Chapter 15 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Fluid Pressure in a U-Tube A U-tube is filled with water, and the two arms are capped. The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube. Part A A one-inch depth of sand is poured onto the cap on each arm. After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Pressure in the Ocean The pressure at 10 below the surface of the ocean is about 2.00×105 . Part A higher lower the same height m Pa Which of the following statements is true? You did not open hints for this part. ANSWER: Part B Now consider the pressure 20 below the surface of the ocean. Which of the following statements is true? You did not open hints for this part. ANSWER: Relating Pressure and Height in a Container Learning Goal: To understand the derivation of the law relating height and pressure in a container. The weight of a column of seawater 1 in cross section and 10 high is about 2.00×105 . The weight of a column of seawater 1 in cross section and 10 high plus the weight of a column of air with the same cross section extending up to the top of the atmosphere is about 2.00×105 . The weight of 1 of seawater at 10 below the surface of the ocean is about 2.00×105 . The density of seawater is about 2.00×105 times the density of air at sea level. m2 m N m2 m N m3 m N m The pressure is twice that at a depth of 10 . The pressure is the same as that at a depth of 10 . The pressure is equal to that at a depth of 10 plus the weight per 1 cross sectional area of a column of seawater 10 high. The pressure is equal to the weight per 1 cross sectional area of a column of seawater 20 high. m m m m2 m m2 m In this problem, you will derive the law relating pressure to height in a container by analyzing a particular system. A container of uniform cross-sectional area is filled with liquid of uniform density . Consider a thin horizontal layer of liquid (thickness ) at a height as measured from the bottom of the container. Let the pressure exerted upward on the bottom of the layer be and the pressure exerted downward on the top be . Assume throughout the problem that the system is in equilibrium (the container has not been recently shaken or moved, etc.). Part A What is , the magnitude of the force exerted upward on the bottom of the liquid? You did not open hints for this part. ANSWER: Part B What is , the magnitude of the force exerted downward on the top of the liquid? A  dy y p p + dp Fup Fup = Fdown You did not open hints for this part. ANSWER: Part C What is the weight of the thin layer of liquid? Express your answer in terms of quantities given in the problem introduction and , the magnitude of the acceleration due to gravity. You did not open hints for this part. ANSWER: Part D Since the liquid is in equilibrium, the net force on the thin layer of liquid is zero. Complete the force equation for the sum of the vertical forces acting on the liquid layer described in the problem introduction. Express your answer in terms of quantities given in the problem introduction and taking upward forces to be positive. You did not open hints for this part. ANSWER: Fdown = wlayer g wlayer = Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). A Submerged Ball A ball of mass and volume is lowered on a string into a fluid of density . Assume that the object would sink to the bottom if it were not supported by the string. Part A  = = i Fy,i mb V f What is the tension in the string when the ball is fully submerged but not touching the bottom, as shown in the figure? Express your answer in terms of any or all of the given quantities and , the magnitude of the acceleration due to gravity. You did not open hints for this part. ANSWER: Archimedes’ Principle Learning Goal: To understand the applications of Archimedes’ principle. Archimedes’ principle is a powerful tool for solving many problems involving equilibrium in fluids. It states the following: When a body is partially or completely submerged in a fluid (either a liquid or a gas), the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body. As a result of the upward Archimedes force (often called the buoyant force), some objects may float in a fluid, and all of them appear to weigh less. This is the familiar phenomenon of buoyancy. Quantitatively, the buoyant force can be found as , where is the force, is the density of the fluid, is the magnitude of the acceleration due to gravity, and is the volume of the displaced fluid. In this problem, you will be asked several qualitative questions that should help you develop a feel for Archimedes’ principle. An object is placed in a fluid and then released. Assume that the object either floats to the surface (settling so that the object is partly above and partly below the fluid surface) or sinks to the bottom. (Note that for Parts A through D, you should assume that the object has settled in equilibrium.) Part A Consider the following statement: The magnitude of the buoyant force is equal to the weight of fluid displaced by the object. Under what circumstances is this statement true? T g T = Fbuoyant = fluidgV Fbuoyant fluid g V You did not open hints for this part. ANSWER: Part B Consider the following statement: The magnitude of the buoyant force is equal to the weight of the amount of fluid that has the same total volume as the object. Under what circumstances is this statement true? You did not open hints for this part. ANSWER: Part C Consider the following statement: The magnitude of the buoyant force equals the weight of the object. Under what circumstances is this statement true? for every object submerged partially or completely in a fluid only for an object that floats only for an object that sinks for no object submerged in a fluid for an object that is partially submerged in a fluid only for an object that floats for an object completely submerged in a fluid for no object