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l butyl benzene
c)
2-ethyl-7-fluoro -3,6-dimethyl 4-octyne
d)
2-propyl-1,4-cyclohexadiene
e)
2-benzyl-4-butyl-2-iodo heptane

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2.Q1) (15 points) In the diagram below, M1 = 50 Kg, M2 = 20 Kg, mass and radius of the ...

g and 30 cm each, respectively. Both M1 and M2 rest on frictionless surfaces and the system starts from rest.
(a) Draw the fbd for each of M1, M2 and the pulley.
(b) Write the equations of motion for each of M1, M2 and the pulley.
(c) Calculate the linear acceleration of the two masses, as well as the angular acceleration of the pulley.
(d) Calculate the angular velocity of the pulley after M1 and M2 have been displaced linearly by 2 m.
Q2) (10 points) A basketball is thrown with an initial speed v0 of 10.8 m/s at 400 above horizontal, and it enters the hoop from above. The ball is released at 2.00 m above the ground. The hoop is 3.05 m above the ground and 10.0 m away from the player.
(a) Find the time at which the ball passes through the hoop.
(b) Find the ball’s velocity (express in component form) just when it enters the hoop.
(c) Find the ball’s maximum height.
Q3) (5 Points) An object is thrown up from the top of a building of height of 400 m with an initial velocity of 20 m/s.
(a) Find the position and the velocity of the object 5 s later.
(b) With what velocity will it hit the ground?
(c) At the same time the first object is thrown up, a second object is thrown up from the ground at 100 m/s. Will the two objects collide? If yes, calculate when and where,

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y aces or twos, you lose the game immediately. You also lose if you draw picture cards(J,Q,K) more than twice. In this question, you’ll study the probability of winning this game.(a) What is the probability of drawing no aces or twos after thirteen draws?(b) Given you have drawn thirteen times, none of which is aces or twos, what is the probability that you draw at most two picture cards?(c) What is the probability to win this game?
12. Suppose you are tossing an unbiased coin for100times.(a) What is the probability of getting50heads and50tails?(b) LetXbe the random variable counting the number of heads you observe in this exper-iment. What is the expected value ofX? What is the variance ofX? What is thestandard deviation ofX?
13. The following are probability distributions for two random variablesX,Y.
kPr(X=k)
0,0.4
1,0.3
2,0.3
kPr(Y=k)
0,0.5
1,0.3
2,0.2
(a) Construct the probability distribution table for the random variableXY.(b) Find E[X],E[Y] and E[XY]. Is is true that E[XY] =E[X]E[Y]?(c) Find the variances σ2X,σ2Y,σ2XY of X,Y and XY. Is it true that σ2XY=σ2Xσ2Y?
14. The aliens who are fond of gambling came back to play another game with you. In this game, you first toss a coin5times. If you observe3or fewer tails, you roll a die3times. If youobserve4or more tails, you roll a die20times. What is the probability that you end up with at most two6’s in your dice rolls?
15. (Challenge question, worth2points) You have two bags, each of which contains10marbles.Each time you remove a marble from a random bag. What is the probability that after one of the bags is emptied, there are still exactly3marbles in the other bag?

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vice. The company has four stores located at malls and is planning on expanding to other locations. Each store has a manager, a technician, and between one and four sales reps.
The owners want to create a personnel records database, and they asked you to review a table that they had designed. They suggested fields for Store Number, location, store telephone, manager name, and manager home telephone. They also want fields for technician name and technician home telephone and fields for up to four sales rep names and sales rep home telephones.
Draw an Entity Relationship Diagram modeling their suggested design.
Analyze their original design using the normalization concepts you learned in Module 9. For this part of the question, make sure you begin with the original table in an unnormalized form as requested by the company. Work your way through 1st, 2nd, and 3rd normal forms. At each point, be sure you use the standard notation format to show the changes in the structure of your table(s) (Module 9; 9.6.1). During your analysis, be sure to explicitly illustrate/write about the reason behind the design decisions you make. Additionally, each normal form should have it's own section/heading.
Draw a final ERD showing your final analysis showing the relationship among the entities you identified during normalization

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rvice. The company has four stores located at malls and is planning on expanding to other locations. Each store has a manager, a technician, and between one and four sales reps.
The owners want to create a personnel records database, and they asked you to review a table that they had designed. They suggested fields for Store Number, location, store telephone, manager name, and manager home telephone. They also want fields for technician name and technician home telephone and fields for up to four sales rep names and sales rep home telephones.
a. Draw an Entity Relationship Diagram modeling their suggested design.
b. Analyze their original design using the normalization concepts you learned in Module 9. For this part of the question, make sure you begin with the original table in an unnormalized form as requested by the company. Work your way through 1st, 2nd, and 3rd normal forms. At each point, be sure you use the standard notation format to show the changes in the structure of your table(s) (Module 9; 9.6.1). During your analysis, be sure to explicitly illustrate/write about the reason behind the design decisions you make. Additionally, each normal form should have it's own section/heading.
c. Draw a final ERD showing your final analysis showing the relationship among the entities you identified during normalization

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given in a local coordinate frame.
Draw the result of applying each of the following transformations to the flag.
Label the new coordinates for the four vertices labelled above. Show values to 1 decimal place.
R(-90°)
S(-2,1)
T(1,2) R(180°)
R(90°) T(-1,0)
S(1,2) R(-45°)
R(-45°) S(1,2)

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2,3,4,7). If it lands tails, a fair six-sided die is
thrown (with values 3,4,5,6,7,9). Regardless of which die is used, Alice
eats n grains of rice, where n is the largest prime factor of the die result
(for example, the largest prime factor of 9 is 3).
(a) What is the conditional probability that the coin lands heads, given
that Alice eats three grains of rice?
(b) Suppose that the entire experiment is conducted twice on the following day (starting with a new coin toss on the second run-through).
What is the conditional probability that the coin lands heads on both
run-throughs, given that Alice eats a total of five grains of rice during the two run-throughs?
(Do not count the two grains from part (a) in part (b); we assume
two brand new experiments, each with a new coin toss. Start your
solution by defining a suitable partition of the sample space. Please
use an appropriate notation and/or justification in words, for each
value that you give as part of your solution.)
Exercise 5) Alice and Bob throw an unfair coin repeatedly, with probability 2/5 of landing heads. Alice starts with £2 and Bob starts with £3 .
Each time the unfair coin lands heads, Alice gives Bob £1 . Each time
the unfair coin lands tails, Bob gives Alice £1 . The game ends when one
player has £5 .
(a) Draw a labelled Markov chain describing the problem, and write
down a transition matrix P. Write down the communication classes,
and classify them as either recurrent or transient.
(b) Using the transition matrix, calculate the probability that Alice loses
all of her money in exactly four tosses of the unfair coin.
(c) Calculate the (total) probability that Alice loses all of her money
(before Bob loses all of his).
(d) Calculate the expected (mean) number of tosses of the unfair coin,
for the game to end.

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0.5 kilometers.
a) Draw a figure to represent the above problem. Let l and w represent the length and width of the rectangle, respectively.
b) Write the area A of the rectangular region as a function of I and in meters (not kilometers).
c) Write the area A of the rectangular regional as a function of w and in meters (not kilometers).

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subgame perfect Nash equilibrium?
Question 3: In which situations should we need the mixed extension of a game?
Question 4: Find, if any, all Nash equilibria of the following famous matrix game:
L R
U (2,0) (3,3)
D (3,4) (1,2)
Question 5: What is the difference between a separating equilibrium and a pooling equilibrium
in Bayesian games?
Question 6: Give another name for, if it exists, the intersection of the players’ best-response
« functions » in a game?
Question 7: assuming we only deal with pure strategies, the Prisoner’s Dilemma is a situation
with:
No Nash equilibrium One sub-optimal Nash equilibrium
One sub-optimal dominant profile No dominant profile
Question 8: If it exists, a pure Nash equilibrium is always a profile of dominant strategies:
True False
Question 9: All games have at least one pure strategy Nash equilibrium:
True False
Question 10: If a tree game has a backward induction equilibrium then it must also be a Nash
equilibrium of all of its subgames:
Tr
2/2
Question 11: The mixed Nash equilibrium payoffs are always strictly smaller than the pure
Nash equilibrium payoffs:
True False
Question 12: Which of the following statements about dominant/dominated strategies is/are
true?
I. A dominant strategy dominates a dominated strategy in 2x2 games.
II. A dominated strategy must be dominated by a dominant strategy in all games.
III. A profile of dominant strategies must be a pure strategy Nash equilibrium.
IV. A dominated strategy must be dominated by a dominant strategy in 2x2 games.
I, II and IV only I, II and III only II and III only
I and IV only I, III and IV only I and II only
Question 13: A pure strategy Nash equilibrium is a special case of a mixed strategy Nash
equilibrium:
True False
Question 14: Consider the following 2x2 matrix game:
L R
U (3,2) (2,4)
D (-1,4) (4,3)
The number of pure and mixed Nash equilibria in the above game is:
0 1
2 3
Exercise (corresponding to questions 15 to 20 below): assume a medical doctor (M)
prescribes either drug A or drug B to a patient (P), who complies (C) or not (NC) with each of
this treatment. In case of compliance, controlled by an authority in charge of health services
quality, the physician is rewarded at a level of 1 for drug A and 2 for drug B. In case of noncompliance, the physician is « punished » at -1 level for non-compliance of the patient with
drug A and at -2 level for non-compliance with drug B. As for the compliant patient, drug A
should give him back 2 years of life saved and drug B, only 1 year of life saved. When noncompliant with drug A, the same patient wins 3 years of life (due to avoiding unexpected
allergic shock for instance), and when non-compliant with drug B, the patient loses 3 years of
life.
Question 15: You will draw the corresponding matrix of the simultaneous doctor-patient game.
Question 16: Find, if any, the profile(s) of dominant strategies of this game.
Question 17: Find, if any, the pure strategy Nash equilibrium/equilibria of this game.
Question 18: Find, if any, the mixed strategy Nash equilibrium/equilibria of this game.
Questions 19 and 20: Now the doctor prescribes first, then the patient complies or not: draw
the corresponding extensive-form game (= question 19) AND find the subgame perfect Nash
equilibrium/equilibria (=

