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Let a be the set that is defined recursively in the following way basis case

 
 

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1.C.1377. How many 6-digit cube-numbers are there? C.1378. Somebody calculated the exact values of and in the decimal system. ...

and in the decimal system. How many digits are there in these two numbers all together? C.1379. Alex and Burt took their rabbits to a whole salesman to sell them to him at once. Each of them got as many dollars for each of their rabbits as many as the rabbits they each took to him. But, because their rabbits were so beautiful, they each got as many extra dollars for their rabbits from the salesman as many as the rabbits they each sold him. This way Alex received $202 more than Burt. How many rabbits did they each sell to the salesman? C.1380. How many {a, b, c} sets are there containing three positive whole elements, where the product of a, b, and c is 2310? C.1381. Let a, b, c, and d be different digits. Find their values so that the following sum has the least possible number of divisors, but the sum itself is the greatest possible. C.1382. Fill in a 25×25 grid by using the numbers +1 and -1. Create the products of the 25 numbers in each column and in each row. Could the sum of these 50 numbers be: a) 0 b) 10 c) 17? C.1383. Is there such a triangle in which the heights are 1, 2, and 3 units long? C.1384. You put a plain on each side of a regular, square-based pyramid. How many sections do these 5 planes divide the space?
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2.Scenario: A chair with a mass of 20.0 kg is attached to one end of a frictionless pulley system via a ...

a strong massless rope. The other end of the rope is attached to a steel water tank sitting on a flat horizontal concrete surface (see the image to the right). The coefficient of static friction between steel and concrete is 0.45 and the coefficient of kinetic friction between the surfaces is 0.30. The water tank, which is full of water, has sprung a leak. The combined mass of the water and the tank is 500 kg. This mass slowly decreases as the water leaks from the hole. You (i.e. your entire mass) are sitting at rest in the seat. You and the seat will remain at rest as long as the force of static friction is strong enough to hold you. Task: LET [DOWN] and [RIGHT] be positive. Using your knowledge of physics, determine the following: Draw the FBD of the system of you and the chair while at rest. Using the LET statement above, write out the net force equation. [2] Draw the FBD of the system of the water tank at rest on the flat horizontal surface. Using the LET statement above, write out the net force equations for both the vertical and horizontal planes. [3] Using the net force equations, determine the minimum mass of water that must be lost (i.e. leaked out) from the water tank in order for you and the seat to begin falling? [4] As soon as the chair begins to move, static friction between the steel tank and concrete surface becomes kinetic friction. Determine the magnitude of the kinetic friction. [3] Using Newton’s 2nd law, determine the acceleration of the system at the instant that the static friction becomes kinetic friction. [6]
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3. Let A, B be a m ×n matrix and n× m matrix respectively. Prove or disprove the following statements: (a) ...

s: (a) (5 marks) (A + B) T = AT + BT . (b) (5 marks) (AB) T = BT AT . (c) (5 marks) AT A is symmetric. (d) (5 marks) AT A = AAT .
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4.Hi, Is the article below non-fiction or creative non-fiction? What makes it either of these titles? Rose By: Tomson Highway Should ...

