Category: Writing

“What Does the Working Man Want?” (1890), the speech by Samuel L. Gompers. The American Federation of Labor was founded in 1886. It organized only skilled workers in craft unions. Federation leaders felt that, since employers could easily replace unskilled workers during a strike, those workers would not have enough bargaining power to make them valuable union members. The union also excluded African Americans, women, and recent immigrants. Samuel L. Gompers, a cigar maker by trade, was the AFL’s president from 1886 to 1924. He was against militant unionism as a way to gain labor’s goals. During World War I, he directed the War Committee on Labor and did much to make unionism acceptable to the American public. In the following excerpt from a speech delivered in 1890, Gompers explains the goals of the AFL.

… Why, when you reduce the hours of labor, say an hour a day, just think what it means. Suppose men who work ten hours a day had the time lessened to nine, or men who work nine hours a day have it reduced to eight hours; what does it mean? It means millions of golden hours and opportunities for thought. Some men might say you will go to sleep. Well, some men might sleep sixteen hours a day; the ordinary man might try that, but he would soon find he could not do it long. He would have to do something. He would probably go to the theater one night, to a concert another night, but he could not do that every night. He would probably become interested in some study and the hours that have been taken from manual labor are devoted to mental labor, said that we will want more; that last year we got and the mental labor of one hour will produce for an advance of ten cents and now we want more. We do want more. You will find that a man generally wants more.

… You ask a workingman who is getting two dollars a day, and he will say that he wants ten cents more. Ask a man who gets five dollars a day and he will want fifty cents more. The man who receives five thousand dollars a year wants six thousand dollars a year, and the hundred fold, we insist that it has been brought to make it a million, while the man who has his about by the intelligence and energy of the millions will want everything he can by his hands workingmen, and while we find that it is now harder to live. We do want more, and when it becomes more, we shall still want more. And we shall never cease to demand more until we have received the results of our labor.

Now answer Numbers 1 through 8. Base your answers on the speech “What Does the Working Man Want?”

(1) Why were unskilled workers not allowed into craft unions?
A. They could not be relied upon to go on strike
B. They would not be helpful to the union in a strike
C. They were uneducated and could not speak English
D. They were largely made up of women and minorities

(2) According to Gompers, how could “millions of golden hours” be created?
F. by allowing people to sleep as much as they want
G. by reducing the number of hours people must work
H. by increasing the opportunities for meaningful work
I. by using militant unionism to reach the union’s goals

(3) Gompers believed that the greatest wealth is brought about by
A. long work hours.
B. hard physical work.
C. interesting mental work.
D. better working conditions.

(4) Why were Gompers and the rest of the union workers accused of being selfish?
F. They let only skilled workers join the union
G. They would not allow poor people in their union
H. Once they got what they asked for, they always asked for more
L. Once they became rich, they would protest poor workers getting a raise

(5) According to Gompers, who was responsible for the great wealth of the nineteenth century?
A. workers
B. inventors
C. businesspeople
D. union leaders

(6) Gompers claimed that they would stop making demands when
F. the high costs of living went down.
G. they got what they deserved for their hard work.
H. modern inventions made working conditions better.
I. millionaires stopped protesting against pay raises for the poor.

(7) What was the purpose of Gompers’s speech?
A. to persuade workers to join the labor union
B. to list the accomplishments made by the labor union
C. to explain why the workers were making their demands
D. to describe the contributions made by the workers

(8) According to Gompers, how are all people ALIKE?
F. No matter what they achieve, they will always want more.
G. No matter how hard they work, they will never get what they deserve.
H. No matter how rich they are, they will never appreciate what they have.
I. No matter who they are, they will always prefer leisure time to working.

