Here are some useful facts: 1) The set of all languages (over some nonempty alphabet) is uncountable. 2) The union of two countable sets is always countable, 3) The set of Turing machines is countable and 4) Every deciable language is decided by some TM. You now have everything you need to do the following problems quickly and easily Required:
Show that the class of decidable languages is countable.

Write a function that draws a pool ball. this function should take as parameters, the color, the number that should go on the pool ball, and the location of the center of the pool ball. the radius of the pool balls should be pool_ball_radius, and the font of the number should be pool_ball_font. the text of the pool ball font should be white. drawpoolball(color. orange, 5, 100, 100); drawpoolball(color. green, 6, 50, 200); drawpoolball(color. red, 3, 150, 350); drawpoolball(color. blue, 2, 250, 140); to center the numbers on the pool ball, you should use the getwidth() and getheight() methods. you are allowed to call these methods on your text object, such as txt.

Write a car class having two private member variables called tank and speed. write public methods called pumpgas and gofast. the method pumpgas gets an integer for gas that must be pumped. that value needs to be added to tank (no more than 20 gallons). it must return the amount of gas that is purchased ($4 per gallon). the method gofast should increase the speed by 5 each time it is called. write a constructor for the above class that initialized both variables to zero. write a tostring to display both the tank and speed when the car is printed. modify the car class to implement the interface comparable and an interface called carinter having the public methods in carinter. write the main program to create an array of size 5 of type car. create 5 car objects having each location of the array to refer to one of the cars. test the pumpgas, gofast, equals method on the array items. write an enhanced loop to print all the car values (using a tostring written last time).write a generic method to find the minimum of four items. pass int, double, char, string and car objects to test this method.

Assume that there is a 4% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?