With probability 1/2 the pivot selected will be between n/2 and 3n/4 (i. e. a good pivot). Also with probability 1/2 the pivot selected will be between 1 and n/4 or between 3n/4 and n (i. e. a bad pivot). (1 points) 1. State a recurrence that expresses the worst case for bad pivots.

Required:
a. State a recurrence that expresses the worst case for bad pivots.
b. State a recurrence that expresses the worst case for good pivots.
c. State a recurrence that expresses the expected worst case by combining the first two recurrences.
d. Prove by induction that your recurrence is in O(nlog n).

Write the quartstogallons java class that declares a named constant to hold the number of quarts in a gallon (4). also declare a variable to represent the number of quarts needed for a painting job, and assign an appropriate value—for example, 18. compute and display the number of gallons and quarts needed for the job. display explanatory text with the values, for example:

Singing in the rain: this first part of the film shows the early history of motion picture. how accurate do you think the portrayal of the early motion picture industry is? why? is historical accuracy important in films and theater productions? explain.

Assume the existence of a bankaccount class. define a derived class, savingsaccount that contains two instance variables: the first a double, named interestrate, and the second an integer named interesttype. the value of the interesttype variable can be 1 for simple interest and 2 for compound interest. there is also a constructor that accepts two parameters: a double that is used to initialize the interestrate variable, and a string that you may assume will contain either "simple", or "compound", and which should be used to initialize the interesttype variable appropriately. there should also be a pair of functions getinterestrate and getinteresttype that return the values of the corresponding data members (as double and int respectively).