Can Someone please help me with this question? this is due on Thursday night.
The major assignment involves producing a Pacman style game in Clara Online.
Spring 2022> The Major Assignment > Pac-Man Game For your convenience, all important requirements specified in this brief are re-listed here: – Clara and the Ghosts must be able to move from one side of the game to the other with the “wrapAroundWorld()” method – Clara must be capable of being controlled with at least the arrow keys on the keyboard – Clara must not move in the game until after an arrow key pressed – Clara must stop before hitting trees or the ghost wall – Clara must be able to eat leaves, and play the appropriate sound when doing so – When all the leaves are eaten, the game must progress to the next level – When each level starts the intro sound must be played once for each level and Clara and the Ghosts must not be able to move until after the intro sound has completed playing – Ghosts must move slower than Clara when moving normally and when scared – Ghosts must stop before hitting trees – Ghosts must randomly decide on a direction to go in when they find themselves in an intersection – When Clara and a Ghost collide, and the Ghost is neither dead nor scared, she must die, and play the appropriate sound – When Clara is dead the player must not be able to continue controlling her – Clara must be able to eat mushrooms, and this must make the Ghosts scared – When the Ghosts are scared, they must run the appropriate animation – When Clara and a Ghost collide, and the Ghost is scared, the Ghost must die, play the appropriate sound and play the appropriate animation – When Ghosts are dead they must attempt to return to the Ghost Healer – When Ghosts collide with the Ghost Healer they must no longer be dead – You must make, at a minimum, one extra level – All files must compile and the game must run. While in the past you only had to work with one file, this time you will have to edit Ghost for all the logic related to the Ghosts as well as MyClara for all the Clara functionality. Important note 2 Do not let the following list of commands scare you, as they are further explained in the assignment brief and your tutors will help you to select those commands that you need for each task. Important note 3 For this assignment you should no longer have a main loop (for or while) inside act(). Instead you should rely on the act() method being executed repetitively (similar to how you did in Practical 2). The stop(); command MUST NOT be used in this assignment. Cnrineranon, Tho Maine Accirnmants Dar-MAan Famo Spring 2022> The Major Assignment > Pac-Man Game – down if Clara is getDirection() Gets which direction Clara is facing. Nothing. facing toward the bottom of the screen. right if Clara is facing to the right side of the screen. left if Clara is facing to the left side of the screen. – A String, which specifies which direction you want face. – “up” – face – Makes Clara face a specific direction. Spring 2022> The Major Assignment > Pac-Man Game – Makes Clara face a specific top of the Spring 2022> The Major Assignment > Pac-Man Game – For more information, see makeScared() the “isScared() function in Nothing. the Ghost’s vocabulary. Also see the section “Part 10 – Eating Mushrooms and Making Ghosts Eatable” Spring 2022> The Major Assignment > Pac-Man Game animateDead() For more information, see  Nothin the section “Part 9 – Ghosts Colliding With Clara and Losing” – Nothing. – Will show an Spring 2022 > The Major Assignment > Pac-Man Game Spring 2022> The Major Assignment > Pac-Man Game An integer Spring 2022 > The Major Assignment > Pac-Man Game Spring 2022 > The Major Assignment > Pac-Man Game Note that this method is Ghost. relative to the screen, not Nothing. the Ghost. That is, regardless  false if there is of the direction of the Ghost, not a below a tree that is below it, will the Ghost. always be below it. – Astring which represents the direction the Ghost is facing. “up” if the Ghost is facing up toward the top of the screen. “down” if the Ghost is facing toward the bottom of the screen. “right” if the Ghost is facing to the right side of the screen. “left” if the Ghost is facing to the left side of the screen. The Major Assignment > Pac-Man Game – Astring, which specifies which direction you want the Ghost to face. “up” if you want it to face toward the top of the screen. “down” if you want it to face Nothing. toward the bottom of the screen. “right” if you want it to face toward the right side of the screen. “left” if you want it to face Spring 2022> The Major Assignment > Pac-Man Game “left” if you want it to face toward the left side of the screen. Spring 2022 > The Major Assignment > Pac-Man Game – The Ghosts continues its death animation by one frame.
animateDead()
the more information, see “Part 10 – Eating
Mushrooms and Making
Ghosts Eatable”
?
Nothing.
