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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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 Rational-functions/86978: This question is really bothering me. Please help. Express f(x) = x2 + │x+3│ - 1 without the absolute values and hand-graph. Hint: │x│= x if x ≥ 0 or = –x if x < 01 solutions Answer 62938 by stanbon(57387)   on 2007-06-30 18:09:43 (Show Source): You can put this solution on YOUR website!Express f(x) = x^2 + │x+3│ - 1 without the absolute values and hand-graph. ---------- Note: |x+3| = x+3 if x+3>=0; that is x>=-3 |x+3| = -(x+3) if x+3 <0; that is x<-3 -------------------- So, for x<-3 your equation becomes: f(x) = x^2 -x-3-1 f(x) = x^2-x-4 Graph this parabola to the left of x=-3. ------------- And for x>=-3 you equation becomes: f(x) = x^2+x+3-1 f(x) = x^2+x+2 Graph this parabola at and to the right of x=-3 ================== Cheers, Stan H. -----------------------
 Miscellaneous_Word_Problems/86986: This question is from textbook Saxon, Algebra 1 Pressure varies inversly as volume. When the pressure is 16 pascals, the volume is 84 liters. What would the volume be if the pressure is reduced to 12 pascals?1 solutions Answer 62936 by stanbon(57387)   on 2007-06-30 18:01:56 (Show Source): You can put this solution on YOUR website!Pressure varies inversely as volume. When the pressure is 16 pascals, the volume is 84 liters. What would the volume be if the pressure is reduced to 12 pascals? -------------- P = k/V Need to find k. 16 = k/84 k= 1344 EQUATIOn: P = 1344/V 12 = 1344/V V=1344/12 V = 112 liters ======================= Cheers, Stan H.
 Travel_Word_Problems/86985: This question is from textbook Saxon, Algebra 1 At noon, the hot air ballon headed north at 8 miles per hour. Three hours later, the glider headed south from the same location at 16 miles per hour. At what time will the hot air ballon be 168 miles from the glider?1 solutions Answer 62935 by stanbon(57387)   on 2007-06-30 17:56:12 (Show Source): You can put this solution on YOUR website!At noon, the hot air ballon headed north at 8 miles per hour. Three hours later, the glider headed south from the same location at 16 miles per hour. At what time will the hot air ballon be 168 miles from the glider? ------------ Ballon DATA: rate = 8mph ; time = x hr ; distance = 8x miles --------------- Glider DATA: rate = 16mph ; time = x-3 ; distance = 16(x-3) miles -------------------- EQUATION: distance + distance = 168 miles 8x + 16x-48 = 168 24x = 216 x= 9 hrs. noon + 9 hrs = 9;00 PM ======================= Cheers, stan H.
 expressions/86982: Tutor could I please get your help? My problem is: how do I simplify this expression: 3y^2+5yz+2z^2 over 2y^2+3yz+z^2 Thank you!1 solutions Answer 62934 by stanbon(57387)   on 2007-06-30 17:45:48 (Show Source): You can put this solution on YOUR website!simplify this expression: 3y^2+5yz+2z^2 over 2y^2+3yz+z^2 ------------------- [3y^2+5yz+2z^2] / [2y^2+3yz+z^2] = [3y2+3yz+2yz+z^2] / [2y^2+2yz+yz+z^2] = [3y(y+z)+2z(y+z)] / [2y(y+z)+z(y+z)] = [(y+z)(3y+2z)] / [(y+z)(2y+z)] =(3y+2z) / (2y+z) ======================== Cheers, Stan H.
 Money_Word_Problems/86984: This question is from textbook Saxon, Algebra 1 David deposited \$10,000 in a acount that pays 5% interest compounded annually. How much money was earned the first 10 years?1 solutions Answer 62932 by stanbon(57387)   on 2007-06-30 17:35:25 (Show Source): You can put this solution on YOUR website!David deposited \$10,000 in a acount that pays 5% interest compounded annually. How much money was earned the first 10 years? ---------- A(t) = P(1+r/n)^(nt) A(10) = 10000(1+0.05/1)^(1*10) A(10) = \$16288.95 --------------- Cheers, Stan H.
