Use the master theorem to find (if applicable) the run time of the cost function T(n) = 5T(n/1) + 2lg(n!). REQUIRED: Show all work and logic. - No text entered -
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- Determine whether ∀x(P (x) ↔ Q(x)) and ∀x P (x) ↔∀xQ(x) are logically equivalent. Justify your answerUse a computer to plot formula 2.22 directly, as follows. Define z = qA/q, so that (l-z) = qB/q. Then, aside from an overall constant that we'll ignore, the multiplicity function is [4z(1-z)]N, where z ranges from 0 to 1 and the factor of 4 ensures that the height of the peak is equal to 1 for any N. Plot this function for N = 1, 10, 100, 1000, and 10,000. Observe how the width of the peak decreases as N increases.3. Use Indirect proof for the following problem. BE SURE TO SHOW ALL OF YOUR WORK. 1. ~P > Q 2. ~R > (~P . ~S) 3. ~S > ~Q / R
- Convert the given i-system to an e-system using slack variables. Then construct a table of all basic solutions of the e-system. For each basic solution, indicate whether or not it is feasible. Show your work and explanations. x1+x2≤8 x1+3x2≤12 x1≥0 x2≥0The tableau is not optimal for either maximization or a minimization problem. Thus, when a nonbasic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering nonbasic variable. Basic Z 0 -5 0 4 -1 -10 0 0 598 0 3 0 -2 -3 -1 5 1 12 0 1 1 3 1 0 3 0 6 1 -1 0 0 6 -4 0 0 0 Categorize the variables as basic and nonbasic and provide the current values of all the variables. AP [8] Assuming that the problem is of the maximization type, identify the nonbasic variables that have the potential to improve the value of If each such variable enters the basic solution, determine the associated leaving…I don't need a code for these questions. I just need them answered Nine steel specimens were submerged in seawater at various temperatures, and the corrosion rates were measured. The results are presented in the following table:Temperature (OC)Corrosion(mm/yr.)26.6 1.5826 1.4527.4 1.1321.7 0.9614.9 0.9911.3 1.0515 0.828.7 0.688.2 0.59a. Construct a scatterplot of corrosion (y) vs. temperature (x). Verify that a linear model is appropriate.b. What is the least-square line (trendline/regression line) for predicting corrosion from temperature?c. Two steel specimens whose temperatures differ by 10OC are submerged in seawater. By how much would you predict their corrosion rates differ?d. Predict the corrosion rate for steel submerged in seawater at a temperature of 20OC.e. Construct a table with predicted values from the original dataset.f. Compute the residuals. Which point has the residual with the largest magnitude?g. What is the correlation between temperature and corrosion rate? What…
- Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solutions including original diagram for part a!Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solution!(b) To compare two kids of bumper guards, 6 of each kid were mounted on a car and then the car was run into A concrete wall. The following are the cost of repairs. Guard 1 107 148 123 165 102 119 Guard 2 134 115 112 151 133 129
- Using the banker’s algorithm, determine whether this is in a safe state, where the available resources are (for A, B, and C) 1, 2, and 1.Question 15 pap Suppose we have a Monte Carlo algorithm, A, and a deterministic algorithm, B, for testing if the output of A is correct. How can we use A and B to construct a Las Vegas algorithm? Also, if A succeeds with probability ½ and both A and B run O(n) time, what is the expected running time of the Las Vegas algorithm that is produced? Full explain this question and text typing work only We should answer our question within 2 hours takes more time then we will reduce Rating Dont ignore this lineProve or disprove the following statements, using the relationship among typical growth-rate functions. a) n! is O(4^n) b) n^22 log n + n^7 is Ω(n^6 log n) c) n^9 + 8000n^7 is Ω(n^16) PLEASE SOLVE ALL. PLEASEEEEE. I SOLVED THESE, BUT I'M NOT SURE ABOUT MY ANSWER, ESP a) and b)