Algebra Paper on Inequalities - example attached.

Question Description

I’m studying and need help with a Algebra question to help me learn.


Read the following instructions in order to complete this assignment and review the example, ATTACHED,  of how to complete the math required for this assignment:

  • Read the article about Body Mass Index (BMI) on page 151 of Elementary and Intermediate Algebra. Use the formula given using pounds and inches for finding the BMI at the end of the first paragraph for the following four intervals:

    • 17 < BMI <= 22  might have a longer life span than average 
    • 23 < BMI <= 25  probably not overweight
    • 25 < BMI <= 30   probably overweight 
    •  BMI > 30        obese
You will use your height to plug into the formula to solve for W, the weight range that will go with each category. You may prefer to solve the formula for the variable W before plugging in values, which is fine.
  • Write a two- to three-page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, do the following:

    • Demonstrate your solution to the above problem, making sure to include all mathematical work.
    • Explain why the computed weight ranges could be misleading.
    • Choose one of the four BMI regions and express the region using set notation and interval notation. Include a simple graph of the region. Please see the example for some ideas of how to do this. 
    • 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; but integrate them into your discussion):

      • Inequality 
      • Equivalent 
      • Compound inequality 
      • Interval 
      • Infinity

Unformatted Attachment Preview

Running Head: INEQUALITIES 1 Running head should use a shortened version of the title if the title is long! All capital letters for the title and the words Running and Head should be capitalized as well. Inequalities (full title; centered horizontally & vertically) First Name Last Name MAT 221 Dr. XXXXXXX XXXXXXXX Date INEQUALITIES 2 Inequalities Be sure to have a centered title on page 1 of your papers!! [The introductory paragraph must be written by each individual student and the content will vary depending on what the student decides to focus on in the general information of the topic. YOUR INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! The following paragraph is not an introduction to the paper but rather the beginning of the assignment.] Students, you are perfectly welcome to format your math work just as I have done in these examples. However, the written parts of the assignment MUST be done in your own words. You are NOT to simply copy my wording into your posts! On page 151 of the textbook (Dugopolski, 2012) is the formula for Body Mass Index or BMI as follows: BMI = 703W H2 Where W = one’s weight in pounds, and H = one’s height in inches. Using personal height, four intervals must be found using compound inequalities. The height used in these problems is 67.25 inches. The specified intervals include three compound “between” inequalities and one regular inequality. Body Mass Index, or BMI, shows up in the inequalities and this formula will be substituted to solve the inequality for W to specify the weight ranges that fit each category for the height being used. The first interval shows who might have a longer life span than average. The compound inequality for this is: 17 < BMI < 22 17 < 703W < 22 This is an equivalent inequality replacing BMI with the formula. H2 17 < 703W < 22 (67.25)2 H2 has been replaced by the height in inches. INEQUALITIES 3 17 < 703W < 22 4522.5625 The denominator was square and then multiplied times each term in the numerator: 17, 703W, and 22. 17(4522.5625) < 703W(4522.5625) < 22(4522.5625) Cancelling is done. 4522.5625 76883.5625 < 703W < 99496.375 The multiplications were carried out. 76883.5625 < 703W < 99496.375 All three terms divided by 703 to isolate W. 703 703 703 109 < W< 141.5 This solution shows the range for weight. People of height 67.25 inches might have a longer than average life span if they weigh between 109 lbs. and 141.5 lbs. In the next problem, a different process will be used since the first problem includes some of the same work. To solve the second inequality formula, a solution for W will be found prior to substituting in the height. 23 < 703W < 25 First, multiply all terms by H2 to take it out of the denominator. H2 23H2 < 703W < 25H2 703 703 Divide all terms by 703 to isolate W. 703 23H2 < W < 25H2 This is an equivalent inequality to solve for the second 703 weight interval. The height squared (4522.5625) is substituted into 703 the formula find the second weight interval. 23(4522.5625) < W < 25(4522.5625) 703 703 INEQUALITIES 4 104018.9375 < W < 113064.0625 703 Multiplication carried out. 703 148 < W < 161 Division carried out. People of height 67.25 inches who weigh between 148 lbs. and 161 lbs. are probably not overweight. This method is much more efficient than the first method so it will be used to find the next two intervals as well. The third weight interval indicates the range for probably overweight for this height. Values substituted into the above compound inequality in place of 23 and 25 are 25.1 and 29.9. 25.1(4522.5625) < W < 29.9(4522.5625) 703 703 113516.31875 < W < 135224.61875 703 Multiplications carried out. 703 161.5 < W < 192 Division carried out People of height 67.25 inches who weigh between 161.5 and 192 are probably overweight. The fourth weight interval indicates the range for those who are obese at this height. This is not a compound inequality so only the middle and right terms of the basic inequality are used with the opposite pointing arrow and substitute 30 for 29.9. W ≥ 30(4522.5625) 703 W ≥ 135676.875 703 W ≥ 193 Division carried out. Multiplication carried out. INEQUALITIES 5 People of height 67.25 inches who weigh 193 lbs. or above are most likely obese and would benefit from some serious life-style changes. Although this interval theoretically extends to positive infinity, the weight of a human is eventually self-limiting. [Student answers to part 3 are going to vary according to their math and understanding of the article.] In English the following was written: People of height 67.25 inches who weigh between 148 lbs. and 161 lbs. are probably not overweight. In set notation this could be written as follows: Let X = the set of those who are probably not overweight for the specified height. Then X = {w | w > 148 and w < 161} where w represents the weight of the individual. Because the weight is between 148 and 161, “w” has to be larger than the smallest number (148) and smaller than the larger number (161). In interval notation this would be written as follows: X = (148, 161) Parentheses are used because of the > and < symbols from the inequality. This demonstrates neither number is included in the solution set. Graphed on a number line this interval could look like this: <-------------(----------------------------------)--------------------> 148 161 [The conclusion paragraph must be written by each individual student and the content will vary depending on what the student decides to include in their summary. DO NOT INCLUDE PERSONAL NARRATIVE LIKE “I LEARNED…” OR “WE CAN DO….”. BE SURE TO SUMMARIZE WHY THE CONCEPT(S) ARE IMPORTANT AND HOW THEY CAN BE CONNECTED TO OTHER CONCEPTS.] INEQUALITIES 6 Reference Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing. Use the word ‘Reference’ or ‘References’ as the title. THERE IS NO COLON OR UNDERLINE. Textbook should ALWAYS be included in every assignment! Be sure to use appropriate indentation (hanging), font (Arial or Times New Roman), and size (12). ...
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Final Answer

Ian N (109)
University of Maryland

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