the quantity, q, of a product manufactures depends on the number of workers. W , and the amount of capital invested, K, and is represented by the Cobb-Douglas function q = 64W^3/4 K^1/4 . Suppose further that labor costs $18 per worker and capital costs $28 per unit, and the budget is $4600. Let λ be the Lagrange multiplier. Does increasing

the quantity, q, of a product manufactures depends on the number of workers. W , and the amount of capital invested, K, and is represented by the Cobb-Douglas function q = 64W^3/4 K^1/4 . Suppose further that labor costs $18 per worker and capital costs $28 per unit, and the budget is $4600. Let λ be the Lagrange multiplier. Does increasing

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 23E

See similar textbooks

Similar questions

The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. Units made with aluminum wire have a defect rate of 10%. A redesigned manufacturing process, involving the use of gold wire, is being investigated. The goal is to reduce the rate of defects to 5% or less. Out of the first 100 units manufactured with gold wire, only 4 are defective. True or false: a) Since only 4% of the 100 units were defective, we can conclude that the goal has been reached. b) Although the sample percentage is under 5%, this may represent sampling variation, so the goal may not yet be reached. c) There is no use in testing the new process, because no matter what the result is, it could just be due to sampling variation. d) If we sample a large enough number of units, and if the percentage of defective units is far enough below 5%, then it is reasonable to conclude that the goal has been reached.
A researcher is testing the effect of a new cold and flu medication on reaction time. A sample of n = 16 students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student's reaction time is measured. The scores for the sample averaged M = 220 milliseconds with SS = 6000. Assuming that reaction time for students in the regular population averages μ = 200 milliseconds, are the data sufficient to conclude that the medication has a significant effect on reaction time? Test at the .05 level of significance. Make a point estimate and a 95% confidence interval estimate for the treated population mean.
Before 1918, approximately 55% of the wolves in a region were male, and 45% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 70% of wolves in the region are male, and 30% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.) (a) Before 1918, in a random sample of 10 wolves spotted in the region, what is the probability that 7 or more were male? What is the probability that 7 or more were female?What is the probability that fewer than 4 were female?(b) For the period from 1918 to the present, in a random sample of 10 wolves spotted in the region, what is the probability that 7 or more were male?What is the probability that 7 or more were female?What is the probability that fewer than 4 were female?
Before 1918, approximately 55% of the wolves in a region were male, and 45% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 70% of wolves in the region are male, and 30% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.) (a) Before 1918, in a random sample of 11 wolves spotted in the region, what is the probability that 8 or more were male?What is the probability that 8 or more were female?What is the probability that fewer than 5 were female?
Before 1918, approximately 55% of the wolves in a region were male, and 45% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 70% of wolves in the region are male, and 30% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.) (a) Before 1918, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? What is the probability that 9 or more were female? What is the probability that fewer than 6 were female? For the period from 1918 to the present, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? What is the probability that 9 or more were female? What is the probability that fewer than 6 were female?
Suppose your utility function for income takes the form U(I) = square root of I (i.e. square root of Income), where I represents thousands of euros. You are considering a self-employment opportunity that may pay €25,000 or €64,000 per year with probability of 0.75 for an outcome of €25,000 and a probability of 0.25 for an outcome of €64,000. Your current salary is €49,000 per year.What is your expected utility from the self-employed position? A. 5B. 5.75C. 7.25D. 7
A pharmcuticle company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of Mercury) for 9 patients before taking the new drug and 2 hours after taking the drug are shown in the table below. is there enough evidence support the company's claim? Let D =(blood pressure before taking new drug)- (blood pressure after taking new drug).use significant levels of a=their 0.05 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patience both Before & After taking the new drug. 1.State the null and alternative hypothesis for the test. 2. Find the value of the standard deviation of the paired differences. Round to one decimal place. 3.compute the value of the test statistic. Round to three decimal places 4.determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion to three decimals. 5.make decision for the hypothesis test.
This cardiologist gets a report on his patients' sugar consumption from the nutritionist. He becomes concerned that his patients seem to consume even more sugar that what is in a typical American diet. He decides to take a random sample of 100 of his patients and calculate the mean sugar consumption, x̅, of these 100 patients. The mean sugar consumption for these 100 patients is 17.3 teaspoons. Let's assume, for the moment, that his patients are no different than the general population of Americans with µ (daily sugar consumption) = 16.1 teaspoons and σ = 3.5 teaspoons and that his sample of 100 patients is one random sample from this population. What is the probability of obtaining a mean sugar consumption of 17.3 teaspoons (or more) in his sample of 100 patients if his patients are similar to the general population? What is the probability that the average (x̅) is greater than 17.3?
The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1% . When 1.25% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p, where pis the proportion of defective light bulbs in a sample of 4400when there is no malfunction. (b)Find the standard deviation of p . (c)Compute an approximation for P≥p0.0125 , which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.
At the end of summer, the total weight of seeds accumulated by a nest of seed-gathering ants will vary from nest to nest. If the total weight of seeds accumulated by a nest is exponentially distributed with parameter λ = 1/5, (a) What is the probability that the total combined weight of the seeds gathered by 100 nests will be larger than 4 95 pounds by the end of next summer? (b) What is the probability that the average weight of the seeds gathered by the 100 nests is larger than 5.3 ? (c) What assumptions are you making to answer parts (a) and (b)? Do you think those assumptions make sense in the context of this problem? Explain. (d) Tell us about the possibility that the total combined weight of the seeds gathered by 2 nests follows a normal distribution. Justify your answer in the speciﬁc context of this problem (ants, nests, seed-gathering). That is, do not just make generic statements that you think apply to every context in the world.
A simple random sample X1, …, Xn is drawn from a population, and the quantities ln X1, …, ln Xn are plotted on a normal probability plot. The points approximately follow a straight line. True or false: a) X1, …, Xn come from a population that is approximately lognormal. b) X1, …, Xn come from a population that is approximately normal. c) ln X1, …, ln Xn come from a population that is approximately lognormal. d) ln X1, …, ln Xn come from a population that is approximately normal.
The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1%. When 1.25% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p, where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction. (b)Find the standard deviation of p. (c)Compute an approximation for P≥p0.0125, which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.