2. For the matrix-vector DE ' = }}} |x with initial condition ☞ (0) = [−8] a. Find the specific solution using eigenvalues and eigenvectors. b. Sketch the phase portrait. Draw the eigenvector lines and use arrows to note whether they exhibit growth or decay. Then fill in some curved trajectories through the rest of the space. C. The origin x = O is an equilibrium solution. What type (node, saddle, spiral), and what is its stability (unstable, stable, semi-stable)?
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- Use the RAND function and the Copy command to generate 100 random numbers. a. What fraction of the random numbers are smaller than 0.5? b. What fraction of the time is a random number less than 0.5 followed by a random number greater than 0.5? c. What fraction of the random numbers are larger than 0.8? d. Freeze these random numbers. However, instead of pasting them over the original random numbers, paste them onto a new range. Then press the F9 recalculate key. The original random numbers should change, but the pasted copy should remain the same.Bad simulations Explain why each of the followingsimulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to representthe number of heads when 9 coins are tossed. b) A basketball player takes a foul shot. Look at a ran-dom digit, using an odd digit to represent a good shot and an even digit to represent a miss.c) Use random numbers from 1 through 13 to represent thedenominations of the cards in a five-card poker hand.When will you use scatter diagram?a. For 2 variables that have relationshipb. For 2 variables that have no relationshipc. For data that are inversely proportionald. For data that are directly proportionale. None of the above
- For the next 6 numbers: Refer to the Management Scientist output of a maximization LP problem. The constraints are defined as follows: Constraint 1: advertising budget ( ) Constraint 2: sales force availability ( ) Constraint 3: production level (=) Constraint 4: retail stores requirement ( ) Optimal Solution Objective Function Value - Variable. Constraint X1 X2 X1 X2 X3 X4 X3 X4 1 2 Variable 1 2 3 3 4 OBJECTIVE COEFFICIENT RANGES 4 Constraint RIGHT HAND SIDE RANGES Value Slack/Surplus Lover Limit 25.000 425.000 150.000 0.000 84.000 50.000 No Lover Linit No Lover Linit Lover Limit 48450.000 0.000 25.000 0.000 0.000 4950.000 1775.000 515.000 0.000 Reduced Costs Dual Prices Current Value 90.000 84.000 70.000 60.000 Current Value 0.000 0.000 0.000 45.000 5000.000 1800.000 600.000 150.000 3.000 0.000 60.000 -17.000 Upper Limit No Upper Linit 90.000 87.000 105.000 Upper Linit 5850.000 No Upper Limit 603.571 200.000Maximize z=4x+5y Subject to: x+y<or=4 x-y>or=-2 x<or=3 x>or=0, y>or=0Show that Jσ_(ij)D_(ij)=T_(iL)F_(iL˙)=S(AB)E_(AB˙) [Hints: (a) to prove the first equation, use the relationship between F_(iL)˙ and L_(ij), and expand L_(ij) into symmetric and antisymmetric parts. Note the symmetry of σ_(ij). (b) To prove the second equation, first express E_(AB)˙ using F_(iL), then take the time derivative. Substitute into the definition of S_(AB )in index form and simplify.]
- typing clearly urjentGiven a normal distribution with μ= 105 and σ = 20, and given you select a sample of n = 16, complete parts (a) through (d). a. What is the probability that X is less than 92? P(X<92) 0.0047 (Type an integer or decimal rounded to four decimal places as needed.) b. What is the probability that X is between 92 and 93.5? P(92 X 93.5)= 0.0061 (Type an integer or decimal rounded to four decimal places as needed.) c. What is the probability that X is above 105.2? P(X 105.2)= 0.4840 (Type an integer or decimal rounded to four decimal places as needed.) d. There is a 67% chance that X is above what value? X = (Type an integer or decimal rounded to two decimal places as needed.)do fast currect answer
- When it first debuted, Telsa was selling its Model 3 sedan for $35,000. The Model 3 was priced substantially less than Tesla’s other models at the time, however, it had similar quality and input costs. In charging such a low price, it is most likely that Tesla is trying to: A. Create more value without capturing more value B. Capture more value without creating more value C. Create and capture more value D. None of the abovePlease do not give solution in image format thankuSolve (xex + y) dx − x dy = 0