...Solving Proportions MAT222 Week 1 Assignment September 22, 2014 Solving Proportions Solving for a proportion can be used within numerous real-world problems, such as finding the population of an area. Conservationists are able to predict the population of bear’s in their area by comparing information collected from two experiments. In this problem, 50 bears in Keweenaw Peninsula were tagged and released so conservationists could estimate the bear population. One year later, the conservationist took random samples of 100 bears from the same area, proportions are able to be used in order to determine Keweenaw Peninsula’s bear population. “To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population (Dugolpolski, 2012)?” In order to figure the estimated population, some variables need to first be defined and explain the rules for solving proportions. The ratio of originally tagged bears to the entire population is (50/x). The ratio of recaptured tagged bears to the sample size is (2/100). 50x=2100 is how the proportion is set up and is now ready to be solved. Cross multiplication is necessary for this problem. The extremes are (100) and (50). The means are (x) and (2). 100(50)=2x New equation, and now solve for (x). 50002=2x2 Divide both...
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...This work MAT 222 Week 2 Discussion Questions 1 contains solutions on the following questions on One-Variable Compound Inequalities: According to the first initial of your last name, find the pair of compound inequalities assigned to you in the table below. Solve the compound inequalities as demonstrated in Elementary and Intermediate Algebra and the Instructor Guidance in the left navigation toolbar, being careful of how a negative x-term is handled in the solving process. Show all math work arriving at the solutions. Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean, and then display a simple line graph for each solution set as demonstrated in the Instructor Guidance in the left navigation toolbar. Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.) Mathematics - Algebra MAT/222 MAT 222 MAT222 Week 2 - Individual Discussion Question Board - A+ Original Guaranteed! MAT 222 MAT/222 MAT222 Algebra Ashford University Original, cited, no plagiarism Use as a guide! If you purchase this: Thanks for purchasing my tutorial! Open the attached file to get the paper/solutions. If you have any questions, comments, or concerns, please let me know! I can help you with future courses. Thanks again...
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...Sailboat Stability MAT222 Ms. Scarf July 29, 2014 Sailboat Stability This weeks assignment is found on page 605 of our math book, question number 103. Focus is solving formulas and using a vocabulary that describes the steps in the equations in mathmatical terms. This weeks focus is radical equations/formulas. The specific problem assigned gives real world value in understanding sailboats and the mathematical understanding of when the stability could be compromised or ideal. The problem is as follows: Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2. For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function. C=4d-1/3 b (Dugopolski,2012) There are three parts to this problem a, b, and c. Each one will be worked out. a)Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam 13.5ft. Using the formula and substituting the values given for the variables of d and b: C=4(23245)-1/3(13.5) First work the exponent by using the reciprocal due to the negative value C=4(.035)(13.5) Multiply all C=1.89 This is the capsize screening value(notice it is below 2 as needed) b) Solve for d of the formula C=4d-1/3b Start isolating d by dividing both sides by 4b C/4b=d-1/3 Now resolve...
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...WEEK 1 ASSIGNMENT: Solving Proportion MAT222: Intermediate Algebra Page 437 #56.) Bear Population: To estimate the size of the bear population on the Keweenaw Peninsula, conservationist captured, tagged, and released 500 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population? x500=1002 2x2=500002 x=25000 In this problem we are seeking to find a total amount. We must use the information we have to locate this amount. To solve we utilize the proportions formula. For this formula we use the total amount divided by the known tagged amount. Once we plug in the given amounts along with the “x” variable, we can begin to solve. First we cross multiply then finally we divide. The outcome is the total amount. Page 444 #10.) Simplify: y-1x+3=-13 3y-1=-1x+3 3y-3=-x-3 y=-x3 In this problem we have two fractional equations better known as a proportion. Next we cross using the extreme means property. The next step is to appropriately distribute on both sides. In order to solve for “y” we must move everything away from “y”. We start by subtracting, and then we divide. The final results are the equivalence of “y”. Upon going back to the top of problem#10 to check to see whether the solution is correct. I was unable to obtain a clear defined solution due to the negative fraction. However it is also unclear as to whether the problem is extraneous. One observation...
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...Composition and Inverse MAT222: Week 5 Assignment April 6, 2014 Composition and Inverse For this week’s assignment we are given the task of learning how to solve Composition and Inverse math problems. This week’s assignment focuses on the following problem: f(x)=2x+5 g(x)=x2-3 h(x)= 7-x / 3 The first thing I will do is compute (f – h)(4). (f – h)(4)=f(4) – h(4). Each function may be calculated separately and will be subtracted due to the rules of composition. f(4)=2(4)+5 We will then substitute the 4 from the problem and plug it into the x. f(4)=8 +5 We will be using order of operations in order to evaluate the function. f(4)=13 h(4)=(7-4) / 3 The same process will be used in this function where we will plug in f(4) and h(4) then the problem will look like: h(4)=3/3 h(4) = 1 (f – h)(4)=13-1 (f – h)(4)=12 This is the solution after substituting the values into the problem. The next step will consist of the two pairs of functions will composed into each other. In order to do this I will first have to find the solution for the function g(x). In order to do this I will be calculating it and then substituting for the x value in the f(x). This rule will function because the g function will be replacing the f function. Therefore this rule will help us (f▫g)(x)= f(g(x)). (f▫g)(x)=f(g(x)) (f▫g)(x)=f(x2-3) f will work on the rule of g and g will be replacing x. (f▫g)(x)=2(x2 - 3)-5 we will be using the rule of f and it will be applied...
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...Two-Variable Inequalities MAT222: Intermediate Algebra November 03, 2014 This week assignment has to do with solving two variable equalities that have to do with practical situations. The main problem on this assignment is objects that would have to be shipped together that would need to fit in an eighteen wheeler trailer. “The accompanying graph shows all of the possibilities for the number of refrigerators and the number of TVs that will fit into an 18-wheeler. a) Write an inequality to describe this region. b) Will the truck hold 71 refrigerators and 118 TVs? c) Will the truck holds 51 refrigerators and 176 TVs?” Dugopolski, M (2012). I will now start out to solve problem 68 on page 539 in our textbook of Elementary and Intermediate Algebra. The graph is going to show a triangle region that would be shaded. This is where I would have to write the inequality to describe the region. When looking at the graph it will show the number of refrigerators. This will be shown on the graph as “x” axis and the number will be “p” for television for the “y” axis. The points on the graph are going to show on the graph as (0,330) and (110, 0) these numbers are given to determine on how the slope is going to be placed on the graph in which will be known as the slope form. (Part A.) p = y1-y2 / X1-x2 = 330 – 0 / 0-110 = -3/1 the slope is -3/1 or -3 Y – y1 = p(x – x1) Y – 330 = - 3 / 1(x-0) Y = - 3x/1 + 330 -3x/1 +330 = y expression switch by place the y on the right hand...
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