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# Recent problems solved by 'stanbon'

stanbon answered: 57151 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 , 57150..57179, >>Next

 Equations/483467: Find the equation of the line satisfying the given conditions, giving it in slope-intercept form if possible: Through (-4,1), parallel to x+3y=51 solutions Answer 330848 by stanbon(57219)   on 2011-08-19 19:12:34 (Show Source): You can put this solution on YOUR website!Find the equation of the line satisfying the given conditions, giving it in slope-intercept form if possible: Through (-4,1), parallel to x+3y=5 ----------------- Slope of the given line = ? y = (-1/3)x + (5/3) --- slope = -1/3 ---- Any line parallel to the given line must have slope = -1/3 ------------------------------------ Equation Form: y = mx + b Solve for "b": 1 = (-1/3)(-4) + b --- 1 = (4/3) + b b = -1/3 ------------- Equation: y = (-1/3)x - (1/3) ====================== Cheers, Stan H.
 Linear-equations/483466: (5, l)is a solution to the equation 2x-3y=7. What does this mean?1 solutions Answer 330846 by stanbon(57219)   on 2011-08-19 19:05:45 (Show Source): You can put this solution on YOUR website!(5, l)is a solution to the equation 2x-3y=7. What does this mean? --- If you put 5 in place of "x" and you put 1 in place of "y" you will get a true statement: 2*5-3*1 = 10-3 = 7 ======================= Cheers, Stan H.
 Equations/483457: i need to solve this inequality and i don't know how to solve it : x^4-5x^3-25x^2+65x+84(greater than or equal to)01 solutions Answer 330845 by stanbon(57219)   on 2011-08-19 18:57:25 (Show Source): You can put this solution on YOUR website!x^4-5x^3-25x^2+65x+84(greater than or equal to)0 ---- Find the zeroes: Use synthetic division: --- -1)....1....-5....-25.....65....84 .......1.....-6....-19......84...|..0 7).....1......1.....-12....|..0 ========================================= Solve x^2+x-12 = 0 (x+4)(x-3) = 0 x = -4 or x = 3 =============================== =============================== Draw a number line and plot x = -4,-1,3,7 These values satisfy the EQUALITY. --------------- Test a value in each of the 5 intervals to find the solution set: INEQUALITY: (x+4)(x+1)(x-3)(x-7) > 0 Let x = -10 to get -*-*-*- > 0 ; true Let x = -2 to get +*-*-*- > 0 ; false Let x = 2 to get +*+*-1*- > 0 ; true Let x = 5 to get +*+*+*- > 0 ; false Let x = 10 to get +*+*+*+ > 0 ; true --------------- Solution: (-oo,-4]U[-1,3]U[7,+oo) ============== Cheers, Stan H.
 Rational-functions/483445: i can't figure out the steps to find the zeros of this equation: y=125x^3-81 solutions Answer 330841 by stanbon(57219)   on 2011-08-19 18:01:47 (Show Source): You can put this solution on YOUR website!figure out the steps to find the zeros of this equation: y=125x^3-8 ---- Solve: 125x^3-8 = 0 --- (5x)^2-2^3 = 0 --- Factor: (5x-2)(25x^2+10x+4) = 0 ---- x = 2/5 and x is the zeroes of 25x^2+10x+4 = 0 ---- Solve: 25x^2+10x+4 = 0 --- x = [-10 +- sqrt(100-4*25*4)]/50 ---- x = [-10 +- sqrt(-300)]/50 ------ x = [-10 +- 10sqrt(3)i]/50 ------ x = (-1/5)-(1/5)sqrt(3)i pr x = (-1/5)+(1/5)sqrt(3)i --- Note: There are 3 solutions ----------------------------------- Cheers, Stan H.
