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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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 Travel_Word_Problems/289721: A car travels at an average speed of 75 km per hour. How long will it take to travel 50 km?1 solutions Answer 209775 by stanbon(57347)   on 2010-04-07 19:07:17 (Show Source): You can put this solution on YOUR website!A car travels at an average speed of 75 km per hour. How long will it take to travel 50 km? ----------------------------- time/distance = time/distance ---- t/50 km = 1/75 --- t = 50(1/75) t = 2/3 hr. ================= Cheers, Stan H.
 Rational-functions/289717: i need to simplify this problem: x+1/x+1/x-11 solutions Answer 209773 by stanbon(57347)   on 2010-04-07 19:03:53 (Show Source): You can put this solution on YOUR website!i need to simplify this problem: x+1/x+1/x-1 ----- = x+1/x+(1-x)/x --- = (x^2+1)/x + (1-x)/x --- = (x^2 + 1 + 1-x)/x --- = (x^2 -x + 2)/x --- = [(x-2)(x+1)]/x ======================= I doubt this is the answer you are looking for but your post has no parentheses so it allows for many interpretations. ======================= Cheers, Stan H.
 Divisibility_and_Prime_Numbers/289718: What is the prime factorization of 385 Please show the steps1 solutions Answer 209771 by stanbon(57347)   on 2010-04-07 18:57:10 (Show Source): You can put this solution on YOUR website!What is the prime factorization of 385 Please show the steps ------------- 385 = 5*77 = 5*7*11 ========================= Cheers, Stan H.
 Trigonometry-basics/289716: Find the values of the six trigonometric functions of the angle in standard position with the terminal side passing through the point P(-4, 3)1 solutions Answer 209770 by stanbon(57347)   on 2010-04-07 18:55:20 (Show Source): You can put this solution on YOUR website!Find the values of the six trigonometric functions of the angle in standard position with the terminal side passing through the point P(-4, 3) ----------------- Since x = -4 and y = 3, r = sqrt(4^2 + 3^2) = 5 ------------------------------- sin = y/r = 3/5 cos = x/r = -4/5 tan = y/x = -3/4 --- csc = r/y = 5/3 sec = r/x = -5/4 cot = x/y = -4/3 ======================= Cheers, Stan H.
 Signed-numbers/289698: -3/5+(8/35)= 1 solutions Answer 209769 by stanbon(57347)   on 2010-04-07 18:50:21 (Show Source): You can put this solution on YOUR website! -3/5+(8/35) --- least common denominator: 35 = (-3*7)/lcd + 8/lcd --- = [-21 + 8]/lcd --- = [-13/lcd] --- = -13/35 ====================== Cheers, Stan H. -----
 Probability-and-statistics/289666: if one member is chosen at random from a club that has 12 girls and 9 boys, what is the probability that a girl will be selected? 1 solutions Answer 209765 by stanbon(57347)   on 2010-04-07 17:51:45 (Show Source): You can put this solution on YOUR website!if one member is chosen at random from a club that has 12 girls and 9 boys, what is the probability that a girl will be selected? ------------------------------- P(select a girl) = 12/21 = 4/7 ======================================== Cheers, Stan H.
 Probability-and-statistics/289489: 2. General Buck Twigidson is preparing to make his annual budget presentation to the U.S. senate and is speculating about his chances of getting all or part of his requested budget approved. From his 20 years of experience in making these requests, he has deduced that his chances of getting between 50 and 74 per cent of his budget approved are twice as good as those of getting between 75 and 99 per cent approved, and two and one-half times as good as those of getting between 25 and 49 per cent approved. Further, the general believes that there is no chance of less than 25 per cent of his budget being approved. Finally, the entire budget has been approved only once during the General's tenure and the General do not expect this pattern to change. What are the probabilities of 0-24 per cent, 25-49 per cent, 50-74 per cent, 75-99 per cent, and 100 per cent approval, according to the general? 1 solutions Answer 209653 by stanbon(57347)   on 2010-04-07 06:45:03 (Show Source): You can put this solution on YOUR website!From his 20 years of experience in making these requests, he has deduced that his chances of getting between 50 and 74 per cent of his budget approved are twice as good as those of getting between 75 and 99 per cent approved, and two and one-half times as good as those of getting between 25 and 49 per cent approved. Further, the general believes that there is no chance of less than 25 per cent of his budget being approved. Finally, the entire budget has been approved only once during the General's tenure and the General does not expect this pattern to change. --------------- What are the probabilities of a) 0-24 per cent, b) 25-49 per cent, c) 50-74 per cent, d) 75-99 per cent, e) 100 per cent ---- Equations: a + b + c + d + e = 1 c = 2d c = 2.5b a = 0 e = 0 ------------------- Substitute 0 + (2/5)c + c + (1/2)c + 0 = 1 Simplify: (19/10)c = 1 c = 10/19 --- Solve for d and b: d = (1/2)c = 5/19 b = (2/5)c = 4/19 =========================== Cheers, Stan H.
