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Probability And Statistics For Engineering And The Sciences 9th Edition Jay L. Devore - Solutions

Reconsider the situation described in Exercise 7, in which x = accelerated strength of concrete and y = 28day cured strength. Suppose the simple linear regression model is valid for x between 1000 and 4000 and that β1 = 1.25 and ( = 350. Consider an experiment in which n = 7, and the x values at
During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. The article "Composition Optimization of High-Strength Steels for Sulfide Cracking Resistance Improvement" (Corrosion Science, 2009: 2878-2884) reported on a study in which the composition
Exercise 16 of Section 12.2 gave data on x = rainfall volume and y = runoff volume (both in m3). Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff, and then calculate a confidence interval for the true average change in runoff
Exercise 15 of Section 12.2 included Minitab output for a regression of flexural strength of concrete beams on modulus of elasticity. a. Use the output to calculate a confidence interval with a confidence level of 95% for the slope β1 of the population regression line, and interpret the resulting
Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article
How does lateral acceleration-side forces experienced in turns that are largely under driver control-affect nausea as perceived by bus passengers? The article "Motion Sickness in Public Road Transport: The Effect of Driver, Route, and Vehicle" (Ergonomics, 1999: 1646-1664) reported data on x =
Mist (airborne droplets or aerosols) is generated when metalremoving fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. The article "Variables Affecting Mist
Magnetic resonance imaging (MRI) is well established as a tool for measuring blood velocities and volume flows. The article "Correlation Analysis of Stenotic Aortic Valve Flow Patterns Using Phase Contrast MRI," referenced in Exercise 1.67, proposed using this methodology for determination of valve
Refer to the data on x = liberation rate and y = NOx emission rate given in Exercise 19.a. Does the simple linear regression model specify a useful relationship between the two rates? Use the appropriate test procedure to obtain information about the P-value, and then reach a conclusion at
Carry out the model utility test using the ANOVA approach for the filtration rate-moisture content data of Example 12.6. Verify that it gives a result equivalent to that of the t test?
The accompanying data on y = ammonium concentration (mg/L) and x = transpiration (ml/h) was read from a graph in the article "Response of Ammonium Removal to Growth and Transpiration of Juncus effusus During the Treatment of Artificial Sewage in Laboratory-Scale Wetlands" (Water Research, 2013:
Use the rules of expected value to show that β0 is an unbiased estimator for β0 (assuming that β1 is unbiased for β1)?
a. Verify that E(1) = β1 by using the rules of expected value from Chapter 5. b. Use the rules of variance from Chapter 5 to verify the expression for V (1) given in this section?
Verify that if each xi is multiplied by a positive constant c and each yi is multiplied by another positive constant d, the t statistic for testing H0: β1 = 0 versus Ha: β1 ≠ 0 is unchanged in value (the value of will change, which shows that the magnitude of b ^ 1 is not by itself indicative
The probability of a type II error for the t test for H0: Î²1 = Î²10 can be computed in the same manner as it was computed for the t tests of Chapter 8. If the alternative value of Î²1 is denoted by Î²'1, the value ofIs first calculated, then the
Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in Exercise 15 of Section 12.2 resulted in = 7.592, sY^ = .179 when x = 40 and y^ = 9.741, sY^ = .253 for x = 60. a. Explain why sY ^ is larger when x = 60 than when x
Reconsider the filtration rate-moisture content data introduced in Example 12.6 (see also Example 12.7). a. Compute a 90% CI for β1 + 125 β1, true average moisture content when the filtration rate is 125. b. Predict the value of moisture content for a single experimental run in which the
Astringency is the quality in a wine that makes the wine drinker's mouth feel slightly rough, dry, and puckery. The paper "Analysis of Tannins in Red Wine Using Multiple Methods: Correlation with Perceived Astringency" (Amer. J. of Enol. and Vitic., 2006: 481-485) reported on an investigation to
The simple linear regression model provides a very good fit to the data on rainfall and runoff volume given in Exercise 16 of Section 12.2. The equation of the least squares line is y = 21.128 + .82697x, r2 = .975, and s = 5.24.a. Use the fact that sY^ = 1.44 when rainfall volume is 40 m3 to
The catch basin in a storm-sewer system is the interface between surface runoff and the sewer. The catch-basin insert is a device for retrofitting catch basins to improve pollutantremoval properties. The article "An Evaluation of the Urban Stormwater Pollutant Removal Efficiency of Catch Basin
You are told that a 95% CI for expected lead content when traffic flow is 15, based on a sample of n = 10 observations, is (462.1, 597.7). Calculate a CI with confidence level 99% for expected lead content when traffic flow is 15?
