Listing 6.7, PrimeNumberFunction.py, provides the isPrime(number) function for testing whether a number is prime. Use this function to find the number of prime numbers less than 10,000.
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Listing 6.7, PrimeNumberFunction.py, provides the isPrime(number) function for testing whether a number is prime. Use this function to find the number of prime numbers less than 10,000.
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- Cyclops numbersdef is_cyclops(n):A nonnegative integer is said to be a cyclops number if it consists of an odd number of digits so that the middle (more poetically, the “eye”) digit is a zero, and all other digits of that number are nonzero. This function should determine whether its parameter integer n is a cyclops number, and return either True or False accordingly n Expected result 0 True 101 True 98053 True 777888999 False 1056 False 675409820 FalseSum of two squares def sum_of_two_squares(n): Some positive integers can be expressed as a sum of two squares of some positive integers greater than zero. For example, 74 = 49 + 25 = 7^2 + 5^2. This function should find and return a tuple of two positive integers whose squares together add up to n, or return None if the parameter n cannot be broken into a sum of two squares.To facilitate the automated testing, the returned tuple must present the larger of its two numbers first. Furthermore, if some integer can be broken down to a sum of squares in several ways, return the breakdown that maximizes the larger number. For example, the number 85 allows two such representations 7^2 + 6^2 and 9^2 + 2^2 , of which this function must return (9, 2).The technique of two approaching indices that start from the beginning and end of a sequence, respectively, and approach each other until they meet somewhere is directly applicable to this problem. In this problem, these indices crawl towards each…Q3: Interplanetary Spaceflight Milan Tusk is the richest person in the universe. After devoting decades of his life to further our space exploration technologies, he’s finally ready to retire. Being a space enthusiast, the first thing he wants to do is visit n planets p1, p2, …, pn, in this order. He’s currently on planet p0. Milan knows that the distance between planets pi and pi + 1 (for 0 ≤ i < n) is d[i]light years. His spaceship uses 1 tonne of fossil fuels per light year. He starts with a full tank and can fill up his tank at any of the n planets (but he must not run out in between two planets). There’s a huge cost to set up the spaceship for refuelling. Due to financial constraints (he’s not THAT rich), he can fill up his tank at most ktimes. In order to save money and make his spaceship lighter, Milan is looking for the smallest possible fuel tank that enables him to complete his space travel and reach planet pn. What is the smallest tank capacity that enables him to do so?…
- Credit Card Number Check. The last digit of a credit card number is the check digit, which protects against transcription errors such as an error in a single digit or switching two digits. The following method is used to verify actual credit card numbers but, for simplicity, we will describe it for numbers with 8 digits instead of 16:• Starting from the rightmost digit, form the sum of every other digit. For example, if thecredit card number is 4358 9795, then you form the sum 5 + 7 + 8 + 3 = 23.• Double each of the digits that were not included in the preceding step. Add all digits ofthe resulting numbers. For example, with the number given above, doubling the digits,starting with the next-to-last one, yields 18 18 10 8. Adding all digits in these valuesyields 1 + 8 + 1 + 8 + 1 + 0 + 8 = 27.• Add the sums of the two preceding steps. If the last digit of the result is 0, the number isvalid. In our case, 23 + 27 = 50, so the number is valid.Write a program that implements this…Credit Card Number Check. The last digit of a credit card number is the check digit, which protects against transcription errors such as an error in a single digit or switching two digits. The following method is used to verify actual credit card numbers but, for simplicity, we will describe it for numbers with 8 digits instead of 16:• Starting from the rightmost digit, form the sum of every other digit. For example, if thecredit card number is 4358 9795, then you form the sum 5 + 7 + 8 + 3 = 23.• Double each of the digits that were not included in the preceding step. Add all digits ofthe resulting numbers. For example, with the number given above, doubling the digits,starting with the next-to-last one, yields 18 18 10 8. Adding all digits in these valuesyields 1 + 8 + 1 + 8 + 1 + 0 + 8 = 27.