The document discusses pollution from vehicles and provides calculations related to carbon dioxide (CO2) emissions from a car's fuel consumption. It includes:
1) A calculation of the kg of CO2 emitted from a car traveling 378 km getting 13.5 km per liter of gas, emitting 2.7 kg CO2 per liter.
2) A polynomial equation relating CO2 emissions (g/km) to speed (km/h) between 20-40 km/h based on sample data.
3) Additional math word problems on topics like geometry, functions, progressions, and probabilities.
GEOMETRIA ESPACIAL - POLIEDROS E CORPOS REDONDOS - PROF TARCÍSIO - www.profta...Tarcísio Filho
This document discusses geometric solids including polyhedra, prisms, pyramids, cylinders, cones, and their properties. It states Euler's formula for convex polyhedra that the number of vertices plus the number of faces equals the number of edges plus two. Formulas are provided for calculating the volume of prisms, pyramids, parallelepipeds, cylinders, cones, and converting between units of volume like cubic meters, liters and cubic centimeters.
This document contains solutions to multiple questions about calculating geometric properties of pyramids and tetrahedrons. It provides step-by-step working to determine measures like base area, lateral area, height, volume, and edge length given various known values for regular pyramids and tetrahedrons.
This document contains 13 math and physics problems from a Brazilian university entrance exam (Unicamp 2012). The problems cover a range of topics including geometry, trigonometry, matrices, linear systems, probability, functions, and more. For each problem, the solutions are provided in mathematical notation or as numerical answers within the document.
This document contains 13 math problems related to geometry, algebra, and other topics. Some key details:
- Problem 1 involves finding parameters of linear functions relating shoe size and length for Brazil and the US.
- Problem 2 analyzes data from Felix Baumgartner's skydive record, calculating velocity at a given time and when he broke the sound barrier.
- Problem 3 involves matrix multiplication and finding the value of a parameter for a system of equations to have a solution.
- Problems 4-6 cover marketing discounts on course enrollments, volume calculations for a pool with dimensions in geometric progression, and nutrient content relationships in fertilizers.
- Later problems analyze triangles, polynomials,
The document describes a linear programming problem to minimize costs for a pipe manufacturing company over 7 months. It provides production capacities, costs, demand forecasts, and inventory holding costs. The assistant formulates the LP with decision variables for regular and overtime production and inventory levels. The objective is to minimize total costs of production, inventory holding and meeting demand over the 7 months. The LP is set up and solved in a spreadsheet, finding the optimal solution that meets all constraints with a total minimum cost of $558,250.
This document contains several multi-part calculus problems involving estimating areas under curves using Riemann sums with rectangles. The problems ask the student to:
- Estimate areas under graphs using left, right, and midpoint Riemann sums with varying numbers of rectangles
- Interpret Riemann sums as approximations of definite integrals involving the area under a curve
- Evaluate definite integrals using properties such as interpreting them in terms of areas under curves
The document appears to contain exam questions for an Operations Management course. It includes questions related to topics like linear trend analysis, capacity planning, aggregate planning, inventory management, MRP, and supply chain management. It also contains exam questions for other engineering courses on subjects like control systems, power plants, and nuclear power. The questions generally provide relevant context and ask students to define terms, explain concepts, calculate values, or discuss strategies related to the various operations, engineering, and management topics.
The document provides information about an examination for Operations Management. It includes 10 questions across two parts (A and B) assessing various topics related to operations management. Part A questions cover topics like defining operation management, service vs goods production differences, decision making frameworks, capacity analysis, forecasting methods, breakeven analysis and aggregate planning models. Part B questions assess topics such as inventory management, manufacturing models, supply chain components, and capacity planning strategies. The document provides context and questions for an exam, assessing students' understanding of key operations management concepts.
GEOMETRIA ESPACIAL - POLIEDROS E CORPOS REDONDOS - PROF TARCÍSIO - www.profta...Tarcísio Filho
This document discusses geometric solids including polyhedra, prisms, pyramids, cylinders, cones, and their properties. It states Euler's formula for convex polyhedra that the number of vertices plus the number of faces equals the number of edges plus two. Formulas are provided for calculating the volume of prisms, pyramids, parallelepipeds, cylinders, cones, and converting between units of volume like cubic meters, liters and cubic centimeters.
This document contains solutions to multiple questions about calculating geometric properties of pyramids and tetrahedrons. It provides step-by-step working to determine measures like base area, lateral area, height, volume, and edge length given various known values for regular pyramids and tetrahedrons.
This document contains 13 math and physics problems from a Brazilian university entrance exam (Unicamp 2012). The problems cover a range of topics including geometry, trigonometry, matrices, linear systems, probability, functions, and more. For each problem, the solutions are provided in mathematical notation or as numerical answers within the document.
This document contains 13 math problems related to geometry, algebra, and other topics. Some key details:
- Problem 1 involves finding parameters of linear functions relating shoe size and length for Brazil and the US.
- Problem 2 analyzes data from Felix Baumgartner's skydive record, calculating velocity at a given time and when he broke the sound barrier.
- Problem 3 involves matrix multiplication and finding the value of a parameter for a system of equations to have a solution.
- Problems 4-6 cover marketing discounts on course enrollments, volume calculations for a pool with dimensions in geometric progression, and nutrient content relationships in fertilizers.
- Later problems analyze triangles, polynomials,
The document describes a linear programming problem to minimize costs for a pipe manufacturing company over 7 months. It provides production capacities, costs, demand forecasts, and inventory holding costs. The assistant formulates the LP with decision variables for regular and overtime production and inventory levels. The objective is to minimize total costs of production, inventory holding and meeting demand over the 7 months. The LP is set up and solved in a spreadsheet, finding the optimal solution that meets all constraints with a total minimum cost of $558,250.
This document contains several multi-part calculus problems involving estimating areas under curves using Riemann sums with rectangles. The problems ask the student to:
- Estimate areas under graphs using left, right, and midpoint Riemann sums with varying numbers of rectangles
- Interpret Riemann sums as approximations of definite integrals involving the area under a curve
- Evaluate definite integrals using properties such as interpreting them in terms of areas under curves
The document appears to contain exam questions for an Operations Management course. It includes questions related to topics like linear trend analysis, capacity planning, aggregate planning, inventory management, MRP, and supply chain management. It also contains exam questions for other engineering courses on subjects like control systems, power plants, and nuclear power. The questions generally provide relevant context and ask students to define terms, explain concepts, calculate values, or discuss strategies related to the various operations, engineering, and management topics.
The document provides information about an examination for Operations Management. It includes 10 questions across two parts (A and B) assessing various topics related to operations management. Part A questions cover topics like defining operation management, service vs goods production differences, decision making frameworks, capacity analysis, forecasting methods, breakeven analysis and aggregate planning models. Part B questions assess topics such as inventory management, manufacturing models, supply chain components, and capacity planning strategies. The document provides context and questions for an exam, assessing students' understanding of key operations management concepts.
This document contains 8 questions regarding mathematics and physics problems. Some key details:
- Question 1 involves probabilities of outcomes when rolling dice in a board game.
- Question 2 involves calculating areas and volumes of geometric shapes given side lengths.
- Question 3 analyzes a decay curve for a radioactive isotope to determine initial amount, half-life, and other values.
- Question 4 requires calculating amounts paid to workers based on an original contract amount and number of workers.
- Question 5 uses a diagram of a cable car to calculate distances and times given information about slope and velocities.
The document continues with additional geometry, algebra, and physics problems through Question 8. It provides illustrations to supplement the written problems and
This document presents the process for designing and implementing a 4-to-15 bit decoder circuit to display a 9-letter word on a 15-segment display. Karnaugh maps are used to simplify the logic expressions for each display segment. A truth table is constructed showing the logic values for each segment corresponding to the input codes needed to display the word "IMPOSTURA". Don't care conditions are applied to simplify the implementation.
Developing barcode scan system of a small-scaled reverse vending machine to s...TELKOMNIKA JOURNAL
Reduce, Reuse, and Recycle is a campaign which aims to reduce the production of waste. Industry used plastic bottle and cans to store the beverage. A research was done by University of Georgia, United States and was published by Wall Street Journal stated that Indonesia is the second predicate country which produced and mismanaged plastic waste in the world. This condition shoud be overcome and this research project was intended to develop reverse vending machine (RVM) to sorting waste of beverage containers either plastic bottles or cans as a campaign to reduce the production of waste. This RVM machine uses barcode scanning as the sorting system to determine whether the plastic bottle or can could be recycled or not. In order to check the weight of the beverage container, a load cell sensor is used to check whether the beverage container is empty or not. The machine will receive the container from the conveyor station, check the weight, and finally transfer it to the sorting station. The container will be sorted as cans or plastic bottle by the aid of barcode scanning and compare it to database. Furthermore, the plastic bottle will be sorted as clear or colored plastic bottle. Unrecyclable plastic or can container or any unemptied container will be classified as rejected container and be returned to the user through the outlet passage. The performance testing was done with 12 different types of plastic bottle and can and 10 samples for each type, so there were total 120 items tested and the result showed that the success rate was 94% while the processing time was varying in between 8 to 13 seconds.
1) The document describes the design of a compensation filter for a Generalized Comb Filter (GCF) using a Maximally-Flat minimization technique.
2) The coefficients of the proposed compensation filter are obtained by solving two linear equations to minimize passband droop.
3) The compensation filter operates at a lower rate than the GCF and significantly reduces passband droop when cascaded with the GCF.
The document provides information about different types of scales used for measurement and their construction. It discusses plain scales, which measure up to one decimal place, diagonal scales, which measure up to two decimals, and Vernier scales. Examples are given for constructing each type of scale along with sample measurement problems. Comparative scales are also introduced, which use the same representative fraction but graduate different units, like miles and kilometers. Step-by-step instructions teach how to determine the representative fraction and layout the scales according to the given measurements.
This document contains a summary of an engineering mathematics exam with questions covering various topics including:
1) Solving differential equations using Taylor series, Runge-Kutta, and Picard's methods.
2) Computing values for functions that satisfy given differential equations using Runge-Kutta and Milne's methods.
3) Analyzing functions in complex plane including Cauchy-Riemann equations and conformal mappings.
4) Solving problems involving Legendre polynomials, addition theorems of probability, and Poisson and normal distributions.
5) Testing hypotheses using statistical methods and fitting distributions to data.
The document discusses optimizing the dimensions of a box made from a 4m by 4m sheet of plastic to maximize its volume, and then optimizing the number of holes in the box to maximize oxygen intake and minimize carbon dioxide intake.
To maximize volume, the squares cut from the box corners should be 2/3m by 2/3m, giving a maximum volume of 4.7407m3.
To optimize gas rates, the number of holes was modeled with accumulation functions. Taking derivatives and finding critical points indicated 20 holes maximizes oxygen intake and minimizes carbon dioxide, ensuring proper ventilation for animals inside.
