Self-disclosure can be a useful tool in a clinical setting or it can blur boundary lines if used incorrectly. While it is a controversial approach, research shows that clients who have counselors who disclose some information about themselves have lower stress levels than those whose counselors do not (Barrett & Berman, 2001). Review Karen’s approach below and determine what she could do to utilize self-disclosure in a helpful way. Write a paragraph about your feelings on how she used self-disclosure and write 1-2 sentences on how Karen could have used self-disclosure in a way that would have been more helpful to Joe.

Karen is a counselor in a residential treatment facility. Her client, Joe, shared that he went to jail an altercation he had when he was drunk. Karen responded, “I know what you mean. When I was younger I was almost arrested when I was drunk. I had some crazy times in college!”

You are a private teacher who conducts one-on-one home tuition in economics for senior college students. You are considering growing your business. In particular you are considering vertical and horizontal integration. Using the theory of the optimal boundary of the firm, discuss the make-orbuy decision as well as the scope for horizontal integration and diversification of your business. What stages of the vertical chain should you consider conducting inhouse? What other horizontal markets may you integrate into?

A survey asked, "Do you currently have tattoos on your body?" Of the 1239 males surveyed, 179 responded that they had at least one tattoo. Of the 1057 females surveyed, 141 responded that they had at least one tattoo. Test if the male population proportion is greater in having tattoos at a 95 % confidence level.

A. What is the test statistics?

B. What is the critical value?

C. What is the test conclusion?

D. What is the left boundary of the 95% C.I. of the group proportion difference?

a) What are the two primary mechanisms of mass transfer (molecular transport)?

b) If ??_?? is positive, is species ?? being consumed or generated by the reaction?

c) Are gas-phase diffusivities smaller or larger than liquid-phase diffusivities, and why?

d) What is a heterogeneous reaction? Describe the difference between a reaction-limited and mass-transfer-limited heterogeneous reaction.

e) If the diffusivity is increased, with all else held constant in a tubular heterogeneous reactor, would the diffusion boundary-layer thickness increase or decrease?

A recent survey asked 64 CMU students, “In the past year, about how many books did your read?” The results indicated a mean of 16.8 books with a S.D. of 6,7 books.

a. What is the Standard Error of the estimate of the population mean?

b. What is the Margin of Error at a C.L. of 97%?

c. What is the right boundary of the C.I. at a C.L. of 97%?

d. At a 99% C.L., if the researcher wants to limit the error within 1.5 book range, what size of the sample is needed?

Consider the following one-dimensional partial differentiation wave equation. Produce the solution u(x, t) of this equation. 4Uxx = Utt 0 < x 0 Boundary Conditions: u (0, t) = u (2π, t) = 0, Initial Conditions a shown below: consider g(x)= 0 in both cases.

(a) u (x, 0) = f(x) = 3sin 2x +3 sin7x , 0 < x <2π

(b) u (x, 0) = x +2, 0 < x <2π

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.

(x-6)(x+3)>0

Use the inequality in the form f(x)>0, to write the intervals determined by the boundary points as they appear from left to right on a number line.

Interval Sign

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(Simplify yours answers. Type your answer in interval notation. Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expressions.)

h Consider a solid T enclosed by the paraboloid z = x^2 +y^2 and the plane z = 4 (the solid above the paraboloid and below the plane). Let M the (closed) surface representing the boundary surface of T. The surface M consists of two surfaces: the paraboloid M1 and the lid M2. Orient M by an outward normal. Let F=(z,2y,-2)

Compute the integral using the Divergence theorem. Carry out the computation of the triple integral using the spherical coordinates.

Masses coupled through springs is a model for the behavior of atoms in a crystal. Consider a one-dimensional crystal, what if we have a crystal made of two kinds of atoms with different masses? Consider a one-dimensional lattice made up of alternating large and small masses, M and m, respectively. Assume periodic boundary conditions. (a) Calculate the normal modes of this lattice (you should find two normal modes). (b) Describe the relative motion of the two types of masses for each mode.

Now assume that a larger sample of 64 student scores is taken. The sample has a mean score of 29.5 and a standard deviation of 3.2. If you were to construct a 95% confidence interval for the ACT scores of this high school class, what would the lower boundary of the interval be?

You've constructed your confidence interval. Statistically, what does this confidence interval tell us? Can it be used to tell us the true population value of the mean ACT score for this high school class? Why or why not?