Use the information provided to write the equation of each circle. 1 Center: (0, 0) Radius: 6 2 Center: (-5, -8) Radius: 8 3 Center: (10,-14) Radius: √22
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- A study of the relation between the rate of reproduction in Drosophila (fruit flies) bred in bottles and the density of the mated population found that the number of imagoes(sexually mature adults) per mated female per day (y) can beapproximated bylog y = 1.54 - 0.008x - 0.658 log x,where x is the mean density of the mated population (measuredas flies per bottle) over a 16-day period. Source: Elements ofMathematical Biology.a. Show that the above equation is equivalent toy = 34.711.01862-xx-0.658.b. Using your answer from part a, find the number of imagesper mated female per day when the density isi. 20 flies per bottle;ii. 40 flies per bottle.c. Using your answer from part a, find the rate of change inthe number of imagoes per mated female per day with respect to the density when the density isi. 20 flies per bottle;ii. 40 flies per bottleResearchers have created every possible "knockout" line in yeast. Each line has exactly one gene deleted and all the other genes present (Steinmetz et al. 2002). The growth rate—how fast the number of cells increases per hour—of each of these yeast lines has also been measured, expressed as a multiple of the growth rate of the wild type that has all the genes present. In other words, a growth rate greater than 11 means that a given knockout line grows faster than the wild type, whereas a growth rate less than 11 means it grows more slowly. The growth rate of a random sample of knockout lines is 0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01 What is the standard deviation and variance of growth rate for this sample?The prices of stocks or other financial instruments are often modeled with a lognormal distribution. An investor is considering purchasing stock in one of two companies, A or B. The price of a share of stock today is $1 for both companies. For company A, the value of the stock one year from now is modeled as lognormal with parameters μ = 0.05 and σ = 0.1. For company B, the value of the stock one year from now is modeled as lognormal with parameters μ = 0.02 and σ = 0.2. a) Find the mean of the price of one share of company A one year from now. b) Find the probability that the price of one share of company A one year from now will be greater than $1.20. c) Find the mean of the price of one share of company B one year from now. d) Find the probability that the price of one share of company B one year from now will be greater than $1.20.
- Suppose that consumers have utility function U(C) = log(C) where C is the consumption level and log is the natural logarithm. Consumers have initial consumptionlevels of 100 and are exposed to the following risk of loss: lose 10 with probability0.4 and lose 5 with probability 0.6. They are considering buying insurance to coverthese losses What is the maximum amount consumers are willing to pay for the insurance?At a one man barber shop, customers arrive according to poison distribution with a mean arrival rate of 5 per hour and hair cutting time was exponentially distributed with an average hair cutting time was exponentially distributed with an average haircut taking 19 minutes. It is assumed that because of excellent reputation, customerswere always willing to wait. Calculate the following a. Average number of customers in the shop and average numbers waiting for a hair cut b .Percentage of time arrival can walk in right without having to wait c. The percentage of customers who have to wait before getting into the barber’s chairThe temperature of Earth's surface is strongly influenced by the amount of carbon in the atmosphere. Each year, human activity adds another 9 gigatons of carbon to the atmosphere. 2 gigatons of this carbon is absorbed by the oceans, and 3 gigatons of this carbon is absorbed by plant growth (photosynthesis). There is currently 900 gigatons of carbon in the atmosphere. Assume that these are the only flows of carbon into/out of the atmosphere, and that the given rates stay constant over time. Write down a differential equation for the total amount of carbon in the atmosphere over time. Solve the equation and use the solution to predict how much carbon there will be in the atmosphere in 25 years.
- And what's logistic model mean here?An investigator modeled the log-odds of getting stomach cancer as a function of number of servings of vegetables per week and the number of servings of red mean per week using logistic regression. The odds that a person gets stomach cancer if they have 4 servings of red meat a week are 1.2 times the odds of cancer for someone who has 3 servings of red meat a week. suppose in the example, where the regression coefficient for servings of vegetables is -0.105, we have also obtained from the SAS output a Standard Error from the output of 0.097. Since our estimates are maximum likelihood estimates, we can assume that they follow a normal distribution. As such we can create confidence intervals for the regression coefficients using standard practices for estimates that have normal sampling distributions. Calculate a 95% confidence interval for the ODDS RATIO given above (odds ratio representing the change in odds of stomach cancer for a one-serving increase in vegetables. Give the…Plot the percentage of machines not running as a function of the service factor for a population of 20 machines with exponential arrivals and services (a) if a single channel is employed and (b) if two channels are employed.
- After constant complaints about the long wait from his customers, Ryan - the owner of shop - hasdecided to hire a second mechanic to handle installations. Customers, who arrive at a rate ofabout 3 per hour (Poisson), will wait in a single line until one of the two mechanics is free. Eachmechanic can serve about four customers per hour (Exponential).Do you think the improvement on customer experience will be significant? Computethe key waiting line characteristics BEFORE and AFTER the second mechanic is hired tosupport your answer.How is this integratet. S = stock price, Mu =expected retrn. Mu question is where does the exponential come fromThe success of a project depends on the effort level of a worker. In case of successthe revenues will be 400,000 TL whereas in case of no-success the revenues will be 0. The workercan provide a low effort level or a high effort level. The effort level cannot be observed by theprincipal. The worker requires an expected salary of 60,000 TL to provide the low effort leveland an expected salary of 80,000 TL to provide the high effort level. The success probabilitiesfor the project are 40% in case of low effort level and 80% in case of high effort level. Whatshould be the minimum bonus (that is awarded in addition to the base salary in case of success)and the base salary for the worker so that the worker has the incentives to provide the higheffort level?