This document provides instructions for a computing engineering laboratory assignment involving root finding methods in MATLAB. It consists of 9 tasks testing skills with false position, Newton-Raphson, secant, and modified secant methods. Students are asked to write M-files to locate roots of equations describing physical systems like bungee jumping, chemical reactions, and tank volumes. They must analyze solutions, compare methods, and debug provided code. The tasks involve both numerical techniques and plotting/graphical analysis skills relevant to engineering applications.
The document contains 20 multiple choice questions about functions. Each question provides context about a function or functions, such as their definitions, graphs, or properties. The questions then ask the examinee to determine properties of the functions or choose the best representation of a function based on the information provided.
This document contains 10 multi-part questions related to mathematics. The questions cover topics such as functions, probability, geometry, and trigonometry. For example, question 1 involves calculating values of functions, finding where two functions are equal, and sketching their graphs. Question 4 analyzes the distances traveled by two planes flying routes between cities.
The document discusses different types of scales used for measurement and their construction. It describes plain scales which can measure up to a single decimal place, diagonal scales which can measure up to two decimals, and Vernier scales which also measure up to two decimals. It provides examples of problems and step-by-step solutions for constructing each type of scale. Comparative scales that measure the same distance in different units are also discussed. Formulas for calculating representative factors and scale lengths are presented.
The document contains advice from Dr. APJ Abdul Kalam about achieving success. It states that to shine brightly like the sun, one must be willing to burn brightly by working hard. It then quotes Abraham Lincoln saying that to accomplish a big task, it is important to properly prepare in advance.
This document discusses combinational circuits and their components. It begins by defining combinational circuits as circuits whose outputs only depend on the current inputs, not previous states. It then discusses Karnaugh maps, which are used to simplify Boolean expressions through grouping variables. Various types of combinational components are covered, including adders, subtractors, and their half and full versions. Finally, it provides the procedures for designing, analyzing, and obtaining truth tables from combinational circuits.
This document contains exam questions from multiple subjects including Engineering Mathematics, Material Science and Metallurgy, Applied Thermodynamics, and Production Technology and Tool Engineering. The questions cover a wide range of topics testing knowledge of calculus, differential equations, material properties, phase diagrams, thermodynamic cycles, refrigeration, and mechanisms. Students are instructed to answer 5 full questions by selecting at least 2 questions from each part of the exam.
1) The document contains 6 questions regarding matrices, geometry, trigonometry, and statistics.
2) The first question involves calculating the product of two matrices and solving a linear system.
3) The second question determines the number of vertices and edges of a polyhedron given its dimensions, and calculates its volume.
The document contains 12 math problems from a Brazilian university entrance exam (Unicamp 2014). Some key details:
- Problem 1 involves finding the 6th term of a harmonic progression and a property of harmonic progressions.
- Problem 2 concerns quadratic functions of the form f(x) = ax^2 + bx and their graphs.
- Problem 3 deals with modeling plant growth over time using logarithmic and composite functions.
- Problem 4 is about a water bill pricing scheme and sketching the associated cost function.
- The remaining problems cover topics like matrices, probability, geometry, polynomials, statistics, and consumer preferences for pizza types.
This document presents a multi-part math problem involving a polygon with sides of decreasing length forming an arithmetic progression. It provides information about the polygon and asks the reader to analyze several propositions related to distances traveled by a formic along the polygon's path. It then asks the reader to identify which of the propositions are true.
This document discusses Latin square designs, which are experimental designs used to study the effects of multiple factors. A Latin square design has the same number of treatments, rows, and columns, with each treatment occurring once in each row and column. This allows researchers to study the effects of treatments, rows, and columns while controlling for interactions between them. The document provides examples of 3x3 and 4x4 Latin squares and explains how to analyze the results using ANOVA.
· 8.6 A large laboratory has four types of devices used to determi.docxoswald1horne84988
· 8.6 A large laboratory has four types of devices used to determine the pH of soil samples. The laboratory wants to determine whether there are differences in the average readings given by these devices. The lab uses 24 soil samples having known pH in the study, and randomly assigns six of the samples to each device. The soil samples are tested and the response recorded is the difference between the pH reading of the device and the known pH of the soil. These values, along with summary statistics, are given in the following table
Devise
Sample
Response
A
1
-0.307
A
2
-0.294
A
3
0.079
A
4
0.019
A
5
-0.136
A
6
-0.324
B
1
-0.176
B
2
0.125
B
3
-0.013
B
4
0.082
B
5
0.091
B
6
0.459
C
1
0.137
C
2
-0.063
C
3
0.24
C
4
-0.05
C
5
0.318
C
6
0.154
D
1
-0.042
D
2
0.69
D
3
0.201
D
4
0.166
D
5
0.219
D
6
0.407
a. Based on your intuition, is there evidence to indicate any difference among the mean differences in pH readings for the four devices?
b. Run an analysis of variance to confirm or reject your conclusion of part (a). Use a = .05
c. Compute the p-value of the F test in part (b).
d. What conditions must be satisfied for your analysis in parts (b) and (c) to be valid?
e. Suppose the 24 soil samples have widely different pH values. What problems may occur by simply randomly assigning the soil samples to the different devices?
· 8.7 - It is conjectured that when fields are overgrazed by cattle there will be a substantial reduction in the available grass during the subsequent grazing season due to the compaction of the soil. A horticulturist at the state agricultural experiment station designs a study to evaluate the conjecture. Twenty-one plots of land of nearly the same soil texture and suitable for grazing are selected for the study. Three grazing regimens selected for evaluation are randomly assigned to 7 plots each. After the 21 plots are subjected to the grazing regimens for four months, the researcher randomly selects 10 soil cores from each plot and measures the bulk density (g/cm3) in each soil core. The mean soil density of the 10 cores from each plot is given in the following table.
1
2
3
5
19
25
17
10
15
12
9
12
10
7
9
4
5
8
a. Do the grazing regimens appear to yield different degrees of effect on the amount of compacting in the soil? Justify your answer using an α = .05 test.
b. Provide the level of significance of your test.
c. Do any of the conditions necessary for conducting your test appear to be violated? Justify your answer.
8.18 – Refer to Example 7.8. The consumer testing agency was interested in evaluating whether there was a difference in the mean percentage increase in mpg of the three additives. In Example 7.9, we showed that the data did not appear to have a normal distribution.
a. Apply the natural logarithm transformation to the data. Do the conditions for applying the AOV F test appear to hold for the transformed data?
b. Test for a difference in the means of the three additives using a = .05..
O documento apresenta 17 questões do Exame Nacional do Ensino Médio (ENEM) sobre diversos assuntos como: corrida de regularidade, monitoramento de substâncias no sangue, crescimento populacional de médicos, modelos predador-presa, crescimento exponencial de bactérias, ativação de rádio automotivo por código secreto e frequências de transmissão de aparelhos sem fio. As questões envolvem cálculos, interpretação de gráficos e tabelas e raciocínio sobre probabilidades.
O documento apresenta três questões sobre um teste realizado com um novo modelo de carro. A primeira questão descreve que 50 litros de combustível foram colocados no tanque do carro e ele foi dirigido em uma pista de testes até o combustível acabar. A segunda questão fornece um gráfico que relaciona a quantidade de combustível no tanque com a distância percorrida. A terceira questão pede a expressão algébrica que relaciona essas duas grandezas.
This document contains 8 questions regarding mathematics and physics problems. Some key details:
- Question 1 involves probabilities of outcomes when rolling dice in a board game.
- Question 2 involves calculating areas and volumes of geometric shapes given side lengths.
- Question 3 analyzes a decay curve for a radioactive isotope to determine initial amount, half-life, and other values.
- Question 4 requires calculating amounts paid to workers based on an original contract amount and number of workers.
- Question 5 uses a diagram of a cable car to calculate distances and times given information about slope and velocities.
The document continues with additional geometry, algebra, and physics problems through Question 8. It provides illustrations to supplement the written problems and
This document presents the process for designing and implementing a 4-to-15 bit decoder circuit to display a 9-letter word on a 15-segment display. Karnaugh maps are used to simplify the logic expressions for each display segment. A truth table is constructed showing the logic values for each segment corresponding to the input codes needed to display the word "IMPOSTURA". Don't care conditions are applied to simplify the implementation.
Developing barcode scan system of a small-scaled reverse vending machine to s...TELKOMNIKA JOURNAL
Reduce, Reuse, and Recycle is a campaign which aims to reduce the production of waste. Industry used plastic bottle and cans to store the beverage. A research was done by University of Georgia, United States and was published by Wall Street Journal stated that Indonesia is the second predicate country which produced and mismanaged plastic waste in the world. This condition shoud be overcome and this research project was intended to develop reverse vending machine (RVM) to sorting waste of beverage containers either plastic bottles or cans as a campaign to reduce the production of waste. This RVM machine uses barcode scanning as the sorting system to determine whether the plastic bottle or can could be recycled or not. In order to check the weight of the beverage container, a load cell sensor is used to check whether the beverage container is empty or not. The machine will receive the container from the conveyor station, check the weight, and finally transfer it to the sorting station. The container will be sorted as cans or plastic bottle by the aid of barcode scanning and compare it to database. Furthermore, the plastic bottle will be sorted as clear or colored plastic bottle. Unrecyclable plastic or can container or any unemptied container will be classified as rejected container and be returned to the user through the outlet passage. The performance testing was done with 12 different types of plastic bottle and can and 10 samples for each type, so there were total 120 items tested and the result showed that the success rate was 94% while the processing time was varying in between 8 to 13 seconds.
1) The document describes the design of a compensation filter for a Generalized Comb Filter (GCF) using a Maximally-Flat minimization technique.
2) The coefficients of the proposed compensation filter are obtained by solving two linear equations to minimize passband droop.
3) The compensation filter operates at a lower rate than the GCF and significantly reduces passband droop when cascaded with the GCF.
The document provides information about different types of scales used for measurement and their construction. It discusses plain scales, which measure up to one decimal place, diagonal scales, which measure up to two decimals, and Vernier scales. Examples are given for constructing each type of scale along with sample measurement problems. Comparative scales are also introduced, which use the same representative fraction but graduate different units, like miles and kilometers. Step-by-step instructions teach how to determine the representative fraction and layout the scales according to the given measurements.
This document contains a summary of an engineering mathematics exam with questions covering various topics including:
1) Solving differential equations using Taylor series, Runge-Kutta, and Picard's methods.
2) Computing values for functions that satisfy given differential equations using Runge-Kutta and Milne's methods.
3) Analyzing functions in complex plane including Cauchy-Riemann equations and conformal mappings.
4) Solving problems involving Legendre polynomials, addition theorems of probability, and Poisson and normal distributions.
5) Testing hypotheses using statistical methods and fitting distributions to data.
The document discusses optimizing the dimensions of a box made from a 4m by 4m sheet of plastic to maximize its volume, and then optimizing the number of holes in the box to maximize oxygen intake and minimize carbon dioxide intake.
