Why does Elizabeth want John to go to Salem?

Find the exact value of each trigonometric function.

$$\cos \frac { 3 \pi } { 4 }$$

A certain experiment produces the data (1, 1.8), (2, 2.7), (3, 3.4), (4, 3.8), (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form $y=\beta_{1} x+\beta_{2} x^{2}$. Such a function might arise, for example, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price to be set for the product. a. Give the design matrix, the observation vector, and the unknown parameter vector. b. Find the associated least-squares curve for the data.

The president of ChemTech is trying to decide whether to start a new product line or purchase a small company. It is not financially possible to do both. To make the product for a 3-year period will require an initial investment of $250,000. The expected annual cash flows with probabilities in parentheses are:$75,000 (0.5), $90,000 (0.4), and$150,000 (0.1). To purchase the small company will cost $450,000 now. Market surveys indicate a 55% chance of increased sales for the company and a 45% chance of severe decreases with an annual cash flow of$25,000. If decreases are experienced in the first year, the company will be sold immediately (during year 1) at a price of $200,000. Increased sales could be$100,000 the first 2 years. If this occurs, a decision to expand after 2 years at an additional investment of $100,000 will be considered. This expansion could generate cash flows with indicated probabilities as follows:$120,000 (0.3), $140,000 (0.3), and$175,000 (0.4). If expansion is not chosen, the current size will be maintained with anticipated sales to continue. Assume there are no salvage values on any investments. Use the description given and a 15% per year return to do the following. (a) Construct a decision tree with all values and probabilities shown. (b) Determine the expected PW values at the “expansion/no expansion” decision node after 2 years, provided sales are up. (c) Determine what decision should be made now to offer the greatest return possible for ChemTech. (d) Explain in words what would happen to the expected values at each decision node if the planning horizon were extended beyond 3 years and all cash flow values continued as forecasted in the description.

What two things does Elizabeth say she is unable to do for John?

What is ironic when John Proctor is reciting his Ten commandments to Rev. Hale in Act II?

Explain how direct democracy differs from representative democracy.

What is the meaning of "Four legs good bad and two legs bad" in the "Animal Farm"?

What is a key source of school-related stress for adolescents?

$$\begin{array} { l } { \text { Let } G = G L ( 2 , \mathbf { R } ) \text { and } H = S L ( 2 , \mathbf { R } ) . \text { Let } A \in G \text { and suppose that } } \\ { \text { det } A = 2 . \text { Prove that } A H \text { is the set of all } 2 \times 2 \text { matrices in } G \text { that } } \\ { \text { have determinant } 2 } \end{array}$$

Each individual letter of the word TENNESSEE is placed on a piece of paper and all 9 pieces of paper are placed in a hat. If one letter is selected at random from the hat, determine the probability that the letter T or E is selected.

Evaluate the integral. Integral x^3+x^2+2x+1/(x^2+1)(x^2+2)dx

Give an example of a discrete random variable of interest to a psychologist.

What evidence is used to back up Abigail Williams's assertion that Elizabeth Proctor is guilty of witchcraft? Do you think the evidence is convincing? Why or why not?