In class we described a method, known as chain matrix multiplication (CMM), which determines the fastest way to multiply

Raquel is going on a really long trip, and will need many toys to be entertained. Prof. Brito allows her to use two bags, with capacities respectively. Design a Dynamic Programming algorithm for Raquel such that: given an array W and L for toys numbered , where W is the weight of toy i, and L is the liking coefficient for each toy (the higher L, the more she likes toy i), your algorithm outputs the maximum sum of the L values of both bags. For now, Raquel only has 1 of each toy. Example: W=, L=, , your algorithm should return 8=5+3 as a result of placing toy 2 in the second bag, and toy 4 in the first bag. Note that you can fill the second bag with toys 1 and 4, and place toy 3 in the first bag, but the sum of the L values in this case is 2+3+1=6

Recall the algorithm discussed in lecture to perform fast multiplication of two integers of n bits. It proposes to recursively compute three multiplications of some integers of n/2 bits, and combine the results using linear many operations. Its runtime is

Recall the algorithm discussed in lecture to perform fast multiplication of two integers of n bits. It proposes to recursively compute three multiplications of some integers of n/2 bits, and combine the results using linear many operations. Its runtime is

The DP table below is the output from the Longest Increasing Subsequence (LIS) algorithm from class, which was run on a sequence A.    1 1 1 2 2 3 4 4   Based on this table, answer questions 12-15.

Let A be an array of integers , sorted in increasing order. A shift of A by k, denoted by , means removing the last k elements and placing them at the beginning. For example, if A= {1, 2, 3, 4, 5, 6, 7} and k = 3, then  = {5, 6, 7, 1, 2, 3, 4}. Design a divide and conquer algorithm that takes as input a sorted array A that has been shifted by an unknown 0

On your scratch paper, make a t-table and a set of axes. Find five ordered pair solutions of the following function. Be sure to include values where x is positive and negative. Graph the equation on your set of axes.  Type EXACTLY two of your ordered pair solutions in the box below and explain how you would know by looking at the equation if this is exponential growth or decay.   (If the equation below is missing the base, here is another version y=1/2(2)^x   The base 2 is raised to the power x.   The equation editor is being strange on some devices. y =       

Given the following set of data from a survey performed on a group of 97 students, answer the following questions in the answer box below. Type in your answers labeled a-e. (All data is made up, except we all know that math is everyone’s favorite subject.) a. What are the cases? b. List the quantitative variables. c. What is the median for the # of hours worked per week? Round to the nearest tenth if needed. d. What is the mode for the # of credits this quarter? e. Which variables are categorical?   NAME Favorite subject # of credits this quarter Snack of choice # of computer/tablets # of hours working per week Favorite hobby Matthew Math 16 spumoni ice cream 2 10 Baking artisan bread Cybil Math 16 Popcorn 3 12 crochet Cheyenne Math 12 Tim’s Jalapeno chips 1 15 gardening Melissa Math 15 goldfish crackers 1 0 hiking Zaida Math 11 celery with peanut butter 2 10 rock climbing Grace Math 12 Popcorn 1 0 extreme couponing

Given the following set of data from a survey performed on a group of 97 students, answer the following questions in the answer box below. Type in your answers labeled a-e. (All data is made up, except we all know that math is everyone’s favorite subject.) a. What are the cases? b. List the quantitative variables. c. What is the median for the # of hours worked per week? Round to the nearest tenth if needed. d. What is the mode for the # of credits this quarter? e. Which variables are categorical?   NAME Favorite subject # of credits this quarter Snack of choice # of computer/tablets # of hours working per week Favorite hobby Matthew Math 16 spumoni ice cream 2 10 Baking artisan bread Cybil Math 16 Popcorn 3 12 crochet Cheyenne Math 12 Tim’s Jalapeno chips 1 15 gardening Melissa Math 15 goldfish crackers 1 0 hiking Zaida Math 11 celery with peanut butter 2 10 rock climbing Grace Math 12 Popcorn 1 0 extreme couponing

Identify the bone in the image above.  Indicate RIGHT or LEFT