Find at least 4 non zero terms of the power series (around 0) for the solution to the initial value problem

y"+ (4 + x)y' − 2y = sin(4x), y(0) = −1, y' (0) = 2.

Over what interval is the solution analytic and why? What is the radius of convergence of the series solution around 0?

Consider a wire of length 4 ft that is cut into two pieces. One pieces form a radius for circle and other forms a square of side x. 1) choose x to maximize the sum of area. 2) choose x to minimize the sum of their areas. WHERE I got x=4/(x+pie).But i am not sure...

A voltaic cell consists of a Mn/Mn²⁺ electrode (E° = –1.18 V) and a Zr/Zr⁴⁺ electrode (E° = –1.53 V). Calculate [Mn²⁺] if [Zr⁴⁺ ] = 1.0x10⁻⁴ M and E_cell = 0.40 V at 25°C.

(1) 0.49 M           (2) 0.24 M           (3) 0.040 M         (4) 1.8 M            (5) 2.0 M

Find the measures of center for following.

mode =

median =

mean =  (round to 4 decimal places)

A company considers investing in a project that will cost $80 million up front. The company expects the project to generate the following cash flows over the next 4 years:

The applicable discount rate is 10%. What is the project's discounted payback period?

You would like to evaluate TSLA's stock. You find out the following about TSLA needed to do so:

(1) Their CAPM beta is 1.6.

(2) The weighted-average YTM on TSLA's bonds is 4%.

(3) Tesla's effective tax-rate is 25%.

(4) TSLA's capital structure mix is 96% equity and only 4% debt. TSLA has 932 million shares outstanding.

(5) The risk-free rate is currently .5% and the market risk-premium is 6%.

(6) Below are TSLA's expected OCFs (operating cash flows) for the next 5 years:

Year 1: $2,400,000,000

Year 2: $3,000,000,000

Year 3: $3,700,000,000

Year 4: $4,600,000,000

Year 5: $5,900,000,000

After year 5, TSLA is expected to grow its OCFs at a very impressive 6% per annum, indefinitely. Tesla is currently trading at $425 a share.

What is TSLA's fair stock price per share, given the above assumptions?

3. According to the above table, at what usage of labor does diminishing marginal product begin?

A) 1 worker

B) 2 workers

C) 4 workers

D) 5 workers

Need to calculate the MPL for all labor in a third column. Show your work.

4. According to the above table, what is the marginal product of the 4th unit of labor?      

A) 3 units of total product

B) 5 units of total product

C) 6 units of total product

D) 7 units of total product

5. According to the above table, what is the average product of labor when three laborers are employed?   

A) 3 units of TP

B) 4 units of TP

C) 5 units of TP

D) 6 units of TP

(a)Evaluate the following set of data for possible and probable outliers.
5 8 2 9 5 3 7 4 2 7 4 10 4 3 17

(b) A firm pays 5/12 of its labor force an hourly wage of $5, 1/3 of the labor force a wage
of $6 and ¼ a wage of $7. Determine the average wage paid by the firm.

(c)For the same amount of capital invested in each of 3 years, an investor earned a rate of
return of 1%during the first year, 4% during the second year and 16% during the third.
Find the simple arithmetic mean and the geometric mean. Which do you think is a more
appropriate in this case? Explain.

(d) A plane travelled 200 miles at 600 mph and 100 miles at 500mph. What was the
average speed for the entire journey?

(e) A driver purchased $10 worth of gasoline at $0.90 per gallon and another $10 at
$1.10 per gallon. What is the average price per gallon?

1. A researcher who works for a national retail chain is interested in changes in employee satisfaction during the holiday season. The table below contains employee satisfaction scores taken at two time points (August 1^st and December 1^st) from a sample of 12 employees. Higher scores indicate more satisfaction. Conduct a hypothesis test to determine if there is an increase or decrease in employee satisfaction from Time 1 to Time 2. Use alpha .05.

1. State the null alternative hypothesis.
2. Conduct the hypothesis test.
3. State your findings.
4. Report an effect size measure. Please use the formula that we used in class