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ibes either drug A or drug B to a patient (P), who complies (C) or not (NC) with each of
this treatment. In case of compliance, controlled by an authority in charge of health services
quality, the physician is rewarded at a level of 1 for drug A and 2 for drug B. In case of noncompliance, the physician is « punished » at -1 level for non-compliance of the patient with
drug A and at -2 level for non-compliance with drug B. As for the compliant patient, drug A
should give him back 2 years of life saved and drug B, only 1 year of life saved. When noncompliant with drug A, the same patient wins 3 years of life (due to avoiding unexpected
allergic shock for instance), and when non-compliant with drug B, the patient loses 3 years of
life.
Question 15: You will draw the corresponding matrix of the simultaneous doctor-patient game.
Question 16: Find, if any, the profile(s) of dominant strategies of this game.
Question 17: Find, if any, the pure strategy Nash equilibrium/equilibria of this game.
Question 18: Find, if any, the mixed strategy Nash equilibrium/equilibria of this game.
Questions 19 and 20: Now the doctor prescribes first, then the patient complies or not: draw
the corresponding extensive-form game (= question 19) AND find the subgame perfect Nash
equilibrium/equilibria (=

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Jays winning each game is 0.375. If the Jays win the first game in this series, what is the probability they will win the series? (Hint: draw a tree diagram and consider each case that would lead to the Jays winning the series.)

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adrants of the coordinate plane
b) Reflect in the line: y = 8
c) Translate: (x, y) (x + 13, y+4)
d) Reflect in the line: y = -x + 3
e) Rotate: 90°
2) Color each image a different color and outline it in black.
3) Color each quadrant in a different color (not the same color as the image or images on the letter in it).
Use a mapping chart to describe each transformation. Use of notation is important. For example, T2,3 or ry=1, or R90° must be used in the mapping chart.
Write a paragraph explaining who M. C. Escher and what contribution he made to art using tessellation. Define tessellation.

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rts to the fireworks platforms: one part is on the ground and the
other part is on top of a building. You are going to graph all of your results on one
coordinate plane. Make sure to label each graph with its equation. Use the following
equations to assist with this assignment.
• The function for objects dropped from a height where t is the time in
seconds, h is the height in feet at time it t, and 0 h is the initial height is
2
0 ht t h ( ) 16 =− + .
• The function for objects that are launched where t is the time in seconds, h is
the height in feet at time t, 0 h is the initial height, and 0 v is the initial velocity
in feet per second is 2
0 0 ht t vt h ( ) 16 =− + + .
Select the link below to access centimeter grid paper for your portfolio.
Centimeter Grid Paper
Task 1
First, conduct some research to help you with later portions of this portfolio
assessment.
• Find a local building and estimate its height. How tall do you think the
building is?
• Use the Internet to find some initial velocities for different types of fireworks.
What are some of the initial velocities that you found?
Task 2
Respond to the following items.
1. While setting up a fireworks display, you have a tool at the top of the
building and need to drop it to a coworker below.
a. How long will it take the tool to fall to the ground? (Hint: use the first
equation that you were given above, 2
0 ht t h ( ) 16 =− + . For the building’s
height, use the height of the building that you estimated in Task 1.)
b. Draw a graph that represents the path of this tool falling to the
ground. Be sure to label your axes with a title and a scale. Your graph
should show the height of the tool, h, after t seconds have passed.
Label this line “Tool”.

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14.a) Draw a diagram to represent each of the following reactions. Then balance each equation. b) ...

Include all states of matter.
c) Remember to stay consistent in your representation of atoms. For example if you decide to represent the hydrogen atom as a blue sphere then you must continue to use this symbol and colour in all equations that contain the hydrogen atom.

