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- When you borrow money to buy a house, a car, or for some other purpose, you repay the loan by making periodic payments over a certain period of time. Of course, the lending company will charge interest on the loan. Every periodic payment consists of the interest on the loan and the payment toward the principal amount. To be specific, suppose that you borrow $1,000 at an interest rate of 7.2% per year and the payments are monthly. Suppose that your monthly payment is $25. Now, the interest is 7.2% per year and the payments are monthly, so the interest rate per month is 7.2/12 = 0.6%. The first months interest on $1,000 is 1000 0.006 = 6. Because the payment is $25 and the interest for the first month is $6, the payment toward the principal amount is 25 6 = 19. This means after making the first payment, the loan amount is 1,000 19 = 981. For the second payment, the interest is calculated on $981. So the interest for the second month is 981 0.006 = 5.886, that is, approximately $5.89. This implies that the payment toward the principal is 25 5.89 = 19.11 and the remaining balance after the second payment is 981 19.11 = 961.89. This process is repeated until the loan is paid. Write a program that accepts as input the loan amount, the interest rate per year, and the monthly payment. (Enter the interest rate as a percentage. For example, if the interest rate is 7.2% per year, then enter 7.2.) The program then outputs the number of months it would take to repay the loan. (Note that if the monthly payment is less than the first months interest, then after each payment, the loan amount will increase. In this case, the program must warn the borrower that the monthly payment is too low, and with this monthly payment, the loan amount could not be repaid.)arrow_forwardWe usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits" {0, 1,...,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0, 1, ...,9, A, B, C, D, E, F}. So for example, a 3 digit hexadecimal number might be 2B8. a. How many 4-digit hexadecimals are there in which the first digit is E or F? 8192 b. How many 5-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? c. How many 3-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)?arrow_forwardWe usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different "digits" {0,1,...9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0,1,....,9,A,B,C,D,E,F}. So for example, a 3 digit hexadecimal number might be 2B8. a. How many 4-digit hexadecimals are there in which the first digit is E or F? b. How many 5-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? c. How many 2-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)?arrow_forward
- We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits” {0,1,…,9}.{0,1,…,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0,1,…,9,A,B,C,D,E,F}.{0,1,…,9,A,B,C,D,E,F}.So for example, a 3 digit hexadecimal number might be 2B8. How many 2-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)?arrow_forwardA 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…arrow_forwardIn 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…arrow_forward
- 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.arrow_forwardLet A = {a, b, c} and B = {u, v}. Write a. A × B b. B × Aarrow_forwardIn number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1² +3² = 10 and 1² + 0² = 1. On the other hand, 4 is not a happy number because the sequence starting with 4² 16 and 126² = 37 and eventually reaches to 4 that is the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. Write, Compile and Execute a Java method that computes whether a given number is happy or sad.arrow_forward
- 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?…arrow_forward1.In an ancient land, the beautiful princess Eve had many suitors. She decided on the following procedure to determine which suitor she would marry. First, all of the suitors would be lined up one after the other and assigned numbers. The first suitor would be number 1, the secondnumber 2, and so on up to the last suitor, number n. Starting at the first suitor she would then count three suitors down the line (because of the three letters in her name) and the third suitor would be eliminated from winning her hand and removed from the line. Eve would then continue, counting three more suitors, and eliminating every third suitor. When she reached the end of the line she would continue counting from the beginning. For example, if there were 6 suitors then the elimination process would proceed as follows:123456 initial list of suitors, start counting from 112456 suitor 3 eliminated, continue counting from 41245 suitor 6 eliminated, continue counting from 1125 suitor 4 eliminated, continue…arrow_forwardpython In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills.Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:• Each square of the board contains at most one rook.• There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2).• The number of rooks is at least 8N.Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists.InputThe first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test case…arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage LearningC++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr