Fertilizer is sold in 100 pound bags labelled with the amount of nitrogen (N), phosphoric acid (P205), and potash (K2O) present. The mixture of these nutrients varies from one type of fertilizer to the next.For example, a 100 pound bag of Vigoro Ultra Turf fertilizer contains 29 pounds of nitrogen, 3 pounds of phosphoric acid, and 4 pounds of potash.Another type of fertilizer, Parker's Premium Starter, has 18 pounds of nitrogen, 25 pounds of phosphoric acid, and 6 pounds of potash per 100 pounds.Determine the amount of each type required to yield a mixture containing the 134 pounds of nitrogen, 37 pounds of phosphoric acid, and 22 pounds of potash.The mixture contains pounds of Vigoro, and pounds of Parker's.Hint: Let 1 be the amount of 100 pound bags of Vigoro, and 2 the amount of 100 pound bags of Parker. Set up and solve the system in the unknowns ₁ and 2 and then multiply the solution by 100 tofind the number of pounds.

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Answered: Fertilizer is sold in 100 pound bags…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 17PS: Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There...

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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.
Researchers are investigating the effectiveness of using a fungus to control the spread of an insect that destroystrees. The researchers will create four different concentrations of fungus mixtures: 0 milliliters per liter (ml/L),1.25 ml/L, 2.5 ml/L, and 3.75 ml/L. An equal number of the insects will be placed into 20 individual containers.The group of insects in each container will be sprayed with one of the four mixtures, and the researchers willrecord the number of insects that are still alive in each container one week after spraying. (b) Does the experiment have a control group? Explain your answer.
Researchers are investigating the effectiveness of using a fungus to control the spread of an insect that destroystrees. The researchers will create four different concentrations of fungus mixtures: 0 milliliters per liter (ml/L),1.25 ml/L, 2.5 ml/L, and 3.75 ml/L. An equal number of the insects will be placed into 20 individual containers.The group of insects in each container will be sprayed with one of the four mixtures, and the researchers willrecord the number of insects that are still alive in each container one week after spraying. (c) Describe how the treatments can be randomly assigned to the experimental units so that each treatmenthas the same number of units.
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…
Fertilizer is sold in 100 pound bags labelled with the amount of nitrogen (N), phosphoric acid (P2O5), and potash (K2O) present. The mixture of these nutrients varies from one type of fertilizer to the next. For example, a 100 pound bag of Vigoro Ultra Turf fertilizer contains 29 pounds of nitrogen, 3 pounds of phosphoric acid, and 4 pounds of potash. Another type of fertilizer, Parker's Premium Starter, has 18 pounds of nitrogen, 25 pounds of phosphoric acid, and 6 pounds of potash per 100 pounds. Determine the total amount of nitrogen, phosphoric acid, and potash in the mixture of 200 pounds of Vigoro and 300 pounds of Parker's. The mixture contains pounds of potash. pounds of nitrogen, pounds of phosphoric acid, and
The following below shows the calories, fat, and carbohydrates per ounce for three brands of cereal, and the total amount of calories, fat, and carbohydrates required for a special diet: Cereal Brand X- 50 calories , 0 fat , 22 carbohydrates Cereal Brand Y - 108 calories, 0.1 fat, 25.5 carbohydrates Cereal Brand Z- 127 calories, 5.5 fat , 18 carbohydrates Total Required - 393 calories, 5.7 fat , 91 carbohydrates a) Using the information in the table above, write a system of three equations.b) Write a system in matrix form Ax = b c) Using the Cramer's Rule or Inverse Method, find the amount of each brand of cereal that will give the level of nutrition required.
