1-Two notions serve as the basis for all torts: wrongs and compensation. True False 2-The goal of tort law is to put a defendant in the position that he or she would have been in had the tort occurred to the defendant. True False 3-Hayley is injured in an accident precipitated by Isolde. Hayley files a tort action against Isolde, seeking to recover for the damage suffered. Damages that are intended to compensate or reimburse a plaintiff for actual losses are: compensatory damages. reimbursement damages. actual damages. punitive damages. 4-Ladd throws a rock intending to hit Minh but misses and hits Nasir instead. On the basis of the tort of battery, Nasir can sue: Ladd. Minh. the rightful owner of the rock. no one. 4-Luella trespasses on Merchandise Mart’s property. Through the use of reasonable force, Merchandise Mart’s security guard detains Luella until the police arrive. Merchandise Mart is liable for: assault. battery. false imprisonment. none of the choice 6-The extreme risk of an activity is a defense against imposing strict liability. True False 7-Misrepresentation in an ad is enough to show an intent to induce the reliance of anyone who may use the product. True False 8-Luke is playing a video game on a defective disk that melts in his game player, starting a fire that injures his hands. Luke files a suit against Mystic Maze, Inc., the game’s maker under the doctrine of strict liability. A significant application of this doctrine is in the area of: cyber torts. intentional torts. product liability. unintentional torts 9-More than two hundred years ago, the Declaration of Independence recognized the importance of protecting creative works. True False 10-n 2014, Cloud Computing Corporation registers its trademark as provided by federal law. After the first renewal, this registration: is renewable every ten years. is renewable every twenty years. runs for life of the corporation plus seventy years. runs forever. 11-Wendy works as a weather announcer for a TV station under the character name Weather Wendy. Wendy can register her character’s name as: a certification mark. a trade name. a service mark. none of the choices 12-Much of the material on the Internet, including software and database information, is not copyrighted. True False 13-In a criminal case, the state must prove its case by a preponderance of the evidence. True False 14-Under the Fourth Amendmentt, general searches through a person’s belongings are permissible. True False 15-Maura enters a gas station and points a gun at the clerk Nate. She then forces Nate to open the cash register and give her all the money. Maura can be charged with: burglary. robbery. larceny. receiving stolen property. 16-Reno, driving while intoxicated, causes a car accident that results in the death of Santo. Reno is arrested and charged with a felony. A felony is a crime punishable by death or imprisonment for: any period of time. more than one year. more than six months. more than ten days. 17-Corporate officers and directors may be held criminally liable for the actions of employees under their supervision. True False 18-Sal assures Tom that she will deliver a truckload of hay to his cattle ranch. A person’s declaration to do a certain act is part of the definition of: an expectation. a moral obligation. a prediction. a promise. 19-Lark promises to buy Mac’s used textbook for $60. Lark is: an offeror. an offeree a promisee. a promisor. 20-Casey offers to sell a certain used forklift to DIY Lumber Outlet, but Casey dies before DIY accepts. Most likely, Casey’s death: did not affect the offer. shortened the time of the offer but did not terminated it. extended the time of the offer. terminated the offer.

1-Two notions serve as the basis for all torts: wrongs and compensation. True False 2-The goal of tort law is to put a defendant in the position that he or she would have been in had the tort occurred to the defendant. True False 3-Hayley is injured in an accident precipitated by Isolde. Hayley files a tort action against Isolde, seeking to recover for the damage suffered. Damages that are intended to compensate or reimburse a plaintiff for actual losses are: compensatory damages. reimbursement damages. actual damages. punitive damages. 4-Ladd throws a rock intending to hit Minh but misses and hits Nasir instead. On the basis of the tort of battery, Nasir can sue: Ladd. Minh. the rightful owner of the rock. no one. 4-Luella trespasses on Merchandise Mart’s property. Through the use of reasonable force, Merchandise Mart’s security guard detains Luella until the police arrive. Merchandise Mart is liable for: assault. battery. false imprisonment. none of the choice 6-The extreme risk of an activity is a defense against imposing strict liability. True False 7-Misrepresentation in an ad is enough to show an intent to induce the reliance of anyone who may use the product. True False 8-Luke is playing a video game on a defective disk that melts in his game player, starting a fire that injures his hands. Luke files a suit against Mystic Maze, Inc., the game’s maker under the doctrine of strict liability. A significant application of this doctrine is in the area of: cyber torts. intentional torts. product liability. unintentional torts 9-More than two hundred years ago, the Declaration of Independence recognized the importance of protecting creative works. True False 10-n 2014, Cloud Computing Corporation registers its trademark as provided by federal law. After the first renewal, this registration: is renewable every ten years. is renewable every twenty years. runs for life of the corporation plus seventy years. runs forever. 11-Wendy works as a weather announcer for a TV station under the character name Weather Wendy. Wendy can register her character’s name as: a certification mark. a trade name. a service mark. none of the choices 12-Much of the material on the Internet, including software and database information, is not copyrighted. True False 13-In a criminal case, the state must prove its case by a preponderance of the evidence. True False 14-Under the Fourth Amendmentt, general searches through a person’s belongings are permissible. True False 15-Maura enters a gas station and points a gun at the clerk Nate. She then forces Nate to open the cash register and give her all the money. Maura can be charged with: burglary. robbery. larceny. receiving stolen property. 16-Reno, driving while intoxicated, causes a car accident that results in the death of Santo. Reno is arrested and charged with a felony. A felony is a crime punishable by death or imprisonment for: any period of time. more than one year. more than six months. more than ten days. 17-Corporate officers and directors may be held criminally liable for the actions of employees under their supervision. True False 18-Sal assures Tom that she will deliver a truckload of hay to his cattle ranch. A person’s declaration to do a certain act is part of the definition of: an expectation. a moral obligation. a prediction. a promise. 19-Lark promises to buy Mac’s used textbook for $60. Lark is: an offeror. an offeree a promisee. a promisor. 20-Casey offers to sell a certain used forklift to DIY Lumber Outlet, but Casey dies before DIY accepts. Most likely, Casey’s death: did not affect the offer. shortened the time of the offer but did not terminated it. extended the time of the offer. terminated the offer.

