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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Polynomials-and-rational-expressions/133041: Could someone show me how to solve this equation using the subsitution method? 1 solutions Answer 97261 by stanbon(57219)   on 2008-03-20 22:42:04 (Show Source): You can put this solution on YOUR website!5x+2y=-2 x=26-7y ------------- Substitute the value of x in the 2nd equation into the 1st equation: 5(26-7y)+2y = -2 130-35y+2y = -2 -33y = -132 y = 132/33 ------------------ Substitute that into x = 26-7y to solve for "x": x = 26-7(132/33) x = 858/33 - 924/33 x = -66/33 = -2 =================== Solution: (-2,(132/33)) Cheers, Stan H.
 Quadratic-relations-and-conic-sections/133047: how can you tell if the equation is a circle, an ellipse, parabola or hyperbola with out graphing or putting it in standard form? for example: x^2 + 4x + y^2 +4y - 8 = 0 is a circle, but how do you tell w/o putting it in standard form? please help differ all shapes. 1 solutions Answer 97260 by stanbon(57219)   on 2008-03-20 22:32:52 (Show Source): You can put this solution on YOUR website!If the x^2 and the y^2 have the same coefficient you have a circle. ------------------- If they have the same sign but different coefficients you have an ellipse -------------------- If they have different signs you have a hyperbola. -------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/133042: I cant seem to remember how to multiply this equation could someone please help me? 1 solutions Answer 97259 by stanbon(57219)   on 2008-03-20 22:19:06 (Show Source): You can put this solution on YOUR website!(-5/3)*(-3/2) The 3's cancel leaving you with: (-5/-2) = 5/2 =========== Cheers, Stan H.
 Polynomials-and-rational-expressions/133043: HOw do I translate this into an algebraic equation? The product of 43% and some number?1 solutions Answer 97258 by stanbon(57219)   on 2008-03-20 22:15:31 (Show Source): You can put this solution on YOUR website!HOw do I translate this into an algebraic equation? The product of 43% and some number? y = (43%)x = (43/100)x = 0.43x ================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/133044: How do i find the domain of a function? 1 solutions Answer 97257 by stanbon(57219)   on 2008-03-20 22:12:30 (Show Source): You can put this solution on YOUR website!How do i find the domain of a function? g(x)=1/(9-7) Simplify: g(x) = 1/2 The domain is "all Real Numbers" because there is no restriction on "x". ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/133045: How do I find the slope? x=41 solutions Answer 97256 by stanbon(57219)   on 2008-03-20 22:09:41 (Show Source): You can put this solution on YOUR website!How do I find the slope? x=4 ------------- The slope is "undefined". --------------- Why? Take two points (4,5) and (4,10) on the line. ----------------- slope = (10-5)(4-4) = 5/0 = "undefined" ============================================= Cheers, Stan H.
 Polynomials-and-rational-expressions/133046: Could someone please help me solve this equation? 1 solutions Answer 97255 by stanbon(57219)   on 2008-03-20 22:06:21 (Show Source): You can put this solution on YOUR website!0.4x+7<1.2x-4 Add 4 to both sides: 0.4x + 11 < 1.2x Multipl thru by 10 to get: 4x + 110 < 12x Subtract 4x from both sides: 8x > 110 x > 55/4 x > 13 3/4 ====================== Cheers, Stan H.
