if the sum of the first m terms of m AP is the same as the sum of its first n terms, show that the sum of its first (m+n) terms is zero.​

The bonds issued by the south foot bear a coupon rate of 7.5 percent, payable semiannually. the bonds mature in 6.5 years, sell at par, and have a $1,000 face value. what is the yield to maturity

Upscale hotels in the united states recently cut their prices by 20 percent in an effort to bolster dwindling occupancy rates among business travelers. a survey performed by a major research organization indicated that businesses are wary of current economic conditions and are now resorting to electronic media, such as the internet and the telephone, to transact business. assume a company's budget permits it to spend $5,000 per month on either business travel or electronic media to transact business. graphically illustrate how a 20 percent decline in the price of business travel would impact this company's budget set if the price of business travel was initially $1,000 per trip and the price of electronic media was $500 per hour. suppose that, after the price of business travel drops, the company issues a report indicating that its marginal rate of substitution between electronic media and business travel is 1. is the company allocating resources efficiently? explain.

Acompany that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. prior to buying the new equipment, the company used 6 workers, who produced an average of 79 carts per hour. workers receive $16 per hour, and machine coast was $49 per hour. with the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $11 per hour while output increased by four carts per hour. a) compute the multifactor productivity (mfp) (labor plus equipment) under the prior to buying the new equipment. the mfp (carts/$) = (round to 4 decimal places). b) compute the productivity changes between the prior to and after buying the new equipment. the productivity growth = % (round to 2 decimal places)