 Inequalities/86981: how do you solve the problem 1= 5x Over 6 + 2x Over 3 1 solutions Answer 62931 by stanbon(57387)   on 2007-06-30 17:28:55 (Show Source): You can put this solution on YOUR website!solve the problem 1= 5x Over 6 + 2x Over 3 ------------ 1= 5x/6 + 2x/3 Multiply both sides by 6 to get: 6 = 5x + 4x 9x = 6 x= 2/3 =============== Cheers, Stan H.
 Money_Word_Problems/86870: what formulas do i use for these problems: Problem #5 John lee saving account has a balance of \$2449 after 7 years what will the amount of interest be at 8% compounded semiannually? Problem #7 Southwest dry cleaners believes that it will need new equipment in 5 years the equipment will cost \$26000 what lump sum should be invested today at 8% compounded semiannually to yield 26000? 1 solutions Answer 62892 by stanbon(57387)   on 2007-06-29 22:42:31 (Show Source): You can put this solution on YOUR website!John lee saving account has a balance of \$2449; after 7 years what will the amount of interest be at 8% compounded semiannually? A(t) = P (1+r/n)^(nt) A(7) = 2449(1+0.08/2)^(2*7) A(7) = 4240.88 Interest earned = 4240.88 - 2449 = \$1791.88 =============== Problem #7 Southwest dry cleaners believes that it will need new equipment in 5 years the equipment will cost \$26000 what lump sum should be invested today at 8% compounded semiannually to yield 26000? --------- 260000 = P(1+0.08/2)^(2*5) P = \$175646.68 (Amount to invest today) =============== Cheers, stan H.
 Money_Word_Problems/86932: An investmest of \$5600 is made at an annual simple interest of 6.5%. How much additional money must be invested at an annual simple interest rate of 9% so that the total interest earned is 8% of the total investment.1 solutions Answer 62890 by stanbon(57387)   on 2007-06-29 22:09:29 (Show Source): You can put this solution on YOUR website!An investmest of \$5600 is made at an annual simple interest of 6.5%. How much additional money must be invested at an annual simple interest rate of 9% so that the total interest earned is 8% of the total investment. --------------- Amt. invested at 6.5% = \$5600 : interest on this is 0.065*5600 = \$364.00 Amt invested at 9% = x dollars: interest on this is 0.09x dollars Amt invested at 8% = (5600+x) ; interest on this is 0.08(5600+x) = 448+0.08x --------------- EQUATION: interest + interest = interest 364 + 0.09x = 448+0.08x 0.01x = 84 x = \$8400 (Amt that must be invested at 9%) =============== Cheers, Stan H.
 Linear-equations/86939: Graph 3x+y=3 I know I have to solve for y...and x is equals to 0? this is what I come up with... 3(0)+ y = 3 y=3-3 y= 0 is this correct?1 solutions Answer 62889 by stanbon(57387)   on 2007-06-29 21:59:41 (Show Source): You can put this solution on YOUR website!Graph 3x+y=3 You need two points to graph a line. Let x=0, then y=3 giving you point (0,3) Let y=0, then 3x=3 and x=1 giving you point (1,0) - --------- Plot those two points and draw a line thru them. Cheers, Stan H.
 Money_Word_Problems/86935: A real estate agent received a 5.5% commission on the sale of a home. If the home sold for \$133,000, how much was his commission?1 solutions Answer 62888 by stanbon(57387)   on 2007-06-29 21:56:28 (Show Source): You can put this solution on YOUR website!A real estate agent received a 5.5% commission on the sale of a home. If the home sold for \$133,000, how much was his commission? ----------- 0.05*133,000 = \$6650.00 ========== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/86937: Consider the function P(x)=x(30-x). Is this function odd, even or neither? What do you expect if you graph this function?1 solutions Answer 62887 by stanbon(57387)   on 2007-06-29 21:51:46 (Show Source): You can put this solution on YOUR website!P(x)=x(30-x) = 30x-x^2 P(-x) = -x(30+x) = -30x-x^2 -P(-x) = 30x+x^2 ============= Since P(x) does not equal P(-x) P(x) is not even Since P(x) does not equal -P(-x) P(x) is not odd ------------------ The graph will not be symmetric to the y axis or to the origin. ================= Cheers, Stan H.