partially or completely submerged in a fluid You did not open hints for this part. ANSWER: Part D Consider the following statement: The magnitude of the buoyant force is less than the weight of the object. Under what circumstances is this statement true? ANSWER: Now apply what you know to some more complicated situations. Part E An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a denser liquid. What would you observe? You did not open hints for this part. ANSWER: for every object submerged partially or completely in a fluid for an object that floats only for an object that sinks for no object submerged in a fluid for every object submerged partially or completely in a fluid for an object that floats for an object that sinks for no object submerged in a fluid Part F An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a less dense liquid. What would you observe? You did not open hints for this part. ANSWER: Part G Two objects, T and B, have identical size and shape and have uniform density. They are carefully placed in a container filled with a liquid. Both objects float in equilibrium. Less of object T is submerged than of object B, which floats, fully submerged, closer to the bottom of the container. Which of the following statements is true? ANSWER: The object would sink all the way to the bottom. The object would float submerged more deeply than in the first container. The object would float submerged less deeply than in the first container. More than one of these outcomes is possible. The object would sink all the way to the bottom. The object would float submerged more deeply than in the first container. The object would float submerged less deeply than in the first container. More than one of these outcomes is possible. Object T has a greater density than object B. Object B has a greater density than object T. Both objects have the same density. ± Buoyant Force Conceptual Question A rectangular wooden block of weight floats with exactly one-half of its volume below the waterline. Part A What is the buoyant force acting on the block? You did not open hints for this part. ANSWER: Part B W The buoyant force cannot be determined. 2W W 1 W 2 The density of water is 1.00 . What is the density of the block? You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). g/cm3 2.00 between 1.00 and 2.00 1.00 between 0.50 and 1.00 0.50 The density cannot be determined. g/cm3 g/cm3 g/cm3 g/cm3 g/cm3 Flow Velocity of Blood Conceptual Question Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel. Imagine a healthy artery, with blood flow velocity of and mass per unit volume of . The kinetic energy per unit volume of blood is given by Imagine that plaque has narrowed an artery to one-fifth of its normal cross-sectional area (an 80% blockage). Part A Compared to normal blood flow velocity, , what is the velocity of blood as it passes through this blockage? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C v0 = 0.14 m/s  = 1050 kg/m3 K0 =  . 1 2 v20 v0 80v0 20v0 5v0 v0/5 This question will be shown after you complete previous question(s). For parts D – F imagine that plaque has grown to a 90% blockage. Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). ± Playing with a Water Hose Two children, Ferdinand and Isabella, are playing with a water hose on a sunny summer day. Isabella is holding the hose in her hand 1.0 meters above the ground and is trying to spray Ferdinand, who is standing 10.0 meters away. Part A Will Isabella be able to spray Ferdinand if the water is flowing out of the hose at a constant speed of 3.5 meters per second? Assume that the hose is pointed parallel to the ground and take the magnitude of the acceleration due to gravity to be 9.81 meters per second, per second. You did not open hints for this part. v0 g ANSWER: Part B This question will be shown after you complete previous question(s). Tactics Box 15.2 Finding Whether an Object Floats or Sinks Learning Goal: To practice Tactics Box 15.2 Finding whether an object floats or sinks. If you hold an object underwater and then release it, it can float to the surface, sink, or remain “hanging” in the water, depending on whether the fluid density is larger than, smaller than, or equal to the object’s average density . These conditions are summarized in this Tactics Box. Yes No f avg TACTICS BOX 15.2 Finding whether an object floats or sinks Object sinks Object floats Object has neutral buoyancy An object sinks if it weighs more than the fluid it displaces, that is, if its average density is greater than the density of the fluid: . An object floats on the surface if it weighs less than the fluid it displaces, that is, if its average density is less than the density of the fluid: . An object hangs motionless in the fluid if it weighs exactly the same as the fluid it displaces. It has neutral buoyancy if its average density equals the density of the fluid: . Part A Ice at 0.0 has a density of 917 . A 3.00 ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. What is the density of the oil, ? Express your answer in kilograms per meter cubed to three significant figures. ANSWER: Part B Once the ice cube melts, what happens to the liquid water that it produces? You did not open hints for this part. ANSWER: avg > f avg < f avg = f 'C kg/m3 cm3 oil oil = kg/m3 Part C What happens if some ethyl alcohol of density 790 is poured into the container after the ice cube has melted? ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. The liquid water sinks to the bottom of the container. The liquid water rises to the surface and floats on top of the oil. The liquid water is in static equilibrium at the location where the ice cube was originally placed. kg/m3 A layer of ethyl alcohol forms between the oil and the water. The layer of ethyl alcohol forms at the bottom of the container. The layer of ethyl alcohol forms on the surface.