 Evaluation_Word_Problems/132967: The church youth group is planning a trip to Washington. A total of 127 people need rides. The church has available buses that hold 40 passengers, and several parents have volunteered station wagons that hold 8 passengers or sedans that hold 5 passengers. The youth leader is planning to use nine vehicles to transport the people. One parent said that if they didn't use any buses, tripled the number of station wagons, and doubled the number of sedans, they would be able to transport 126 people. How many buses, station wagons and sedans are they planning to use if they use 9 vehicles? Where: B = Bus W = Wagon S = Sedan Indicate the algebraic equations used to solve this problem and then solve for the unknowns.1 solutions Answer 97248 by stanbon(57219)   on 2008-03-20 20:57:20 (Show Source): You can put this solution on YOUR website!The church youth group is planning a trip to Washington. A total of 127 people need rides. The church has available buses that hold 40 passengers, and several parents have volunteered station wagons that hold 8 passengers or sedans that hold 5 passengers. The youth leader is planning to use nine vehicles to transport the people. One parent said that if they didn't use any buses, tripled the number of station wagons, and doubled the number of sedans, they would be able to transport 126 people. How many buses, station wagons and sedans are they planning to use if they use 9 vehicles? Where: B = # of Busses W = # of Wagons S = # of Sedans Indicate the algebraic equations used to solve this problem and then solve for the unknowns. -------------------- Vehicles: S + W + B = 9 People : 5S + 8W + 40B = 127 People : 2S + 3W + 0 = 126 --------------------------------------- I used the Matrix function of a TI calculator to get: S = -81 W = 96 B = -5.9 --------- Comment: These answers dont make any sense. I suggest you check the statement of your problem. =================== Cheers, stan H.
 Functions/133029: Could I have some help understanding how to solve this & what the n stands for. Thank you. A={2,4,6} B={-3,-2-1,0} Find n of A and B. 1 solutions Answer 97247 by stanbon(57219)   on 2008-03-20 20:40:09 (Show Source): You can put this solution on YOUR website!Could I have some help understanding how to solve this & what the n stands for. Thank you. A={2,4,6} B={-3,-2-1,0} Find n of A and B. ------------------ It depends on your text, but frequently "n" means "number of elements in". Your Problem: A and B = "the null set" because there are no elements common to A and B. Therefore n(A and B) = 0 ============================ Cheers, Stan H.
 Radicals/132993: Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. (sqrt (c) - sqrt (d)) / (sqrt (c) + sqrt (d))1 solutions Answer 97246 by stanbon(57219)   on 2008-03-20 20:37:18 (Show Source): You can put this solution on YOUR website!Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. (sqrt (c) - sqrt (d)) / (sqrt (c) + sqrt (d)) --------------- Multiply numerator and denominator by (sqrt(c)-sqrt(d)) to get: [sqrt(c)-sqrt(d)]^2/[c-d] = [c+d -2sqrt(cd)]/(c-d) ============================ Cheers, Stan H.
 Polynomials-and-rational-expressions/132994: Simplify by removing factors of 1. m^2-4 / (m+2)^2 This should look like a fraction.1 solutions Answer 97245 by stanbon(57219)   on 2008-03-20 20:33:31 (Show Source): You can put this solution on YOUR website!(m^2-4) / (m+2)^2 Factor: = [(m-2)(m+2)/(m+2)^2] Cancel (m+2) in numerator and denominator to get: = (m-2)/(m+2) ================= Cheers, Stan H.
 Miscellaneous_Word_Problems/133028: you have the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 You have to find the number of possible solutions for a four digit code. numbers can be used more than once I tried 10X4 and got 40 but i think its to low1 solutions Answer 97243 by stanbon(57219)   on 2008-03-20 20:28:49 (Show Source): You can put this solution on YOUR website!you have the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 You have to find the number of possible solutions for a four digit code. numbers can be used more than once ---------------------- Choose the 1st digit: 10 ways Choose the 2nd digit: 10 ways Choose the 3rd digit: 10 ways Choose the 4th digit: 10 ways -------------------------------- Total number of code words = 10^4 = 10,000 ================================== Cheers, Stan H.
 Radicals/132995: Simplify by taking roots of the numberator and the denominator. Assume that all expressions under radicals represent positive numbers. root (3,512x^8/y^3)1 solutions Answer 97242 by stanbon(57219)   on 2008-03-20 20:26:06 (Show Source): You can put this solution on YOUR website!root (3,512x^8/y^3) = sqrt((4x^8/y^2)* (878/y)) = (2x^4/y)*sqrt(878/y) ============= Cheers, Stan H.
