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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...

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1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2
A diesel engine uses Type A filter and high-grade lubricating oil costing P5.50 per liter. With this filter, the oil and the filter have to be changed every 500 hours of operation, and 5 liters of coil have to be added every 100 hours. This filter costs P148 a piece. Eighty liters of coil fill the engine. Another type, filter B, costing P120 may be used with a lower grade of oil costing P4.80 per liter. However, if this filter is used, the oil and filter have to be changed every 300 hours, and 10 liters are added after each 150 hours the engine is used. Which type of filter and oil would you recommend?
b. Determine the average daily rates that separate the:(i) top 8% of average daily rates from the rest of the daily rates or from the bottom 92% of average daily ratesx= Round to 2 decimal places. (ii) bottom 15% of average daily rates from the rest of the daily ratesx= Round to 2 decimal places. (iii) middle 70% of average daily rates from the rest of the daily rates = ? < x < ? Round to 2 decimal places.
An existing mall (Circuit Mall) is located near the residential area and has the following characteristics: Shopping Center Distance from residential area of Zone A (miles) Commercial Floor Space (thousand ft2) Circuit Mall 2.1 220 Three malls are to be built to rival the existing mall and there are currently three proposals. A total of 5000 shopping trips are generated from the residential area. Use n=1.5 Shopping Center Distance from residential area of Zone A (miles) Commercial Floor Space (thousand ft2) SM City 1 3.25 150 SM City 2 5.68 300 SM City 3 6.75 600 How many trips would Circuit Mall make compared to the new competitors?
It is often said that the economy of Arizona depends on the “Five C’s”: Copper, Cattle, Cotton, Citrus, andClimate. Assume a (highly simplified) model of the Arizona Economy that depends only on C1, C2, C3, C4,and C5, which represent the number of economic units (pennies, pounds, etc) purchased of each of the FiveC’s, respectively. Further assume that the Utility, or Economic Value (which is different from DollarValue), can be described by the function:U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5As a mathematical function, does U have a maximum or minimum value? What values of Ci correspond tothe minimum value of U? What values of Ci correspond to the maximum value of U? Do these values of Cimake sense from an economic standpoint?
A company manufacture two different types of call phone F and E, each unit of call phone S costs (OR .7)and each unit of call phone E costs (OR. 6). The company insists that total costs for the two types call phone be (OR .400). Assuming that company manufactures in total 88 products. How many products are of type Fand E? (solve the problem using Crammer's Rule)
Option 1: 2(lw + lh + wh), l + w + h, lwh Option 2: 3 layers of 10, 7 layers of 21, 3 layers of 21, 7 layers of 3 Option 3: volume, edge lengths, base area Option 4: equal to, less than, greater than
An engineer is studying the mileage performance characteristics of 5 types of gasoline additives. In the road test he wishes to use cars as blocks; however, because of a time constraint, he must use an incomplete block design. He runs the balanced design with the five blocks that follow. Car Additive 1 2 3 4 5 1 NA 17 14 13 12 2 14 14 NA 13 10 3 12 NA 13 12 9 4 13 11 11 12 NA 5 11 12 10 NA 8 - Verify that this is a balanced incomplete block design - Obtain the estimates of the treatment means and the treatments effects
You’re a quality control engineer working for Tinker Air Force Base. The length, width, andheight of a manufactured part used in the maintenance, repair, and overhaul of a particularaircraft type are classified as being either within or outside specified tolerance limits. In aquality inspection, 86% of the parts are found to be within the specified tolerance limits forwidth, but only 80% of parts are within specified limits for all three dimensions. Further, 2% ofthe parts are within the limits for width and length but not for height, and 3% of parts arewithin limits for width and height but not length. Also, 92% of parts are within limits for eitherwidth or height or both. If a part is within the specified tolerance limits for height, what is theprobability that it will also be within the specified limits for width?
Consider a school that similar to Jacob university. Jacob university has 65% graduation rate and a student-faculty ration of 19:1, 37% of the classes have fewer than 20 students, 23% of the classes have more than 50 students, and have a freshman retention rate of 80%. Should Jacob university giving rate be greater or less than 8%? I need help sugesting giving rates and I am confused on what the corrent one is School SFR LT20 GT50 GRAD FRR GIVE Arizona State 24 42% 16% 59% 81% 8% Arkansas State —Jonesboro 19 49% 4% 37% 69% 11% Auburn 18 24% 17% 66% 87% 31% Air Force Academy 8 74% 0.10% 81% 88% 11% Military Academy 8 95% 0% 86% 92% 28% Akron 20 39% 6% 35% 69% 15% Arizona 20 35% 17% 60% 79% 5% Arkansas 18 28% 18% 58% 83% 23% Ball State 18 34% 12% 57% 78% 11% Baylor 14 49% 9% 71% 85% 14% Boise State 21 33% 11% 27% 67% 8% Boston College 14 47% 6% 91% 96% 27% Bowling Green State 19 33% 7% 61% 75% 8% Brigham Young —Provo 21…
Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $13,000. Assuming the college wishes to offer a total of six sections, accommodate 210 students, and bring in $253,000in revenues, how many sections of each course should it offer? Finite Math section(s)Applied Calculus section(s) Computer Methods section(s)
ata Set 12 “Passive and Active Smoke” in Appendix B includes cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, Mean = 60.58 ng>mL, s = 138.08 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, Mean = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke. 1. Find the degrees of freedom using the conversative estimate formula. What is it? 2. Find the critical value. What is it? 3. Sketch a normal distribution curve and highlight the region of significance.

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