To maximize volume, the squares cut from the box corners should be 2/3m by 2/3m, giving a maximum volume of 4.7407m3.
To optimize gas rates, the number of holes was modeled with accumulation functions. Taking derivatives and finding critical points indicated 20 holes maximizes oxygen intake and minimizes carbon dioxide, ensuring proper ventilation for animals inside.
This document provides instructions for a computing engineering laboratory assignment involving root finding methods in MATLAB. It consists of 9 tasks testing skills with false position, Newton-Raphson, secant, and modified secant methods. Students are asked to write M-files to locate roots of equations describing physical systems like bungee jumping, chemical reactions, and tank volumes. They must analyze solutions, compare methods, and debug provided code. The tasks involve both numerical techniques and plotting/graphical analysis skills relevant to engineering applications.
The document contains 20 multiple choice questions about functions. Each question provides context about a function or functions, such as their definitions, graphs, or properties. The questions then ask the examinee to determine properties of the functions or choose the best representation of a function based on the information provided.
This document contains 10 multi-part questions related to mathematics. The questions cover topics such as functions, probability, geometry, and trigonometry. For example, question 1 involves calculating values of functions, finding where two functions are equal, and sketching their graphs. Question 4 analyzes the distances traveled by two planes flying routes between cities.
The document discusses different types of scales used for measurement and their construction. It describes plain scales which can measure up to a single decimal place, diagonal scales which can measure up to two decimals, and Vernier scales which also measure up to two decimals. It provides examples of problems and step-by-step solutions for constructing each type of scale. Comparative scales that measure the same distance in different units are also discussed. Formulas for calculating representative factors and scale lengths are presented.
The document contains advice from Dr. APJ Abdul Kalam about achieving success. It states that to shine brightly like the sun, one must be willing to burn brightly by working hard. It then quotes Abraham Lincoln saying that to accomplish a big task, it is important to properly prepare in advance.
This document discusses combinational circuits and their components. It begins by defining combinational circuits as circuits whose outputs only depend on the current inputs, not previous states. It then discusses Karnaugh maps, which are used to simplify Boolean expressions through grouping variables. Various types of combinational components are covered, including adders, subtractors, and their half and full versions. Finally, it provides the procedures for designing, analyzing, and obtaining truth tables from combinational circuits.
This document contains exam questions from multiple subjects including Engineering Mathematics, Material Science and Metallurgy, Applied Thermodynamics, and Production Technology and Tool Engineering. The questions cover a wide range of topics testing knowledge of calculus, differential equations, material properties, phase diagrams, thermodynamic cycles, refrigeration, and mechanisms. Students are instructed to answer 5 full questions by selecting at least 2 questions from each part of the exam.
1) The document contains 6 questions regarding matrices, geometry, trigonometry, and statistics.
2) The first question involves calculating the product of two matrices and solving a linear system.
3) The second question determines the number of vertices and edges of a polyhedron given its dimensions, and calculates its volume.
The document contains 12 math problems from a Brazilian university entrance exam (Unicamp 2014). Some key details:
- Problem 1 involves finding the 6th term of a harmonic progression and a property of harmonic progressions.
- Problem 2 concerns quadratic functions of the form f(x) = ax^2 + bx and their graphs.
- Problem 3 deals with modeling plant growth over time using logarithmic and composite functions.
- Problem 4 is about a water bill pricing scheme and sketching the associated cost function.
- The remaining problems cover topics like matrices, probability, geometry, polynomials, statistics, and consumer preferences for pizza types.
This document presents a multi-part math problem involving a polygon with sides of decreasing length forming an arithmetic progression. It provides information about the polygon and asks the reader to analyze several propositions related to distances traveled by a formic along the polygon's path. It then asks the reader to identify which of the propositions are true.
This document discusses Latin square designs, which are experimental designs used to study the effects of multiple factors. A Latin square design has the same number of treatments, rows, and columns, with each treatment occurring once in each row and column. This allows researchers to study the effects of treatments, rows, and columns while controlling for interactions between them. The document provides examples of 3x3 and 4x4 Latin squares and explains how to analyze the results using ANOVA.
· 8.6 A large laboratory has four types of devices used to determi.docxoswald1horne84988
· 8.6 A large laboratory has four types of devices used to determine the pH of soil samples. The laboratory wants to determine whether there are differences in the average readings given by these devices. The lab uses 24 soil samples having known pH in the study, and randomly assigns six of the samples to each device. The soil samples are tested and the response recorded is the difference between the pH reading of the device and the known pH of the soil. These values, along with summary statistics, are given in the following table
Devise
Sample
Response
A
1
-0.307
A
2
-0.294
A
3
0.079
A
4
0.019
A
5
-0.136
A
6
-0.324
B
1
-0.176
B
2
0.125
B
3
-0.013
B
4
0.082
B
5
0.091
B
6
0.459
C
1
0.137
C
2
-0.063
C
3
0.24
C
4
-0.05
C
5
0.318
C
6
0.154
D
1
-0.042
D
2
0.69
D
3
0.201
D
4
0.166
D
5
0.219
D
6
0.407
a. Based on your intuition, is there evidence to indicate any difference among the mean differences in pH readings for the four devices?
b. Run an analysis of variance to confirm or reject your conclusion of part (a). Use a = .05
c. Compute the p-value of the F test in part (b).
d. What conditions must be satisfied for your analysis in parts (b) and (c) to be valid?
e. Suppose the 24 soil samples have widely different pH values. What problems may occur by simply randomly assigning the soil samples to the different devices?