 Rate-of-work-word-problems/289413: It takes 10 hours to fill a pool with the inlet pipe. It can be emptied in 15 hours with the outlet pipe. If the pool is half full to begin with, how long will it take to fill it from there if both pipes are open? i think i have it at here but im not sure i worked it out to be.. 1/10-1/15=1/2t1 solutions Answer 209620 by stanbon(57347)   on 2010-04-06 22:28:14 (Show Source): You can put this solution on YOUR website!It takes 10 hours to fill a pool with the inlet pipe. 5 hrs to fill half the pool: rate = 1/5 hrs/half-pool --------------------------------- It can be emptied in 15 hours with the outlet pipe. (15/2) hrs to empty half the pool rate = (2/15) hrs/half-pool --------------------------------- Working together let rate = x hrs/half-pool ----- Equation: 1/5 - 2/15 = 1/x 3x - 2x = 15 x = 15 hrs (time to fill half of the pool) ========================== If the pool is half full to begin with, how long will it take to fill it from there if both pipes are open? i think i have it at here but im not sure i worked it out to be.. 1/10-1/15=1/2t Using your equation: Multiply thru by 30t to get: 3t-2t = 15 t = 15 hrs. (time to fill half of the pool) ================================================= Cheers, Stan H. =================================================
 Polynomials-and-rational-expressions/289411: I am not understanding how to do this problem... Most I am getting however, this one is driving me tired... Please help and thank you!! (x-2)/(x-8)-1/x=(x-7)/x Please show me how to work the problem... to get the correct answers... Blessings & Miracles Alberta... 1 solutions Answer 209616 by stanbon(57347)   on 2010-04-06 22:16:40 (Show Source): You can put this solution on YOUR website![(x-2)/(x-8)]-[1/x] = [(x-7)/x] ------ Multiply thru by x(x-8) to get rid of the denominators: ------ x(x-2) - (x-8) = (x-8)(x-7) --- x^2 - 2x -x + 8 = x^2-15x+56 -------------------- -3x + 8 = -15x + 56 12x = 48 x = 4 -------------------------------- Cheers, Stan H. =====================
 Miscellaneous_Word_Problems/289408: Judy has three more dimes than nickels and twice as many nickels as quarters. If altogether she has 85 cents in nickels, dimes, and quarters, how many of each coin does she have? 1 solutions Answer 209614 by stanbon(57347)   on 2010-04-06 22:12:05 (Show Source): You can put this solution on YOUR website!Judy has three more dimes than nickels and twice as many nickels as quarters. If altogether she has 85 cents in nickels, dimes, and quarters, how many of each coin does she have? ----- Equations: d = n+3 n = 2q 5n + 10d + 25q = 85 cents ------------------------ Substitute and solve for "n" 5n + 10(n+3) + 25(n/2) = 85 Multiply thru by 2 to get: 10n + 20n + 60 + 25n = 170 55n = 110 n = 2 (# of nickels) d = n+3 = 5 (# of dimes) q = (1/2)n = 1 (# of quarters) ================================== Cheers, Stan H.