– The Ghosts continues its scared animation by one frame. animateScared() For more information, see Nothing. Nothing. the section “Part 10 – Eating Mushrooms and Making Ghosts Eatable” –  Gets Clara. Spring 2022> The Major Assignment > Pac-Man Game –  Gets Clara. – Is to be used with the Is to be used with the getClara() “isAboveMe”, “isBelowMe”,  Nothing. “isToMyLeft” and “isToMyRight” commands, explained below. – Gets the Ghost Healer. – Is to be used with the “isAboveMe” “isBelowMe”,  Nothing.  Ghost Healer. “isToMyLeft” and “isToMyRight” commands, explained below. – true if specified Spring 2022> The Major Assignment > Pac-Man Game ne Spring 2022> The Major Assignment > Pac-Man Game One of your first tasks – is to learn how to process keyboard input of the player by using Keyboard.isKeyDown(String) method. Try passing the movement constants defined inside MyClara.java as input for Keyboard.isKeyDown(String) and see what happens when you press the arrow keys. Try starting with using System.out.println() to print which of the keys was pressed to make yourself familiar with keyboard input. Next thing for you to do – is to make sure that Clara can be controlled with the arrow keys. You may add extra functionality, such as controls for left handed players, but that is not compulsory. You will need to use Clara’s “setDirection(String)” method, which can be sent one of the following commands; “up”, “down”, left” or “right” (a good idea is to use the same movement constants defined inside MyClara rather than using those String literals inside your code). Passing the aforementioned String values to setDirection(String) method will set Clara’s direction to the command you specify. Note that the “setDirection(String)” method will not change Clara to a specified direction if there is a tree in that direction. Once you’re able to process keyboard input and make Clara respond to it by turning in the right direction – now it’s time to make Clara move. In order to make Clara move, you will need to use the “move(int)” method. Note that it can be passed any integer, and that a bigger integer will make Clara move faster. The integer that it is passed will determine how fast Clara moves. It will be up to you to determine a suitable speed for Clara. Please note that it is not a good programming practice to arbitrarily pass numbers to methods, and that it is always a good idea to instead, make a constant that will hold the value that you wish to pass. Then you will need to somehow stop Clara from automatically moving at the start of the game, and only start continuously moving after a single key is pressed. Note that as per the original Pacman game, it is only necessary to stop Clara from moving before the initial key press, and that after that, it is perfectly acceptable to have Clara continuously move in the direction that was last selected. Once you have determined, and tested, a suitable speed, you might notice Clara disappearing off the edge of the world. It is important that Clara, and the Ghosts, at some point call the method “wrapAroundWorld()” to deal with this issue. This will enable them to reappear on the opposite side of the world that they disappear off. Part 2 – Animating Clara’s Movement In order to animate Clara, you will need to call the “animate()” method. You may notice, that if you just call the “animate()” method, that it cycles through Clara’s animation very quickly. This is because every time the method is called, it advances Clara’s animation to the next frame. You will need to figure out a way of not calling it every time the act method is run, but every so many times that the act method is run. HINT: If you are having trouble, try only calling “animate()” every second time the act method is called. Then try editing that attempt to work only every third time the act method is called. It will ultimately be up to you to determine what looks best. Part 3 – Clara Collisions with Trees and Ghost Walls Obviously, Clara really shouldn’t be floating through the world; she should stop before hitting trees. She will also need to stop before hitting the Ghost Wall, as only the Ghosts are allowed to pass through it. It will be up to you to figure out how to stop Clara from passing through either. HINT: You will need to use the “ghostWallFront()” method. Part 4 – Eating Leaves and Winning Clara will need to eat all of the leaves in order to win. First, she will need to be capable of eating leaves. If you Clara will need to eat all of the leaves in order to win. First, she will need to be capable of eating leaves. If you are unsure of how to do this, please revise practicals 1 and 2. Once you’ve got Clara eating leaves, you’ll need to play the right sound. To do so, you’ll need to call the method “playLeafEatenSound()” at an appropriate point in your code. When you have Clara happily eating leaves, you’ll need to check that all leaves have been eaten and progress to the next level. You will need to use the “allLeavesEaten()”, “advanceToLevel(char[][])” and “getCurrentLevelNumber()” methods. You will need to somehow check what the current level is, and either advance to the next available level, or, if there are no more available levels, advance back to the first level again. Note that if you wish to return back to the first level, all you need to do is send LEVEL_1 or null to the “advanceToLevel(char[][])” method. Please note that actually adding levels to the “advanceToNextLevel()” method is covered in “Part 12 – Making and Adding Levels”. Once you can advance to new levels, or return to the first level after player completes it, it’s time to play the famous Pacman intro music at the start of each level. Note that it is a requirement to not allow Clara or the Ghosts to move until after the intro music has finished playing and the intro music must only play once for each level. You will need to use the methods “playPacmanlntro()” and “isPacmanIntroStillPlaying()”. For now, just focus on stopping Clara from moving while it is playing. Note that after doing the above, you may wish to comment out the code that plays the intro music and prevents movement while testing the game, but remember to uncomment it and add it back in when you’re ready to submit. Part 5 – Moving Ghosts Making the Ghosts move is very similar to making Clara move, but all your corresponding code must now be placed inside Ghost.java. You will need to call the “move(int)” method and determine a suitable speed for Ghosts. Note that they should