FIRST CRSE.IN DIFF.EQUAT..-ACCESS
11th Edition
ISBN: 9781337652469
Author: ZILL
Publisher: CENGAGE L
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Chapter 3.2, Problem 31E
To determine
The distance walked by the swimmer along the beach to reach point (0, 0).
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Answer question S8 stepwise
Answer questions 8.2.11 and 8.2.12 respectively
8.4.2 An article in Knee Surgery, Sports Traumatology, Arthroscopy [“Arthroscopic Meniscal Repair with an
Absorbable Screw: Results and Surgical Technique” (2005, Vol.
13, pp. 273–279)] showed that only 25 out of 37 tears (67.6%)
located between 3 and 6 mm from the meniscus rim were healed.
a. Calculate a two-sided 95% confidence interval on the proportion of such tears that will heal.
b. Calculate a 95% lower confidence bound on the proportion of such tears that will heal.
8.4.3 An article in the Journal of the American Statistical Association [“Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling” (1990, Vol. 85, pp.
972–985)] measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats.
a. Calculate a 95% two-sided confidence interval on the true
proportion of rats that would show underweight from the
experiment.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95%…
Chapter 3 Solutions
FIRST CRSE.IN DIFF.EQUAT..-ACCESS
Ch. 3.1 - The population of a community is known to increase...Ch. 3.1 - Suppose it is known that the population of the...Ch. 3.1 - The population of a town grows at a rate...Ch. 3.1 - The population of bacteria in a culture grows at a...Ch. 3.1 - The radioactive isotope of lead, Pb-209, decays at...Ch. 3.1 - Initially 100 milligrams of a radioactive...Ch. 3.1 - Determine the half-life of the radioactive...Ch. 3.1 - Consider the initial-value problem dA/dt = kA,...Ch. 3.1 - When a vertical beam of light passes through a...Ch. 3.1 - When interest is compounded continuously, the...
Ch. 3.1 - Carbon Dating Archaeologists used pieces of burned...Ch. 3.1 - The Shroud of Turin, which shows the negative...Ch. 3.1 - Newtons Law of Cooling/Warming A thermometer is...Ch. 3.1 - A thermometer is taken from an inside room to the...Ch. 3.1 - A small metal bar, whose initial temperature was...Ch. 3.1 - Two large containers A and B of the same size are...Ch. 3.1 - A thermometer reading 70 F is placed in an oven...Ch. 3.1 - At t = 0 a sealed test tube containing a chemical...Ch. 3.1 - A dead body was found within a closed room of a...Ch. 3.1 - The rate at which a body cools also depends on its...Ch. 3.1 - A tank contains 200 liters of fluid in which 30...Ch. 3.1 - Solve Problem 21 assuming that pure water is...Ch. 3.1 - A large tank is filled to capacity with 500...Ch. 3.1 - In Problem 23, what is the concentration c(t) of...Ch. 3.1 - Solve Problem 23 under the assumption that the...Ch. 3.1 - Determine the amount of salt in the tank at time t...Ch. 3.1 - A large tank is partially filled with 100 gallons...Ch. 3.1 - In Example 5 the size of the tank containing the...Ch. 3.1 - A 30-volt electromotive force is applied to an...Ch. 3.1 - Prob. 30ECh. 3.1 - A 100-volt electromotive force is applied to an...Ch. 3.1 - A 200-volt electromotive force is applied to an...Ch. 3.1 - An electromotive force E(t)={120,0t200,t20 is...Ch. 3.1 - An LR-series circuit has a variable inductor with...Ch. 3.1 - Air Resistance In (14) of Section 1.3 we saw that...Ch. 3.1 - How High?No Air Resistance Suppose a small...Ch. 3.1 - How High?Linear Air Resistance Repeat Problem 36,...Ch. 3.1 - Skydiving A skydiver weighs 125 pounds, and her...Ch. 3.1 - Rocket Motion Suppose a small single-stage rocket...Ch. 3.1 - Rocket MotionContinued In Problem 39 suppose of...Ch. 3.1 - Evaporating Raindrop As a raindrop falls, it...Ch. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Constant-Harvest model A model that describes the...Ch. 3.1 - Drug Dissemination A mathematical model for the...Ch. 3.1 - Memorization When forgetfulness is taken into...Ch. 3.1 - Heart Pacemaker A heart pacemaker, shown in Figure...Ch. 3.1 - Sliding Box (a) A box of mass m slides down an...Ch. 3.1 - Sliding Box—Continued
In Problem 48 let s(t) be...Ch. 3.1 - What Goes Up (a) It is well known that the model...Ch. 3.2 - The number N(t) of supermarkets throughout the...Ch. 3.2 - The number N(t) of people in a community who are...Ch. 3.2 - A model for the population P(t) in a suburb of a...Ch. 3.2 - Census data for the United States between 1790 and...Ch. 3.2 - (a) If a constant number h of fish are harvested...Ch. 3.2 - Investigate the harvesting model in Problem 5 both...Ch. 3.2 - Repeat Problem 6 in the case a = 5, b = 1, h = 7.Ch. 3.2 - (a) Suppose a = b = 1 in the Gompertz differential...Ch. 3.2 - Two chemicals A and B are combined to form a...Ch. 3.2 - Solve Problem 9 if 100 grams of chemical A is...Ch. 3.2 - Leaking cylindrical tank A tank in the form of a...Ch. 3.2 - Leaking cylindrical tank—continued When friction...Ch. 3.2 - Leaking Conical Tank A tank in the form of a...Ch. 3.2 - Inverted Conical Tank Suppose that the conical...Ch. 3.2 - Air Resistance A differential equation for the...Ch. 3.2 - How High?Nonlinear Air Resistance Consider the...Ch. 3.2 - That Sinking Feeling (a) Determine a differential...Ch. 3.2 - Solar Collector The differential equation...Ch. 3.2 - Tsunami (a) A simple model for the shape of a...Ch. 3.2 - Evaporation An outdoor decorative pond in the...Ch. 3.2 - Doomsday equation Consider the differential...Ch. 3.2 - Doomsday or extinction Suppose the population...Ch. 3.2 - Skydiving A skydiver is equipped with a stopwatch...Ch. 3.2 - Prob. 27ECh. 3.2 - Old Man River In Figure 3.2.8(a) suppose that the...Ch. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Time Drips By The clepsydra, or water clock, was a...Ch. 3.2 - (a) Suppose that a glass tank has the shape of a...Ch. 3.2 - Prob. 35ECh. 3.3 - We have not discussed methods by which systems of...Ch. 3.3 - In Problem 1 suppose that time is measured in...Ch. 3.3 - Use the graphs in Problem 2 to approximate the...Ch. 3.3 - Construct a mathematical model for a radioactive...Ch. 3.3 - Potassium-40 Decay The chemical element potassium...Ch. 3.3 - Potassium-Argon Dating The knowledge of how K-40...Ch. 3.3 - Consider two tanks A and B, with liquid being...Ch. 3.3 - Use the information given in Figure 3.3.6 to...Ch. 3.3 - Two very large tanks A and B are each partially...Ch. 3.3 - Three large tanks contain brine, as shown in...Ch. 3.3 - Consider the Lotka-Volterra predator-prey model...Ch. 3.3 - Show that a system of differential equations that...Ch. 3.3 - Determine a system of first-order differential...Ch. 3.3 - Prob. 16ECh. 3.3 - SIR Model A communicable disease is spread...Ch. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Mixtures Solely on the basis of the physical...Ch. 3.3 - Newtons Law of Cooling/Warming As shown in Figure...Ch. 3 - Answer Problems 1 and 2 without referring back to...Ch. 3 - Answer Problems 1 and 2 without referring back to...Ch. 3 - Prob. 3RECh. 3 - Air containing 0.06% carbon dioxide is pumped into...Ch. 3 - tzi the Iceman In September of 1991 two German...Ch. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Suppose a cell is suspended in a solution...Ch. 3 - Suppose that as a body cools, the temperature of...Ch. 3 - According to Stefans law of radiation the absolute...Ch. 3 - Suppose an RC-series circuit has a variable...Ch. 3 - A classical problem in the calculus of variations...Ch. 3 - A model for the populations of two interacting...Ch. 3 - Initially, two large tanks A and B each hold 100...Ch. 3 - Prob. 15RECh. 3 - When all the curves in a family G(x, y, c1) = 0...Ch. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Sawing Wood A long uniform piece of wood (cross...Ch. 3 - Solve the initial-value problem in Problem 20 when...Ch. 3 - Prob. 22RE
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- 8.4.8 Use the data from Exercise 8.4.2 to compute the two-sided Agresti-Coull CI on the proportion of tears that heal. Compare and discuss the relationship of this interval to the one computed in Exercise 8.4.2.arrow_forwardAnswer questions 8.3.7 and 8.4.1 respectivelyarrow_forwardDon't do 14. Please solve 19arrow_forward
- 8.4.7 Use the data from Exercise 8.4.5 to compute the two-sided Agresti-Coull CI on the proportion of digits read correctly. Compare and discuss the relationship of this interval to the one computed in Exercise 8.4.5.arrow_forward8.6.5 Consider the fuel rod enrichment data described in Exercise 8.2.11. Compute a 90% prediction interval on the enrichment of the next rod tested. Compare the length of the prediction interval with the length of the 99% CI on the population mean.arrow_forward8.4.4 The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed limits from 65 mph to 75 mph. How many residents does the department need to survey if it wants to be at least 99% confident that the sample proportion is within 0.05 of the true proportion? 8.4.5 The U.S. Postal Service (USPS) has used optical character recognition (OCR) since the mid-1960s. In 1983, USPS began deploying the technology to major post offices throughout the country (www.britannica.com). Suppose that in a random sample of 500 handwritten zip code digits, 466 were read correctly. a. Construct a 95% confidence interval for the true proportion of correct digits that can be automatically read. b. What sample size is needed to reduce the margin of error to 1%? c. How would the answer to part (b) change if you had to assume that the machine read only one-half of the digits correctly?arrow_forward
- 8.6.4 Consider the test on the compressive strength of concrete described in Exercise 8.2.9. Compute a 90% prediction interval on the next specimen of concrete tested. 8.6.5 . SS Consider the fuel rod enrichment data described in Exercise 8.2.11. Compute a 90% prediction interval on the enrichment of the next rod tested. Compare the length of the prediction interval with the length of the 99% CI on the population mean.arrow_forwardAnswer questions 8S10 and 8S11 respectively.arrow_forward8.4.6 Information on a packet of seeds claims that 93% of them will germinate. Of the 200 seeds that were planted, only 180 germinated. a. Find a 95% confidence interval for the true proportion of seeds that germinate based on this sample. b. Does this seem to provide evidence that the claim is wrong? 8.6.1 Consider the tire-testing data described in Exercise 8.2.3. Compute a 95% prediction interval on the life of the next tire of this type tested under conditions that are similar to those employed in the original test. Compare the length of the prediction interval with the length of the 95% CI on the population mean.arrow_forward
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