Can a closed linear map be unbounded?

In Python

iOverlap (a1, a2, b1, b2)

Write the function iOverlap that tests whether 2 closed intervals overlap. It takes 4 numbers (ints or floats) a1, a2, b1, b2 that describe the two closed intervals [a1,a2] and [b1,b2] of the real number line, and returns True if these two closed intervals overlap (even if at only one point) and False otherwise. If a1>a2, then the interval [a1,a2] is empty. If b1>b2, then the interval [b1,b2] is empty. Both intervals are closed, so contain their endpoints. For example, the intervals [1,2] and [2,3] overlap at the point 2.

I want to know how long basketball shoes last for people on average. I rubbed a dusty coffee pot and a genie popped out to tell me that the standard deviation for the lifespan of all basketball shoes is 4.2 months. I polled 1225 people at the PEIF (before it closed) on how long their shoes lasted, and I got an average of 27 months.

(a) What is the 95% confidence interval for the population mean lifespan of a basketball shoe?

(b) What is the 99.7% confidence interval for the population mean lifespan of a basketball shoe?

(c) Draw appropriate shaded bell curves to show the difference between these.

Case Study Instructions: Read this case study and answer the questions that follow: Virgin was founded in 1970 by Richard Branson and is classified as a holding company for multiple ventures under the Virgin Group. When it comes to innovation Virgin is one of the top companies in the world. What began as a mail order record company has evolved into one of the most diverse companies in existence. Virgin invests in and builds companies that revolve around delivering fantastic customer experience and change the scope of industries. They do everything from space tourism to air travel, make comic books and video games. The company now holds over 200 companies and operates in 29 countries. They’ve found that the most successful ideas they get are the ones that are marketing, sales, and customer focused, sit under the Virgin brand, have a well-defined and differentiated customer offer and oftentimes are delivered in partnership with experts in their field.
Virgin takes the ideas it gets and boils them down into several categories. Anything that doesn’t quite fit into an existing company gets sent to corporate development for review. They take the time to read and respond to every proposal. They do not disclose how rewards are awarded but there are substantial ones for good ideas that are implemented. Internally Virgin also sources business plans and ideas from employees. Once a flight attendant had an idea. It got presented to the CEO and before long she had a considerable role in starting up Virgin Brides (which beyond being a fantastic idea didn’t quite work out in the market place). It’s incredible that a flight attendant can have an idea that makes it that far in a company. Notice that Virgin has over 200 companies under it. If you stop for a second you’ll realize just how massive that number is. That is a lot of innovation for a company only 40 years old. Financially they do quite well so obviously something has been working out for them. Not a lot of firms innovate this much or support this much innovation but that’s kind of the key – they don’t just source great ideas, they act on them. Sourcing this many fantastic ideas isn’t easy – it’s a lot of hard work for the company and they have to devote time and resources to going through all of them never mind actually taking the time to respond. But it shows that they care and that they’re serious about this. All great innovations come from an idea. Some go so far as to say it’s the most important part of the process (Seth Godin would likely disagree and say that shipping is the most important). Some companies looking at Virgin’s requirements might find them surprisingly strict, others surprisingly loose. No matter how you view it the only thing that remains true at the end of the day is that Virgin’s strategy works – and it works well.

Required:
Business excellence is about strategy. From the case study which strategies has Virgin used to achieve continuous creativity and innovation.

The following condensed income statements of the Jackson Holding Company are presented for the two years ended December 31, 2021 and 2020:

On October 15, 2021, Jackson entered into a tentative agreement to sell the assets of one of its divisions. The division qualifies as a component of an entity as defined by GAAP. The division was sold on December 31, 2021, for $5,480,000. Book value of the division’s assets was $4,720,000. The division’s contribution to Jackson’s operating income before-tax for each year was as follows:

Assume an income tax rate of 25%.

Required: (In each case, net any gain or loss on sale of division with annual income or loss from the division and show the tax effect on a separate line.)
1. Prepare revised income statements according to generally accepted accounting principles, beginning with income from continuing operations before income taxes. Ignore EPS disclosures.
2. Assume that by December 31, 2021, the division had not yet been sold but was considered held for sale. The fair value of the division’s assets on December 31 was $5,480,000. Prepare revised income statements according to generally accepted accounting principles, beginning with income from continuing operations before income taxes. Ignore EPS disclosures.
3. Assume that by December 31, 2021, the division had not yet been sold but was considered held for sale. The fair value of the division’s assets on December 31 was $4,060,000. Prepare revised income statements according to generally accepted accounting principles, beginning with income from continuing operations before income taxes. Ignore EPS disclosures.
  

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Prepare revised income statements according to generally accepted accounting principles, beginning with income from continuing operations before income taxes. Ignore EPS disclosures. (Amounts to be deducted should be indicated with a minus sign.)

Distributors sells snack and candy to local stores. On March 1, 2010, Borges issued $4,000,000 of 5-year, 13% bonds at an effective interest rate of 11%. Interest is payable semiannually on March 1 and September 1. Journalize the entries to record the following:

1. Sale of bonds on March 1, 2010. Use the tables on present values in Appendix A of your textbook to determine the present value of the bond issue. Round to nearest dollar.

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2. First interest payment on September 1, 2010, and amortization of bond premium for six months, using the straight-line method. Round to the nearest dollar.  

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Fireflies Limited began retail operations on 1/1/2010. On that date, it issued 10,000 shares of $1 par value common stock for $50,000. On 1/1/2010, Fireflies also borrowed $20,000 from a local bank. The loan will be due in three years, with 8% interest rate. Fireflies pays interests every quarter. On 1/31, Fireflies used $36,000 of the proceeds to rent a store, paying in advance for the next one year. Fireflies also purchased $12,000 of merchandise on credit, agreeing to pay the supplier within 30 days. Prepare, a balance sheet as of 1/31/2010.

Satisfied?A poll taken by the General Social Survey in 2010 asked people in the United States whether they were satisfied with their financial situation. A total of 478 out of 2038 people said they were satisfied. The same question was asked in 2014, and 698 out of 2532 people said they were satisfied.

a. Construct a 95% confidence interval for the difference between the proportion of adults who said they were satisfied in 2014 and the proportion in 2010.

b. A sociologist claims that the proportion of people who are satisfied increased from 2010 to 2014 by more than 0.05. Does the confidence interval contradict this claim?

4. Assume a company's January 1, 2010, financial position was: Assets, $75,000 and Liabilities, $30,000. During January 2010, the company completed the following transactions: (a) paid on a note payable $5,000; (b) collected an accounts receivable, $4,000; (c) paid an accounts payable, $3,000; and (d) purchased a truck using $2,000 cash, and a $13,000 note payable. The company's January 31, 2010 financial position is

Assets Liabilities Stock holders equity

A) $83,000 $38,000 $45,000

B) $65,000 $35,000 $30,000

C) $78,000 $37,000 $41,000

D) $80,000 $35,000 $45,000

Consider the following price data from 2002 to 2010

a. Compute the simple price index using 2002 as the base year. (Round your answers to 2 decimal places.)

b. Update the index numbers with a base year revised from 2002 to 2005. (Round your answers to 2 decimal places.)