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mathematics
college mathematics for business
Questions and Answers of
College Mathematics For Business
If the conditional proposition p is a contingency, is ¬ p a contingency, a tautology, or a contradiction? Explain.
If the conditional proposition p is a contradiction, is ¬ p a contingency, a tautology, or a contradiction? Explain.
In Problem find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class:Let the universal set U be the set of all 120 students in the class,
A jewelry store chain with 8 stores in Georgia, 12 in Florida, and 10 in Alabama is planning to close 10 of these stores.(A) How many ways can this be done?(B) The company decides to close 2 stores
How many subsets does each of the following sets contain?(A) {a}(B) {a, b}(C) {a, b, c}(D) {a, b, c, d}
There are 8 standard classifications of blood type. An examination for prospective laboratory technicians consists of having each candidate determine the type for 3 blood samples. How many different
Because of limited funds, 5 research centers are chosen out of 8 suitable ones for a study on heart disease. How many choices are possible?
A nominating convention will select a president and vice-president from among 4 candidates. Campaign buttons, listing a president and a vice-president, will be designed for each possible outcome
For U = {7, 8, 9, 10, 11} and A = {7, 11} , find A′.
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.¬q ∧ (p → q)
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.¬ p ∧ q
In Problem refer to the Venn diagram below and find the indicated number of elements.n(B′) U A B 21 42 18 19
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.¬p → (p → q)
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.¬(p V ¬q)
In Problem determine whether the given set is finite or infinite. Consider the set Z of integers to be the universal set, and letE ∪ K M = {n e Z|n < 10°} %3D K = {n e Z|n > 10'} E = {n e Z|n is
Using the English alphabet, how many 5-character case-sensitive passwords are possible?
In Problem refer to the Venn diagram below and find the indicated number of elements.n(A′) U A B 21 42 18 19
In Problem determine whether the given set is finite or infinite. Consider the set Z of integers to be the universal set, and letM ∩ K M = {n e Z|n < 10°} %3D K = {n e Z|n > 10'} E = {n e Z|n is
In Problem refer to the Venn diagram below and find the indicated number of elements.n(A ∩ B′) U A B 21 42 18 19
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.¬ p → q
In Problem determine whether the given set is finite or infinite. Consider the set Z of integers to be the universal set, and letK′ M = {n e Z|n < 10°} %3D K = {n e Z|n > 10'} E = {n e Z|n is even}
Using the English alphabet, how many 5-character case-sensitive passwords are possible if each character is a letter or a digit?
In Problem refer to the Venn diagram below and find the indicated number of elements.n( (A ∩ B)′ ) U A B 21 42 18 19
How many ways can a 3-person subcommittee be selected from a committee of 7 people? How many ways can a president, vice-president, and secretary be chosen from a committee of 7 people?
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.q ∧ (p ∨ q)
In Problem determine whether the given set is finite or infinite. Consider the set Z of integers to be the universal set, and letE ∩ M M = {n e Z|n < 10°} %3D K = {n e Z|n > 10'} E = {n e Z|n is
In Problem refer to the Venn diagram below and find the indicated number of elements.n(B ∩ A′) U A B 21 42 18 19
In Problem refer to the Venn diagram below and find the indicated number of elements.n(A′ ∩ B′) U A B 21 42 18 19
In Problem refer to the Venn diagram below and find the indicated number of elements.n(A ∪ A′) U A B 21 42 18 19
Problem refer to the following Venn diagram.Which of the numbers x, y, z, or w must equal 0 if B ⊂ A? A B y
In Problem refer to the Venn diagram below and find the indicated number of elements.n(A ∩ A′) U A B 21 42 18 19
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.p → (p ∧ q)
Problem refer to the following Venn diagram.Which of the numbers x, y, z, or w must equal 0 if A and B are disjoint? A B y
A man has 5 children. Each of those children has 3 children, who in turn each have 2 children. Discuss the number of descendants that the man has.
Problem refer to the following Venn diagram.Which of the numbers x, y, z, or w must equal 0 if A ∪ B = A ∩ B? A B y
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.(p → q) → ¬ p
Solve the following problems using nPr or nCr:(A) How many 3-digit opening combinations are possible on a combination lock with 6 digits if the digits cannot be repeated?(B) Five tennis players have
Problem refer to the following Venn diagram.Which of the numbers x, y, z, or w must equal 0 if A ∪ B = U? A B y
A group of 75 people includes 32 who play tennis, 37 who play golf, and 8 who play both tennis and golf. How many people in the group play neither sport?
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.q → (¬ p ∧ q)
In Problem write the resulting set using the listing method.{x| x3 - x = 0}
In Problem determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set.{n ∈ N| n > 100}
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.q → (p ∨ ¬q)
In Problem write the resulting set using the listing method.{x |x is a positive integer and x! < 100}
In Problem determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set.{n ∈ N| n < 1000}
A group of 100 people touring Europe includes 42 people who speak French, 55 who speak German, and 17 who speak neither language. How many people in the group speak both French and German?