 Trigonometry-basics/483438: Given sinB =11/18 find angle B in degrees. Round your answer to the nearest hundredth.1 solutions Answer 330840 by stanbon(57219)   on 2011-08-19 17:40:45 (Show Source): You can put this solution on YOUR website!Given sinB =11/18 find angle B in degrees. Round your answer to the nearest hundredth. -------------- sin^-1(11/18) = 37.67 degrees -------------------------------- Cheers, Stan H. ========================
 Linear-equations/483437: Could someone please help with is problem? Thank you. find the x- and y-intercepts for the equation y= -6x-8? please show work and then graph the equation. Thank you again.1 solutions Answer 330835 by stanbon(57219)   on 2011-08-19 17:13:04 (Show Source): You can put this solution on YOUR website!find the x- and y-intercepts for the equation y= -6x-8 ----- x-intercept ? Let y = 0; then -6x-8 = 0; and 6x = -8; and x = -4/3 ------------------- y-intercept ? Let x = 0; then y = -6*0-8; and y = -8 ---- PLot (-4/3),0) and (0,-8) and draw a line thru them: Cheers, Stan H.
 Finance/483417: im having troubles learning logarithms and im stuck at this problem log(1 over 10^-3) + 10^41 solutions Answer 330824 by stanbon(57219)   on 2011-08-19 16:13:38 (Show Source): You can put this solution on YOUR website!log(1 over 10^-3) + 10^4 --- = log(10^3) + 10^4 ---- = 3 + 10000 ---- = 10003 =============== Cheers, Stan H.
 Numeric_Fractions/483418: I need help with dividing fractions, I am very confused on how to simplify my problem and keep it in the indicated operation. Here is an example of what I mean; 4/3 divided by 5/7? Please get back to me asap Thanks alot!1 solutions Answer 330823 by stanbon(57219)   on 2011-08-19 16:11:40 (Show Source): You can put this solution on YOUR website!4/3 divided by 5/7? --- Multiply numerator and denominator by (7/5) to get: --- [(7/5)(4/3)]/[(7/5)(5/7)] ---- = (28/15)/1 --- = (28/15) --------------------- Note: The general rule for dividing a fraction by a fraction is "invert the denominator and multiply". ----- Example: (2/3)/(5/4) = (2/3)(4/5) = 8/15 =============================================== Cheers, Stan H.
 Probability-and-statistics/483293: Data is collected for a total of 100 driving trips. Informatiom is gathered on whether the driver takes a map and whether the driver gets lost (see the table below). The driver then goes on 2 additional trips. ..................Gets lost...............Doesn't get lost..........Totals ....................10..........................30.......................40 ....................40..........................20.......................60 ....................50..........................50.......................100 Find the probability that the driver gets lost both times, whether a map is brought or not. a. 0.010 b. 0.200 c. 0.247 d. 0.250 1 solutions Answer 330822 by stanbon(57219)   on 2011-08-19 16:07:55 (Show Source): You can put this solution on YOUR website!Data is collected for a total of 100 driving trips. Informatiom is gathered on whether the driver takes a map and whether the driver gets lost (see the table below). The driver then goes on 2 additional trips. ..................Gets lost...............Doesn't get lost..........Totals ....................10..........................30.......................40 ....................40..........................20.......................60 ....................50..........................50.......................100 Find the probability that the driver gets lost both times, whether a map is brought or not. ------------- P(gets lost on a trip) = 50/100 = 1/2 --- P(gets lost on 2 trips) = (1/2)(1/2) = 1/4 = 0.25 ========== Cheers, Stan H. ========== a. 0.010 b. 0.200 c. 0.247 d. 0.250
 Polynomials-and-rational-expressions/483408: Multiply: (a-2/5)(a+5/2) 1 solutions Answer 330819 by stanbon(57219)   on 2011-08-19 15:55:13 (Show Source): You can put this solution on YOUR website!Multiply: (a-2/5)(a+5/2) ----- = (a(a+(5/2))-(2/5)(a+(5/2)) ----- = a^2 + (5/2)a -(2/5)a - 1 ----- = a^2 + [(5/2)-(2/5)]a -1 ----- = a^2 + [(25-4)/10]a -1 ---- = z^2 + (21/10)a -1 ========================== Cheers, Stan H.