· 8.7 - It is conjectured that when fields are overgrazed by cattle there will be a substantial reduction in the available grass during the subsequent grazing season due to the compaction of the soil. A horticulturist at the state agricultural experiment station designs a study to evaluate the conjecture. Twenty-one plots of land of nearly the same soil texture and suitable for grazing are selected for the study. Three grazing regimens selected for evaluation are randomly assigned to 7 plots each. After the 21 plots are subjected to the grazing regimens for four months, the researcher randomly selects 10 soil cores from each plot and measures the bulk density (g/cm3) in each soil core. The mean soil density of the 10 cores from each plot is given in the following table.
1
2
3
5
19
25
17
10
15
12
9
12
10
7
9
4
5
8
a. Do the grazing regimens appear to yield different degrees of effect on the amount of compacting in the soil? Justify your answer using an α = .05 test.
b. Provide the level of significance of your test.
c. Do any of the conditions necessary for conducting your test appear to be violated? Justify your answer.
8.18 – Refer to Example 7.8. The consumer testing agency was interested in evaluating whether there was a difference in the mean percentage increase in mpg of the three additives. In Example 7.9, we showed that the data did not appear to have a normal distribution.
a. Apply the natural logarithm transformation to the data. Do the conditions for applying the AOV F test appear to hold for the transformed data?
b. Test for a difference in the means of the three additives using a = .05..
O documento apresenta 17 questões do Exame Nacional do Ensino Médio (ENEM) sobre diversos assuntos como: corrida de regularidade, monitoramento de substâncias no sangue, crescimento populacional de médicos, modelos predador-presa, crescimento exponencial de bactérias, ativação de rádio automotivo por código secreto e frequências de transmissão de aparelhos sem fio. As questões envolvem cálculos, interpretação de gráficos e tabelas e raciocínio sobre probabilidades.
O documento apresenta três questões sobre um teste realizado com um novo modelo de carro. A primeira questão descreve que 50 litros de combustível foram colocados no tanque do carro e ele foi dirigido em uma pista de testes até o combustível acabar. A segunda questão fornece um gráfico que relaciona a quantidade de combustível no tanque com a distância percorrida. A terceira questão pede a expressão algébrica que relaciona essas duas grandezas.
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Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
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Unicamp 2011 - aberta
1. UNICAMP 2011 - ABERTA
1
01. (Unicamp 2011) Uma grande preocupação atual é a poluição, particularmente aquela emitida pelo crescente número
de veículos automotores circulando no planeta. Ao funcionar, o motor de um carro queima combustível, gerando CO2,
além de outros gases e resíduos poluentes.
a) Considere um carro que, trafegando a uma determinada velocidade constante, emite 2,7 kg de CO2 a cada litro de
combustível que consome. Nesse caso, quantos quilogramas de CO2 ele emitiu em uma viagem de 378 km, sabendo
que fez 13,5 km por litro de gasolina nesse percurso?
b) A quantidade de CO2 produzida por quilômetro percorrido depende da velocidade do carro. Suponha que, para o carro
em questão, a função c(v) que fornece a quantidade de CO2, em g/km, com relação à velocidade v, para velocidades
entre 20 e 40 km/h, seja dada por um polinômio do segundo grau. Determine esse polinômio com base nos dados da
tabela abaixo.
Velocidade
(km/h)
Emissão de
CO2 (g/km)
20 400
30 250
40 200
2. UNICAMP 2011 - ABERTA
2
02. (Unicamp 2011) Uma placa retangular de madeira, com dimensões 10 x 20 cm, deve ser recortada conforme mostra
a figura abaixo. Depois de efetuado o recorte, as coordenadas do centro de gravidade da placa (em função da medida w)
serão dadas por ( ) ( )
( )
2
CG CG
400 w 20
400 15w
x w e y w ,
80 2w 80 2w
+ −
−
= =
− −
em que xCG é a coordenada horizontal e yCG é a
coordenada vertical do centro de gravidade, tomando o canto inferior esquerdo como a origem.
a) Defina A(w), a função que fornece a área da placa recortada em relação a w. Determine as coordenadas do centro de
gravidade quando A(w) = 150 cm2
.
b) Determine uma expressão geral para w(xCG), a função que fornece a dimensão w em relação à coordenada xCG, e calcule
yCG quando xCG = 7/2 cm.
3. UNICAMP 2011 - ABERTA
3
03. (Unicamp 2011) Define-se como ponto fixo de uma função f o número real x tal que f(x) = x. Seja dada a função
( )
1
f x 1.
1
x
2
= +
+
a) Calcule os pontos fixos de f(x).
b) Na região quadriculada abaixo, represente o gráfico da função f(x) e o gráfico de g(x) = x, indicando explicitamente os
pontos calculados no item (a).
4. UNICAMP 2011 - ABERTA
4
04. (Unicamp 2011) No mês corrente, uma empresa registrou uma receita de R$ 600 mil e uma despesa de R$ 800 mil. A
empresa estuda, agora, alternativas para voltar a ter lucro.
a) Primeiramente, assuma que a receita não variará nos próximos meses, e que as despesas serão reduzidas,
mensalmente, em exatos R$ 45 mil. Escreva a expressão do termo geral da progressão aritmética que fornece o valor
da despesa em função de n, o número de meses transcorridos, considerando como mês inicial o corrente. Calcule em
quantos meses a despesa será menor que a receita.
b) Suponha, agora, que a receita aumentará 10% a cada mês, ou seja, que a receita obedecerá a uma progressão
geométrica (PG) de razão 11/10. Nesse caso, escreva a expressão do termo geral dessa PG em função de n, o número
de meses transcorridos, considerando como mês inicial o corrente. Determine qual será a receita acumulada em 10
meses. Se necessário, use 1,12
= 1,21; 1,13 ≈ 1,33 e 1,15
≈ 1,61.