Chapter 15 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Fluid Pressure in a U-Tube A U-tube is filled with water, and the two arms are capped. The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube. Part A A one-inch depth of sand is poured onto the cap on each arm. After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Pressure in the Ocean The pressure at 10 below the surface of the ocean is about 2.00×105 . Part A higher lower the same height m Pa Which of the following statements is true? You did not open hints for this part. ANSWER: Part B Now consider the pressure 20 below the surface of the ocean. Which of the following statements is true? You did not open hints for this part. ANSWER: Relating Pressure and Height in a Container Learning Goal: To understand the derivation of the law relating height and pressure in a container. The weight of a column of seawater 1 in cross section and 10 high is about 2.00×105 . The weight of a column of seawater 1 in cross section and 10 high plus the weight of a column of air with the same cross section extending up to the top of the atmosphere is about 2.00×105 . The weight of 1 of seawater at 10 below the surface of the ocean is about 2.00×105 . The density of seawater is about 2.00×105 times the density of air at sea level. m2 m N m2 m N m3 m N m The pressure is twice that at a depth of 10 . The pressure is the same as that at a depth of 10 . The pressure is equal to that at a depth of 10 plus the weight per 1 cross sectional area of a column of seawater 10 high. The pressure is equal to the weight per 1 cross sectional area of a column of seawater 20 high. m m m m2 m m2 m In this problem, you will derive the law relating pressure to height in a container by analyzing a particular system. A container of uniform cross-sectional area is filled with liquid of uniform density . Consider a thin horizontal layer of liquid (thickness ) at a height as measured from the bottom of the container. Let the pressure exerted upward on the bottom of the layer be and the pressure exerted downward on the top be . Assume throughout the problem that the system is in equilibrium (the container has not been recently shaken or moved, etc.). Part A What is , the magnitude of the force exerted upward on the bottom of the liquid? You did not open hints for this part. ANSWER: Part B What is , the magnitude of the force exerted downward on the top of the liquid? A  dy y p p + dp Fup Fup = Fdown You did not open hints for this part. ANSWER: Part C What is the weight of the thin layer of liquid? Express your answer in terms of quantities given in the problem introduction and , the magnitude of the acceleration due to gravity. You did not open hints for this part. ANSWER: Part D Since the liquid is in equilibrium, the net force on the thin layer of liquid is zero. Complete the force equation for the sum of the vertical forces acting on the liquid layer described in the problem introduction. Express your answer in terms of quantities given in the problem introduction and taking upward forces to be positive. You did not open hints for this part. ANSWER: Fdown = wlayer g wlayer = Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). A Submerged Ball A ball of mass and volume is lowered on a string into a fluid of density . Assume that the object would sink to the bottom if it were not supported by the string. Part A  = = i Fy,i mb V f What is the tension in the string when the ball is fully submerged but not touching the bottom, as shown in the figure? Express your answer in terms of any or all of the given quantities and , the magnitude of the acceleration due to gravity. You did not open hints for this part. ANSWER: Archimedes’ Principle Learning Goal: To understand the applications of Archimedes’ principle. Archimedes’ principle is a powerful tool for solving many problems involving equilibrium in fluids. It states the following: When a body is partially or completely submerged in a fluid (either a liquid or a gas), the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body. As a result of the upward Archimedes force (often called the buoyant force), some objects may float in a fluid, and all of them appear to weigh less. This is the familiar phenomenon of buoyancy. Quantitatively, the buoyant force can be found as , where is the force, is the density of the fluid, is the magnitude of the acceleration due to gravity, and is the volume of the displaced fluid. In this problem, you will be asked several qualitative questions that should help you develop a feel for Archimedes’ principle. An object is placed in a fluid and then released. Assume that the object either floats to the