 Miscellaneous_Word_Problems/86938: I can't seem to understand how to do this also I will like to see if you can verify my answer on the second exersize? 1.Evaluate. | –9 | – | 2 | 2. Multiply. Multiply. (-5/8)(40)= -5/8 x 40/1= 200/8= 25 I found the common denominator for 200 and 8 then I divided and then equal 25 1 solutions Answer 62886 by stanbon(57387)   on 2007-06-29 21:46:45 (Show Source): You can put this solution on YOUR website!1.Evaluate. | –9 | – | 2 | = 9 - 2 = 7 -------------------------- 2. Multiply. Multiply. (-5/8)(40)= -5/8 x 40/1= 200/8= 25 I found the common denominator for 200 and 8 then I divided and then equal 25 Don't forget the negative sign. Ans: -25 ============================= Cheers, Stan H.
 Money_Word_Problems/86936: Of 30 students in a class, 15 passed. What percentage of the students passed?1 solutions Answer 62885 by stanbon(57387)   on 2007-06-29 21:40:37 (Show Source): You can put this solution on YOUR website!15/30 = 1/2 = = 0.50 = 50% --------- Or you could do it this way: 15/30 = x/100 30x=1500 x= 50 Therefore 15/30 = 50/100 = 50% ------------- Cheers, Stan H.
 Probability-and-statistics/86761: This question is from textbook Basic Practice of Statistics Here are some probabilities estimated by a medical care study. The entries in the table are the probabilities that both of two events occur; for example, .321 is the probability that a patient is under 65 years of age and the tests were done. The 4 probabilities in the table have a sum 1 beacuse the table lists all possible outcomes. Tests Done? Yes No Age<65 0.321 0.124 Age>or=65 0.365 0.190 1) What is the probability that a pt. is under 65? That a pt. is 65 or over? 2) What is the probability that the tests were done for a pt.? That they were not done? 3) Are the events A= (the pt. was 65 or older) and B= (the tests were done independent? Were the tests omitted on older pts. more or less frequently than would be the case if testing were independent of age?1 solutions Answer 62883 by stanbon(57387)   on 2007-06-29 21:25:29 (Show Source): You can put this solution on YOUR website!Tests Done? .........Yes... No......|Total Age<65 0.321...0.124....|0.445 Age>=65 0.365...0.190....|0.555 -------- ---- Total...0.686...0.314.... 1.000 -------------------------- 1) What is the probability that a pt. is under 65? Ans: 0.455 That a pt. is 65 or over ? Ans: 0.555 ----------------------------------- 2) What is the probability that the tests were done for a pt.? Ans: 0.686 That they were not done? Ans: 0.314 --------------------------------- 3) Are the events A= (the pt. was 65 or older) and B= (the tests were done independent? P(A)*P(B) = 0.555*0.686 = 0.38073 P(A|B) = 0.365 Ans: Since these are not the same the A and B are dependent. -------------------- Were the tests omitted on older pts. more or less frequently than would be the case if testing were independent of age? Ans: Yes, the percentage would be up to 38% instead of 36.5% ============= Cheers, Stan H.
 expressions/86912: Tutor could you help me please: I need to multiply and simplify the following: 6x^2/10x^3*5x/12 AND 9/y-6*y/5 Thank you!!!!1 solutions Answer 62879 by stanbon(57387)   on 2007-06-29 21:01:04 (Show Source): You can put this solution on YOUR website![6x^2/10x^3] * [5x/12] = [3/5] * [5x/12] = [x/4] ---------------------- AND --------- [9/y-6] * [y/5] Question: Is the denominator of the 1st fraction "y" or is it "y-6"? You can avoid this question by properly using parentheses. ============== Cheers, Stan H.