• Add the sums of the two preceding steps. If the last digit of the result is 0, the number isvalid. In our case, 23 + 27 = 50, so the number is valid.Write a program that implements this…Sum of two squares def sum_of_two_squares(n): Some positive integers can be expressed as a sum of two squares of some positive integers greater than zero. For example, 74 = 49 + 25 = 72 + 52. This function should find and return a tuple of two positive integers whose squares together add up to n, or return None if the parameter n cannot be broken into a sum of two squares. To facilitate the automated testing, the returned tuple must present the larger of its two numbers first. Furthermore, if some integer can be broken down to a sum of squares in several ways, return the breakdown that maximizes the larger number. For example, the number 85 allows two such representations 72 + 62 and 92 + 22 , of which this function must return (9, 2). The technique of two approaching indices that start from the beginning and end of a sequence, respectively, and approach each other until they meet somewhere, used in the function two_summers in one of our class examples, is directly applicable to this…
- Sum of two squares def sum_of_two_squares(n): Some positive integers can be expressed as a sum of two squares of some positive integers greater than zero. For example, 74 = 49 + 25 = 72 + 52. This function should find and return a tuple of two positive integers whose squares together add up to n, or return None if the parameter n cannot be broken into a sum of two squares.To facilitate the automated testing, the returned tuple must present the larger of its two numbers first. Furthermore, if some integer can be broken down to a sum of squares in several ways, return the breakdown that maximizes the larger number. For example, the number 85 allows two such representations 72 + 62 and 92 + 22 , of which this function must return (9, 2).The technique of two approaching indices that start from the beginning and end of a sequence, respectively, and approach each other until they meet somewhere, used in the function two_summers in one of our class examples, is directly applicable to this…3. Randomly generate a number in range [1, 12]. Map this number to a season: if the number is 3, 4, or 5, map it to “Spring", if the number is 6, 7, or 8, map it to "Summer", if the number is 9, 10, or 11, map it to "Fall", and if the number 12, 1, or 2, map it to "Winter". Display season nameBrussel's choice def brussels_choice_step(n, mink, maxk): This problem is adapted from another jovial video "The Brussel's Choice" of Numberphile (a site so British that you just know there has to be a Trevor and a Colin somewhere in there) whose first five minutes you should watch to get an idea of what is going on. This function should compute and return the list of all numbers that the positive integer n can be converted to by treating it as a string and replacing some substring m of its digits with the new substring of either 2*m or m/2, the latter substitution allowed only when m is even so that dividing it by two produces an integer. This function should return the list of numbers that can be produced from n in a single step. To keep the results more manageable, we also impose an additional constraint that the number of digits in the chosen substring m must be between mink and maxk, inclusive. The returned list must contain the numbers in ascending sorted order.
- le.com/forms/d/e/1FAlpQLSc6PlhZGOLJ4LOHo5cCGEf9HDChfQ-tT1bES-BKgkKu44eEnw/formResponse The following iterative sequence is defined for the set of positive integers: Sn/2 3n +1 ifn is odd if n is even Un = Using the rule above and starting with 13, we generate the following sequence: 13 u13 = 40 u40 =20 u20 = 10→ u10 =5 u5 = 16 u16 = 8 ug = 4 → Us =2 u2 =1. It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. The below function takes as input an integer n and returns the number of terms generated by the sequence starting at n. function i-Seq (n) u=n; i=%3; while u =1 if statement 1 u=u/2; else statement 2 end i=i+1; end statement 1 and statement 2 should be replaced by: None of the choices statement 1 is "mod(u,2)=D%3D0" and statement 2 is "u = 3*u+1;" statement 1 is "u%2" and statement 2 is "u = 3*u+1;" O statement 1 is "mod(n,2)=30" and statement 2 is "u = 3*n+1;"def sind_approx(x: float) -> float: """ sind_approx(x) returns the Bhaskara I's sine approximation for sine in degrees. This approximation is only valid within the range [0, 180]. The sine approximation is given as: 4 * x * (180 - x) / (40500 - x * (180 - x)) example: sind_approx(90.0) -> 1.0 example: sind_approx(0.0) -> 0.0 example: sind_approx(180.0) -> 0.0 example: sind_approx(45.0) -> 0.7058823529... TODO: add param and return descriptions here """ pass # TODO: replace 'pass' with the function implementationPHP ATM machines allow 4 or 6 digit PIN codes and PIN codes cannot contain anything but exactly 4 digits or exactly 6 digits. *With user input ($pinNumbers), create a function that takes a string and returns true if the PIN is valid and false if it's not. Examples validatePIN("$1234") ➞ true validatePIN("12345") ➞ false validatePIN("a234") ➞ false validatePIN("") ➞ false Notes ● Some test cases contain special characters. ● Empty strings must return false.