 Points-lines-and-rays/483404: 1. Determine whether the lines will be perpendicular when graphed. 3x - 2y = 6 2x + 3y = 6 1 solutions Answer 330817 by stanbon(57219)   on 2011-08-19 15:51:06 (Show Source): You can put this solution on YOUR website!Determine whether the lines will be perpendicular when graphed. 3x - 2y = 6 2x + 3y = 6 --- slope of 1st equation: 3/2 --- slope of 2nd equation: -2/3 ----- Sice their product is -1, the lines are perpendicular. ================ Cheers, Stan H. ================
 Miscellaneous_Word_Problems/483413: In a certain lake, it is estimated that the fish population has been doubling in size every 80 weeks. Write an exponential growth equation of the form y=ae^kt that models the growth of the fish population, where t is given in weeks, if the initial population was 5000.1 solutions Answer 330815 by stanbon(57219)   on 2011-08-19 15:44:37 (Show Source): You can put this solution on YOUR website!In a certain lake, it is estimated that the fish population has been doubling in size every 80 weeks. Write an exponential growth equation of the form y=ae^kt that models the growth of the fish population, where t is given in weeks, if the initial population was 5000. ---------------------- A(t) = 5000*2^(t/80) where t is given in weeks. ======== Cheers, Stan H.
 Expressions-with-variables/483382: I need help solving this literal equation for x. I need to show all work. I would appreciate it if you can help me. d^2 - 4 (x+2) = d(x-2)1 solutions Answer 330807 by stanbon(57219)   on 2011-08-19 14:26:58 (Show Source): You can put this solution on YOUR website!d^2 - 4 (x+2) = d(x-2) --- Get the "x" terms on one side: ---- d(x-2)+4(x+2) = d^2 --- Factor: (x+2)(d+4) = d^2 --- Solve for "x": x+2 = d^2/(d+4) --- x = [d^2/(d+4)]-2 ========================== Cheers, Stan H.
 Radicals/483375: I need help solving this radical so no radicals are in the denominator. 8 / 2- sqrt 21 solutions Answer 330805 by stanbon(57219)   on 2011-08-19 14:23:43 (Show Source): You can put this solution on YOUR website!I need help solving this radical so no radicals are in the denominator. 8 / (2-sqrt(2)) ----------------------- Multiply numerator and denominator by (2+sqrt(2)) to get: --- = [8(2+sqrt(2)]/[4+2] --- = (4/3)(2+sqrt(2) ---- = (8/3) + (4/3)sqrt(2) ================= Cheers, Stan H.
 Linear-equations/483385: I need help finding the equation of the line in slope-intercept form (y=mx + b) using the given information. the answer is supposed to be y= 5 bu ti don't know how to get to the answer. The equation goes through (5,5) (10,12)1 solutions Answer 330799 by stanbon(57219)   on 2011-08-19 14:14:40 (Show Source): You can put this solution on YOUR website!I need help finding the equation of the line in slope-intercept form (y=mx + b) using the given information. the answer is supposed to be y= 5 bu ti don't know how to get to the answer. The equation goes through (5,5) (10,12) ---- y = 5 is not the answer. ---------------------------- slope = (12-5)/(10-5) = 7/5 ---- Form: y = mx + b Solve for "b": 5 = (7/5)*5 + b b = -2 ---- Equation: y = (7/5)x - 2 ================== Cheers, Stan H. ==================
 Probability-and-statistics/483299: please help me to explain this discussin question in detail with an example....Discuss the effects that the level of confidence have on the confidence interval......my instructor says that I need to state some kind of relationship like if the interval of confidence decreases then the confidence interval get bigger or something of that nature...I am not really sure how to explain it can you please help ASAP!!!PLEASE!!!!1 solutions Answer 330761 by stanbon(57219)   on 2011-08-19 09:17:28 (Show Source): You can put this solution on YOUR website!Discuss the effects that the level of confidence have on the confidence interval. ----- The confidence interval is ALWAYS 2*ME --- And ME = z*s/sqrt(n) --- The level of confidence determines the value of "z". If the level increases, z must increase. As z increases, ME must increase because ME and z are directly proportional. As ME increases the confidence interval gets wider, i.e. we have more confidence when the interval is wider. We can have absolute confidence if the interval is infinitely wide. ========== Cheers, Stan H. ==========
 Polynomials-and-rational-expressions/483277: pls i need help on this: factorise by grouping y2+4y+3+hy+3h 1 solutions Answer 330755 by stanbon(57219)   on 2011-08-19 09:01:18 (Show Source): You can put this solution on YOUR website!(y^2+4y+3) + (hy+3h) ---------- (y+3)(y+1) + h(y+3) ---- = (y+3)[y+1+h) ================== Cheers, Stan H. ===========
 Volume/483296: Hello Tutors of Algebra.com, I don't if is the right section but here goes A lab technician has a 40% alcohol solution and a 60% alcohol solution. He needs to make 100 mL of solution that is 48% alcohol . How much of each available solution should he use ? thanks in advance :D1 solutions Answer 330754 by stanbon(57219)   on 2011-08-19 08:57:03 (Show Source): You can put this solution on YOUR website!A lab technician has a 40% alcohol solution and a 60% alcohol solution. He needs to make 100 mL of solution that is 48% alcohol . How much of each available solution should he use ? -------- Equation: alcohol + alcohol = alcohol --------- 0.40x + 0.60(100-x) = 0.48*100 --- Multiply thru by 100 to get: 40x + 60*100 - 60x = 48*100 -20x = -12*100 x = 60 mL (amt. of 40% solution needed) 100-x = 40mL (amt. of 60% solution needed) ============ Cheers, Stan H.