1-Two notions serve as the basis for all torts: wrongs … Read More...
Problems Marking scheme 1. Let A be a nonzero square matrix. Is it possible that a positive integer k exists such that ?? = 0 ? For example, find ?3 for the matrix [ 0 1 2 0 0 1 0 0 0 ] A square matrix A is nilpotent of index k when ? ≠ 0 , ?2 ≠ 0 , … . . , ??−1 ≠ 0, ??? ?? = 0. In this task you will explore nilpotent matrices. 1. The matrix in the example given above is nilpotent. What is its index? ( 2 marks ) 2. Use a software program to determine which of the following matrices are nilpotent and find their indices ( 12 marks ) A. [ 0 1 0 0 ] B. [ 0 1 1 0 ] C. [ 0 0 1 0 ] D. [ 1 0 1 0 ] E. [ 0 0 1 0 0 0 0 0 0 ] F. [ 0 0 0 1 0 0 1 1 0 ] 3. Find 3×3 nilpotent matrices of indices 2 and 3 ( 2 marks ) 4. Find 4×4 nilpotent matrices of indices 2, 3, and 4 ( 2 marks ) 5. Find nilpotent matrix of index 5 ( 2 marks ) 6. Are nilpotent matrices invertible? prove your answer ( 3 marks ) 7. When A is nilpotent, what can you say about ?? ? prove your answer ( 3 marks ) 8. Show that if ? is nilpotent , then ? − ? is invertible ( 4 marks ) 30% 2. A radio transmitter circuit contains a resisitance of 2.0 Ω, a variable inductor of 100 − ? ℎ?????? and a voltage source of 4.0 ? . find the current ? in the circuit as a function of the time t for 0 ≤ ? ≤ 100? if the intial curent is zero. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 3. An object falling under the influence of gravity has a variable accelertaion given by 32 − ? , where ? represents the velocity. If the object starts from rest, find an expression for the velocity in terms of the time. Also, find the limiting value of the velocity. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 4. When the angular displacement ? of a pendulum is small ( less than 60), the pendulum moves with simple harmonic motion closely approximated by ?′′ + ? ? ? = 0 . Here , ?′ = ?? ?? and ? is the accelertaion due to gravity , and ? is the length of the pendulum. Find ? as a function of time ( in s ) if ? = 9.8 ?/?2, ? = 1.0 ? ? = 0.1 and ?? ?? = 0 when ? = 0 . sketch the cuve using any graphical tool. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 5. Find the equation relating the charge and the time in a electric circuit with the following elements: ? = 0.200 ? , ? = 8.00 Ω , ? = 1.00 ?? , ? = 0. In this circuit , ? = 0 and ? = 0.500 ? when ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 6. A spring is stretched 1 m by ? 20 − ? Weight. The spring is stretched 0.5 m below the equilibrium position with the weight attached and the then released. If it is a medium that resists the motion with a force equal to 12?, where v is the velocity, sketch and find the displacement y of the weight as a function of the time. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 7. A 20?? inductor, a 40.0 Ω resistor, a 50.0 ?? capacitor, and voltage source of 100 ?−100?are connected in series in an electric circuit. Find the charge on the capacitor as a function of time t , if ? = 0 and ? = 0 ?ℎ?? ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 10% quality and neatness and using Math equations in MS word. –