 Polynomials-and-rational-expressions/133008: Solve. (x + 17)(x - 8)(x + 8) > 01 solutions Answer 97240 by stanbon(57219)   on 2008-03-20 20:08:46 (Show Source): You can put this solution on YOUR website!Solve. (x + 17)(x - 8)(x + 8) > 0 ----------------------------- Draw a number line: Plot the points x= -17, x= -8, x= 8 on the line. ----------------------------- Check a test point in each interval to see where the solutions lie: Test -20: (-)(-)(-) < 0 , so no solutions in (-inf,-17) Test -10: (+)(-)(-) > 0 . so solutions in (-17,-8) Test 0 : (+)(-)(+) < 0 , so no solutions in (-8,8) Test 10 : (+)(+)(+) > 0 , so solutions in (8,+inf) ------------------------ Final Solution: (-17,-8)U(8,+inf) Cheers, Stan H.
 Functions/133021: Could I please have some help with the following problem. Let P={-3,-2,0,1,5} Let T={0,1,6,9} Let S={-3,1,6} Find T and S Find P and T1 solutions Answer 97237 by stanbon(57219)   on 2008-03-20 20:01:15 (Show Source): You can put this solution on YOUR website!Let P={-3,-2,0,1,5} Let T={0,1,6,9} Let S={-3,1,6} Find T and S = {1,6} Find P and T = {1} ================== Cheers, Stan H.
 Quadratic_Equations/132998: Television sets: What does it mean to refer to a 20-in TV set or a 25-in TV set? A 15-in TV set also has a width of 12-inches. What is its height? I am stumped on how to set up the problem into an equation. Can someone help me?1 solutions Answer 97228 by stanbon(57219)   on 2008-03-20 19:00:31 (Show Source): You can put this solution on YOUR website!What does it mean to refer to a 20-in TV set or a 25-in TV set? It means the diagonal measurement is 20 in or 25 in. --------------------------------------------------------- A 15-in TV set also has a width of 12-inches. What is its height? Use Pythagoras to get: height^2 + width^2 = diagonal^2 h^2 + 12^2 = 15^2 h^2 = 225-144 h^2 = 89 h = 9.43 inches ===================== Cheers, Stan H.
 Probability-and-statistics/132971: Please help. Found the question but the calculations were not available. Thank you in advance. Can people really identify their favorite brand of cola? Volunteers tasted coca-cola classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: at alpha=.05, is the correctness of the prediction different for the two types of cola drinker? Could you identify your favorite brand in this kind of test? Since it is a 2x2 table, try also a two taled two sample z test for п1= п2 and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why? Show how the degrees of freedom are calculated, find the critical value of chi-square, and interpret the p-value. Is the conclusion sensitive to the level of significance chosen? Correct? Regular Cola Diet Cola Row Total Yes, got it right 7 7 14 No, got it wrong 12 20 32 Col total-------- 19 27 46 1 solutions Answer 97226 by stanbon(57219)   on 2008-03-20 18:48:12 (Show Source): You can put this solution on YOUR website!Can people really identify their favorite brand of cola? Volunteers tasted coca-cola classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. ----------------------------------------------------------------- Correct?............ Reg Cola Diet Cola Row Total Yes, got it right 7 7 14 No, got it wrong 12 20 32 Col total-------- 19 27 46 ----------------------------------------------------------------- Research question: at alpha=.05, Is the correctness of the prediction different for the two types of cola drinker? Ho: They are the same Ha: They are different ------------------------- un a Chi-Sq. Test on the 2X2 data: Reg Cola: 7....12 DietCola: 7....20 ------- Test statistic: Chi-Sq = 0.62768... p-value = 0.428207... Show how the degrees of freedom are calculated, df= (# of rows -1)(# of columns) = 1*1 = 1 ---------------------- Find the critical value of chi-square for alpha = 5% and df=1, Left margin = 0.001; Right margin is 7.879 ------------------------------------- Interpret the p-value. At least 43.8% of test results could provide stronger evidence for rejecting Ho. ------------------------ Since p-value is greater then alpha = 5%, Fail to Reject Ho. Conclusion: Correctness of the predictions of RegCola and DietCola drinkers is not different. --------------------- Could you identify your favorite brand in this kind of test? Probably not since this test group was wrong in their identification 32 out of 46 times. --------------------- Since it is a 2x2 table, try also a two tailed two sample z test for p1= p2 and verify that z2 is the same as your chi-square statistic. Ho: p1-p2=0 Ha: p1-p2 is not 0 ---------- Critical Value for 2-tail 2-proportion z test with alpha=5%: z = +/-1.96 -------------------------- If data is pooled p-bar = (x1+x2)/(n1+n2) =14/46 = 0.304 Test statistic: z(7/19 - 7/27) = 0.10916/sqrt[(0.304*0.696/19) + (0.304*0.696/27)] = 0.10916/sqrt(0.01897) = 0.015056... ----------------------------------- Conclusion: Since the test statistic is between -1.96 and +1.96, Fail to Reject Ho. The proportions are the same. ------------------------------------- Show how the degrees of freedom are calculated, df= (# of rows -1)(# of columns) = 1*1 = 1 ---------------------- Find the critical value of chi-square, Left margin = 0.001; Right margin is 7.879 ------------------------------------- p-value for the test statistic = 2P(z > 0.015056...) = 98.8% Interpret the p-value: 98.8% of the test results could have provided stronger evidence to reject Ho.. Is the conclusion sensitive to the level of significance chosen? Not when the p-value is as large as 98.9% ----------------- Which test do you prefer? Why? The Chi-Sq is much easier to run and interpret. --------------------------- Cheers, Stan H.