 Probability-and-statistics/483295: A bag contains 9 balls numbered 1 through 9. A person draws 4 balls from the bag at the same tome, and then the person writes down the numbers on the balls in increasing order. What is the probability that the sequence 2, 5, 7, 9 will be written down? a. 0.00031 b. 0.00794 c. 0.04167 d. 0.22222 1 solutions Answer 330753 by stanbon(57219)   on 2011-08-19 08:52:02 (Show Source): You can put this solution on YOUR website!A bag contains 9 balls numbered 1 through 9. A person draws 4 balls from the bag at the same time, and then the person writes down the numbers on the balls in increasing order. What is the probability that the sequence 2, 5, 7, 9 will be written down? --- There are 9C4 = (9*8*7*6)/(1*2*3*4) = 126 sequences of 4 digits. Only 1 is correct. ---- P(correct sequence) = 1/126 = 0.00794 ======= Cheers, Stan H. ========= a. 0.00031 b. 0.00794 c. 0.04167 d. 0.22222
 Probability-and-statistics/483285: Can someone please help me on this one, I have no clue of what to do! Thank you Consider a die with eight sides, marked one, two, three, and so on. Assuming equally likely outcomes, find the probability that the sum of two dice is the given number. (Enter the answer either as a fracion or as a decimal rounded to three places. (a) P(3)= (b) P(4)= (c) P(7)= (d) P(10)= (e) P(12)= (f) P(13)= 1 solutions Answer 330751 by stanbon(57219)   on 2011-08-19 08:47:43 (Show Source): You can put this solution on YOUR website!Consider a die with eight sides, marked one, two, three, and so on. Assuming equally likely outcomes, find the probability that the sum of two dice is the given number. (Enter the answer either as a fracion or as a decimal rounded to three places. --------- This is "what to do". Sketch an 8 by 8 rectangle with rows labled 1-8 and columns labled 1-8 --- Enter the sum of each row-label + column-label in the row/column position: You should get the following in the 1st few rows: 2/3/4/5/6/7/8/9/10 3/4/5/6/7/8/9/10/11 4/5/6/7/8/9/10/11/12 etc. ----------- (a) P(3)= You see there are a total of 8*8 = 64 sums and 2 of the sums is "3". So P(3) = 2/64 ---- (b) P(4)= 3/64 etc. ---- (c) P(7)= (d) P(10)= (e) P(12)= (f) P(13)= ================= Cheers, Stan H.