A diet supplies 0.8 grams of calcium per day, in addition to the nutrients listed in the table to the right. The amounts of calcium per unit (100 g) supplied by the three ingredients in the diet are as follows: 1.25 g from nonfat milk, 0.18 g from soy flour, and 0.8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 78 g of protein, 0 g of carbohydrate, 3.6 g of fat, and 0.15 g of calcium. Complete parts (a) and (b) below. 0.42 X₁ x2 X3 11 34 45 3 0.8 CIES X4 (Type an integer or decimal for each matrix element.) Amounts (g) Supplied per 100 Amounts (g) g of Ingredient Supplied by Diet in One Day a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply precise amounts of protein, carbohydrate, fat, and calcium in the diet. Nutrient Nonfat Soy Whey Milk flour 36 Protein Carbohydrate 52 0 Fat 50 14 33 75 7 1.2 34 45 3
Daniel is on a diet and he wants to limit his food intake to 109 g carbohydrate, 103 g fat, and 153 g calories per day. According to his food nutritionist, he should have 3 g carbohydrate, 14 g fat, and 13 g calories for breakfast; for lunch he should have 5 g carbohydrate, 7 g fat, and 15 g calories; and at dinner he should have 9 g carbohydrate, 15 g fat, and 6 g calories. What is the determinant of the given matrix in the problem?
A bakery in Cape Town would like to produce a koeksister that could be marketed to consumers that are health conscious. They experimented with 4 different fats to see which fat was least absorbed by the koeksisters during the deep-frying process. Each fat was used for six batches of one dozen koeksisters each, and the table shows the grams of fat absorbed by each batch of koeksisters g Fat Absorbed in Batch Fat 1 64 72 68 77 56 95 72 13.34 Fat 2 78 91 97 82 85 77 85 7.77 Fat 3 75 93 78 71 63 76 76 9.88 Fat 4 55 66 49 64 70 68 62 8.22 S df MS F p-value Treatment 1636.5 3 545.4 5.41 0.0069 Error 2018.0 20 100.9 Total 3654.5 23 4.1 At the 0.05 level of significance, test whether the mean fat absorbed by the four different fats are significantly different. Interpret your results. (Ensure you use all the steps for your hypothesis test) 4.2 Given the table below, what can you conclude about the mean fat absorbed by the four different fats 95% Confidence Interval for x – x Fat 1- Fat 2 -13…
Select the correct answer. A veterinarlan is mixing three different types of feed to produce a mixture that contains 44 grams of fat, 48 grams of carbohydrates, and 132 grams of protein. • Each serving of the first type of feed, x, contains 11 grams of fat, 24 grams of carbs, and 3 grams of protein. Each serving of the second type of feed, y, contains 4 grams of fat, 8 grams of carbs, and 31 grams of protein. • Each serving of the third type of feed, z, contains 10 grams of fat, 0 grams of carbs, and 18 grams of protein. Which matrix represents the system of equations that will give the number of servings of each type of feed the veterinarian should include? O A. 3 11 4 10 24 8 31 18 44 48 132 11 4 101 O B. 24 8 0 3 31 18 C. |組 O D. 4 10 44 24 8 0 48 3 31 18 132 All rights reserved.
Animals and people that take in more energy than they expend will get fatter. Here are data on 12 rhesus monkeys: 6 lean monkeys (4% to 9% body fat) and 6 obese monkeys (13% to 14% body fat). The data report the energy expended in 24 hours (kilojoules per minute) and the lean body mass (kilograms, leaving out fat) for each monkey. Lean Obese Body Mass Energy Body Mass Energy 6 1.13 8.2 0.91 8 1 9 1.32 9.2 1.46 10.4 1.18 10.5 1.62 12.7 1.46 9.2 1.02 12.2 1.28 9 1.16 10.6 1.37 (a) What is the mean lean body mass of the lean monkeys? ANSWER x¯=x¯= kilograms. (b) What is the mean lean body mass of the obese monkeys? ANSWER x¯=x¯= kilograms.
Newcor’s steel mill has received an order for 25 tonsof steel. The steel must be 5% carbon and 5% molybdenumby weight. The steel is manufactured by combining threetypes of metal: steel ingots, scrap steel, and alloys. Foursteel ingots are available for purchase. The weight (in tons),cost per ton, carbon and molybdenum content of each ingotare given in Table 97.Three types of alloys can be purchased. The cost per tonand chemical makeup of each alloy are given in Table 98.Steel scrap may be purchased at a cost of $100 per ton.Steel scrap contains 3% carbon and 9% molybdenum.Formulate a mixed integer programming problem whosesolution will tell Newcor how to minimize the cost of fillingtheir order.

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