Let a : {12, 13, 14, 15, 16, 17, 18, 19, 20} → Z be the function defined by a(x) equals thelargest prime number that divides x.(a) Write down the set of ordered pairs which corresponds to a.(b) What is the range of a?
Can someone please help me with this assignment
Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use StatKey or Minitab Express include the appropriate output (copy + paste) along with an explanation. Output without explanation will not receive full credit. Round all answers to at least 3 decimal places. If you have any questions, post them to the course discussion board.
1. According to U.S. News and World Reports, 18.60% of all Penn State World Campus students have military experience. In a random sample of 40 students enrolled in World Campus sections of STAT 200, 5 reported having military experience. [30 points]
A. Compute the sample proportion (p-hat) for this sample of n=40 STAT 200 students.
B. Should the exact method or normal approximation method be used to construct a sampling distribution in this situation? Explain your reasoning.
C. Using StatKey, construct a sampling distribution for p=0.1860 and n=40. Generate at least 5,000 samples. Take a screenshot of your sampling distribution and paste it here.
D. If the population proportion is 18.60%, what is the probability of taking a random sample of n=40 and finding a sample proportion more extreme than the one observed in this sample? Use StatKey to determine this proportion. Include a screenshot of your sampling distribution with this proportion highlighted.
E. Given your results from part D, do you think that the proportion of all STAT 200 students who have military experience is different from the overall population of World Campus students where p=0.1860? Explain your reasoning.
2. For the following questions, assume a normally distributed population. [20 points]
A. Given μ=50, σ=15, and n=25, compute the standard error of the mean.
B. Given μ=50, σ=15, and n=500, compute the standard error of the mean.
C. Given μ=50, σ=3, and n=25, compute the standard error of the mean.
D. Given μ=500, σ=15, and n=25, compute the standard error of the mean.
E. How does the standard error of the mean change when the population mean, population standard deviation, and sample size change?
3. Using StatKey you are going to construct a sampling distribution for a mean. Select a population distribution that is NOT normal (e.g., the built in Hollywood Movies, Rock Bands, or Baseball Players datasets, or a skewed distribution of your own). Using the same population distribution for each, construct the distribution of sample means for N=4 and N=30. Take at least 5,000 samples. [20 points]
A. Include a screen shots of your parent population and your two sampling distributions here.
B. How are your two distributions of sample means similar? How are they different?
C. Describe how your results relate to the Central Limit Theorem.
4. In the population ACT scores are normally distributed with a mean of 18 and a standard deviation of 6. Suppose that we are taking a simple random sample of 60 students from one high school. [30 points]
A. Calculate the standard error of the mean.
B. If we were to repeatedly pull samples of 60 individuals from the population of all ACT test takers, the distribution of sample means would have a mean of ____ and a standard deviation of ____.
C. Given the values from part B, 95% of random samples of n=60 will have sample means between ___ and ___.
D. What is the probability that you would pull a random sample of 60 individuals from the population of all test takers and they would have a sample mean of 19 or higher?
E. Suppose that the high school in question boasts that their students (i.e., the population of all of their students) have an average ACT score above the national average of 18. Given your results from part D, do you believe that there is evidence that the mean ACT score at this high school is greater than 18? Explain your reasoning.
Let A = {1,2,3,4,5,6}. In each case, give an example of a function f : A −→ A with the indicated properties, or explain why no such function exists.
(a) f is not the identity function on A, but f is bijective.
(b) f is one-to-one, but not onto
Lesson 4 Tax 515
1. Discuss the different requirements for disclosing items to both the IRA owner and the IRS and when each applies.
2. List out the different reports required by the IRA owner and the IRS for an IRA account and what the use of each is.
3. Taxpayers are required to report and pay taxes on certain distributions from IRA accounts. Explain the criteria for when a distribution is made as to when a taxpayer must pay tax or not on the distribution amount.
4. After reviewing the different types of penalties that might apply to an IRA owner and their actions, explain the different types of penalties and when each would be in effect.
5. Discuss the general filing information requirements for IRA accounts, to include the various forms and the use of each.
6. In reviewing the different forms that are required through the IRA and tax process that impacts the IRA account owner, discuss who is required to fill out each of these forms, as well as who is responsible for withholding the funds for inclusion in the IRA account.
Professional Development Question
Professional Development Question
Assume you are sitting down with an investment advisor to discuss the opening of either a
Traditional or Roth IRA account for you future. Determine what types of questions you would ask this advisor, specific to the penalties, distributions, filings, and withholding rules you might expect. How would the answers to these questions impact your choice bet
Let ζ8 ∈ C be a primitive 8-th root of unity.