move slower than Clara at this point. It is also a good idea to add the code to stop them from moving when the intro is playing. You will need to use the method “isPacmanlntroStillPlaying()”. Don’t forget to call the “wrapAroundWorld()” method, so that Ghosts correctly move after reaching the edge of the world. Part 6 – Animating Ghosts’ Movement Making the Ghosts animated works in the similar way as animating Clara. The method you call is exactly the same. Just like Clara, you will need to figure out a way of calling the “animate()” method every so often that the act method is called, and that it is up to you to determine how often they should animate. Part 7 – Ghosts and Tree Collisions Making the Ghosts detect that a tree is in the way, and stop, is achieved in a similar way as making Clara do so, you will even need the same methods. Although, unlike Clara, there is no human player to tell the Ghosts where to go after they hit a tree. It is up to you to decide what they should generally do when they hit one. Note that telling the Ghosts where to face will involve using the “setDirection(string)” method, just like with Clara. It may assist your general Ghost logic if you use the “getDirection()” method, which returns a string just like you would send the “setDirection(string)” method, and that the string will be either “up”, “down”, “left” or “right”. It is not necessary to use the “getDirection()” method, but you may find it helpful while testing and Note that telling the Ghosts where to face will involve using the “setDirection(string)” method, just like with Clara. It may assist your general Ghost logic if you use the “getDirection()” method, which returns a string just like you would send the “setDirection(string)” method, and that the string will be either “up”, “down”, “left” or “right”. It is not necessary to use the “getDirection()” method, but you may find it helpful while testing and debugging your code. Note that, just like Clara, the “setDirection(string)” method will not change the Ghost to a specified direction if there is a tree in that direction. Part 8 – Al and Intersections An important part of making your Ghosts intelligent – is detecting an intersection and deciding which way to go. You should start with simply selecting a random direction at an intersection by using random numbers covered in the lectures. You will need to use the methods “treeAbove()”, “treeBelow()”, “treeToLeft()” and “treeToRight()” to detect an intersection. It should be noted that, unlike most sensor commands that you’ve used before, like “treeFront()” and “treeleft()”, these commands are not relative to the direction that the Ghost is facing, they are relative to the screen itself. This means that a tree that is above the Ghost, will always be above the ghost, regardless of which direction it is facing. This basic logic is true for all four aforementioned commands. Test them out in order to understand them. Drag one of the Ghosts around and see what is the result of calling those methods. It should be noted that, for the most part, an intersection can be defined as a location where there are three or more directions to go to. HINT: You might want to check to make sure the Ghost has passed the intersection it is currently at before running the code to choose a direction at an intersection. (Otherwise, it might just hang around the same intersection and not go anywhere). For more advanced students, use the “isAboveMe()”, “isBelowMe()”, “isToMyLeft()”, “isToMyRight()” and “getClara()” methods to give them a 50% chance of moving in the Clara’s direction at every intersection. Note that the “isAboveMe()”, “isBelowMe()”, “isToMyLeft()”, “isToMyRight()” methods are further explained in the “Part 11 – Ghosts and Regeneration”. Part 9 – Ghosts Colliding with Clara and Losing The Ghosts must pose a threat to Clara, and as such, they must kill her if they catch her. In order to do so, you will need to check if they have collided with Clara. To do so, you will need to use the methods “intersects(Actor)”, “getClara()” and “makeClaraDead()” inside the Ghost class. Clara will need to use the method “isClaraDead()” to signal that the game is over. It is important for the Ghosts to be continually checking whether they have caught Clara, and it is important for Clara to check whether she is dead to prevent further movement and animation. Once you have Clara capable of checking whether she is dead, you will need to show the appropriate death image, with Clara’s method “animateDead()” and play the appropriate sound with the method “playClaraDieSound()”. It is important that the method “playClaraDieSound()” is only called once. It is also important that you stop processing keyboard input from the player at the point of Clara’s death. Note that Clara’s “animateDead()” method only contains one frame, and so it is acceptable to run it every time the act method is called after Clara is dead. Part 10 – Eating Mushrooms and Making Ghosts Eatable Clara will need to able to eat mushrooms and get her super power. In order to do so, you will need to use methods “onMushroom()” and “removeMushroom()”. Then you will need to appropriately place the method “makeScared()” when Clara has eaten a mushroom. The Clara will need to able to eat mushrooms and get her super power. In order to do so, you will need to use methods “onMushroom()” and “removeMushroom()”. Then you will need to appropriately place the method “makeScared()” when Clara has eaten a mushroom. The Ghosts will need to check whether or not they should be scared, and switch to the appropriate animation when they are. You will need to use the methods “isScared()” and “animateScared()”. Note that the “animateScared()” method will need to be run every so many times that the act method is called, just like the “animate()” method. It is acceptable, but not compulsory to increase the Ghosts’ speed when they are scared, but they should be slower than Clara. You will then need to ensure that the Ghosts don’t kill Clara when they collide with her if they are scared, and instead, die themselves. It will be up to you to create your own variable that checks if the Ghosts are dead. You will need the “animateDead()”and “playGhostEatenSound()” methods. It is important to note that the Ghosts do not stop moving when they are dead, and that the Ghost’s “animateDead()” method will need to be run every so many times that the act method is called, just like the “animate()” method. It is also important that the Ghosts should not harm Clara when they are scared or when they are dead. Also note that the game will automatically decide how long the Ghosts should be scared for. Part 11 – Ghosts and Regeneration When a Ghost is dead, it will need to return to the Ghost Healer, which is the red object near where the Ghosts start. It will be up to you to decide how they should logically make their way back to the Ghost Healer object. You will need to use the “isAboveMe(Actor)”, “isBelowMe(Actor)”, “isToMyLeft(Actor)”, “isToMyRight(Actor)” and “getGhostHealer()” methods to make this happen. Note that the “isAboveMe(Actor)”, “isBelowMe(Actor)”, “isToMyLeft(Actor)”, “isToMyRight(Actor)” methods need to be sent an Actor, and that only two are available to you, through the “getGhostHealer()” and “getClara()” methods. You will need to send those ‘get’ methods to the ‘is’ methods in order to get an appropriate answer. An example of how to use the above functions is below: “isAboveMe( getGhostHealer() );” If the above example returns true, then the Ghost Healer is above the Ghost. When the Ghost returns to the Ghost Healer object, it will need to make itself no longer dead. You will need the “intersects(Actor)” and “getGhostHealer()” methods to make this work. Part 12 – Making and Adding Levels It’s time to understand how Clara’s world is designed in this game, and how to design and add your own levels. When you first opened up “MyClara”, you may have noticed the first level at the top of the code. This is the format you will need to use in order to create your own levels. See the image below for what you should roughly see when first opening up “MyClara”. You’ll notice that a level is simply an array of characters that visually represent the level that they make. The characters used are as follows: – ‘#’ represents a tree, which is an obstacle to both Clara and the Ghosts. – “. represents a leaf, which Clara needs to eat in order to progress to the next level. – ‘ ‘ represents nothing, which is essentially an empty tile. – ‘%’ represents a Ghost. At least one must be present in every level you make. – ‘?’ represents a Ghost Healer, which the Ghosts return to when eaten in order to come back to life. At least one must be present in every level you make. – ‘I’ represents a Ghost Wall, which is an obstacle that only Ghosts may pass through, and not Clara. It is connected to the group of trees that make up the initial room that the Ghosts start in. At least one must be present in every level you make. – ‘$’ represents a mushroom, which can be eaten by Clara in order to make the Ghosts scared and capable of being killed by Clara. – ‘@’ represents Clara, it is where she will start at the beginning of the level. Only one must be present in every level you make. The characters that make up the array of a level in Clara’s world are each surrounded by single quotes (‘) and the characters in a single row are separated by commas (,). A single row in a level is surrounded by curly braces({}), and the end of a row of a level, that is not the end of the whole level, is indicated by a comma after the closing curly brace (},). Now you should have a rough understanding of how Clara’s world is constructed. or peing Killea py Liara. – ‘@’ represents Clara, it is where she will start at the beginning of the level. Only one must be present in every level you make. The characters that make up the array of a level in Clara’s world are each surrounded by single quotes (‘) and the characters in a single row are separated by commas (,). A single row in a level is surrounded by curly braces({}), and the end of a row of a level, that is not the end of the whole level, is indicated by a comma after the closing curly brace (},). Now you should have a rough understanding of how Clara’s world is constructed. In order to build your own level, all you have to do is delete all of the streets of the level and write your own level in there, following the above rules in order to present it and write it properly. Then write your own level, in between the curly braces that are left after you delete what was highlighted. After you’re done, you’ll need to go to where you call the “advanceToLevel(char[][])” method and figure out a way of sending it “LEVEL_2” when the player has finished “LEVEL_1”. Now add a new level, and test it. To add another level, simply copy and paste “LEVEL_2” inside MyClara and change it to “LEVEL_3”, and modify it just like you did for level 2. Add as many levels as you want, although technically you are only required to add one more level. Part 13 – Life is Good Now tidy up your code, add more levels if you want, but be sure to properly comment what you’ve coded. You’re ready to hand in your assignment. Life is good!
Clara’s vocabulary
For this assignment, the following commands are available for Clara right from the start:
Ghost’s vocabulary
Making the Game

