Financial application: investment amount. Suppose you want to deposit a certain amount of money into a savings account with a fixed annual interest rate. We are interested in calculating the amount needed to deposit in order to have, for instance, $5000 in the account after three years. The initial deposit amount can be obtained using the following formula: finalAccountValue (1 + monthlylnterestRate)numberofMonths initialDepositAmount
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Max Function
Statistical function is of many categories. One of them is a MAX function. The MAX function returns the largest value from the list of arguments passed to it. MAX function always ignores the empty cells when performing the calculation.
Power Function
A power function is a type of single-term function. Its definition states that it is a variable containing a base value raised to a constant value acting as an exponent. This variable may also have a coefficient. For instance, the area of a circle can be given as:
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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.)Interest Rates Savings accounts state an interest rate and a compounding period. If theamount deposited is P, the stated interest rate is r, and interest is compounded m timesper year, then the balance in the account after one year is P⋅(1+rm)m. For instance, if$1000 is deposited at 3% interest compounded quarterly (that is, 4 times per year), thenthe balance after one year is1000⋅(1+.034)4=1000⋅1.00754=$1,030.34.Interest rates with different compounding periods cannot be compared directly.The concept of APY (annual percentage yield) must be used to make the comparison. TheAPY for a stated interest rate r compounded m times per year is defined byAPY=(1+rm)m−1.(The APY is the simple interest rate that yields the same amount of interest after oneyear as the compounded annual rate of interest.) Write a program to compare interestrates offered by two different banks and determine the most favorable interest rate. SeeFig. 4.24.Problem Description The hailstone sequence is defined as the integer sequence that results from manipulating a positive integer value n as follows: If n is even, divide it by 2 (using floor division) • If n is odd, multiply it by 3 and then add 1 Repeat this process until you reach 1. For example, starting with n = 5, we get the sequence 5, 16, 8, 4, 2, 1. If n is 6, we get the sequence 6, 3, 10, 5, 16, 8, 4, 2, 1. If n is 7, we get 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. If n is 8, we get the sequence 8, 4, 2, 1. As far as anyone can tell, this process will eventually reach 1 for any starting value, although mathematicians have been unable to formally prove this property as of yet. a. Write a Python function named hail () that takes a single integer argument. hail() should print out the sequence of numbers generated by applying the process above to the function parameter. This function does not return any value.
- Problem Description: In the Whimsical Library, each book is enchanted with a magical code to ensure the protection of knowledge. The validation process for these magical codes involves a combination of mathematical spells. The validation process is described as follows: Take the sum of the digits at odd positions from left to right. Take the sum of the squared digits at even positions from left to right. If the absolute difference between the results from step 1 and step 2 is a prime number, the book code is considered valid; otherwise, it is invalid. Example 1: Consider the magical book code 86420137. Step 1. Take the sum of the digits at odd positions from left to right. 8+4+0+3=15 Step 2. Take the sum of the squared digits at even positions from left to right. 6^2+2^2+1^2+7^2=36+4+1+49 = 90 Step 3. If the absolute difference between the results from step 1 and step 2 is a prime number. 115-901 75 (not a prime number) Book code 86420137 is invalid. Example 2: Now, let's examine the…Python Knapsack: you are carrying a knapsack with capacity to hold a total of weight C. You are selecting among n items with values A={a1, a2, ... , an} and associated weights W={w1, w2, ... , wn}. Here the weights and values are all positive. You wish to maximize the total value of the items you select not exceeding the given weight capacity, example, maximize sum_{a in A} such that sum_{w in W} <= C. Note that you can only select your items once. In Python, create function DP_K (C, A, W) as stated above. Input an array to the function to hold the backtrace. What is the best set of items for C = 30, A = [40, 110, 100] and w = [20, 30, 40]? This can be shown using auxiliary printing function.Brute force equation solver this is python program. Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 38 3 -5 -1 Then the output is: 3 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: No solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy. ''' Read in first equation, ax + by = c '''a = int(input())b = int(input())c = int(input()) ''' Read in…
