Concept explainers
(a)
To calculate: The stockpiles in each of the next two years, if in an arm race is held between two superpowers, each nation stores its own enemy’s nuclear arsenal each year and has a policy of undoing a certain percentage of its stockpile each year and adding that same percentage of its competitor’s stockpile.
Nation A has
(b)
To calculate: The stockpiles in each of the preceding two years, if in an arm race which is held between two superpowers, each nation stores its own enemy’s nuclear arsenal each year and has a policy of undoing a certain percentage of its stockpile each year and adding that same percentage of its competitor’s stockpile.
Nation A has
(c)
To prove: That the missile gap is decreased by
An arm race is held between two superpowers, each nation stores its own enemy’s nuclear arsenal each year and has a policy of undoing a certain percentage of its stockpile each year and adding that same percentage of its competitor’s stockpile. Nation A has
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Finite Mathematics & Its Applications (12th Edition)
- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forwardCholesterol 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.arrow_forwardA certain closed economy consists of two sectors: goods and services.Suppose that 60% of all goods and 30% of all services. are used in theproduction of goods. What proportion of the total economic output is usedin the production of goods?arrow_forward
- Suppose that a region has two hospitals. Hospital A has about 10 births per day, and hospital B has about 50 births per day. About 50% of all babies are boys, but the percentage who are boys varies at each hospital from day to day. Over the course of a year, which hospital will have more days on which 60% or more of the births are boys? The smaller Hospital A, the larger B, or will Hospital A and B have nearly the same number of days?arrow_forwardThe population of Boomtown is currently 12000 and expected to grow by 2.6% over the next year. What will its population be by then? The population of Dullsville, on the other hand, is currently 9000 and expected to decrease by 3% over the next year. What will its population be by then?arrow_forwardO A commuter owns two cars. One is a compact and the other is a standard model. About of the time he uses the compact to travel to work and about - of the time the larger car is used. When he uses the compact car, he usually gets home by 5 : 30 P.M. about 75% of the time. If he uses the standard sized car he gets home by 5 : 30 P.M. about 60% of the time. If he gets home by 5 : 35 P.M., what is the probability that he used the compact car?arrow_forward
- 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 $100 per ton.Steel scrap contains 3% carbon and 9% molybdenum.Formulate a mixed integer programming problem whosesolution will tell Newcor how to minimize the cost of fillingtheir order.arrow_forwardb) A mining company runs copper mines with various levels of fertility, where the profits per tonne of copper extracted are greater in more fertile mines. A greater annual quantity of copper can also be extracted from more fertile mines. As per the sample of mines in the table below, mine A is of highest fertility, mine D is of lowest fertility. Profit per tonne of Annual copper extracted ($) Tonnes of Copper Extracted 300 Mine Mine A 50 Mine B 200 30 Mine C 150 20 Mine D 100 10 What is mean, median and mode profit per tonne of copper extracted? As a shareholder, which measure would you be more concerned with? i. Given that the above table is an unbiased sample of data, what is the variance, standard deviation and coefficient of variation of profit per tonne of copper extracted? ii. Test the hypothesis that the population mean profit per tonne of copper extracted is $250 at the 5% level of significance. iii. If you were told the population variance of profit per tonne of copper…arrow_forwardCompany A receives large shipments of microprocessors from Company B. It must try to ensure the proportion of microprocessors that are defective is small. Suppose Company A decides to test ten microprocessors out of a shipment of thousands of these microprocessors. Suppose that if at least one of the microprocessors is defective, the shipment is returned. Complete parts a through c. a. If Company B's shipment contains 12% defective microprocessors, calculate the probability the entire shipment will be returned. The probability is nothing. (Round to four decimal places as needed.) If Company B and Company A agree that Company B will not provide more than 5% defective chips, calculate the probability that the entire shipment will be returned even though only 5% are defective. The probability is (please show how you achieved answer).arrow_forward
- Company A receives large shipments of microprocessors from Company B. It must try to ensure the proportion of microprocessors that are defective is small. Suppose Company A decides to test 10 microprocessors out of a shipment of thousands of these microprocessors. Suppose that if at least one of the microprocessors is defective, the shipment is returned. Complete parts a through c.a. If Company B's shipment contains 8% defective microprocessors, calculate the probability the entire shipment will be returned.The probability is0.5656.(Round to four decimal places as needed.) I only need answer to B below:b. If Company B and Company A agree that Company B will not provide more than 3% defective chips, calculate the probability that the entire shipment will be returned even though only 3% are defective.The probability is (Round to four decimal places as needed.)arrow_forwardA conglomerate corporation develops, manufactures, and markets a wide range of products, including medical diagnostic imaging devices, jet engines, lighting products, and chemicals. In 2013, the stock price rose 33.55%, and in 2014, the stock price declined 9.2%. If one purchased $1,000 of some social media stock at the start of 2013, its value would be $2,926.83 at the end of 2014. Complete parts (a) through (c) below. a. Compute the geometric mean rate of return per year of the two-year period 2013-2014. (Hint: Denote an increase of 33.55% as R₁ = 0.3355). % per year. The geometric mean rate of return is (Round to two decimal places as need.) b. If you purchased $1,000 of this conglomerate corporation's stock at the start of 2013, what was its value at the end of 2014? The value of this stock at the end of 2014 was $ (Round to the nearest cent as needed.) c. Compare the result of (b) to the value of the $1,000 of the social media stock. Choose the correct answer below and fill in the…arrow_forwardDina Drink stall sells three types of drinks daily. Each type of drink is made from totally milk and rose syrup. Sixty liters of milk and twenty-five liters of rose syrup should be consumed daily since stocks are nearing their expiration dates. The composition of each type of drink per liter and the profit earned from each drink is shown below: Drink Type Milk (L) Rose syrup (L) Profit (P) 1 0.7 0.3 35 0.8 0.2 25 0.9 0.1 30 Past experiences indicate that the total amount of drink of Type 1 and Type 2 is sold not more than the total amount of drink of Type 3 sold. Formulate an LP that will maximize profit.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning