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Questions and Answers of Mathematics Economics Business

In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. V355-60V/35 = 5√7-6√5
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.The square roots of 2√6 – 5 are √3 – √2 and √2 – √3.
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. 3/7-5√2 = 1 V2
In Problem evaluate using a calculator.223/2
In Problem evaluate using a calculator.155/4
In Problem evaluate using a calculator.827–3/8
In Problem evaluate using a calculator.103–3/4
In Problem evaluate using a calculator.37.097/3
In Problem evaluate using a calculator.2.8768/5
You have inherited $10,000 just prior to a presidential election and wish to invest it in solar energy and oil stocks. An investment advisor provides you with a payoff matrix that indicates your
A corporate farm grows both wheat and rice. Rice does better in wetter years, and wheat does better in normal or drier years. Based on records over the past 20 years and current market prices, a
Reduce each fraction to lowest terms.(A)(B) 1.2.3.4 1.2.3.4.5.6
Factor out all factors common to all terms.(A) 3x3y – 6x2y2 – 3xy3(B) 3y(2y + 5) + 2(2y + 5)
Reduce each fraction to lowest terms. (A) 1.2.3.4.5 1.2.1.2.3 (B) 1.4.9.16 1.2.3.4
State the real number property that justifies the indicated statement.(A) 8 + (3 + y) = (8 + 3) + y(B) (x + y) + z = z + (x + y)(C) (a + b) (x + y) = a(x + y) + b(x + y)(D) 5xy + 0 = 5xy(E) If xy =
Factor out all factors common to all terms.(A) 2x3y – 8x2y2 – 6xy3 (B) 2x(3x – 2) – 7(3x – 2)
(A) Given the polynomial 6x5 + 7x3 – 2, what is the degree of the first term? The second term? The third term? The whole polynomial?(B) Given the polynomial 2u4v2 – 5uv3, what is the degree of
Remove parentheses and simplify:(A) 3(u2 – 2v2) + (u2 + 5v2)(B) (m3 – 3m2 + m – 1) – (2m3 – m + 3)(C) (x3 – 2) – [2x3 – (3x + 4)]
Factor by grouping.(A) 3x2 – 3x – x + 1(B) 4x2 – 2xy – 6xy + 3y2(C) y2 + xz + xy + yz
Round 22/7 + 18/19 to the nearest integer.
Reduce each rational expression to lowest terms.(A)(B) 6x² + x1 2x² x 1 -
Remove parentheses and simplify:(A) 2(3x2 – 2x + 5) + (x2 + 3x – 7)(B) (x3 – 2x – 6) – (2x3 – x2 + 2x – 3)(C) [3x2 – (2x + 1)] – (x2 – 1)
Round 6/93 to the nearest integer.
Factor by grouping.(A) 6x2 + 2x + 9x + 3(B) 2u2 + 6uv – 3uv – 9v2(C) ac + bd + bc + ad
Add horizontally and vertically:3x4 – 2x3 – 4x2, x3 – 2x2 – 5x, and x2 + 7x – 2
Factor, if possible, using integer coefficients.(A) 4x2 – 4x – 3 (B) 2x2 – 3x – 4 (C) 6x2 – 25xy + 4y2
Perform the indicated operations and reduce to lowest terms.(A)(B) 10x³y 3xy +9y x² - 9 X 4x² - 12x
Find the sales tax that is owed on a purchase of $947.69 if the tax rate is 6.5%.
Perform the indicated operations and reduce to lowest terms.(A)(B) 12x²y³3 2xy² + 6ху y2 + бу + 9 3у³ + 9y2
Add horizontally and vertically:x4 – 3x3 + x2, –x3 – 2x2 + 3x, and 3x2 – 4x – 5
You intend to give a 20% tip, rounded to the nearest dollar, on a restaurant bill of $78.47. How much is the tip?
Factor, if possible, using integer coefficients.(A) 2x2 + 11x – 6(B) 4x2 + 11x – 6(C) 6x2 + 5xy – 4y2
Combine into a single fraction and reduce to lowest terms.(A)(B)(C) 3 10 + 556 11 45
Subtract 2x2 – 5x + 4 from 5x2 – 6, both horizontally and vertically.