surface (settling so that the object is partly above and partly below the fluid surface) or sinks to the bottom. (Note that for Parts A through D, you should assume that the object has settled in equilibrium.) Part A Consider the following statement: The magnitude of the buoyant force is equal to the weight of fluid displaced by the object. Under what circumstances is this statement true? T g T = Fbuoyant = fluidgV Fbuoyant fluid g V You did not open hints for this part. ANSWER: Part B Consider the following statement: The magnitude of the buoyant force is equal to the weight of the amount of fluid that has the same total volume as the object. Under what circumstances is this statement true? You did not open hints for this part. ANSWER: Part C Consider the following statement: The magnitude of the buoyant force equals the weight of the object. Under what circumstances is this statement true? for every object submerged partially or completely in a fluid only for an object that floats only for an object that sinks for no object submerged in a fluid for an object that is partially submerged in a fluid only for an object that floats for an object completely submerged in a fluid for no object partially or completely submerged in a fluid You did not open hints for this part. ANSWER: Part D Consider the following statement: The magnitude of the buoyant force is less than the weight of the object. Under what circumstances is this statement true? ANSWER: Now apply what you know to some more complicated situations. Part E An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a denser liquid. What would you observe? You did not open hints for this part. ANSWER: for every object submerged partially or completely in a fluid for an object that floats only for an object that sinks for no object submerged in a fluid for every object submerged partially or completely in a fluid for an object that floats for an object that sinks for no object submerged in a fluid Part F An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a less dense liquid. What would you observe? You did not open hints for this part. ANSWER: Part G Two objects, T and B, have identical size and shape and have uniform density. They are carefully placed in a container filled with a liquid. Both objects float in equilibrium. Less of object T is submerged than of object B, which floats, fully submerged, closer to the bottom of the container. Which of the following statements is true? ANSWER: The object would sink all the way to the bottom. The object would float submerged more deeply than in the first container. The object would float submerged less deeply than in the first container. More than one of these outcomes is possible. The object would sink all the way to the bottom. The object would float submerged more deeply than in the first container. The object would float submerged less deeply than in the first container. More than one of these outcomes is possible. Object T has a greater density than object B. Object B has a greater density than object T. Both objects have the same density. ± Buoyant Force Conceptual Question A rectangular wooden block of weight floats with exactly one-half of its volume below the waterline. Part A What is the buoyant force acting on the block? You did not open hints for this part. ANSWER: Part B W The buoyant force cannot be determined. 2W W 1 W 2 The density of water is 1.00 . What is the density of the block? You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). g/cm3 2.00 between 1.00 and 2.00 1.00 between 0.50 and 1.00 0.50 The density cannot be determined. g/cm3 g/cm3 g/cm3 g/cm3 g/cm3 Flow Velocity of Blood Conceptual Question Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel. Imagine a healthy artery, with blood flow velocity of and mass per unit volume of . The kinetic energy per unit volume of blood is given by Imagine that plaque has narrowed an artery to one-fifth of its normal cross-sectional area (an 80% blockage). Part A Compared to normal blood flow velocity, , what is the velocity of blood as it passes through this blockage? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C v0 = 0.14 m/s  = 1050 kg/m3 K0 =  . 1 2 v20 v0 80v0 20v0 5v0 v0/5 This question will be shown after you complete previous question(s). For parts D – F imagine that plaque has grown to a 90% blockage. Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). ± Playing with a Water Hose Two children, Ferdinand and Isabella, are playing with a water hose on a sunny summer day. Isabella is holding the hose in her hand 1.0 meters above the ground and is trying to spray Ferdinand, who is standing 10.0 meters away. Part A Will Isabella be able to spray Ferdinand if the water is flowing out of the hose at a constant speed of 3.5 meters per second? Assume that the hose is pointed parallel to the ground and take the magnitude of the acceleration due to gravity to be 9.81 meters per second, per second. You did not open hints for this part. v0 g ANSWER: Part B This question will be shown after you complete previous question(s). Tactics Box 15.2 Finding Whether an Object Floats or Sinks Learning Goal: To practice Tactics Box 15.2 Finding whether an object floats or sinks. If you hold an object underwater and then release it, it can float to the surface, sink, or remain “hanging” in the water, depending on whether the fluid density is larger than, smaller than, or equal to the object’s average density . These conditions are summarized in this Tactics Box. Yes No f avg TACTICS BOX 15.2 Finding whether an object floats or sinks Object sinks Object floats Object has neutral buoyancy An object sinks if it weighs more than the fluid it displaces, that is, if its average density is greater than the density of the fluid: . An object floats on the surface if it weighs less than the fluid it displaces, that is, if its average density is less than the density of the fluid: . An object hangs motionless in the fluid if it weighs exactly the same as the fluid it displaces. It has neutral buoyancy if its average density equals the density of the fluid: . Part A Ice at 0.0 has a density of 917 . A 3.00 ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. What is the density of the oil, ? Express your answer in kilograms per meter cubed to three significant figures. ANSWER: Part B Once the ice cube melts, what happens to the liquid water that it produces? You did not open hints for this part. ANSWER: avg > f avg < f avg = f 'C kg/m3 cm3 oil oil = kg/m3 Part C What happens if some ethyl alcohol of density 790 is poured into the container after the ice cube has melted? ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. The liquid water sinks to the bottom of the container. The liquid water rises to the surface and floats on top of the oil. The liquid water is in static equilibrium at the location where the ice cube was originally placed. kg/m3 A layer of ethyl alcohol forms between the oil and the water. The layer of ethyl alcohol forms at the bottom of the container. The layer of ethyl alcohol forms on the surface.

please email info@checkyourstudy.com Chapter 15 Practice Problems (Practice – no … Read More...
In the country of Wiknam, there is only one firm that produces and sells soccer ball. Initially international trade is prohibited in the country. The following equations describe the monopolist’s demand, marginal revenue, total cost and marginal cost: Demand: P = 10 – Q Marginal Revenue: MR = 10 – 2Q Total Cost: TC = 3 + Q + 0.5Q2 Marginal Cost: MC = 1 + Q Q stands for quantity and P is the price measured in Wiknamian dollars. a) [20 marks] How many soccer balls does the monopolist produce? At what price are they sold? What is the monopolist’s profit? Show all your calculations. b) [10 marks] One day, the King of Wiknam decrees that henceforth, there will be free trade- either imports or exports- of soccer balls at the world price of $6. The firm now becomes a price taker in a competitive market. What happens to domestic production of soccer balls? What happens to domestic consumption? Does Wiknam export or import soccer balls? c) [10 marks] Suppose that the world price was not $6, but instead, happens to be exactly the same as the domestic price without trade as determined in part a) above. Would allowing trade change anything for the Wiknamian economy? Explain

In the country of Wiknam, there is only one firm that produces and sells soccer ball. Initially international trade is prohibited in the country. The following equations describe the monopolist’s demand, marginal revenue, total cost and marginal cost: Demand: P = 10 – Q Marginal Revenue: MR = 10 – 2Q Total Cost: TC = 3 + Q + 0.5Q2 Marginal Cost: MC = 1 + Q Q stands for quantity and P is the price measured in Wiknamian dollars. a) [20 marks] How many soccer balls does the monopolist produce? At what price are they sold? What is the monopolist’s profit? Show all your calculations. b) [10 marks] One day, the King of Wiknam decrees that henceforth, there will be free trade- either imports or exports- of soccer balls at the world price of $6. The firm now becomes a price taker in a competitive market. What happens to domestic production of soccer balls? What happens to domestic consumption? Does Wiknam export or import soccer balls? c) [10 marks] Suppose that the world price was not $6, but instead, happens to be exactly the same as the domestic price without trade as determined in part a) above. Would allowing trade change anything for the Wiknamian economy? Explain