 Probability-and-statistics/483266: sorry if am adding more questions but please i need your help. The next question is a. A study considered risk factors for HIV infection among intravenous drug users. It found that 40% of users who had 100 injections per month (light users) and 55% of users who had >100 injections per month (heavy users) were HIV positive. i. What is the probability that exactly 3 out of 5 light users are HIV positive? ii. What is the probability that at least 3 light users are HIV positive? 1 solutions Answer 330748 by stanbon(57219)   on 2011-08-19 08:05:23 (Show Source): You can put this solution on YOUR website!a. A study considered risk factors for HIV infection among intravenous drug users. -------------------------- It found that 40% of users who had 100 injections per month (light users) and -------------------------- 55% of users who had >100 injections per month (heavy users) were HIV positive. ------------------------ i. What is the probability that exactly 3 out of 5 light users are HIV positive? Binomial Problem with n = 5 and p = 0.40 P(x = 3) = 5C3(0.4)^3*(0.6)^2 = 0.2304 ---------- ii. What is the probability that at least 3 light users are HIV positive? P(3<= x <=5) = 1 - binomcdf(5,0.4,2) = 0.3174 ====================== Cheers, Stan H. =========
 Probability-and-statistics/483268: Following is the frequency distribution of systolic blood pressure for smokers and nonsmokers: Class interval nonsmokers smokers Total 90-109 10 5 15 110-129 24 15 39 130-149 18 10 28 150-169 9 3 12 170-189 2 2 4 190-209 0 2 2 Total 63 37 100 Suppose, A: a nonsmoker B: a smoker C: a systolic blood pressure of 170 or greater Find a. P(A) b. P(B) c. P(C) d. P(C ) e. P(C f. Compare d and e, and comment. Are smoking status and blood pressure level independent event? 1 solutions Answer 330746 by stanbon(57219)   on 2011-08-19 07:58:58 (Show Source): You can put this solution on YOUR website!Following is the frequency distribution of systolic blood pressure for smokers and nonsmokers: Class interval nonsmokers smokers Total 90-109 ::::::::::::::10 5 15 110-129 ::::::::::::::24 15 39 130-149 ::::::::::::::18 10 28 150-169 :::::::::::::::9 3 12 170-189 :::::::::::::::2 2 4 190-209 :::::::::::::::0 2 2 Total ::::::::::::::63 37 100 Suppose, A: a nonsmoker B: a smoker C: a systolic blood pressure of 170 or greater Find a. P(A) = 63/100 b. P(B) = 37/100 c. P(C) = 6/100 d. P(C|A) = 2/100 e. P(C|B) = 4/100 f. Compare d and e, and comment. Are smoking status and blood pressure level independent event? Ans: No. -------------- Cheers, Stan H.
 Probability-and-statistics/483269: In a clinical trial 250 patients are randomly assigned to receive either a proposed stroke prevention medication ( ) or a placebo ( ) and are followed over the course of a 5-years study period. These results are given in the following table: Treatment Group Event Stroke No Stroke Total 12 108 120 28 102 130 Total 40 210 250 a. Estimate the risk of stroke comparing those on the medication to those on placebo and interpret the result. b. Interpret your result in part a. 1 solutions Answer 330744 by stanbon(57219)   on 2011-08-19 07:49:53 (Show Source): You can put this solution on YOUR website!In a clinical trial 250 patients are randomly assigned to receive either a proposed stroke prevention medication ( ) or a placebo ( ) and are followed over the course of a 5-years study period. These results are given in the following table: Treatment Group Event Stroke No Stroke Total ::::::12 108 120 ::::::28 102 130 Total 40 210 250 -------------------- I'll assume the "12" refers to the treatment group and the 28 is the not-treatment group. --- So p-hat = 12/120 = 0.10 for the treatment group and p-hat = 28/130 = 0.22 for the non-treatment group ---- Ho: p1-p2 = 0 H1: p1-p2 < 0 --- test stat: (0.10-0.22)/sqrt[(0.1*0.9/120)+(0.22*0.78/130)] = -2.6375 --- p-value = P(z < -2.6375) = 0.0042 ---------- Conclusion: Since the p-value is less than 1%, reject Ho at the 1% significance level. ================================================== a. Estimate the risk of stroke comparing those on the medication to those on placebo and interpret the result. b. Interpret your result in part a. The non-treatment group is twice as liable have a stroke. ============================================================ Cheers, Stan H.
 Quadratic_Equations/483204: y^2+6y+34=0 solve by "completing the square"1 solutions Answer 330690 by stanbon(57219)   on 2011-08-18 22:45:27 (Show Source): You can put this solution on YOUR website!y^2+6y+34=0 solve by "completing the square" --- y^2+6y + ? = -34 + ? --- y^2+6y+9 = -34+9 ---- (y+3)^2 = -25 ---- y + 3 = 5i or y+3 = -5i ----- y = -3+5i or y = -3-5i =========================== cheers, stan H.