 Quadratic_Equations/132946: Determine whether the following equations have a solution or not? Justify your answer. (7)1/2y2 - 6y - 13(7)1/2 = 0 Please help with this difficult question.1 solutions Answer 97137 by stanbon(57219)   on 2008-03-20 09:36:54 (Show Source): You can put this solution on YOUR website!(7)1/2y^2 - 6y - 13(7)1/2 = 0 Multiply thru by 2 to get rid of the fractions: 7y^2 -12y -91 = 0 y = [12 +-sqrt(12^2-4*7*-91)]/14 y = [12 +- 51.8845]/14 y = 4.5632... or y = -2.8489.. Cheers, Stan H.
 Equations/132912: Please help me to find the vertex form of .1 solutions Answer 97110 by stanbon(57219)   on 2008-03-19 22:34:08 (Show Source): You can put this solution on YOUR website!find the vertex form of . ------------------- 2x^2+16x = -(y+32) 2(x^2+8x+16) = -y-32+2*16 2(x+4)^2 = -y (x+4) = (-1/2)(y-0) ------------------- Vertex: (-4,0) ------------------- --------------------- Cheers, Stan H.
 Linear-equations/132913: determine the slope of the line that goes through each pair (0,4) and (5,0)1 solutions Answer 97109 by stanbon(57219)   on 2008-03-19 22:25:05 (Show Source): You can put this solution on YOUR website!determine the slope of the line that goes through each pair (0,4) and (5,0) ---------------- slope = change in y/ change in x = (0-4)/(5-0) = -4/5 ============================= Cheers, stan H.
 Linear-equations/132915: Determine teh equation. Write the answer in standard for using only integers as the coefficients. the line through (-2,0) with slope -3/41 solutions Answer 97108 by stanbon(57219)   on 2008-03-19 22:22:20 (Show Source): You can put this solution on YOUR website!Write the answer in standard for using only integers as the coefficients. the line through (-2,0) with slope -3/4 ---------------- Form: y = mx + b You know x,y, and m; solve for "b": 0 = (-3/4)*(-2) + b 0 = (3/2) + b b = -3/2 ---------------- EQuATION: y = (-3/4)x -(3/2) Multiplythru by 4 to get: 4y = -3x - 6 Rearrange: 3x+4y = -6 ================ Cheers, Stan H.
 Probability-and-statistics/132907: This question is from textbook Applied Statistics in Business and Economics Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill. (a) State the appropriate hypotheses. (b) Obtain a test statistic and p-value. Interpret the results at α = .01. (c) Is normality assured? (d) Is the difference large enough to be important? (e) What else would medical researchers need to know before prescribing this drug widely? 1 solutions Answer 97105 by stanbon(57219)   on 2008-03-19 22:02:19 (Show Source): You can put this solution on YOUR website!this was answered yesterday. Cheers, Stan H.