Factor completely.(A) 4m2 – 12mn + 9n2 (B) x2 – 16y2 (C) z3 – 1(D) m3 + n3(E) a2 – 4(b + 2)2
Combine into a single fraction and reduce to lowest terms. (A) (C) 5 28 - 1 + 10 - 2 6 35 2 X 4x + 4 1 - 1 x-2 (B) - 4x² 2x + 1 3x³ + 3 12x
Subtract 4x2 – 3x + 5 from x2 – 8, both horizontally and vertically.
Factor completely:(A) x2 + 6xy + 9y2 (B) 9x2 – 4y2 (C) 8m3 – 1(D) x3 + y3z3 (E) 9(m – 3)2 – 4n2
Multiply: (2x – 3)(2x2 + 3x – 2)
Express as a simple fraction reduced to lowest terms: (A) 1 5+h h 1 5 (B) 는 y X X X y
Factor completely.(A) 3x3 – 48x (B) 3u4 – 3u3v – 9u2v2(C) 3m2 – 24mn3 (D) 3x4 – 5x2 + 2
Express as a simple fraction reduced to lowest terms:(A)(B) 1 2+h h — 2
Multiply: (2x – 3)(3x2 – 2x + 3)
Factor completely.(A) 18x3 – 8x(B) 4m3n – 2m2n2 + 2mn3(C) 2t4 – 16t(D) 2y4 – 5y2 – 12
Multiply mentally, where possible.(A) (4u – 3v)(2u + v) (B) (2xy + 3)(2xy – 3)(C) (m + 4n)(m – 4n) (D) (2u – 3v)2(E) (2x – y)3
Multiply mentally, where possible.(A) (2x – 3y)(5x + 2y) (B) (3a – 2b)(3a + 2b)(C) (5x – 3)2 (D) (m + 2n)3
In Problem indicate true (T) or false (F).5(8m) = (5 · 8)m
Perform the indicated operations and simplify:(A) 2t – {7 – 2[t – t(4 + t)]}(B) (u – 3v)2 – (2u – v)(2u + v)
Perform the indicated operations and simplify:(A) 3x – {5 – 3[x – x(3 – x)]}(B) (x – 2y)(2x + 3y) – (2x + y)2
In Problem perform the indicated operations and simplify.2(u – 1) – (3u + 2) – 2(2u – 3)
In Problem perform the indicated operations and simplify.4a – 2a[5 – 3(a + 2)]
In Problem perform the indicated operations and simplify.(3x – 5)(2x + 1)
In Problem factor completely. If a polynomial cannot be factored, say so.2x2 + 5x – 3
In Problem factor completely. If a polynomial cannot be factored, say so.x2 – 4xy – 12y2
In Problem factor completely. If a polynomial cannot be factored, say so.x2 + x – 4
In Problem factor completely. If a polynomial cannot be factored, say so.w2x2 – y2
In Problem factor completely. If a polynomial cannot be factored, say so.25m2 – 16n2
If uv = 1, does either u or v have to be 1? Explain.
If uv = 0, does either u or v have to be 0? Explain.
In Problem factor completely. If a polynomial cannot be factored, say so.u2 + 81
In Problem factor completely. If a polynomial cannot be factored, say so.4u3v – uv3
In Problem factor completely. If a polynomial cannot be factored, say so.x3y – 9xy3
In Problem factor completely. If a polynomial cannot be factored, say so.8x3 – 27y3
In Problem factor completely. If a polynomial cannot be factored, say so.5x3 + 40y3
Find the tax owed on a purchase of $182.39 if the state sales tax rate is 9%. (Round to the nearest cent).
