Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
14th Edition
ISBN: 9780134677972
Author: Barnett
Publisher: PEARSON
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Textbook Question
Chapter 1.1, Problem 31E
In Problems 19-32, find the solution set.
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Assume {u1, U2, u3, u4} does not span R³.
Select the best statement.
A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set.
B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³.
C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set.
D. {u1, U2, u3} cannot span R³.
E. {U1, U2, u3} spans R³ if u̸4 is the zero vector.
F. none of the above
Select the best statement.
A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors
are distinct.
n
B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0
excluded spans Rª.
○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n
vectors.
○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors
spans Rn.
E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn.
F. none of the above
Assume {u1, U2, u3, u4} does not span R³.
Select the best statement.
A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set.
B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³.
C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set.
D. {u1, U2, u3} cannot span R³.
E. {U1, U2, u3} spans R³ if u̸4 is the zero vector.
F. none of the above
Chapter 1 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Ch. 1.1 - According to equality property 2, multiplying both...Ch. 1.1 - Replace ? with < or > in each of the following:...Ch. 1.1 - The solution to Example 5B shows the graph of the...Ch. 1.1 - Solve and check: 3x2(2x5)=2(x+3)8Ch. 1.1 - Solve and check: x+13x4=12Ch. 1.1 - Matched Problem 3 If a cardboard box has length L,...Ch. 1.1 - Replace each question mark with either < or >....Ch. 1.1 - (A) Write 7,4 as a double inequality and graph....Ch. 1.1 - Solve and graph: 3(x1)5(x+2)5Ch. 1.1 - Solve and graph: 83x57
Ch. 1.1 - Mary paid 8.5 sales tax and a 190 title and...Ch. 1.1 - How many bike computers would a company have to...Ch. 1.1 - What net annual salary in 1973 would have had the...Ch. 1.1 - In Problems 1-6, solve for x. 5x+3=x+23Ch. 1.1 - In Problems 1-6, solve for x. 7x6=5x24Ch. 1.1 - In Problems 1-6, solve for x. 9(4x)=2(x+7)Ch. 1.1 - In Problems 1-6, solve for x. 3(x+6)=52(x+1)Ch. 1.1 - In Problems 1-6, solve for x. x+14=x2+5Ch. 1.1 - In Problems 1-6, solve for x. 2x+135x2=4Ch. 1.1 - In Problems 7-12, write the interval as an...Ch. 1.1 - In Problems 7-12, write the interval as an...Ch. 1.1 - In Problems 7-12, write the interval as an...Ch. 1.1 - In Problems 7-12, write the interval as an...Ch. 1.1 - In Problems 7-12, write the interval as an...Ch. 1.1 - In Problems 7-12, write the interval as an...Ch. 1.1 - In Problems 13-18, write the solution set using...Ch. 1.1 - In Problems 13-18, write the solution set using...Ch. 1.1 - In Problems 13-18, write the solution set using...Ch. 1.1 - In Problems 13-18, write the solution set using...Ch. 1.1 - In Problems 13-18, write the solution set using...Ch. 1.1 - In Problems 13-18, write the solution set using...Ch. 1.1 - In Problems 19-32, find the solution set. x4+12=18Ch. 1.1 - In Problems 19-32, find the solution set. m34=23Ch. 1.1 - In Problems 19-32, find the solution set. y532Ch. 1.1 - In Problems 19-32, find the solution set. x456Ch. 1.1 - In Problems 19-32, find the solution set....Ch. 1.1 - In Problems 19-32, find the solution set....Ch. 1.1 - In Problems 19-32, find the solution set....Ch. 1.1 - In Problems 19-32, find the solution set. 34x=5x+1Ch. 1.1 - In Problems 19-32, find the solution set. 3y4y3Ch. 1.1 - In Problems 19-32, find the solution set. x22x5Ch. 1.1 - In Problems 19-32, find the solution set. x5x6=65Ch. 1.1 - In Problems 19-32, find the solution set. y4y3=12Ch. 1.1 - In Problems 19-32, find the solution set. m5335m2Ch. 1.1 - In Problems 19-32, find the solution set. u223u3+2Ch. 1.1 - In Problems 33-36, solve and graph. 