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Recent problems solved by 'stanbon'

stanbon answered: 57146 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next

Graphs/89569: Graph the following. Find the asymptotes, if any. State the domain and range, and describe the concavity. y = __1_ x + 1 1 solutions Answer 65106 by stanbon(57214)   on 2007-07-22 22:09:47 (Show Source): You can put this solution on YOUR website! Find the asymptotes, if any. State the domain and range, and describe the concavity. y = __1_ x + 1 --------------------------------------------------------- Domain: all Real Numbers except x=-1 Range: all Real Numbers -------------------------------------- Vertical asymptote at x=-1 ------------------------------------- ------- Concave on the interval (-1,+inf) =================== Cheers, Stan H.

Graphs/89568: Graph the following and state the domain and range. y = (x - 1)^3 1 solutions Answer 65103 by stanbon(57214)   on 2007-07-22 22:04:23 (Show Source): You can put this solution on YOUR website! Domain: all Real numbers Range: all Real numbers -------------- ================ Cheers, Stan H.

Rational-functions/89509: Write a rational function satisfying the following criteria: Vertical assymptote: x=1 Assymptote: y=x+1 zero of the function: x=-2 1 solutions Answer 65099 by stanbon(57214)   on 2007-07-22 21:34:23 (Show Source): You can put this solution on YOUR website! Write a rational function satisfying the following criteria: Vertical asymptote: x=1 so f(x) must have a factor of (x-1) in the denominator ------------------- Asymptote: y=x+1 So, f(x) = g(x)/(x-1) = x+1 + k/(x-1) Need to find g(x) and k -------- zero of the function: x=-2 so f(x) must have a factor of (x+2) in the numerator. -------------------------------- Working the problem: f(x) = [(x+2)(ax+b)/(x-1)] = x+1 + k/(x-1) Then: f(-2) = 0 = -2+1+k/(-2-1) k/-3 = 1 k = -3 --------------- f(x) = [(ax^2+(b+2a)x+2b)/(x-1)] = x+1 -3/(x-1) Need to find a and b: Divide ax^2+(b+2a)x+2b by (x-1) to force a quotient of (x+1) and remainder =-3: This will happen if a=1 and b = -2 ---------------- So, f(x)= [(x+2)(x-2)/(x-1)] ================== Checking: (x^2-4)/(x-1) = x+1 -3/(x-1) which has a vertical asymptote at x=1, a zero at x=-2, and an asymptote of x+1 =================== Cheers, Stan H.

Square-cubic-other-roots/89517: This question is from textbook intermediate algebra 3 square root of 27k to the ninth power 1 solutions Answer 65088 by stanbon(57214)   on 2007-07-22 20:52:45 (Show Source): You can put this solution on YOUR website! 3 square root of 27k to the ninth power -------- 3sqrt(27k^9) = 3sqrt(9k^8)sqrt(3k) = 3*3*k^4 sqrt(3k) = 9k^4 sqrt(3k) =================== Cheers, Stan H.

Linear-equations/89538: A small firm produces both AM and AM/FM car radios. The AM radios take 15 h to produce, and the AM/FM radios take 20 h. The number of production hours is limited to 300 h per week. The plant’s capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 AM radios and at least 3 AM/FM radios be produced per week. Write a system of inequalities representing this situation. Then, draw a graph of the feasible region given these conditions, in which x is the number of AM radios and y the number of AM/FM radios 1 solutions Answer 65086 by stanbon(57214)   on 2007-07-22 20:49:33 (Show Source): You can put this solution on YOUR website! A small firm produces both AM and AM/FM car radios. Let x is the number of AM radios and y the number of AM/FM radios. The AM radios take 15 hr to produce, and the AM/FM radios take 20 hr. The number of production hours is limited to 300 hrs. per week. Production EQUATION: 15x+20y <=300 hrs ------------------ The plant’s capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 AM radios and at least 3 AM/FM radios be produced per week. 4<=x<=18 3<=y<=18 ------------------- Write a system of inequalities representing this situation. Then, draw a graph of the feasible region given these conditions, Draw a vertical line at x=4 and at x=18. ============ Cheers, Stan H. ------------