Problems Marking scheme 1. Let A be a nonzero square matrix. Is it possible that a positive integer k exists such that ?? = 0 ? For example, find ?3 for the matrix [ 0 1 2 0 0 1 0 0 0 ] A square matrix A is nilpotent of index k when ? ≠ 0 , ?2 ≠ 0 , … . . , ??−1 ≠ 0, ??? ?? = 0. In this task you will explore nilpotent matrices. 1. The matrix in the example given above is nilpotent. What is its index? ( 2 marks ) 2. Use a software program to determine which of the following matrices are nilpotent and find their indices ( 12 marks ) A. [ 0 1 0 0 ] B. [ 0 1 1 0 ] C. [ 0 0 1 0 ] D. [ 1 0 1 0 ] E. [ 0 0 1 0 0 0 0 0 0 ] F. [ 0 0 0 1 0 0 1 1 0 ] 3. Find 3×3 nilpotent matrices of indices 2 and 3 ( 2 marks ) 4. Find 4×4 nilpotent matrices of indices 2, 3, and 4 ( 2 marks ) 5. Find nilpotent matrix of index 5 ( 2 marks ) 6. Are nilpotent matrices invertible? prove your answer ( 3 marks ) 7. When A is nilpotent, what can you say about ?? ? prove your answer ( 3 marks ) 8. Show that if ? is nilpotent , then ? − ? is invertible ( 4 marks ) 30% 2. A radio transmitter circuit contains a resisitance of 2.0 Ω, a variable inductor of 100 − ? ℎ?????? and a voltage source of 4.0 ? . find the current ? in the circuit as a function of the time t for 0 ≤ ? ≤ 100? if the intial curent is zero. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 3. An object falling under the influence of gravity has a variable accelertaion given by 32 − ? , where ? represents the velocity. If the object starts from rest, find an expression for the velocity in terms of the time. Also, find the limiting value of the velocity. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 4. When the angular displacement ? of a pendulum is small ( less than 60), the pendulum moves with simple harmonic motion closely approximated by ?′′ + ? ? ? = 0 . Here , ?′ = ?? ?? and ? is the accelertaion due to gravity , and ? is the length of the pendulum. Find ? as a function of time ( in s ) if ? = 9.8 ?/?2, ? = 1.0 ? ? = 0.1 and ?? ?? = 0 when ? = 0 . sketch the cuve using any graphical tool. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 5. Find the equation relating the charge and the time in a electric circuit with the following elements: ? = 0.200 ? , ? = 8.00 Ω , ? = 1.00 ?? , ? = 0. In this circuit , ? = 0 and ? = 0.500 ? when ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 6. A spring is stretched 1 m by ? 20 − ? Weight. The spring is stretched 0.5 m below the equilibrium position with the weight attached and the then released. If it is a medium that resists the motion with a force equal to 12?, where v is the velocity, sketch and find the displacement y of the weight as a function of the time. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 7. A 20?? inductor, a 40.0 Ω resistor, a 50.0 ?? capacitor, and voltage source of 100 ?−100?are connected in series in an electric circuit. Find the charge on the capacitor as a function of time t , if ? = 0 and ? = 0 ?ℎ?? ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 10% quality and neatness and using Math equations in MS word. –

Problems Marking scheme 1. Let A be a nonzero square … Read More...
. What behaviors indicate psychological distress? Name 5 and explain.

. What behaviors indicate psychological distress? Name 5 and explain.

The term ‘distress’ is commonly used in nursing literature to … Read More...
Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

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Question One: There are 4 legal reasons why an agreement would lack consideration. Your assignment is to list each of the four legal reasons. Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . . b) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . c) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . d) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion. Question One: There are 4 legal reasons why an agreement would lack consideration. Your assignment is to list each of the four legal reasons. Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . . b) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . c) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . d) An agreement would lack consideration if ___________ 

 factual example: X and Y . . .

Question One: There are 4 legal reasons why an agreement would lack consideration. Your assignment is to list each of the four legal reasons. Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . . b) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . c) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . d) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion. Question One: There are 4 legal reasons why an agreement would lack consideration. Your assignment is to list each of the four legal reasons. Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . . b) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . c) An agreement would lack consideration if ___________ 

 factual example: X and Y . . . d) An agreement would lack consideration if ___________ 

 factual example: X and Y . . .

Ans. All given agreements are not contracts. The agreement which … Read More...
Question One: There are 4 legal reasons why an agreement would lack assignment is to list each of the four legal reasons.  Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if  ___________   

    factual example: X and Y . . . . b) An agreement would lack consideration if  ___________ 

    factual example: X and Y . . . c) An agreement would lack consideration if ___________    

    factual example: X and Y . . . d) An agreement would lack consideration if ___________    

    factual example: X and Y . . .  Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion.

Question One: There are 4 legal reasons why an agreement would lack assignment is to list each of the four legal reasons.  Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if  ___________   

    factual example: X and Y . . . . b) An agreement would lack consideration if  ___________ 

    factual example: X and Y . . . c) An agreement would lack consideration if ___________    

    factual example: X and Y . . . d) An agreement would lack consideration if ___________    

    factual example: X and Y . . .  Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion.

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BI 102 Lab 1 Writing Assignment How did the different concentrations of sucrose impact osmotic rate? This assignment requires you to evaluate a hypothesis and communicate the results of your experiment on the rate of osmosis into sucrose solutions of varying concentrations. The questions below are meant to guide you to reporting the key findings of your experiment and help you think through how to explain the findings and draw conclusions from them in a scientific manner. ASSIGNMENT: Please respond to the following questions to complete your laboratory write up. For this assignment you will only focus on the osmosis of water into sucrose concentrations of varying concentration. Make sure that your write up is accurate, and clearly written so that it is easily readable. A grading rubric is provided on the second page of this assignment. To earn full points on your write up, you must provide answers that align to the “meets” column of your grading rubric as well as meeting all “Quality of Writing and Mechanics” elements described in the rubric. There are also some tips on pages 3-4 of this assignment to help you succeed. FORMAT: • Type your responses, using 1.5 or double spacing. • Include the section headings (Hypothesis, Results, Analysis) and question number (example: 1, 2, 3, etc) in your answers but do not rewrite the question. • Graphs may be made with a computer program (example: Microsoft excel, Mac numbers, etc) or may be neatly produced with a ruler on graphing paper. • Print out the cover sheet on page 2 of this assignment, read and sign the academic honesty statement, and submit it with your write up. Your instructor WILL NOT accept a write up without the signed cover sheet. DUE DATE: Your write up is due at the beginning of class next week. Late assignments will have 1 point deducted per day up to 5 days, at which point the assignment will be assigned 0 points. Hypothesis and Prediction – Part 1 of Rubric 1. What did you think was going to happen in this experiment and why? You may find it helpful to state your answers to these questions as an “if-then” hypothesis-prediction. Be sure you have included a biological rationale that explains WHY you made this hypothesis/prediction. (You worked on this in question 2 on page 10 of this lab activity) Results – Part 2 of Rubric 2. How did the different concentrations of sucrose impact osmotic rate? Answer this question by creating a line graph that shows the results of your experiment. If you need assistance building a graph, there is a Guide to Graphing resource available on your Moodle lab course site. Analysis- Part 3 of Rubric 3. Explain why you think that the results shown in your graph support or refute your hypothesis (remember we never “prove” anything in science). Consider all your data and the overall data pattern as you answer this question. Don’t ignore unusual data that may not seem to fit into a specific patterns (“outliers”). Explain what you think might be behind these unusual data points. 4. What is the biological significance of your results? What biological concepts explain completely why these events happened in the experiment? How do these results help you understand the biology of the cell and how materials move back and forth across the cell membrane? (A hint: refer back to questions 1A-1F on page 10 of this lab activity). Think about giving a specific example. References- Mechanics Checklist 5. Provide at least one full citation (make sure you include an in-text citation that pinpoints where you used this resource) for a resource you made use of in performing the experiment, understanding the concepts and writing this assignment. (Perhaps your lab manual? Your textbook? A website?) If you used more than one resource, you need to cite each one! If you need help with citations, a Guide to Citing References is available on your Moodle lab course site. Please print out and submit this cover sheet with your lab writeup! Lab Writeup Assignment (1) Assessment Rubric-­‐ 10 points total Name: ________________________________________ Element Misses (1 point) Approaches (2 points) Meets (3 points) Hypothesis Clarity/Specificity Testability Rationale ___Hypothesis is unclear and hardto- understand ___Hypothesis is not testable ___No biological rationale for hypothesis or rationale is fully inaccurate ___Hypothesis included is clearly stated, but not specific or lacks specific details __Hypothesis is testable, but not in a feasible way in this lab ___Some foundation for hypothesis, but based in part on biological inaccuracy ___Hypothesis included is clearly stated and very specific ___Hypothesis is testable and could be tested within lab parameters ___Rationale for hypothesis is grounded in accurate biological information Graph Title Axes Variables Key Graph clarity Data accuracy ___Graph lacks a title ___Axes are not labeled ___Variables not addressed in graph ___No key or way to tell data points apart ___Graph is hard to read and comparisons cannot be made: Inappropriate graph type or use of scale ___Data graphed is inaccurate or does not relate to experiment ___Graph has a title that is not very descriptive ___Axes are either unlabeled, or units are unclear or wrong ___Variables addressed in graph, but not on correct axes ___Key included, but is hard to understand ___Graph is somewhat readable, comparisons can be made with difficulty: Appropriate graph type, but not scaled well ___Data graphed is partially accurate; some data is missing ___Graph has a concise, descriptive title ___Axes are labeled, including clarification of units used ___Variables on correct axes ___A clear, easy-to-use key to data points is included ___Graph is clearly readable and comparisons between treatments are easy to make: Graph type and scale are appropriate to data ___Data graphed is accurate and includes all relevant data, including controls (if needed) Analysis Hypothesis Scientific language Data addressed Explanation ___Hypothesis is not addressed ___Hypothesis is described using language like proven, true, or right ___No explanations for data patterns observed in graph or data does not support conclusions. ___No biological explanation for data trends or explanations are completely inaccurate ___Hypothesis is mentioned, but not linked well to data ___Hypothesis is not consistently described as supported or refuted ___Some data considered in conclusions but other data is ignored. Any unusual “outliers” are ignored ___Explanations include minimal or some inaccurate biological concepts ___Hypothesis is evaluated based upon data ___Hypothesis is consistently described as supported or refuted ___All data collected is considered and addressed by conclusions, including presence of outliers, ___Explanations include relevant and accurate biological concepts Quality of Writing and Mechanics: Worth 1 point. Writeup should meet all of the following criteria! Yes No ☐ ☐ Write up includes your name, the date, and your lab section ☐ ☐ Write up is free from spelling and grammatical errors (make sure you proofread!!) ☐ ☐ Write up is clear and easy-to-understand ☐ ☐ Write up includes full citation for at least one reference with corresponding in-text citation ☐ ☐ All portions of write up are clearly labeled, and question numbers are included Plagiarism refers to the use of original work, ideas, or text that are not your own. This includes cut-and-paste from websites, copying directly from texts, and copying the work of others, including fellow students. Telling someone your answers to the questions (including telling someone how to make their graph, question #2), or asking for the answers