Biologists stock a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 10, 000. The number of fish tripled in the first year.
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- Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. LineSpeed Number ofDefectiveParts Found 20 23 20 21 30 19 30 15 40 16 40 18 50 14 50 10 (a) Develop a scatter diagram with the line speed as the independent variable. A…Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plasticsm conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. a. Develop a scatter diagram with the line speed as the independent variable. b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? c. Use…Our family brought lots of hot dogs along on our latest camping trip. However, after setting up the tent, we didn’t take care to make sure that the food was safe – and raccoons ate 1/3 of the hot dogs! Grumbling, we cleaned up the mess, then ate 6 hot dogs for lunch. But we forgot to put the rest away when we went hiking, and lost 1/4 of our dwindling supply to jays! Just as a precaution, Mom went to the store and bought enough hot dogs to increase our supply by 2/3. Our campsite neighbors, however, ran out of food, so we gave them 2/9 of our remaining hot dogs and then ate 11 hot dogs for our dinner. That night, bears got 3/4 of the last part of our supply, and in the morning there were only 6 hot dogs left! How many hot dogs did we start with? (Next time maybe we should just bring granola bars...)
- Rivers in North Carolina contain small concentrations of mercury that can accumulate in fish over their lifetimes. The concentration of mercury in fish tissue can be obtained by catching fish and sending samples to a lab for analysis. A study was conducted on fish from the Waccamaw and Lumber Rivers to investigate mercury levels in tissues of largemouth bass. At several stations along each river a group of fish were caught, weighed and measured; in addition a filet from each fish was sent to a lab so that the tissue concentration of mercury could be determined. In all, 171 fish were caught at 15 different research stations along the Waccamaw and Lumber Rivers. Data from fish caught at one of these stations is shown in the followinng table: length weight 1616 47.0 48.7 1862 2855 55.7 45.2 1199 1320 44.7 1225 43.8 870 38.5 1455 45.8 1220 44.0 1033 40.4 Compute the correlation between length and weight for these fish. (Assume the correlation conditions have been satisfied and round your…Ross White recently opened a landscaping division , that advises home owners and businesses on landscaping and lawn maintenance. The operations manager, Ms. Priya Johnson, is trying to determine the amount of fertilizer that should be applied to a particular lawn in a residential area in San Juan. Ms. Johnson’s analysis has determined that the lawn needs at least 60kg of Nitrogen, 24kg of Phosphorous compounds and 40kg of Potassium compounds for the current season. After checking nearby home and garden centres, Ms. Johnson has found that one of the suppliers is currently having a sale on packaged fertilizer. One type on sale called Xynis, is a 20-5-20 mixture, containing 20% Nitrogen, 5% phosphorous compounds and 20% potassium compounds. It sells at $4 for a 20kg bag. The other type called Yield-all is a 10-10-5 mixture (10% Nitrogen, 10% phosphorous compounds and 5% potassium compounds) selling for $5 for a 40kg bag. Ms. Johnson would like to know how many bags of each type she…Intensive care units (ICUS) generally treat the sickest patients in a hospital. ICUS are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUS as efficiently as possible in hospital. According to a 2017 large-scale study of elderly ICU patients, the average length of stay in the ICU is 3.4 days (Critical Care Medicine journal article). Assume that this length of stay in the ICU has an exponential distribution. Do not round intermediate calculations. a. What is the probability that the length of stay in the ICU is one day or less (to 4 decimals)? b. What is the probability that the length of stay in the ICU is between two and three days (to 4 decimals)? c. What is the probability that the length of stay in the ICU is more than five days (to 4 decimals)?
- The US Department of Agriculture collected nutrient data on various types of cheeses. Two nutrients of concern to people trying to eat healthier are saturated fat and sodium. The given JMP applet shows scatterplots of the amount of sodium in milligrams by the amount of saturated fat in grams for these cheeses.t O JMP Applet jmp ? Sodium (mg) By Saturated Fat (g) Sodium (mg) By Saturated Fat (15 g - 21 g) 2000 2000 1500- 1500 1000- 1000- 500- 500- 0- 0- 20 15 16 20 21 Saturated Fat (g) Saturated Fat (g) Sodium (1,000 mg - 2,000 mg) By Saturated Fat (g) 1800- 1000- 1400- 1200- 1000- 10 15 20 Saturated Fat (g) II (Bu) unipos III (Bu) unipos (Bu) uniposBrawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. LineSpeed Number ofDefectiveParts Found 20 23 20 21 30 19 30 16 40 15 40 17 50 14 50 11 Use the least squares method to develop the estimated regression equation (to 1…An fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 127 pounds, and will sell for $4.6 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 2.1 pounds, while the price per pound will decrease by $0.07. A) How many weeks should the grower wait before harvesting the apples in order to maximize the sales revenue per tree? (Round your answer to the nearest tenth of a week.) Answer: __________ (rounded to the nearest tenth) B) Use your answer in part A to find the actual maximum revenue that can be expected. (Round your answer to the nearest dollar.) Answer: ____________ dollars (rounded to the nearest dollar)
- At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint takes exactly 2 minutes (this is constant). The average total time in the system is 6.0 minutes. 8.0 minutes. 5.4 minutes. 2.5 minutes.A survey looked at how long it takes a typical company to recoup an investment in research. The survey determined that 39% of the corporations took six months or less to recoup their investment. The data table below shows a sample of the time, in months, it might have taken 20 corporations to recoup their investment. Complete parts a and b. 9.0 8.0 4.0 4.0 7.0 8.0 7.0 7.0 9.5 5.5 7.5 12.0 8.5 5.5 10.5 10.0 7.5 4.5 7.0 7.5 a. Determine the number of corporations that recovered their investement in research in six months or less. There were 5 corporations that recovered their investment in research in six months or less. b. Calculate the probability of obtaining at most the number of corporations that you determined in part a if the percent of those recovering their investment is as indicated by the survey. The probability (Round to four decimal places as needed.)A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 60 cells.