23x714Ch. 1.1 - In Problems 33-36, solve and graph. 45x+621Ch. 1.1 - In Problems 33-36, solve and graph. 495C+3268Ch. 1.1 - In Problems 33-36, solve and graph. 123t+511Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 43 and 44, solve and graph. 347x18Ch. 1.1 - In Problems 43 and 44, solve and graph. 1083u6Ch. 1.1 - If both a and b are positive numbers and b/a. is...Ch. 1.1 - If both a and b are negative numbers and b/a is...Ch. 1.1 - Ticket sales. A rock concert brought in $432,500...Ch. 1.1 - Parking meter coins. An all-day parking meter...Ch. 1.1 - IRA. You have $500,000 in an IRA (Individual...Ch. 1.1 - IRA. Refer to Problem 49. How should you divide...Ch. 1.1 - Car prices. If the price change of cars parallels...Ch. 1.1 - Home values. If the price change in houses...Ch. 1.1 - Retail and wholesale prices. Retail prices in a...Ch. 1.1 - Retail and sale prices. Sale prices in a...Ch. 1.1 - Equipment rental. A golf course charges $52 for a...Ch. 1.1 - Equipment rental. The local supermarket rents...Ch. 1.1 - Sales commissions. One employee of a computer...Ch. 1.1 - Sales commissions. A second employee of the...Ch. 1.1 - Break-even analysis. A publisher for a promising...Ch. 1.1 - Break-even analysis. The publisher of a new book...Ch. 1.1 - Break-even analysis. The publisher in Problem 59...Ch. 1.1 - Break-even analysis. The publisher in Problem 60...Ch. 1.1 - Wildlife management. A naturalist estimated the...Ch. 1.1 - Temperature conversion. If the temperature for a...Ch. 1.1 - Psychology. The IQ (intelligence quotient) is...Ch. 1.1 - Psychology. Refer to Problem 65. If the IQ of a...Ch. 1.2 - (A) As noted earlier, (4,3) is a solution of the...Ch. 1.2 - (A) Graph y=x+b for b=5,3,0,3 and 5 simultaneously...Ch. 1.2 - Graph:4x3y=12Ch. 1.2 - Graph 4x-3y=12 on a graphing calculator and find...Ch. 1.2 - (A) Graph x=5andy=3 simultaneously in the same...Ch. 1.2 - Find the slope of the line through each pair of...Ch. 1.2 - Write the equation of the line with slope 12 and y...Ch. 1.2 - (A) Find an equation for the line that has slope...Ch. 1.2 - Answer parts (A) and (B) in Example 7 for fixed...Ch. 1.2 - At a price of $12.59 per box of grapefruit, the...Ch. 1.2 - \ Problems 1-4 refer to graphs (A)-(D). Identify...Ch. 1.2 - Problems 1-4 refer to graphs (A)-(D). Identify the...Ch. 1.2 - Problems 1-4 refer to graphs (A)-(D). Identify the...Ch. 1.2 - Problems 1-4 refer to graphs (A)-(D). Identify the...Ch. 1.2 - In Problems 5-8, sketch a graph of each equation...Ch. 1.2 - In Problems 5-8, sketch a graph of each equation...Ch. 1.2 - In Problems 5-8, sketch a graph of each equation...Ch. 1.2 - In Problems 5-8, sketch a graph of each equation...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 15-20, find the slope and x intercept...Ch. 1.2 - In Problems 15-20, find the slope and x intercept...Ch. 1.2 - In Problems 15-20, find the slope and x intercept...Ch. 1.2 - In Problems 15-20, find the slope and x intercept...Ch. 1.2 - In Problems 15-20, find the slope and x intercept...Ch. 1.2 - In Problems 15-20, find the slope and x intercept...Ch. 1.2 - In Problems 21-24, write an equation of the line...Ch. 1.2 - In Problems 21-24, write an equation of the line...Ch. 1.2 - In Problems 21-24, write an equation of the line...Ch. 1.2 - In Problems 21-24, write an equation of the line...Ch. 1.2 - In Problems 25-28, use the graph of each line to...Ch. 1.2 - In Problems 25-28, use the graph of each line to...Ch. 1.2 - In Problems 25-28, use the graph of each line to...Ch. 1.2 - In Problems 25-28, use the graph of each line to...