 Probability-and-statistics/86873: can someone help me with these three problems i just still don't understand them can someone show me step by step thanks... Problem #1 Sect:2 Write a sample space for the given experiment A box contains 3 blue cards numbered 1 through 3 , and 4 green cards numbered 1 through 4. A blue card is picked , followed by a green card. Problem #2 sect 2 Write the indicated event in set notation the even that charlie is selected as a board memeber when three board members are selected at random from the following group: Allison, Betty, Charlie, Dave, and Emily. [the possible outcomes can be represented as follows. ABC/ABD/ABE/ACD/ACE ADE/BCD/BCE/BDE/CDE] *I USED THE "/" TO SEPARATE THEM HOW IT LOOKS IN THE BOOK* 1 solutions Answer 62878 by stanbon(57387)   on 2007-06-29 20:54:37 (Show Source): You can put this solution on YOUR website!show me step by step thanks... Problem #1 Sect:2 Write a sample space for the given experiment A box contains 3 blue cards numbered 1 through 3 , and 4 green cards numbered 1 through 4. A blue card is picked , followed by a green card. --------- I'm going to write these outcomes as a pair where the 1st of the pair is one of the blue cards and the 2nd of the pair is one of the green cards: b1,g1 ; b1,g2 ; b1,g3 ; b1,g4 b2,g1 ; b2,g2 ; b2,g3 ; b2,g4 b3,g1 ; b3,g2 ; b3,g3 ; b3,g4 =================================== Problem #2 sect 2 Write the indicated event in set notation the event that charlie is selected as a board memeber when three board members are selected at random from the following group: Allison, Betty, Charlie, Dave, and Emily. [the possible outcomes can be represented as follows. ABC/ABD/ABE/ACD/ACE ADE/BCD/BCE/BDE/CDE] --------- Since "C" is Charlie, C must appear in the selection. {CAB , CAD ,CAE, CBD, CBE, CDE} ================== Cheers, Stan H.
 Equations/86931: solve and check 6(2 – x) = 4x1 solutions Answer 62876 by stanbon(57387)   on 2007-06-29 20:36:33 (Show Source): You can put this solution on YOUR website!solve and check 6(2 – x) = 4x 12 - 6x = 4x 12 = 10x x= 6/5 ================ Checking: 6(2-(6/5)) = 4(6/5) 12-36/5 = 24/5 60/5 - 36/5 = 24/5 24/5 = 24/5 ================= Cheers, Stan H.
 logarithm/86910: Approximately how long will it take \$100 to grow to \$500 at 8% annual interest and compounded 12 times per year?1 solutions Answer 62875 by stanbon(57387)   on 2007-06-29 20:33:49 (Show Source): You can put this solution on YOUR website!Approximately how long will it take \$100 to grow to \$500 at 8% annual interest and compounded 12 times per year? ------------ A(t) = P(1+r/n)^(nt) 500 = 100(1+0.08/12)^(12t) 5 = 1.0066666666^12t Take the log of both sides to get: 12t(log1.006666666...)= log5 12t = [log5]/[log1.006666666...] 12t = 242.22 t = 20.18 years =============== Cheers, Stan H.
 Probability-and-statistics/86928: This question is from textbook elementary statistics in social research A researcher was interested in studying the phenomenon known as social distance, the reluctance of people to associate with members of different ethnic and racial groups. She designed an experiment in which students enrolled in a lecture course were asked to choose a discussion group (all meeting at the same time in the same building) based only on the ethnic-racial stereotype associated with the names of the teaching assistant: Group Teaching Assistant Room Enrollment _____________________________________________________ A Cheng 106 10 B Schultz 108 24 C Goldberg 110 10 D Rodriguez 112 16 ___________________________________________________ Based on the enrollments, use the one-way chi-squre to test the null hypothesis that the ethnic-racial name made no difference in students' selection of a discussion group.1 solutions Answer 62872 by stanbon(57387)   on 2007-06-29 20:28:06 (Show Source): You can put this solution on YOUR website!Group Teaching Assistant Room Enrollment _____________________________________________________ A Cheng 106 10 B Schultz 108 24 C Goldberg 110 10 D Rodriguez 112 16 ---------------- Ho: choices are uniformly distributed Ha: choices are not uniformly distributed Critical Value: df=4-1=3; Chi-Sq = 7.815 for alpha = 5% ------------ Note: Expected value for each teacher's attendance = (1/4)60=15 --------- Test Statistic: Chi-Sq =[(10-15)^2]/15 + [(24-15)^2]/15 + [(10-15)^2]/15 +[(16-15)^2]/15 Chi-Sq = [25/15] + [81/15] + [25/15] + 1/15 = 132/15 = 8.8 ------------ Since 8.8 > 7.815, reject Ho. The test shows significant statistical support for the conclusion that the selection is influenced by racial bias. ============ Cheers, Stan H.
