A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 34, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.

1. At what value should the control limit be set? (Round z values to two decimal places. Round your answers to 2 decimal places.)
2. If the population mean shifts to 7.6, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
3. If the population mean shifts to 8.7, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)

Crestview sells a particularly popular Christmas card once a year and distributes the cards to gift shops. It costs Crestview $0.5 per card to order from a printing company, and Crestview receives $1.0 for each card sold. The printing company costs $0.30 to print each card. Because the cards have the current year printed on them, those cards that are not sold are discarded at no value. Crestview has estimated that the demand for the coming Christmas season follows a normal distribution with a mean of 200,000 and standard deviation of 50,000.

A. Determine the optimal number of cards Crestview should order for the coming Christmas season.

B. Suppose Crestview has purchased a printing machine and will print cards themselves. The cost to print each card is still $0.30. Determine the optimal number of cards Crestview should print for the coming Christmas season.

C. Interpret the difference between the results in a) and b).

You have a cold gas of gold atoms, and you observe that if you shine light consisting of photons with energy 10.2 eV through the gas, some free electrons are observed, implying that a photon of this energy is able to ionize an atom in the gas. You find that the emitted electrons have a kinetic energy of 1.0 eV. What is the ionization energy of the gold atom? What is its ground state energy K + U?

you shine light with continuous energy distribution, and you observe absorption lines at the following photon energies: 1.1 eV, 2.7 eV, 4.6 eV, 5.1eV, 6.7eV, and 7.2eV.

Q/ Using the information from the two experiments describes above, draw a diagram of the energy levelsof one of the atoms in this gas. Draw the diagram expermintly to scale. Label the energy levels with their Values and label the transitions observed from the absorption line Data.

12. What is the molarity of 0.31 mol of NaCl in enough water to make 2.0 L of solution?

13. What is the molarity of the nitrate ions when 0.60 mol of barium nitrate, Ba(NO₃)₂, is dissolved in enough water to make 2.0 L of solution?

14. Calculate the molarity of calcium hydroxide that has been prepared by dissolving 2.24 g of calcium hydroxide in water and diluting the solution to a final volume of 4.00 L.

15. Calculate the molarity of the hydroxide ions in a solution that has been prepared by dissolving 70.3 g of barium hydroxide (Ba(OH)₂) in water and diluting the solution to a final volume of 4.00 L. (M.W's: Ba 137.3 g/mol., O 16.0 g/mol, and H 1.0 g/mol)

16. How many moles of H⁺ are in 181 mL of 0.71 M nitric acid, HNO₃?

Question 36

There are two firms: Firm U and Firm L. Both firms have $50M total assets and $8M EBIT (earnings before interest and taxes). Firm U is an unleveraged firm without debt. Firm L is a leveraged firm with 50% of debt and 50% of common equity. The pre-tax cost of debt for Firm L is 10%. Both firms have 40% corporate tax rate. Calculate the return on equity (ROE) for firm U.

Question 37

Based on the information from Question 36, what’s the return on equity (ROE) for firm L

Question 38

Based on the information from Question 36, what’s the difference of the total dollars paid to all investors in Firm L and Firm U?

Assume that you use Purchasing Power Parity (PPP) to forecast exchange rates. Suppose you expect that inflation in the UK the next year will be 1.0%, and inflation in the US will be 5.0%. Assume that you are considering the purchase of five one-year British pound call options from PHLX with a strike price of $1.265/£. The premium is $0.014 per £. The spot rate of the pound is $1.25/£ and the one-year forward rate is $1.26/£ today.

1. Based on your PPP analysis, what will be your expected spot exchange of $/£ in one year?

2. Graph the call option cash flow schedule at maturity. Mark option’s strike price and break-even point.

c. Determine your expected profit (or loss) if the pound appreciates to your expected future spot rate.

d. Determine your expected profit (or loss) if the pound appreciates to the forward rate.

Here we will look at an example of subatomic elastic collisions. High-speed neutrons are produced in a nuclear reactor during nuclear fission processes. Before a neutron can trigger additional fissions, it has to be slowed down by collisions with nuclei of a material called the moderator. In some reactors the moderator consists of carbon in the form of graphite. The masses of nuclei and subatomic particles are measured in units called atomic mass units, abbreviated u, where 1u=1.66×10−27kg. Suppose a neutron (mass 1.0 u) traveling at 2.6×107m/s makes an elastic head-on collision with a carbon nucleus (mass 12 u) that is initially at rest. What are the velocities after the collision? If the neutron's kinetic energy is reduced to 3649 of its initial value in a single collision, what is the mass of the moderator nucleus? Express your answer in atomic mass units as an integer.

A 0.25 kg block slides down a ramp that is 0.6 m tall, 0.8 m long and has a diagonal length of 1.0 m. The block starts at rest and arrives at the bottom with a speed of 1.3m/s. a.) How much heat was created by friction? b.)What is the average frictional force acting on the block? At what rate is kinetic energy being dissipated into heat near the bottom of the ramp? c.)Instead of a block, a cart with a mass of 0.33 kg rolls without any frictional losses. It collides with a horizontally mounted spring at the bottom of the ramp. If the spring has a spring constant of 215 N/m, how far will it be compressed. d.)Draw energy bar graphs for the following four moments: a. the moment of release, b. halfway down the ramp, c. at the base of the ramp d. when the spring has reached maximum compression.

a. A hydrogen atom in the n=5 state decays to the n=3 state. What is the wavelength of the photon that the hydrogen atom emits? Use hc=1240 nm eV.

nm

b. While in the first excited state, a hydrogen atom is illuminated by various wavelengths of light. What happens to the hydrogen atom when illuminated by each wavelength?

486.3 nm?

491.3 nm?

335.1 nm?

For each wavelength pick from the following choices:

"stays in n=2 state" , "jumps to n=3 state", "jumps to n=4 state", "jumps to n=5 state", "jumps to n=6 state", "is ionized"

Note: For a transition between bound states (finite n) you need to match the correct wavelength to about 8 significant figures. For this problem, treat a transition as happening if the wavelength is within 1.0 nm.

Water at 34 ^oC is reacted with 2.34 tonne h^-1 of gaseous thionyl chloride, SO₂Cl₂, at 43 ^oC and the product stream leaves as liquid. The reaction is given by:

SO₂Cl₂ (g) + 2H₂O (aq) → H₂SO₄ (aq)           + 2HCl (aq)

1. Complete the mass balance if three times the stoichiometric quantity of water is used.
2. Calculate the amount of heat released in kW.
3. If 65% of the heat released is removed by a cooling coil, calculate the temperature of the product stream. Use a temperature datum of 15^oC.

DATA

Heat of reaction, ΔH_R,            = - 2.5 × 10⁵ kJ kmol^-1 Liquid specific heat = 4.2 kJ kg^-1K^-1

Gas specific heat                     = 1.0 kJ kg^-1K^-1 Relative atomic masses

MW Data

C = 12,     H = 1,       O = 16,        S = 32,     N= 14, Cl=35.5