A study was conducted concerning the effects of varying lengths of unemployment on ability to concentrate. Data represent participants' proofreading scores (number of errors found). Finding fewer errors on the proofreading task is a behavioral indicator of stress. Length of unemployment was regarded by the researchers as an indicator of exposure to chronic stress. Fifteen participants were included in the study and followed across three periods: employment (control), short-term unemployment and long-term unemployment. (20%) Data were collected and are shown below: Length of Unemployment

Control: 8 10 9 8 10. Short: 0 1 2 7 5 Long: 6 7 7 6 9

Please analyze the data fully (including appropriate follow-up tests) and provide a brief written summary of the results.

Determine all maximal planar graphs G of order 3 or more such that the number of regions in a planar embedding of G equals its order.

Give an example of two non-isomorphic maximal planar graphs of the same order.

FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below.

The company needs to develop a linear programming model whose solution would tell them how many ounces of each mix to put into the TrailTime blend. TrailTime is packaged in boxes that will hold between three and four cups. The blend should contain no more than 1,100 calories and no more than 30 grams of fat. Dried fruit must be at least 25% of the volume (in cups) of the mixture, and nuts must be no more than 20% of the weight (in ounces) of the mixture.

Use Excel's Solver to obtain the optimal solution for this problem. In other words: what is the most cost effective way to create the TrailTime blend? What is the cost?

True or False? For any two events A and B, P(A∩ B) ≥ 1 − P(A∪ B)

True or False? For any two independent events A and B, P(A| B) = P(A| Bc )

Compute B(6, .2, 2)

Find the matrix A representing the follow transformations T. In each case, check that Av = T(v)
Step by step please.

A. T(x,y,z) = (x-3y+4z, 6x-2z, 8x-y-4z)

B. T(x,y) = (x,y,y-x,x+y, 6x-9y)

Thank you!

Find the general solution to the differential equation 3x''+2x'+2x=0. Use  and  to denote arbitrary constants.

6a. Show that 2/n = 1/3n + 5/3n and use this identity to obtain the unit fraction decompositions of 2/25 , 2/65 , and 2/85 as given in the 2/n table in the Rhind Mathematical Papyrus.

6b. Show that 2/mn = 1/ (m ((m+n)/ 2 )) + 1/ (n ((m+n)/ 2 )) and use this identity to obtain the unit fraction decompositions of 2/7 , 2/35 , and 2/91 as given in the 2/n table in the Rhind Mathematical Papyrus.

6c. Verify that 2/ n = 1/n + 1/2n + 1/3n + 1/6n and use this identity to obtain the unit fraction decompositions of 2/101 as given in the 2/n table in the Rhind Mathematical Papyrus.

IN EXCEL: 5.2.1 At time t = 0, a yeast culture weighs 0.5 g. Two hours later, it weighs 2 g. The maximum weight of the culture is 8 g.

1. Create a spreadsheet to model the population using a logistic equation. Use a scroll bar to vary the value of k.

2. Use the scroll bar to find a value of k so that the condition y(2) = 2 is satisfied.

3. At what time is the weight increasing most rapidly? Support your answer numerically.

Find the eigenvalues

λ_n

and eigenfunctions

y_n(x)

for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.)

x²y'' + xy' + λy = 0,  y'(e⁻¹) = 0,  y(1) = 0

Answer the following questions.
(a) What is the implication of a correlation matric not being positive-semidefinite?
(b) Why are the diagonal elements of a correlation matrix always 1?
(c) Making small changes to a positive-semidefinite matrix with 100 variables will have no effect on the matrix. Explain this statement

Answer ”True” or ”False” for each of the following:

(i) If f,g : R → R and are both continuous at a number c, then the composition function f ◦g is continuous at c.

(ii) If functions h1, h2 : R → R and are both uniformly continuous on a non-empty set of real numbers E, then the product h1h2 is uniformly continuous on E.

(iii) If a function g : R → R, then there exists a function G : R → R such that G0(x) = g(x) for all x ∈ R. (iv) If A ⊂ B and A is countable, then B is uncountable.

(v) If f : R → R is continuous and positive at a number c, then f is differentiable at c. (vi) If K is a non-empty compact set of real numbers, then either K is finite or uncountable.

An investor is considering purchasing one of three stocks. Stock A is regarded as conservative, stock B as speculative, and stock C as highly risky. If the economic growth during the coming year is strong, then stock A should increase in value by $3000, stock B by $6000, and stock C by $15,000. If the economic growth during the next year is average, then stock A should increase in value by $2000, stock B by $2000, and stock C by $1000. If the economic growth is weak, then stock A should increase in value by $1000 and stocks B and C decrease in value by $3000 and $10,000, respectively.

(a) Give the pay off matrix for this problem and decide if the game is strictly determined or not.

(b) What is the optimal strategy for the investor?

(c) What is the value or expected value of the game?