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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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 Rectangles/488923: A farmer owns two rectangular fields. The length of the larger field is twice the length of the smaller field, and the width of the larger field is four times the width of the smaller field. If the smaller field has an area of 1 acre, what is the area of the larger field?1 solutions Answer 333489 by stanbon(57274)   on 2011-08-31 08:31:19 (Show Source): You can put this solution on YOUR website!A farmer owns two rectangular fields. The length of the larger field is twice the length of the smaller field, and the width of the larger field is four times the width of the smaller field. If the smaller field has an area of 1 acre, what is the area of the larger field? --- Area of smaller field = LW ------ Area of larger field = (2L)(4W) = 8LW ---- Area of larger field = 8(LW) = 8(1) = 8 acres ================== Cheers, Stan H. ==================
 Linear-equations/488926: if one-third of a number is added to twice of a number, the answer is 10. What is the number1 solutions Answer 333487 by stanbon(57274)   on 2011-08-31 08:28:41 (Show Source): You can put this solution on YOUR website!if one-third of a number is added to twice of a number, the answer is 10. --- Equation: (1/3)x + 2x = 10 --- Multiply thru by 3 to get: x + 6x = 30 7x = 30 x = 30/7 ============ Cheers, Stan H. ============
 Quadratic_Equations/488918: N(x) = -0.4x^2 +8x + 12 IS the formula. What day will the ticket sales peak on? and how many tickets will be sold on that day.1 solutions Answer 333486 by stanbon(57274)   on 2011-08-31 08:26:25 (Show Source): You can put this solution on YOUR website!N(x) = -0.4x^2 +8x + 12 IS the formula. What day will the ticket sales peak on? and how many tickets will be sold on that day. ------ a = -0.4 ; b = 8 ; c = 12 --- Max tickets sales occurs when x = -b/(2a) = -8/(2*-0.4) = 10 --- Max ticket sales = N(10) = -0.4^10^2 + 8*10 +12 = -40 + 80 + 12 = 52 ========== Cheers, Stan H.
 percentage/488925: What is the percentage of 320 out of 359?1 solutions Answer 333485 by stanbon(57274)   on 2011-08-31 08:22:52 (Show Source): You can put this solution on YOUR website!What is the percentage of 320 out of 359? --- x/100 = 320/359 --- x = 100(320/359) --- x = 100*0.8914 --- x = 89.14% ============ Cheers, Stan H.
 Rate-of-work-word-problems/488920: Pipe M can fill a tank in 36 hours, and pipe N can fill it in a certain time. If both pipes are opened simultaneously, the tank gets filled in 24 hours. Find the time it takes pipe N alone to fill the tank.1 solutions Answer 333484 by stanbon(57274)   on 2011-08-31 08:20:50 (Show Source): You can put this solution on YOUR website!Pipe M can fill a tank in 36 hours, and pipe N can fill it in a certain time. If both pipes are opened simultaneously, the tank gets filled in 24 hours. Find the time it takes pipe N alone to fill the tank. ---- Pipe M rate: 1/36 job/hr --- Pipe N rate: 1/x job/hr --- Together rate: 1/24 job/hr ----- Equation: rate + rate = together rate 1/36 + 1/x = 1/24 24x + (24*36) = 36x 12x = (24*36) x = 72 hrs (time for Pipe N to fill the tank alone) ================ Cheers, Stan H.
 Signed-numbers/488912: I need help awnsering x+y2+3x+xy ? I dont get it . It say combine like terms.1 solutions Answer 333481 by stanbon(57274)   on 2011-08-31 07:15:32 (Show Source): You can put this solution on YOUR website!x+y2+3x+xy ---- The only "like" terms you have are x and 3x. --- = y^2 + xy + 4x ==================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/488911: 2 men and 5 women can together complete the work in 4 days while 3 mens and 6 women can finish it in 3 days .find the time taken by one man and women each to complete the work.1 solutions Answer 333480 by stanbon(57274)   on 2011-08-31 07:13:35 (Show Source): You can put this solution on YOUR website!2 men and 5 women can together complete the work in 4 days while 3 mens and 6 women can finish it in 3 days .find the time taken by one man and women each to complete the work. ---- Let a man's rate be "m"; Let a women's rate be "w": ---- Equations: 2m + 5w = 1/4 3m + 6w = 1/3 ------------------------ Modify: 8m + 20w = 1 9m + 18w = 1 ------------- Modify: 72m + 180w = 9 72m + 144w = 8 -------------------- Subtract and solve for "w": 36w = 1 w = 1/36 Note: Since a woman's rate is 1/36 job/day, a woman's time to do the job is 36 days/job. +++++++++++++++++++++++++++++++++ Solve for "m": 9m + 18w = 1 9m + 18(1/36) = 1 9m + (1/2) = 1 9m = 1/2 m = 1/18 Note: Since a man's rate is 1/18 job/day, a man's time to do the job is 18 days/job ============================================= Cheers, Stan H.