5. UNICAMP 2011 - ABERTA
5
05. (Unicamp 2011) O perfil lipídico é um exame médico que avalia a dosagem dos quatro tipos principais de gorduras
(lipídios) no sangue: colesterol total (CT), colesterol HDL (conhecido como “bom colesterol”), colesterol LDL (o “mau
colesterol”) e triglicérides (TG). Os valores desses quatro indicadores estão relacionados pela fórmula de Friedewald: CT
= LDL + HDL + TG/5. A tabela abaixo mostra os valores normais dos lipídios sanguíneos para um adulto, segundo o
laboratório SangueBom.
Indicador Valores normais
CT Até 200 mg/dl
LDL Até 130 mg/dl
HDL Entre 40 e 60 mg/dl
TG Até 150 mg/dl
a) O perfil lipídico de Pedro revelou que sua dosagem de colesterol total era igual a 198 mg/dl, e que a de triglicérides era
igual a 130 mg/dl. Sabendo que todos os seus indicadores estavam normais, qual o intervalo possível para o seu nível
de LDL?
b) Acidentalmente, o laboratório SangueBom deixou de etiquetar as amostras de sangue de cinco pessoas. Determine de
quantos modos diferentes seria possível relacionar essas amostras às pessoas, sem qualquer informação adicional. Na
tentativa de evitar que todos os exames fossem refeitos, o laboratório analisou o tipo sanguíneo das amostras, e
detectou que três delas eram de sangue O+
e as duas restantes eram de sangue A+
. Nesse caso, supondo que cada
pessoa indicasse seu tipo sanguíneo, de quantas maneiras diferentes seria possível relacionar as amostras de sangue às
pessoas?
6. UNICAMP 2011 - ABERTA
6
06. (Unicamp 2011) Um grupo de pessoas resolveu encomendar cachorros-quentes para o lanche. Entretanto, a
lanchonete enviou apenas 15 sachês de mostarda e 17 de catchup, o que não é suficiente para que cada membro do grupo
receba um sachê de cada molho. Desta forma, podemos considerar que há três subgrupos: um formado pelas pessoas
que ganharão apenas um sachê de mostarda, outro por aquelas que ganharão apenas um sachê de catchup, e o terceiro
pelas que receberão um sachê de cada molho.
a) Sabendo que, para que cada pessoa ganhe ao menos um sachê, 14 delas devem receber apenas um dos molhos,
determine o número de pessoas do grupo.
b) Felizmente, somente 19 pessoas desse grupo quiseram usar os molhos. Assim, os sachês serão distribuídos
aleatoriamente entre essas pessoas, de modo que cada uma receba ao menos um sachê. Nesse caso, determine a
probabilidade de que uma pessoa receba um sachê de cada molho.
7. UNICAMP 2011 - ABERTA
7
07. (Unicamp 2011) A caixa de um produto longa vida é produzida como mostra a sequência de figuras abaixo. A folha de
papel da figura 1 é emendada na vertical, resultando no cilindro da figura 2. Em seguida, a caixa toma o formato desejado,
e são feitas novas emendas, uma no topo e outra no fundo da caixa, como mostra a figura 3.
Finalmente, as abas da caixa são dobradas, gerando o produto final, exibido na figura 4. Para simplificar, consideramos as
emendas como linhas, ou seja, desprezamos a superposição do papel.
a) Se a caixa final tem 20 cm de altura, 7,2 cm de largura e 7 cm de profundidade, determine as dimensões x e y da menor
folha que pode ser usada na sua produção.
b) Supondo, agora, que uma caixa tenha seção horizontal quadrada (ou seja, que sua profundidade seja igual a sua
largura), escreva a fórmula do volume da caixa final em função das dimensões x e y da folha usada em sua produção.
8. UNICAMP 2011 - ABERTA
8
08. (Unicamp 2011) Considere uma gangorra composta por uma tábua de 240 cm de comprimento, equilibrada, em seu
ponto central, sobre uma estrutura na forma de um prisma cuja base é um triângulo equilátero de altura igual a 60 cm,
como mostra a figura. Suponha que a gangorra esteja instalada sobre um piso perfeitamente horizontal.
a) Desprezando a espessura da tábua e supondo que a extremidade direita da gangorra está a 20 cm do chão, determine
a altura da extremidade esquerda.
b) Supondo, agora, que a extremidade direita da tábua toca o chão, determine o ângulo α formado entre a tábua e a
lateral mais próxima do prisma, como mostra a vista lateral da gangorra, exibida abaixo.
9. UNICAMP 2011 - ABERTA
9
09. (Unicamp 2011) Suponha um trecho retilíneo de estrada, com um posto rodoviário no quilômetro zero. Suponha,
também, que uma estação da guarda florestal esteja localizada a 40 km do posto rodoviário, em linha reta, e a 24 km de
distância da estrada, conforme a figura a seguir.
a) Duas antenas de rádio atendem a região. A área de cobertura da primeira antena, localizada na estação da guarda
florestal, corresponde a um círculo que tangencia a estrada. O alcance da segunda, instalada no posto rodoviário,
atinge, sem ultrapassar, o ponto da estrada que está mais próximo da estação da guarda florestal. Explicite as duas
desigualdades que definem as regiões circulares cobertas por essas antenas, e esboce essas regiões no gráfico abaixo,
identificando a área coberta simultaneamente pelas duas antenas.
b) Pretende-se substituir as antenas atuais por uma única antena, mais potente, a ser instalada em um ponto da estrada,
de modo que as distâncias dessa antena ao posto rodoviário e à estação da guarda florestal sejam iguais. Determine
em que quilômetro da estrada essa antena deve ser instalada.
