Suppose the number of inches a plant grows each day is linearly related to the hours the plant is exposed to sunlight. Given that the plant grows 2.5 inches a day if it gets 7 hours of sunlight, and it grows 3 inches if it gets 9 hours of sunlight. How many hours of sunlight did the plant get if it grew 1.2 inch a day?
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- An economist believes there is a linear relationship between the marketprice of a particular commodity and the number of units suppliers of thecommodity are willing to bring to the marketplace. Two sampleobservations indicate that when the price equals $15 per unit, the weekly supply equals 30,000 units; and when the price equals $20 per unit, theweekly supply equals 48,000 units (i) If price per unit, p, is plotted on the horizontal axis and the quantitysupplied q is plotted on the vertical axis, determine the slope-intercept formof the equation of the line which passes through these two points.(ii) Interpret the slope of the equation in this application.(iii) Predict the weekly supply if the market price equals $25 per unit.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, 126 pounds, and will sell for $4.7 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 1.8 pounds, while the price per pound will decrease by $0.06.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.)The Organization for Economic Cooperation and Development (OECD) consists of 20 industrialized countries. For these nations, the prediction equation relating y = child poverty rate (in percentage points) to x = social expenditure as a percentage of gross domestic product (GDP) is = 22-1.3x. In 2000, the actual child poverty rate ranged from 2.8% (in Finland) to 21.9% (in the U.S.). Social expenditure as a percentage of GDP ranged from 2% (in the United States) to 16% (in Denmark). Using the linear prediction equation and plugging in the actual x-values (social expenditure rates) provided above, find the predicted child poverty rates for the United States and for Denmark. The x-values for both of these countries are provided above in the description of the study. (Note: You do not need to convert the percentages into proportions before or after plugging them into the equation.) The predicted child poverty rate for the U.S.: The predicted child poverty rate for Denmark:
- The Organization for Economic Cooperation and Development (OECD) consists of 20 industrialized countries. For these nations, the prediction equation relating y = child poverty rate (in percentage points) to x = social expenditure as a percentage of gross domestic product (GDP) is = 22-1.3x. In 2000, the actual child poverty rate ranged from 2.8% (in Finland) to 21.9% (in the U.S.). Social expenditure as a percentage of GDP ranged from 2% (in the United States) to 16% (in Denmark). What is the residual for the United States? You can use the information on the actual y-value given in the description of the study as well as information from your response to Question 3 to calculate this. Residual for the U.S. =At the BMV, suppose that the length of time you must wait before speaking to a customer service representative is linearly related to the number of people who are in line in front of you. If there are 8 people in line in front of you, you will wait 44 minutes, and if there are 14 people in front of you, you will wait 68 minutes. How long will you wait if there are 10 people in front of you?The percentage of male workers who prefer a female boss over a male boss increased approximately linearly from 7 % in 1977 to 14 % in 2005 . Predict when 22 % of male workers will prefer a female boss.
- The number of days a barrel of water lasts varies inversely with the people who consume it. If a barrel of water lasts four days for five people, how long will it last if the consumer will be ten people? 1. As you have observed on your solution, what happen to the number of days a barrel of water could last as the number of persons increases from 5 up to 10 people? 2. Dealing with the same problem, crrate your ow questio regarding the number of days the barrel could last if there is a certain number of consumers. Also show your solution to your problem.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, 130 pounds, and will sell for $0.6 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 7 pounds, while the price per pound will decrease by $0.02.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)Suppose that a company has determined that a 70% experience curve accurately describes the evolution of its production costs for a new line. If the first unit costs $100 to produce, what should the 1,000th unit cost based on the experience curve?
- Suppose now that the government decides to increase the number of quotas available to 72 units, but keeps the price support at the current level of $72. calculate the consumer surplus the producer surplus Deadweight loss which if the two options would be preferred by the producers? which of the two options would be preferred by a society as a whole?A multimedia company anticipates that there will be a demand for 20,000 copiesof a certain DVD during the next year. It costs the company $0.40 to store a DVD for one year. Each time it must make additional DVDs, it costs $250 to set up the equipment. How many DVDs should the company make during each production run to minimize its total storage and setup costs?A farmer wants to start raising cows, horses, goats, and sheep and desires to have a rectangular pasture for the animals to graze in. However, no two different kinds of animals can graze together. In order to minimize the amount of fencing she will need, she has decided to enclose a large rectangular area and then divide it into four equally sized pens by adding three segments of fence inside the large rectangle that are parallel to two existing sides (see attached image). She has decided to purchase 7500 ft of fencing. What is the maximum possible area that each of the four pens will enclose? Make sure to include units in your answer.