Linear-equations/89477: The height h in feet of an object after t seconds is given by the function h = –16t^2 + 90t + 3. How long will it take the object to hit the ground? Round your answer to the nearest thousandth, and explain which solution is the correct one. 1 solutions Answer 65082 by stanbon(57214)   on 2007-07-22 20:36:27 (Show Source): You can put this solution on YOUR website! The height h in feet of an object after t seconds is given by the function h = –16t^2 + 90t + 3. How long will it take the object to hit the ground? -------------------- h=0 when the object is on the ground. -16t^2+90t+3 = 0 t = [-90+-sqrt(90^2-4*-16*3)]/-32 t = 5.66 seconds =============== Cheers, Stan H.

Quadratic_Equations/89462: Which two expressions are equivalent? Explain your reasoning. -sqrt36, sqrt-36, -6 1 solutions Answer 65080 by stanbon(57214)   on 2007-07-22 20:28:59 (Show Source): You can put this solution on YOUR website! -sqrt36 = -6 --------- Cheers, Stan H.

Functions/89514: What is a relation? And can you give an example? 1 solutions Answer 65078 by stanbon(57214)   on 2007-07-22 20:27:18 (Show Source): You can put this solution on YOUR website! Any set of pairs of numbers is a relation: {(1,2),(3,5),(0,10)} is a relation ================= Cheers, stan H.

Radicals/89520: This question is from textbook algebra I am asked to find the equilibrium for demand and supply equations d=-5p+40 S=-p^2+30p-8 so far I have -p^2+30p-8=-5+40 0=p^2-30p+48 so, p=35+ sq rt(-35)^2-4(48)/2 =35+ sqrt701/2 4 options a.)$1.43 b.)$1.57 c.)1.71 d.)$1.29 how do I simplify this? please help 1 solutions Answer 65076 by stanbon(57214)   on 2007-07-22 20:12:46 (Show Source): You can put this solution on YOUR website! I am asked to find the equilibrium for demand and supply equations d=-5p+40 S=-p^2+30p-8 so far I have -p^2+30p-8=-5p+40 0=p^2-35p+48 so, p = [35+- sqrt((-35)^2-4(48)]/2 p = [35+-sqrt(1033)]/2 p = $33.57 o $1.43 ======================== ================= Cheers, Stan H. 4 options a.)$1.43 b.)$1.57 c.)1.71 d.)$1.29 how do I simplify this? please help

logarithm/89526: During 1991, 200,000 people visited a particular amusement park. During 1996, the number had grown to 604,000. Find an exponential model for this data, lettingrepresent the number of visitors in any year andrepresent the number of years since 1991. 1 solutions Answer 65075 by stanbon(57214)   on 2007-07-22 19:57:27 (Show Source): You can put this solution on YOUR website! Comment: Two words are missing from your posted problem. Cheers, Stan H.

logarithm/89527: Condense the expression to the logarithm of a single quantity. 2log10(x)-5log10(x-7) 1 solutions Answer 65074 by stanbon(57214)   on 2007-07-22 19:55:18 (Show Source): You can put this solution on YOUR website! 2log10(x)-5log10(x-7) Comment: Just keep in mind it is all base 10. =logx^2 - log(x-7)^5 = log[x^2/(x-7)^5] ================ Cheers, stan H.

Equations/89532: 5263=235,000 / 100 - x 140,000 = 4,250,00 / x-50 1 solutions Answer 65073 by stanbon(57214)   on 2007-07-22 19:50:47 (Show Source): You can put this solution on YOUR website! 5263=235,000 / 100 - x 100 - x = 235000/5263 x = -44.65+100 x= 55.35 ================== 140,000 = 4,250,00 / x-50 x-50 = 4250000/140000 x-50 = 30.36 x = 80.36 ================== Cheers, Stan H.