Rose By: Tomson Highway Should Only Native Actors Have the Right to Play Native Roles? Deep in my Cree heart of hearts, I had two-millennium projects on the go, though this only in hindsight. One was for the year 2000, the other for 2001, and thus just to make sure I had the right year for actually beginning this brand new, and incredibly exciting, millenium. Those two projects? For the year 2000, an English language production, in Toronto, of the third play in what I call my “Rez Septology,” a play called Rose. And for the year 2001, the Japanese-language premiere, in Tokyo, of the second play in the septology, a play called Dry Lips Oughta Move to Kapuskasing. And this is how the two projects affected me and my life: When it dawned on me, one cloudy day, that my career as a playwright had been destroyed by political correctness, I just about died. I wanted to throw myself under a subway train and just call it a day. I was horrified! After all that work? After all those years of struggle and of hope and of prayer and of pain and of tears and of more struggle, against odds that were impossible to begin with? But how can it be? How can the voice of a playwright be silenced? By a method so brutally effective as political correctness? In a country supposedly as civilized as Canada? Questions like this, and others like them, resounded through my brain over and over and over again. As they do to this day. Permit me, therefore, to start off with the “backdrop” before I go into “the projects,” please: First of all, I don’t happen to have the good fortune of coming from a city such as Montreal or Vancouver or Toronto or Ottawa or New York or any other major city where educational (and employment) opportunities, right from age one, are virtually unlimited (believe me, you can be a movie star by age one in such cities!). And I don’t come from a city where English (or French) is the language of the day. I come, instead, from one of the tiniest, most remote, most inaccessible, most underprivileged and most troubled Indian reserves in the country, Brochet, Manitoba, population 700, one thousand five hundred kilometers directly north of Winnipeg (further than Churchill but on the opposite side of the province). I come from a place where the language spoken is Cree. AND Dene, incidentally; because we are located so far north, we spill over into the land of such sub-arctic peoples as the Dene (linguistically speaking) to the Navajo and other southwest Native nations. In fact, to fly from Toronto (my home until recently) to Brochet costs more than a ticket to Sydney, Australia or to Rio de Janeiro. To fly home to visit my family (which I do regular as clockwork), I could fly from Toronto to London, England and back - three times each way- for the same amount of money, easy. No jumping in a taxi or a car or on a bus or a train or a “seat sale” seat on a plane from Toronto to Vancouver for the likes of us, not to go have lunch with Mom, not to go to a funeral. Plane ticket prices for Canada’s northerners? Brutal. Brutal, brutal, brutal. And that’s just the distance barrier, never mind the linguistic. For Cree is as different from English as English is from Cantonese; not one shred of resemblance exists. In fact, the two languages are often completely at odds with each other. In one language, for instance, God is male, in the other, female. And that’s just the start… So along comes this little Indian boy from one such remote northern Native community and into the big, big city of Toronto and he dares to dream of a career in the theatre, or, at the very least, in the world of Canadian letters. Fat chance, baby! Forget it. He doesn’t listen. He goes ahead anyway. “No matter how they laugh, let them laugh. I can do it,” he says to himself. And he puts his shoulder to the grindstone, as they say in movies. People always say The Rez Sisters was my first play. That’s not true. It’s not true at all. It may have been my first play to be successful with the general public. But there were five plays that came before that, every one of them self-produced, with money from my very own pocket. And some of these plays were awful, some of them were good, at least two of them were very, very good. But only with The Rez Sisters did my work suddenly, finally get noticed by, as I say, a wider public. By which time, I was almost forty. And what I had to go through to get those first five plays self-produced, you don’t even wanna know! How do you make money standing with your back against the wall in some big city, downtown back alley? Late, late at night? Guess. When it came to that “first” play, however - and I speak here about The Rez Sisters, which, in fact, was my sixth - it was the fall of 1986. In those days, of course, you could count the number of professional Native actors in this country on the fingers on one hand alone. In my wildest dreams - keeping in mind that my work was totally unknown then - I dared to write this play for “them,” meaning for those four or five professional Native actors then in existence. The reason? I adored them. I just absolutely adored these people AND their work. They were my heroes. They kept my