 Exponents/289406: i need help!!!! way behind on home work and have no idea how to do this algebra! im working on perfect square trinomials. and factoring polynomials. what would 6bsquared+11b+3 how do i solve? and x squared-18x+81=0 how do i solve????1 solutions Answer 209609 by stanbon(57347)   on 2010-04-06 21:50:19 (Show Source): You can put this solution on YOUR website!6bsquared+11b+3 how do i solve? --- You cannot "solve" it because it is not an equation. You can factor it: 6b^2 + 11b + 3 Think of two numbers whose product is 6*3 = 18 and whose sum is 11. The numbers are 9 and 2 Rewrite the problem but replace 11b by 9b+2b --- 6b^2 + 9b + 2b + 3 Factor the 1st two and the last two terms: 3b(2b+3) + (2b+3) Factor again: (2b+3)(3b+1) =========================================== and x squared-18x+81=0 x^2 - 18x + 81 Think of two numbers whose product is 81 and sum is -18. The numbers are -9 and -9 ------------------------------ Rewrite the problem: x^2 -9x -9x + 81 = 0 x(x-9) -9(x-9) = 0 (x-9)(x-9) = 0 x = 9 with multiplicity 2 ============================== Cheers, Stan H. ============================== -----------------
 Probability-and-statistics/289363: Assuming that boys and girls are equally likely, estimate the probability of getting more than 3600 girls in 6400 births.1 solutions Answer 209597 by stanbon(57347)   on 2010-04-06 20:44:20 (Show Source): You can put this solution on YOUR website!Assuming that boys and girls are equally likely, estimate the probability of getting more than 3600 girls in 6400 births. ------- mean = np = (1/2)6400 = 3200 std = sqrt(npq) = sqrt(1600) = 40 ------------------------ Find the z-score of 3600 z(3600) = (3600-3200)/40 = 400/40 = 10 --- P(x > 3600) = P(z > 10) = 7.8 x 10^(-24) ============================================== Cheers, Stan H.
 Quadratic_Equations/289365: The height of an object thrown in the air is given by h = t2 – 7t + 3, where h is in feet and t is the time in seconds the object has been in motion. At what time (to the nearest tenth) is the object 11 feet in the air? Could you help to solve this equation? Thank you. Cynthia 1 solutions Answer 209596 by stanbon(57347)   on 2010-04-06 20:29:10 (Show Source): You can put this solution on YOUR website!The height of an object thrown in the air is given by h = t2 – 7t + 3, where h is in feet and t is the time in seconds the object has been in motion. At what time (to the nearest tenth) is the object 11 feet in the air? ---- h is the height so make it 11 and solve for "t": t^2-7t+3 = 11 --- t^2 -7t -8 = 0 (t-8)(t+1) = 0 Positive solution: t = 8 seconds (time at which the object is at a height of 11 ft. ===================================== Cheers, Stan H.
 Probability-and-statistics/289348: Suppose that the wrapper of a candy bar lists its weight as 8 ounces. The actual weights of individual candy bars naturally vary to some extent. Suppose that these actual weights vary according to a normal distribution wth mean 8.5 ounces and standard deviation .325 ounces What proportion of he candy bars weigh less less than adverised 8 ounces? If the manufacturer wants to decrease this proportion from a) by changing the man of its candy bar weigts, should it increase or decrease that mean? If the manufacturer wants to decrease this proportion from a) by changing the standard deviation of its candy bar weight should it increase or decrease that standard deviation? Not sure what I need to do ....Thank you for your help1 solutions Answer 209594 by stanbon(57347)   on 2010-04-06 20:24:49 (Show Source): You can put this solution on YOUR website!Suppose that the wrapper of a candy bar lists its weight as 8 ounces. The actual weights of individual candy bars naturally vary to some extent. Suppose that these actual weights vary according to a normal distribution wth mean 8.5 ounces and standard deviation .325 ounces ----------------------------- What proportion of the candy bars weigh less less than adverised 8 ounces? Find the z-value of 8: z(8) = (8-8.5)/0.325 = -1.5385 P(x < 8) = P(z < -1.5385) = 0.062 weigh less than then 8 ounces. ------------------------- If the manufacturer wants to decrease this proportion from a) by changing the mean of its candy bar weights, should it increase or decrease that mean? Increase it. ------------------------- If the manufacturer wants to decrease this proportion from a) by changing the standard deviation of its candy bar weight should it increase or decrease that standard deviation? Decrease it to pull the distribution close to the mean. ================ Cheers, Stan H.
