You have to communicate a signal in a language that has 3 symbols a, b and c. the probability of observing a is 50% while that of observing b and c is 25% each. design an appropriate encoding for this language. what is the entropy of this signal in bits?

1. package newton’s method for approximating square roots (case study 3.6) in a function named newton. this function expects the input number as an argument and returns the estimate of its square root. the script should also include a main function that allows the user to compute square roots of inputs until she presses the enter/return key. 2. convert newton’s method for approximating square roots in project 1 to a recursive function named newton. (hint: the estimate of the square root should be passed as a second argument to the function.) 3. elena complains that the recursive newton function in project 2 includes an extra argument for the estimate. the function’s users should not have to provide this value, which is always the same, when they call this function. modify the definition of the function so that it uses a keyword parameter with the appropriate default value for this argument, and call the function without a second argument to demonstrate that it solves this problem. 4. restructure newton’s method (case study 3.6) by decomposing it into three cooperating functions. the newton function can use either the recursive strategy of project 1 or the iterative strategy of case study 3.6. the task of testing for the limit is assigned to a function named limitreached, whereas the task of computing a new approximation is assigned to a function named improveestimate. each function expects the relevant arguments and returns an appropriate value. 5. a list is sorted in ascending order if it is empty or each item except the last one is less than or equal to its successor. define a predicate issorted that expects a list as an argument and returns true if the list is sorted, or returns false otherwise. (hint: for a list of length 2 or greater, loop through the list and compare pairs of items, from left to right, and return false if the first item in a pair is greater.)

Which syntax error in programming is unlikely to be highlighted by a compiler or an interpreter? a variable name misspelling a missing space a comma in place of a period a missing closing quotation mark

Create a function (prob3_6) that will do the following: input a positive scalar integer x. if x is odd, multiply it by 3 and add 1. if the given x is even, divide it by 2. repeat this rule on the new value until you get 1, if ever. your program will output how many operations it had to perform to get to 1 and the largest number along the way. for example, start with the number 3: because 3 is odd, we multiply by 3 and add 1 giving us 10. 10 is even so we divide it by 2, giving us 5. 5 is odd so we multiply by 3 and add one, giving us 16. we divide 16 (even) by two giving 8. we divide 8 (even) by two giving 4. we divide 4 (even) by two giving 2. we divide 2 (even) by 2 to give us 1. once we have one, we stop. this example took seven operations to get to one. the largest number we had along the way was 16. every value of n that anyone has ever checked eventually leads to 1, but it is an open mathematical problem (known as the collatz conjectureopens in new tab) whether every value of n eventually leads to 1. your program should include a while loop and an if-statement.