A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flows into the tank at a rate of Rin=80 L/minutes (min). The fluid mixes instantaneously and is pumped out at a specified rate Rout. Let y(t) denote the quantity of salt in the tank at time t. Assume that Rout=40L/min. (a) Set up and solve the differential equation for y(t). (b) What is the salt concentration when the tank overflows?

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general 9 months ago 5281

Suppose a random sample of n = 16 observations is selected from a population that is normally distributed with mean equal to 101 and standard deviation equal to 12. (a) Give the mean and the standard deviation of the sampling distribution of the sample mean x(with a line above). (Enter your standard deviation to two decimal places.)mean = standard deviation = (b) Find the probability that x(line above it) exceeds 107. (Round your answer to four decimal places.)Answer:(c) Find the probability that the sample mean deviates from the population mean μ = 101 by no more than 4. (Round your answer to four decimal places.)

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general 9 months ago 8140

A group of 56 computer science students were taught introductory computer programming class with an innovative teaching method that used a graphical interface and drag-and-drop methods of creating computer programs. At the end of the class, 43 of these students said that they felt confident in their ability to write computer programs. Another group of 41 students were taught the same material using a standard method. At the end of class, 25 of these students said they felt confident. Assume that each class contained a simple random sample of students. Let pX represent the population proportion of students taught by the innovative method who felt confident and let pY represent the population proportion of students taught by the standard method who felt confident. Find a 99% confidence interval for the difference pX−pY . Round the answers to four decimal places.

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general 9 months ago 1196

In a recent poll, 600 people were asked if they liked soccer, and 72% said they did. Based on this, construct a 99% confidence interval for the true population proportion of people who like soccer.As in the reading, in your calculations:--Use z = 1.645 for a 90% confidence interval--Use z = 2 for a 95% confidence interval--Use z = 2.576 for a 99% confidence interval.Give your answers as decimals, to 4 decimal places.Out of 500 people sampled, 80 had kids. Based on this, construct a 90% confidence interval for the true population proportion of people with kids.As in the reading, in your calculations:--Use z = 1.645 for a 90% confidence interval--Use z = 2 for a 95% confidence interval--Use z = 2.576 for a 99% confidence interval.Give your answers to three decimalsGive your answers as decimals, to three decimal places.

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general 9 months ago 8656

5. [12 points] Minor surgery on horses under field conditions requires a reliable short-term anesthetic producing good muscle relaxation, minimal cardiovascular and respiratory changes, and a quick, smooth recovery with minimal aftereffects so that horses can be left unattended. A research article reports that, for a sample of 73 horses to which ketamine was administered under certain conditions, the sample average lying-down time was 18.9 minutes. Does this data suggest that the true mean lying-down time is less than 20 minutes? Assume that lying-down time varies according to a normal distribution with population standard deviation 8.6 minutes. Test using the level of significance α = 0.10.

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general 9 months ago 3550