What is the degree of the sum of the two polynomials in Problem 51?Data from Problem 51If you are given two polynomials, one of degree m and the other of degree n, where m is greater than n, what is
In Problem factor completely. If a polynomial cannot be factored, say so.4(A + B)2 – 5(A + B) – 6
How does the answer to Problem 51 change if the two polynomials can have the same degree?Data from Problem 51If you are given two polynomials, one of degree m and the other of degree n, where m is
How does the answer to Problem 52 change if the two polynomials can have the same degree?Data from Problem 52What is the degree of the sum of the two polynomials in Problem 51?Data from Problem 51If
In Problem factor completely. If a polynomial cannot be factored, say so.m4 – n4
In Problem factor completely. If a polynomial cannot be factored, say so.15x2(3x – 1)4 + 60x3(3x – 1)3
Four thousand tickets are to be sold for a musical show. If x tickets are to be sold for $20 each and three times that number for $30 each, and if the rest are sold for $50 each, write an algebraic
Solve the two-finger Morra game introduced at the beginning of this section.Data from two-finger Morra game Nonstrictly Determined Games: Example Now we consider some interesting nonstrictly
In Problem given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement.36.1
Solve the following matrix game by using geometric methods to solve the corresponding linear programming problems. M = -2 1 4 -3
A company claims that 60% of the households in a given community use its product. A competitor surveys the community, using a random sample of 40 households, and finds only 15 households out of the
Suppose that a and k are both saddle values of the matrix(A) Show that a must equal k after explaining why each of the following must be true: a ≤ c, c ≤ k, a ≥ i, and i ≥ k.(B) Show that c
Solve the following matrix game using geometric linear programming methods: 2-4 3 M = [-² -1
Solve the following version of the two-finger Morra game (which is equivalent to the penny-matching game): M -41 -1 =
In Problem calculate the matrix product. [10] 2 -1 -3 ][] 4
Show thatis a strictly determined matrix game. Nevertheless, apply the geometric procedure given for nonstrictly determined matrix games to M. Does something go wrong? Do you obtain the correct
In Problem find the smallest integer k ≥ 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs. -3 2 -57 -6]
Two large shopping centers have competing home-improvement discount stores, Riteway (R) in one center and Cashmart (C) in the other. Every week, each store chooses one, and only one, of the following
Repeat Example 1 for the HDTV game matrix discussed at the beginning of this section:Data from Example 1Two large shopping centers have competing home-improvement discount stores, Riteway (R) in one
An investor wishes to invest $10,000 in bonds and gold. He knows that the return on the investments will be affected by changes in interest rates. After some analysis, he estimates that the return
Suppose that the investor in Example 1 wishes to invest $10,000 in long- and short-term bonds, as well as in gold, and he is concerned about inflation. After some analysis, he estimates that the
Outline a procedure for solving the 4 × 5 matrix gamewithout actually solving the game. M = 2 -3 5 -4 -2 -1 6 -6 4 -1 6 0 2 7 3 63 - -7 4 -5
Let(A) Show that if the row minima belong to the same column, at least one of them is a saddle value.(B) Show that if the column maxima belong to the same row, at least one of them is a saddle
In Problem solve each matrix game. [ 4 0 -1 2.
In Problem, is the matrix game strictly determined? 5 -4 -3 2
(A) Using Theorem 4, give conditions on a, b, c, and d to guarantee that the nonstrictly determined matrix gameis fair.(B) Construct the matrix of payoffs for a two-finger Morra game that is
Solve the matrix game: M = -1 -3 1 0 0 -2 40 3 1-3 -3 2
Solve the matrix game: M = -1 3 -1 -1 2 - 1 2 -4 3
In Problem calculate the matrix product. 2 -3 唱歌 0 [0 1]
In Problem find the smallest integer k ≥ 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs. [도 4 -1 2
Determine whether the following matrix games are strictly determined: A = -1 5 2 -2 -3 4 3 0 2 -1 -8 10 -5 -3 0 24 B = 4 8
Determine which of the matrix games below are nonstrictly determined: A = - 1 0 -2 -1 3 2 -4 0 B = 2 -3 -6 -1 0 10 5 -8
In Problem solve each matrix game. 1 2 0 -1 -2 1
In Problem, is the matrix game strictly determined? -1 4 -2 1
In Problem determine the value v of the matrix game. Is the game fair? 5 3 -2 0]

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