DISCRETE MATHEMATICS-CONNECT ACCESS ONLY
8th Edition
ISBN: 9781264309696
Author: ROSEN
Publisher: MCG
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Chapter 2.6, Problem 13E
To determine
To show:
Matrix multiplication holds associative law.
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The table shows the total square footage (in billions) of retailing space at shopping centers and their sales (in billions of dollars) for 10 years. Construct a 90% prediction interval for sales when the
total square footage is 5.7 billion. The equation of the regression line is y = 567.939x - 1985.560.
Total
4.9 5.2 5.3 5.4
5.5
5.6
5.9
5.9 5.9 6.1
Square Footage, x
Sales, y
880.1 935.5 989.5 1056.9 1100.7 1201.9 1283.4 1346.3 1434.8 1549.5
Click the icon to view a table of critical values for the t-distribution.
Construct a 90% prediction interval for the sales when the total square footage is 5.7 billion. Choose the correct prediction interval below, rounded to the nearest million dollars.
The maximum weights (in kilograms) for which one repetition of a half squat can be performed and the times (in seconds) to run a 10-meter sprint for 12 international soccer players are shown in the
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The new correlation coefficient r
(Round to three decimal places a
going from 0.941 to
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gets stronger,
gets weaker,
stays the same,
You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 31 students. You want to test this claim. You randomly select 18
classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At α = 0.05, can you support the university's claim? Complete parts (a) through (d)
below. Assume the population is normally distributed.
36
28
25
27
29
35
32
39
31
28
380
22
26
29
24
27
24
30吋
24
(a) Write the claim mathematically and identify Ho and Ha.
Which of the following correctly states Ho and H₂?
○ A. Ho: μ31
Нa: μ≤31
E. Ho: "=31
Ha: μ 31
OF. Ho: μ=31
Нa: μ31
Chapter 2 Solutions
DISCRETE MATHEMATICS-CONNECT ACCESS ONLY
Ch. 2.1 - List the members of these sets. { xx is a real...Ch. 2.1 - Use set builder notation to give a description of...Ch. 2.1 - Which of the intervals (0, 5), (0, 5], [0, 5), [0,...Ch. 2.1 - For each of these intervals, list all its elements...Ch. 2.1 - For each of these pairs of sets, determine whether...Ch. 2.1 - For each of these pairs of sets, determine whether...Ch. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - For each of the following sets, determine whether...Ch. 2.1 - Prob. 10E
Ch. 2.1 - Determine whether each of these statements is true...Ch. 2.1 - Determine whether these statements are true or...Ch. 2.1 - Determine whether each of these statements is true...Ch. 2.1 - Prob. 14ECh. 2.1 - Use a Venn diagram to illustrate the set of all...Ch. 2.1 - Prob. 16ECh. 2.1 - Use a Venn diagram to illustrate the re1ationships...Ch. 2.1 - Use a Venn diagram to illustrate the relationships...Ch. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - What is the cardinality of each of these sets? {a}...Ch. 2.1 - What is the cardinality of each of these sets? {}...Ch. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - How many elements does each of these sets have...Ch. 2.1 - Determine whether each of these sets is the power...Ch. 2.1 - Prove that P(A)P(B) if and only if AB .Ch. 2.1 - Show that if AC and BD , then ABCDCh. 2.1 - Let A={a,b,c,d} and B={y,z} . Find AB . BA .Ch. 2.1 - Prob. 30ECh. 2.1 - That is the Cartesian product ABC , where A is the...Ch. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Let A={a,b,c} , B={x,y} , and C={0,l} . Find ABC ....Ch. 2.1 - Find A2 if A={0,1,3} A={1,2,a,b}Ch. 2.1 - Find A3 if A={a} A={0,a}Ch. 2.1 - How many different elements does AB have if A has...Ch. 2.1 - How many different elements does ABC have if A has...Ch. 2.1 - How many different elements does An have when A...Ch. 2.1 - Show that ABBA , when A and B are nonempty, unless...Ch. 2.1 - Explain why ABC and (AB)C are not the same.Ch. 2.1 - Explain why (AB)(CD) and A(BC)D are not the same.Ch. 2.1 - Prove or disprove that if A and B are sets, then...Ch. 2.1 - Prove or disprove that if A, B, and C are nonempty...Ch. 2.1 - Translate each of these quantifications into...Ch. 2.1 - Translate each of these quantifications into...Ch. 2.1 - Find the truth set of each of these predicates...Ch. 2.1 - Find the truth set of each of these predicates...Ch. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.1 - Prob. 51ECh. 2.2 - Prob. 1ECh. 2.2 - Suppose that A is the set of sophomores at your...Ch. 2.2 - Let A={1,2,3,4,5} and B={0,3,6} . Find AB . AB ....Ch. 2.2 - Let A={a,b,c,d,e} and B={a,b,c,d,e,f,g,h} . Find...Ch. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - TABLE 1 Set Identities. Identity Name AU=AA=A...Ch. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Show that if A and B are sets in a universe U then...Ch. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Let A, B, and C be sets. Show that (AB)C=(AC)(BC)...Ch. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Let A and B be subsets of a universal set U. Show...Ch. 2.2 - Let A, B, and C be sets. Use the identity AB=AB ,...Ch. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prove or disprove that for all sets A, B, and C,...Ch. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - Prob. 44ECh. 2.2 - Prob. 45ECh. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - Prob. 52ECh. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - Prob. 54ECh. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - Prob. 58ECh. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - The symmetric difference of A and B, denoted by AB...Ch. 2.2 - Prob. 64ECh. 2.2 - Prob. 65ECh. 2.2 - Prob. 66ECh. 2.2 - Prob. 67ECh. 2.2 - Prob. 68ECh. 2.2 - Prob. 69ECh. 2.2 - The successor of the set A is the set A{A} ....Ch. 2.2 - The Jaccard similarity J(A,B) of the finite sets A...Ch. 2.2 - Prob. 72ECh. 2.2 - Prob. 73ECh. 2.2 - Prob. 74ECh. 2.2 - Prob. 75ECh. 2.3 - Why is f not a function from R to R if f(x)=1/x?...Ch. 2.3 - Determine whether f is a function from Z to R if...Ch. 2.3 - Prob. 3ECh. 2.3 - Find the domain and range of these functions. Note...Ch. 2.3 - Find the domain and range of these functions. Note...Ch. 2.3 - Find the domain and range of these functions. the...Ch. 2.3 - Find the domain and range of these functions. the...Ch. 2.3 - Find these values. 1.1 1.1 0.1 0.1 2.99 2.99 12+12...Ch. 2.3 - Find these values. 34 78 34 78 3 1 12+32 1252Ch. 2.3 - Prob. 10ECh. 2.3 - Which functions in Exercise 10 are onto? Determine...Ch. 2.3 - Determine whether each of these functions from Z...Ch. 2.3 - Prob. 13ECh. 2.3 - Determine whether f:ZZZ is onto if f(m,n)=2mn ....Ch. 2.3 - Determine whether the function f:ZZZ is onto if...Ch. 2.3 - Consider these functions from the set of students...Ch. 2.3 - Consider these functions from the set of teachers...Ch. 2.3 - Specify a codomain for each of the functions in...Ch. 2.3 - Specify a codomain for each