1. Open the start file EX2019-Challenge Yourself-2-4-ALT. The file will be renamed automatically to include your name Change the project file name it directed to do so by your instructor, and save it 2. If the workbook opens in Protected View, click the Enable Editing button in the Message Bar at the top of the workbook so you can modify it 3. Center and merge the title across cells A1:41 4. Apply the Title cell style to the merged cells. 5. Merge and center the four section titles across the appropriate cells (Monthly Income Available income, Monthly Expenses and Preschool Expenses) 6. Apply cell styles to the section titles as follows: a. Monthly Income Accent b. Available income Accent2 cMonthly Expenses – Accent d. Preschool Expenses Accent1 7. Add the Green, Accent 6, Lighter 80% fill color to cells A4:B4. It is the last color in the second row under Theme Colors 8. Bold cells A4:34 9. Copy only the formatting of cells A4:B4 to the headers in the other sections (cells A12:B12, 04:E4, and D12:E12). 10. The line item for Transportation (cells A21:321) is in the wrong category. Cut the cells and insert them into cells D15:15 shifting the other cells down. Do not overwrite the existing data 11. Delete the empty cells A21:B21 shifting the other cells up. IMPORTANT: You must complete step 11 correctly in order to receive points for completing the next steps. Check your work carefully 12. Cell E7 has the wrong number format applied. Copy the formatting from cell E6 and apply it to cell E7 13. Apply conditional formatting to cells B13:B23 to display the 3 Arrows (gray) icon in each cell, 14. The text in cell A21 appears cutoff. Apply text wrapping to the cell, 15. Apply the default All Borders border style to the following cell ranges: A4:B7, 04:08 A12:824, and D12:E16 16. Save and close the workbook 17. Upload and save your project file 18. Submit project for grading A1 for Household Budget E G Amount $ 48,800.00 $ 28,240.00 $4,379.00 $ 16,181.00 B ? D 1 Household Budget 2 3 Monthly Income Available income 4 Income Source Amount Expense 5 Estimated monthly net incorr S 10,800.00 Monthly Income 6 Other income $ 1,400.00 Monthly expenses 7 Total $ 12,200.00 Preschool expenses 8 Difference 9 10 11 Monthly Expenses Preschool Expenses 12 Expense Amount Expense 13 Rent S 2,200.00 Tuition 14 Utilities $ 250.00 Other fees 15 Cellphone $ 200.00 Total 16 Groceries S 500.00 17 Auto expenses S 550.00 Preschool semester length (months) 18 Other loans S 19 Credit cards 2,000.00 20 Insurance 160.00 21 Transportation 200.00 22 Medical, dental, and vision ex $ 500.00 23 Entertainment S 250.00 24 Miscellaneous S 250.00 25 Total S 7,060.00 26 27 Amount $ 4,304.00 $ 75.00 $ 4,379.00 4

