(a) Prove that there are no degenerate bound states in an infinite (−∞ < x < ∞) one-dimensional space. That is, if ψ1(x) and ψ2(x) are two bound-state solutions of − (h^2/2m) (d^2ψ dx^2) + V (x)ψ = Eψ for the same energy E, it will necessarily follow that ψ2 = Cψ1, where C is just a constant (linear dependence). Bound-state solutions should of course vanish at x → ±∞.

(b) Imagine now that our particle is restricted to move along a circular ring of radius R. It would still be a 1D system as we need only one coordinate x (as measured along the ring) to specify the position. It is, however, different from case (a) as x is limited to the circumference of the ring.

We want to find all stationary states (that is, eigenfunctions, including normalization factors) and energy values for the particle on this ring in the absence of an external potential (V (x) = 0 ). The main consideration here is that the wave function is single-valued – you are thus faced with what is called “periodic boundary conditions”: after going around the circle, you get to the same point. In addition to finding stationary states, you are asked to assess the degeneracy of all energy levels and relate your observations to the result of case (a). For better clarity, you are suggested to use both standing-wave (like sin(kx)) and running-wave (like exp(ikx)) solutions in your analysis. Any commentary and interpretations are welcome, including comparisons to states in the infinite square well potential.

Find all the steady states of the system

? ′ = ?(10 − ? − ?) ? ′ = ?(30 − 2? − ?)

Then find the eigenvalues for every steady state and classify them

What types of powers are given to the states by the Constitution?

what is the process to calculate the payoff in both states?

18 –List the various states of Maslow’s theory.

Shaftel Ready Mix is a processor and supplier of concrete, aggregate, and rock products. The company operates in the intermountain western United States. Currently, Shaftel has 14 cement-processing plants and a labor force of more than 375 employees. With the exception of cement powder, all materials (e.g., aggregates and sand) are produced internally by the company. The demand for concrete and aggregates has been growing steadily nationally. In the West, the growth rate has been above the national average. Because of this growth, Shaftel has more than tripled its gross revenues over the past 10 years.

Of the intermountain states, Arizona has been experiencing the most growth. Processing plants have been added over the past several years, and the company is considering the addition of yet another plant to be located in Scottsdale. A major advantage of another plant in Arizona is the ability to operate year round, a feature not found in states such as Utah and Wyoming.

In setting up the new plant, land would have to be purchased and a small building constructed. Equipment and furniture would not need to be purchased. These items would be transferred from a plant that opened in Wyoming during the oil boom period and closed a few years after the end of that boom. However, the equipment needs some repair and modifications before it can be used. The equipment has a book value of $200,000, and the furniture has a book value of $30,000. Neither has any outside market value. Other costs, such as the installation of a silo, well, electrical hookups, and so on, will be incurred. No salvage value is expected. The summary of the initial investment costs by category is as follows:

After reviewing these data, Karl Flemming, vice president of operations, argued against the proposed plant. Karl was concerned because the plant would earn significantly less than the normal 8.3% return on sales. All other plants in the company were earning between 7.5 and 8.5% on sales. Karl also noted that it would take more than 5 years to recover the total initial outlay of$582,000. In the past, the company had always insisted that payback be no more than 4 years. The company's cost of capital is 10%. Assume that there are no income taxes.

Required:

1. Prepare a variable-costing income statement for the proposed plant. Compute the ratio of net income to sales.
2. (A) Compute the payback period for the proposed plant.  (B) Suppose you were told that the equipment being transferred from Wyoming could be sold for its book value; what is the payback period?
3. Compute the NPV for the proposed plant.
4. (A)Compute the cubic yards of cement that must be sold for the new plant to break even. Using this break-even volume, compute the NPV.  (B)How can a plant that is breaking even be generating a sufficient NPV?

Please answer number  differently from the answer key

5.

California and Washington state both started reporting COVID-19 cases at approximately the same time. Suppose a researcher wants to study the fatality rate of diagnosed COVID-19 cases in the 2 states.

a. What null hypothesis should be used? Pick one and explain.

i. California has a higher fatality rate than Washington.
ii. California has lower higher fatality rate than Washington.
iii. California has a different fatality (possibly higher, possibly lower) rate than Washington. iv. California and Washington have the same fatality rate.

b. What alternate hypothesis should be used? Pick one and explain.

i. California has a higher fatality rate than Washington.
ii. California has lower higher fatality rate than Washington.
iii. California has a different fatality (possibly higher, possibly lower) rate than Washington. iv. California and Washington have the same fatality rate.

c. As of 3/24/2020, California had 2220 cases and 100 fatalities, compared to 111 fatalities in 2221 cases in Washington. Use your calculator to carry out a suitable hypothesis test. Report the p-value of the test, determine whether or not to reject the null, and state what should be concluded. Use ? = .05.