Tuesday, March 17, 2020
Gambling essays
Gambling essays Have you ever felt remorse after gambling? Has gambling affected your reputation? Do you often gamble until your last dollar is gone? Do you ever borrow to finance your gambling? After a win do you have a strong urge to return and win more? A compulsive gambler will often reply yes to most of these questions, but many simply wont admit the fact that they have a problem. Admitting that their behaviour is compulsive is like accepting defeat. Gamblers spend most of their time trying to win, so giving in doesnà ¡t come easy. Gambling has been seen as a problem in society, ever since it was made legal in Nevada and Atlantic City in 1976. Since then, pro-gambling lobbyists have fought to get a form of legalized gambling in every state, but the National Coalition Against Legalized Gambling has prevailed. In 1987 however, the Supreme Court ruled that Native Americans, who are without state regulation, could offer legal gambling far outside Indian reservations. This decision has contributed to the rising numbers of compulsive gamblers in many states. More than 6% of adult gamblers are now considered to be addicted, and the numbers are continuing to grow. At present, Americans will wager over 550 billion dollars a year, a! 3,200% increase since 1976. Solutions to this problem are beginning to come forward, much to the gambling industryà ¡s dislike, as the four percent of pathological gamblers may account for as much as 52% of an average casinoà ¡s The causes of compulsive gambling are similar to those which alcoholics and drug addicts encounter. Compulsive gamblers are preoccupied with seeking out gambling and gamble longer than intended, and with more money than intended. There is also the equivalent of à ¡toleranceà ¡ when gamblers have to increase the size of their bets or the odds against them in order to create the desired amount of excitement. (Lesieur 2) à ¡The cause of the addicti...
Sunday, March 1, 2020
Functions on SAT Math Linear, Quadratic, and Algebraic
Functions on SAT Math Linear, Quadratic, and Algebraic SAT / ACT Prep Online Guides and Tips SAT functions have the dubious honor of being one of the trickiest topics on the SAT math section. Luckily, this is not because function problems are inherently more difficult to solve than any other math problem, but because most students have simply not dealt with functions as much as they have other SAT math topics. This means that the difference between missing points on this seemingly tricky topic and acing them is simply a matter of practice and familiarization. And considering that function problems generally show up on average of three to four times per test, you will be able to pick up several more SAT math points once you know the rules and workings of functions. This will be your complete guide to SAT functions. We'll walk you through exactly what functions mean, how to use, manipulate, and identify them, and exactly what kind of function problems you'll see on the SAT. What Are Functions and How Do They Work? Functions are a way to describe the relationship between inputs and outputs, whether in graph form or equation form. It may help to think of functions like an assembly line or like a recipe- input eggs, butter, and flour, and the output is a cake. Most often you'll see functions written as $f(x) =$ an equation, wherein the equation can be as complex as a multivariable expression or as simple as an integer. Examples of functions: $f(x) = 6$ $f(x) = 5x âËâ 12$ $f(x) = x^2 + 2x âËâ 4$ Functions can always be graphed and different kinds of functions will produce different looking graphs. On a standard coordinate graph with axes of $x$ and $y$, the input of the graph will be the $x$ value and the output will be the $y$ value. Each input ($x$ value) can produce only one output, but one output can have multiple inputs. In other words, multiple inputs may produce the same output. One way to remember this is that you can have "many to one" (many inputs to one output), but NOT "one to many" (one input to many outputs). This means that a function graph can have potentially many $x$-intercepts, but only one $y$-intercept. (Why? Because when the input is $x=0$, there can only be one output, or $y$ value.) A function with multiple $x$-intercepts. You can always test whether a graph is a function graph using this understanding of inputs to outputs. If you use the "vertical line test," you can see when a graph is a function or not, as a function graph will NOT hit more than one point on any vertical line. No matter where we draw a vertical line on our function, it will only intersect with the graph a maximum of one time. The vertical line test applies to every type of function, no matter how "odd" looking. Even "strange-looking" functions will always pass the vertical line test. But any graph that fails the vertical line test (by intersecting with the vertical line more than once) is automatically NOT a function. This graph is NOT a function, as it fails the vertical line test. Too many obstacles in the way of the ascent works out as well for functions as it does for real life (which is to say: not well at all). Function Terms and Definitions Now that we've seen what functions do, let's talk about the pieces of a function. Functions are presented either by their equations, their tables, or by their graphs (called the "graph of the function"). Let's look at a sample function equation and break it down into its components. An example of a function: $f(x) = x^2 + 5$ $f$ is the name of the function (Note: we can call our function other names than $f$. This function is called $f$, but you may see functions written as $h(x)$, $g(x)$, $r(x)$, or anything else.) $(x)$ is the input (Note: in this case our input is called $x$, but we can call our input anything. $f(q)$ or $f(\strawberries)$ are both functions with the inputs of $q$ and strawberries, respectively.) $x^2 + 5$ gives us the output once we plug in the input value of $x$. An ordered pair is the coupling of a particular input with its output for any given function. So for the