John Roberts is 55 years old and has been asked to accept early retirement from his company. On July 1, the company offered John three alternative compensation packages to induce John to retire: (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) 1. $180,000 cash payment to be paid immediately. 2. A 20-year annuity of $16,000 beginning immediately. 3. A 10-year annuity of $50,000 beginning on July 1 of the year John reaches age 65 (after 10 years). Required: Determine the present value, assuming that he is able to invest funds at a 7% rate, which alternative should John choose? (Round your final answers to nearest whole dollar amount.)

Each of the following scenarios is based on facts in anactual fraud. categorize each scenario as primarily indicating (1) anincentive to commit fraud, (2) an opportunity to commit fraud, or(3) a rationalization for committing fraud. also state your reasoningfor each scenario.a. there was intense pressure to keep the corporation ' stock from declining further. this pressure came from investors, analysts,and the ceo, whose financial well-being was significantly dependent on the corporation ' s stock price.b. a group of top-level management was compensated (mostly in the form of stock-options) well in excess of what would be considered normal for their positions in this industry.c. top management of the company closely guards internal financial information, to the extent that even some employees on a “need-to-know basis” are denied full access.d. managing specific financial ratios is very important to the company, and both management and analysts are keenly observant of variability in key ratios. key ratios for the company changed very little even though the ratios for the overall industry were quite volatile during the time period.e. in an effort to reduce certain accrued expenses to meet budget targets, the cfo directs the general accounting department to reallocate a division’s expenses by a significant amount. the general accounting department refuses to acquiesce to the request, but the journal entry is made trough the corporate office. an accountant in the general accounting department is uncomfortable with the journal entries required to reallocate divisional expenses. he brings his concerns to the cfo, who assures him that everything will be fine and that the entries are necessary. the accountant considers resigning, but he does not have another job lined up and is worried about supporting his family. therefore, he never voices his concerns to either the internal or external auditors.f. accounting records were either nonexistent or in a state of such disorganization that significant effort was required to locate or compile them.

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.

Which stage of group development involves members introducing themselves to each other?