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# Recent problems solved by 'stanbon'

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 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 logarithm/158685: 5^x=12 use log to solve for x.1 solutions Answer 116867 by stanbon(57361)   on 2008-09-23 23:43:04 (Show Source): You can put this solution on YOUR website!5^x=12 use log to solve for x. ----------- Take the log of both sides to get: x(log5) = log12 x = [log12] / [log5] ------------ I don't have a calculator with me so maybe you do and can perform the division to solve for "x". ------------------ Cheers, Stan H.
 Equations/158682: This question is from textbook Prealgebra -5w+2+6w=-4+9 This is what I got; I know I need to find the like terms, which are -5w & 6w. -5w + 6w = 1w + 2 = 5 I know I need to balance each side out equally...but not sure how to do that. I'm stuck! Also, not sure how to check my work. This problem is in my text book: Prealgebra Third Edition by Lial Hestwood page 115 #39. Thank you for your help! Pauline1 solutions Answer 116866 by stanbon(57361)   on 2008-09-23 23:38:03 (Show Source): You can put this solution on YOUR website!-5w+2+6w=-4+9 Simplify the left side and the right side of the equation: w + 2 = 5 Subtract 2 from both sides to get: w = 3 ============ Checking; substitute 3 in place of "x" in the original equation: -5*3 + 2 + 6*3 = -4+9 -15 + 2 + 18 = 5 5 = 5 ============== Cheers, Stan H.
 Polynomials-and-rational-expressions/158540: I need help with this multiplication: 3x over 2y * y^2 over 6 = ? Thank you for your help.1 solutions Answer 116800 by stanbon(57361)   on 2008-09-23 08:21:39 (Show Source): You can put this solution on YOUR website!3x over 2y * y^2 over 6 = ? --------------------------------- (3x/2y)* (y^2/6) -------- Cancel any factors that are common to a numerator and a denominator, such as y, and 3, to get: =(x/2)* (y/2) Now multiply the numerators and multiply the denominators to get: =(xy)/4 --------- Cheers, Stan H.
 Functions/158479: Find the domain of the following: 1.f(x)=4.5e 2. g(x)=2^x Show your work and explain how you obtained your answer 3. h(x)=-e^x Description of transformation Equation(s) for the Horizontal Asymptote(s). y-intercept in (x,y) form:1 solutions Answer 116787 by stanbon(57361)   on 2008-09-22 23:52:30 (Show Source): You can put this solution on YOUR website!Find the domain of the following: 1.f(x)=4.5e Domain: all Real Numbers Description: horizontal line thru all points where y = 4.5*2 Horizontal Asymptote: none y-intercept: Let x = 0, then y = 4.5e intercept is (0,4.5e) ------------------------------ 2. g(x)=2^x Show your work and explain how you obtained your answer Domain: all Real Numbers Description: increasing exponential function Horizontal Asymptote: y = 0 y-intercept: Let x=0, then y = 1 Intercept is (0,1) ------------------------------ 3. h(x)=-e^x Domain: all Real Numbers Description: decreasing exponential function Horizontal Asymptote: y = 0 y-intercept: Let x = 0, then y = -1 Intercept is (0,-1) =================================== Cheers, Stan H.
 Exponents/158496: This question is from textbook Math Connections I'm Having A Hard Time Trying To Get This Question Answered. "Can each of the following be expressed as a power of two? If Yes, do so. If No, Explain why not." Problem A: 2^3 * 2^85 I Don't Know What The Questions Means/Wants.1 solutions Answer 116786 by stanbon(57361)   on 2008-09-22 23:35:16 (Show Source): You can put this solution on YOUR website!"Can each of the following be expressed as a power of two? If Yes, do so. If No, Explain why not." Problem A: 2^3 * 2^85 = 2^(3+85) = 2^88 ============= Cheers, Stan H.