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - Given Ax+By=12, graph each of the following three...Ch. 1.2 - Given Ax+By=24, graph each of the following three...Ch. 1.2 - Graph y=25x+200,x0.Ch. 1.2 - Graph y=40x+160,x0.Ch. 1.2 - (A) Graph y=1.2x4.2 in a rectangular coordinate...Ch. 1.2 - (A) Graph y=0.8x+5.2 in a rectangular coordinate...Ch. 1.2 - In Problems 47-50, write the equations of the...Ch. 1.2 - In Problems 47-50, write the equations of the...Ch. 1.2 - In Problems 47-50, write the equations of the...Ch. 1.2 - In Problems 47-50, write the equations of the...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - Discuss the relationship among the graphs of the...Ch. 1.2 - Discuss the relationship among the graphs of the...Ch. 1.2 - Cost analysis. A donut shop has a fixed cost of...Ch. 1.2 - Cost analysis. A small company manufactures picnic...Ch. 1.2 - Cost analysis. A plant can manufacture 80 golf...Ch. 1.2 - Cost analysis. A plant can manufacture 50 tennis...Ch. 1.2 - Business-Markup policy. A drugstore sells a drug...Ch. 1.2 - Business-Markup policy. A clothing store sells a...Ch. 1.2 - Business-Depreciation. A farmer buys a new tractor...Ch. 1.2 - Business-Depreciation. A charter fishing company...Ch. 1.2 - Boiling point. The temperature at which water...Ch. 1.2 - Boiling point. The temperature at which water...Ch. 1.2 - Flight conditions. In stable air, the air...Ch. 1.2 - Flight navigation. The airspeed indicator on some...Ch. 1.2 - Demographics. The average number of persons per...Ch. 1.2 - Demographics. The median household income divides...Ch. 1.2 - Cigarette smoking. The percentage of female...Ch. 1.2 - Cigarette smoking. The percentage of male...Ch. 1.2 - Supply and demand. At a price of $9.00 per bushel,...Ch. 1.2 - Supply and demand. At a price of $3.20 per bushel,...Ch. 1.2 - Physics. Hooke’s law states that the relationship...Ch. 1.2 - Physics. The distance d between a fixed spring and...Ch. 1.3 - As illustrated in Example 1A, the slope m of a...Ch. 1.3 - As stated previously, we used linear regression to...Ch. 1.3 - The equation a=28.55w+118.7 expresses BSA for...Ch. 1.3 - A 400-pound load of grain is dropped from an...Ch. 1.3 - Prices for emerald-shaped diamonds from an online...Ch. 1.3 - Using the model of Example 4, estimate the...Ch. 1.3 - Figure 5 shows the scatter plot for white spruce...Ch. 1.3 - Ideal weight. Dr. J. D. Robinson published the...Ch. 1.3 - Ideal weight. Dr. J. D. Robinson also published...Ch. 1.3 - Underwater pressure. At sea level, the weight of...Ch. 1.3 - Underwater pressure. Refer to Problem 3. In fresh...Ch. 1.3 - Rate of descent Parachutes. At low altitudes, the...Ch. 1.3 - Rate of descent Parachutes. The U.S Army is...Ch. 1.3 - Speed of sound. The speed of sound through air is...Ch. 1.3 - Speed of sound. The speed of sound through sea...Ch. 1.3 - Energy production. Table 5 lists U.S. fossil fuel...Ch. 1.3 - Energy consumption. Table 6 lists U.S. fossil fuel...Ch. 1.3 - Cigarette smoking. The data in Table 7 shows that...Ch. 1.3 - Cigarette smoking. The data in Table 7 shows that...Ch. 1.3 - Licensed drivers. Table 8 contains the state...Ch. 1.3 - Licensed drivers. Table 9 contains the state...Ch. 1.3 - Net sales. A linear regression model for the net...Ch. 1.3 - Operating income. A linear regression model for...Ch. 1.3 - Freezing temperature. Ethylene glycol and...Ch. 1.3 - Freezing temperature. A linear regression model...Ch. 1.3 - Forestry. The figure contains a scatter plot of...Ch. 1.3 - Forestry. The figure