 Points-lines-and-rays/289314: what is the measure, in degrees of each angle of a regular hexagon1 solutions Answer 209588 by stanbon(57347)   on 2010-04-06 19:03:55 (Show Source): You can put this solution on YOUR website!what is the measure, in degrees of each angle of a regular hexagon ------------------- Sum of the angles of a regular hexagon: (6-2)180 = 720 degrees ----------------- Measure of each interior angle: 720/6 = 120 degrees ================= Cheers, Stan H.
 logarithm/289308: Hi I couldnt figure out how to do this problem LOG6(x+3)+LOG6(x-2)=11 solutions Answer 209587 by stanbon(57347)   on 2010-04-06 18:59:08 (Show Source): You can put this solution on YOUR website!Hi I couldnt figure out how to do this problem LOG6(x+3)+LOG6(x-2)=1 ------------ log6[(x+3)(x-2)] = 1 --- x^2+x-6 = 6^1 --------------- x^2+x-12 = 0 (x-4)(x+3) = 0 --- Acceptable solution: x = 4 Note: x cannot be -3 because log(x-3) would be log(0) which does not exist. ============ Cheers, Stan H.
 Complex_Numbers/289304: what is [(1/3)^-2-(-3)^-1]/[(1/2)^-1-(-2)^-2]1 solutions Answer 209586 by stanbon(57347)   on 2010-04-06 18:54:28 (Show Source): You can put this solution on YOUR website!what is [(1/3)^-2-(-3)^-1]/[(1/2)^-1-(-2)^-2] ------------ = [(1/9) +(1/3)]/[2 + -(1/4)] ----- = [4/9] / [7/4] --- = 16/63 ============= Cheers, Stan H. =============
 Proportions/289294: 35 out of 50 bike injuries in the state last year were head injuries. Of each 10 bike injuries how many are to the head? I tried to figure the proportion but can't quite get it... THANKS!1 solutions Answer 209585 by stanbon(57347)   on 2010-04-06 18:46:17 (Show Source): You can put this solution on YOUR website!35 out of 50 bike injuries in the state last year were head injuries. Of each 10 bike injuries how many are to the head? I tried to figure the proportion but can't quite get it... ----------------------- head/bike injuries = head/bike injuries --- x/10 == 35/50 --- x = 10(35/50) x = 7 ======================== Cheers, Stan H. ========================
 Quadratic_Equations/289278: 1 solutions Answer 209583 by stanbon(57347)   on 2010-04-06 18:23:58 (Show Source): You can put this solution on YOUR website!y=-3x^2+6x+1 ------------------------ Find the x-intercepts: Quadratic Formula: x = [-6 +- sqrt(36-4*-3*1)]/-6 ------- x = [-6 +- sqrt(48)]/-6 --- x = [-6 +-4sqrt(3)]/-6 --- x = 1 +- (2/3)sqrt(3) --- Find the y-intercept: y = 0+0+1 y = 1 ---- y=-3x^2+6x+1 Find the vertex: x = -b/2a = -6/(-6) = 1 f(1) = -3+6+1 = 4 Vertex at (1,4) --------------------- Graph: ================================================ Cheers, Stan H.
