Regional. ANS. Simply plug above information into equation given and solve for N.

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Ilene Norman
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1 #1 The sum of the iterior agles of a polygo with N equal sides is 180(N-). If the measure of oe of the iterior agles is 1 degrees, how may side are there? a) 4 b) 6 c) 8 d) 10 e) 1 ANS. Simply plug above iformatio ito equatio give ad solve for N. 180( N ) 1 180N 60 1N 4N 60 N 8 N # A tet that has a triagular profile was ot built evely. Oe of the sides is 6 ft log, but the other side is oly. feet log. If the base of the tet is 6. feet across, how high is the highest poit of the tet? (roud to earest teth of a foot) a).9 feet b) 4.4 feet c) 4.7 feet d).0 feet e). feet ANS: Oe possible solutio uses algebra ad the Pythagorea theorem. If we split c ito x ad 6. x, the we get two expressios that ivolve the height h. These are x + h 6 ad (6.-x) +h.. By substitutio, we ca fid that 6 - x. - (6.-x). After a bit of expasio ad cacellatio, we fid that x.69, ad the through the Pythagorea theorem, the height is 4.7 feet. It is also possible to use Law of Cosies to fid oe base agle, the use simple trigoometry to fid the height of the tet. If we let a 6, b., ad c 6., the the agle d betwee a ad c ca be foud usig b a + c ac cos d. This gives a agle measure of.0 degrees. Usig simple trigoometry, si.0 height / 6, or height 4.7 feet, just as before. # (PY, trig, med) State the rule of a sie fuctio with a amplitude 8, period of ad vertical shift of 6 up. a. 8 si( x) + 6 b. 8 si(pi/ x) + 6 c. 8 si(pi x) + 6 d. -6 si(pi/ x) + 8 e. Noe of the above ANS: Period, p, is foud by the relatioship, p pi/ b. So, pi/ b which makes b pi/. The vertical shift of 6 is the costat at the ed so the correct equatio is 8 si(pi/ x) + 6 which is choice b.

2 #4 [cot(x) + ta(x) ] / sec(x) ca also be writte as: a) csc(x) b) sec(x) c) cos(x) d) si(x) ANS: cos( x) si( x) cos ( x) + si ( x) + cot( x) + ta( x) si( x) cos( x) si( x)cos( x) 1(cos( x)) 1 csc( x) sec( x) 1 1 si( x)cos( x) si( x) cos( x) cos( x) # What is the legth of the vector created by addig the vectors i + j ad i - 4j? a) - b) c) d) ANS: Addig the vectors creates the vector -i j. The legth of this vector is foud as ormal. It is the square root of the sum of the squares of the compoets, or. #6 (PY,trig, med) What is the phase shift of y cos( x - pi) relative to y cos x. a. pi/ to the right b. pi/ to the left c. to the right d. to the left e. oe of the above ANS: Distribute out the i y cos( x - pi) to get y cos (x - pi/). The resultig expressio (x - pi/) deotes a horizotal or phase shift of pi/ to the right.

3 #7 The probabilty that a car door is opeed is 1/. There are 8 keys hagig o the wall, of which, will ope the door ad you select oe key at radom. What is the probability that you ca ope the door without havig to select aother key? a) 0. b) 0. c) 0.4 d) 0. e) 0.6 ANS: There are two ways that the door will ope: oe way is if it is already ope that has a probability of 1/ OR the other way is if the door is locked AND you have the opeig key havig the probability of (/)(1/4) 1/6 ad 1/ + 1/6 1/ d #8 Cosider the set of umbers S { -1, 0, 0, 1,,, 9}. Which of the followig is true about S? a) mea < media < mode b) media < mode < mea c) mode < media < mea d) mea < media < mode e) mode < mea media ANS: Simple calculatios of the above data yields: mea, media 1 ad mode 0, so aswer c #9 This Thaksgivig you decide to go ito the Frech apple pie busiess to ear moey for Christmas. Two years ago whe you sold the pies for $ each you sold 8 pies. Last year you raised your price to $9.0 but oly sold 1 pies. Assumig that demad is liear, how may pies would you sell if you sold them for $7.? a) Approximately 61 pies b) Approximately 67 pies c) Approximately 7 pies d).approximately 119 pies e) Noe of the above ANS: The rate of chage (slope) of price/quatity sold is foud by the quotiet ( - 9.0)/(8-1) The y - itercept is foud by solvig () - b or (1) + b. So, solvig for b, you get b You liear demad equatio is y x where y is the demad ad x is the price. Fially, if you substitute 7. for x, you have a total demad of approximately 67 pies.