to any question, is cheating. (Asking someone how to make the graph for this assignment is NOT the same as asking for help learning excel or some other software). All forms of cheating, including plagiarism and copying of work will result in an immediate zero for the exam, quiz, or assignment. In the case of copying, all parties involved in the unethical behavior will earn zeros. Cheating students will be referred to the Student Conduct Committee for further action. You also have the right to appeal to the Student Conduct Committee. I have read and understand the plagiarism statement. ____________________________________________________ Signature Guidelines for Good Quality Scientific Reports Hypothesis and Prediction: The hypothesis is a tentative explanation for the phenomenon. Remember that: • A good hypothesis and prediction is testable (and should be testable under the conditions of our lab environment; For example, if your hypothesis requires shooting a rocket into space, then its not really testable under our laboratory conditions). • Your explanation can be ruled out through testing, or falsified. • A good hypothesis and prediction is detailed and specific in what it is testing. • A good hypothesis provides a rationale or explanation for why you think your prediction is reasonable and this rationale is based on what we know about biology. • A good prediction is specific and can be tested with a specific experiment. Examples*: I think that diet soda will float and regular soda will sink. {This hypothesis misses the goal. It is not specific as we don’t know where the sodas are floating and sinking, and it does not provide any explanation to explain why the hypothesis makes sense} Because diet soda does not contain sugar and regular soda does, the diet soda will float in a bucket of water, while regular soda will sink. {This hypothesis approaches the goal. It is more specific about the conditions, and it provides a partial explanation about why the hypothesis makes sense, but the connection between sugar and sinking is unclear} If diet soda does not contain sugar, then its density (mass/volume) is lower than that of regular soda which does contain sugar, and so diet soda will float in a bucket of water while regular soda sinks. {This hypothesis meets the goal. It is specific and the rationale- sugar affects density and density is what determines floating or sinking in water- is clearly articulated} *Note that these examples are for different experiments and investigations and NOT about your osmosis lab. They are provided only to help you think about what you need to include in your write up. Graph: The graph is a visual representation of the data you gathered while testing your hypothesis. Remember that: • A graph needs a concise title that clearly describes the data that it is showing. • Data must be put on the correct axes of the graph. In general, the data you collected (representing what you are trying to find out about) goes on the vertical (Y) axis. The supporting data that that describes how, when or under what conditions you collected your data goes on the horizontal (X) axis. (For this reason time nearly always goes on the X-axis). • Axes must be labeled, including the units in which data were recorded • Data points should be clearly marked and identified; a key is helpful if more than one group of data is included in the graph. • The scale of a graph is important. It should be consistent (there should be no change in the units or increments on a single axis) and appropriate to the data you collected Examples: {This graph misses the goal. There is no title, nor is there a key to help distinguish what the data points mean. The scale is too large- from 0 to 100 with an increment of 50, when the maximum number in the graph is 25- and makes it hard to interpret this graph. The x-axis is labeled, but without units (the months) and the y-axis has units, but the label is incomplete- number of what?} {This graph meets the goal. There is a descriptive title, and all of the axes are clearly labeled with units. There is a key so that we can distinguish what each set of data points represent. The dependent variable (number of individuals) is correctly placed on the y-axis with the independent variable of time placed on the x-axis. The scale of 0-30 is appropriate to the data, with each line on the x-axis representing an increment of 5.} 0 50 100 Number Month 0 5 10 15 20 25 30 March April May June July Number of individuals Month (2011) Population size of three different madtom catiCish in the Marais de Cygnes River in Spring/Summer 2011 Brindled madtom Neosho madtom Slender madtom Analysis: You need to evaluate your hypothesis based on the data patterns shown by your graph. Remember that: • You use data to determine support or refute your hypothesis. It is only possible to support a hypothesis, not to “prove” one (that would require testing every possible permutation and combination of factors). Your evaluation of your hypothesis should not be contradicted by the pattern shown by your data. • Refer back to the prediction you made as part of your hypothesis and use your data to justify your decision to support or refute your hypothesis. • In the “if” part of your hypothesis you should have provided a rationale, or explanation for the prediction you made in your hypothesis (“then” part of hypothesis”). Use this to help you explain why you think you observed the specific pattern of data revealed in your graph. • You should consider all of the data you collected in examining the support (or lack of support for your hypothesis). If there are unusual data points or “outliers” that don’t seem to fit the general pattern in your graph, explain what you think those mean. Examples: I was right. Diet Pepsi floated and so did Apricot Nectar. Regular Pepsi sank. Obviously the regular Pepsi was heavier. This helps us understand the concept of density, which is a really important one. {This analysis misses the goal. The hypothesis isn’t actually mentioned and the data is only briefly described. There is no explanation of the importance of the Apricot Nectar results. Finally, there is no connection to how these results help understand density or why it is biologically important} I hypothesized that diet soda would float, and all three cans of diet Pepsi did float while the regular Pepsi sank. This supports my hypothesis. Both types of Pepsi were 8.5 fluid ounces in volume, but the regular Pepsi also contained 16 grams of sugar. This means that the regular Pepsi had 16 more grams of mass provided by the sugar in the same amount of volume. This would lead to an increase in density, which explains why the regular soda cans sank. When we put in a can of Apricot Nectar, which had 19 grams of sugar, it floated. This was unexpected, but I think it is explained by the fact that an Apricot Nectar can had a volume of 7 fluid ounces, but the dimensions of the can are the same as that of a Pepsi can. A same-sized can with less liquid probably has an air space that helped it float. The results of this experiment help us understand how the air bladder of a fish, which creates an air space inside the fish, helps it float in the water and also how seaweeds and other living things with air spaces or other factors that decrease their density keep from sinking to the bottom of the water. {This analysis meets the goal. It clearly ties the hypothesis to the results and outlines what they mean. It describes how the results support the hypothesis, but also explains a possible reason behind the unusual results of the Apricot Nectar. Finally, there is a link to how this experiment helps us understand biology}