Probability-and-statistics/89502: I need help with these problems please explain them to me step by step thanks....I have an exam tomorrow i want to really understand them;..... Problem #1 Find the percent of the total area under a normal curve that is contained within the specified interval. Between the mean and 1.64 standard deviations from the mean Problem #2 Find the percent of the total area under the standard normal curve between the given z-scores. z= -1.10 and z = -0.36 1 solutions Answer 65060 by stanbon(57214)   on 2007-07-22 15:59:38 (Show Source): You can put this solution on YOUR website! Problem #1 Find the percent of the total area under a normal curve that is contained within the specified interval. Between the mean and 1.64 standard deviations from the You need a z-chart or a calculator with z capability, like a TI 83 or 84 On the z cart find z=1.64. The chart tells you the area over the interval [0,1.64] = 0.9495-0.5000 = 0.4495 -------------------- Problem #2 Find the percent of the total area under the standard normal curve between the given z-scores. z= -1.10 and z = -0.36 Look up z = 1.10 = 0.8643-0.5000 = 0.3643 Look up z = 0.36 = 0.6406-0.5000 = 0.1406 Subtract the 2nd area from the 1st to get 0.2237 -------- Comment: Your z-chart might be arranged differently but the final figure you get should be the same as the one I have. =============== Cheers, Stan H.

Functions/89505: A. Find the function of the circle's center. B. Find the radius of the cirle. C. Use your answer from part (a) and (b) to write the standard form of the cirle's equation. y | |(3,6) | * | *(5,4) |_____________x 1 solutions Answer 65056 by stanbon(57214)   on 2007-07-22 15:14:24 (Show Source): You can put this solution on YOUR website! I think you left something out of your posting or it was dropped by the site in transmitting. Cheers, Stan H.

Matrices-and-determiminant/89489: PLEASE HELP ME!!!! I need help because i am confused i am not getting this please explain these two problems step by step so i can refocuse on what i have to do....If someone has afew thank i really appreciate all your help... Problem #1 (*I used the underscore to separate the numbers*) find the inverse, if it exists, for the matrix -2_1_3 3_-1_2 -4_2_0 Problem #2 Solve the matrix equation AX=B for X by finding A to power * Matrix A is a 3X3 A = 2_-1_3 -3_4_-5 -4_0_6 and matrix b is a 3X1 B= 9 6 -9 1 solutions Answer 65054 by stanbon(57214)   on 2007-07-22 13:55:08 (Show Source): You can put this solution on YOUR website! Problem #1 (*I used the underscore to separate the numbers*) find the inverse, if it exists, for the matrix -2_1_3 3_-1_2 -4_2_0 --------.........[-4...6...5] Inverse = (1/6) [-8..12..13] .................[2....0..-1] I'll let you do the work to show that is correct. ===================== Problem #2 Solve the matrix equation AX=B for X by finding A to power * Matrix A is a 3X3 A = 2_-1_3 -3_4_-5 -4_0_6 and matrix b is a 3X1 B= 9 6 -9 ------- A^(-1)B = [5.43] ..........[8.22] ..........[2.12] =================================== Cheers, Stan H.

Polynomials-and-rational-expressions/89387: I would like some help with the following problems. Please explain to me how these problems have to be worked out. Find the value of the following polynomial for the given value of the variable. -x2-5x-6,x=-3 and = -2( first 2 is a exponent) What expression raised to the fourth power is 81x12y8z16?( the numers after the variables are exponents) The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w+13.3 Find the cost when 375 wing nuts are made. What is the average cost to manufacture one wing nut? Thank you for taking tie to help me out. Thanks. 1 solutions Answer 65053 by stanbon(57214)   on 2007-07-22 13:31:47 (Show Source): You can put this solution on YOUR website! Find the value of the following polynomial for the given value of the variable. -x2-5x-6,x=-3 and = -2( first 2 is a exponent) ------ -2^2-5*2-6 =-4-10-6 =-20 =============== What expression raised to the fourth power is 81x12y8z16?( the numers after the variables are exponents) x^4 = 81x^12y^8z^16 x = 3x^3y^2z^4 ===================== The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w+13.3 Find the cost when 375 wing nuts are made. Cost = (0.07*375+13.3) = 39.55 ------------- What is the average cost to manufacture one wing nut? 39.55/375 = 0.1055 ================= Cheers, Stan H.