The article "Objective Measurement of the Stretchability of Mozzarella Cheese" (J. of Texture Studies, 1992: 185-194) reported on an experiment to investigate how the behavior of mozzarella cheese varied with temperature. Consider the accompanying data on x = temperature and y = elongation (%) at
Silicon-germanium alloys have been used in certain types of solar cells. The paper "Silicon-Germanium Films Deposited by Low-Frequency Plasma-Enhanced Chemical Vapor Deposition" (J. of Material Res., 2006: 88-104) reported on a study of various structural and electrical properties. Consider the
Refer to Example 12.12 in which x = test track speed and y = rolling test speed. a. Minitab gave S 0 + 0 (45) = .120 and S 0 + 0 (47) = .186. Why is the former estimated standard deviation smaller than the latter one? b. Use the Minitab output from the example to calculate a 95% CI for expected
Plasma etching is essential to the fine-line pattern transfer in semiconductor processes. The article "Ion Beam- Assisted Etching of Aluminum with Chlorine" (J. of the Electrochem. Soc., 1985: 2010-2012) gives the accompanying data (read from a graph) on chlorine flow (x, in SCCM) through a nozzle
Consider the following four intervals based on the data of Exercise 12.17 (Section 12.2): a. A 95% CI for mean porosity when unit weight is 110 b. A 95% PI for porosity when unit weight is 110 c. A 95% CI for mean porosity when unit weight is 115 d. A 95% PI for porosity when unit weight is
The height of a patient is useful for a variety of medical purposes, such as estimating tidal volume of someone in an intensive care who requires artificial ventilation. However, it can be difficult to make an accurate measurement if the patient is confused, unconscious, or sedated. And measurement
Verify that V(0 + ix) is indeed given by the expression in the text?
The article "Bone Density and Insertion Torque as Predictors of Anterior Cruciate Ligament Graft Fixation Strength" (The Amer. J. of Sports Med., 2004: 1421-1429) gave the accompanying data on maximum insertion torque (N · m) and yield load (N), the latter being one measure of graft
The article "Behavioural Effects of Mobile Telephone Use During Simulated Driving" (Ergonomics, 1995: 2536-2562) reported that for a sample of 20 experimental subjects, the sample correlation coefficient for x = age and y = time since the subject had acquired a driving license (yr) was .97. Why do
The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. The article "Dependence of Oxidation Stability of Steam Turbine Oil on Base Oil Composition" (J. of the Society of
Toughness and fibrousness of asparagus are major determinants of quality. This was the focus of a study reported in "Post-Harvest Glyphosphate Application Reduces Toughening, Fiber Content, and Lignification of Stored Asparagus Spears" (J. of the Amer. Soc. of Hort. Science, 1988: 569-572). The
The authors of the paper "Objective Effects of a Six Months' Endurance and Strength Training Program in Outpatients with Congestive Heart Failure" (Medicine and Science in Sports and Exercise, 1999: 1102-1107) presented a correlation analysis to investigate the relationship between maximal lactate
The article "Quantitative Estimation of Clay Mineralogy in Fine-Grained Soils" (J. of Geotechnical and Geoenvironmental Engr., 2011: 997-1008) reported on various chemical properties of natural and artificial soils. Here are observations on x = cation exchange capacity (CEC, in meq/100 g) and y =
Physical properties of six flame-retardant fabric samples were investigated in the article "Sensory and Physical Properties of Inherently Flame-Retardant Fabrics" (Textile Research, 1984: 61-68). Use the accompanying data and a .05 significance level to determine whether a linear relationship
The accompanying data on x = UV transparency index and y = maximum prevalence of infection was read from a graph in the article "Solar Radiation Decreases Parasitism in Daphnia" (Ecology Letters, 2012: 47-54):Summary quantities include Sxx = 25.5224, Syy = 5593.0588, and Sxy = 264.4882. a.