(a) Determine the minimal polynomial of ζ8 over Q. – I have found that the min poly is x4 +1
need help With the following two parts, with a good explanation please (particularly showing the Q(8)/Q is galois)
(b) Show that Q(ζ8)/Q is Galois and determine its Galois group
(c) Determine all the subfields of Q(ζ8)
Let S=$300, K=$300, r=10% risk-free interest rate, (continuously compounding), T=3 years, n=3, three-period binomial tree,
Let 5 = $300, K = $300, 1= 10% risk – free interest rate , ( continuously compounding ) ,T = 3 years , n = 3, three – period binomial tree , ${_ 6.5%6 , continuous dividend yield onthe stock , 4 = 1. 25, and d = 0. 7 .a ) Construct the binomial tree for the stock .b ) Compute the prices of American and European calls .c ) Compute the prices of American and European puts by using risk – neutralapproach .d ) What is your replicating portfolio today for European Call and Put optionsin part ( b ) and ( C ) ?"e ) What is your replicating portfolio today for American Call and Put options inpart ( b ) and ( c ) ?
Letπi , i = 1, . . . , n be positive numbers that sum to 1. LetQbe an irreducible
transition probability matrix with transition probabilities q(i, j ), i, j =
1, . . . , n. Suppose that we simulate a Markov chain in the following manner:
if the current state of this chain is i , then we generate a random variable that
is equal to k with probability q(i, k), k = 1, . . . , n. If the generated value is j
then the next state of the Markov chain is either i or j , being equal to j with
probability π j q( j,i )
πi q(i, j )+π j q( j,i ) and to i with probability 1 − π j q( j,i )
πi q(i, j )+π j q( j,i ) .
(a) Give the transition probabilities of the Markov chain we are simulating.
(b) Show that {π1, . . . , πn} are the stationary probabilities of this chain.
3. Let 31;, i = l, . . . , n be positive numbers that sum to 1. Let Q be an irreducibletransition probability matrix with transition probabilities q(i, j ), i, j =l, . . . , 11. Suppose that we simulate a Markov chain in the following manner:if the current state of this chain is i, then we generate a random variable thatis equal to k with probability q(i, k), k = 1, . . . , at. If the generated value is jthen the next state of the Markov chain is either i or j, being equal to j with probability W W) 31′ jfiIUJ) —:r;q(i,j)+njq(j,i) and to; With probab111ty l — —Kt_q(1.7j) +Jrthjai)’ (a) Give the transition probabilities of the Markov chain we are simulating.(b) Show that {31], . . . , 31”} are the stationary probabilities of this chain.
thank you for your assistance in working out this math problem.
21. Let “`^( 2) State the domainAnswer *( 6) State the horizontal asymptotesAnswer :`( c ) State the vertical asymptote (‘s )*Answer .( }) Which of the following represents the graph of from) -^ ^`Answer :GRAPH AGRAPH BTO`GRAPHICGRAPHDfor .
Please provide full solution with the answer. This is a calculus question.
Let( 2 2 – 2xx + a , if * < ]9 ( 20 ) =3 .if ac = ]bac + 2 .far > 1 .( a ) Determine values of a and 6 for which , is continuous at ac = ] .( b) For what values of a and & is a continuous from the left at ac = 1 , but not continuous from the rightat ac = 1 ?( C ) For what values of a and & is a continuous from the right at ac = 1 , but not continuous from the leftat ac = 1 ?
Lester’s Home Healthcare Services (LHHS) was organized on January 1, 2005, by four friends. Each organizer invested $10,000 in the company and, in turn, was issued 8,000 shares of stock. To date, they are the only stockholders. During the first month (January 2005), the company had the following six events:2. During the first month, the records of the company were inadequate. You were asked to prepare the summary of the preceding transactions. To develop a quick assessment of their economic effects on Lester’s Home Healthcare Services, you have decided to complete the spreadsheet that follows and to use plus (+) for increases and minus (-) for decreases for each account. The first transaction is used as an example.1. Collected a total of $40,000 from the organizers and, in turn, issued the shares of stock.2. Purchased a building for $65,000, equipment for $16,000 and three acres of land for $12,000; paid $13,000 in cash and signed a note for the balance, which is due to be paid in 15 years.3. One stockholder reported to the company that 500 shares of his Lester’s stock had been sold and transferred to another stockholder for $5,000 cash. 4. Purchased supplies for $3,000 cash. 5. Sold one acre of land for $4,000 cash to another company. 6. Lent one of the shareholders $5,000 for moving costs, receiving a signed six-month note from the shareholder.After the spreadsheet is done I need to answer these questions1. Was Lester’s Home Healthcare Services organized as a partnership or corporation? Explain the basis for your answer. 1. Did you include the transaction between the two stockholders-event c-in the spreadsheet? Why? 2. Based only on the completed spreadsheet, provide the following amounts (show computations):3. Total assets at the end of the month. 4. Total liabilities at the end of the month. 5. Total stockholders’ equity at the end of the month. 6. Cash balance at the end of the month.7. Total current assets at the end of the month.8. As of January 31, 2005, has the financing for LHHS’S investment in assets primarily come from liabilities or stockholders’ equity?
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