Question I need help with a, b, and c. I don't know how to do them. Please, help.1. A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered:A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes.A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes.A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money for customers arriving at the window. The average service time for this alternative is 2 minutes for each server.For each of the three design alternatives, answer the following questions. Then, recommend one of the design options.a. What is the probability that no cars are in the system?b. What is the average number of cars waiting for service?c. What is the average number of cars in the system?

A data related to air pollution in 10 U.S. cities. The dependent variable Y is the annual mean concentration of sulfur dioxide, in micrograms per cubic meter. The explanatory variable X records the number of manufacturing enterprises employing 20 or more workers. Below is R output of the relationship between X and Y. a) Write the regression equation with parameters from the R output. b) Suppose that the number of manufacturing enterprises employing 20 or more workers in Irvine is 250, could you predict that the annual mean concentration of sulfur dioxide in Irvine? c) What is the residual if in Irvine the annual mean concentration of sulfur dioxide is 15 micrograms per cubic meter. d) What is the value of the correlation coefficient? e) Calculate a 95% confidence interval for the slope of the model. f) Based on the confidence interval, is there a linear relationship between X and Y? Adata related to air pollution in 10 U.S. cities. The dependent variable Y is the annual mean concentration of sulfur dioxide, in micrograms per cubic meter. The explanatory variable X records the number of manufacturing enterprises employing 20 or more workers. Below is Routput of the relationship between X and Y. Coefficients: Estimate Std. Error t value Pro> tl) (Intercept) 9.4764 9.6266 0.98 0.354 2.0315 0.0070 4.51 0.CO2 ** X Signif. codes: 9 ****' 0.001 ***' 0.01 **' 0.05, 0.1' '1 Residual standard error: 17.9 on 8 degrees of freedom Multiple R-squared: 0.717, Adjusted R-squared: 0.682 F-statistic: 20.3 on 1 and 8 DF, p-value: 0.00198

Help please A thin walled cylindrical pressure vessel is subjected to an internal pressure which varies from 750 KPa to 3550 KPa continuously. The diameter of the shell is 1.5 m. Find the required thickness of the cylinder wall based on yield point of 480 MPa, net endurance limit of 205 MPa and a factor of safety of 2.5. A camshaft 19 mm. in diameter is mounted on ball bearings and carries a cam midway from the bearings. The follower, which weighs 2.8 KN, is out of adjustment so that impact is produced when it is contacted by the cam. The height h of fall equals 0.254 mm. The shaft is made of AISI C1045 steel. Determine the maximum bending stress in the shaft.

Consider the following diagram: Internet Modem Wireless AP Switch Wireless AP DO Wireless AP Server 2.1 Using a table, compare 4 types of area networks. Consider the size of the network and the transmission media that is most likely to be found in each type of network. (8) 2.2 Based on the information given in 2.1, which type if network is shown in the Consider the following diagram: Internet Modem Wireless AP Switch Wireless AP DO Wireless AP Server 2.1 Using a table, compare 4 types of area networks. Consider the size of the network and the transmission media that is most likely to be found in each type of network. (8) 2.2 Based on the information given in 2.1, which type if network is shown in the diagram? Motivate your (2) answer. 2.3 This network has wireless access points. Compare three modulation techniques, using sketches, that could be used by these access points to transmit data. Use the bit-stream 10000101111. (6)

Biostatistics ESSAY A firm investigates the length of telephone conversations of their office staff. Ten consecutive conversations had lengths, in minutes: 10.7, 9.5, 11.1, 7.8, 11.9, 4.1, 10.0, 9.2, 6.5, 9.2. Derive a 95% confidence interval for the mean conversation length. Test whether the mean length of a conversation is eight minutes.(25 MARKS)

P3.5 The sales revenue, food cost of sales, and guests served for a small fast- food carryout division of a restaurant for the past six months are given below. Sales Month Cost of Revenue Guests Served Sales, Food 1 2. 4 $258,200 274,800 285,600 289,400 298,300 304,600 $ 96,200 104,300 110,500 113,100 118,900 123,700 10,200 10,400 10,300 10,100 10,400 10,500 6 For each of the six months calculate average check and average costs of sales food. Using these averages, calculate an index number. Set the in- dex for month 1 at 100 and complete index numbers for the remaining five months. With the index numbers identified, convert sales revenue and cost of sales food from historic to current dollars.

A cylindrical rock sample has a length of 6 cm, a diameter of 4 cm, and a dry weight of 166.4 g. When fully saturated with an oil of density 0.85 g/cm3, the weight of this sample is 176.9 g. Assuming constant temperature, find: i) The porosity of the sample ii) The pore compressibility of the sample, given that 0.2 cm of oil leaves the sample when a pressure of 3200 psig is applied on it iii) The amount of oil that can be extracted from the sample when a pressure of 2000 psig is applied on it