three vertices has at most three edges.a. Trueb. False
A multigraph with three vertices has at most three edges.a. Trueb. False
If vertex \(a\) is adjacent to vertex \(b\), and vertex \(b\) is adjacent to vertex \(c\), then vertex \(a\) must be adjacent to vertex \(c\).a. Trueb. False
A complete graph with four vertices must have exactly four edges.a. Trueb. False
In a cycle, every vertex has degree two.a. Trueb. False
The number of vertices in a graph is twice the number of edges.a. Trueb. False
The cycle \((a,b, c, d)\) can also be called \((c,b, a, d)\).a. Trueb. False
The cycle \((a,b, c, d)\) can also be called \((a,b, d, c)\).a. Trueb. False
The only cliques that are cycles are cliques of three vertices.a. Trueb. False
A student found that the sum of the degrees of the vertices in a graph was 13 . Why is that impossible?
A student finds the number of edges in a complete graph by taking half the number of vertices, then subtracting one from the number of vertices, then multiplying these two values together. Will the student get the correct result?
Two graphs are isomorphic, and the graphs have the same structure.Determine whether each statement is always true, sometimes true, or never true.
A graph with four vertices is isomorphic to a graph with five vertices.Determine whether each statement is always true, sometimes true, or never true.
The sums of the degrees of the vertices of two graphs are equal, but the two graphs are not isomorphic.Determine whether each statement is always true, sometimes true, or never true.
Two graphs are isomorphic, but the graphs have a different number of edges.Determine whether each statement is always true, sometimes true, or never true.
One graph can be transformed to look like a second graph without removing or adding any connections, and the two graphs are isomorphic.Determine whether each statement is always true, sometimes true, or never true.
Two graphs are isomorphic, and there is more than one isomorphism between the two graphs.Determine whether each statement is always true, sometimes true, or never true.
Two graphs have the same number of vertices, but there is no isomorphism between them.Determine whether each statement is always true, sometimes true, or never true.
There is a correspondence between the vertices of Graph \(A\) and the vertices of Graph \(B\) such that the adjacent vertices in Graph \(A\) always correspond to vertices of Graph \(B\), but the two graphs are not isomorphic Determine whether each statement is always true, sometimes true, or never
Two graphs have the same number of edges, the same number of vertices, vertices of the same degree, and have all the same subgraphs, but they are not isomorphic Determine whether each statement is always true, sometimes true, or never true.
Two graphs are isomorphic, and the sum of the degrees of the vertices of one equals the sum of the degrees of the other graph.Determine whether each statement is always true, sometimes true, or never true.
If two graphs are isomorphic, then their complements are isomorphic.Determine whether each statement is always true, sometimes true, or never true.
A trail is a path.Determine whether each statement is always true or sometimes true.
A trail is a walk.Determine whether each statement is always true or sometimes true.
A walk is a path.Determine whether each statement is always true or sometimes true.
A circuit is a trail.Determine whether each statement is always true or sometimes true.
A directed cycle is a path.Determine whether each statement is always true or sometimes true.
A circuit is a directed cycle.Determine whether each statement is always true or sometimes true.
A directed cycle is a circuit.Determine whether each statement is always true or sometimes true.
If a graph has an \(n\)-coloring, then its chromatic number is \(n\).Determine whether each statement is always true or sometimes true.
If the chromatic number of a graph is \(n\), then it has an \(n\)-coloring.Determine whether each statement is always true or sometimes true.
If a graph is planar, then it has a chromatic number of at most four.Determine whether each statement is always true or sometimes true.
A walk that ____________ is a trail.Fill in the blanks to make the statement true.
A trail that ______________ is a circuit.Fill in the blanks to make the statement true.
A circuit that ______________ is a directed cycle.Fill in the blanks to make the statement true.
A closed walk that ______________ is a circuit.Fill in the blanks to make the statement true.
A complete graph with \(n\) vertices has a chromatic number of ______________.Fill in the blanks to make the statement true.
A graph with a clique with \(n\)-vertices has a chromatic number of ______________ n.Fill in the blanks to make the statement true.
A disconnected graph has only one component.Determine whether each statement is always true, sometimes true, or never true.
A graph that has all vertices of even degree is connected.Determine whether each statement is always true, sometimes true, or never true.
There is a route through the city of Konigsberg that a person may pass over each bridge exactly once and return to the starting point.Determine whether each statement is always true, sometimes true, or never true.
A graph with vertices of all even degree is Eulerian.Determine whether each statement is always true, sometimes true, or never true.
An Eulerian graph has all vertices of even degree.Determine whether each statement is always true, sometimes true, or never true.
An Euler circuit is a closed trail.Determine whether each statement is always true, sometimes true, or never true.
An Euler circuit is a closed path Determine whether each statement is always true, sometimes true, or never true.
To eulerize a graph, add new edges between previously nonadjacent vertices until no vertices have odd degree.Determine whether each statement is always true, sometimes true, or never true.
To eulerize a graph, add duplicate edges between adjacent vertices until no vertices have odd degree.Determine whether each statement is always true, sometimes true, or never true.
The number of duplicate edges required to eulerize a graph is half the number of vertices of odd degree.Determine whether each statement is always true, sometimes true, or never true.
An Euler trail is a trail that visits each _________________ exactly once.Fill in the blank to make the statement true.
_________________ algorithm is a procedure for finding an Euler trail or circuit.Fill in the blank to make the statement true.
An Euler _________________ always begins and ends at the same vertex, but an Euler \( \qquad \) does not.Fill in the blank to make the statement true.
When a bridge is removed from a graph, the number of _________________ is increased by one.Fill in the blank to make the statement true.
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