e maximum value of the following function F(x)=2x3 , using the genetic algorithm, performing two iterations

Euclid’s Algorithm states the following: gcd(a, b) - a and b are integers b ≠ 0 r is the remainder of integer division At each step, the remainder, r, decreases by at least 1 r must eventually become 0 Use Euclid’s Algorithm to calculate gcd(96, 128).

Write a fraction calculator program. Your program should check for the division by 0, have and use the following functions: abs - returns the absolute value of a given integer. min - returns the smallest of two positive integers. gcd - returns the greatest common divisor of two positive integers. reduce - reduces a given fraction. flip - reduces a given fraction and flips the sign if the denominator is negative. the program should run repeatedly until the user wants to quit.

In rare cases, it's not such a great idea to "round prematurely." Consider the following function: ALG3(n): count := 0 for i = 0,..., n for j = 1,..., 21 return count count := count +1 (a) Give big-O estimates for the number of iterations of each loop, and use those estimates to give a big-O estimate for the return value count. (b) Give an exact formula for the return value count, and then simplify it using big-0 notation. (Hint: you might need the formula for the sum of a geometric series.) Is this better than your answer in part (a)?

Does the following algorithm produce a unit vector (i.e. with length one) starting fromthe origin towards a random direction? Verify your answer by writing a program thatvisualizes the angle distributions with respect to the x-axis.My-Vector()out: unit vector (x, y) towards a random direction1: x ← 2 · Random-Unit() − 12: y ← 2 · Random-Unit() − 13:
← x2 + y2 Distance from (0, 0) to (x, y).4: return (x/
, y/
) Scale to the unit circle.

1. Design an algorithm to find the weighted sum of four test scores (https://en.wikipedia.org/wiki/Weight_function). Assume that the weights have been accurately calculated in advance such that their sum equals one. Your algorithm must-read in the four test scores and four corresponding weights in the following order: score1 weight1 score2 weight2 score3 weight3 score4 weight4 Write your algorithm such that it can be run with any set of data values. However, you can test your algorithm on the following sample data to verify that the result is 70: 90 0.10 80 0.20 70 0.30 60 0.40 2. Write an algorithm that prompts the user for the radius, in inches, and price of a pizza, and then reads in those values. Finally, have the algorithm compute and output the pizza’s cost per square inch. 3. Sports exercise advisor algorithm. In this algorithm you will start out with a temperature value in Celsius, so you do not need to ask the user for it. First, convert the temperature to Fahrenheit....

n and n+1 are integers with the same number of positive divisions. Find the integers n from 1<n<107. For example, the positive divisors of 14 are 1, 2, 7, 14, and 15 are 1, 3, 5, 15. (P.s.: You have to done it by C++.)

y f(x)=x+4 10 Use the figures to calculate the left and right Riemann sums for f on the given interval and the given value of n. f(x)=x+4 on [2,7]; n = 5 The left Riemann sum is The right Riemann sum is 864 C 2 4 6 (Simplify your answer.) (Simplify your answer.) LV f(x)=x+4 N- 2 4 6 Ax

You have to run Prim's algorithm for the problem defined by adjacency matrix: 1 2 3 4 5 6 7 8 9 1 0 10 9 999 999 17 999 999 999 2 3 69 10 0 14 4 2 999 999 13 999 14 0 7 999 999 999 999 999 4 999 4 7 0 999 2 8 999 999 5 999 2 999 999 0 6 999 1 999 6 17 999 999 2 6 0 999 7 999 7 999 999 999 8 999 999 0 11 4 8 999 13 999 999 1 7 11 9 999 999 999 999 999 999 4 80 8 0 1. We started from the vertex vl, so initially we have Y = {v1}: initial 1 2 3 4 5 6 7 8 9 nearest 1 1 1 1 1 1 1 1 1 distance -1 10 9 999 999 17 999 999 999 Print out the values stored in the nearest and distance arrays after first iteration of Prim's algorithm. Specify the value of vnear and the next vertex that has to be added to Y Hint: use (copy) the table above to record your answer.

Write a fraction calculator program that adds, subtracts, multiplies, and di-vides fractions. Your program should check for the division by 0, have and use the following functions:(a) subtract - finds the reduced difference of a pair of given fractions, by makingthe second fraction negative then using the add function.(b) multiply - finds the reduced product of a pair of given fractions.(c) divide - finds the reduced quotient of a pair of given fractions by inverting the second fraction then using the multiply function

Order the following functions by asymptotic growth rate (number 1 is the best algorithm, and number 3 is the worst). 4nlog n+2n 2log n n3 + 2

Practicing Comparing Growth Rates Exercise Current score: O out of 3 You are given this set of growth functions: n!, 2", 2n2, 5n log n, 20n, 10n For the growth function 10n, type a value (a positive integer) for which this function is the most efficient of the six. If there is no integer value for which it is most efficent, type "none".

Programming Exercise 10 in Chapter 6 asks you find the mean and standard deviation of five numbers. Extend this programming exercise to find the mean and standard deviation of up to 100 numbers. Suppose that the mean (average) of n numbers x1, x2, . . ., xn is x. Then the standard deviation of these numbers is:S=sqrt(((x1-x)^2+(x2-x)^2+...+(xi-x)^2+...+(xn-x)^2)/n)