A biologist doing an experiment has a bacteria populationcultured in a petri dish. After measuring, she finds that there are98.5 million bacteria infected with the zeta-virus and 26.4 millioninfection-free bacteria. Her theory predicts that 20% ofinfected bacteria will remain infected over the next hour, while theremaining of the infected manage to fight off the virus in that hour.Similarly, she predicts that 20% of the healthy bacteria willremain healthy over the hour while the remaining of the healthy willsuccumb to the affliction. Modeling this as a Markov chain,use her theory to predict the population of non-infectedbacteria after 1 hour(s). [Round to 3 significant figures.]O a) 25 millionOb) 84.1 millionO c) 40.8 milliond) 99.9 million

Infected Non- Infected 20% 80% Infected 80% 20% Non- Infected To find - The population…

Answered: A biologist doing an experiment has a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Lycopene is a bright red pigment which has been shown to have powerful antioxidant and anticarcinogenic properties. A biological research company conducts experiments in which seeds from cherry tomatoes are exposed to a series of pulsations of ultra-violet radiation with the aim of triggering a genetic mutation to increase lycopene production. It is well established from past experiments that the lycopene content for untreated cherry tomatoes is 12.7 mg/100g. A random sample of 36 treated seeds from a population of seeds of an identical variant was selected and were planted and grown in identical conditions. The mean lycopene content of the treated seeds was determined via mass spectrometry to be 13.1 mg/100g and a standard deviation of 1.2. A histogram indicates that the distribution of the lycopene content appears to be roughly normally distributed. Select the appropriate set of hypotheses to determine if the radiation treatment effectively increases lycopene content in cherry…
A sports physiologist is investigating whether water or Gatorade provides the best hydration for athletes after training. A sample of 50 athletes between the ages of 18 and 30 was selected. On two consecutive days, each athlete ran 5 miles at a steady rate on a treadmill in a 75-degree room. On one of these days, 32 ounces of water was consumed after running. On the other day, 32 ounces of Gatorade was consumed after running. For each athlete, which beverage was consumed first was randomized. Hydration one hour after beverage consumption was measured, and results for the two beverages were compared. Which of the following is the best description of this study? (A) An experiment using a completely randomized design (B) An experiment using a matched-pairs design (C) An observational study using a simple random sample (D) An observational study using a cluster sample (E) An observational study using a stratified sample
Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. Independent random samples from two regions gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions. Region I: x,; n, = 15 853 1,551 1,230 1,080 2,330 1,850 1,860 875 2,340 1,080 910 1,130 1,450 1,260 1,010 Region II: x,; n, = 14 540 1,230| 1,770 808 790 960 1,650 860 890 640 1,180 1,160 | 1,050 1,020 In USE SALT (a) Use a calculator with mean and standard deviation keys to verify that x,, S,, x2, and s,. (Round your answers to four decimal places.) x, = X1 ppm S1 ppm X2 ppm S2 , = ppm (b) Let…
Explain the Stationarity in the AR(1) Model?
Medical researchers have developed a radiotracer dye that can bind to specific dopaminergic cell receptor sites in the brain, which can be viewed using PET imaging. The radiotracer has a reported half-life of 14 hours, where its radioactivity will be below detection threshold. A random sample of 40 solutions of the dye is made up at the same concentration and their specific activities measured by a scintillation counter. The average half-life of these dyes is 14.3 hours. Assume that half-life is normally distributed with a standard deviation of 0.58 hours. Is there evidence to support the claim that the mean half-life exceeds 14 hours? Use a 5% level of significance. Your answer should include:  State the statistical hypotheses (using the appropriate notation).  Indicate whether the alternative hypothesis is non-directional or directional (and how you know).  Set the decision rules, which will include: o State alpha o Providing the critical value for the test statistic o Sketch…
A cohort study is conducted to assess the association between hypertension and the risk of stroke. The study involves n=1,250 participants who are free of stroke at the study start. Each participant is assessed at study start (baseline) and every year thereafter for five years. The following table displays data on hypertension status measured at baseline and hypertension status measured two years later. 2 Years: Not Hypertensive 2 Years: Hypertensive Baseline: Not Hypertensive 850 148 Baseline: Hypertensive 45 207 Compute the cumulative incidence of hypertension over 2 years. Group of answer choices 17.1%
The null hypothesis: H. :|| The alternative hypothesis: H :0 1 The type of test statistic: (Choose one) v The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Can we reject the researchers' claim that the mean recovery time when treated with multivitamin is less than or equal to the mean recovery time when treated with vitamin C only? Yes No
Researchers are studying pomegranate’s antioxidant properties to see if it might have any beneficial effects in the treatment of cancer. One such study investigated whether pomegranate fruit extract (PFE) was effective in slowing the growth of prostate cancer tumors. In this study, 24 mice were injected with cancer cells, then the mice were randomly assigned to one of three treatment groups. The data on y = average tumor volume (in mm3) and x = number of days after injection of cancer cells for the mice that received plain drinking water is shown in picture below: a. Find (to three decimal places) zy, and zxzy for the pair (23,580): zy = zxzy = b. Compute Pearson’s sample correlation coefficient for the given data to four decimal places. c. Compute the slope, b, for the least-squares regression line to two decimal places d. Use b to calculate a and write the equation for the least-squares regression line a= y= e. Predict the average tumor volume (y) for a mouse 20 days…
Osteoporosis is a degenerative disease that primarily affects women over the age of 60. A research analyst wants to forecast sales of StrongBones, a prescription drug for treating this debilitating disease. She uses the model Sales = β0 + β1Population + β2Income + ε, where Sales refers to the sales of StrongBones (in $1,000,000s), Population is the number of women over the age of 60 (in millions), and Income is the average income of women over the age of 60 (in $1,000s). She collects data on 38 cities across the United States and obtains the following regression results: Coefficients StandardError t Stat p-Value Intercept 10.35 4.02 2.57 0.0199 Population 8.47 2.71 3.12 0.0062 Income 7.62 6.63 1.15 0.2661 a. What is the sample regression equation? (Enter your answers in millions rounded to 2 decimal places.) b-1. Interpret the coefficient of population. multiple choice 1 As the number of women over the age of 60 increases by 1 million, sales of StrongBones…
The cuttlefish, a cephalopod and first cousin of the octopus, has the ability to camouflage to almost any natural sea environment instantaneously (within a few milliseconds). They are also able to camouflage to non-natural environments but not quite as quickly. A cognitive psychologist is interested in whether cuttles exhibit learning (by showing a reduction in reaction time) after repeated exposure to the same environment. Initially, 10 baby cuttlefish are individually placed in a tank with a checkerboard bottom and their reaction time (time to camouflage) is recorded. Over the next month the samecuttlefish are exposed to the same environment daily and at the end of the month each cuttlefish's reaction time is recorded again. The data are recorded in the table below. Reaction Time (seconds) Subject Before After 1 58 41 2 48 45 3 54 40 4 56 42 5 55 48 6 55 41 7 43 32 8 51 44 9 62 38 10 35…
Consider a two component parallel system in which both components have times to failure and times to 0.0024 f/hr and µ1 = = 0.001 f /hr, 12 repair that are exponentially distributed. The data is 1, 0.003 r/hr and µ2 = 0.005 r/hr. Evaluate the reliability or probability of success for a mission of 1000 hr. (hint: form a history for each component using the data for failure rate and repair rate)
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