math for computing ( assignments)

please answers

(3,4,5,7)

3. A technician takes X hours to visit the stores in a couple of streets in one shift, and when he finishes his tour, another technician revisits the same stores again, needing other X hours to finish the second shift, and so on. For example, if the first technician started his shift at 1:00pm, he finishes it at 7:00pm and the second technician starts his shift at 7:00pm and finishes it at 1:00am, and so on. The supervisors used to make a quick meeting with all technicians twice a day at 1:00 am and 1:00 pm, so they need to finish their tours exactly 1:00. Identify the mathematical notation for the number of shifts should be made by the technicians in order to achieve this, write the name of this mathematical value, and find it for two tours, one with X=7 and another with X=11. 4. The marketing department in the computer company is studying the pattern of the stores' orders for better understanding of the customers' needs. Some of the study findings are: 50% of the customers buy hardware products, while 50% buy software products. There is a 40% probability that a customer is interested in computer gaming, if he/she buys a hardware product. The probability that a customer buys a software product and is a computer programs developer is 30%. Based on this information, find the following: a) The probability that a random customer is interested in computer gaming and buys hardware products. b) The probability that a random customer is a computer programs developer if they buy software products. c) The probability that 6 out of the next 11 new customers are buying hardware products. Consider that the company income follows a normal distribution with average =10,000 S, and standard deviation-2000 S: d) Calculate the probability that the company income for October will be above 15.000 5. If the study of orders is also conducted by the manufacturer in order to keep production on target by fulfilling the companies' orders. The following table shows a detailed list of the number of items and the number of times they ordered in the study dedicated to 200 orders: Product Number of items Number of times ordered Headsets 119 20 Webcams 87 22 Keyboards 78 24 RAM sticks 63 62 SSDs 66 28 Other 43 44 Based on the study conducted, what is the expected number of items to be ordered next? 6. Based on your understanding of Prime Numbers and its importance, create a detailed report discussing one application of using Prime Numbers in the Computing field and the reason behind using them rather than other numbers. 7. Assess the application of probability theories in hashing and load balancing techniques by explaining both techniques and how probability theories can work for it with an example