Consider the grammar g1: s → ε, s → as, s → asbs and the language l that contains exactly those strings of a's and b's such that every prefix has at least as many a's as b's. we want to prove the claim: g1 generates all strings in l. we take the following inductive hypothesis to prove the claim: for n < k, g1 generates every string of length n in l. to prove the inductive step we argue as follows: "for each string w in l either ) or ) holds. in both cases we use the inductive hypothesis and one of the rules to show that string w can be generated by the grammar. in the first case we use rule s → as and in the second case we use rule s → asbs." which phrases can replace the so that this argument is correct

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.

What is used to analyze and summarize your data without graphical support

Barbara is interested in pursuing a career in the science and math pathway. which qualifications will her reach that goal? a.an advanced knowledge of physics and math b.an advanced knowledge of engineering and math c. an advanced knowledge of physics and robotics an d. advanced knowledge of machinery and math