info@checkyourstudy.com
Transportation 1. What would be some major benefits to a city investing in mass transit? • Reduces congestion and fuel usage o 2011 – U.S. public transportation use saved 865 million hours in travel time and 450 million gallons of fuel in 498 urban areas o Decrease the need for road enhancements o Can be quicker to get to work when roads are congested o Incentivizes exercise o Mass transit can have less land use requirements • Provides economic opportunities o revitalization of cities o Provides jobs in transportation o City makes money off of transit revenue o More appealing to tourists • Air quality o Cuts carbon emissions by 37 million metric tons annually o Air quality improvement for the city (less smog) • Safety o Reduce the number of accidents 2. What would be some major benefits to the users of mass transit? • Traffic o Reduces frustration of driving in traffic o Reduces the need for gas in traffic o Reliable and predictable time of arrival o More options to travel o No waiting in DMV lines • Economics o Public transit vs. owning, driving, and parking a car = $803/month average savings (~$10,000 a year) o Connects people who don’t have a car to jobs, healthcare, home o Provides jobs in transportation o No longer have to pay car insurance • Social o Can interact/meet new people every day o Connects communities o Can do other things, like read, on the train or bus o Reduce in stress o • Safety o Reduce risk of accidents

Transportation 1. What would be some major benefits to a city investing in mass transit? • Reduces congestion and fuel usage o 2011 – U.S. public transportation use saved 865 million hours in travel time and 450 million gallons of fuel in 498 urban areas o Decrease the need for road enhancements o Can be quicker to get to work when roads are congested o Incentivizes exercise o Mass transit can have less land use requirements • Provides economic opportunities o revitalization of cities o Provides jobs in transportation o City makes money off of transit revenue o More appealing to tourists • Air quality o Cuts carbon emissions by 37 million metric tons annually o Air quality improvement for the city (less smog) • Safety o Reduce the number of accidents 2. What would be some major benefits to the users of mass transit? • Traffic o Reduces frustration of driving in traffic o Reduces the need for gas in traffic o Reliable and predictable time of arrival o More options to travel o No waiting in DMV lines • Economics o Public transit vs. owning, driving, and parking a car = $803/month average savings (~$10,000 a year) o Connects people who don’t have a car to jobs, healthcare, home o Provides jobs in transportation o No longer have to pay car insurance • Social o Can interact/meet new people every day o Connects communities o Can do other things, like read, on the train or bus o Reduce in stress o • Safety o Reduce risk of accidents

info@checkyourstudy.com
Ryan and Ben are best friends. Ryan regularly runs marathons and is a member of the Marathon Runners Club at his university. Ben also wants to join the club, but he is not a very strong runner. Ben decides to start running every day so that he can participate in marathons and become a member of the club. Given this information, the Marathon Runners Club can be categorized as a(n) _____.

Ryan and Ben are best friends. Ryan regularly runs marathons and is a member of the Marathon Runners Club at his university. Ben also wants to join the club, but he is not a very strong runner. Ben decides to start running every day so that he can participate in marathons and become a member of the club. Given this information, the Marathon Runners Club can be categorized as a(n) _____.

aspirational reference group
A life insurance salesman sells on the average 33 life insurance policies per week. Use Poisson’s law to calculate the probability that in a given week he will sell Some policies 22 or more policies but less than 55 policies. Assuming that there are 55 working days per week, what is the probability that in a given day he will sell one policy?

A life insurance salesman sells on the average 33 life insurance policies per week. Use Poisson’s law to calculate the probability that in a given week he will sell Some policies 22 or more policies but less than 55 policies. Assuming that there are 55 working days per week, what is the probability that in a given day he will sell one policy?

A life insurance salesman sells on the average 33 life … Read More...