4 #10 A, B, ad C toss a 6-side die begiig with A ad the first to throw a 1 or a wis. What is the probability that A wis? a) 1/ b) 6/1 c) 8/1 d) 9/19 e) 1/ ANS: Cosider the followig data: A wis o 1st try d try rd try 4th try P( A wis) ( ) ( ) ( ) ( ) etc Ad so this a ifiite geometric sequece that eeds to be summed up. The above is: ( ) ( ) ( )... ( ) 1 ( ) ( )... D #11 If A 1 ad B 1 1 0, the AB a) b) c) 1 0 d) e) This operatio caot be doe ANS: This is the simple matrix operatio of multiplicatio. as B #1 What is (M - N),? 0 x x 0 N 1 7x x / M 1 1/ x x 6 a) b) 4 c) x d) 4x e) -Noe of the above ANS: The, i the (M - N), otatio refers to the secod row ad third colum. Therefore, (M - N),, x - (x/) x - x 4x

5 #1 The roots to a polyomial are located at x -1, x 1 ad x. Which of the followig polyomials COULD be represeted by this iformatio? a) x b) x c) x 4 x 6x x d) both B ad C e) oe of x + 8x x + these + 6x 9 ANS: This is pretty much a trial ad error problem. If c is a root, the (x-c) is a biomial factor of the polyomial. So,...(x + 1)(x - 1)(x - ) as. C. Also, because aswer B is a polyomial of degree 4, there could be a double root. By observig the edig term, the oly possible double root might be at, so (x + 1)(x - 1)(x - )(x - ) as. B So, correct aswer is D #14 A woodsma makes two differet trails from his cabi to tow. The first path goes through meadows ad takes three hours to travel. This path heads east for five miles, the goes orth three miles ito tow. The other path goes directly through the woods from the woodsma s cabi to tow ad takes oly two ad a half hours to travel to travel. O which route is the woodsma travelig faster? a) Forest route by 0.0 miles per hour b) Forest route by 0. miles per hour c) Meadow route by 0.4 miles per hour d) Meadow route by 0. miles per hour e) The speed is the same for both routes ANS: Before calculatig speed, we must first determie the legth of each path. The meadow path is the sum of the legths, or 8 miles. The forest path is foud usig the Pythagorea theorem or trigoometry, ad is.810 miles. If we the use the expressio rate distace / time, we fid that the speed o the forest path is.810 miles /. hours, or. mph. The speed o the meadow path is 8 /, or.67 mph, which is 0.4 mph greater tha the speed o the forest path. #1 Covert 7 o '8" to decimals. a) 7.47 o b) 7.8 o c) o d)7.00 o e) Noe of the above ANS: The coversio is 7 + /60 + 8/ which is a.

6 #16 A tub ca be filled by a large faucet i 10 miutes while a small faucet ca fill the same tub i miutes. The drai at the bottom of the tub ca empty the tub i 1 miutes. If both faucets are tured o at the same time, ad oe miute later the drai is opeed, how may miutes does it take to fill the tub from the start? (earest miute) a) 11 b) 1 c) 1 d) 17 ANS: Let: x time the faucets are ruig ad x-1 time the drai is ope x x x 1 1x 6x 10( x 1) x 10x x 140 x 140/ #17 What is the average rate of chage of y -x + 1 from x -1 to x? a) -9 b) - c) 1 d) e) oe of the above ANS: Cosider the slope of the lie from (-1, 9) to (, 0) (the first iput / output to the secod iput / output pai. The slope of this lie is (9-0)/(-1-), or - #18 Let f(x) x - p. If the cos(k).4, what is the value of cos(f(k))? a) 4 b) -.4 c). d) -. e) Noe of the above ANS: cos(f(k)) cos(k p). Sice this is a phase shift of p to the right, the cos(k p) cos(k).4 which is choice a. #19 Determie the quatity of: 8 ( 1+ i) a)-16 b) -4 c ) 0 d) 4 e) 16 4 ( 1+ i) 1+ i 1 i ( 1+ i) i( 1+ i) i ( 1+ i) ( i )( 1+ i) i i 4 so aswer E

7 #0 If you flip a fair coi five times, what is the probability that you will get heads o at least three of these flips? a) 0.01 b) 0.1 c) 0.1 d) 0. e) 0.6 ANS: A biomial distributio, with ad p 1/. ad, P(at least )P(X)+P(X4)+P(X) gettig: #1 (PY, t, med) A satellite trackig statio is located i Tucso, AZ. If a satellite followig a circular orbit passes over Tucso 17 miles above the earth, how far alog the Earth s surface ca the statio track the satellite before it moves below the horizo? (Assume the earth is a sphere with radius 960 miles). a. 116 miles b miles c miles d. 107 miles e. Noe of the above Aswer: a Ratig II # Determie x if: log 8 ( x) 1 a) 8 b) 16 c) d) 64 e) 18 ANS: Start by addig / to each side the re-write as follows: log8 ( x) x 8 x 8 # (PY, t, m) What is the equatio of the lie taget to the circle ( x 1) + ( y + ) at poit (, 0)? a) 4x + y 0

8 Aswer: d b) x + 4y 0 c) x + 4y 0 d) 4x + y 0 e) Noe of the above #4 What is the product of the roots of the equatio: 6x 17x 14 0 a) -7/ b) -/7 c) -1/ d) 1/ ANS: After factorig we get: as a ( x 7)(x + ) 0 x 7 / or x / # Cosider the equatio below ad solve it for W. W ( 1+ W Pr Pr(1 + a) W 1 (1 + Pr(1 + b) W 1 (1 + 1 (1 + c) W Pr(1 + 1 (1 + d) W Pr(1 + W W Pr ( 1+ [ W Pr]( 1+ W W(1+ Pr1 ( + adw [(1 + 1] Pr( 1+ Pr( 1+ W (1+ 1 W W(1+ W Pr( 1+ #6 Determie the sie fuctio, that has a rage from y -1 to y 4., a period of π, ad a phase shift of π/6 to the left.