dreams alive. So it came to the casting of the show. Finally, my play was going to get done! I was so excited I could hardly sleep at night. So then I approached them, these Native actors, for you see, as always, I was the producer, again, or at least in this case, one of the two co-producers, god bless the other co-producer, may he rest in peace. These Native actors, however, all said “no.” They were all too busy working on other projects, many of them on Native subject matter written by - horrors! - white people! I pleaded with them and pleaded with them and pleaded with them but, still, they said “no.” God bless them and their courageous careers but they made me cry. They made me want to give up and die. So what choice did I have? Either I forget the play and kill myself. OR I go right ahead and hire - horrors! - white actors! Which is what I did, exactly. And these white actors, they were SO generous, they were so kind, so supportive, so confidence generating that, with their help as with that of those Native actors who did say “yes,” god bless them - I simply bloomed. The play opened. The play was successful. And it has never really stopped playing ever since, somewhere in the world, giving continued employment to many, many, many actors both Native and non-Native. As it will do probably forever - your grandchildren will be playing in The Rez Sisters! - something that would NEVER have happened if not for the help of extremely generous people who happened NOT to be Native, actors who happened to be white! Several years later, I experienced a similar situation. This time, it was with a play called Rose. Again I wrote it for Native actors - of which, by this time (1991), there were many more - actors whom I absolutely adored, whose work I absolutely adored. And again, for some strange reason, they said “no.” They were NOT interested. I couldn’t get them interested. If their objective was to make me cry, then they were certainly utterly successful. So then I waited ten years. Ten years! And by this time, I’m almost fifty years old, okay? Until some incredibly generous non-Native person comes along and offers to produce it, albeit, in a university setting, that is, a non-professional (i.e., non-paying) setting. I was thrilled. I was so thrilled I could have danced myself to shreds! So then they went to work on it, this group of “white kids,” none of whom was older than twenty-five. And they worked. And they worked and they worked and they worked and they worked. Never seen such a group of people work so hard. And with so much faith and so much conviction and so much love. It was a blessing from heaven to be sitting there beside them, to be in the same room as them. They glowed, they glowed like lightbulbs. You’ve never seen people so happy, so high. And by the time the show opened, you couldn’t get a ticket; it had been sold out way before opening; hundreds of people were turned away. On virtually no advertising; it all happened by word of mouth. And, to me -as to most people who saw it - the production was FANTASTIC! It was rich, it was beautiful, it was spectacular, it was moving, it was...miraculous! Not perfect, perhaps, but pretty gall-darned good. But these were the things about this experience that most struck me, that most stayed with me: Not one of these actors got paid; they were students; in fact, because they were students of the drama programme at the University of Toronto, they were paying for the experience through their tuition fees which, if I understand correctly, can be as much as $8,000 a year at that particular institution. Pardon me - ONE of those actors DID get paid, a little girl we needed who, of course (being little), came from outside the drama programme. And she, by the way - and god bless her - was the only performer in that production who was Native. But how many Native actors do YOU know who would be willing to pay $8,000 to be in a show? Any show? That question stunned me. All the other performers? Well, we had French-Canadians and Anglo-Canadians and Dutch-Canadians and Polish-Canadians and Ukrainian-Canadians and Jewish-Canadians and Peruvian-Canadians and Lebanese-Canadians and Portuguese-Canadians and god only knows what else! And none of them have even met a Native person, up until then. They pretty well all came from the city of Toronto, or somewhere very close by (such as Barrie, or Sudbury) so they had never, ever been privy to any even remotely “Native experience” in their lives. Now, for the first time, in their third year of university, at ages 21-25, here they were getting this heavy-duty immersion course in “Native Studies,” meaning Native culture, Native history, Native spirituality, Native language - they were learning to speak Cree for god’s sake, something you can’t get Cree kids to do these days! - Native art, Native music, and just generally, Native life in this country, today. And you know what? They all fell in love with it. Now, as the direct result of such an experience, what they have for Native culture and people and languages is endless respect, even awe. And love. And what’s more, they will pass on that knowledge and that love and respect - and wisdom - on to their children and their grandchildren and their great grandchildren, etc., etc., etc…. The experience changed their lives. And both communities - Native AND non-Native - will benefit from it, both in the long term AND permanently. The experience certainly changed MY life. It shocked me. The shock? That generosity and kindness and love know no racial boundaries. And that, contrariwise, UN generosity and lack of kindness and just plain cruelty ALSO know no racial boundaries. Coming out of Rose, I ended up with the immense gift of, minimum, 30 gorgeous, fantastically kind new friends, people whose friendship and generosity - and laughter - I will cherish right up until the day I die. And the icing on the cake? A show was born that otherwise would never have been born, that otherwise would have died forever. A show was born that will give useful, meaningful, enriching employment - and enjoyment - to many, many people for many, many years. Like, I say, the whole thing was a shock. And it took ten years! One more story before I close off on my point, the story, that is of my second “millennium project,” so-called. As it turns out, I’m writing this from Japan, specifically Tokyo, where the Japanese-language production of another play of mine, Dry Lips Oughta Move to Kapuskasing, just opened. It was awesome. And, again, it wasn’t so much the production - which was absolutely stunning! Imagine, if you will, the Seven Samurai doing Dry Lips.. - that move me so much as the generosity of the cast and crew, Japanese every one of them. That generosity, that kindness, that largeness of heart, just astonished me. It made me cry. To be the beneficiary of kindness on that scale is a gift one could easily die for. As a result of just that one project, I now have a hundred friends, easy, in Japan. For the rest of my life! I LOVE Tokyo! And again, none of these people had ever met a Native person - well, two had, but…- much less knew anything about Native culture first hand. By the end of the six-week rehearsal process, however, some of them were speaking Cree AND some Ojibway. And let me tell you, to hear your own Native tongue being spoken with a Japanese accent is a bittersweet experience indeed. (I mean, come on, folks! To be unilingual in a language that’s not even your own? If the Japanese can learn Cree, YOU can learn Ojibway!) And, again, these people will pass their respect for Native people and culture on to their children, their grandchildren, their great great grandchildren etc., etc., etc…. The experience changed their lives. It changed mine. The one question I kept being asked over and over? How does it feel to have Japanese actors playing Native parts? (In the aforementioned Canadian production of The Rez Sisters, it was more like, “how dare these two white women STEAL Native parts from Native actors!” Well, good grief! The show would never have been born without them in the first place!) Anyway, my answer to the question in Japan was this: 1) These Japanese actors, they’re human beings, for god’s sake. What they are, first, foremost and last, is real-life, flesh-and-blood human beings with feelings, human beings who happen to be incredibly talented. And incredibly generous. If they hadn’t agreed to do it, it would never, EVER have happened. 2)To me, saying that only Native actors have the right to play Native roles - on stage, anyway, as opposed to film, which another thing entirely and not at all what I’m talking about here - well, that’s like saying only Italian actors have the right to play in Romeo and Juliet, or only Danish actors have the right to play in Hamlet, or only Spanish actors have the right to play in Blood Wedding. It would be like saying to someone like Canadian film-maker Atom Egoyan, “you have the right to work with Armenian actors only,” which, of course, would automatically bring his career to a standstill; it would destroy it, it would kill it, right there on the spot. Or as I asked, one sunny day, a respected, much admired Jewish theatre artist, “how would you like to work with no but Jews for the rest of your life?” You could almost see his hair stand on end; the very thought horrified him. My argument with someone else at that same summer gathering? “Theatre is about illusion, the better the magic, the more profound the experience.” Besides, working in a situation of cultural, ethnic and linguistic diversity can be the most empowering, most liberating, most exhilarating experience in anyone’s life. Working in a pressure cooker environment by comparison? Working in the context of a “ghetto” of any kind whatsoever, be that “ghetto” Native or black or French or English or Jewish or female or male or gay or…? Remember the expression, “familiarity breeds contempt”? Well, only too frequently, such a working environment can only mean THAT kind of disaster. Or one of plain, out-and-out hatred. And hatred, as who doesn’t know, kills and kills completely. It kills relationships, it kills communities, it kills love. Look at what the Argentinians did TO EACH OTHER during the so-called “dirty war” of the 1970s. Look at what the Spanish did TO EACH OTHER during the