example function $f(x) = x^2 + 5$, with an input of 3, we can have an ordered pair of: $f(x) = x^2 + 5$ $f(3) = 3^2 + 5$ $f(3) = 9+5$ $f(3) = 14$ So our ordered pair is $(3, 14)$. Ordered pairs also act as coordinates, so we can use them to graph our function. Now that we understand our function ingredients, let's see how we can put them together. Different Types of Functions We saw before that functions can have all sorts of different equations for their output. Let's look at how these equations shape their corresponding graphs. Linear Functions A linear function makes a graph of a straight line. This means that, if you have a variable on the output side of the function, it cannot be raised to a power higher than 1. Why is this true? Because $x^2$ can give you a single output for two different inputs of $x$. Both $âËâ3^2$ and $3^2$ equal 9, which means the graph cannot be a straight line. Examples of linear functions: $f(x) = x âËâ 12$ $f(x) = 4$ $f(x) = 6x + 40$ Quadratic Functions A quadratic function makes a graph of a parabola, which means it is a graph that curves to open either up or down. It also means that our output variable will always be squared. The reason our variable must be squared (not cubed, not taken to the power of 1, etc.) is for the same reason that a linear function cannot be squared- because two input values can be squared to produce the same output. For example, remember that $3^2$ and $(âËâ3)^2$ both equal 9. Thus we have two input values- a positive and a negative- that give us the same output value. This gives us our curve. (Note: a parabola cannot open side to side because it would have to cross the $y$-axis more than once. This, as we've already established, would mean it was not a function.) This is NOT a quadratic function, as it fails the vertical line test. A quadratic function is often written as: $f(x) = ax^2 + bx + c$ The $\bi a$ value tells us how the parabola is shaped and the direction in which it opens. A positive $\bi a$ gives us a parabola that opens upwards. A negative $\bi a$ gives us a parabola that opens downwards. A large $\bi a$ value gives us a skinny parabola. A small $\bi a$ value gives us a wide parabola. The $\bi b$ value tells us where the vertex of the parabola is, left or right of the origin. A positive $\bi b$ puts the vertex of the parabola left of the origin. A negative $\bi b$ puts the vertex of the parabola right of the origin. The $\bi c$ value gives us the $y$-intercept of the parabola. This is wherever the graph hits the $y$-axis (and will only ever be one point). (Note: when $b=0$, the $y$-intercept will also be the location of the vertex of the parabola.) Don't worry if this seems like a lot to memorize right now- with practice, understanding function problems and their components will become second nature. Want to learn more about the SAT but tired of reading blog articles? Then you'll love our free, SAT prep livestreams. Designed and led by PrepScholar SAT experts, these live video events are a great resource for students and parents looking to learn more about the SAT and SAT prep. Click on the button below to register for one of our livestreams today! Typical Function Problems SAT function problems will always test you on whether or not you properly understand the relationship between inputs and outputs. These questions will generally fall into four question types: #1: Functions with given equations #2: Functions with graphs #3: Functions with tables #4: Nested functions There may be some overlap between the three categories, but these are the main themes you'll be tested on when it comes to functions. Let's look at some real SAT math examples of each type. Function Equations A function equation problem will give you a function in equation form and then ask you to use one or more inputs to find the output (or elements of the output). In order to find a particular output, we must plug in our given input for $x$ into our equation (the output). So if we want to find $f(2)$ for the equation $f(x) = x + 3$, we would plug in 2 for $x$. $f(x) = x + 3$ $f(2) = 2 + 3$ $f(2) = 5$ So, when our input $(x)$ is 2, our output $(y)$ is 5. Now let's look at a real SAT example of this type: $g(x)=ax^2+24$ For the function $g$ defined above, $a$ is a constant and $g(4)=8$. What is the value of $g(-4)$? A) 8 B) 0 C) -1 D) -8 We can start this problem by solving for the value of $a$. Since $g(4) = 8$, substituting 4 for $x$ and 8 for $g(x)$ gives us $8= a(4)^2 + 24 = 16a + 24$. Solving this equation gives us $a=-1$. Next, plug that value of $a$ into the function equation to get $g(x)=-x^2 +24$ To find $g(-4)$, we plug in -4 for $x$. From this we get $g(-4)=-(-4)^2 + 24$ $g(-4)= -16 + 24$ $g(-4)=8$ Our final answer is A, 8. Function Graphs A function graph question will provide you with an already graphed function and ask you any number of questions about it. These questions will generally ask you to identify specific elements of the graph or have you find the equation of the function from the graph. So long as you understand that $x$ is your input and that your equation is your output, $y$, then these types of questions will not be as tricky as they appear. The minimum value of a function corresponds to the $y$-coordinate of the point on the graph where it's lowest on the $y$-axis. Looking at the graph, we can see the function's lowest point on the $y$-axis occurs at $(-3,-2)$. Since we're looking for the value of $x$ when the function is at it's minimum, we need the x-coordinate, which is -3. So our final answer is B, -3. Function Tables The third way you may see a function is in its table. You will be given a table of values both for the input and the output and then asked to either find the equation of the function or the graph of the function. Oftentimes the best strategy for these types of questions is to plug in answers to make our lives simpler. This way, we don't have to actually find the equation on our own- we can simply test which answer choices match the inputs and outputs we are given in our table. Let's test the second ordered pair, $(3,13)$ with each answer option. For