For Day 19 Homework Cover Sheet Name:_________________________________________________ Read Pages from 294-315, or watch the videos listed below Introduction to Division http://www.youtube.com/watch?v=7gZ4yW1nr9Y (13 min) Introduction to Division of Rational Numbers http://www.youtube.com/watch?v=9LTICGxqwKE (10 min) Division of Decimal Numbers and Rational Expressions http://www.youtube.com/watch?v=BGReDOGObbk (7 min) Division Algorithm for Decimal Numbers and Polynomials http://www.youtube.com/watch?v=XXr0ixy8PfA (8 min) Division Algorithm for Decimal Polynomials http://www.youtube.com/watch?v=PQrlt8PhFAE (11 min) Attempt problems from workbook pages 91-97 Summary of the lectures you watched should include answers to the following questions. When doing division of rational expressions or numbers, what allows us to multiply by the reciprocal of the divisor instead? For example, 3/4÷3/5=3/4×5/3 or (x^2-1)/x÷(x+1)/(x-2)=(x^2-1)/x×(x-2)/(x-1) List any parts of the video lecture (if there are any) that were unclear or you had trouble understanding. Please be specific and do not just say “All of it”. Questions you had difficulty with or felt stuck on- List the number for the ALEKS topics you were stuck on from the list at the end of the video logs-   ALEKS Topics Mastered Division facts Division involving a whole number and a fraction Division involving quotients with intermediate zeros Division of a decimal by a power of ten Division with carry Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Division without carry Fraction division Integer multiplication and division Multiplying or dividing numbers written in scientific notation Quotient and remainder: Problem type 1 Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Rationalizing the denominator of a radical expression Simplifying a product and quotient involving square roots of negative numbers The reciprocal of a number Writing a ratio as a percentage without a calculator

For Day 19 Homework Cover Sheet Name:_________________________________________________ Read Pages from 294-315, or watch the videos listed below Introduction to Division http://www.youtube.com/watch?v=7gZ4yW1nr9Y (13 min) Introduction to Division of Rational Numbers http://www.youtube.com/watch?v=9LTICGxqwKE (10 min) Division of Decimal Numbers and Rational Expressions http://www.youtube.com/watch?v=BGReDOGObbk (7 min) Division Algorithm for Decimal Numbers and Polynomials http://www.youtube.com/watch?v=XXr0ixy8PfA (8 min) Division Algorithm for Decimal Polynomials http://www.youtube.com/watch?v=PQrlt8PhFAE (11 min) Attempt problems from workbook pages 91-97 Summary of the lectures you watched should include answers to the following questions. When doing division of rational expressions or numbers, what allows us to multiply by the reciprocal of the divisor instead? For example, 3/4÷3/5=3/4×5/3 or (x^2-1)/x÷(x+1)/(x-2)=(x^2-1)/x×(x-2)/(x-1) List any parts of the video lecture (if there are any) that were unclear or you had trouble understanding. Please be specific and do not just say “All of it”. Questions you had difficulty with or felt stuck on- List the number for the ALEKS topics you were stuck on from the list at the end of the video logs-   ALEKS Topics Mastered Division facts Division involving a whole number and a fraction Division involving quotients with intermediate zeros Division of a decimal by a power of ten Division with carry Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Division without carry Fraction division Integer multiplication and division Multiplying or dividing numbers written in scientific notation Quotient and remainder: Problem type 1 Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Rationalizing the denominator of a radical expression Simplifying a product and quotient involving square roots of negative numbers The reciprocal of a number Writing a ratio as a percentage without a calculator

No expert has answered this question yet. You can browse … Read More...