Quadratic_Equations/89423: If Corliss invested $100 at an annual rate of 8% compounded continuously, what amount to the nearest cent will be in her account after 2 years? 1 solutions Answer 65050 by stanbon(57214)   on 2007-07-22 13:14:50 (Show Source): You can put this solution on YOUR website! If Corliss invested $100 at an annual rate of 8% compounded continuously, what amount to the nearest cent will be in her account after 2 years? ---------- A = Pe^(rt) A = 100e^(0.08*2) A = $117.35 ============= Cheers, Stan H.

Polynomials-and-rational-expressions/89431: I cant seem to figure this out and need some help: What value of x must be excluded in the following fraction? x+8/5 Thank you 1 solutions Answer 65049 by stanbon(57214)   on 2007-07-22 13:10:41 (Show Source): You can put this solution on YOUR website! None Cheers, Stan H.

Graphs/89441: Under what conditions is the graph of a function y = f(x)said to be symmetric through the origin? 1 solutions Answer 65048 by stanbon(57214)   on 2007-07-22 13:09:12 (Show Source): You can put this solution on YOUR website! When f(x) = -f(-x) ========== Cheers, stan H.

Quadratic_Equations/89478: Find the axis of symmetry. Your answer should be the equation that represents the axis of symmetry. y = –x^2 + 10x – 1 1 solutions Answer 65046 by stanbon(57214)   on 2007-07-22 13:00:03 (Show Source): You can put this solution on YOUR website! y = –x^2 + 10x – 1 Complete te square on the x terms: y = -(x^2-10x+?)-1--? y = -(x^2-10x+25)-1+25 y = -(x-5)^2+24 axis of symmetry is x=5 ================ Cheers, Stan H.

Polynomials-and-rational-expressions/89486: Is the following trinomial a perfect square? Please explain your answer. x2 + 10x + 25 1 solutions Answer 65044 by stanbon(57214)   on 2007-07-22 12:52:20 (Show Source): You can put this solution on YOUR website! Yes; the 1st and the 3rd terms are perfect squares. The 2nd term is twice the product of the square-roots of the 1st and the 3rd terms. Those conditions make it a perfect trinomial square. ============== Cheers, Stan H.

Expressions-with-variables/89474: Please help me solve this problem: 50,000 -10,000(P) = 25,000(P) Thanks 1 solutions Answer 65038 by stanbon(57214)   on 2007-07-22 11:45:18 (Show Source): You can put this solution on YOUR website! 50,000 -10,000(P) = 25,000(P) 50,000 = 35000p p = 50/35 p = 10/7 ================ Cheers, stan H.

Quadratic_Equations/89473: The length of a rectangle is 2 cm more than 5 times its width. If the area of the rectangle is 65 cm2, find the dimensions of the rectangle to the nearest thousandth Hint: Call the width x. Then the length is 5x + 2. Now write your equation and solve. 1 solutions Answer 65037 by stanbon(57214)   on 2007-07-22 11:42:14 (Show Source): You can put this solution on YOUR website! The length of a rectangle is 2 cm more than 5 times its width. If the area of the rectangle is 65 cm2, find the dimensions of the rectangle to the nearest thousandth -------------- Area = lw Let width = x Then length = 5x+2 ---------- EQUATION: x(5x+2) = 65 5x^2+2x = 65 5x^2+2x-65=0 x=[-2+-sqrt(4-4*5*-65)]/10 x=[-2+-sqrt1304]/10 x=[-2+-36.11..]/10 Positive solution: x=[-2+36.11...]/10 x=4.411 (width) 5x+2 - 19.06 (length) ============= Cheers, stan H. Positive solution: x=-1+sqrt14 = 2.74... (width) 5x+2 = 15.71..

