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Get college assignment help at uniessay writers Alice thinks of a number that is either -1 or 1 with equal probability. She tells this number to Tom who is supposed to relay the number to Bob. However, it is known that Tom lies with probability p, where 0 <= p <= 1. For example, suppose that Alice told the number 1 to Tom, Tom will tell the number -1 to Bob with probability p, or the number 1 to Bob with probability 1- p. (a) Determine the MAP decision rule that Bob will employ to guess the number Alice chose. Draw a figure to illustrate the decision rule. (Hint: Consider each of the two cases p 0.5 separately.) (b) What is the probability of error, i.e. what is the probability that Bob guesses wrongly. (c) For what value of p will the probability of error be the largest? Justify your answer.

The block B is suspended from a cable that is attached to the block at E, wraps around three pulleys, and is tied to the back of a truck. If the truck starts from rest when xD is zero, and moves forward with a constant acceleration of aD = 5 m/s2, determine the speed of the block at the instant xD = 3 m.

a.Explain in around 100 words why burning wood has advantages over coal in respect of greenhouse gas emissions. (4 marks) b.If the heat of combustion of the wood is 9.8 MJ kg–1 and the power station will generate electricity with an efficiency of 31% when burning wood, calculate how much electricity can be produced (in units of MW) if the station burns 10 tonnes of wood per hour. Give your final answer to 1 decimal place. (6 marks) c.How much wood would need to be burned per hour to maintain an output of 500 MW from the power? Give your answer to 2 significant figures. (2 marks) d.The wood is to be stored under cover and the plant operators wish to keep two weeks supply of wood on site. If the bulk density of the wood is 300 kg m-3, calculate the minimum volume of storage that will be required for the 500 MW plant. (3 marks)

