Professor bunyan thinks he has discovered a remarkable property of binary search trees. suppose that the search for key kk in a binary search tree ends up in a leaf. consider three sets: aa, the keys to the left of the search path; bb, the keys on the search path; and cc, the keys to the right of the search path. professor bunyan claims that any three keys a \in aa∈a, b \in bb∈b, and c \in cc∈c must satisfy a \le b \le ca≤b≤c. give a smallest possible counterexample to the professor's claim.

Robots with telescoping arms are sometimes used to perform tasks (e.g., welding or placing screws) where access may be difficult for other robotic types. during a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. use a computer program to plot the path of tip a in x and y coordinates for 0 ≤ t ≤ 4s.

Shown below is the start of a coding region within the fist exon of a gene. 5'--3' 3'--5' how many cas9 pam sequences are present?

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.