Quadratic_Equations/89470: Simplify. Express your answer in simplified radical form sqrt5x/sqrt3 1 solutions Answer 65036 by stanbon(57214)   on 2007-07-22 11:15:24 (Show Source): You can put this solution on YOUR website! sqrt5x/sqrt3 --------- Multiply numerator and denominator by sqrt3 to get [sqrt15x]/3 ============== Cheers, stan H.

Quadratic_Equations/89456: Would someone help me please. The directions are to divide. x^3+2x^2+x+12/x+3. I have four choices for the answer A)x^2-x+4, B)x^2+x-14, C) x^2-x-4, and D) x^2+x-4. Please show me step by step how you got this answer, and what method or formula you used to solve? Thank you 1 solutions Answer 65035 by stanbon(57214)   on 2007-07-22 10:55:00 (Show Source): You can put this solution on YOUR website! x^3+2x^2+x+12/x+3 ----- Using synthetic division: --------- -3)....1....2....1....12 ........1....-1....4..|..0 ================= Remainder: 0 Quotient: x^2-x+4 ===================== Cheers, Stan H.

Quadratic-relations-and-conic-sections/89448: PLEASE HELP ME WITH THIS FOUR PROBLEMS ABOUT WRITING AN EQUATION FOT THE CONIC SECTION THANK U I APPRECIATE YOUR SUPPORT I NEEDED FOR THIS MONDAY 24 ,JULY, 07 1. CIRCLE WITH CENTER AT (4, -3) AND A RADIUS OF 8. 2. PARABOLA WITH VERTIX OF (2,-4) AND FOCUS OF ( 2,2). 3. ELIPSE WITH VERTIXES (-4,0) AND (4,0) AND CO-VERTICES (0,-9) AND (0,9). 4. HYPERBOLA WITH VERTICES (1,2) AND (5,2) AND FOCI (-1,2) AND (7,2). THANK YOU!!!!! 1 solutions Answer 65034 by stanbon(57214)   on 2007-07-22 10:40:34 (Show Source): You can put this solution on YOUR website! For each of these you should draw the picture so you see how vertices, foci,radius, etc. relate to one another. 1. CIRCLE WITH CENTER AT (4, -3) AND A RADIUS OF 8. (x-4)^2+(y+3)^2 = 64 ------------------- 2. PARABOLA WITH VERTIX OF (2,-4) AND FOCUS OF ( 2,2). Form: (x-h)^2 = 4p(y-k) (x-2)^2 = 4*6(y+4) x^2-4x+4 = 24y+96 x^2-4x-92 = 24y y = (1/24)x^2 -(1/6)x-(23/6) ------------------ 3. ELIPSE WITH VERTIXES (-4,0) AND (4,0) AND CO-VERTICES (0,-9) AND (0,9). x^2/16 + y^2/81 = 1 ----------------- 4. HYPERBOLA WITH VERTICES (1,2) AND (5,2) AND FOCI (-1,2) AND (7,2). Form: (x-h)^2/a^2 - (y-k)^2/b^2 = 1 --------- Vertices at (1,2),(5,2) implies center is at (3,2) Center at (3,2)and vertex at (5,2) implies a=2 Center at (3,2) and focus at (7,2) implies c=4 For ellipe b^2=c^2-a^2 b^2 = 4^2-2^2 = 12 ----------- EQUATION: (x-3)^2/4 - (y-2)^2/12 = 1 ============ Cheers, stan H.