Students are divided into groups of three or four. Each member in a group is required to submit a comprehensive report for the Superpave mix design and a similar report for the Marshall mix design. All of the laboratory procedures follow both the American Association of State Highway and Transportation Officials (AASHTO) and the American Society for Testing and Materials (ASTM). The following subsections summarize the viscosity test and the Marshall mix design procedure with samples of the students work when applicable. Viscosity of the asphalt Asphalt cement can be graded using a special designation which starts with the letters “PG”, that stands for Performance Graded and is followed by two numerical values which represent temperatures for the high and low temperature grade, such as PG 64-22. For this binder, “64” is the high temperature grade and is the 7-day maximum pavement design temperature in degrees centigrade for the pavement temperature. The low temperature grade, “-22,” is the minimum pavement design temperature in degrees centigrade considered for the design. PG 64-22 is the asphalt cement used in this laboratory. The first test conducted in the laboratory is the measurement of the viscosity of the asphalt that will be used in preparing the HMA specimen so that temperature ranges of mixing and compaction of the HMA can be determined. The procedure is given to the students as a summary of the detailed procedure stated in “ASTM D4402 – Viscosity Determinations of Unfilled Asphalt Using the Brookfield Thermosel Apparatus”. Students are required to report the results of their viscosity measurments at 135° C and 165° C respectively and plot the viscosity vs temperature on a semilog scale. The desired viscosity range for mixing is between 0.15 and 0.19 Pa-s and 0.25 and 0.31 Pa-s for compaction. Figure 7 shows an example of the students’ results for viscosity test. For the chart shown, mixing temperature range is found to be (146-151) ° C and compaction temperature is found as (158-163) ° C. Results of a viscosity test to determine the mixing and compaction temperature Marshall mix design Marshall mix design is one of the oldest design methods used. Developed by Bruce Marshall for the Mississippi Highway Department in the late 30’s, this method is still widely used by most states. The Marshall method criteria allows the engineer to choose an optimum asphalt content to be added to specific aggregate blend to a mix where the desired properties of density, stability and flow are met. The Marshall method uses standard HMA samples that are 4 inches in diameter and 2 1/2 inches high. The preparation procedure is carefully specified, and involves heating, mixing, and compacting asphalt/aggregate mixtures. Once prepared, the samples are subjected to a density-voids analysis and to a stability-flow test. The procedure is given to the students as a summary of the detailed procedure stated in: “ASTM D1559-Resistance to Plastic Flow of Bituminous mixtures using Marshall Apparatus”, “ASTM D2726 Bulk Specific Gravity of Compacted Bituminous Mixtures”, and ” ASTM D 1559 Marshall stability and flow of asphalt concrete”. All materials for the asphalt laboratory are donated by local companies and vendors. Four different types of aggregates are used for the trial blend: #7 Gravel (58%), Manufactured Sand (7%), #10 soft volcanic materials (25%), and Natural sand (10%). They are placed in the oven to dry to a constant temperature at 165° C. Figure 8-a shows the aggregates used in the laboratory. Due to a tight laboratory schedule, aggregate proportions, specific gravities, grain size distribution, and other aggregate properties are obtained from the aggregate provider. Students are already familiar-from previous courses- with the basic tests that determine aggregate properties. The asphalt binder used is a PG 64-22 and shown in Figure 8-b. Three specimens are prepared at each of the four percentages of the asphalt at 4.5%, 5.0%, 5.5%, and 6.0% (Percentage of weight of the total mixture). The heated aggregates and the asphalt cement are mixed thoroughly in the mixer as seen in Figure 8-c. Each mix is prepared to weigh 2200 grams for each specimen. A portion of the loose mix (1000 g) is used to establish the maximum specific gravity (Gmm) test (Rice test) and the rest of the loose mix are poured in the 4 in mold. The Gmm test is conducted following the AASHTO T 209-94 “Theoretical Maximum Specific Gravity and Density of Bituminous Paving Mixtures” and using the Rice test apparatus shown in Figure 2. The HMA in the mold is compacted using the Marshall compactor described previously. Both faces of the specimen are compacted with 75 blows to simulate a heavy traffic greater than 1 million Equivalent Single Axle Load (ESAL). Samples are extruded from molds and left to cool down before starting the bulk specific gravity (Gmb) test: ASTM D2726 Bulk Specific Gravity of Compacted Bituminous Mixtures. The stability and flow tests are run using the semi-circular test head in conjunction with the Marshall testing machine shown in Figure 5 above. The stability of the sample is determined at the peak load crushing the sample in the loading head in Newtons. The flow is also measured as the highest deflection at the peak load in increments of 0.01 in. (a) (b) (c) (a) 4 types of aggregate (b) Asphalt binder PG 64-22 and (c) weighing material in mixing bowl Gmm and Gmb densities are then used to calculate the volumetric parameters of the HMA. Measured void expressions are usually: Air voids (Va), sometimes called voids in the total mix (VTM), Voids in the mineral aggregate (VMA), and Voids filled with asphalt (VFA). Equations 1, 2, and 3 show how to calculate the volumetric parameters Where, Pb is the percentage of binder content used and Gsb is the bulk specific gravity for the blended aggregate. …equation (1) …equation (2) …equation (3) The optimum asphalt binder content is finally selected based on the combined results of Marshall Stability and flow, density analysis and void analysis. Plots of asphalt binder content versus measured values of air voids, unit weight, flow, Marshall stability, %VFA, and %VMA are generated. Best fit of the plotted points generally have the trends shown in Figure 9. Optimum asphalt content is selected corresponding to air voids of 4%. The values of the other properties at this percentage of asphalt binder are determined and compared to specifications. Example of specifications used is shown in Table1. To complete the Marshall Mix design, students are required to write a detailed report using the results of the work done with a discussion of the results and conclusions drawn. Students are also required to complete standard forms for the measurements and calculations obtained through the design process. Asphalt binder % vs measured values Table 1 Typical Marshall Design Criteria [AI, 2] Mix Criteria Light Traffic (106 ESALs) Min. Max. Min. Max. Min. Max. Compaction (number of blows on each end of the sample) 35 50 75 Stability 2224 N (500 lbs.) 3336 N (750 lbs.) 6672 N (1500 lbs.) Flow (0.25 mm (0.01 in)) 8 20 8 18 8 16 Percent Air Voids 3 5 3 5 3 5

3. [M, None, 4.x]Consider a CMOS inverter followed by a wire of length L. Assume that in the reference design, inverter and wire contribute equally to the total propagation delay tpref. You may assume that the transistors are velocity-saturated. The wire is scaled in line with the ideal wire scaling model. Assume initially that the wire is a local wire. a. Determine the new (total) propagation delay as a a function of tpref, assuming that technology and supply voltage scale with a factor 2. Consider only first-order effects. b. Perform the same analysis, assuming now that the wire scales a global wire, and the wire length scales inversely proportional to the technology.

If a meter’s range selection switch is set to the R 10 range and the meter reading is 22 , what is the actual measured resistance of the circuit? A. 2.2 C. 220 B. 22 D. 2,200

A pressurized oil reservoir surrounds the centre section BC of a metal rod AD. There are O-ring seals at B and C to allow the rod to slide longitudinally as needed. The ends of the rod A and D are fixed to rigid supports (not shown in the diagram). Lengths BC and AD are 12 inches and 20 inches respectively, and the rod diameter is 1.5 inches. E = 23 x 106 psi and v = 0.29. For an oil pressure p = 619 psi, what is the longitudinal stress in the rod? (If you wish, you may assume that the rod is 1.5 inches square instead of circular. The computer will accept either answer.) Give the answer in psi. Figure for question in the attachment

In the network shown, you can choose RL. Given VS=9 V, α=4, R1=4 kΩ and R2=5 kΩ, what is the maximum power you can transfer to RL (in mW)?