BI 102 Lab 1 Writing Assignment How did the different concentrations of sucrose impact osmotic rate? This assignment requires you to evaluate a hypothesis and communicate the results of your experiment on the rate of osmosis into sucrose solutions of varying concentrations. The questions below are meant to guide you to reporting the key findings of your experiment and help you think through how to explain the findings and draw conclusions from them in a scientific manner. ASSIGNMENT: Please respond to the following questions to complete your laboratory write up. For this assignment you will only focus on the osmosis of water into sucrose concentrations of varying concentration. Make sure that your write up is accurate, and clearly written so that it is easily readable. A grading rubric is provided on the second page of this assignment. To earn full points on your write up, you must provide answers that align to the “meets” column of your grading rubric as well as meeting all “Quality of Writing and Mechanics” elements described in the rubric. There are also some tips on pages 3-4 of this assignment to help you succeed. FORMAT: • Type your responses, using 1.5 or double spacing. • Include the section headings (Hypothesis, Results, Analysis) and question number (example: 1, 2, 3, etc) in your answers but do not rewrite the question. • Graphs may be made with a computer program (example: Microsoft excel, Mac numbers, etc) or may be neatly produced with a ruler on graphing paper. • Print out the cover sheet on page 2 of this assignment, read and sign the academic honesty statement, and submit it with your write up. Your instructor WILL NOT accept a write up without the signed cover sheet. DUE DATE: Your write up is due at the beginning of class next week. Late assignments will have 1 point deducted per day up to 5 days, at which point the assignment will be assigned 0 points. Hypothesis and Prediction – Part 1 of Rubric 1. What did you think was going to happen in this experiment and why? You may find it helpful to state your answers to these questions as an “if-then” hypothesis-prediction. Be sure you have included a biological rationale that explains WHY you made this hypothesis/prediction. (You worked on this in question 2 on page 10 of this lab activity) Results – Part 2 of Rubric 2. How did the different concentrations of sucrose impact osmotic rate? Answer this question by creating a line graph that shows the results of your experiment. If you need assistance building a graph, there is a Guide to Graphing resource available on your Moodle lab course site. Analysis- Part 3 of Rubric 3. Explain why you think that the results shown in your graph support or refute your hypothesis (remember we never “prove” anything in science). Consider all your data and the overall data pattern as you answer this question. Don’t ignore unusual data that may not seem to fit into a specific patterns (“outliers”). Explain what you think might be behind these unusual data points. 4. What is the biological significance of your results? What biological concepts explain completely why these events happened in the experiment? How do these results help you understand the biology of the cell and how materials move back and forth across the cell membrane? (A hint: refer back to questions 1A-1F on page 10 of this lab activity). Think about giving a specific example. References- Mechanics Checklist 5. Provide at least one full citation (make sure you include an in-text citation that pinpoints where you used this resource) for a resource you made use of in performing the experiment, understanding the concepts and writing this assignment. (Perhaps your lab manual? Your textbook? A website?) If you used more than one resource, you need to cite each one! If you need help with citations, a Guide to Citing References is available on your Moodle lab course site. Please print out and submit this cover sheet with your lab writeup! Lab Writeup Assignment (1) Assessment Rubric-­‐ 10 points total Name: ________________________________________ Element Misses (1 point) Approaches (2 points) Meets (3 points) Hypothesis Clarity/Specificity Testability Rationale ___Hypothesis is unclear and hardto- understand ___Hypothesis is not testable ___No biological rationale for hypothesis or rationale is fully inaccurate ___Hypothesis included is clearly stated, but not specific or lacks specific details __Hypothesis is testable, but not in a feasible way in this lab ___Some foundation for hypothesis, but based in part on biological inaccuracy ___Hypothesis included is clearly stated and very specific ___Hypothesis is testable and could be tested within lab parameters ___Rationale for hypothesis is grounded in accurate biological information Graph Title Axes Variables Key Graph clarity Data accuracy ___Graph lacks a title ___Axes are not labeled ___Variables not addressed in graph ___No key or way to tell data points apart ___Graph is hard to read and comparisons cannot be made: Inappropriate graph type or use of scale ___Data graphed is inaccurate or does not relate to experiment ___Graph has a title that