Miscellaneous_Word_Problems/89455: can you direct me on the right path to solve this problem. A store sells tents, sleeping bags, an camp stools. A customer buys a tent, 3 sleeping bags and 2 camp stools for $175. The price of the tent is 6 times the cost of a camp stool. The cost of the sleeping bag is $40 more then the cost of a camp stool. I have to find the cost of each item. Now I know i have to solve for X which will be the price of the stool but I'm unsure what is next. 1 solutions Answer 65032 by stanbon(57214)   on 2007-07-22 09:24:16 (Show Source): You can put this solution on YOUR website! A customer buys a tent, 3 sleeping bags and 2 camp stools for $175. The price of the tent is 6 times the cost of a camp stool. The cost of the sleeping bag is $40 more then the cost of a camp stool. ---------------- t+3b+2s = 175 t=6s b=s+40 ----------------- EQUATION: Substitute to solve for s: 6s+3(s+40)+2s=175 6s+3s+120+2s=175 11s = 55 s = $5 (price of a stool) t=6s=$30 (price of a tent) b=s+40=$45 (price of a bag) ================== Cheers, Stan H.

Length-and-distance/89454: I have a problem that has thrown me for a loop. I am to find all values of y such that the distance between (3,y) and (-2,9) is 12. I tried to solve this problem by using the distance formula (X1,Y1)and (X2,Y2). Which looks like this d=the square root of (X2-X1)2 + (Y2-Y1)2 ***this is all under the square root symble and the 2 are squares** (-2-3)2+(3-y)2 remember the 2's are sqrares and the problem is under the sqrare root symbole (5)2+ (3-y)2 100+9-y2 109-Y2 I'm not sure if I am on the right path. Please help! (sorry i do not know how to put the root symbole or make the 1 by the X and Y small on the computer) 1 solutions Answer 65031 by stanbon(57214)   on 2007-07-22 09:15:30 (Show Source): You can put this solution on YOUR website! find all values of y such that the distance between (3,y) and (-2,9) is 12. --------- d = sqrt((3--2)^2 + (y-9)^2) 12 = sqrt( 25 + (y-9)^2) 144 = 25 + (y-9)^2 119 = (y-9)^2 y = sqrt119 +9 or y = -sqrt119+9 y=19.909 or y= -1.909 ======== Cheers, stan H.

Equations/89443: figure out the y-intercept of the graph of the equation y=x2 (this is x squared) 6x = 9 and -3/2 (x-6)2 (squared). 1 solutions Answer 65030 by stanbon(57214)   on 2007-07-22 09:01:32 (Show Source): You can put this solution on YOUR website! According to Newton's Law of Gravitation the force of attraction between two objects varies jointly as their masses and inversely square of the distance between them. How does the force change if each of their masses is tripled but the distance between them is cut to one-third? --------------- a = k(m1*m2/d^2) ---------- After change: a = k(3m1*3m2/((1/3)d)^2 a = k(9m1*m2/((1/9)d^2) a = 81k(m1*m2/d^2) =============== Cheers, stan H.

Quadratic_Equations/89453: Please help me on how to figure out the y-intercept of the graph of the equation y=x2 (this is x squared) 6x = 9 and -3/2 (x-6)2 (squared). 1 solutions Answer 65027 by stanbon(57214)   on 2007-07-22 08:44:04 (Show Source): You can put this solution on YOUR website! figure out the y-intercept of the graph of the equation y=x2 (this is x squared) 6x = 9 and -3/2 (x-6)2 (squared). ------.-- Do you mean y = x^2+6x+9 and y=(-3/2)(x-6)^2 =================== Cheers, Stan H

Quadratic_Equations/89451: Please help me on how to figure out the vertex of the equation 2y=x2(this is x squared)-2x-5. 1 solutions Answer 65025 by stanbon(57214)   on 2007-07-22 08:37:37 (Show Source): You can put this solution on YOUR website! Please help me on how to figure out the vertex of the equation 2y=x2(this is x squared)-2x-5. ---------------- 2y=x^2-2x-5 Complete the square on the x-terms and keep the equation balanced: 2y+5+1 = x^2-2x+1 2(y+3) = (x-1)^2 ----------- The vertex is at (1,-3) ----------------------- Another way to find it: y = (1/2)x^2-x-(5/2) The vertex occus when x=(-b)/(2a) = 1/(2*(1/2)) = 1/1=1 Solve for y to get the y coordinate: y = (1/2)1^2-1-(5/2) = (1/2)-1(-5/2) = -6/2 = -3 =============== Cheers, Stan H.