the correct answer, when we plug the $x$-value (3) into the equation, we'll end up with the correct $y$-value (13). A) $f(x) = 2(3) +3 = 9$. This equation is incorrect since 9 doesn't equal 13. B) $f(x) =3(3) +2 = 1$. This equation is also incorrect. C) $f(x) = 4(3) +1=13$. It's a match! This equation is correct so far. D) $f(x)= 5(3)= 15$. This equation is also incorrect. It looks like C is the correct answer choice, but let's plug the first and third ordered pairs in to make sure. For the first ordered pair $(1,5)$: $f(x) = 4(1) +1=5$ That's correct! For the third ordered pair $(5,21)$ $f(x) = 4(5) +1=21$ That's also correct! Our final answer is C, $f(x) = 4x +1$ Nested Functions The final type of function problem you might encounter on the SAT is called a "nested" function. Basically, this is an equation within an equation. In order to solve these types of questions, think of them in terms of your order of operations. You must always work from the inside out, so you must first find the output for your innermost function. Once you've found the output of your innermost function, you can use that result as the input of the outer function. Let's look at this in action to make more sense of this process. What is $f(g(xâËâ2))$ when $f(x) = x^2 âËâ 6$ and $g(x) = 3x + 4?$ A. $3x âËâ 2$ B. $3x^2 + 12x âËâ 6$ C. $9x^2 + 24x + 10$ D. $9x^2 âËâ 12x + 4$ E. $9x^2 âËâ 12x âËâ 2$ Because $g(x)$ is nested the deepest, we must find its output before we can find $f(g(xâËâ2))$. Instead of a number for $x$, we are given another equation. Though this may look different from earlier problems, the principle is exactly the same- replace whatever input we have for the variable in the output equation. $g(x) = 3x + 4$ $g(xâËâ2) = 3(xâËâ2) + 4$ $g(xâËâ2) = 3x âËâ 6 + 4$ $g(xâËâ2) = 3x âËâ 2$ So our output of $g(xâËâ2)$ is $3xâËâ2$. Again, this is an equation and not an integer, but it still works as an output. Now we must finish the problem by using this output of $g(x)$ as the input of $f(x)$. (Why do we do this? Because we are finding $f(g(x))$, which positions the result/output of $g(x)$ as the input of $f(x)$.) $f(x) = x^2 âËâ 6$ $f(g(xâËâ2)) = (3xâËâ2)^2 âËâ 6$ Now, we have a bit of a complication here in that we must square an equation. If you remember your exponent rules, you know you cannot simply distribute the square across the elements of the equation; you must square the entire expression. So let's take a moment to expand $(3xâËâ2)^2$ before we find the solution for the entire equation. $(3x âËâ 2)^2$ $(3x âËâ 2)(3x âËâ 2)$ $(3x*3x) + (3x*-2) + (âËâ2*3x) + (âËâ2*-2)$ $9x^2 âËâ 6x âËâ 6x + 4$ $9x^2 âËâ 12x + 4$ Now, let us add this expanded form of the equation back into the output. $f(g(xâËâ2)) = (9x^2 âËâ 12x + 4) âËâ 6$ $f(g(xâËâ2)) = 9x^2 âËâ 12x âËâ 2$ So our final solution for $f(g(xâËâ2))$ is $9x^2 âËâ 12x âËâ 2$. Our final answer is E, $9x^2 âËâ 12x âËâ 2$. Functions within functions, dreams within dreams. Make sure not to lose yourself along the way. Strategies for Solving Function Problems Now that you've seen all the different kinds of function problems in action, let's look at some tips and strategies for solving function problems of various types. For clarity, we've split these strategies into multiple sections- tips for all function problems and tips for function problems by type. So let's look at each strategy. Strategies for All Function Problems: #1: Keep careful track of all your pieces and write everything down Though it may seem obvious, in the heat of the moment it can be far too easy to confuse your negatives and positives or misplace which piece of your function (or graph or table) is your input and which is your output. Parenthesis are crucial. The creators of the SAT know how easy it is to get pieces of your function equations confused and mixed around (especially when your input is also an equation), so keep a sharp eye on all your moving pieces and don't try to do function problems in your head. #2: Use PIA and PIN as necessary As we saw in our function table problem above, it can save a good deal of effort and energy to use the strategy of plugging in answers. You can also use the technique of plugging in your own numbers to test out points on function graphs, work with any variable function equation, or work with nested functions with variables. For instance, let's look at our earlier nested function problem using PIN. (Remember- most any time a problem has variables in the answer choices, you can use PIN). What is $f(g(xâËâ2))$ when $f(x)= x^2 âËâ 6$ and $g(x) = 3x + 4?$ A. $3x^2 + 24x âËâ 2$ B. $3x^2 + 12x âËâ 6$ C. $9x^2 âËâ 24x + 10$ D. $9x^2 âËâ 12x + 4$ E. $9x^2 âËâ 12x âËâ 2$ If we remember how nested functions work (that we always work inside out), then we can plug in our own number for $x$ in the function $g(xâËâ2)$. That way, we won't have to work with variables and can use real numbers instead. So let us say that the $x$ is the $g(xâËâ2)$ function is 5. (Why 5? Why not!) Now $xâËâ2$ will be $5âËâ3$, or 3. This means $g(xâËâ2)$ will be $g(3)$. $g(xâËâ2) = 3x + 4$ $g(3) = 3(3) + 4$ $g(3) = 9 + 4$ $g(3) = 13$ Now, let us plug this number as the value for our $g(xâËâ2)$ function into our nested function $f(g(xâËâ2))$. $f(x) = x^2 âËâ 6$ $f(g(3)) = (13)^2 âËâ 6$ $f(g(3)) = 169 âËâ 6$ $f(g(3)) = 163$ Finally, let us test our answer choices to see which one matches our found answer of 163. Let us, as usual when using PIA or PIN, start in the middle with answer choice C. $9x^2 âËâ 24x + 10$ Now, we replace our $x$ value with the $x$ value we chose originally- 5. $9x^2 âËâ 24x + 10$ $9(5)^2 âËâ 24(5) + 10$ $9(25) âËâ 120 + 10$ $225 âËâ 120 + 10$ 5 Unfortunately, this number is too small. Let us try answer choice D instead. $9x^2 âËâ 12x + 4$ $9(5)^2 âËâ 12(5) + 4$ $9(25) âËâ 60 + 4$ $225 âËâ 60 + 4$ $165 + 4$ 169 This value is still too large, but we can see that it is awfully close to the final answer we want. Just by looking over our answer choices, we can see that answer choice E is exactly the same expression as answer choice D, except for the final integer value. If we were to subtract 2 from 165 instead of