9 a).7 si (p x + p/6) b) 4. si (/ x + p/9) c).7 si (/ x + p/6) d).7 si (/ x + p/9) e) Noe of the above Solutio: The amplitude ad vertical shift are foud from the rage of y -1 to y 4.. The distace betwee the max ad mi is. with the midpoit of 1.7. Therefore the vertical shift is 1.7 ad the amplitude is./.7. From the period of π we kow that p π/b. Therefore, π π/b so b /. Fially a phase shift of π/6 to the left is traslated to the expressio (x + π/6) so that the fial formula is: f(x).7 si /(x + π/6) si ( / x + π/9) which is aswer d. #7 (TF, alg, easy) You have $1,000 to ivest with two optios: Fud A ears 6% ad Fud B ears 1%. How much should you ivest ito Fud A so that you ear $1,00 total from both fuds i 1 year? (earest dolla a) $4,8 b) $6,7 c) $7,908 d) $9,07 e) $10,714 ANS: Let x amt i Fud A ad x amt i Fud B, the we get:. 06x +.1(1000 x) x x 70 x ( ) #8 The equatio of a ellipse is: 4x + 8x + y 6y 0 At what poit o the graph is the maximum located at? a) (-1, 7 ) b) ( -1, 16) c) ( -1, ) d) ( -1, 1) ANS: First, complete the square, the determie the stadard form (is the verticle or horizotal axis the major axis?). 4x + 8x+ y 6y 4( x + x) + ( y 6y) 4( x + x+ 1) + ( y 6y + 9) ( x+ 1) ( x ) 4( x+ 1) + ( x ) maxat ( 1, + 4) ( 1, 7) 4 16 #9 (TF, log,easy) How log will it take for $1,000 to accumulate to $,000 assumig 14% iterest compouded semi-aually? a)

10 ANS: A easy problem t t l() ( / ) (1.07) t t 4 l(1.07) #0 (PY,la,med) Cosider a triagle ABC with vertices at A(-1, ), B(1, ), ad C(7,1) uder the trasformatio T(x, y) (x, y ). The ratio of the areas of the origial triagle over the trasformed triagle is approximately: a. 1: b. 1: c. 1:4 d. 1: e. Noe of the above ANS: a #1 (TF, alg, med) It takes Sally 4 hours to paddle upstream while it oly takes her hours to paddle dowstream.if Sally ca paddle 4. mph i still water, what is the total distace i miles that Sally travels? a) 1. b) 6 c) 1 d) 4 e) ca t be determied ANS: Let x rate of the stream, so 4. + x rate dowstream ad 4. - x rate upstream d d r t r t ( 4. + x) (4. x)4 9 + x 18 4x 6x 9 x 1. up dow up up dow dow distace (oe way) ( ) 1 ad 4 is correct. # (TF, alg, easy) What is the sum of the slope ad y-itercept of the equatio: x - y 6 a) -4/ b) -/ c) / d) 4/ e) oe of the above x y 6 y x + 6 y x ad ANS: Simple calculatios yield: a #. The sum of two umbers is 49 ad the quotiet is 6. What is the product of the two umbers? 4

11 a. 94 b. 8 c. 86 d. 416 e. oe of the above x + y 49 ad y x 6 x 6y 6y + y 49 y 7 x 4 ad 4 ( 7 94 ANS: a #4 ANS. Be careful writig dow the equatio: 10x x 8x 1 x 7 x x ad # ANS. Begi by squarig both sides gettig: 4 x 1+ ( ) ( )( ) ( 8) ± ± 176 x x.66or 0.66 ( 4) 8 #6 ANS. By ispectio, these are perpedicular #7 ANS. For this problem, we use the formula: a a ( 1) d + ( 1) #8 ANS. After careful calculatio, the above umbers yield: #9 ANS. After you multiply the umerator you get: 1 1 ( 6x 11x + ) ( ) 6x 11x + lim lim x x x x + 14x 1 14 ( x + 14x) + x x #40 ANS. Usig the hyper-geometric distributio, we get: 1(4C)1(4C).1% C x + + x + 1 x x + 1 4x + 4x 0 4 ( )( ) ( ) ( ) ( ) 19 4( x + ) 4x 8x 7 0 ( ) 7

FUNCTIONS (11 UNIVERSITY)

FUNCTIONS (11 UNIVERSITY) FINAL EXAM REVIEW FOR MCR U FUNCTIONS ( UNIVERSITY) Overall Remiders: To study for your eam your should redo all your past tests ad quizzes Write out all the formulas i the course to help you remember