 Polynomials-and-rational-expressions/132883: I need a little help solving this equation and finding the solution to the system. Could someone please help me? 1 solutions Answer 97096 by stanbon(57219)   on 2008-03-19 20:55:50 (Show Source): You can put this solution on YOUR website!x+7y=7}}} x=4-7y ------------ substitute the value of "x" in the 2nd equation into the 1st to get: 4-7y+7y=7 4 = 7 ---------- This happened because I assumed the x and y in the one equation were the same as the x and y in the other. That assumption lead to the contradiction. The system of equation is said to be inconsistent. There is no solution. If you graph the two equation you will get two parallel lines. =============== Cheers, Stan H.
 Quadratic_Equations/132874: Solve : 3(2^(2x)) - 2^(x+2) +1=0 I am having real trouble with this one , I hope someone can help me:)1 solutions Answer 97094 by stanbon(57219)   on 2008-03-19 20:47:06 (Show Source): You can put this solution on YOUR website!Solve : 3(2^(2x)) - 2^(x+2) +1=0 3(2^(2x) -[2^x*2^2] + 1 = 0 3(2^2x) -4(2^x] + 1 = 0 ------------- Let 2^x = w ------------- Rewrite the equation in "w": 3w^2 -4w + 1 = 0 Factor: (3w-1)(w-1) = 0 w = 1/3 or w = 1 ------------------ Rewrite in terms of "x": 2^x = (1/3) or 2^x = 1 x = [log(1/3)]/[log2] or x = [log1]/[log2] x = -1.58496... or x = 0 ============================= Cheers, Stan H.
 Equations/132870: I am still a little confused on this one could someone shoe me how to solve the domain of a function? 1 solutions Answer 97092 by stanbon(57219)   on 2008-03-19 20:36:07 (Show Source): You can put this solution on YOUR website!domain of a function? --------------- Your domain is "all Real Numbers" because you can put any Real Number you want to in place of "x". ------------------ You have a restriction on the domain if: 1) you are taking an even root of an expression with a variable in it; like y = sqrt(x+2) OR 2) you have a denominator with an expression with a variable in it: like y = 3/(2x+1) OR 3) you have a log expression like y = log2(x-3) --------------- All of these cause you to have a restricted domain. #1: x must be >= -2 #2: x must not be -1/2 #3: x must be > 3 ======================= Cheers, Stan H.
 Graphs/132864: I need a litle help could some one show me how to graph this on a plane? 1 solutions Answer 97089 by stanbon(57219)   on 2008-03-19 20:20:52 (Show Source): You can put this solution on YOUR website!graph this on a plane? ------------------- Solve for "Y": y < (-5/6)x +6 ------------------- Graph the boundary as a dashed line y = (-5/6)x+30 If x=0, y= 30 giving you point (0,30) If x = 6, y = 25, giving you point (6,25) --------------------- Plot (0,30) and (6.25) and draw a dashed line thru them. Note: That is the boundary for the solution; it is not the solution. ------------- Since you want y LESS THAN (-5/6)x+30, shade the half-plane BELOW the boundary line. That is the graph of the inequality. ----------------------- ======================== Cheers, Stan H.
 Quadratic_Equations/132847: 3. The speed of sound in air is 1100 feet per second. The speed of sound in steel is 16500 per second. Robin, one ear pressed against the railroad track, hears a sound through the rail six seconds before hearing the same sound through the air. To the nearest foot, how far away is the source of that sound?1 solutions Answer 97087 by stanbon(57219)   on 2008-03-19 20:12:44 (Show Source): You can put this solution on YOUR website!The speed of sound in air is 1100 feet per second. The speed of sound in steel is 16500 per second. Robin, one ear pressed against the railroad track, hears a sound through the rail six seconds before hearing the same sound through the air. To the nearest foot, how far away is the source of that sound? --------------- Time difference = 6 seconds ----------------------- Rail DATA: Distance = x ft ; Rate = 16,500 ft/sec ; Time = d/r = x/16500 sec ---------------- Air DATA: Distance = x ft ; Rate = 11000 ft/sec ; Time = d/r = x/11000 sec ----------------- EQUATION: air time - rail time = 6 seconds x/11000 - x/16500 = 6 (16500x - 11000x) = 6(11000*16500) 5500x = 6*11000*16500 x = 198,000 ft.(distance the train was when it initiated the sound heard by Robin) ================ Cheers, Stan H.