12 pts) Use Mathematical Induction to prove that a_n=n³+5n is divisible by 6 when ever n≥0. You may explicitly use without proof the fact that the product n(n+1) of consecutive integers n and n+1 is always even, that is, you must state where you use this fact in your proof.Write in complete sentences since this is an induction proof and not just a calculation. Hint:Look up Pascal’s triangle.

(a)

Verify the initial case n= 0.

(b)

State the induction hypothesis.

(c)

Perform the induction

Companies often have different mutual funds to serve different investment time horizons. Use the tab titled BESTFUNDS to determine if there is a difference between in the three-year annualized return for small cap growth, mid-cap growth, and large cap growth mutual funds.

(a) Identify which type of test you plan to use and why.

(b) Analyze and report your findings.

(c) Put the findings into meaningful words (i.e., explain what the test allows you to conclude about the types of mutual funds).

(d) Does your result from

(b) give you statistical permission to probe group differences, yes or no?

Companies often have different mutual funds to serve different investment time horizons. Use the tab titled BESTFUNDS to determine if there is a difference between in the three-year annualized return for small cap growth, mid-cap growth, and large cap growth mutual funds. (a) Identify which type of test you plan to use and why. (b) Analyze and report your findings. (c) Put the findings into meaningful words (i.e., explain what the test allows you to conclude about the types of mutual funds). (d) Does your result from (b) give you statistical permission to probe group differences, yes or no?

1.) Articulate and describe two separate advantages of being a high self-monitor and two separate advantages of being a low self-monitor.

2.) Using concrete examples, articulate and explain three of the risks of self-disclosure identified in your text

3.) The United States is sometimes criticized for being as individualistic as it is. What are some good things about growing up in an individualist culture? In what ways would growing up in a collectivistic culture be better? Explain and defend your answer.

4.) Using concrete examples, articulate and explain how perceptual accuracy can be influenced by social and occupational roles.

5.) Identify and define each of the four types of language rules articulated in your text.

1. Diatomic nitrogen's oscillation frequency is about 6.2 x 10¹³ Hz. What is the spacing between excited vibration energy states of nitrogen? Give your answer in eV.

1a. What is the zero-point energy of the vibration mode of diatomic nitrogen if its oscillation frequency is 6.2 x 10¹³ Hz? Give your answer in eV.

1c. Per the equipartition theorem in thermodynamics, each degree of freedom of a system has (on average) of energy. Vibration modes of molecules like nitrogen do not share this degree of freedom until the available thermal energy can excite molecules into the first excited state (above the zero-point energy). At what temperature would correspond to this energy? Give your answer in Kelvin. Assume the vibration mode frequency is 6.2 x 10¹³ Hz.

Describe and explain why the USA health system is considered to be neither a decentralized health market nor a centralized health system and what is the impact on health care reform of the combined federal-state responsibility with substantial federal oversight and funding, imbued with state innovation and implementation?

Describe and explain why the USA health system is considered to be neither a decentralized health market nor a centralized health system and what is the impact on health care reform of the combined federal-state responsibility with substantial federal oversight and funding, imbued with state innovation and implementation

4.170 Change in Stock Prices. Standard & Poor's maintains one of the most widely followed indices of large-cap American stocks: the S&P 500. The index includes stocks of 500 companies in industries in the US economy. A random sample of 50 of these companies was selected, and the change in the price of the stock (in dollars) over the 5-day period from August 2 to 6, 2010 was recorded for each company in the sample. The data are available in StockChanges.

a. Use StatKey to calculate a 95% confidence interval for the mean change in all S&P stock prices over these dates using the bootstrap percentiles method. Include a screen shot of your Statkey output with your homework submission, and write the confidence interval below.

b. Use only the confidence interval you created (do not find a p-value) to predict the results of a hypothesis test to see if the mean change for all S&P 500 stocks over this period is different from zero.

i. Define the parameter.

ii. State the hypotheses.

iii. What significance level are you able to use based on the confidence interval?

iv. State the conclusion using nontechnical language.

c. If any error were to occur in the decision to reject or fail to reject, would it be a Type I error or a Type II error?

d. Explain what an error of this type would mean in context.

SPChange
0.29
-0.06
0.34
0.7
0.42
0.22
0.12
0.03
-0.5
0.36
0.03
0.09
-0.12
0.03
-0.47
-3.27
0.35
-0.06
0.01
0.6
0.12
4.86
-0.77
-0.03
0.39
0.1
-0.12
0.47
-0.05
0.06
-0.03
0.15
0.31
-0.15
0.32
-2.66
0.22
-0.03
0.09
0.29
0.16
0.38
0.1
0.21
0.09
0.33
0.18
1.93
0.14
0.03

In your own words explain what a theoretical plate is . What is the relationship between the number of theoretical plates and resolution? How is theoretical plate height related to resolution? Now quantitatively, answer the following question: How many theoretical plates, N, must a packed column have to achieve a resolution of 1.5 between 2 peaks that elute at 5.42 minutes and 5.63 minutes. At a resolution of 1.5 are these peaks considered resolved?