 Probability-and-statistics/289273: How much pizza is left if 7 people ate 3/8 each of 4 pizzas?1 solutions Answer 209581 by stanbon(57347)   on 2010-04-06 18:04:31 (Show Source): You can put this solution on YOUR website!How much pizza is left if 7 people ate 3/8 each of 4 pizzas? -------------------- The 7 people ate 7(3/8) = 21/8 pizza ---------------- The 4 pizzas can be written as 32/8 pizza ---------------- Then 32/8 - 21/8 = 11/8 pizza (amount of pizza that is left) =================== Cheers, Stan H. ===================
 Length-and-distance/289185: The circle x^2+y^2-6x-8y=0 intersects the y axis at A& B and is a tangent to the x axis at C. (a) write down the coordinates of pt C (b) find the length of the chord AB i figured that a line or something touches (6,8) i think because of -6x and -8y thx!!!!1 solutions Answer 209537 by stanbon(57347)   on 2010-04-06 15:00:55 (Show Source): You can put this solution on YOUR website!The circle x^2+y^2-6x-8y=0 intersects the y axis at A& B and is a tangent to the x axis at C. -------------- Complete the square to find the center and radius of the circle: x^2-6x+9 + y^2-8y+16 = 25 (x-3)^2 + (y-4)^2 = 25 center at (3,4); radius = 5 ----------------- Draw the picture of that circle putting the center at (3,4) and making the radius = 5. ------ y-intercepts = ? Let x = 0 and solve for "y": y^2-8y = 0 y(y-8) = 0 y = 0 or y = 8 --- The y-intercepts are (0,0) and (0,8) The chord AB has length = 8 --------------------------------------- (a) write down the coordinates of pt C Note: The circle is not tangent to the x-axis. C is directly below (3,4) C is (3,0) if it is on the x-axis -------------------------- (b) find the length of the chord AB: 8 ============================================== Cheers, Stan H. ==============================================
 Expressions-with-variables/289184: Perform the indicated operation (multiplication) and simplify your answer. I appreciate the help, thank you.1 solutions Answer 209532 by stanbon(57347)   on 2010-04-06 14:47:22 (Show Source): You can put this solution on YOUR website!(x^4/2)(x/3) Perform the indicated operation (multiplication) and simplify your answer. = (x^5/6) ========== Cheers, Stan H. ===========
 Miscellaneous_Word_Problems/289183: A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle? Can you all help me with this one??? Thank you :)1 solutions Answer 209529 by stanbon(57347)   on 2010-04-06 14:44:31 (Show Source): You can put this solution on YOUR website! A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle? ---------------- Equations: d = L + 3.6 d = W + 7.1 --------------------- length = d-3.6 ft width = d-7.1 ft --------------------- Cheers, Stan H.
 Length-and-distance/289179: if the diagonal of a rhombus are 12 and 16 then a side of the rhombus will measure? a) 10 b) 12 c) 16 d) 20 and how did you do it?1 solutions Answer 209527 by stanbon(57347)   on 2010-04-06 14:39:09 (Show Source): You can put this solution on YOUR website!if the diagonal of a rhombus are 12 and 16 then a side of the rhombus will measure? Draw a rhombus (all sides are equal) The diagonal are perpendicular bisectors of one-another. --- Diagonal pieces are 6,6 and 8,8. Use Pythgoras: side^2 = 6^2 + 8^2 side = sqrt[100] side = 10 ------------- Cheers, Stan H. ======================= a) 10 b) 12 c) 16 d) 20 =======================
 expressions/289141: Using a standard American keyboard, how do I enter a square root symbol ? How do I enter an exponent ? How do I enter a pi symbol ? How do I enter a greater than or less than symbol ? How do I enter does not equal symbol ? If you can add any other 'problematic' keyboard entries it would be greatly appreciated. 1 solutions Answer 209508 by stanbon(57347)   on 2010-04-06 12:45:24 (Show Source): You can put this solution on YOUR website! Using a standard American keyboard, how do I enter a square root symbol ?:: use "sqrt" How do I enter an exponent ?::: use ^(power) or "to the---power" How do I enter a pi symbol ?::: use 3.14 or (22/7) How do I enter a greater than or less than symbol ?::: use > or "greater than" ; use < or "less than" How do I enter does not equal symbol ?::: use "is not equal to" How to enter e ::: use 2.1828.. If you can add any other 'problematic' keyboard entries it would be greatly appreciated. ==================== Cheers, Stan H.
 logarithm/289140: 3^x+2 x 3^x=81 Also 3[logx]=61 solutions Answer 209506 by stanbon(57347)   on 2010-04-06 12:39:50 (Show Source): You can put this solution on YOUR website!3^(x+2)*3^x=81 3^(x+2+x) = 3^4 2x+2 = 4 2x = 2 x = 1 ----------------------- Also 3[logx]=6 log(x) = 2 x = 10^2 x = 100 ================= Cheers, Stan H.
