Archie has to go to school this morning for an important test, but he woke up late. He can either take the bus or take his unreliable car. If he takes the car, Archie knows from experience that he will make it to school without breaking down with probability 0.2. However, the bus to school runs late 65% of the time. Archie decides to choose between these options by tossing a coin. Suppose that Archie does, in fact, make it to the test on time. What is the probability that he took his car? Round your answer to two decimal places.

An enzyme acts as a catalyst in the fermentation of A to form product R. An aqueous feed stream containing the enzyme and compound A flows into a CSTR at 25 L/min, and the initial concentration of A is 2 mol*L^-1 . Determine the volume of the CSTR (in Liters, expressed to the nearest integer ) needed to achieve 98% conversion of reactant A. You may assume that the enzyme concentration and volumetric flowrates are constant. The maximum rate of destruction of the substrate is 0.4 mol/(L min). When the substrate concentration is 0.5 mol/L, the rate of destruction of the substrate is 0.2 mol/(L min), i.e. half of the maximum rate.

1. The ordinates of a 6- hr unit hydrograph are given below. A storm had three successive 6 – hr intervals of rainfall magnitude of 3, 5, and 4 cm respectively. Assuming a Φ- index of 0.2 cm/hr and a base flow of 30 m³/s, determine the resulting hydrograph of flow (total flow).

The following data are monthly sales of jeans at a local department store. The buyer would like to forecast sales of jeans for the next month, July.

(a) Forecast sales of jeans for March through June using the naïve method, a two-period moving average, and exponential smoothing with an ? = 0.2. (Hint: Use naïve to start the exponential smoothing process.)
(b) Compare the forecasts using MAD and decide which is best.
(c) Using your method of choice, make a forecast for the month of July.

A charge of -1.0 µC is located at the origin, a second charge of 1 µC is located at x = 0, y = 0.1 m, and a third charge of 11 µC is located at x = 0.2 m, y = 0. Find the forces that act on each of the three charges.

(values for q=-1 is correct but all other values are wrong please show all work)

A metal bar of length 30 cm, is initially at 25 ^oC. Then through an electrical wire heat is generated at a rate of 0.5 cal/cm³s. The left end (x = 0 cm ) is contacted with a medium at 10 ^oC. At the right end there is a heat loss due to the air convection at a flux of 0.6 cal/cm²s. The physical properties are, k = 2 cal/cm ^oC s, r = 8 g/cm³, Cp = 0.2 cal/g ^oC.

Use M = 0.25, Dx = 5 cm. Solve the model numerically to find the temperature at the length of 22.5 cm after 10 seconds.

Determine the area of a flat piece of metal according to the data in the table below. The answer will need to be correctly stated as: (mean value ± σ_m) units. For example: Area = (3.2 ± 0.2 cm²).

(a)

Determine the mean, standard deviation, and the standard deviation of the mean for the measurements. (Hint: Use Logger Pro to help you make the calculations. Enter your mean values to at least four decimal places, and enter your standard deviations to at least five decimal places.)

Q#1

The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.10 years and a standard deviation of 2.00 years. Random samples of size 12 are drawn from the population and the mean of each sample is determined. Round the answers to the nearest hundredth.

Q#2

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be less than 12.1 ounces. Find the probability if the sample is just 1 cup.

An individual has three umbrellas, some at his office, and some at home. If he is leaving home in the morning (or leaving work at night) and it is raining, he will take an umbrella, if there is one there. Otherwise, he gets wet. Assume that, independent of the past, it rains on each trip with probability 0.2. To formulate a Markov chain, let Xn be the number of umbrellas at his current location “before” he starts his n-th trip. Note that “current location” can either be home or office, depending on whether the trip is from home to office or vice versa. Find the transition probabilities of this Markov chain

Consider the following.

a. What is the duration of a two-year bond that pays an annual coupon of 9 percent and whose current yield to maturity is 14 percent? Use $1,000 as the face value. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))
b. What is the expected change in the price of the bond if interest rates are expected to decrease by 0.2 percent? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

a. duration of bond

b. expected change in the price