Spanish Civil War. Look at what the Chileans have done TO EACH OTHER. Look at the Irish in Northern Ireland. Look at the Balkans, at Cambodia in the ‘80s, at Haiti, at Rwanda, etc., etc., etc…. Does anybody out there actually want to live like that? Internally directed hatred, internally directed violence - which, in essence, is what civil war is - well, there is nothing more destructive, we all know that. Diversity! What we all need is diversity! What we all need, desperately, is room to breathe! That’s what makes Canada work as a society; precisely its diversity. If we - all of us - were Cree, I would have had my head macheted off a long, long time ago! All by way of saying the following: “Only Native actors have the right to play Native roles?” Music to Native actor’s ears, perhaps, yes, god bless them. But death to a Native playwright’s career. Because chances are that the show will NEVER, ever get done. No producer in the country has balls that size, balls big enough, that is to say, of going against the political grain. Not today. Not tomorrow. Stop it, you people! It’s killing us! Myself, I had to move out of the country, finally. I could no longer live there, not really. I kind of live, well...all over the world now. I do where I can find work. Because I certainly am NOT finding it in my own country. I go where I can find the kindness, I go where I can find the generosity, I go where I can find the friendship and support. The working situation in Canada, for someone like me? Well, it has simply become unworkable. I find it stultifying, asphyxiating. I CAN’T work under such artificial constraints. No one can. Sooner or later, it will drive you crazy. Not to mention kill your imagination. AND your career. All as you watch, with envious eyes, the careers of your non-Native playwright colleagues (whom you love) bloom like a garden everywhere around you… It seems to me that what we have here are two distinct choices: a) either we cast a show politically correctly (meaning only Native actors play Native parts) and the show never, ever gets produced (trust me; I waited ten years for Rose to happen, more for others which will NEVER get done), or b) cast it any way you want, in whatever way you can afford it budget-wise (plane tickets are a waste of money, trust me), let the show be born, let the show become successful, and THEN it will live on forever to employ many, many, many more actors, Native and otherwise, for many, many, many more years. And the upshot of the latter arrangement? Having Native and non-Native actors working side by side like that? There is no better healing agent for bringing two only-too-frequently disparate, disharmonious communities together. And, in the process, making our country an even better, richer, healthier country than it is already. The life of an artist is so incredibly challenging, after all, a Native artist’s most especially, in Canada today, or anywhere in the world. Everywhere you turn, insurmountable obstacles meet you square in the face. Everywhere you turn, events, or people, conspire to bring you down, to destroy you. What those artists need, and need most desperately, is as much breathing space as you can give them, the freedom to create, the freedom to employ, the freedom to fly with their souls and imaginations. Don’t hold them down. Don’t shoot them down. You will kill them. Or drive them away. They need all the help they can possibly acquire. They’ve already almost killed themselves just to get to where they are today. Someone said to me one day: “Artists are here to break down barriers, not to create them.” So, myself, I’ve moved away. I’ve left my own country, to continue helping to break down barriers in whatever way I still can, at my age, in the only way I know how, and to have a good time doing it. The thing is, I can do that. I can take it. I’ve had, as they say in the business, my “fifteen minutes of fame.” Enough already. I’ve been very, very lucky (not to mention being the beneficiary of extraordinary teachers, absolutely extraordinary parents and many dear, dear friends). And I’ve moved on, to other things. I have had, after all, no choice. The sad thing is this: what about the next generation of Native playwrights? Will they, too, one day find themselves standing on that subway platform - late, late at night, stoned, drunk out of their skulls, not a penny in their pockets, no future in sight - and those long, silvery tracks down below gleaming up at them in a manner most, most enticing?
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5.Customers arrive at a soft drink dispensing machine according to a Poisson process with rate λ per hour. Let N(t) ...

hour. Let N(t) be the number of custoer arrivals up to time t, with hour as the unit. There are two types of soft drinks, type A and B, stored in the machine. Suppose that each time a customer deposits money, the machine dispenses one soft drink A with probability p1, or one soft drink B with probability p2. We have p1 + p2 = 1, p1 > 0, p2 > 0. Let X(t) be the number of type A soft drinks dispensed up to time t; and Y (t) be the number of type B soft drinks dispensed up to time t.