10. UNICAMP 2011 - ABERTA
10
10. (Unicamp 2011) Para certo modelo de computadores produzidos por uma empresa, o percentual dos processadores
que apresentam falhas após T anos de uso é dado pela seguinte função: P(T) = 100(1 − 2−0,1T
).
a) Em quanto tempo 75% dos processadores de um lote desse modelo de computadores terão apresentado falhas?
b) Os novos computadores dessa empresa vêm com um processador menos suscetível a falhas. Para o modelo mais
recente, embora o percentual de processadores que apresentam falhas também seja dado por uma função na forma
( )
cT
Q(T) 100 1 2
= − , o percentual de processadores defeituosos após 10 anos de uso equivale a 1/4 do valor observado,
nesse mesmo período, para o modelo antigo (ou seja, o valor obtido empregando-se a função P(T) acima). Determine,
nesse caso, o valor da constante c. Se necessário, utilize log2(7) ≈ 2,81.
11. UNICAMP 2011 - ABERTA
11
11. (Unicamp 2011) Uma empresa imprime cerca de 12000 páginas de relatórios por mês, usando uma impressora jato
de tinta colorida. Excluindo a amortização do valor da impressora, o custo de impressão depende do preço do papel e dos
cartuchos de tinta. A resma de papel (500 folhas) custa R$ 10,00. Já o preço e o rendimento aproximado dos cartuchos de
tinta da impressora são dados na tabela abaixo.
Cartucho
(cor/modelo)
Preço
(R$)
Rendimento
(páginas)
Preto BR R$ 90,00 810
Colorido BR R$ 120,00 600
Preto AR R$150,00 2400
Colorido AR R$ 270,00 1200
a) Qual cartucho preto e qual cartucho colorido a empresa deveria usar para o custo por página ser o menor possível?
b) Por razões logísticas, a empresa usa apenas cartuchos de alto rendimento (os modelos do tipo AR) e imprime apenas
em um lado do papel (ou seja, não há impressão no verso das folhas). Se 20% das páginas dos relatórios são coloridas,
quanto a empresa gasta mensalmente com impressão, excluindo a amortização da impressora? Suponha, para
simplificar, que as páginas coloridas consomem apenas o cartucho colorido.
12. UNICAMP 2011 - ABERTA
12
12. (Unicamp 2011) Um engenheiro precisa interligar de forma suave dois trechos paralelos de uma estrada, como mostra
a figura abaixo. Para conectar as faixas centrais da estrada, cujos eixos distam d metros um do outro, o engenheiro planeja
usar um segmento de reta de comprimento x e dois arcos de circunferência de raio r e ângulo interno .
α
a) Se o engenheiro adotar 45 ,
α
= ° o segmento central medirá x d 2 2r( 2 1).
= − − Nesse caso, supondo que d 72 m,
= e
r 36 m,
= determine a distância y entre as extremidades dos trechos a serem interligados.
b) Supondo, agora, que 60 ,
α
= ° r 36 m
= e d 90 m,
= determine o valor de x.
13. UNICAMP 2011 - ABERTA
13
QUESTÃO 1
2
1
c(v) v 40v 1000.
2
= − +
QUESTÃO 2
a) 𝑥𝑥CG(10) =
25
6
𝑐𝑐𝑐𝑐 e 𝑦𝑦CG(10) =
25
3
𝑐𝑐𝑐𝑐
b) 𝑦𝑦CG(15) =
17
2
𝑐𝑐𝑐𝑐
QUESTÃO 3
a) 𝑥𝑥 = −1 ou 𝑥𝑥 =
3
2
b) ( 1, 1)
− − e
3 3
, ,
2 2
cujas abscissas são os pontos fixos
de f.
QUESTÃO 4
a) após 6 1 5
− = meses a despesa será menor do que a
receita.
b)
10 5 2
1,1 1 (1,1 ) 1
600000 600000
1,1 1 0,1
6000000 (2,5921 1)
R$ 9.552.600,00.
− −
⋅ = ⋅
−
≅ ⋅ −
=
QUESTÃO 5
a) [112,130].
b) 6 2 12.
⋅ =
QUESTÃO 6
a) 14 9 23
+ = pessoas.
b)
13
.
19
QUESTÃO 7
a) 𝑥𝑥 = 28,4𝑐𝑐𝑐𝑐
b)
𝑥𝑥2
16
⋅ �𝑦𝑦 −
𝑥𝑥
4
� 𝑐𝑐𝑐𝑐³
QUESTÃO 8
a) 100cm.
b) 𝛼𝛼 = 30°
QUESTÃO 9
a)
b) 𝑥𝑥 = 25 𝑘𝑘𝑘𝑘
QUESTÃO 10
a) 𝑇𝑇 = 20 anos
b) 𝑐𝑐 = −0,019
QUESTÃO 11
a) O cartucho Colorido BR é o que apresenta menor
custo.
b) 𝑅𝑅$ 1.380,00
QUESTÃO 12
a) 72 √2 m
b) 36 √3