of the functions in...Ch. 2.3 - Prob. 20ECh. 2.3 - Give an explicit formula for a function from the...Ch. 2.3 - Determine whether each of these functions is a...Ch. 2.3 - Determine whether each of these functions is a...Ch. 2.3 - Let f:RR and let f(x)0 for all xR . Show that f(x)...Ch. 2.3 - Let f:RR and 1et f(x)0 for all xR . Show that f(x)...Ch. 2.3 - Prove that a strictly increasing function from R...Ch. 2.3 - Prob. 27ECh. 2.3 - Show that the function f(x)=ex from the set of...Ch. 2.3 - Prob. 29ECh. 2.3 - Let S={1,0,2,4,7} . Find f(S) if f(x)=1 ....Ch. 2.3 - Let f(x)=x2/3 . Find f(S) if S={2,1,0,1,2,3}...Ch. 2.3 - Let f(x)=2x where the domain is the set of real...Ch. 2.3 - Prob. 33ECh. 2.3 - Suppose that g is a function from A to B and f is...Ch. 2.3 - Prob. 35ECh. 2.3 - If f and fog are one-to-one, does it follow that g...Ch. 2.3 - Prob. 37ECh. 2.3 - Find fog and gof where f(x)=x2 and g(x)=x+2 , are...Ch. 2.3 - Prob. 39ECh. 2.3 - Let f(x)ax+b and g(x)=cx+d , where a, b, c, and d...Ch. 2.3 - Show that the function f(x)ax+b from R to R, where...Ch. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Let f be the function from R to R defined by...Ch. 2.3 - Let g(x)=|x| . Find g1({0}) . g1({1,0,1}) ....Ch. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Show x+12 is the closest integer to the number x...Ch. 2.3 - Prob. 49ECh. 2.3 - Show that if x is a real number, then xx=1 if x is...Ch. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Show that if x is a real number and n is an...Ch. 2.3 - Prob. 55ECh. 2.3 - Prove that if x is a real number, then x=x and x=x...Ch. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - How many bytes are required to encode n bits of...Ch. 2.3 - How many bytes are required to encode n bits of...Ch. 2.3 - How many ATM cells (described in Example 30) can...Ch. 2.3 - Data are transmitted over a particular Ethernet...Ch. 2.3 - Draw the graph of the function f(n)=1n2 from Z to...Ch. 2.3 - Draw the graph of the function f(x)=2x from R to...Ch. 2.3 - Draw the graph of the function f(x)=x/2 from R to...Ch. 2.3 - Prob. 67ECh. 2.3 - Draw the graph of the function f(x)=x+x/2 from R...Ch. 2.3 - Draw graphs of each of these functions. f(x)=x+12...Ch. 2.3 - Prob. 70ECh. 2.3 - Find the inverse function of f(x)=x3+1 .Ch. 2.3 - Suppose that f is an invertible function from Y to...Ch. 2.3 - Let S be a subset of a universal set U. The...Ch. 2.3 - Suppose that f is a function from A to B, where A...Ch. 2.3 - Prove or disprove each of these statements about...Ch. 2.3 - Prove or disprove each of these statements about...Ch. 2.3 - Prove that if x is a positive real number, then...Ch. 2.3 - Let x be a real number. Show that 3x=x+x+13+x+23 .Ch. 2.3 - For each of these partial functions, determine its...Ch. 2.3 - Prob. 80ECh. 2.3 - Prob. 81ECh. 2.3 - Show that a set S is infinite if and only if there...Ch. 2.4 - Find these terms of the sequence {an} , where...Ch. 2.4 - What is the term a8 of the sequence {an} if an ,...Ch. 2.4 - What are the terms a0,a1,a2 , and a3 of the...Ch. 2.4 - What are the terms a0,a1,a2 , and a3 of the...Ch. 2.4 - List the first 10 terms of each of these...Ch. 2.4 - List the first lo terms of each of these...Ch. 2.4 - Find at least three different sequences beginning...Ch. 2.4 - Find at least three different sequences beginning...Ch. 2.4 - Find the first five terms of the sequence defined...Ch. 2.4 - Find the first six terms of the sequence defined...Ch. 2.4 - Let an=2n+53n for n=0,1,2,,... Find a0,a1,a2,a3 ,...Ch. 2.4 - Show that the sequence {an} is a solution of the...Ch. 2.4 - Is the sequence {an} a solution of the recurrence...Ch. 2.4 - For each of these sequences find a recurrence...Ch. 2.4 - Show that the sequence {an} is a solution of the...Ch. 2.4 - Find the solution to each of these recurrence...Ch. 2.4 - Find the solution to each of these recurrence...Ch. 2.4 - A person deposits $1000 in an account that yields...Ch. 2.4 - Suppose that the number of bacteria in a colony...Ch. 2.4 - Assume that the population of the world in 2017...Ch. 2.4 - A factory makes custom sports cars at an...Ch. 2.4 - An employee joined a company in 2017 with a...Ch. 2.4 - Find a recurrence relation for the balance B(k)...Ch. 2.4 - Find a recurrence relation for the balance B(k)...Ch. 2.4 - For each of these lists of integers, provide a...Ch. 2.4 - For each of these lists of integers, provide a...Ch. 2.4 - *27. Show that if an denotes the nth positive...Ch. 2.4 - Let an , be the nth term of the sequence 1, 2, 2,...Ch. 2.4 - What are the values of these sums? k=15(k+1)...Ch. 2.4 - What are the values of these sums, where...Ch. 2.4 - What is the value of each of these sums of terms...Ch. 2.4 - Find the value of each of these sums. j=08(1+ ( 1...Ch. 2.4 - Compute each of these double sums. i=12j=13( i+j)...Ch. 2.4 - Compute each of these double sums. i=13j=12( i+j)...Ch. 2.4 - Show that j=1n(aja j1)=ana0 , where a0,a1,...,an...Ch. 2.4 - Use the identity 1/(k(k+1))=1/k1/(k+1) and...Ch. 2.4 - Sum both sides of the identity k2(k21)2=2k1 from...Ch. 2.4 - Use the technique given in Exercise 35, together...Ch. 2.4 - Find k=100200k . (Use Table 2.) TABLE 2 Some...Ch. 2.4 - Prob. 40ECh. 2.4 - Find k=1020k2(k3) . (Use Table 2.) TABLE 2 Some...Ch. 2.4 - Find . k=1020(k1)(2k2+1) (Use Table 2.) TABLE 2...Ch. 2.4 - Find a formula for k=0mk , when m is a positive...Ch. 2.4 - Find a formula for k=0mk3 , when m is a positive...Ch. 2.4 - There is also a special notation for products. The...Ch. 2.4 - Express n! using product notation.Ch. 2.4 - Find j=04j! .Ch. 2.4 - Find j=04j! .Ch. 2.5 - Prob. 1ECh. 2.5 - Determine whether each of these sets is finite,...Ch. 2.5 - Determine whether each of these sets is countable...Ch. 2.5 - Determine whether each of these sets is countable...Ch. 2.5 - Show that a finite group of guests arriving at...Ch. 2.5 - Suppose that Hilbert’s Grand Hotel is fully...Ch. 2.5 - Suppose that Hilbert’s Grand Hotel is fully...Ch. 2.5 - Show that a countably infinite number of guests...Ch. 2.5 - Suppose that a countably infinite number of buses,...Ch. 2.5 - Give an example of two uncountable sets A and B...Ch. 2.5 - Give an example of two uncountable sets A and B...Ch. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Show that a subset of a countable set is also...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Show that if |A|=|B| and |B|=|C| , then |A|=|C| .Ch. 2.5 - Prob. 21ECh. 2.5 - Suppose that A is a countable set. Show that the...Ch. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Show that the union of a countable number of...Ch. 2.5 - Show that the set Z+Z+ is countableCh. 2.5 - Prob. 29ECh. 2.5 - Show that the set of real numbers that are...Ch. 2.5 - Show that Z+Z+ t is countable by showing that the...Ch. 2.5 - Show that when you substitute (3n+1)2 for each...Ch. 2.5 - Prob. 33ECh. 2.5 - Show that (0, 1) and R have the same cardinality...Ch. 2.5 - Prob. 35ECh. 2.5 - Prob. 36ECh. 2.5 - Show that the set of all computer programs in a...Ch. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Show that if S is a set, then there does not exist...Ch. 2.5 - In this exercise, we prove the Schröder-Bernstein...Ch. 2.6 - Let A=[111320461137] . What size is A? What is the...Ch. 2.6 - Find A + B, where A=[104122022],B=[135223230]...Ch. 2.6 - Find AB if A=[2132],B=[0413] A=[110123],B=[321102]...Ch. 2.6 - Find the product AB, where...Ch. 2.6 - Find a matrix A such that [2314]A=[3012] . [Hint:...Ch. 2.6 - Find a matric A such that [132211403]A=[713103137]Ch. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - In this exercise we show that matrix...Ch. 2.6 - Prob. 13ECh. 2.6 - The nn matrix A=[aij] is called a diagonal matrix...Ch. 2.6 - Let A=[1101] . Find a formula for An , whenever n...Ch. 2.6 - Show that (At)t=A .Ch. 2.6 - Prob. 17ECh. 2.6 - Show that [231121113] Is the inverse of...Ch. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Let A=[1101] and B=[0110] Find AB . AB . AB .Ch. 2.6 - Prob. 27ECh. 2.6 - Find the Boolean product of A and B, where...Ch. 2.6 - Prob. 29ECh. 2.6 - Let A be a zeroone matrix. Show that AA=A . AA=A .Ch. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - In this exercise we will show that the Boolean...Ch. 2 - Prob. 1RQCh. 2 - What is the empty set? Show that the empty set is...Ch. 2 - Define |S|, the cardinality of the set S. Give a...Ch. 2 - Define the power set of a set S. When is the empty...Ch. 2 - Define the union. intersection, difference, and...Ch. 2 - Prob. 6RQCh. 2 - Explain the relationship between logical...Ch. 2 - Prob. 8RQCh. 2 - Prob. 9RQCh. 2 - Define the inverse of a function. When does a...Ch. 2 - Prob. 11RQCh. 2 - Conjecture a formula for the terms of the sequence...Ch. 2 - Prob. 13RQCh. 2 - What is the sum of the terms of the geometric...Ch. 2 - Show that the set of odd integers is countable.Ch. 2 - Prob. 16RQCh. 2 - Prob. 17RQCh. 2 - Prob. 18RQCh. 2 - Prob. 1SECh. 2 - Prob. 2SECh. 2 - Prob. 3SECh. 2 - Prob. 4SECh. 2 - Prob. 5SECh. 2 - Prob. 6SECh. 2 - Prob. 7SECh. 2 - Prob. 8SECh. 2 - Prob. 9SECh. 2 - Prob. 10SECh. 2 - Prob. 11SECh. 2 - Prob. 12SECh. 2 - Prob. 13SECh. 2 - Prob. 14SECh. 2 - Prob. 15SECh. 2 - *16. Suppose that f is a function from the set A...Ch. 2 - Prob. 17SECh. 2 - Prob. 18SECh. 2 - Prob. 19SECh. 2 - Prob. 20SECh. 2 - Prob. 21SECh. 2 - Prob. 22SECh. 2 - Prob. 23SECh. 2 - Prove that if x is a real number, then x/2/2=x/4 .Ch. 2 - Prob. 25SECh. 2 - Prob. 26SECh. 2 - Prove that if m is a positive integer and x is a...Ch. 2 - We define the Ulam numbers by setting u1=1 and...Ch. 2 - Prob. 29SECh. 2 - Determine a rule for generating the terms of the...Ch. 2 - Prob. 31SECh. 2 - Prob. 32SECh. 2 - Prob. 33SECh. 2 - Show that the set of all finite subsets of the set...Ch. 2 - Prob. 35SECh. 2 - Prob. 36SECh. 2 - Prob. 37SECh. 2 - Prob. 38SECh. 2 - Prob. 39SECh. 2 - Prob. 40SECh. 2 - Prob. 41SECh. 2 - Prob. 1CPCh. 2 - Prob. 2CPCh. 2 - Prob. 3CPCh. 2 - Prob. 4CPCh. 2 - Prob. 5CPCh. 2 - Prob. 6CPCh. 2 - Prob. 7CPCh. 2 - Prob. 8CPCh. 2 - Prob. 9CPCh. 2 - Prob. 10CPCh. 2 - Prob. 11CPCh. 2 - Prob. 12CPCh. 2 - Prob. 1CAECh. 2 - Prob. 2CAECh. 2 - Use a computational program or programs you have...Ch. 2 - Prob. 4CAECh. 2 - Prob. 5CAECh. 2 - Use a computational program or programs you have...Ch. 2 - Prob. 1WPCh. 2 - Research where the concept of a function first...Ch. 2 - Explain the different ways in which the...Ch. 2 - Define the recently invented EKG sequence and...Ch. 2 - Prob. 5WPCh. 2 - Expand the discussion of the continuum hypothesis...