Distribution of the Sample Mean and Linear Combinations – Examples Example 1 Let X1;X2; : : : ;X100 denote the actual net weights of 100 randomly selected 50-pound bags of fertilizer. a. If the expected weight of each bag is 50 pounds and the standard deviation is 1 pound, approximate P(49:75 • ¹X • 50:25) using the CLT. b. If the expected weight is 49.8 pounds rather than 50 pounds, so that on average bags are under…lled, approximate P(49:75 • ¹X • 50:25). Example 2 The breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 500 psi. a. What is the approximate probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,900 psi and 10,200 psi? b. If the sample size had been 15 rivets rather than 40 rivets, could the probability requested in part a be approximated from the given information? Why or why not? Example 3 The lifetime of a certain type of battery is normally distributed with mean 8 hours and standard deviation 1 hour. There are four batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages? Example 4 Suppose your waiting time for a bus in the morning is uniformly distributed on [0; 5], while waiting time in the evening is uniformly distributed on [0; 10]. Assume that evening waiting time is independent of morning waiting time. a. If you take the bus each morning and evening for a week, what is your total expected waiting time. b. What is the variance of your total waiting time? expected value and variance of the di¤erence between morning and evening waiting time on a given day? d. What are the expected value and variance of the di¤erence between total morning waiting time and total evening waiting time for a particular week? 2 Example 5 Three di¤erent roads feed into a particular freeway entrance. Suppose that during a …xed time period, the number of cars coming from each road onto the freeway is a random variable, with expected value and standard deviation as given in the following table: Road 1 Road 2 Road 3 Expected Value 800 1000 600 Standard Deviation 16 25 18 : a. What is the expected total number of cars entering the freeway at this point during the period? b. What is the variance of the total number of entering cars? Have you made any assumptions about the relationship between the number of cars on the di¤erent roads? c. With Xi denoting the number of cars entering from road i during the period, suppose that Cov(X1;X2) = 80, Cov(X1;X3) = 90, and Cov(X2;X3) = 100 (so that the three streams of tra¢c are not independent). Compute the expected total number of entering cars and the standard deviation of the total. Example 6 In an area having sandy soil, 50 small trees of a certain type were planted, and another 50 trees were planted in an area having clay soil. Let X be the number of trees planted in sandy soil that survive one year and Y be the number of trees planted in clay soil that survive one year. If the probability that a tree planted in sandy soil will survive one year is 0.7 and the probability of one-year survival in clay soil is 0.6, compute an approximation to P(¡5 • X ¡ Y • 5). For the purposes of this exercise, ignore the continuity correction.

Distribution of the Sample Mean and Linear Combinations – Examples Example 1 Let X1;X2; : : : ;X100 denote the actual net weights of 100 randomly selected 50-pound bags of fertilizer. a. If the expected weight of each bag is 50 pounds and the standard deviation is 1 pound, approximate P(49:75 • ¹X • 50:25) using the CLT. b. If the expected weight is 49.8 pounds rather than 50 pounds, so that on average bags are under…lled, approximate P(49:75 • ¹X • 50:25). Example 2 The breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 500 psi. a. What is the approximate probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,900 psi and 10,200 psi? b. If the sample size had been 15 rivets rather than 40 rivets, could the probability requested in part a be approximated from the given information? Why or why not? Example 3 The lifetime of a certain type of battery is normally distributed with mean 8 hours and standard deviation 1 hour. There are four batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages? Example 4 Suppose your waiting time for a bus in the morning is uniformly distributed on [0; 5], while waiting time in the evening is uniformly distributed on [0; 10]. Assume that evening waiting time is independent of morning waiting time. a. If you take the bus each morning and evening for a week, what is your total expected waiting time. b. What is the variance of your total waiting time? expected value and variance of the di¤erence between morning and evening waiting time on a given day? d. What are the expected value and variance of the di¤erence between total morning waiting time and total evening waiting time for a particular week? 2 Example 5 Three di¤erent roads feed into a particular freeway entrance. Suppose that during a …xed time period, the number of cars coming from each road onto the freeway is a random variable, with expected value and standard deviation as given in the following table: Road 1 Road 2 Road 3 Expected Value 800 1000 600 Standard Deviation 16 25 18 : a. What is the expected total number of cars entering the freeway at this point during the period? b. What is the variance of the total number of entering cars? Have you made any assumptions about the relationship between the number of cars on the di¤erent roads? c. With Xi denoting the number of cars entering from road i during the period, suppose that Cov(X1;X2) = 80, Cov(X1;X3) = 90, and Cov(X2;X3) = 100 (so that the three streams of tra¢c are not independent). Compute the expected total number of entering cars and the standard deviation of the total. Example 6 In an area having sandy soil, 50 small trees of a certain type were planted, and another 50 trees were planted in an area having clay soil. Let X be the number of trees planted in sandy soil that survive one year and Y be the number of trees planted in clay soil that survive one year. If the probability that a tree planted in sandy soil will survive one year is 0.7 and the probability of one-year survival in clay soil is 0.6, compute an approximation to P(¡5 • X ¡ Y • 5). For the purposes of this exercise, ignore the continuity correction.