The balance sheet for Bearing Industries Inc. at the end of the current fiscal year indicated the following:

Income before income tax was $238,000, and income taxes were $36,400, for the current year. Cash dividends paid on common stock during the current year totaled $41,580. The common stock was selling for $22 per share at the end of the year.

Determine each of the following. Round answers to one decimal place, except for dollar amounts which should be rounded to the nearest whole cent. Use the rounded answers for subsequent requirements, if required.

The following figure represents experimental results from study designed after the Beadle and Tatum experiment.  

Assume the mutants are homozygous for recessive alleles causing their phenotypes.

a. Create an ordered pathway of nutrients and mutants (pull down the correct mutant for M1-M4 and the correct nutrient for Nut1-Nut4):

#1. M1

a). Mutant 1

b.) Mutant 2

c.) Mutant 3

d.) Mutant 4

e.) Mutant 5

f.) Mutant 1 and 2

g.) Mutant 2 and 5

h.) Mutant 2 and 3

i.) Mutant 1 and 5

#2. M2

a). Mutant 1

b.) Mutant 2

c.) Mutant 3

d.) Mutant 4

e.) Mutant 5

f.) Mutant 1 and 2

g.) Mutant 2 and 5

h.) Mutant 2 and 3

i.) Mutant 1 and 5

#3. M3

a). Mutant 1

b.) Mutant 2

c.) Mutant 3

d.) Mutant 4

e.) Mutant 5

f.) Mutant 1 and 2

g.) Mutant 2 and 5

h.) Mutant 2 and 3

i.) Mutant 1 and 5

j.) Mutant 3 and 4

k.) Mutant 4 and 5

#4. M4

a). Mutant 1

b.) Mutant 2

c.) Mutant 3

d.) Mutant 4

e.) Mutant 5

f.) Mutant 1 and 2

g.) Mutant 2 and 5

h.) Mutant 2 and 3

i.) Mutant 1 and 5

j.) Mutant 3 and 5

k.) Mutant 1 and 2

l.) Mutant 1 and 3

#5. Nut 1

a.) Nutrient A

b.) Nutrient B

c.) Nutrient C

d.) Nutrient D

#6. Nut 2

a.) Nutrient A

b.) Nutrient B

c.) Nutrient C

d.) Nutrient D

#7 Nut 3

a.) Nutrient A

b.) Nutrient B

c.) Nutrient C

d.) Nutrient D

#8 Nut 4

a.) Nutrient A

b.) Nutrient B

c.) Nutrient C

d.) Nutrient D

b. If you crossed mutants 1 and 5, what would the nutrient requirements of the offspring be?

c. If you crossed mutants 1 and 4, what would the nutrient requirements of the F₁ be?

d. If you conducted an F₁xF₁ cross of mutants 1 and 4, what would the phenotypic ratios of the F₂ be?

1) There is a continuous function from [1, 4] to R that is not uniformly continuous. True or False and justify your answer.

2) Suppose f : D : →R be a function that satisfies the following condition: There exists a real number C ≥ 0 such that |f(u) − f(v)| ≤ C|u − v| for all u, v ∈ D. Prove that f is uniformly continuous on D

Definition of uniformly continuous: A function f: D→R is called uniformly continuous iff for all sequences {a_n} and {b_n} in D if (a_n) - (b_n)→ 0 then f(a_n) - f(b_n)→ 0

1. A 1 kilogram mass is attached to a spring with a spring constant of 4 N/m. Write the equation of motion if the spring is stretched 25 cm below the equilibrium position and released.

a) Suppose the system experiences a constant forcing function downwards of 4 N. (Note that one would need to divide by the mass, but the mass is 1 kg so we don’t see a difference here.) Solve the non-homogeneous equation. (Keep everything else about the initial value problem the same.) How does the forcing function change the solution/motion?

b) Suppose the forcing function is the periodic function ?(?) = 4 cos ?. Solve that nonhomogeneous equation. What is the period and amplitude of the motion in this system?

c) Suppose the forcing function is the periodic function ?(?) = 4 cos 2?. Solve this nonhomogeneous equation. How does the period and amplitude of the motion change? How would you describe the motion?

1) Use MATLAB to solve this differential equation. ??/?? = .25? (1 − ?/4 ) - a

2) Use MATLAB to graph solution curves to this system with several different initial values. Be sure to show at least one solution curve for each of the scenarios found in ??/?? = .25? (1 − ?/4 ) - a ( let a = 0.16)

Express the inverse transform as an integral s(s+3)/[(s^2+4)(s^2+6s+10)]

The thermal decomposition of dimethyl ether CH 3 2 O g CH 4 g H 2 g CO g is to be carried out in an isothermal 2.00-liter laboratory reactor at 600°C. The reactor is charged with pure dimethyl ether at a pressure of 350 torr. After about two hours, the reactor pressure is 875 torr. (a) Has the reaction proceeded to completion at the end of the two-hour period? If not, what percentage of the dimethyl ether has decomposed? (b) Taking elemental species [C(s), H2(g), O2(g)] at 25°C as references, prepare and fill in an inlet-outlet enthalpy table. (See Example 9.5-2.) Use tabulated data for methane, hydrogen, and carbon monoxide, and the following data for dimethyl ether: Δ H f 180.16 kJ mol C p J mol K 26.86 0.1659 T 4.179 10 5 T 2 T in kelvins (c) Calculate Δ H r 600 C and Δ U r 600 C for the dimethyl ether decomposition reaction. (d) How much heat (kJ) was transferred to or from the reactor (state which it is) during the two-hour period of the reaction? (e) Suppose the reaction were instead carried out in an expandable reactor at 600°C at a constant pressure of 350 torr, with the same final percentage decomposition of dimethyl ether. Calculate the final volume of the reactor and the required amount of heat transfer. (Note: These should both be quick calculations.) Explain why the values of Q calculated in Part d and in this part are different, even though the initial conditions and extents of reaction are the same.

a.  For the following probability density function:

                f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2

                       = 0 otherwise

           find its expectation and variance.

b. The two regression lines are 2X - 3Y + 6 = 0 and 4Y – 5X- 8 =0 , compute mean of X and mean of Y. Find correlation coefficient r , estimate y for x =3 and x for y = 3.

Chapter 11 Estimation and Confidence Intervals - Please answer 2-4

Practice 2) Estimation for the one-sample t Test

In chapter 9, we computed a one-sample t test examining the social functioning of relatives of individuals with OCD compared to the general healthy population.

In 18 participants, M = 62.00; SD = 20.94

Find the 95% CI for these data

Practice 3) Estimation for the two-independent-sample t test

In chapter 9, we tested the mean difference of calorie consumption between two independent groups given the same buffet: One group was instructed to eat fast, and another group was instructed to eat slowly. In a sample of 12 participants, we recorded M=600 in Grout Eating Slowly and M=650 in Group Eating Fast with an estimated standard error for the difference of S_M1-M2 = 82.66. Here we will find the 95% confidence interval for these data.

Practice 4) Estimation for the Related-Sample t Test

In chapter 10, we tested if teacher supervision influences the time that elementary school children read. The difference in time spent reading in the presence versus absence of a teacher was M_D=15 (n=8); the estimated standard error for the difference was S_MD=5.35. Here we will find the 95% confidence interval for these data.

2. Provide one example of technological determinism from units 2, 3 or 4. Describe two reasons why your chosen example highlights the problems associated with technological determinism.