 Expressions-with-variables/158514: Define a variable, write an inequality for: Four more than the quotient of a number and 3 is at least that number. I'm stuck about showing the quotient. I wrote 4 + 1/x + 3 > x Please help and thanks, Justin1 solutions Answer 116785 by stanbon(57361)   on 2008-09-22 23:32:26 (Show Source): You can put this solution on YOUR website!Define a variable, write an inequality for: Four more than the quotient of a number and 3 is at least that number. ---------------- Let the number be "x". INEQUALITY: (x/3) + 4 >= x ===================== Cheers, Stan H.
 expressions/158526: This question is from textbook Algerbra 1 Placing planks at equel length end to end, jewels found that three planks where one foot short of the portch length, while four planks were two feet to long. How long was each plank?1 solutions Answer 116784 by stanbon(57361)   on 2008-09-22 23:21:48 (Show Source): You can put this solution on YOUR website!Placing planks at equal length end to end, jewels found that three planks where one foot short of the porch length, while four planks were two feet to long. How long was each plank? ------------------- EQUATION: porch length = porch length 3p+1 = 4p-2 p = 3 ft. Cheers, Stan H.
 Word_Problems_With_Coins/158293: Susan has saved \$85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have. I have tried this a zillion times using 2 separate equations and the elimination method a variety of ways, but cannot seem to get an answer that fits back. If someone can show me the proper equation to be using please then I can solve from there. Thanks. 1 solutions Answer 116670 by stanbon(57361)   on 2008-09-21 23:49:38 (Show Source): You can put this solution on YOUR website!Susan has saved \$85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have. ------------------------ I believe a "looney" is one dollar. If that is right you get the following equations: Value Equation: 25Q + 100L = 8575 Quantity Equation: Q = (3/4)L + 1 ----------------------------------- Rearrange the equations: 4Q - 3L = 4 25Q + 100L = 8575 ------------------------ Multiply the 1st equation by 25; Multiply the 2nd equation by 4. 100Q - 75L = 100 100Q + 400L = 4*8575 ---------------------- Subtract the 1st equation from the 2nd to get: 475L = 4*8575 - 100 ------------------------ I don't have a calculator with me so I'll leave solving "L" to you. When you get "L" substitute into one of the early equation to solve for Q. -------------------------- Cheers, Stan H.
 Travel_Word_Problems/158306: Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive each way. (i'm in 8th grade, and it just doesn't make sense to me) But I think this is what I am supposed to do, but I don't understand why it works.. if it does. 1 solutions Answer 116669 by stanbon(57361)   on 2008-09-21 23:39:29 (Show Source): You can put this solution on YOUR website!Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive each way. ------------------------------------- School to home DATA: rate = 20 mph ; distance = x miles ; time = d/r = x/20 hrs --------------------------- home to school DATA: rate = 30 mph ; distance = x miles ; time = d/r = x/30 hrs ----------------------------- EQUATION: time + time = 1.5 hours x/20 + x/30 = 3/2 Multiply thru by 60 to get: 3x + 2x = 90 5x = 90 x = 18 miles (distance each way) ----------- time to drive from home to school = 18/20 = 9/10 hr = 54 minutes time to drive from school to home = 18/30 = 3/5 hr = 36 minutes ====================== Cheers, Stan H.
 Square-cubic-other-roots/158307: How do you solve...?... (x+4)exponent5=-1 ...??? ...Thanks1 solutions Answer 116667 by stanbon(57361)   on 2008-09-21 23:31:38 (Show Source): You can put this solution on YOUR website!(x+4)exponent5=-1 ------------ Take the 5th root of each side to get: x+4 = -1 x = -5 ========== Cheers, Stan H.
 Percentage-and-ratio-word-problems/158309: Anna has 6 liters of 60% acid. How much water should she add to make a solution that is 40% acid?1 solutions Answer 116666 by stanbon(57361)   on 2008-09-21 23:27:32 (Show Source): You can put this solution on YOUR website!Anna has 6 liters of 60% acid. How much water should she add to make a solution that is 40% acid? --------------------- Acid Equation: 0.6*6 + 0*x = 0.4(6+x) 0.36 = 0.24 + 0.4x 0.4x = 0.12 x = 3 liters (amount of water that must be added) ----------- Cheers, Stan H.
 Geometry_Word_Problems/156936: This question is from textbook PRECALCULUS Mathmatics for Calculus 4th I can't figure out how to even start this: The hypotenuse of a right triangle has length 20 cm. The sum of the lengths of the other two sides is 28 cm. Find the lengths of the other two sides of the triangle.1 solutions Answer 115705 by stanbon(57361)   on 2008-09-14 19:17:01 (Show Source): You can put this solution on YOUR website!Let one of the sides be "x"; Let the other side be "28-x' Use Pythagoras to find "s" and 28-x: EQUATION: x^2 + (28-x)^2 = 20^2 x^2 + 784 - 56x + x^2 = 400 2x^2 -56x + 384 = 0 x^2 - 28x + 192 = 0 (x-12)(x-16) = 0 x = 12 or x = 16 ----------- Cheers, Stan H.