 Probability-and-statistics/86927: This question is from textbook elementary statistics in social research An urban sociologist interested in neighborliness collected data for a sample of 10 adults on (X) how many years they have lived in their neighborhood and (Y) how many of their neighbors they regard as friends. Compute a Pearson's correlation coefficient for these data and determine whether the correlation is significant. X Y ________ 1 1 5 4 6 2 1 3 8 5 2 1 5 2 9 6 4 7 2 0 ________1 solutions Answer 62870 by stanbon(57387)   on 2007-06-29 20:10:09 (Show Source): You can put this solution on YOUR website!An urban sociologist interested in neighborliness collected data for a sample of 10 adults on (X) how many years they have lived in their neighborhood and (Y) how many of their neighbors they regard as friends. Compute a Pearson's correlation coefficient for these data and determine whether the correlation is significant. --------------- Using the TI-83 Linear Regression program I get an r value of 0.61 which indicates weak positive linear correlation. ------------- Hypothesis Test Setup: Ho: rho = 0 (meaning there is no linear correlation) Ha: rho is not equal to 0 (meaning there is some linear correlation) Using a Pearson Product-Moment Correlation Coefficient Table you find (for 10-2 degrees of freedom) the critical value is 0.632 for a two-tailed ted with alpha=5%. Since 0.61 (the test statistic) is not greater than 0.632 you fail to reject Ho; you conclude this test did not show significant statistic evidence of strong linear correlation in the data. ============= Cheers, Stan H.
 Polynomials-and-rational-expressions/86920: multiply -3a^2b over 35a^5 multiplied by 14a^3b^2 over -9b^41 solutions Answer 62867 by stanbon(57387)   on 2007-06-29 19:42:37 (Show Source): You can put this solution on YOUR website!multiply [-3a^2b/35a^5] * [14a^3b^2/-9b^4] = [-3b/35a^3] * [14a^3/-9b^2] = [1/5] * [2/3b] =[2/15b] ======================= Cheers, Stan H.
 Miscellaneous_Word_Problems/86886: The odds against a horse winning the race are 6 to 5. What is the probability of the horse winning the race?1 solutions Answer 62864 by stanbon(57387)   on 2007-06-29 18:33:07 (Show Source): You can put this solution on YOUR website!The odds against a horse winning the race are 6 to 5. What is the probability of the horse winning the race? --------------- Odds against winning = [P(losing)]/P(winning)] = 6:5 P(losing) = 6/11 P(winning) = 5/11 =================== Cheers, Stan H.
 Miscellaneous_Word_Problems/86826: A box contains 4 blue balls 5 green balls and 3 yellow balls. You randomly select 3 balls, one at a time, from the box without replacing a selected ball. What is the probability of selecting a blue, a green, a yellow in that order?1 solutions Answer 62817 by stanbon(57387)   on 2007-06-28 22:11:43 (Show Source): You can put this solution on YOUR website!A box contains 4 blue balls 5 green balls and 3 yellow balls. You randomly select 3 balls, one at a time, from the box without replacing a selected ball. What is the probability of selecting a blue, a green, a yellow in that order? ------------- P(blue)*P(green)*P(yellow) = 4/12 * 5*11 * 3/10 = 5/110 = 1/22 =============== Cheers, Stan H.