adding 4 (as we did with answer choice D), we would get our final answer of 163. As you can see. $9x^2 âËâ 12x âËâ 2$ $9(5)^2 âËâ 12(5) âËâ 2$ $9(25) âËâ 60 âËâ 2$ $225 âËâ 60 âËâ 2$ $165 âËâ 2$ 163 So our final answer is E, $9x^2 âËâ 12x âËâ 2$. #3: Practice, practice, practice Finally, the only way to get truly comfortable with any math topic is to practice as many different kinds of questions on that topic as you can. If functions are a weak area for you, then be sure to seek out more practice questions. For Function Graphs and Tables: #1: Start by finding the $\bi y$-intercept Generally, the easiest place to begin when working with function graphs and tables is by finding the y-intercept. From there, you can often eliminate several different answer choices that do not match our graph or our equation (as we did in our earlier examples). The y-intercept is almost always the easiest piece to find, so it's always a good place to begin. #2: Test your equation against multiple ordered pairs It is always a good idea to find two or more points (ordered pairs) of your functions and test them against a potential function equation. Sometimes one ordered pair works for your graph and a second does not. You must match the equation to the graph (or the equation to the table) that works for every coordinate point/ordered pair, not just one or two. For Function Equations and Nested Equations: #1: Always work inside out Nested functions can look beastly and difficult, but take them piece by piece. Work out the equation in the center and then build outwards slowly, so as not to get any of your variables or equations mixed up. #2: Remember to FOIL It is quite common for SAT to make you square an equation. This is because many students get these types of questions wrong and distribute their exponents instead of squaring the entire expression. If you don't properly FOIL, then you will get these questions wrong. Whenever possible, try not to let yourself lose points due to these kinds of careless errors. For instance, let's say that you must square an expression. Square the expression $x + 3$. We are told to square the entire expression, so we would say: $(x + 3)^2$ Now you must FOIL this out properly. $(x + 3)(x + 3)$ $(x*x)+(3*x)+(3*x)+(3*3)$ $x^2 + 3x + 3x + 9$ $x^2 + 6x + 9$ The final expression, once you have squared $x + 3$, is: $x^2 + 6x + 9.$ (Note: It is a common error for students to distribute the square and say: $(x + 3)^2 = x^2 + 9$ but this is wrong. Do not fall into this kind of trap!) You're all leveled-up- time to fight the big boss and put knowledge to action! Test Your Knowledge Now let's put your function knowledge to the test against real SAT math problems. 1. Let the function $f$ be defined bye $f(x)=5x-2a$, where $a$ is a constant. If $f(10)+f(5)=55$, what is the value of $a$? A) -5 B) 0 C) 5 D) 10 2. A function $f$ satisfies $f(2)=3$ and $f(3)=5$. A function $g$ satisfies $g(3)=2$ and $g(5)=6$. What is the value of $f(g(3))$? A) 2 B) 3 C) 5 D) 6 3. 4. Answers: C, B, A, D Answer Explanations: 1. As you can see here, we are given our equation as well as two inputs and their combined output. We must use this knowledge to find an element of our output (in this case, the value of $a$.) So let us find our outputs for each input we are given. $f(x) = 5x âËâ 2a$ $f(10) = 5(10) âËâ 2a$ $f(10) = 50 âËâ 2a$ And $f(x) = 5x âËâ 2a$ $f(5) = 5(5) âËâ 2a$ $f(5) = 25 âËâ 2a$ Now, let us set the sum of our two outputs equal to 55 (as was stipulated in the question). $50 âËâ 2a + 25 âËâ 2a = 55$ $75 âËâ 4a = 55$ $âËâ4a = âËâ20$ $a = 5$ Our final answer is C, $a=5$. 2. We're told in the question that $g(3)=2$. To find the value of $f(g(3))$, we need to substitute 2 for $g(3)$. We'll use that value in the $f(x)$ equation. Substituting 2 for $g(3)$ gives us $f(g(3))$ = $f(2)$. We're also told that $f(2)=3$, so that means 3 is the correct answer. Our final answer is B, 3. 3. As per our strategies, we will start by finding the $y$-intercept. We can see in this graph that the $y$-intercept is +2, which means we can eliminate answer choices C and E. (Why did we eliminate answer choice E? Because it had no $y$-intercept, which means that its $y$-intercept would be 0). We can see that the vertex of the graph is at $x=0$ and so it is not shifted to the right or left of the $y$-axis. This means that, in our quadratic equation $ax^2+bx+c$, our $b$ value has to be 0. If it were anything other than 0, our graph would be shifted left or right of the $y$-axis. Now answer choices B and D are squaring expressions, so let us properly FOIL them in order to see the equation properly. Answer choice B gives us: $y=(x+2)^2$ $y=(x+2)(x+2)$ $y=x^2+2x+2x+4$ $y=x^2+4x+4$ This equation would give us a parabola whose $y$-intercept was at +4 and whose vertex was positioned to the left of the $y$-axis (remember, a positive $b$ value shifts the graph to the left.) We can eliminate answer choice B. By the same token, we can also eliminate answer choice D, as it would give us: $y=(xâËâ2)^2$ $y=(xâËâ2)(xâËâ2)$ $y=x^2âËâ4x+4$ Which would give us a graph with a $y$-intercept at +4 and a vertex positioned to the right of the $y$-axis. By process of elimination, we are left with answer choice A. But, for the sake of double-checking, let us test a coordinate point on the graph against the formula. We already know that our equation matches the coordinate points of $(0, 2)$, as that is our $y$-intercept, but there are several more places on the graph that hit at even coordinates. By looking at the graph, we can see that the parabola hits the coordinates $(1, 3)$, so let us test this point by plugging our input (1) into our equation, in hopes that it will match our output of 3. $y=x^2+2$ $y=(1)^2+2$ $y=1+3$ $y=3$ Our equation matches two sets of ordered pairs on the graph. We can reasonably say that this is the correct equation for the graph. Our final solution is A, $y=x^2+2$ 4. Instead of using $x$ for our input, this problem has us use $t.