 Linear-equations/289137: solve by substitution I need help finding the response to these sentences 2m+n=16 m-3n=151 solutions Answer 209502 by stanbon(57347)   on 2010-04-06 12:36:18 (Show Source): You can put this solution on YOUR website!2m+n=16 m-3n=15 ----- Comment: It's up to you to decide which variable you are going to eliminate. If you want to eliminate the "n" terms, Multiply thru the 1st equation by 3, then add the two equations: 6m + 3n = 48 m - 3n = 15 -------------- 7m = 63 m = 9 ---- Substitute into either of the original equations and solve for "n": 9-3n = 15 -3n = 6 n = -2 ------------------- Cheers, Stan H. =====================
 Equations/289131: In testing an engine, various mixtures of gasoline and methanol are being tried. How much of a 90% gasoline mixture and a 75% gasoline mixture are needed for 1200 L of an 85% gasoline mixture?1 solutions Answer 209500 by stanbon(57347)   on 2010-04-06 12:32:16 (Show Source): You can put this solution on YOUR website!How much of a 90% gasoline mixture and a 75% gasoline mixture are needed for 1200 L of an 85% gasoline mixture? -------------- Equation: gas + gas = gas 0.90x + 0.75(1200-x) = 0.85*1200 ---- Multiply thru by 100 and solve for "x": 90x + 75*1200 - 75x = 85*1200 15x = 10*1200 x = (2/3)1200 x = 800 L (amt. of 90% gasoline needed in the mixture) --- 1200-x = 400 L (amt. of 75% gasoline needed in the mixture) ==================================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/289107: a 90% antifreeze solution is to be mixed with a 75% solution to make 30 liters of an 80% solution. How many liters of the 90% and 75% solutions should be used?1 solutions Answer 209471 by stanbon(57347)   on 2010-04-06 11:19:42 (Show Source): You can put this solution on YOUR website!A 90% antifreeze solution is to be mixed with a 75% solution to make 30 liters of an 80% solution. How many liters of the 90% and 75% solutions should be used? ----------------------------- Equation: alcohol + alcohol = alcohol 0.9x + 0.75(30-x) = 0.30(80) --- Multiply thru by 100 and solve for "x": 90x + 75*30 - 75x = 30*80 15x = 5*30 x = 6 liters (amt. of 90% antifreeze needed in the mixture) --- 30-x = 24 liters (amt. of 75% antifreeze needed in the mixture) ==================================== Cheers, Stan H. ====================================
 Square-cubic-other-roots/289104: square root of 14 over the square root of 3 1 solutions Answer 209467 by stanbon(57347)   on 2010-04-06 11:12:37 (Show Source): You can put this solution on YOUR website!square root of 14 over the square root of 3 --------------- [sqrt(14)]/[sqrt(3)] ---- Multiply numerator and denominator by sqrt(3) to get: ---- = [sqrt(42)]/3 ================ Cheers, Stan H. ================
 Polynomials-and-rational-expressions/289102: Missing ages. Molly’s age is twice Anita’s. If the sum of the squares of their ages is 80, then what are their ages? I started this problem and took 80 divided by two which gave me 40, then this is where i got stuck. Am i doing this right ro do i need to go about it differently?1 solutions Answer 209465 by stanbon(57347)   on 2010-04-06 11:08:47 (Show Source): You can put this solution on YOUR website!Missing ages. Molly’s age is twice Anita’s. If the sum of the squares of their ages is 80, then what are their ages? ----------------------------------- Equations: m = 2a m^2 + a^2 = 80 ---- Substitute for "m" and solve for "a": (2a)^2 + a^2 = 80 4a^2 + a^2 = 80 5a^2 = 80 a^2 = 16 a = 4 (Anita's age) --- Since m = 2a, m = 8 (Molly's age) =================================== Cheers, Stan H. ===================================