 Exponents/86846: Q WHAT IS THE VALUE OF (-1) TO THE POWER IRRATIONAL NUMBER 1 solutions Answer 62816 by stanbon(57387)   on 2007-06-28 22:01:49 (Show Source): You can put this solution on YOUR website!Try it: (-1)^(sqrt(3)) There is no answer. ================ Cheers, Stan H.
 Money_Word_Problems/86842: solve and check What interest will you pay on a \$4900 loan for 1 year if the interest rate is 7%?1 solutions Answer 62815 by stanbon(57387)   on 2007-06-28 21:58:07 (Show Source): You can put this solution on YOUR website!What interest will you pay on a \$4900 loan for 1 year if the interest rate is 7%? --------- Interest = .07*4900 = \$343.00 ===================== Cheers, Stan H.
 Quadratic_Equations/86833: simplify: sqrt75a^2/sqrt51 solutions Answer 62814 by stanbon(57387)   on 2007-06-28 21:55:11 (Show Source): You can put this solution on YOUR website!simplify: sqrt75a^2/sqrt5 ---------- =[(5a)sqrt(3)]/[sqrt(5)] Multiply numerator and denominator by sqrt(5) to get: = [(5a)sqrt(15)]/5 Cancel the 5's to get: = a*sqrt(15) ============== Cheeers, Stan H.
 Quadratic_Equations/86834: Simplify. Assume x represents a positive number. sqrt45x^4 1 solutions Answer 62813 by stanbon(57387)   on 2007-06-28 21:46:56 (Show Source): You can put this solution on YOUR website!sqrt45x^4 = sqrt(9x^4)*sqrt(5) = 3x^2*sqrt(5) ================= Cheers, stan H.
 Probability-and-statistics/86763: This question is from textbook The Basic Practice of Statistics I use Moore's 4th Ed. The Basic Practice of Statistics. I need help setting up and finding the appropriate formula for questions 11.46 on pg. 301, and 11.38 on pg. 298. Thank you1 solutions Answer 62812 by stanbon(57387)   on 2007-06-28 21:40:56 (Show Source): You can put this solution on YOUR website!I don't have the book. Can you post the problems? Cheers, Stan H.
 Quadratic_Equations/86802: solve the equation by completeing the square a2(squared)-12a+27=01 solutions Answer 62803 by stanbon(57387)   on 2007-06-28 20:50:33 (Show Source): You can put this solution on YOUR website!solve the equation by completing the square a^2-12a+27=0 ----------- a^2-12a+? = -27+? Complete the square. a^2-12a+(12/2)^2 = -27 + (12/2)^2 (a-6)^2 = -27 + 36 (a-6)^2 = 9 (a-6) = 3 or (a-6) = -3 a = 9 or a = 3 ======================= Cheers, Stan H.
 Quadratic_Equations/86811: Simplify: square root of 5001 solutions Answer 62802 by stanbon(57387)   on 2007-06-28 20:40:05 (Show Source): You can put this solution on YOUR website!Simplify: square root of 500 sqrt(500) = [sqrt100] =10 sqrt(5) ====================== cheers, Stan H.
 Geometry_Word_Problems/86803: Here is the question that I am having trouble with: Two blocks, each of length x, width x+4, and height x, are cut out of a block of length 3x+4, width x+4, and height x. All dimensions are given in centimeters. Find the volume of the resulting solid. Am I suppose to figure out the volume of the original block and then subtract the cut out block? Also since it states that there were two blocks cut out do I have to double everything for the cout out volume? Can you help me set this up? Thank you very much. 1 solutions Answer 62801 by stanbon(57387)   on 2007-06-28 20:36:02 (Show Source): You can put this solution on YOUR website!Two blocks, each of length x, width x+4, and height x, are cut out of a block of length 3x+4, width x+4, and height x. All dimensions are given in centimeters. Find the volume of the resulting solid. ------------- Volume of original block: Vo = (3x+4)(x+4)(x) Volume of one of the two smaller blocks: Vs = x*x*(x+4) EQUATION: Vo/Vs = 2 Solve for x. Find Vo and find Vs; one of them is the "so-called" resulting solid. =========== Cheers, Stan H.