$ If you become very used to using $f(x)$, this may seem disorienting, so you can always rewrite the problem using $x$ in place of $t$. In this case, we will continue to use $t$, just so that we can keep the problem organized on the page. First, let us find the $y$-intercept. The $y$-intercept is the point at which $x=0$, so we can see that we are already given this with the first set of numbers in the table. When $t=0$, $f(t) = âËâ1$ Our $y$-intercept is therefore -1, which means that we can automatically eliminate answer choices B, C, and E. Now let's use our strategy of plugging in numbers again. Our answer choices are between A and D, so let us first test A with the second ordered pair. Our potential equation is: $f(t) = t âËâ 1$ And our ordered pair is: $(1, 1)$ So let us put them together. $f(t) = t âËâ 1$ $f(1) = 1 âËâ 1$ $f(1) = 0$ This is incorrect, as it would mean that our output is 0 when our input is 1, and yet the ordered pair says that our output will be 1 when our input is 1. Answer choice A is incorrect. By process of elimination, let us try answer choice D. Our potential equation is: $f(t) = 2t âËâ 1$ And our ordered pair is again: $(1, 1)$ So let us put them together. $f(1) = 2(1) âËâ 1$ $f(1) = 2 âËâ 1$ $f(1) = 1$ This matches the input and output we are given in our ordered pair. Answer choice D is correct. Our final answer is D, $f(t) = 2t âËâ 1$ You did it! High fives all around. The Take Aways Many students have not dealt a lot with functions, but don't let these kinds of questions intimidate or confuse you when you see them on the SAT. The principles behind functions are a simple matter of input, output, and plugging in values. The test will try to muddy the waters when they can, but always remember that these questions will appear to be more complex than they truly are. Though it can be easy to make a error with your signs or variables, the actual problems are simple at their core. So pay close attention, double-check your work, and you'll soon be able to work through functions problems with little trouble. What's Next? Speaking of quadratic functions, how's your grasp of completing the square? Learn how and when to complete the square with this guide. Phew! Knowing your functions means knowing a significant portion of the SAT math section (round of applause to you!), but there are so many more topics to cover. Take a look at all the topics you'll be tested on in the SAT math section and then mosey on over to our math guides to review any topic you feel rusty on. Not feeling confident about your exponent rules? How about your understanding of polygons? Need to review your slopes? Whatever the topic, we've got you covered! Looking for help with more basic math? Refresh your memory on the distributive property, perfect squares, and how to find the mean of a set of numbers here. Think you need a math tutor? Check out our guides on how to find the tutor that best meets your needs (and your budget). Running out of time on the SAT math section? Not to worry! We have the tools and strategies to help you beat the clock and maximize your point gain. Trying for a perfect score? Check out how to push your score to its maximum potential with our guide to getting an 800 on the SAT math, written by a perfect scorer. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:
Friday, February 14, 2020
Swimming Pool Chemistry Term Paper Example | Topics and Well Written Essays - 1250 words
Swimming Pool Chemistry - Term Paper Example To be more specific, the regular use to which swimming pools are put requires that they be cleaned on a regular basis. Exposed as they are, and frequented by a lot of people, swimming pools are places that are especially prone to infection if neglected. This paper, then, is intended as an explanation of the various measures taken by operators of swimming pools as to how to keep their waters safe, as well as how the public can do their part. The Importance of Swimming Pool Sanitation As detailed in a report by the World Health Organization (2006), swimming pools are vulnerable to pollutants such as bird droppings or even the rain. And while indoor pools are much safer, even they need to be cleaned at least once in a while just to be absolutely sure. Either way, as noted by the Centers for Disease Control and Prevention (2009), pathological contaminants often abound in swimming pools, which can cause a myriad of conditions such as diarrhea. A pool that is cleaned regularly is in effect guaranteed to be safe for the public to enjoy ââ¬â guaranteed safe for them to swim in. ...In the words of the Division for Environmental Health (2011), the only way to maintain safe and consistent swimming pool operation is through proper water chemistry. The exact process involved is often rather varied, not only in the chemicals that may be used but also in the methods employed. For one thing, disinfectants may be used to rid the water of harmful, objectionable or otherwise unwanted microorganisms. Alkalinity and pH adjusters may also be used to ensure that the poolââ¬â¢s pH and acidity levels remain stable, while algaecide and filter aids respectively kill any algae and prevent foreign material from spreading in the water. Swim Kingââ¬â¢s (2011) official website also tells us that the balance between these chemicals needs to be just right so as to keep the water free of any unwanted ââ¬Ëlurkersââ¬â¢, yet still be safe for those of us who feel like taking a swim. For instance, free chlorine residual refers to the amount of chlorine which has yet to react with any other substance in the water besides the water itself, and should ideally be anywhere between 1-3 ppm. Secondly, combined chlorine refers to chlorine that fits the opposite description ââ¬â that is to say, it has already reacted with a foreign substance. This kind of chlorine is no longer a help to the disinfection process, and indeed, only acts as an irritant. And finally, total chlorine residual is the sum of these two variants of chlorine. Besides chlorine, bromine can also be used to fulfill the function of disinfection. In fact, whereas the former is more prevalent in swimming pools (Sweazy, 2001), it is the latter that is the preferred substance among owners of spas and hot tubs (Wilson, 2002).
