A stock index is currently 990, the risk-free rate is 5%, and the dividend yield on the index is 2%. Use a three-step tree in an excel spreadsheet to value an 18-month American put option with a strike price of 1,000 when the volatility is 20% per annum.

Acompany is developing a new high­performance wax for cross country ski racing. in order to justify the price marketingwants, the wax needs to be very fast. specifically, the mean time to finish their standard test course should be less thanseconds for a former olympic champion. to test it, the champion will ski the course 8 times. the champion's times(selected at random) are 59.9 61.9 48.8 52.2 46.6 45.3 50.6 and 41.1 seconds to complete the test course. complete parts a and b below. a) should they market the wax? assume the assumptions and conditions for appropriate hypothesis testing are metfor the sample. assume=0.05. what are the null and alternative hypotheses? choose the correct answer below. b) suppose they decide not to market the wax after the test, but it turns out that the wax really does lower the champion'saverage time to less thanseconds. what kind of error have they made? explain the impact to the company of such anerror.

When you hire an independent contractor you don't have to pay the contractors what

Wilson center is a private not-for-profit voluntary health and welfare entity. during 2017, it received unrestricted pledges of $638,000, 65 percent of which were payable in 2017, with the remainder payable in 2018 (for use in 2018). officials estimate that 14 percent of all pledges will be uncollectible. a. how much should wilson center report as contribution revenue for 2017? b. in addition, a local social worker, earning $20 per hour working for the state government, contributed 600 hours of time to wilson center at no charge. without these donated services, the organization would have hired an additional staff person. how should wilson center record the contributed service?