- Summary Interest on a credit card's unpaid balance is calculated using the average daily balance. Suppose that netBalance is the balance shown in the bill, payment is the payment made, d1 is the number of days in the billing cycle, and d2 is the number of days payment is made before billing cycle. Then, the average daily balance is: averageDailyBalance = (netBalance * d1 payme If the interest rate per month is, say, 0.0152, then the interest on the unpaid balance is: interest averageDailyBalance * 0.0152 Instructions Write a program that accepts as input netBalance, d1, payment, d2, and interest rate per month ( interestRate).Computer Science Question Lab There is only one list of N ingredients in the menu. Every ingredient has its beauty value that does not depend on its taste, but on the way it looks, which is expressed as a positive integer. To order a dish, the customer asks Ramsay to use all the ingredients from L to R (L is strictly less than R). Ramsay knows that the dish will be tasty and not only beautiful if the sum of its ingredients' beauty values is divisible by K. Ramsay does not want to use all the ingredients, so he always excludes one of them. Which one? - The least beautiful one! (in other words - which has the minimal beauty value). Now he wonders - how many segments (L,R) are there such that the sum of their beauty values will be divisible by K after excluding the least beautiful ingredient. Your assignment is to develop a python code that prints the answer for the problem. Sample test case are given below:Input:3 51 2 3Output:1* Question Completion Status: A Moving to another question will save this response. Question 9 Given the function F(X,Y,Z) =XZ + Z(X'+ XY), the equivalent, most simplified Boolean representation for F is O a. Z+XYZ O b.XZ O c. Z O d.Z+YZ A Moving to another question will save this response. مشمس 36°C
- Broken Cabins Problem Statement: There is an Office consisting of m cabins enumerated from 1 to m. Each cabin is 1 meter long. Sadly, some cabins are broken and need to be repaired. You have an infinitely long repair tape. You want to cut some pieces from the tape and use them to cover all of the broken cabins. To be precise, a piece of tape of integer length t placed at some positions will cover segments 5,5+1-sit-1. You are allowed to cover non-broken cabins, it is also possible that some pieces of tape will overlap. Time is money, so you want to cut at most k continuous pieces of tape to cover all the broken cabins. What is the minimum total length of these pieces? Input Format The first line contains three integers n,m and k(1sns10°, namsloº, Isksn) - the number of broken cabins, the length of the stick and the maximum number of pieces you can use The second line contains n integers bl,b2,bn (Isbism) - the positions of the broken cabins. These integers are given in increasing…Direction Fields Plotting Direction fields can be done using the function quiver: quiver Quiver plot. quiver (X,Y.U.V) plots velocity vectors as arrows with components (u.v) at the points (x,y). The matrices X,Y,U,V must all be the same size and contain corresponding position and velocity components (X and Y can also be vectors to specify a uniform grid). quiver automatically scales the arrows to fit within the grid. Example: xrange = -5:0.5:5; %the domain of x is from -5 up to 5 with 0.5 interval. yrange= -10:1:10; %the values of y is from -10 up to 10 with 1 interval. [x,y] meshgrid(xrange,yrange); Xplot the DE y = x^2+y^2; S = x.^2+y^2; quiver (x,y,ones (size(s)),s) Exercises: Sketch the direction fields of the following differential equations 1. y = 0.25xy² 2. y = sin(x-y) Notes: For the ranges: For Item No.1 Use xr1 = (-5,5) with 0.5 interval yr1 = (-10,10) with 0.5 interval Use s1 for the f(x,y). x1 and y1 as the points in the rectangular coordinate system, For Item No.2 Use xr2…JAVA CODE PLEASE Functions With No Parameters and Return Values Practice ll by CodeChum Admin Create a program that has a global integer variable assigned to a value of 1. Then, create a new function named increment that increments the global variable. In the main function, if the current value of the global variable is divisible by 3, print “Cody!”. Otherwise, print the value of that global variable. Repeatedly call the increment function until the value of the global variable is greater than 15. Output Multiple lines containing a string or an integer 1 2 Cody! 4 5 Cody! 7 8 Cody! 10 11 Cody! 13 14 Cody! Score: