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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.With a terrain and make of concrete, experience from national highways suggests that there are, on the average, 2 potholes per mile after a certain amount of usage. We wish to know how likely it is to find no more than one pothole in a section of 5 miles of a highway. What is the average number of potholes in a section of 5 miles of a certain highway?In baseball, League A allows a designated hitter (DH) to bat for the pitcher, who is typically a weak hitter. In League B, the pitcher must bat. The common belief is that this results in League A teams scoring more runs. In interleague play, when League A teams visit League B teams, the League A pitcher must bat. So, if the DH does result in more runs, it would be expected that league A teams will score more runs in League A park than when visiting League B parks. To test this claim, a random sample of runs scored by league A teams with and without their DH is given in the accompanying table. Complete parts c) through d) below.
- In comparing the average protein content µ1 and µ2 of two brands of dog food, a consumer testing service finds that fifty 5-pund packages of brand A dog food had an average protein content x̅1=11 ounces per package and a s.d of s1 = 1 ounce, while sixty-5 pound packages of brand B dog food has an average protein content x̅2=9ounces per package and a s.d of s2 = 0.5 ounce. A difference of 0.5 ounces is considered to be not sufficiently important to report as a consumer issue. Therefore, a decision was made to test the hypothesis.On the Great Stark island, the likelihood of a residential fire is evenly distributed at 12 per month. Residents are evenly distributed along the 64-mile perimeter of the island. The government is providing fire protection, and a fire department's fixed cost is $60,000 per month. If the travel cost to fight a fire is $2,500 per mile, what is the optimal number of fire departments?nick and Casey are playing darts on the board that has five regions labeled a, b, c, d, and e in which of the regions is a dart most likely to fall?
- An angler fishes half of their time at East Delaney Lake, one quarter of their time at South Delaney Lake, and one quarter of their time at North Delaney Lake. Each lake has only two types of trout, brown trout and cutthroat trout. In East Delaney Lake, 6% of the trout are brown trout. In South Delaney Lake 64% of the trout are brown trout. In North Delaney Lake 69% of the trout are brown trout. Assume that any individual trout fish has the same chance of being caught by an angler spending time at that lake. Given that the angler caught a brown trout, what is the conditional probability that they caught the trout on North Delaney Lake? Use three decimal place accuracy.We know that physical exercise improves the body, but can it also improve the mind? Scientists at The Salk Institute at La Jolla, California, took a random sample of adult mice and divided them into two groups. Both groups were trained to find a platform in a maze filled with cloudy water. (Mice hate swimming, so they seek the platform as the refuge.) The first group of mice exercised on a running wheel, about 5 kilometers per day. The second group remained inactive. After one month, the mice were placed in the maze and timed until each reached the platform. The sample statistics are given below.Active group: n = 15, x ̄ = 17.6, s = 3.0 111Inactive group: n = 12, x ̄ = 27.1, s = 6.3 222(a) At 1% significance level conduct a hypothesis test to determine if exercise im- proves memory in adult mice; in other words, test if the active group is, on average, faster than the inactive group.(i.) State the hypotheses.(ii.) Test for equality of unknown population variances.(iii.) Calculate test…The weather report says that there is a 30% chance it will rain this morning. If you take your umbrella, which cost $25,and it does not rain, there is a 20% chance that you will lose it somewhere. If you do not take your umbrella, and it does rain, you will arrive at class damp and smelly, which you would pay $10 to avoid. Should you take your umbrella?
- If a farmer chose Technique B, what would happen?a. Possibility of a lower yield and lower riskb. Possibility of a higher risk and higher yieldc. Possibility of lower yield with higher risk but sustainabled. Possibility of higher yield and lower riske. No answerBased on Angel et al. (2003). A fertilizer companyis trying to determine the cheapest fertilizer mix thatprovides desired amounts of nutrients. The mix ismade by combining the following fertilizers: SSA,SPO, GUR, TSP, KCI, FERT, and SPF. The mix cannot contain both GUR and TSP. The percentage ofpotassium (K), sulfur (S), calcium (Ca), sodium (Na)and phosphorus (P) in each fertilizer is listed in the fileP06_88.xlsx. For example, a pound of SSA is 16% Kand 26% Na. The mix must contain at least 600 poundsof K, 550 pounds of S, 750 pounds of Ca, 900 poundsof Na, and 750 pounds of P. The mix cannot containboth GUR and TSP, because if both are present in themix, the affect of other fertilizers is nullified. The costper pound (in cents) of each fertilizer is listed in thesame file. Develop a linear integer model to find theminimum-cost fertilizer mixture that meets the statedchemical requirements.Globally, 35% of all ridged brittleshell tortoises have spots on their shells. A herpetologist in Citition collects a sample of 38 ridged brittlesell tortoises and finds that 16 of them have spots on their shells. The herpetologist would like to test the claim that the proportion of ridged brittleshell tortoises in Cititon with spots on their shells is greater than 35%. The herpetologist ends up rejecting the null hypothesis. If the actual proportion of ridged brittleshell tortoises in Cititon with spots on their shells is 41%, then what type of error, if any, has occurred? In the problem above, what is the test statistic?