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- In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, …a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime(int num) b. Write a Java class called PrimeNumbers that: o Reads from the user a natural value n (should be less than or equal 200). o Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run.In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 x 1, involve 5 itself. Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, .. a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime (int num) b. Write a Java class called PrimeNumbers that: Reads from the user a natural value n (should be less than or equal 200). Prints a list of the prime numbers from 2 to n and their number and values. The program has to work EXACTLY as given in the following sample run. Hints: You should create a single dimension array to store the prime…A fish-finder is a device used by anglers to find fish in a lake. If the fish-finder finds a fish, it will sound an alarm. It uses depth readings to determine whether to sound an alarm. For our purposes, the fish-finder will decide that a fish is swimming past if:there are four consecutive depth readings which form a strictly increasing sequence (such as 3 4 7 9) (which we will call "Fish Rising"), orthere are four consecutive depth readings which form a strictly decreasing sequence (such as 9 6 5 2) (which we will call "Fish Diving"), orthere are four consecutive depth readings which are identical (which we will call "Constant Depth").All other readings will be considered random noise or debris, which we will call "No Fish."Create a Python program called "fishfinder_firstname_lastname" that takes 1 input of string of 4 numbers separated with comma. Your program must display "Fish Rising", "Fish Diving.", "Fish At Constant Depth" or "No Fish".Example:30,10,20,20 Must display No…
- A number is called a perfect number if it is equal to the sum of all of its divisors, not including the number itself. For instance, 6 is a perfect number because the divisors of 6 are 1, 2, 3, 6 and 6 = 1 + 2 + 3. As another example, 28 is a perfect number because its divisors are 1, 2, 4, 7, 14, 28 and 28 = 1 + 2 + 4 + 7+ 14. However, 15 is not a perfect number because its divisors are 1, 3, 5, 15 and 15 6= 1 + 3 + 5. Write an algorithm that asks the user to enter a positive integer n and prints all the perfect numbers that are less than n.A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors. The first perfect number is 6, because 1, 2 and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: (1 + 2 + 3 + 6) / 2 = 6. Write a program to display the of sum all perfect numbers found in the first 1000 integers.A decreasing sequence of numbers is a sequence of integers where every integer in the sequence is smaller than all other previous integers in that sequence. For example, •35, 16, 7, 2, 0, -3, -9 is a decreasing sequence of numbers. The length of this sequence is 7 (total numbers in the sequence) and the difference of this sequence is 35 - (-9) -44. • 5 is a decreasing sequence of numbers with length 1 and difference 5-5 = 0 •99,-99 is a decreasing sequence of numbers with length 2 and difference 99-(-99) = 198 •17, 23, 11, 8, -5, -3 is not a decreasing sequence of %3D numbers. Write a program that contains a main() function. The main function repeatedly asks the user to enter an integer if the previously entered integers form a decreasing sequence of numbers. This process stops as soon as the latest user input breaks the decreasing sequence. Then your function should print the length and difference of the decreasing sequence. Finally, call the main() function such that the call will be…
- A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors. The first perfect number is 6, because 1, 2 and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: (1 + 2 + 3 + 6) / 2 = 6.Write a program to display the of sum all perfect numbers found in the first 1000 integers in javaBlackout Math is a math puzzle in which you are given an incorrect arithmetic equation. The goal of the puzzle is to remove two of the digits and/or operators in the equation so that the resulting equation is correct. For example, given the equation 6 - 5 = 15 ^ 4/2 we can remove the digit 5 and the / operator from the right-hand side in order to obtain the correct equality 6 - 5 = 1 ^ 42. Both sides of the equation now equal to 1. Observe how removing an operator between two numbers (4 and 2) causes the digits of the numbers to be concatenated (42). Here is a more complicated example: 288 / 24 x 6 = 18 x 13 x 8 We can remove digits and operators from either side of the equals sign (either both from one side, or one on each side). In this case, we can remove the 2 from the number 24 on the left-hand side and the 1 from the number 13 on the right-hand side to obtain the correct equality 288 / 4 x 6 = 18 x 3 x 8 Both sides of the equation now equal to 432. Here is another puzzle for you…The Fibonacci sequence is listed below: The first and second numbers both start at 1. After that, each number in the series is the sum of the two preceding numbers. Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, ... If F(n) is the nth value in the sequence, then this definition can be expressed as F(1) = 1 F(2) = 1 F(3) = 2 F(4) = 3 F(5) = 5 F(6) = 8 F(7) = 13 F(8) = 21 F(n) = F(n - 1) + F(n - 2) for n > 2 Example: Given n with a value of 4F(4) = F(4-1) + F(4-2)F(4) = F(3) + F(2)F(4) = 2 + 1F(4) = 3 The value of F at position n is defined using the value of F at two smaller positions. Using the definition of the Fibonacci sequence, determine the value of F(10) by using the formula and the sequence. Show the terms in the Fibonacci sequence and show your work for the formula.
- IN JAVA Alice and Bob are playing a board game with a deck of nine cards. For each digit between 1 to 9, there is one card with that digit on it. Alice and Bob each draw two cards after shuffling the cards, and see the digits on their own cards without revealing the digits to each other. Then Alice gives her two cards to Bob. Bob sees the digits on Alice’s cards and lays all the four cards on the table in increasing order by the digits. Cards are laid facing down. Bob tells Alice the positions of her two cards. The goal of Alice is to guess the digits on Bob’s two cards. Can Alice uniquely determine these two digits and guess them correctly? Input The input has two integers p,q (1≤p<q≤9) on the first line, giving the digits on Alice’s cards. The next line has a string containing two ‘A’s and two ‘B’s, giving the positions of Alice’s and Bob’s cards on the table. It is guaranteed that Bob correctly sorts the cards and gives the correct positions of Alice’s cards. Output If Alice can…Blackout Math is a math puzzle in which you are given an incorrect arithmetic equation. The goal of the puzzle is to remove two of the digits and/or operators in the equation so that the resulting equation is correct. For example, given the equation 6 - 5 = 15 ^ 4/2we can remove the digit 5 and the / operator from the right-hand side in order to obtain the correct equality 6 - 5 = 1 ^ 42. Both sides of the equation now equal to 1. Observe how removing an operator between two numbers (4 and 2) causes the digits of the numbers to be concatenated (42). Here is a more complicated example: 288 / 24 x 6 = 18 x 13 x 8 We can remove digits and operators from either side of the equals sign (either both from one side, or one on each side). In this case, we can remove the 2 from the number 24 on the left-hand side and the 1 from the number 13 on the right-hand side to obtain the correct equality 288 / 4 x 6 = 18 x 3 x 8 Both sides of the equation now equal to 432. Here is another puzzle for you…The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid's algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner: 1. Compute the remainder of dividing the larger number by the smaller number. 2. Replace the larger number with the smaller number and the smaller number with the remainder. 3. Repeat this process until the smaller number is zero. The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their GCD. An example of the program input and output is shown below: Enter the smaller number: 5 Enter the larger number: 15 The greatest common divisor is 5