Saturday, February 1, 2020
Compare and contrast functionalist and marxist perspectives including Essay
Compare and contrast functionalist and marxist perspectives including feminist perspectives - Essay Example Interpretive sociology examines the meaning that is given to everyday life by those involved in its construction. The culture in which people live has a profound impact on what is perceived as reality. People act out their social roles, some of which are ascribed or given at birth, and others are achieved or gained through life experiences. The Functionalists and the New Right adopt a consensus perspective and uphold family values based on consensus. On the other hand, Feminism and Marxism are conflict perspectives, ââ¬Å"which view family values as part of the problem in relation to power, control, status and inequalityâ⬠(Squire, 2003: 69). The functionalist perspective of family is comprehensively explained by Parsons (1964), who identifies two major functions of the conjugal family. First, families facilitate the procreation of children and socialize them into adult roles of the kind which are accepted and expected by the social group in which they live. An example is the teaching of adult gender roles by the Western family. This is achieved by ââ¬Å"the way in which children are dressed, the games they are allowed to play, how they are spoken to and the different attitudes of parents towards their childrenââ¬â¢s behaviourâ⬠(Bond, 1994: 95). Children are socialized into identifying with a gender role. Secondly, the family undertakes to re-inforce primary and secondary socialisation; and also stabilizes adult behaviour towards the stereotyped roles of husband and wife. Thus, in traditional conjugal families, parents act as role models for their children, besides influencing the way children identify adult gender roles. In industrialized societies, men usually work to earn money to support the family, hence their activities and interests are more focused outside the home than are those of women whose main occupations are domestic and therefore pertain to the home (Bond, 1994). Thus, the functionalist perspective views the relatively independent-functioning
Friday, January 24, 2020
Luis Valdezs Los Vendidos Essay -- mexico Mexican Los Vendidos Essays
Luis Valdez's Los Vendidos Social science teaches that a personââ¬â¢s self identity is a reflection of that which other people put on the individual, in other words a personââ¬â¢s behavior steams more from what they see of themselves from someone elseââ¬â¢s perspective and less from how they see themselves. In the case of the Mexicans, this concept holds true. From that, which has been studied thus far this semester, Mexicans/ Mexican Americans are good examples of this concept. Their sorted past has resulted in a new kind of Mexican American and perhaps a new kind of Mexican. Certainly the Mexicans Americanââ¬â¢s experience in this country has brought about some changes from the first generation of Mexicans who were born in this country to those who are born here now with native Mexican ancestry. Luis Valdezââ¬â¢z play Los Vendidos is a satirical commentary on not only the sociological concept of self-identity, but also the change that has taken place in the Mexican/Mexican American over the ye ars. What is of particular interest is the meaning of the title of the play. The literal translation is the sold out ones, however a group known as Somos Raza, who are a part of Unià ³n del Barrio (Liberacià ³n Exige Organaizacià ³n), have a somewhat different interpretation of the word. As part of their ten point platform Somos Raza defined the word vendidos as the following: "We recognize Hispanic vendidos as those people who unite with the government and tell us to assimilate with the system - the very same people and system that is oppressing us." The play consists of one scene. The setting is in "Amano Sanchoââ¬â¢s Used Mexicans Dealership"; a store that features used Mexicans for sale. The store carries a wide variety of Mexicans. They range from Mexicans as... ...dnââ¬â¢t deserve fair treatment. The result then is a confused Mexican American in search of some self worth. It was really not until the Brown Power Movement of the 60ââ¬â¢s and 70ââ¬â¢s, which instilled some Mexican pride into those who were born in the US. The play ends with the Raza gathered around a map of the US. The professor reads off all the major cities Mexican have representatives in, one persons speaks out "they think we are robots", he responds "God help us to be humans". All any body wants is to be treated fairly and that is all the vendidos want. To them they best way to do it is wipe out the reflected image whites have put on them, and through it all they have to remain human. Sacrifices have to be made for la causa, but it is for the best. Even if you canââ¬â¢t be what you want for a little while, like Tequi, who was not Tequi anymore, "Its is Erick now, Chula".
Thursday, January 16, 2020
Automotive Service Essay
The career that I have literally chosen is the automotive service technician and mechanics career. The reason why I chose this career itââ¬â¢s becauseâ⬠¦ Well actually I have plenty and many reasons to choose from because I am very passionate about this career and I have lived through it my entire life. One reason is that Auto Mechanics is because to me itââ¬â¢s an interesting field to me. I decided to explore the topic a little more to get a better understanding of what it would take to become a successful automotive technician . I have lived through the auto mechanics field pretty much all through my life. Well actually since I have been born. The reason of this is very simple. That is because my very own dad is an auto mechanic himself. Well actually to be more exact, he owns his own auto mechanic shop. Since I was little I have always helped him at his work because I have always enjoyed working with vehicles. Since the very first day that I started working with him I already knew that the automotive field was the job for me. Since I was a baby my very own parents use to tell me that I would disappear out of their sight. And when they used to find me I used to be playing with the tools besides my dad helping him out. I have pretty much made my mind up about actually going further in this career. Not only because I actually enjoy doing that job but also because of the pay check that you receive. Well actually that is a bonus in it. It does matter to me the money that you earn in it but not as much as I like doing the activity of interacting and working with automobiles. I have faith in me that one day I am not only going to fix cars, but I am also going to own my own shop myself. According to the Bureau of Labor Statistics, an auto mechanic is a technician that inspects, maintains and repair automobiles and light trucks that run on gasoline, electricity or other types of kinds of fuels, like for example ethanol. Auto mechanics play a very important role in maintaining and keeping vehicles up and running not only correctly and normal but also efficiently. The field of auto mechanics reveals a pretty long history. Specialized schooling education and a strong career objectives for anyone that would like to choose this field as a career. There are certain types requirements or abilities that you supposed or have to get or have in order to become an auto mechanic technician. A student can get the basics of automobile repair by taking a vocational class in high their high school time. The course is not really considered training but it gives you a basic information and knowledge of what an actual auto mechanic does. To be considered and known as a qualified auto mechanic technician you will have to complete and finish training at a post secondary school or a community college. Many post secondary schools for graduates have six months to one year of strong , helpful needed intense training. The community college most of the time offers an associate degree for this field and it most of the time takes about two years to complete the coursework and other things necessary. With this kind of type of training you are getting the most up to date training that you will indeed need when you are using with computer systems to detect problems with cars, like for example electrical problems that you can not fix your self without the help of an electronic computer. Another form of training involves you with working as an apprentice to a master technician. This type of fields is pretty much like a helper to the main technician in other words.. When all the formal training is completed and done, the mechanic is considered as a certified They will receive a very own ASE certification. This stands for Automobile Service Excellence certification. The Bureau of Labor statistics suggests and shows that individuals who live in large cities should get certified that says ASE to help them with their search for jobs. This will provide them with a better chance of actually acquiring the job. An auto mechanics basic job function is performed in some type of repair shop. Many mechanics work pretty much around forty hours per week. That is the estimate time of duty hours. In addition to their working time, they also make pretty good money. The median wage salary earnings of automobile technicians and mechanics, including commission, were about $16. 24 in may 2006. And the middle 50 percent is between $11. 96 and $21. 56 per hour. And last but not least the lowest ten percent earned less than $9. 17 and the highest ten percent earn $27. 22 per hour. The person that I interview for this project was my very own dad. His full name is Herminio garcia. His profession is an automotive technician. His place of employment is the boss and owner of an auto mechanic shop. He has been working in this career for about fifteen years. When I asked Mr. Leal how much money I expected to make at the start of my career he told me between ten dollars to 20 dollars an hour. He said it was not a lot but that he enjoyed working with cars and also liked putting smiles on peoples faces. He also told me that the working conditions in that specific field was kind of hard because is a lot of physical work. This lead me to ask him if there were plenty of jobs available in this field and he said that there were because cars will keep needing maintenance for e long time to come. When I ask him about the benefits of this career I did not get that enthusiastic because he told me u really did not get any unless u had car allowance and maybe some medical care. So then we started talking about traveling but he said that traveling had nothing to do with this field. That you stay in one particular spot or place like a shop or garage to fix cars. Another questions that I asked him was about the hours and how they were like. He told me that the average hours he worked a week was about 40 and thatââ¬â¢s not a lot . So then we started talking about family and if there was anytime for them and he told me that I would not have a problem with that, that I would have plenty of time with my family to spent and that put a smile on my face. However, then I asked him if there were any dangers associated with this job and he told me that yes, that there were plenty of risk associated with this job because of the chemicals that you had to deal with and the tools etc. Now that did not leave me very happy. When I ask him about any additional skills and course work associated with this job he told me that yes you will need the most skills, course work and experience you can get to work in this field. He told me that it was really not difficult to get a job in this area because cars always needed maintenance. When I finally made my last question and ask him what advice would he give to some one like me to better prepare me for the challenges of this career, he gave me a very short answer but with a lot of meaning ââ¬Å"Stay in schoolâ⬠.
Wednesday, January 8, 2020
The Middle Ages Was A Great Era For Artists And They...
