We know that 70% of the students shop online (there is a 70% chance that a randomly selected student shops online), and 60% of the students have a credit card (there is a 60% chance that a randomly selected student has a credit card). We also know that 95% of those who have a credit card shop online. A. What is the probability that a student shops online and has a credit card? Show your work. B. What is the probability that a student neither shops online nor has a credit card? Show your work. C. Are the events "shopping online" and "having a credit card" mutually exclusive? Explain. Show your work.

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

Jen left a job paying $75,000 per year to start her own florist shop in a building she owns. the market value of the building is $120,000. she pays $35,000 per year for flowers and other supplies, and has a bank account that pays 5 percent interest. what is the economic cost of jen's business?

Identify at least 3 body language messages that project a positive attitude