A taxi company manager is trying to decide whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same cars were then equipped with regular belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows:
Kilometers per Liter Car123456789101112Radial Tires4.24.76.67.06.74.55.76.07.44.9 6.15.2Belted Tires4.14.96.26.96.84.45.75.86.94.7 6.04.9
Can we conclude that cars equipped with radial tires give better fuel economy than those equipped with belted tires? Assume the populations to be normally distributed. Use a P-value in your conclusion.

Needs to schedule the staffing of the center. it is open from 8am until midnight. larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required: time of dayminimum number of consultants required to be on duty8 am-noon4noon-4 pm84pm-8pm108pm-midnight6 two types of computer consultants can be hired: full-time and part-time. the full- time consultants work for eight consecutive hours in any of the shifts: morning (8am- 4pm), afternoon (noon-8pm) and evening (4pm-midnight). full-time consultants are paid $14 per hour. part-time consultants can be hired to work any of the four shifts listed in the table. part-time consultants are paid $12 per hour. an additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost. formulate this as an lp problem. you must define your variables clearly

Stocks a, b, and c are similar in some respects: each has an expected return of 10% and a standard deviation of 25%. stocks a and b have returns that are independent of one another; i. e., their correlation coefficient, r, equals zero. stocks a and c have returns that are negatively correlated with one another; i. e., r is less than 0. portfolio ab is a portfolio with half of its money invested in stock a and half in stock b. portfolio ac is a portfolio with half of its money invested in stock a and half invested in stock c. which of the following statements is correct? a. portfolio ab has a standard deviation that is greater than 25%.b. portfolio ac has an expected return that is less than 10%.c. portfolio ac has a standard deviation that is less than 25%.d. portfolio ab has a standard deviation that is equal to 25%.e. portfolio ac has an expected return that is greater than 25%.

What is one of the advantages of getting a government-sponsored mortgage instead of a conventional mortgage