2.4.5. Let X be a metric space. Given x E X, prove that {x} is a closed subset of X.

Advanced Math Question

Several states have argued that the 65-mph speed limit has no justification and have refused to enforce it. The federal Department of Transportation (DOT) believes that the 65-mph limit saves lives. To illustrate its contention, the department regressed the number of traffic fatalities (Y) last year in a state on the state’s population (X1), the number of days of snow cover (X2), and the average speed of all cars (X3). The results are shown below. Table 10: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .821 a .780 .613 3.258 a. Predictors: (Constant), population, days of snow, average speed   Table 11: Coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 1.4 2.957   .473 .584 Population .00029 .00003 .0034 9.667 .000 Days of Snow 2.4 .62 .759 3.871 .000 Average Speed 10.3 1.1…

Atlantic hurricanes form off the western coast of Africa. As warm moist air rises, it begins to rotate around a low- pressure system. This rotation is sustained by warm ocean temperatures and a central low pressure. Once a sustained wind speed of 74 miles per hour is reached, the storm is considered a hurricane. As man-made climate change continues to increase the temperature of the Earth's oceans, it is expected that the strength of hurricanes will Typically, a lower central pressure within a hurricane's eye is associated with a higher wind speed. Here, statistical software (R/RStudio) will be used to explore this relationship by applying linear regression methods. Using a database of landfalling hurricanes in the United States, a linear regression will be used to correlate the central pressure of each hurricane to its maximum sustained wind speed. increase. Regression Plot y=942.196-0.884*x R^2=0.768 ----- ----------- -. •... •. 980 1000 940 960 900 920 Independent Variable (x)…