Torsion during hip external rotation and extension may explain why acetabular labral tears occur in professional athletes. The article "Hip Rotational Velocities During the Full Golf Swing" (J. of Sports Science and Med., 2009: 296-299) reported on an investigation in which lead hip internal peak
Consider a time series-that is, a sequence of observations X1, X2,... obtained over time-with observed values x1, x2,..., xn. Suppose that the series shows no upward or downward trend over time. An investigator will frequently want to know just how strongly values in the series separated by a
A sample of n = 500 (x, y) pairs was collected and a test of H0: ( = 0 versus Ha: ( ≠ 0 was carried out. The resulting P-value was computed to be .00032. a. What conclusion would be appropriate at level of significance .001? b. Does this small P-value indicate that there is a very strong linear
The appraisal of a warehouse can appear straightforward compared to other appraisal assignments. A warehouse appraisal involves comparing a building that is primarily an open shell to other such buildings. However, there are still a number of warehouse attributes that are plausibly related to
Refer to the previous exercise, which gives data on truss heights for a sample of warehouses and the corresponding sale prices. a. Estimate the true average change in sale price associated with a one-foot increase in truss height, and do so in a way that conveys information about the precision of
The article "Some Field Experience in the Use of an Accelerated Method in Estimating 28-Day Strength of Concrete" (J. of Amer. Concrete Institute, 1969: 895) considered regressing y = 28day standard-cured strength (psi) against x = accelerated strength spsid. Suppose the equation of the true
Forensic scientists are often interested in making a measurement of some sort on a body (alive or dead) and then using that as a basis for inferring something about the age of the body. Consider the accompanying data on age (yr) and % D-aspertic acid (hereafter %DAA) from a particular tooth ("An
Phenolic compounds are found in the effluents of coal conversion processes, petroleum refineries, herbicide manufacturing, and fiberglass manufacturing. These compounds are toxic, carcinogenic, and have contributed over the past decades to environmental pollution of aquatic environments. In one
The SAS output at the bottom of this page is based on data from the article "Evidence for and the Rate of Denitrification in the Arabian Sea" (Deep Sea Research, 1978: 431-435). The variables under study are x = salinity level (%) and y 5 nitrate level (mM/L). a. What is the sample size n? b.
The presence of hard alloy carbides in high chromium white iron alloys results in excellent abrasion resistance, making them suitable for materials handling in the mining and materials processing industries. The accompanying data on x = retained austenite content (%) and y = abrasive wear loss
The accompanying data was read from a scatter-plot in the article "Urban Emissions Measured with Aircraft" (J. of the Air and Waste Mgmt. Assoc., 1998: 16-25). The response variable is (NOy, and the explanatory variable is DCO.a. Fit an appropriate model to the data and judge the utility of the
An investigation was carried out to study the relationship between speed (ft/sec) and stride rate (number of steps taken/sec) among female marathon runners. Resulting summary quantities included n = 11, ((speed) = 205.4, ((speed) = 205.4, ((speed)2 = 3880.08, ((rate) = 35.16, ((rate)2 = 112.681,
"Mode-mixity" refers to how much of crack propagation is attributable to the three conventional fracture modes of opening, sliding, and tearing. For plane problems, only the first two modes are present, and the mode-mixity angle is a measure of the extent to which propagation is due to sliding as
Open water oil spills can wreak terrible consequences on the environment and be expensive to clean up. Many physical and biological methods have been developed to recover oil from water surfaces. The article "Capacity of Straw for Repeated Binding of Crude Oil from Salt Water and Its Effect on
In Section 12.4, we presented a formula for V(0 + 1x*) and a CI for 0 + 1x*. Taking x* = 0 gives (20 and a CI for 0. Use the data of Example 12.11 to calculate the estimated standard deviation of 0 and a 95% CI for the y-intercept of the true regression line?
Show that SSE = Syy - 1 Sxy, which gives an alternative computational formula for SSE?
Referring to Exercise 7, The article "Some Field Experience in the Use of an Accelerated Method in Estimating 28-Day Strength of Concrete" (J. of Amer. Concrete Institute, 1969: 895) considered regressing y = 28day standard-cured strength (psi) against x = accelerated strength spsid. Suppose the
Suppose that x and y are positive variables and that a sample of n pairs results in r ≈ 1. If the sample correlation coefficient is computed for the (x, y2) pairs, will the resulting value also be approximately 1? Explain.
Let sx and sy denote the sample standard deviations of the observed x's and y's, respectively [that is, s2x = ((xi - xÌ…)2 / (n - 1) and similarly for s2y].a. Show that an alternative expression for the estimated regression line y = 0 + 1x isb. This expression for the regression line
Verify that the t statistic for testing H0: β1 = 0 in Section 12.3 is identical to the t statistic in Section 12.5 for testing H0: ( = 0?
Use the formula for computing SSE to verity that r2 = 1 - SSE / SST?
In biofiltration of wastewater, air discharged from a treatment facility is passed through a damp porous membrane that causes contaminants to dissolve in water and be transformed into harmless products. The accompanying data on x = inlet temperature (°C)
Normal hatchery processes in aquaculture inevitably produce stress in fish, which may negatively impact growth, reproduction, flesh quality, and susceptibility to disease. Such stress manifests itself in elevated and sustained corticosteroid levels. The article "Evaluation of Simple Instruments for
The article "Evaluating the BOD POD for Assessing Body Fat in Collegiate Football Players" (Medicine and Science in Sports and Exercise, 1999: 1350-1356) reports on a new air displacement device for measuring body fat. The customary procedure utilizes the hydrostatic weighing device, which measures
Reconsider the situation of Exercise 73, in which x = retained austenite content using a garnet abrasive and y = abrasive wear loss were related via the simple linear regression model Y = Î²0 + Î²1x + Îµ. Suppose that for a second type of abrasive, these variables
The flow rate y (m3 / min) in a device used for air-quality measurement depends on the pressure drop x (in. of water) across the device's filter. Suppose that for x values between 5 and 20, the two variables are related according to the simple linear regression model with true regression line y =-
Suppose the variables x = commuting distance and y = comuting time are related according to the simple linear regression model with s = 10. a. If n = 5 observations are made at the x values x1 = 5, x2 = 10, x3 = 15, x4 = 20, and x5 = 25, calculate the standard deviations of the five corresponding
a. Show that Σnn=1 ei when the ei's are the residuals from a simple linear regression. b. Are the residuals from a simple linear regression independent of one another, positively correlated, or negatively correlated? Explain. c. Show that Σnn=1xiei for the residuals from a simple linear
a. Express the ith residual Yi - Ŷi (where Ŷi = β̂0 + β̂1xi) in the form ΣjYj, a linear function of the Yj's. Then use rules of variance to verify that V(Yi - Ŷ) id is given by Expression (13.2). b. It can be shown that Ŷi and Yi - Ŷi (the ith predicted value and residual) are
a. Could a linear regression result in residuals 23, -27, 5, 17, -8, 9, and 15? Why or why not? b. Could a linear regression result in residuals 23, -27, 5, 17, -8, -12, and 2 corresponding to x values 3, -4, 8, 12, -14, -20, and 25? Why or why not?