is not very descriptive ___Axes are either unlabeled, or units are unclear or wrong ___Variables addressed in graph, but not on correct axes ___Key included, but is hard to understand ___Graph is somewhat readable, comparisons can be made with difficulty: Appropriate graph type, but not scaled well ___Data graphed is partially accurate; some data is missing ___Graph has a concise, descriptive title ___Axes are labeled, including clarification of units used ___Variables on correct axes ___A clear, easy-to-use key to data points is included ___Graph is clearly readable and comparisons between treatments are easy to make: Graph type and scale are appropriate to data ___Data graphed is accurate and includes all relevant data, including controls (if needed) Analysis Hypothesis Scientific language Data addressed Explanation ___Hypothesis is not addressed ___Hypothesis is described using language like proven, true, or right ___No explanations for data patterns observed in graph or data does not support conclusions. ___No biological explanation for data trends or explanations are completely inaccurate ___Hypothesis is mentioned, but not linked well to data ___Hypothesis is not consistently described as supported or refuted ___Some data considered in conclusions but other data is ignored. Any unusual “outliers” are ignored ___Explanations include minimal or some inaccurate biological concepts ___Hypothesis is evaluated based upon data ___Hypothesis is consistently described as supported or refuted ___All data collected is considered and addressed by conclusions, including presence of outliers, ___Explanations include relevant and accurate biological concepts Quality of Writing and Mechanics: Worth 1 point. Writeup should meet all of the following criteria! Yes No ☐ ☐ Write up includes your name, the date, and your lab section ☐ ☐ Write up is free from spelling and grammatical errors (make sure you proofread!!) ☐ ☐ Write up is clear and easy-to-understand ☐ ☐ Write up includes full citation for at least one reference with corresponding in-text citation ☐ ☐ All portions of write up are clearly labeled, and question numbers are included Plagiarism refers to the use of original work, ideas, or text that are not your own. This includes cut-and-paste from websites, copying directly from texts, and copying the work of others, including fellow students. Telling someone your answers to the questions (including telling someone how to make their graph, question #2), or asking for the answers to any question, is cheating. (Asking someone how to make the graph for this assignment is NOT the same as asking for help learning excel or some other software). All forms of cheating, including plagiarism and copying of work will result in an immediate zero for the exam, quiz, or assignment. In the case of copying, all parties involved in the unethical behavior will earn zeros. Cheating students will be referred to the Student Conduct Committee for further action. You also have the right to appeal to the Student Conduct Committee. I have read and understand the plagiarism statement. ____________________________________________________ Signature Guidelines for Good Quality Scientific Reports Hypothesis and Prediction: The hypothesis is a tentative explanation for the phenomenon. Remember that: • A good hypothesis and prediction is testable (and should be testable under the conditions of our lab environment; For example, if your hypothesis requires shooting a rocket into space, then its not really testable under our laboratory conditions). • Your explanation can be ruled out through testing, or falsified. • A good hypothesis and prediction is detailed and specific in what it is testing. • A good hypothesis provides a rationale or explanation for why you think your prediction is reasonable and this rationale is based on what we know about biology. • A good prediction is specific and can be tested with a specific experiment. Examples*: I think that diet soda will float and regular soda will sink. {This hypothesis misses the goal. It is not specific as we don’t know where the sodas are floating and sinking, and it does not provide any explanation to explain why the hypothesis makes sense} Because diet soda does not contain sugar and regular soda does, the diet soda will float in a bucket of water, while regular soda will sink. {This hypothesis approaches the goal. It is more specific about the conditions, and it provides a partial explanation about why the hypothesis makes sense, but the connection between sugar and sinking is unclear} If diet soda does not contain sugar, then its density (mass/volume) is lower than that of regular soda which does contain sugar, and so diet soda will float in a bucket of water while regular soda sinks. {This hypothesis meets the goal. It is specific and the rationale- sugar affects density and density is what determines floating or sinking in water- is clearly articulated} *Note that these examples are for different experiments and investigations and NOT about your osmosis lab. They are provided only to help you think about what you need to include