Discrete Mathematics With Applications
5th Edition
ISBN: 9781337694193
Author: EPP, Susanna S.
Publisher: Cengage Learning,
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Chapter 1.4, Problem 12ES
Another famous puzzle used as an example in the study of artificial intelligence seems first to have
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Recent research suggests that the amount of time that parents spend talking about numbers can have a big impact on the mathematical development
of their children (Levine, Suriyakham, Rowe, Huttenlocher, and Gunderson, 2010). In the study, the researchers visited the children's homes between
the ages of 14 and 30 months and recorded the amount of "number talk" they heard from the children's parents. The researchers then tested the
children's knowledge of the meaning of numbers at 46 months. The following data are similar to the results obtained in the study.
X
5
Complete the following distribution table.
4
3
Children's Knowledge-of-Numbers Scores for Two Groups of Parents
Low Number-Talk Parents
High Number-Talk Parents
3, 4, 5, 4, 5
4, 2, 3, 5, 4
5, 3, 4, 5, 4
2
1
2, 1, 2, 3, 4
3, 3, 2, 2, 1
5, 3, 4, 1, 2
flow
fhigh
Using the following graphing tool, sketch a polygon showing the frequency distributions for children with low number-talk parents and children with
high number-talk…
Chapter 1 Solutions
Discrete Mathematics With Applications
Ch. 1.1 - A universal statement asserts that a certain...Ch. 1.1 - A conditional statement asserts that if one...Ch. 1.1 - Given a property that may or may not be true, an...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - Given any real number, there is a number that is...Ch. 1.1 - The reciprocal of any postive real number is...Ch. 1.1 - Prob. 6ESCh. 1.1 - Rewrite the following statements less formally,...
Ch. 1.1 - For every object J, if J is a square then J has...Ch. 1.1 - For every equation E, if E is quadratic then E has...Ch. 1.1 - Every nonzero real number has a reciropal. All...Ch. 1.1 - Evaery positive number has a positive square root....Ch. 1.1 - There is a real number whose product with every...Ch. 1.1 - There is a real number whose product with ever...Ch. 1.2 - When the elements of a set are given using the...Ch. 1.2 - The symbol R denotes ____.Ch. 1.2 - The symbol Z denotes ______Ch. 1.2 - The symbol Q denotes__Ch. 1.2 - The notation {xP(x)} is read _______Ch. 1.2 - Prob. 6TYCh. 1.2 - Prob. 7TYCh. 1.2 - Given sets A,B, and C, the Cartesian production...Ch. 1.2 - A string of length n over a set S is an ordered...Ch. 1.2 - Prob. 1ESCh. 1.2 - Write in words how to read each of the following...Ch. 1.2 - Is 4={4}? How many elements are in the set...Ch. 1.2 - a. Is 2{2}? b. How many elements are in the set...Ch. 1.2 - Which of the following sets are equal?...Ch. 1.2 - For each integer n, let Tn={n,n2} . How many...Ch. 1.2 - Prob. 7ESCh. 1.2 - Prob. 8ESCh. 1.2 - Is3{1,2,3}? Is 1{1}? Is {2}{1,2}? Is...Ch. 1.2 - Is ((2)2,22)=(22,( 2)2)? Is (5,5)=(5,5)? Is...Ch. 1.2 - Prob. 11ESCh. 1.2 - Prob. 12ESCh. 1.2 - Prob. 13ESCh. 1.2 - Prob. 14ESCh. 1.2 - Let S={0,1} . List all the string of length 4 over...Ch. 1.2 - Let T={x,y} . List all the strings of length 5...Ch. 1.3 - Given sets A and B , relation from A to B is ____Ch. 1.3 - A function F from B is a relation from A to B that...Ch. 1.3 - If F is a function from A to B and x is an element...Ch. 1.3 - Let A={2,3,4} and B={6,8,10} and define a relation...Ch. 1.3 - Let C=D={3,2,1,1,2,3} and define a elation S from...Ch. 1.3 - Let E={1,2,3} and F={2,1,0} and define a relation...Ch. 1.3 - Let G=-2,0,2) and H=4,6,8) and define a relation V...Ch. 1.3 - Define a relations S from R to R as follows: For...Ch. 1.3 - Define a relation R from R to R as follows: For...Ch. 1.3 - Let A={4,5,6} and B={5,6,7} and define relations...Ch. 1.3 - Let A={2,4} and B={1,3,5} and define relations U,...Ch. 1.3 - Find all function from {01,} to {1} . Find two...Ch. 1.3 - Find tour relations from {a,b} to {x,y} that are...Ch. 1.3 - Let A={0,1,2} and let S be the set of all strings...Ch. 1.3 - Let A={x,y} and let S be the set all strings over...Ch. 1.3 - Let A={1,0,1} and B={t,u,v,w} . Define a function...Ch. 1.3 - Let C = (1,2,3,4) and D={a,b,c,d}. Define a...Ch. 1.3 - Let X=2,4,5) and Y=(1,2,4,6) . Which of the...Ch. 1.3 - Let f be the squaring function defined in Example...Ch. 1.3 - Let g be the successor function defined in Example...Ch. 1.3 - Let h be the constant function defined in Example...Ch. 1.3 - Define functions f and g from R to R by the...Ch. 1.3 - Define functions H and K from R to R by the...Ch. 1.4 - A graph consists of two finite sets: ______and...Ch. 1.4 - A loop in a graph is_____Ch. 1.4 - Two distinct edges in a graph are parallel if, and...Ch. 1.4 - Two vertices are called adjacent if, and only if,...Ch. 1.4 - An edge is incident on _______Ch. 1.4 - Two edges incident on the same endpoint...Ch. 1.4 - A vertex on which no edges are incident is________Ch. 1.4 - Prob. 8TYCh. 1.4 - Prob. 9TYCh. 1.4 - In 1 and 2, graphs are represented by drawings...Ch. 1.4 - In 1 and 2, graphs are represented by drawings....Ch. 1.4 - In 3 and 4, draw pictures of the specified graphs....Ch. 1.4 - Prob. 4ESCh. 1.4 - Prob. 5ESCh. 1.4 - In 5-7, show that the two drawings represent the...Ch. 1.4 - In 5-7, show that the two drawings represent the...Ch. 1.4 - For each of the graphs in 8 and 9: (i) Find all...Ch. 1.4 - For each of the graphs in 8 and 9: (i) Find all...Ch. 1.4 - Use the graph of Example 1.4.6 to determine...Ch. 1.4 - Find three other winning sequences of moves for...Ch. 1.4 - Another famous puzzle used as an example in the...Ch. 1.4 - Solve the vegetarians-and-cannibals puzzle for the...Ch. 1.4 - Two jugs A and B have capacities of 3 quarts and 5...Ch. 1.4 - Prob. 15ESCh. 1.4 - In this exercise a graph is used to help solve a...Ch. 1.4 - A deptnn1 war to ithechik final ezans that no...
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- Another famous puzzle used as an example in the study of artificial intelligence seems first to have appeared in a collection of problems, Problems for the Quickening of the Mind, which was compiled about A.D. 775. It involves a wolf, a goat, a bag of cabbage, and a ferryman. From an initial position on the left bank of a river, the ferryman is to transport the wolf, the goat, and the cabbage to the right bank. The difficulty is that the ferryman’s boat is only big enough for him to transport one object at a time, other than himself. Yet, for obvious reasons, the wolf cannot be left alone with the goat, and the goat cannot be left alone with the cabbage. How should the ferryman proceed?arrow_forward. Recent research suggests that the amount of time that parents spend talking about numbers can have a big impact on the mathematical development of their children (Levine, Suriyakham, Rowe, Huttenlocher, & Gunderson, 2010). In the study, the researchers visited the children’s homes between the ages of 14 and 30 months and recorded the amount of “number talk” they heard from the children’s parents. The researchers then tested the children’s knowledge of the meaning of numbers at 46 months. The following data are similar to the results obtained in the study. Children’s Knowledge-of-Numbers Scores for Two Groups of Parents Low Number-Talk Parents High Number-Talk Parents 2, 1, 2, 3, 4 3, 4, 5, 4, 5 3, 3, 2, 2, 1 4, 2, 3, 5, 4 5, 3, 4, 1, 2 5, 3, 4, 5, 4 Sketch a polygon showing the frequency distribution for children with low number-talk parents. In the same graph, sketch a polygon showing the scores for the children with high number-talk…arrow_forwardSection 2.2 (77) Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon Delta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago, they managed to tag all 50,000 of them (with little Epsilon Delta Fraternity tags). This year’s pledge class discovered that last year’s tags had all fallen off, and they wound up tagging a total of 75,000 frogs. a)Find an exponential model for the frog population. b)Assuming exponential population growth and that all this year’s tags have fallen off, how many tags should Epsilon Delta order for next year’s pledge class?arrow_forward
- 2. Another famous puzzle used as an example in the study of artificial intelligence was compiled about A.D. 775. It involves a wolf, a goat, a bag of cabbage, and a ferryman. From an initial position on the left bank of a river, the ferryman is to transport the wolf, the goat, and the cabbage to the right bank. The difficulty is that the ferryman's boat is only big enough for him to transport one object at a time, other than himself. Yet, for obvious reasons, the wolf cannot be left alone with the goat, and the goat cannot be left alone with the cabbage. How should the ferryman proceed?arrow_forwardLet's assume that there are 500 people in a population. The researcher has access to all 500 participants, and sends a questionnaire that is accessed by a hyperlink. Of the 500 possible subjects, 485 complete it. Does this mean that the results generated from this study will be highly-accurate? What might cause the study to be unreliable?arrow_forwardThis question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A die is a cube with dots on each face. The faces have 1, 2, 3, 4, 5, or 6 dots. The table below is a computer simulation (from the software package Minitab) of the results of rolling a fair die 20 times. DATA DISPLAY ROW C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 1 3 2 4 5 4 5 3 5 3 4 2 5 2 2 2 5 3 2 3 1 4 (a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it appropriate that the same number appears more than once? Why?What is the outcome of the sixth roll?(b) If we simulate more rolls of the die, do you expect to get the same sequence of outcomes? Why or why not? Step 1 (a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it…arrow_forward
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