Recall that Î²Ì‚0 + Î²Ì‚1x has a normal distribution with expected value Î²0 + Î²1x and varianceso that has a standard normal distribution. If S = (ˆšSSE/n - 2) is substituted for s, the resulting variable has a t
If there is at least one x value at which more than one observation has been made, there is a formal test procedure for testing H0: µY.x = Î²0 + Î²1x for some values Î²0, Î²1 (the true regression function is linear) versus Ha: H0 is not true (the
No tortilla chip aficionado likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture. The following data on x 5 frying time (sec) and y 5 moisture content (%) appeared in the article "Thermal and Physical Properties of
Polyester fiber ropes are increasingly being used as components of mooring lines for offshore structures in deep water. The authors of the paper "Quantifying the Residual Creep Life of Polyester Mooring Ropes" (Intl. J. of Offshore and Polar Exploration, 2005: 223-228) used the accompanying data as
The following data on mass rate of burning x and flame length y is representative of that which appeared in the article "Some Burning Characteristics of Filter Paper" (Combustion Science and Technology, 1971: 103-120):a. Estimate the parameters of a power function model.b. Construct diagnostic
Failures in aircraft gas turbine engines due to high cycle fatigue is a pervasive problem. The article "Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys" (J. of Engineering for Gas Turbines and Power, 2002: 161-176) gave the accompanying data
Thermal endurance tests were performed to study the relationship between temperature and lifetime of polyester enameled wire ("Thermal Endurance of Polyester Enameled Wires Using Twisted Wire Specimens," IEEE Trans. Insulation, 1965: 38-44), resulting in the following data.a. Does a scatterplot of
The x values and standardized residuals for the chlorine flow/etch rate data of Exercise 52 (Section 12.4) are displayed in the accompanying table. Construct a standardized residual plot and comment on its appearance.
Exercise 14 presented data on body weight x and metabolic clearance rate/body weight y. Consider the following intrinsically linear functions for specifying the relationship between the two variables: (a) ln(y) versus x, (b) ln(y) versus ln(x), (c) y versus ln(x), (d) y versus 1/x, and (e) ln(y)
Mineral mining is one of the most important economic activities in Chile. Mineral products are frequently found in saline systems composed largely of natural nitrates. Freshwater is often used as a leaching agent for the extraction of nitrate, but the Chilean mining regions have scarce freshwater
In each of the following cases, decide whether the given function is intrinsically linear. If so, identify x' and y', and then explain how a random error term e can be introduced to yield an intrinsically linear probabilistic model. a. y = 1/(α + βx) b. y = 1/(1 + eα+βx) c. y = eea+βx (a
Suppose x and y are related according to a probabilistic exponential model Y = aeβx.e, with V(e) a constant independent of x (as was the case in the simple linear model Y = β0 + β1x + e). Is V(Y) a constant independent of x [as was the case for Y = β0 + β1x + e, where V(Y) = (s2)? Explain your
Kyphosis refers to severe forward flexion of the spine following corrective spinal surgery. A study carried out to determine risk factors for kyphosis reported the accompanying ages (months) for 40 subjects at the time of the operation; the first 18 subjects did have kyphosis and the remaining 22
The article "Acceptable Noise Levels for Construction Site Offices" (Building Serv. Engr. Res. Tech., 2009: 87-94) analyzed responses from a sample of 77 individuals, each of whom was asked to say whether a particular noise level (dBA) to which he/she had been exposed was acceptable or
The article "Physical Properties of Cumin Seed" (J. of Agric. Engr. Res., 1996: 93-98) considered a quadratic regression of y 5 bulk density on x 5 moisture content. Data from a graph in the article follows, along with Minitab output from the quadratic fit.May not be copied, scanned, or duplicated,
The following data on y = glucose concentration (g/L) and x = fermentation time (days) for a particular blend of malt liquor was read from a scatterplot in the article "Improving Fermentation Productivity with Reverse Osmosis" (Food Tech., 1984: 92-96):a. Verify that a scatterplot of the data is
The viscosity (y) of an oil was measured by a cone and plate viscometer at six different cone speeds (x). It was assumed that a quadratic regression model was appropriate, and the estimated regression function resulting from the n = 6 observations was y = 2113.0937 + 3.3684x - .01780x2 a. Estimate