in your write up. Graph: The graph is a visual representation of the data you gathered while testing your hypothesis. Remember that: • A graph needs a concise title that clearly describes the data that it is showing. • Data must be put on the correct axes of the graph. In general, the data you collected (representing what you are trying to find out about) goes on the vertical (Y) axis. The supporting data that that describes how, when or under what conditions you collected your data goes on the horizontal (X) axis. (For this reason time nearly always goes on the X-axis). • Axes must be labeled, including the units in which data were recorded • Data points should be clearly marked and identified; a key is helpful if more than one group of data is included in the graph. • The scale of a graph is important. It should be consistent (there should be no change in the units or increments on a single axis) and appropriate to the data you collected Examples: {This graph misses the goal. There is no title, nor is there a key to help distinguish what the data points mean. The scale is too large- from 0 to 100 with an increment of 50, when the maximum number in the graph is 25- and makes it hard to interpret this graph. The x-axis is labeled, but without units (the months) and the y-axis has units, but the label is incomplete- number of what?} {This graph meets the goal. There is a descriptive title, and all of the axes are clearly labeled with units. There is a key so that we can distinguish what each set of data points represent. The dependent variable (number of individuals) is correctly placed on the y-axis with the independent variable of time placed on the x-axis. The scale of 0-30 is appropriate to the data, with each line on the x-axis representing an increment of 5.} 0 50 100 Number Month 0 5 10 15 20 25 30 March April May June July Number of individuals Month (2011) Population size of three different madtom catiCish in the Marais de Cygnes River in Spring/Summer 2011 Brindled madtom Neosho madtom Slender madtom Analysis: You need to evaluate your hypothesis based on the data patterns shown by your graph. Remember that: • You use data to determine support or refute your hypothesis. It is only possible to support a hypothesis, not to “prove” one (that would require testing every possible permutation and combination of factors). Your evaluation of your hypothesis should not be contradicted by the pattern shown by your data. • Refer back to the prediction you made as part of your hypothesis and use your data to justify your decision to support or refute your hypothesis. • In the “if” part of your hypothesis you should have provided a rationale, or explanation for the prediction you made in your hypothesis (“then” part of hypothesis”). Use this to help you explain why you think you observed the specific pattern of data revealed in your graph. • You should consider all of the data you collected in examining the support (or lack of support for your hypothesis). If there are unusual data points or “outliers” that don’t seem to fit the general pattern in your graph, explain what you think those mean. Examples: I was right. Diet Pepsi floated and so did Apricot Nectar. Regular Pepsi sank. Obviously the regular Pepsi was heavier. This helps us understand the concept of density, which is a really important one. {This analysis misses the goal. The hypothesis isn’t actually mentioned and the data is only briefly described. There is no explanation of the importance of the Apricot Nectar results. Finally, there is no connection to how these results help understand density or why it is biologically important} I hypothesized that diet soda would float, and all three cans of diet Pepsi did float while the regular Pepsi sank. This supports my hypothesis. Both types of Pepsi were 8.5 fluid ounces in volume, but the regular Pepsi also contained 16 grams of sugar. This means that the regular Pepsi had 16 more grams of mass provided by the sugar in the same amount of volume. This would lead to an increase in density, which explains why the regular soda cans sank. When we put in a can of Apricot Nectar, which had 19 grams of sugar, it floated. This was unexpected, but I think it is explained by the fact that an Apricot Nectar can had a volume of 7 fluid ounces, but the dimensions of the can are the same as that of a Pepsi can. A same-sized can with less liquid probably has an air space that helped it float. The results of this experiment help us understand how the air bladder of a fish, which creates an air space inside the fish, helps it float in the water and also how seaweeds and other living things with air spaces or other factors that decrease their density keep from sinking to the bottom of the water. {This analysis meets the goal. It clearly ties the hypothesis to the results and outlines what they mean. It describes how the results support the hypothesis, but also explains a possible reason behind the unusual results of the Apricot Nectar. Finally, there is a link to how this experiment helps us understand biology}

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