4. Read a short wav file into MATLAB and pass it through a digital IIR bandstop filter with specifications Approximation: Butterworth Lower passband cutoff frequency: 500 Hz Upper passband cutoff frequency: 2000 Hz Lower stopband cutoff frequency: 1000 Hz Upper stopband cutoff frequency: 1500 Hz Maximum loss in the passband: 2dB (a) Play the sound before and after the filter. (b) Plot the waveforms in the time domain before and after the filter. (c) Plot the spectrums (fft magnitude) before and after the filter. (d) Plot the impulse response, magnitude response, phase response, pole-zero diagram of the filter.

. In a bike speedometer the wheel diameter is 80cm what is the frequency of velocity sensor, which gives 1 pulse per rotation of wheel at a speed of 80Km/H?

Get college assignment help at uniessay writers simply supported beam (L1 L2) m long carries a point load (Gk = A kN, Qk = B kN) at mid-span and its self-weight with fire protection casing gk = g kN/m, and variable action qk = q kN/m as shown. The beam is laterally restrained at the ends and at the points of application of the load. The steel grade is S275. Design a MOST economical Universal Beam size which can carry such actions. Calculate the classification, bending and shear resistances. Also calculate the deflection of the beam to check that it complies with the design limit of L/200. Only variable actions are required for deflection check.

A simply supported beam (L1 L2) m long carries a point load (Gk = A kN, Qk = B kN) at mid-span and its self-weight with fire protection casing gk = g kN/m, and variable action qk = q kN/m as shown. The beam is laterally restrained at the ends and at the points of application of the load. The steel grade is S275. Design a MOST economical Universal Beam size which can carry such actions. Calculate the classification, bending and shear resistances. Also calculate the deflection of the beam to check that it complies with the design limit of L/200. Only variable actions are required for deflection check.

An aluminum rod width w = 2.68 inches and thickness t inches, has a 1 inch hole drilled through its centre. Determine the required thickness t so that the rod can support an axial load P = 2,954 lbs with a failure stress of sigma = 24,967 psi and a safety factor of 2.1. Give the answer in inches. Figure for question is in the attached file

Process control A process with Gp= 2/(2s 1) and Gd=1/(2s 1) experiences a disturbance step change of magnitude 5. The SP remains constant. If a P-controller alone with Kc=1 is used and Ga=Gs=1, then what is the output variable, delta Y(t) versus time? Delta Y(s) = Gd/(Gp*Ga**Gc*Gs 1) * 5/S

A Pitot-‐static probe connected to a water manometer is used to measure the velocity of air. Determine the velocity of the air taking the density of the air to be 1.25 kg/m3

A stationary radar operator determines that a ship is 19 km south of him. An hour later the same ship is 16 km southeast. If the ship moved at constant speed and always in the same direction, what was its velocity during this time? (Hint: Take the origin to be the location of the radar.)

for a neutral surface layer, plot wind speed against height on linear and on semi-log graphs for friction velocity of .5 m/sec and aerodynamic roughness length (m) of: a. 0.001 c. 0.005 d. 0.01 e. 0.02 b. 0.002 f. 0.05 g. 0.1 h. .02

Hi could you please work on all of the problems? thank you

Rod AB is bent into the shape of an arc of circle and is lodged between two pegs D and E. It supports a load P at end B. Neglecting friction and the weight of the rod, determine the distance c corresponding to equilibrium when a 20 mm and R 100 mm.

What is the pH of the solution created by combining 0.90 mL of the 0.10 M NaOH(aq) with 8.00 mL of the 0.10 M HCl(aq)? with 8.00 mL of the 0.10 M HC2H3O2(aq)?

Consider the Bayesian framework where a radio transmitter sends one of four signals on the complex plane: f {1 j, 1 – j,-1 j, -1 – j}, with equal probability (i.e., 0:25 each). The signal is corrupted with noise. Assume that the real and complex parts are independently corrupted with noise, each of which is modeled as a Gaussian random variable with mean zero and unit variance (i.e., variance equals one). Determine the optimal receiver for this system which minimizes the probability of error (derive all expressions involved). Also qualitatively draw the form of the decision rule on the complex plane.

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November 3, 2019