ࡱ> ac`[ bjbj Ůhh$)HvfnSSSS```uuuuuuu$wPznu`>"```uSSv444`SSu4`u44ltSQkvWoLuv0Hvo8z$ztzt``4`````uu4```Hv````z````````` : MAT 218 Final Practice Test Let  EMBED Equation.3 , find  EMBED Equation.3   EMBED Equation.3  Find the domain of the function in two variables  EMBED Equation.3  Find the distance between the points EMBED Equation.3 and  EMBED Equation.3 ; the coordinates of the midpoint. Find the equation of the sphere with the center at  EMBED Equation.3 and radius 4 Show that  EMBED Equation.3 is a level curve of  EMBED Equation.DSMT4  Find  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 for the following functions:  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  Find  EMBED Equation.DSMT4  for the function  EMBED Equation.DSMT4  Multivariate Optimization. Find the critical points of the function and determine if it is a max, min, or saddle point.  EMBED Equation.3  For the function  EMBED Equation.3  Find all the partial derivatives of the first and second order Find the stationary point and classify it by using the second-derivative test. Let  EMBED Equation.3 and  EMBED Equation.3 . Find all first order partial derivatives of EMBED Equation.3 and find the stationary point for f. Find the Extreme points for f over S. Find the max and min points for the following  EMBED Equation.DSMT4 subject to  EMBED Equation.3 and  EMBED Equation.3  Which of the following sets are open, closed, bounded, compact?  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Find the maximum and minimum values of  EMBED Equation.DSMT4  under the constraint  EMBED Equation.DSMT4  Systems, Matrices. Solve the system of equations and determine whether it is independent, dependent, or inconsistent.  EMBED Equation.3  Perform the following operations for the given matrices. If it is impossible, explain why.  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Multiply the given matrices. If it is impossible, explain why.  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Show that the following matrices are inverses of each other:  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Write the system of equations in a form of  EMBED Equation.DSMT4 , find  EMBED Equation.DSMT4 and solve for X using  EMBED Equation.3 .  EMBED Equation.3  Probability. Draw a random card from a standard deck of 52 cards. The sample space is the collection of the 52 cards (outcomes of the draw). Probability of selecting any card is 1/52. Let  EMBED Equation.3   EMBED Equation.3  Find a. EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  Two fair six-sided dice are rolled and the outcomes are recorded. Write a sample space for this event. Find the probabilities of the following events:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  In state lottery five numbers are drawn one at a time without replacement from 1 to 40. The six number power ball is selected from the numbers from 1 to 100. Find the probability of buying a winning lottery ticket. The following table classifies 100 people by their sex and their voting preference. Male ( EMBED Equation.3 )Female ( EMBED Equation.3 )TotalsDemocrat ( EMBED Equation.3 )153550Republican ( EMBED Equation.3 )203050Totals3565100 Compute the following probabilities if one of these 100 students is selected randomly:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Let A and B be two independent events with EMBED Equation.3 and EMBED Equation.3 Compute the probabilities of the following events:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  If  EMBED Equation.3 , EMBED Equation.3 and EMBED Equation.DSMT4  Are these events independent? Explain. Discrete and Continuous Distributions. 20 golden nuggets are randomly weighted in g (grams). Their weights are recorded below. 3 2 3 1 5 4 1 2 3 2 5 2 2 4 3 1 2 5 3 1 Create a histogram of their frequency distribution. Find the standard deviation for the set of ungrouped sample data: 2,4,5,7,3,1,0,7,9,5 Find the standard deviation of the set of grouped sample data Interval2-66-1010-1414-18Frequency2643 A play in the game costs $1.50. The play consists from tossing three coins and the payoff is equal to the number of tails showing up. For example, if there is one tail the net gain is -0.5$, if there are two tails the net gain is $0.5. Find the expected value of the game. Is it a fair game? A payoff table for two courses of action EMBED Equation.3  is given below. Which of the two actions will produce the largest expected value? What is it?  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