contains a scatter plot of...Ch. 1.3 - Undergraduate enrollment. Table 12 lists fall...Ch. 1.3 - Graduate enrollment. Table 13 lists fall graduate...Ch. 1.3 - Climate. Find a linear regression model for the...Ch. 1.3 - Climate. Find a linear regression model for the...Ch. 1.3 - Olympic Games. Find a linear regression model for...Ch. 1.3 - Olympic Games. Find a linear regression model for...Ch. 1.3 - Supply and demand. Table 16 contains price supply...Ch. 1.3 - Supply and demand. Table 17 contains price supply...Ch. 1 - Solve2x+3=7x11.Ch. 1 - Solvex12x33=12.Ch. 1 - Solve2x+5y=9fory.Ch. 1 - Solve3x4y=7forx.Ch. 1 - Solve Problems 5-7 and graph on a real number...Ch. 1 - Solve Problems 5-7 and graph on a real number...Ch. 1 - Solve Problems 5-7 and graph on a real number...Ch. 1 - Sketch a graph of 3x+2y=9.Ch. 1 - Write an equation of a line with x intercept 6 and...Ch. 1 - Sketch a graph of 2x3y=18. What are the intercepts...Ch. 1 - Write an equation in the form y=mx+b for a line...Ch. 1 - Write the equations of the vertical line and the...Ch. 1 - Write the equation of a line through each...Ch. 1 - Write the equation of the line through the two...Ch. 1 - Solve Problems 15-19. 3x+25=5xCh. 1 - Solve Problems 15-19. u5=u6+65Ch. 1 - Solve Problems 15-19. 5x34+x2=x24+1Ch. 1 - Solve Problems 15-19. 0.05x+0.2530x=3.3Ch. 1 - Solve Problems 15-19. 0.2x3+0.05x=0.4Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Given Ax+By=30, graph each of the following cases...Ch. 1 - Describe the graphs of x=3 and y=2 Graph both...Ch. 1 - Describe the lines defined by the following...Ch. 1 - Solve Problems 28 and 29 for the indicated...Ch. 1 - Solve Problems 28 and 29 for the indicated...Ch. 1 - For what values of a and b is the inequality a+bba...Ch. 1 - If a and b are negative numbers and ab, then is...Ch. 1 - Graph y=mx+bandy=1mx+b simultaneously in the same...Ch. 1 - Investing. An investor has $300,000 to invest. If...Ch. 1 - Break-even analysis. A producer of educational...Ch. 1 - Sports medicine. A simple rule of thumb for...Ch. 1 - Linear depreciation. A bulldozer was purchased by...Ch. 1 - Business Pricing. A sporting goods store sells...Ch. 1 - Income. A salesperson receives a base salary of...Ch. 1 - Price demand. The weekly demand for mouthwash in a...Ch. 1 - Freezing temperature. Methanol, also known as wood...Ch. 1 - High school dropout rates. Table 2 gives U.S. high...Ch. 1 - Consumer Price Index. The U.S. Consumer Price...Ch. 1 - Forestry. The figure contains a scatter plot of 20...
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- Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forwardTrolley of the overhead crane moves along the bridge rail. The trolley position is measured from the center of the bridge rail (x = 0) is given by x(t) = 0.5t^3-6t^2+19.5t-14 : 0 <= t <= 3 min. The trolley moves from point A to B in the forward direction, B to C in the reverse direction and C to D again in the forward direction. CONTROL PANEL END TRUCK- RUNWAY BEAM- BRIDGE RAIL HOIST -TROLLEY TROLLEY BUMPER TROLLEY DRIVE LPENDANT TRACK -TROLLEY CONDUCTOR TRACK WIRE ROPE -HOOK BLOCK -BRIDGE DRIVE -END TRUCK BUMPER -RUNWAY RAIL TROLLEY END STOP -CONDUCTOR BAR PENDANT FESTOONING TROLLEY FESTOONING PENDANT CABLE PENDANT x(t)=0.5t^3-6t^2+19.5t-14 v(t)=1.5t^2-12t+19.5 a(t)=(dv(t))/dt=3t-12 Fig. T2.2: The overhead crane Total masses of the trolley, hook block, and the load attached to the hook block are 110 kg, 20 kg, and 150 kg. Damping coefficient, D, is 40 kg/s. What is the total amount of energy required from the trolley motor to move the system [Hint: Use Newton's 2nd law to obtain the…arrow_forward
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