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m 2
After graduating from AUD, Salman plans to start a book publishing company in the Media City. He did some research and found that the printer will cost Dh 230,000. He estimated that the variable cost per book is Dh 170 and the selling price is Dh 390.
a. How many books must he sell to break even? Also calculate the breakeven in dirham.
b. In addition to the costs given above, if he wants to pay himself a salary of Dh 15,400 per year, what is her breakeven point in units and dirham?
c. In the first three months of his business, he sold 400 books. Suddenly the printer breaks down. He spent Dh 25000 to fix the printer. In addition to 400 books sold, how many more books she should sell to breakeven? Assume that this part of the question is independent, and she does not draw any salary.
Problem 8
A furniture store makes tables and chairs from plywood and glass. The store has 30 units of plywood, 24 units of glass. Each table requires 7 units of plywood three units of glass, whereas each chair requires three units of plywood and two units of glass. The demand for chairs is between 2 and 4. The ratio between the table and chair is at least 1 to 2. A table earns $225 in profit and a chair, $145. The store also wants a minimum profit of $5000. The store wants to determine the number of tables and chairs to make in order to maximize profit. Formulate a linear programming model for this problem

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16.An elevator WEIGHS 1.0 x 10⁴ N. {Part A} Draw a free body diagram for each part of this questions ...

to show which force is larger [5 marks] {Part B} Determine the MASS of the elevator [2 marks] {Part C} The elevator begins to accelerate UPWARDS from rest at 5.0 m/s². What is the force tension in the cable? [3 marks] {Part D} The same elevator is moving UPWARDS and starts to DECELERATE at 3.0 m/s². What is the force tension in the cable? [3 marks] {Part E} The elevator moves DOWN at CONSTANT velocity at 10 m/s. What is the force tension in the cable? [2 marks] {Part F} The elevator cable snaps (and everyone screams!). What are the forces working on the elevator now? Draw a diagram [2 marks]

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17.Twenty students are asked to select an integer between 1 and 10. Eight choose either 4, 5 or 6. a If ...

f the students make their choices independently and each is as likely to pick one integer
as any other, what is the probability that 8 or more will select 4,5 or 6?
b Having observed eight students who selected 4, 5, or 6, what conclusion do you draw based
on your answer to part (a)?A missile protection system consists of n radar sets operating independently, each with a
probability of .9 of detecting a missile entering a zone that is covered by all of the units.
a If n = 5 and a missile enters the zone, what is the probability that exactly four sets detect
the missile? At least one set?
b How large must n be if we require that the probability of detecting a missile that enters the
zone be .999?

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k of 10 cards numbered 1-10. I draw 5 cards (each time i draw i put the card back and shuffle). The numbers were 8, 2, 4, 9, and 4. What is the probability that it will be 4 on the 6th time i draw? I know each card has a 10% chance of being drawn. I also know the probability of a 10% event happening twice is 1%. But wouldnt the odds be lower since i drew 4 a couple trials earlier? How exactly would i calculate that. If there is an online calculator that executes the answer id like to know. Just a college student who craves probability. :)

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o C 61.4%; H 3.9%; O 12.6%; Fe 22%. A displays strong IR bands at 2020 cm-1 and 1970 cm-1 and its 1H NMR spectrum shows 2 peaks at 7.12 ppm (integration = 5) and 4.98 ppm (integration = 5). Identify and draw the structure of A and assign the NMR data. Count the electrons for each of A and CpFe(CO)2Cl.

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e based on the provided data set.
You can draw the tree electronically, or draw it by hand and scan or photograph a copy—or use any other appropriate means you wish.
2. How many homoplasies are in the tree? Give the nucleotide position number(s) and tell what character states were independently derived in which species.
3. Two major clades are revealed by the tree. List the species in each clade. What can you say in general about the geographic distribution of each clade?
4. In cases where two species of Map Turtle occupy the same river system, are those species each other’s nearest relatives? Considering their phylogeny and distribution, what speciation events (including such factors as migration, vicariance, etc.) would you predict led to the species found in these rivers and their current distributions?

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21.a 4 feet tall layer shoots a 28 foot shot that was higher than 12 feet but less than 16 ...

l draw and label a graph for each of the situations so that each graph has 3 equations

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n(A)equals14, n(Upper A intersect Upper B intersect Upper C)equals4, n(Upper A intersect Upper C)equals11, n(Upper A intersect Upper B prime)equals8, n(Upper B intersect Upper C)equals9, n(Upper A prime intersect Upper B prime intersect Upper C prime)equals21, n(Upper B intersect Upper C prime)equals4, n(Upper B union Upper C)equals33
Complete the Venn diagram.
\

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics