A real estate company is interested in testing whether, on average, families in Gotham have been living in their homes different amounts of time than families in Metropolis have. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the data on length of residence in current homes. Random samples yield the following results. Gotham: XG= 35 months, SG2= 900 Metropolis: XM= 50 months, SM2= 1050 Assuming equal variances and normal distributions, what is the number of degrees of freedom?

Asmall town wants to build some new recreational facilities. the proposed facilities include a swimming pool, recreation center, basketball court and baseball field. the town council wants to provide the facilities which will be used by the most people, but they face budget and land limitations. the town has $400,000 and 14 acres of land. the pool requires locker facilities which would be in the recreation center, so if the swimming pool is built the recreation center must also be built. also, the council has only enough flat land to build the basketball court or the baseball field. the daily usage and cost of the facilities (in $1,000) are shown below. which facilities should they build? facilityusagecost ($1,000)landswimming pool4001002recreation center5002003basketball court3001504baseball field2001005