The middle ages The Middle Ages was from the end of the Fifth Century through 1485. After the collapse of the Roman Empire, the economy was in shambles and many towns were abandoned. After several centuries of Germanic invasion, new cultures and people emerged, developing into predatory kingdoms that competed for power. After a while, a great artistic culture flourished under the Anglo-Saxons, producers, epic poems, Beowulf and sophisticated metalwork. The middle Ages was a great era for artists and they produced great artistic works that Society: The middle ages were like a system of hierarchy where different people fit into different levels and a pyramid based on their family, strength, or gender. At the top of the pyramid was the king. He was the most important person in medieval society and was protected by his men and knights. The king ruled over many lands and gave part of his land to Lords. Next on the pyramid were the Knights. The Knights were warriors who were taught to protect the king and in return were given land. Only the sons of Lords could become Knights and they had to start at the young age of seven and at the age of thirteen they would become squires and at twenty-one, they would be fully Knights. Next were noble men and noble women. Noble women were wives and daughters of noblemen. Their job was to be housewives and take care of their family. Bishops were the leaders of the church. They had a lot of authority because the churches played aShow MoreRelatedThe Ugly Renaissance Discussion Of Italy1575 Words à |à 7 PagesWhy did the Renaissance originate in Florence and prosper for so many years? In many ways, Italy had benefits over northern Europe in detaching from the feudal system and accumulating enormous amounts of wealth. I think that above all else, geography was Italyââ¬â¢s anchor in this respect. Being a projecting land mass sticking out into the Mediterranean Sea, and beneficially located between the main part of Europe and the Byzantine Empire, cities within Italy had little choice but to weave endeavors ofRead MoreArt in the Middle Ages and The Renaissance and Its Effect in Society1017 Words à |à 5 Pagesperiod also referred to as the Middle Ages was the period of time between the demise of the Roman Empire and the Renaissance era; this was the period from the 5th century to the 17th century in Europe. During this time, society conformed to the feudal system which was based on the hierarchy approach which upper class had control over the lower class. Included in this class structure were kings, lords, neighboring kings, peasants and church leaders. In the Middle Ages, art evolves as humans continueRead MoreThe Art Of The Middle Age897 Words à |à 4 PagesThe Museum in the Middle Age During the Middle Age when governed by Christianity, the churches and monasteries played a role as a treasure storage for collections and exhibitions of precious goods. Even the most of collected and produced objects or art works were the tools for religious ceremony and the ornaments for the interior and exterior of church. The churches used a collection and display of precious goods in a way to attracts the publics to the church unlike that artworks were given secularRead MoreRenaissance And The Renaissance Era915 Words à |à 4 PagesThe Renaissance era was a time of great change in music, art, literature, and science. The Renaissance, which lasted from the 1300 s to the 1600 s began in Italy and spread throughout other countries to England, France, Germany, the Netherlands and Spain. During this time, there was a great deal of agricultural economy and the church were dominate and transform society. The word Renaissance come from the Latin word meaning ââ¬Å"rebirth.â⬠Dur ing the Renaissance period many artists studied art of AncientRead MoreHow Does The Change Made People Pay More Attention?1123 Words à |à 5 PagesThe change made people pay more attention to human traits and to re-focus values of At the beginning of the 14th century, which is also known as the Middle Ages, people started to think more about themselves, and they became less interested in God, heaven, and the saints. The study of government, art, writings, architecture, philosophy, and science significantly influenced peopleââ¬â¢s way of thinking. At that time, Humanism became an important motif for architects, painters, and writers. A large numberRead MoreComparing Art And The Baroque Eras989 Words à |à 4 PagesBaroque Eras The Renaissance and the Baroque eras created some of the most famous works of art produced in the world. The two eras expressed differences in style and theme, but they also have many characteristics in common. To better understand the similarities of the eras it will be described by the characteristics, styles and the influences of each; Renaissance and Baroque works of art. Famous artist from the Renaissance era were Leonard da Vinci and Michelangelo Buonarroti. Famous artist fromRead MoreEssay about ITW1 Task 1 1121304 Words à |à 6 PagesHumanities: Analysis and Interpretation Comparing Classical and Middle Age Art Periods 112.1.2 The Fourth and Fifth centuries brought the Classical Art period to Greece. This was a very significant period for Greek art. Before this time, art lacked dimension and intensity, but the onset of the classical period brought with it influential architecture, vase paintings and sculptures, giving life to its subjects. Many modern day artists draw their creative influence from the classical art period.Read MoreThe Relationship Between Art And Commerce1420 Words à |à 6 Pagesstyle of expression, the Middle Ages to pre modern time saw many individual became some of the greatest artists of all time. But for artists before the modern era, life was dramatically different than it is now. Creative expression followed majorly a patronage style. That is, the work of art is commissioned by usually some persons of power. A patron would agree with the artists upon price, time to complete, subject of work, and other pre specified requirements. This model was followed by one of theRead MoreTh e Carolingian Renaissance1472 Words à |à 6 Pagesï » ¿The Carolingian Renaissance is known for the cultural transitions and great achievements that were obtained in the 8th century under the direction of Charlemagne. Charlemagne, who was also known as Carolus Magnus and Charles the Great, was one of the greatest leaders during the Middle Ages. He was a military man, king of the Franks, and was appointed as Roman emperor in 800 AD. Throughout Europe, he was seen as a great example of an emperor and Christian king. Not only did he revive the politicalRead MoreEssay on The Doni Tondo: Michelangelo1044 Words à |à 5 Pagescontemporary art world, where artists bring interdisciplinary elements and combine them in a mixture of genius and creativity, three and two-dimensional pieces are by no means exclusive in nature. The Donni Tondo, Michelangelo Buonarrotis tempera on panel with oil flourishes, although characteristically High Renaissance, projects a legacy of exploration and grow th that may appeal to contemporary artists whose artistic sensibilities favor the combination of artistic platforms. Michelangeloââ¬â¢s portrayal
Subscribe to:
Posts (Atom)