High-alumina refractory castables have been extensively investigated in recent years because of their significant advantages over other refractory brick of the same class-lower production and application costs, versatility, and performance at high temperatures. The accompanying data on x = $High-alumina refractory castables have been extensively investigated in recent years$
Example 12.6 presented the residuals from a simple linear regression of moisture content y on filtration rate x. a. Plot the residuals against x. Does the resulting plot suggest that a straight-line regression function is a reasonable choice of model? Explain your reasoning. b. Using s 5 .665,
The accompanying data was extracted from the article "Effects of Cold and Warm Temperatures on Springback of Aluminum-Magnesium Alloy 5083- H111" (J. of Engr. Manuf., 2009: 427-431). The response variable is yield strength (MPa), and the predictor is temperature (°C).a. What proportion of
The accompanying data on y = energy output (W) and x 5 temperature difference (Â°K) was provided by the authors of the article "Comparison of Energy and Exergy Efficiency for Solar Box and Parabolic Cookers" (J. of Energy Engr., 2007: 53-62). The article's authors fit a cubic regression model to
The following data is a subset of data obtained in an experiment to study the relationship between x = soil pH and y = A1 Concentration/EC ("Root Responses of Three Gramineae Species to Soil Acidity in an Oxisol and an Ultisol," Soil Science, 1973: 295-302):A cubic model was proposed in the
In many polynomial regression problems, rather than fitting a "centered" regression function using x' = x - xÌ…, computational accuracy can be improved by using a function of the standardized independent variable x' = (x - xÌ…)/sx, where sx is the standard deviation of the
The following data resulted from an experiment to assess the potential of unburnt colliery spoil as a medium for plant growth. The variables are x 5 acid extractable cations and y = exchangeable acidity/total cation exchange capacity ("Exchangeable Acidity in Unburnt Colliery Spoil," Nature, 1969:
The article "The Respiration in Air and in Water of the Limpets Patella caerulea and Patella lusitanica" (Comp. Biochemistry and Physiology, 1975: 407-411) proposed a simple power model for the relationship between respiration rate y and temperature x for P. caerulea in air. However, a plot of
Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction
A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x1 = distance traveled (miles) and x2 = the number of deliveries made. Suppose that the model equation is Y = 2.800 + .060x1 +
Let y = wear life of a bearing, x1 = oil viscosity, and x2 = load. Suppose that the multiple regression model relating life to viscosity and load is Y = 125.0 + 7.75x1 + .0950x2 - .0090x1x2 + e a. What is the mean value of life when viscosity is 40 and load is 1100? b. When viscosity is 30, what
Let y = sales at a fast-food outlet (1000s of $), x1 = number of competing outlets within a 1-mile radius, x2 = population within a 1-mile radius (1000s of people), and x3 be an indicator variable that equals 1 if the outlet has a drive-up window and 0 otherwise. Suppose that the true regression
The accompanying data on y = normalized energy (J/m2) and x = intraocular pressure (mmHg) appeared in a scatterplot in the article "Evaluating the Risk of Eye Injuries: Intraocular Pressure During High Speed Projectile Impacts" (Current Eye Research, 2012: 43-49); an estimated regression function
The article cited in Exercise 49 of Chapter 7 gave summary information on a regression in which the dependent variable was power output (W) in a simulated 200-m race and the predictors were x1 = arm girth (cm), x2 = excess post-exercise oxygen consumption (ml/kg), and x3 = immediate posttest
Researchers carried out a study to see how y = ultimate deflection (mm) of reinforced ultrahigh toughness cementitious composite beams were influenced by x1 = shear span ratio and x2 = splitting tensile strength (MPa), resulting in the accompanying data ("Shear Behavior of Reinforced Ultrahigh
As the air temperature drops, river water becomes supercooled and ice crystals form. Such ice can significantly affect the hydraulics of a river. The article "Laboratory Study of Anchor Ice Growth" (J. of Cold Regions Engr., 2001: 60-66) described an experiment in which ice thickness (mm) was
When the model Y = β0 = β1x1 + β2x2 + β3x21 + β4x22 + β5x1x2 + ε is fit to the data of Exercise 49, the resulting value of SSE is 28.947. Given that the predictors x1, x2, and x1x2 remain in the model, does either of the quadratic predictors x21 or x22 provide additional useful information?

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