 expressions/156695: How do I solve for x in the following: (x x x) - 3 = 8x (the xxx in paranthesis is x times x times x) thank you! (it is a teacher created homework problem and not a problem in text. Even looked in text trying to find a model problem and could not. We are in the Mcdougal Littel Algebra 1 book.)1 solutions Answer 115565 by stanbon(57361)   on 2008-09-13 18:03:43 (Show Source): You can put this solution on YOUR website!solve for x in the following: (x x x) - 3 = 8x x^3 -8x -3 = 0 ------------ I graphed it and found it crossed the x-axis at 2.148177... --------------- Cheers, Stan H.
 Radicals/156659: 3^x-5=31 solutions Answer 115481 by stanbon(57361)   on 2008-09-13 07:45:14 (Show Source): You can put this solution on YOUR website! 3^(x-5) = 3 ----------------- Since the bases are the same, the exponents must be equal: x-5 = 1 x = 6 =========== Cheers, Stan H.
 expressions/156502: This question is from textbook Algebra x^2+3x+2 x^2+5x+4 ________ / _________ x^2+7x+12 x^2+5x+61 solutions Answer 115480 by stanbon(57361)   on 2008-09-13 07:17:27 (Show Source): You can put this solution on YOUR website!x^2+3x+2 x^2+5x+4 ________ / _________ x^2+7x+12 x^2+5x+6 ------------------------------ Factor where you can to get: (x+2)(x+1) (x+4)(x+1) ________ / _________ (x+3)(x+4) (x+3)(x+2) -------------------------------- Invert the denominator and change to multiplication: (x+2)(x+1) (x+3)(x+2) ________ * _________ (x+3)(x+4) (x+4)(x+1) --------------------------------- Cancel factors that are common to a numerator and denominator, such as (x+1), (x+3) (x+2) (x+2) ________ * _________ (x+4) (x+4) -------------------------------- = (x+2)^2 / (x+4)^2 ========================= Cheers, Stan H.
 Polynomials-and-rational-expressions/156628: A biologist estimated the population of seals on a group of islands over a span of 20 years after restrictions were put on hunting. Her data can be modeled by the equation P= 0.6x^4−19x^3+220x^2−850x+1900, where x is the number of years after the restrictions went into place, and P is the total population of seals. Evaluate the population for x = 15. 1 solutions Answer 115479 by stanbon(57361)   on 2008-09-13 06:56:01 (Show Source): You can put this solution on YOUR website!I put P(x) into a calculator. I substituted 15 for x and got P(15) = -39650 ------------------------ Cheers, Stan H.
 Geometry_proofs/156638: This question is from textbook Given: Line segment BD is parallel to line segment AE Prove: Triangle DCB ~ triangle ECA ? Statements Reasons Line segments BD AE are parallel Given Angles CDB CEA, _______________________ CBD, CAE are congruent _______________________ _______________________ Triangles DCB ~ ECA _______________________ _______________________ I don't know why I have such a problem figuring out proofs, but I do, I think at the angle congruent question they are looking for a theorem, and triangles, I think I need to prove, but I don't how. Can you help me. I am about to graduate in less than 2 weeks, and personally, I am losing my mind over proofs.1 solutions Answer 115478 by stanbon(57361)   on 2008-09-13 06:51:01 (Show Source): You can put this solution on YOUR website!Where is point C in the figure? Cheers, San H.
 Miscellaneous_Word_Problems/156616: Suppose Charlie O’Brian hits a baseball straight upward at 150ft/sec from a height of 5 ft. 1 solutions Answer 115477 by stanbon(57361)   on 2008-09-13 06:49:00 (Show Source): You can put this solution on YOUR website!What is the question? Cheers, Stan H.
 Polynomials-and-rational-expressions/156626: g^2 - g - 12/g^2 - 10g + 24 divided by g^2 - 9/g^2 - 7g + 61 solutions Answer 115476 by stanbon(57361)   on 2008-09-13 06:47:19 (Show Source): You can put this solution on YOUR website!(g^2 - g - 12)/(g^2 - 10g + 24) / (g^2 - 9) / (g^2 - 7g + 6) -------------------------------------------------------------- Factor where you can to get; [(g-4)(g+3)] / [(g-6)(g-4)] / [(g-3)(g+3)] / [(g-6)(g-1)] --------------------------------------------------------------- Invert the denominator and change to multiplication: [(g-4)(g+3)] / [(g-6)(g-4)] * [(g-6)(g-1)][(g-3)(g+3)] --------------------------------------------------------------- Cancel factors that are common to a numerator and a denominator, such as (g-4), (g-6), (g+3): [1/1] / [1/1)] * [(g-1)][(g-3)] ---------------------------------------------------------------- = (g-1)/(g-3) ===================== Cheers, Stan H.
 Polynomials-and-rational-expressions/156627: simplify: (q^9)^7/r^61 solutions Answer 115475 by stanbon(57361)   on 2008-09-13 06:30:59 (Show Source): You can put this solution on YOUR website!simplify: (q^9)^7/r^6 -------------------------- = q^63 / r^6 ========================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/156639: A sum of money is made up of \$5 bills and \$10 bills. The total number of \$5 bulls is at least 3 less than double the number of \$10 bulls. That sum of money is a minimum of \$65. What would that look like as an inequality equation?1 solutions Answer 115474 by stanbon(57361)   on 2008-09-13 06:28:27 (Show Source): You can put this solution on YOUR website!A sum of money is made up of \$5 bills and \$10 bills. ------------------------------ The total number of \$5 bills is at least 3 less than double the number of \$10 bills. Quantity Inequality: F >= 2T -3 ---------------- That sum of money is a minimum of \$65. Value Inequality: 5F + 10T >= 65 ---------------- That is what the inequalities look like. =========================================== Cheers, Stan H.
 Inequalities/156642: Use the set builder notation to describe the complete solution. 7/4(3x-1/2)-4/3<5/3 1 solutions Answer 115471 by stanbon(57361)   on 2008-09-13 06:18:20 (Show Source): You can put this solution on YOUR website!Use the set builder notation to describe the complete solution. 7/4(3x-1/2)-4/3<5/3 --------------------------------------------- (21/4)x - (7/8) - (4/3) < (5/3) Add (4/3) to both sides to get: (21/4)x - (7/8) < 3 Multiply thru by 8 to get: 42x - 7 < 24 Add 7 to both sides to get: 42x < 31 x < 31/42 ---------------- Set Builder: {x| x < (31/42)} ================================= Cheers, Stan H.
 Signed-numbers/156623: Find the difference of the given terms: -15a squared b squared - (-6a squared b squared)1 solutions Answer 115468 by stanbon(57361)   on 2008-09-13 06:11:41 (Show Source): You can put this solution on YOUR website!Find the difference of the given terms: -15a squared b squared - (-6a squared b squared) ---------------------------------------------------- -15a^2b^2 - (-6a^2b^2) = -15a^2b^2 + (6a^2b^2) = -9a^2b^2 ============= Cheers, Stan H.
 Rate-of-work-word-problems/156655: An application of rational function is T=(AB)/(A+B) Which gives the time T dictates for 2 workers to complete a particular task where A+B represent the time it would take for each individual worker to complete the identical task. Then how long is would take together. My personal example: It takes me 3.5 hours in 1 day to do my weekly house cleaning chores. It takes my mother 4-5 hrs a day for 4 days to do her housecleaning chores for the week. I need the solution to be showed, and I need you to explain it to me please. Thank you.1 solutions Answer 115466 by stanbon(57361)   on 2008-09-13 06:01:40 (Show Source): You can put this solution on YOUR website!An application of rational function is T=(AB)/(A+B) Which gives the time T dictates for 2 workers to complete a particular task where A+B represent the time it would take for each individual worker to complete the identical task. Then how long is would take together. ------------------------------------------ My personal example: It takes me 3.5 hours in 1 day to do my weekly house cleaning chores. It takes my mother 4-5 hrs a day for 4 days to do her housecleaning chores for the week. -------------------------------------- T=(AB)/(A+B) A = 3.5 hrs B = 5 hrs (Note: You can't say "4 to 5"; you must select a number) ---------- Then T = [3.5*5] / [3.5 + 5] T = 17.5/8.5 T = 2.05.. hrs. ==================== Cheers, Stan H.