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.(¬ p ∧ q) ∧ (q → p)
A catering service offers 8 appetizers, 10 main courses, and 7 desserts. A banquet committee selects 3 appetizers, 4 main courses, and 2 desserts. How many ways can this be done?
In Problem write the resulting set using the listing method.{x| x is a positive integer that is a perfect square and x < 50}
In Problem determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set.{2, 3, 5, 7, 11, 13}
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.(p → ¬q) ∧ (p ∧ q)
A software development department consists of 6 women and 4 men.(A) How many ways can the department select a chief programmer, a backup programmer, and a programming librarian?(B) How many of the
In Problem refer to the table in the graphing calculator display below, which shows y1 = nPr and y2 = nCr for n = 6.Discuss and explain the symmetry of the numbers in the y2 column of the
In Problem determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set.{2, 4, 6, 8, 10, ... }
In Problem construct a truth table to verify each implication.p ⇒ p ∨ q
In Problem would you consider the selection to be a permutation, a combination, or neither? Explain your reasoning.A book club meets monthly at the home of one of its 10 members. In December, the
In Problem refer to the Venn diagram below and find the indicated number of elements.n(A ∪ B) U A B 21 42 18 19
A particular new car model is available with 5 choices of color, 3 choices of transmission, 4 types of interior, and 2 types of engine. How many different variations of this model are possible?
In Problem refer to the Venn diagram below and find the indicated number of elements.n(A ∩ B) U A B 21 42 18 19
In Problem would you consider the selection to be a permutation, a combination, or neither? Explain your reasoning.A student bought 4 books: 1 for his father, 1 for his mother, 1 for his younger
In Problem refer to the Venn diagram below and find the indicated number of elements.n(B) U A B 21 42 18 19
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.(p V ¬p) → (q ∧ ¬q)
In Problem refer to the Venn diagram below and find the indicated number of elements.n(A) A 21 42 18 B 19
In Problem would you consider the selection to be a permutation, a combination, or neither? Explain your reasoning.A student checked out 4 novels from the library.
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.p V (q → p)
In Problem refer to the Venn diagram below and find the indicated number of elements.n(U) U A B 21 42 18 19
In Problem would you consider the selection to be a permutation, a combination, or neither? Explain your reasoning.The university president selected 2 of her vice-presidents to attend the dedication
In Problem state the converse and the contrapositive of the given proposition.If g(x) is a quadratic function, then g(x) is a function that is neither increasing nor decreasing.
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.(p → q) ∧ (q → p)
In Problem would you consider the selection to be a permutation, a combination, or neither? Explain your reasoning.The university president named 3 new officers: a vice-president of finance, a
In Problem state the converse and the contrapositive of the given proposition.If f(x) is a linear function with positive slope, then f(x) is an increasing function.
In Problem simplify each expression assuming that n is an integer and n ≥ 2. (п + 3)! (п + 1)!
In Problem simplify each expression assuming that n is an integer and n ≥ 2. (п + 1)! 21 (п — 1)!
In Problem write the resulting set using the listing method.{x |x is a month starting with M}
In Problem simplify each expression assuming that n is an integer and n ≥ 2. (п + 1)! 3! (п — 2)!
Evaluate the expressions in Problem13C4 . 13C1
In Problem describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false.If 4 is even, then 4 is prime
In Problem write the resulting set using the listing method.{x | x is an odd number between 1 and 9, inclusive}
In Problem simplify each expression assuming that n is an integer and n ≥ 2. n! (п — 2)! n
Evaluate the expressions in Problem8P5
In Problem describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false.7 is odd and 7 is prime
In Problem evaluate the expression. If the answer is not an integer, round to four decimal places. 26C4 52C4
In Problem write the resulting set using the listing method.{x|x4 = 16}
Evaluate the expressions in Problem8C5
In Problem describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false.9 is even or 9 is prime
In Problem write the resulting set using the listing method.{x|x3 = -27}
Evaluate the expressions in Problem 15! 10!5!
In Problem evaluate the expression. If the answer is not an integer, round to four decimal places. 39C5 52C5
Evaluate the expressions in Problem 15! 10!
In Problem describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false.11 is not prime
In Problem write the resulting set using the listing method.{x|x2 = 36}
In Problem evaluate the expression. If the answer is not an integer, round to four decimal places. 3654 36525
In Problem describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false.-3 is not greater than 0
In Problem write the resulting set using the listing method.{x|x2 = 25}
In Problem evaluate the expression. If the answer is not an integer, round to four decimal places. 12P 127
Evaluate the expressions in Problem(10 - 6) !
In Problem describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false.If -3 < 0, then (-3)2 < 0
Use the Venn diagram to find the number of elements in each of the following sets:(A) A ∩ B (B) A ∪ B(C) (A ∩ B)′ (D) (A ∪ B)′ U A B 30 35 40 45
In Problem write the resulting set using the listing method.{-3, -1} ∪ {1, 3}
In Problem(A) Introduce slack, surplus, and artificial variables and form the modified problem.(B) Write the preliminary simplex tableau for the modified problem and find the initial simplex
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