Question Patients arrive randomly at an eye care clinic for eye exam. Suppose that there is only one optometrist. The time required for the exam varies from patient to patient. Arrivals have been found to follow the Poisson process (i.e., exponentially distributed inter-arrival times), and the service times follow the exponential distribution. The average arrival rate is 12 patients per hour, and the average service rate is 20 patients per hour. A patient wait in a waiting room until the optometrist is ready to see them. How many patients, on the average, will be in the waiting room? 4. 1.5 3 0.9 36

Starbucks has a large, global supply chain that must efficiently supply over 17,000 stores. Although the stores might appear to be very similar, they are actually very different. Depending on the location of the store, its size, and the profile of the customers served, Starbucks management configures the store offerings to take maximum advantage of the space available and customer preferences. Starbucks' actual distribution system is much more complex, but for the purpose of our exercise let's focus on a single item that is currently distributed through five distribution centers in the United States. Our item is a logo-branded coffeemaker that is sold at some of the larger retail stores. The coffeemaker has been a steady seller over the years due to its reliability and rugged construction. Starbucks does not consider this a seasonal product, but there is some variability in demand. Demand for the product over the past 13 weeks is shown in the following table. (week –1 is the week before week 1 in the table, -2 is two weeks before week 1, etc.). Management would like you to experiment with some forecasting models to determine what should be used in a new system to be implemented. The new system is programmed to use one of two forecasting models: simple moving average or exponential smoothing. 8 WEEK -5 Atlanta 45 Boston 60 Chicago 62 Dallas 40 LA 44 -4 35 24 23 35 42 -3 30 50 71 40 52 -2 55 40 43 64 45 -1 35 35 45 44 36 1 30 30 45 28 34 2 45 34 33 42 42 3 35 40 23 34 50 4 30 41 53 40 44 5 54 45 48 6 28 48 72 62 72 7 20 54 64 68 40 58 20 27 64 34 9 46 60 25 52 44 10 36 45 96 40 38 11 24 30 34 38 48 12 56 46 45 45 55 13 41 52 47 42 48 50 46 Total 251 159 243 247 195 167 196 182 208 243 282 246 203 227 255 174 247 230 a. Consider using a simple moving average model. Experiment with models using five weeks' and three weeks' past data. (Round your answers to 2 decimal places.) 3-week MA Week ATL BOS CHI DAL LA Total 1 2 3 4 5 6 7 8 9 10 11 12 13

Shelly and Kelly Macdonald met up with Sarah and Tara MacNeill to go fishing in Cape Breton. They found two pools in a stream containing speckled trout (assume equal variance), with the Macdonalds at one pool and the MacNeills at the other, and at the end of the day each team had caught (and released unharmed) 5 fish. For each fish they recorded the length and weight, and the data on length (in cm) is summarized below (Give the answers to 2 places past decimal) Team Macdonald MacNeill Mean 18.1 20.35 Std.Dev 1.4 1.9 a.) To test whether or not the fish have the same mean size in the two pools, the null hypothesis will be: HO: 1-X 2 = -2.25 HO: p1-y2 = -2.25 HO: X 1-8 2 = 0 HO: 1-2 = 0 # Tries 0/1 b.) The alternative hypothesis for this test will be: Ha: * 1- 2 = -2.25 Ha: p1-12 + -2.25 Ha: 81-X 2 = 0 Ha: p1-42 = 0 1236 Tries 0/1 c.) What is the pooled estimate of the variance? 1202 Tries 0/5 d.) Compute the value of the test statistic. 1 Tries 0/5

A 50-g weight is hung at the 20-cm mark of a meterstick and a 100-g weight is hung at the 70-cm mark. At what point must the meterstick be supported for it to be in rotational equilibrium? The weight of the meterstick is negligible. O at the 56.67-cm mark. at the 46.67 cm mark. O at the 53.33-cm mark. O at the 43.33 cm mark.

Part A The post is made of Douglas fir and has a diameter of 100 mm (Figure 1) It is subjected to the load of 20 kN and the soil provides a frictional resistance distributed around the post that is triangular along its sides that is, it varies from w=0 kN/mat y=0 m to w= 15 kN/m at y = 2 m. Neglect the weight of the post Determine the force at its bottom needed for equilibrium Express your answer to three significant figures and include appropriate units. HÅ ? Value Units Submit Request Answer Figure 1 of 1 Part B 20KN What is the displacement of the top of the post with respect to a bottom B? Express your answer to three significant figures and include appropriato unito, ? 2 m 0 = Value Units 12 kN/m Submit Request Answer

​​​​​​​ The bar has a cross-sectional area of \( 1900 \mathrm{~mm}^{2} \) and \( E=250 \mathrm{GPa} \). (Figure 1) Determine the displacement of its end \( A \) when it is subjected to the distributed loading. Express your answer to three significant figures and include the appropriate units. Enter negative value in the case of contraction and positive value in the case of elongation. Figure 1 of 1 X Incorrect; Try Again; 4 attempts remaining

      please solve all tasks A car rental company owns five types of cars: Small, Economy, Standard, Family, Exclusive. The prices for per day rent for each type of the cars aregiven in British pounds by the \( 1 \times 5 \) matrix \[ \mathbf{p}=\left(\begin{array}{lllll} 15 & 19 & 21 & 28 & 37 \end{array}\right) \] The care demand for five days of a week ahead is given by the matrix \[ \mathbf{A}=\left(\begin{array}{ccccc} 2 & 4 & 3 & 1 & 3 \\ 4 & 3 & 3 & 5 & 3 \\ 10 & 11 & 8 & 6 & 9 \\ 4 & 3 & 2 & 3 & 4 \\ 2 & 1 & 3 & 2 & 1 \end{array}\right) \] Calculate the total income in British pounds of the company for this week. a. 10500 b. 3420 C. 2242 d. 4520 Consider the clockwise rotation \( T \) of \( \mathbb{R}^{2} \) by the angle of \( 30^{\circ} \). Mark only correct statements. a. The matrix of \( T \) is \( \left(\begin{array}{cc}-\frac{\sqrt{3}}{2} & \frac{1}{2} \\ \frac{1}{2} & -\frac{\sqrt{3}}{2}\end{array}\right) \) b. The matrix of \( T \) is symmetric. c. The matrix of \( T \) is \( \left(\begin{array}{rr}\frac{\sqrt{3}}{2} & -\frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) d. The matrix of \( T \) is \( \left(\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) e. The matrix of \( T \) is \( \left(\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) A company manufactures three types of perfume-refreshing \( (R) \), standard \( (S) \), and exclusive \( (E) \), in four factories in different countries \( A \), B, C, D. The distributions of costs in producing a single piece of perfume are given in the left table below. The number of pieces of perfume produced in one month at the four locations are given in the right table. a. Location A materials: \( \$ 4500 \) b. Location B: labor \( \$ 8000 \) c. Location A: labor \( \$ 14000 \) d. Location D: materials \( \$ 25000 \) e. Location C: overheads \( \$ 16000 \)