 Linear_Algebra/156658: can i ask u how to show that B is a subset of V as V={(a,b,c)|a-b=c} and B={(0,-1,1),(1,-1,2)}1 solutions Answer 115464 by stanbon(57361)   on 2008-09-13 05:50:30 (Show Source): You can put this solution on YOUR website!can i ask u how to show that B is a subset of V as V={(a,b,c)|a-b=c} and B={(0,-1,1),(1,-1,2)} -------------------------------- V is the set of all triplets of the form (a,b,c) that satisfy the condition that a-b=c. ------------------- But (0,-1,1) is a triplet where 0-(-1)=1; And (1,-1,2) is a triplet where 1-(-1)=2. -------- Since both elements of B satisfy the conditions of V, B is a subset of V. ========================= Cheers, Stan H.
 Expressions-with-variables/156651: 1/2bh When b=14 h=22?1 solutions Answer 115456 by stanbon(57361)   on 2008-09-12 22:50:46 (Show Source): You can put this solution on YOUR website!1/2bh When b=14 h=22 ----------- Area of a triangle = (1/2)bh Area = (1/2)*14*22 Area = 14*11 = 154 ====================== Cheers, Stan H.
 Miscellaneous_Word_Problems/156643: for the following function, c computes a value, where if you add millions of dollars to the value, the result is the cost of implementing a city recycling project when x, as a perentage(not its decimal equivalent) citizens participate. C(x)= 1.5x/100-x a. Using this model, determine the cost if 60% of the citizen's participate. b. Using this model, find the percentage of participation that can be expected if \$5 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.1 solutions Answer 115455 by stanbon(57361)   on 2008-09-12 22:48:16 (Show Source): You can put this solution on YOUR website!C(x)= 1.5x/100-x a. Using this model, determine the cost if 60% of the citizen's participate. C(60) = 1.5*60/(100-60) = 90/40 = 9/4 = \$2.25 million --------------------------------------------------------- b. Using this model, find the percentage of participation that can be expected if \$5 million is spent on this recycling project? 5 = 1.5x/(100-x) 500 -5x = 1.5x 6.5x = 500 x = 76.92% ================ Cheers, Stan H. Set up an equation and solve algebraically. Round to the nearest whole percent.
 Linear_Equations_And_Systems_Word_Problems/156644: Jonathan plays midget hockey. Last season, three times the number of assists he made was less than the number of goals he scored. At the end of the season he had more than 58 points (assists and goals). Write in two inequality equations1 solutions Answer 115449 by stanbon(57361)   on 2008-09-12 22:02:52 (Show Source): You can put this solution on YOUR website!Jonathan plays midget hockey. ------------------------------- Write in two inequality equations ------------------------------- Last season, three times the number of assists he made was less than the number of goals he scored. INEQUALITY: 3a < g -------------- At the end of the season he had more than 58 points (assists and goals). a + g > 58 ---------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/156645: Subtract and simplify (8-v)/(v-2) - (4v-9)/(v-2) i got -v+8/v-2 -4v-9/-v+2... do i go a step further? Is there a step beyond this? 1 solutions Answer 115448 by stanbon(57361)   on 2008-09-12 21:57:40 (Show Source): You can put this solution on YOUR website!Subtract and simplify (8-v)/(v-2) - (4v-9)/(2-v) ------------------------------- Multiply numerator and demoniator of the 2nd fraction by -1 to get: (8-v)/(v-2) + (4v-9)/(v-2) Now the denominators are the same so combine the numerators to get; = [8-v+4v-9] / [v-2] = [3v-1] / [v-2] ======================= Cheers, Stan H.
 Equations/156647: Express the following rational expressions in lowest terms y^5-3y^3+8y^2 over 5y1 solutions Answer 115446 by stanbon(57361)   on 2008-09-12 21:54:25 (Show Source): You can put this solution on YOUR website!Express the following rational expressions in lowest terms y^5-3y^3+8y^2 over 5y ------------------------------------ (y^5-3y^3+8y^2) / (5y) = [y^2(y^3-3y+8)]/[5y] = [y(y^3 - 3y + 8)]/5 ========================== Cheers, Stan H.
 Square-cubic-other-roots/156648: Simplify I thought a - couldnt be a sq rt. Im assuming it is not a real number but im not sure. please help1 solutions Answer 115443 by stanbon(57361)   on 2008-09-12 21:48:51 (Show Source): You can put this solution on YOUR website!Simplify --------------------------------------- = sqrt(-1/2^10) = (1/2^5)i = (1/32)i ============== Cheers, Stan H.