Question Solved1 Answer 3.67. As will be discussed in detail in Chapter 5, the ideal-gas equation of state relates absolute pressure, P(atm); gas volume, V(liters); number of moles of gas, n(mol); and absolute temperature, T(K): (a) Convert the equation to one relating P(psig), V(ft) n(lb-mole), and TCD. (b) A 30.0 mole% CO and 70.0 mole% N2 gas mixture is stored in a cylinder with 3.67. As will be discussed in detail in Chapter 5, the ideal-gas equation of state relates absolute pressure, P(atm); gas volume, V(liters); number of moles of gas, n(mol); and absolute temperature, T(K): (a) Convert the equation to one relating P(psig), V(ft) n(lb-mole), and TCD. (b) A 30.0 mole% CO and 70.0 mole% N2 gas mixture is stored in a cylinder with a volume of 3.5 ta a temperature of 85°F. The reading on a Bourdon gauge attached to the cylinder is 500 psi. Calculate the total amount of gas (lb-mole) and the mass of CO (lbm) in the tank. (e) Approximately to what temperature (F) would the cylinder have to be heated to increase the gas pressure to 3000 psig, the rated safety limit of the cylinder? (The estimate would only be approximate because the ideal gas equation of state would not be accurate at pressures this high.)

4. In humans, the antibiotic Ceftriaxone has the mean values for the apparent volume of distribution 300 L and total clearance CL=14L/h and t1/2= 8 h. . Salmonella infection is susuceptible to Ceftriaxone at concntration above 5 ug/mL and patient gets overdosed at the levels above 80ug/L. Calculate an IV dose ad infusion rate that provides steady-state level of 30ug/mL in human. b)The doctor decides to give a dose of 12 mg and started a constatnt infusion at the same Ro calculated . Ceftriaxone is eliminated as unchanges in the urine and the drug concentrations were recorded as; Time (h.) Con. Ug/L 0 4 12 6 24 6.8 36 7.5 360 10 a) Compute the Vd for patient (10pts) b) Compute the CL (10pts)

Problem 5 The Cauchy probability distribution with location parameter xo E R and scale parameter 7> 0 has the density function 1 p(x) (x ER) - Po 2 1+ 7 0.6 30 = 0,7 = 0.5 X = 0,7 = 1 - T = 0, 7=2 To = -2,7 = 1 0.5 0.4 0.3 0.2 0.1 0.0 0 2 2 a. The proportionality constant is determined by the condition ſple) dx = 1. Find it. | xp() b. Show that the mean value o xp(x) dx does not exist. 00

A substrate is decomposed in the presence of an enzyme according to the Michaelis-Menten equation with the following kinetic parameters: Km= 15 g/L Vmax = 10.5 g/L-min a. Determine the concentration of substrate leaving the second reactor in a two-reactor series of 10-liter CSTRs. The flow rate is 0.75 L/min. The inlet substrate concentration is 67 g/L. The enzyme concentration in the two reactors is maintained at the same value all of the time (20 points). b. Determine the efficiency in terms of substrate conversion of the two-reactor system and the efficiency of a single CSTR equal to the total volume of the two-reactor system. Clearly indicate the configuration with the greater fraction conversion of substrate (10 points).

  3. Opportunity cost and production possibilities Neha is a talented artist who sells hand-crafted goods on her website. Neha currently crafts and sells both crochet hats and embroidered sweaters. She spends 8 hours a day working on crafts. The following table gives different daily output scenarios depending on how much of her time is spent on each good. On the following graph, use the blue points (circle symbol) to plot Neha's initial production possibilities frontier (PPF). Suppose Neha is currently using combination D, producing one crochet hat per day. Her opportunity cost of producing a second crochet hat per day is per day. Now, suppose Neha is currently using combination C, producing two crochet hats per day. Her opportunity cost of producing a third crochet hat per day is per day. From the previous analysis, you can determine that as Neha increases her production of crochet hats, her opportunity cost of producing one more crochet hat Suppose Neha buys a new tool that enables her to produce twice as many crochet hats per hour as before, but it doesn't affect her ability to produce embroidered sweaters. Use the green points (triangle symbol) to plot her new PPF on the previous graph. Because she can now make more crochet hats per hour, Neha's opportunity cost of producing embroidered sweaters is it was previously.

In the last lecture, we covered the basics of hypothesis testing with the HIP mammography study as our example. The study's aim is to determine whether offering mammographies for breast cancer detection reduces the rate of death due to breast cancer. There are 31000 individuals in each of the treatment and control groups; only those in the treatment groups In the last lecture, we covered the basics of hypothesis testing with the HIP mammography study as our example. The study's aim is to determine whether offering mammographies for breast cancer detection reduces the rate of death due to breast cancer. There are 31000 individuals in each of the treatment and control groups; only those in the treatment groups are offered mammographies. We recap the elements of the hypothesis testing framework. In the mammography study, they are: • the Parametric Model. We can write indicator variables for whether each patient in the treatment group dies of breast cancer as X₁,..., X$1000 Bernoulli (π), and we can also approximate the total number of deaths as Y = X₁ + ... + X31000~ Poisson (X). • The null hypothesis Ho: = 0.00203 (equivalently λ = 63, and the alternative hypothesis HA: < 0.00203 (equivalently X < 63). We then decide whether or not to reject the null hypothesis based on a test. • The test statistic T. We define T to simply be the number of deaths Y in the treatment group. Under Ho, it is distributed as T binomial (31000, 0.00203). This distribution can also be approximated as T Poisson (63). The role of T' is to distinguish between Ho and HA • The significance level a = 0.05. This is the probability of rejecting the null hypothesis Ho when it is in fact true (type I error), that is, the probability of concluding there is an effect when there is none. Generally, the threshold of the test statistic for rejecting the null hypothesis is set based on a chosen significance level. • The p-value p. This is the probability that the test statistic, under the null hypothesis, takes a value more extreme (towards the direction of the alternative hypothesis) than the one observed. This probability can be computed from the test statistic T and the given parametric model. The p-value varies with the observed value of data, and when p < a, the Ho is rejected. • The power of the test. This is the probability of rejecting Ho when HA is true (avoiding a type Il error: 1 - P (type II error)). It is useful to write the power as a function of the parameter, when more than one parameter value is considered for HA Throughout the hypothesis test, we focused on the observed death rate in the treatment group as the variable, and compare it to π = 0.00203, the observed death rate in the control group. The question below examines the validity of this approach. Further thinking 1 point possible (graded) Remember our research question is whether offering mammography reduces the death rate from breast cancer. What is a potential problem in the hypothesis test that we have so far that can cause the hypothesis to not represent the research question? There is uncertainty in the death rate of the control, and the estimated death rate 0.00203 of the control is only a realization of a random variable. Therefore, we should not interpret the estimated value as the true death rate in the population without treatment We can conclude from our test that the probability to die from breast cancer in the treatment group is lower than 0.00203, but we cannot conclude that the probability to die from breast cancer in the treatment group is lower than that in the control group. None of the above. Both of the above.

You are trying to determine the number of moles of CO2 you have generated when reacting your unknown CaCO3 tablet with excess HCl according to the lab manual. You have determined the following: Volume of flask: 0.140 L Pi': 46.6 kPa Pf': 133.2 kPa Ti: 21.05 °C Tf: 22.75 °C How much CO2 did you generate in mmol to 2 decimal places?