Describe and correct the error made in writing the system of inequalities epresented by the graph shown to the right. The red boundary line is y = 0.5x +1. Since the line is solid, use s or 2. The blue boundary line is y = -2x +2. Since the line is dashed, use < or >. ys0.5x +1 y< -2x + 2
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- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.A fund-raising company is putting together a student kit of candy bars for a school to use in its annual support campaign. To maximize sales, the company will put more of the most popular candy bar sold in an average day in each kit. The company’s research shows that of the five most popular candies, local vending machines sell 100 of Candy A, 14 of Candy B, 50 of Candy C, 6 of Candy D, and 45 of Candy E on an average day. Which candy on average is the most popular candy? Which averaging method did you use?The analysis of risk and the search for yield in companies is determinant for financial success. In this case, consider the stock price and dividends of the companies Power Electric Industries, Riviera Power Inc. and Nature Energy Corp. for the period from 2014 to 2019. Power Electric Industries Power Electric Industries Riviera Power Inc. Riviera Power Inc. Nature Energy Corp. Nature Energy Corp. year Year Stock price Dividends Year Stock price Dividends Year Stock price Dividends 2019 $18.5 $1.50 $38.5 $4.50 $58.5 $3.50 2018 $15.93 $1.10 $40.93 $3.10 $50.93 $2.10 2017 $10.20 $1.00 $43.20 $3.00 $53.20 $3.00 2016 $9.80 $0.90 $50.80 $2.90 $50.80 $2.90 2015 $8.50 $0.85 $48.50 $2.85 $48.50 $2.75 2014 $8.00 $0.80 $45.00 $2.80 $45.00 $2.60 6. Calculate the percentage volatility (betas) of Power Electric Industries and Riviera Power Inc. by running regressions from the returns.…
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