 Linear-equations/483193: y = 2x + 3 y = 2x + 5 You know by looking at these two problems that the slope is the same for each equation (y = mx + b - the slope is 2) and they have a different y-intercept. First - what is the y-intercept for each of these equations? Second - can you say anything about this system of equations - visualize the solution? 1 solutions Answer 330689 by stanbon(57219)   on 2011-08-18 22:42:07 (Show Source): You can put this solution on YOUR website!y = 2x + 3 y = 2x + 5 You know by looking at these two problems that the slope is the same for each equation (y = mx + b - the slope is 2) and they have a different y-intercept. --------------------------- First - what is the y-intercept for each of these equations? 1st: 3 2nd: 5 ------------------- Second - can you say anything about this system of equations - visualize the solution? The line are parallel. They have no common point. The system has no solution. ---------------------------- Cheers, Stan H.
 Permutations/483194: Hi, here's the question, "how many ways can 3 student representatives be chosen from 100. Here's my work: 100C3 = 100•99•98•97! / 3! 97! But the answer didn't come out right1 solutions Answer 330685 by stanbon(57219)   on 2011-08-18 22:34:48 (Show Source): You can put this solution on YOUR website!"how many ways can 3 student representatives be chosen from 100. Here's my work: 100C3 = 100•99•98•97! / 3! 97! But the answer didn't come out right ----- Cancel the 97! in the numerator and the denominator to get: (100*99*98)/(1*2*3) = 161,700 ========== Cheers, Stan H. ==========
 logarithm/483161: 9=3^2 In a logarithmic form 1 solutions Answer 330683 by stanbon(57219)   on 2011-08-18 22:30:59 (Show Source): You can put this solution on YOUR website!9=3^2 In a logarithmic form ------ "log" means power or exponent. ---- Your problem has exponent = 2, base = 3 and result = 9 --- So, log3(9) = 2 ================== Cheers, Stan H.
 Permutations/483173: 1.I make 5,000 more then 2 times Jack? How do I make this a algabraic equation?1 solutions Answer 330681 by stanbon(57219)   on 2011-08-18 22:19:24 (Show Source): You can put this solution on YOUR website!I make 5,000 more then 2 times Jack? How do I make this a algabraic equation? ---- I = 2J + 5000 ======================= Cheers, Stan H.
 Travel_Word_Problems/483190: Hello! Can anyone pls. answer this problem, it's all about distance/rate problem. I don't know how to start solving this problem. Pls. help me solve this. Problem: An automobile traveling at a certain rate can go from one province to another in 9 hours. If the rate were 12 kilometers per hour faster, the trip would require two hour less. What is the distance between provinces? Pls. do answer this problem. >>Thank You<<1 solutions Answer 330679 by stanbon(57219)   on 2011-08-18 22:17:20 (Show Source): You can put this solution on YOUR website!An automobile traveling at a certain rate can go from one province to another in 9 hours. If the rate were 12 kilometers per hour faster, the trip would require two hour less. What is the distance between provinces? ----------------- 1st trip DATA: time = 9 hrs; rate = x kph ; distance = 9x km --------------- 2nd trip DATA: time = 7 hrs; rate = x+12 kph ; distance = 7(x+12) km -------------------- Equation: distance = distance 9x = 7(x+12) 9x = 7x + 84 --- 2x = 84 x = 42 ---- distance = 9*42 = 378 km ============================ Cheers, Stan H. =============
 absolute-value/483180: 3|p-5|=2p1 solutions Answer 330676 by stanbon(57219)   on 2011-08-18 22:11:22 (Show Source): You can put this solution on YOUR website!3|p-5|=2p ----- |p-5| = (2/3)p --- p-5 = (2/3)p or p-5 = (-2/3)p ------ p = 5 + (2/3)p or p = 5+(-2/3)p (1/3)p = 5 or (5/3)p = 5 --- p = 15 or p = 3 =================== Cheers, Stan H.
 Linear-equations/483185: the speed of an automobile in mph varies directly with its speed in kph. a speed of 64 mph is equivalent to a speed of 103 kph. write a linear equation that relates speed in miles per hour to speed in kph1 solutions Answer 330674 by stanbon(57219)   on 2011-08-18 22:06:27 (Show Source): You can put this solution on YOUR website!the speed of an automobile in mph varies directly with its speed in kph. a speed of 64 mph is equivalent to a speed of 103 kph. write a linear equation that relates speed in miles per hour to speed in kph ---------------- mph = k*kph --- Solve for "k": 64 = k*103 k = 64/103 ---- mph = (64/103)kph ========================== Cheers, Stan H. ============