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- Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed. μ Claim: <4715; α = 0.05 Sample statistics: x = 4917, s = 5501, n = 54 What are the null and alternative hypotheses? Ho: Ha (Type integers or decimals. Do not round.) Find the standardized test statistic t. t = ☐ (Round to two decimal places as needed.) Find the P-value. P = (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. Ho. There enough evidence at the ☐ % level of significance to Fail to reject Reject .... the claim.arrow_forwardNot use ai pleasearrow_forwardA politician claims that the mean salary for managers in his state is more than the national mean, $85,000. Assume the the population is normally distributed and the population standard deviation is $8700. The salaries (in dollars) for a random sample of 30 managers in the state are listed. At α = 0.01, is there enough evidence to support the claim? Use technology. 92,421 81,412 85,143 97,220 99,317 71,884 97,762 86,108 98,385 73,869 81,391 95,997 98,828 86,476 77,893 74,995 90,472 81,330 92,183 94,649 77,880 91,821 90,907 84,640 78,479 81,703 89,573 89,948 70,938 81,300 (a) Identify the null hypothesis and alternative hypothesis. O A. Ho: " =85,000 Нa: μ85,000 D. Hoi u >85,000 Нa: μ≤85,000 (b) Identify the standardized test statistic. Z= B. Hoμ≥85,000 Haμ85,000 Haμ≤85,000 (Round the final answer to two places as needed. Round all intermediate values to three places as needed.) (c) Find the P-value. Use technology. (Round to three decimal places as needed.) (d) Decide whether to reject…arrow_forward
- i need help please and thank youarrow_forwardi need help please and thank youarrow_forwardThe parameters of an RLC circuit with an input voltage of E(t) are given. R=202, L=10 H, C = 0.01 F, E(t) = 200 cos 4t V Using the initial conditions I(0) = 0 and Q(0) = 4, plot both the steady periodic current I sp(t) and the total current I(t) = Isp (t) + Itr(t).arrow_forward
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- - Let f (x) = √x sin( X/12), × 0. D x = ○ Show that f is continuous at x=0. 3 Let f(x) = ( + sin(x2) x +0 ' Lo. X = 6 Show that f is discontinuous at x=0. 9 Let a, b & R, acb. Let f be a real-valued function on [a,b]. 10 (a) Define what we mean by "f is bounded." (b) Assume is bounded and let m = M = inf {f(x): xe [a,b]} sup {f(x): x = [a,b]}. Prove that there exist Xo, & [a,b] such that Хо f(xo) Im and f(x) = M. = น Prove the Intermediate Value theorem for f as in ⑦ that for each yε [m,M] there exists. xe [a, b] such that f(x) = y. Conclude that f([a,b]) = [m, M].arrow_forwardA mass weighing 80 lbs (mass m = 2.5 in fps) is attached to the end of a spring that is stretched 8 in. by a force of 80 lbs. A force Fo cos wt acts on the mass. At what frequency (in hertz) will resonance oscillations occur? Neglect damping.arrow_forward①(a) Let rεR, o≤r<1. Prove directly from defintions. 2 = r ++²+3+... that the series r = 1 is convergent with sum 1-2 +p+.... (b) Prove that the harmonic series 2 ½ is divergent. นะเ n ② (a) Define what is meant by the following: (1) the sequence (an) is convergent. (ii) the sequence (an) is Cauchy. (ii) the sequence (an) is bounded. (b) Prove directly from definitions that a Cauchy Sequence is bounded. ③ (a) Prove diredly from definitions that if a Cauchy Sequence (an) has a convergent subsequence then (an) is convergent. (6) Use the results of 2(b) and 3(a) to deduce that a Counchy sequence is convergent. You may assume the Bolzano- Weierstrass Theorem.arrow_forward
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