MI- Prob. Set #4 DUE: Tuesda, Feb 1, 011 Spring 11 1) Dr. Condie has sport coats, pairs of slacks, 4 shirts and 6 ties that he can choose to wear on an da. a) How man combinations of these four pieces of clothing can he wear if he must wear one of each item? b) Does the answer to part (a) change if he need not wear a sport coat. Eplain wh or wh not. ) A resort has 6 empt rooms and 4 travelers who want rooms. In how man was can the manager assign a room to each traveler, given that no travelers share a room? ) NC Simplif into a single fraction: 7 1 4 1 4) Write a matri equation and give result: (a) (b) (c) (d) that will reflect ABC over the -ais. that will reflect ABC over =. that will rotate ABC 180 about the origin. that will shrink the triangle to fourth its area. ) NC Use the zero product propert to solve each: (be sure to check our answers) (a) 6 7 4 (c) 7 (b) 9 1 (d) 4 1 6 0 IMSA Prob Set 4.1 Rev. S11
MI- Prob. Set #4 DUE: Tuesda, Feb 1, 011 Spring 11 Solving Quadratics b Completing the Square While the zero product propert works well as a method for solving man quadratic equations, other methods are also possible. If a perfect square trinomial is equal to a number, taking the square root of both sides of the equation is a good wa to proceed. For eample: If ( + 4) = then + 4 = ± = 4 ± = 9 or 1 If 9 6 + 1 = 7 then ( 1) = 7 1 = ± 7 = 1 ± 7 = 1 ± 7 or 1 ± 7 6) NC Solve for. Give eact answers. a) ( ) 18 b) ( ) 1 c) 0 4 7) NC Solve for (,): 1 1 1 1 8 IMSA Prob Set 4. Rev. S11
MI- Prob. Set #4 DUE: Tuesda, Feb 1, 011 Spring 11 8) a) Which set below has the larger median? b) How much larger is it? The range of a set of data is the maimum value minus the minimum value. The range and interquartile range are measures of dispersion or spread. The midrange is another measure of central tendenc used in statistics. It is the mean of the minimum and the maimum. 9) a) Give the range for Set A in Problem 8. b) Give the interquartile range for Set A in Problem 8. In a fraction containing radicals, either the numerator or the denominator can be rationalized, that is, multiplied b some epression so that the product is a rational number. For eample, to rationalize the denominator in: E: 1 7 = 1 7 = E: 1 7 = 1 7 1 7 1 7 = = 1 7 6 IMSA Prob Set 4. Rev. S11
MI- Prob. Set #4 DUE: Tuesda, Feb 1, 011 Spring 11 10) Simplif 17 a) b rationalizing the numerator. b) b rationalizing the denominator. 11) Rationalize the denominator and simplif: a) b) 1) State all values of for which the epression in 11b is defined. State answer in interval notation. 1) is not alwas true. a) Find two real values of for which it is false. b) Find two real values of for which it is true. c) Based upon our answers in (a) and (b), state the condition for the statement to be true. 14) The table below gives the life epectanc at birth (in ears) of males born in the United States. Birth ear Life epectanc Birth ear Life epectanc 1900 48. 1960 66.6 1910 1.1 1970 67.1 190. 1980 70.0 190 7.4 1990 71.8 1940 6. 000 7.0 190 6.6 010 7. Give all answers to two decimal places. a) Find a linear model that describes this data giving life epectanc L as a function of time t. For 1900 let t 0, 1910 let t 10 and so on. b) According to our model, what was the life epectanc for a male born 1996? c) According to our model, what was the life epectanc in 1776? Comment on the appropriateness of our model in doing this etrapolation. IMSA Prob Set 4.4 Rev. S11
MI- Prob. Set #4 DUE: Tuesda, Feb 1, 011 Spring 11 1) (Continuation of problem set ) Consider the graph of given b ( h) k. and transformations of the graph a) Eamine the graph of and values of k have upon the graph of eplanation. b) Eamine the graph of and different values of h have upon the graph of sketch) in our eplanation. k for different values of k. What effect do different? Give an eample (both equation and sketch) in our ( h ) for different values of h. What effect do? Give an eample (both equation and c) Generalize our results b what effect both h and k have of the graph of ( h) k. Give an eample (both equation and sketch) in our eplanation. when Save these results along with our results in problem set # for a future problem set. IMSA Prob Set 4. Rev. S11