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6.I just need someone to look over my paper for anatomy and to just let me know what I need ...

t or add. I'll attach the questions, my rubric, as well as my answers I made. It would really help me out please. The questions: 1.) Choose two somatosensory receptors. Please include a description of each receptor, what they sense, and which part of the brain processes the information from the receptor. 2.) Provide a discussion of the thyroid gland. Include the following: Description of the thyroid gland's structure and location. Description of the cells of the thyroid gland. Description of the hormones secreted by the thyroid gland and their functions. Description of how thyroid hormones are controlled by hormones secreted by the hypothalamus and anterior pituitary gland. Description of how the feedback system works in the cases of high or low thyroid hormone levels. 3. Describe the cardiac cycle. Include descriptions of the 3 phases, the pressure changes in each of the heart's chambers, valves are open and closed, and blood flows during each step. My answer: 1.) Exteroceptor - receives external stimuli from outside of the body. An example, the skin (Thermoreceptors) detects the temperature of the outside area of the body. Interceptor - receives stimuli from inside of the body. An example would be blood pressure as well as blood oxygen levels. 2.) Thyroid Gland is located near the front lower part of the neck, beneath Adam's apple. Its structure includes Thyroid Epithelial that form follicles filled with colloid - a protein-rich reservoir of the materials needed for thyroid hormone production. The cells are responsible for releasing hormones that control metabolism (Energy levels). The thyroid gland releases triiodothyronine (T3) and thyroxine (T4). These hormones regulate weight, energy levels, internal temperature, skin, and growth. When the hypothalamus and pituitary function well, they can detect when hormone levels are low, which causes them to produce more TRH and TSH, which stimulates the thyroid to produce hormones. When the hormone levels exceed their limit, they then have less TRH and TSH, which results in reduced hormone production by the thyroid. Feedback is when a product feeds back into its initial cycle. The Feedback includes both positive and negative feedback. Positive Feedback is when a product provides back to increase production: an example, milk production by a mother for her baby. As the baby suckles, nerve messages from the nipple cause the pituitary gland to secrete prolactin. Prolactin, in turn, stimulates the mammary glands to produce milk, so the baby suckles more. Which causes more prolactin to be secreted and more milk to is made. Negative Feedback is when a product feeds back decreases production; it brings down show if they increase past their limit. It also controls insulin secretion by the pancreas. 3.) The Cardiac Cycle takes place from the beginning of a heartbeat to the next. It contains two periods: One is when the heart muscle relaxes and refills with blood, called diastole, following a time when it begins contraction and pumping of blood, systole. Once emptied, the heart then relaxes and expands to receive another inrush of blood coming back from the lungs and other areas of the body. The atrioventricular valves remain open while the semilunar valves are closed. During the middle part of the diastole, a small amount of blood flows into the ventricles. The blood flows from the veins and passes the atria fills the ventricles. The pressure in both ventricles is close to zero as a result.
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7.Let X_1, X_2, ... , X_n be i.i.d. with probability density function f(x | theta) = theta*x^(-theta - 1); I{x>1}, theta ...

- 1); I{x>1}, theta > 1. (a) Show that log Xi has an exponential distribution with a mean of 1/theta. (b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0. (c) Give formula for nding the rejection region for a given value of alpha. Hint: use the result from (a) to fi nd the distribution of the test statistic. (d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}. (e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0. (f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.
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8.Let X_1, X_2, ... , X_n be i.i.d. with probability density function f(x | theta) = theta*x^(-theta - 1); I{x>1}, theta ...

- 1); I{x>1}, theta > 1. (a) Show that log Xi has an exponential distribution with a mean of 1/theta. (b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0. (c) Give formula for nding the rejection region for a given value of alpha. Hint: use the result from (a) to fi nd the distribution of the test statistic. (d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}. (e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0. (f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics