Chapter 1.1, Problem 62E

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.

Cholesterol levels: A national health survey measured the serum HDL cholesterol levels in a large number of women. Following is a sample of 35 HDL levels (in milligrams per deciliter) that are based on the results of that survey. The list has been sorted into numerical order. 28 28 28 30 31 34 34 35 38 38 39 39 40 41 41 41 41 42 42 43 43 44 46 47 48 49 52 53 56 61 63 65 68 68 69 Send data to Excel Part 1 of 2 (a) What is the 17th percentile? The 17" percentile is Part 2 of 2 (b) What is the 72nd percentile? The 72nd percentile is. Check Answer Save For Later Submit Assignment ZUZMCorawl LLC. All Rights Reserved. Terms of Use Privacy Center

Blood pressure: A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters of mercury, for a sample of 7 adults. The following table presents the results. Systolic Diastolic 115 83 133 91 154 94 119 69 123 77 112 75 157 103 Send data to Excel Compute the least-squares regression line for predicting diastolic pressure (y) from systolic pressure (x). Round the intermediate calculations to at least six decimal places. Round the slope and y-intercept values to at least four decimal places. Regression line equation: y = Save For Later Submit Assignment Check Answer Privacy Center © 2021 McGraw Hill LLC. All Rights Reserved. Terms of Use 47°F