The Nutty Professor sells cashews for $6.00 per pound and Brazil nuts for $4.80 per pound. How much of each type should be used to make a 34 pound mixture that sells for $5.47 per pound? Round answers to the nearest pound. pounds of cashews pounds of Brazil nuts
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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 top three sources of oil imports for the United States in the same year were Saudi Arabia, Mexico, and Canada. The three top countries accounted for 47% of oil imports. The United States imported 1.8% more from Saudi Arabia than they did from Mexico, and 1.7% more from Saudi Arabia than they did from Canada. What percent of the United States oil imports were from these three countries?[29]The chart below gives price and fuel efficiency for Ford Escape SUVs with conventional or hybrid engines. Car model price average mileage (mpg) Ford Escape (conventianal) $25,000 24 For escape (Hybrid) $33,500 38 What is the annual cost to drive the conventional Ford Escape for 15,000 miles if gas costs $2.50 per gallon? What is the annual cost to drive the hybrid model Ford Escape for 15,000 miles if gas costs $2.50 per gallon? How much money would you save annually if you bought the hybrid model instead of the conventional Ford Escape, assuming you drove 15,000 miles each year? How many years of driving the more fuel-efficient SUV would it take for you to make up difference in its higher sticker price over the price of the conventional model?
- As GM prepares to begin producing and selling 16-ounce boxes of the new cereal, which it has named Cheerios, management is concerned about the amount of banana-flavored marshmallows. It wants to be careful not to include less than 1.6 ounces or more than 2.4 ounces of banana flavored marshmallows in each 16-ounce box of Cheerios. Tina Finkel, VP of Production for GM, has suggested that the company measure the weight of banana-flavored marshmallows in a random sample of 25 boxes of Cheerios on a weekly basis. Each week GM can count the number of boxes out of the 25 boxes in the sample that contain less than 1.6 ounces or more than 2.4 ounces of banana-flavored marshmallows; if the number of boxes that fail to meet the standard weight of banana-flavored marshmallows is too high, production will be shut down and inspected. Ms. Finkel and her staff have designed the production process so that only 8% of all 16-ounce boxes of Cheerios fail to meet the standard weight of banana-flavored…The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the cars frame. Model DRW is a heavier roll bar that must be welded to the car’s frame. Model DRB requires 20 pounds of a special alloy steel, 40 minutes of manufacturing time, and 60 minutes if assembly time. Model DRW requires 25 pounds of the special alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan’s steel supplier indicated that at most 40,000 pounds of the high alloy steel will be available next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,600 hours of assembly time will be available next quarter. The profit contributions are $200 per unit…The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the cars frame. Model DRW is a heavier roll bar that must be welded to the car’s frame. Model DRB requires 20 pounds of a special alloy steel, 40 minutes of manufacturing time, and 60 minutes if assembly time. Model DRW requires 25 pounds of the special alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan’s steel supplier indicated that at most 40,000 pounds of the high alloy steel will be available next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,600 hours of assembly time will be available next quarter. The profit contributions are $200 per unit…