The volume, V, of a sphere in terms of its radius, r, is given by V (r) = 7³. Express r as a function of V, and find the radius of a sphere with volume of 350 cubic feet. Round your answer for the radius to two decimal places. Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Include a multiplication sign between symbols. For example, a * .
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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.The Porsche Club of America sponsors driver education events that provide highperformance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. DeeganIndustries manufactures two types of roll bars for Porsches. Model DRB is bolted to thecar using existing holes in the car’s frame. Model DRW is a heavier roll bar that must bewelded to the car’s frame. Model DRB requires 20 pounds of a special high-alloy steel, 40minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires25 pounds of the special high-alloy steel, 100 minutes of manufacturing time, and 40minutes of assembly time. Deegan’s steel supplier indicated that at most 40,000 poundsof the high-alloy steel will be available next quarter. In addition, Deegan estimates that2000 hours of manufacturing time and 1600 hours of assembly time will be available nextquarter. The profit contributions are $200 per unit for…The vintage Restaurant is located on Captiva Island, a resort community located near Fort Meyers, Florida. The restaurant, which is owned and operated by Karen Payne, has just completed its third year of operation. During this time, Karen sought to establish a reputation for the restaurant as a high-quality dining establishment that specializes in fresh seafood. The efforts made by Karen and her staff have proved successful, and her restaurant has become one of the best and fastest-growing restaurants on the island. Karen has just concluded that to plan better for the growth of the restaurant in the future, it is necessary to develop a system that will enable her to forecast food and beverage sales by the month for up to 1 year in advance. Karen has the following data available on the total food and beverage sales that were realized during the previous 3 years of operation. Food and Beverage Sales for the Vintage Restaurant ($1000s) Month First Year Second Year Third YearJanuary 242…
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- It has been suggested that daily production of a subassembly would be increased if better lighting were installed and background music and free coffee and doughnuts were provided during the day. Management agreed to try the scheme for a limited time. A listing of the number of subassemblies produced per week before and after the new work environment for each employee follows. Employee Past Production Record Production after Installing, Lighting, Music, etc. JD 23 33 SB 26 26 MD 24 30 RCF 17 25 MF 20 19 UHH 24 22 IB 30 29 WWJ 21 25 OP 25 22 CD 21 23 PA 16 17 RRT 20 15 AT 17 9 QQ 23 Show your work, please. Thanks!It has been suggested that daily production of a subassembly would be increased if better lighting were installed and background music and free coffee and doughnuts were provided during the day. Management agreed to try the scheme for a limited time. A listing of the number of subassemblies produced per week before and after the new work environment for each employee follows. Employee Past Production Record Production after Installing, Lighting, Music, etc. JD 23 33 SB 26 26 MD 24 30 RCF 17 25 MF 20 19 UHH 24 22 IB 30 29 WWJ 21 25 OP 25 22 CD 21 23 PA 16 17 RRT 20 15 AT 17 9 QQ 23 30 FIND: State the decision rule and show your work: Reject H0 if T ≤ : Compute T and arrive at a decision (Show your work). T = ____________ , do not reject H0.In laparoscopic surgery, a video camera and several thin instruments are inserted into the patient's abdominal cavity. The surgeon uses the image from the video camera positioned inside the patient's body to perform the procedure by manipulating the instruments that have been inserted. The Top Gun Laparoscopic Skills and Suturing Program was developed to help surgeons develop the skill set necessary for laparoscopic surgery. Because of the similarity in many of the skills involved in video games and laparoscopic surgery, it was hypothesized that surgeons with greater prior video game experience might acquire the skills required in laparoscopic surgery more easily. Thirty‑three surgeons participated in the study and were classified into three categories, never used, under three hours, and three or more hours—depending on the daily number of hours they played video games at the height of their video game use. They also performed Top Gun drills and received a score based on the time to…