7. A coin pyramid is an arrangement of n coins in rows such that • Coins in each row form a contiguous block • For k > 1, coins in the kth row touch exactly 2 coins from the row beneath it. Here is an example of a coin pyramid with 10 coins in the first row: Let an be the number of coin pyramids with n coins in the first row. We have ai = 1 and a2 = 2. = j=1 = a. The sequence satisfies an 1+1=l(n – j)a; for n > 1. Give a combinatorial proof of this recurrence. Note that this formula also holds for n=1 (which makes life easier for us) b. List all the coin pyramids for n = 1, 2, 3, 4. (You can figure out how many there are using the recurrence.) c. Let A(x) = {mo anx”, the ordinary generating function for coin pyramids. Starting with the recursion above, find a simple closed formula for A(x). .

Getting ready to write your personal memorable event story…
Prewriting graphic organizer. Brainstorm a list of ideas in the boxes based on your own experiences. You can choose any one of these options for describing your experiences.
Vacations or Trips…
? Challenges… First time doing something new…
Successes… Relationships… Growing up… ?
Mistakes or regrets… Celebrations… Decisions…
Choosing your story’s topic (focus, ?main idea). ?
Select one brainstormed idea that was/is important to you.
List & Choose: List specific things about this experience. Read through your ideas AND CHOOSE 1 ?to make the central idea of your personal story. CIRCLE this idea.
?
Important Details: Visualize what happened. List important details that focus on feelings, thoughts, and reactions. *Remember the 5 ?senses! ?
?
Significance: What is the significance of this event or experience FOR YOU!? What has been the effect on you then and/or now?