 Travel_Word_Problems/488890: 2 children are balanced on a seesaw. One of them weighing 40 lbs is 6 feet from the fulcrum. How far from the fulcrum on the other side must the other child sit if he weighs 60 lbs? 1 solutions Answer 333479 by stanbon(57274)   on 2011-08-31 07:01:51 (Show Source): You can put this solution on YOUR website!2 children are balanced on a seesaw. One of them weighing 40 lbs is 6 feet from the fulcrum. How far from the fulcrum on the other side must the other child sit if he weighs 60 lbs? ------------------------ Equation: 40*6 = 60x ----- x = (40*6)/60 --- x = 40/10 -- x = 4 ft. =================== Cheers, Stan H.
 Numbers_Word_Problems/488907: find the four consecutive integers whose sum is 32. 1 solutions Answer 333478 by stanbon(57274)   on 2011-08-31 06:52:43 (Show Source): You can put this solution on YOUR website!find the four consecutive integers whose sum is 32. ----- 1st: x-2 2nd: x-1 3rd: x 4th: x+1 --------------- Equation: sum = 32 4x-2 = 32 4x = 34 x = 8.5 ================ No such consecutive integers exist. Cheers, Stan H.
 logarithm/488910: I not sure if I should move the y to be with the 3 in the problem: 3=Ln(x/y) if I have to solve for y. 1 solutions Answer 333477 by stanbon(57274)   on 2011-08-31 06:47:01 (Show Source): You can put this solution on YOUR website!I not sure if I should move the y to be with the 3 in the problem: 3=Ln(x/y) if I have to solve for y. ------------------------------------- 3=Ln(x/y) ---- x/y = e^3 --- y = x/e^3 ================= Cheers, Stan H.
 Probability-and-statistics/488814: If the random variable z is the standard normal score and a > 0, is it true that P(z < -a) = P(z > a)? Why or why not?1 solutions Answer 333475 by stanbon(57274)   on 2011-08-31 06:44:01 (Show Source): You can put this solution on YOUR website!If the random variable z is the standard normal score and a > 0, is it true that P(z < -a) = P(z > a)? Why or why not? ------------ Ans: Yes, because of the symmetry of the normal curve. P(x > a) = P(x < -a) ======================== Cheers, Stan H.
 Proportions/488767: use two unit multipliers to convert 4000 ft to centimeters.1 solutions Answer 333452 by stanbon(57274)   on 2011-08-30 21:58:46 (Show Source): You can put this solution on YOUR website!use two unit multipliers to convert 4000 ft to centimeters. ------ 4000 ft (1 meter/3.28 ft)(100 cm/1 meter) ------ = (4000*1*100)/(1*3.28*1) cm ------ = 121,951.22 cm ========================= Cheers, Stan H.
 expressions/488763: Please help me with this algebra problem Perform the operation and, simplify if posspible please show all work. Thank you very much. - 2/3 - (- 2/7)1 solutions Answer 333444 by stanbon(57274)   on 2011-08-30 21:41:00 (Show Source): You can put this solution on YOUR website!- 2/3 - (- 2/7) ----- = -(2/3) + (2/7) ----- = (-14+6)/(21) ----- = -8/21 ================= Cheers, Stan H.
 absolute-value/488756: 2 LN 2 - ((LN 36) / 2) + (2/3 LN 27). I think it is: LN [(27 ^ (2/3))(2^2) / (36^.5) Is this how I rewrite it.1 solutions Answer 333442 by stanbon(57274)   on 2011-08-30 21:34:50 (Show Source): You can put this solution on YOUR website! 2 LN 2 - ((LN 36) / 2) + (2/3 LN 27). I think it is: LN [(27 ^ (2/3))(2^2) / (36^.5) Is this how I rewrite it. ========================================================= 2 LN(2) - ((LN(36) / 2) + (2/3) LN 27 ------------------- = ln(4) - ln(36^(1/2)) + ln(27^(2/3)) ------------------- = ln(4) - ln(6) + ln(9) ------ = ln[4*9/6] ------ = ln(6) ================= Cheers, Stan H.
 Inequalities/488755: 4n-5(n-3)>3(n+1)-41 solutions Answer 333439 by stanbon(57274)   on 2011-08-30 21:26:24 (Show Source): You can put this solution on YOUR website! 4n-5(n-3)>3(n+1)-4 ----------- 4n -5n + 15 > 3n + 3 - 4 ----------- -n + 15 > 3n -1 ------------ 4n < 16 ------- n < 4 ================= Cheers, Stan H.
 absolute-value/488719: I am trying to help my daughter and am at a loss.Your help would be very much appreciated We are doing absolute value.Can you solve this equation |x-1| = 5x + 101 solutions Answer 333436 by stanbon(57274)   on 2011-08-30 21:19:34 (Show Source): You can put this solution on YOUR website!|x-1| = 5x + 10 ------- Draw a number line. Plot x = 1 on the line ---- If x < 1, x-1 is negative. So |x-1| = 1-x Solve: |x-1| = 5x+10 1-x = 5x+10 6x = -9 x = -3/2 ======================= If x > 1, x-1 is positive. So |x-1| = x-1 Solve: x-1 = 5x+10 4x = 11 x = 11/4 ======================= Cheers, Stan H.
 Travel_Word_Problems/488673: A long distance trucker traveled 180 miles in one direction during a snow storm. The return trip in rainy weather was accompolished at double spped and took 3 hours less time. Find the speed going? The speed going was ____mph1 solutions Answer 333432 by stanbon(57274)   on 2011-08-30 20:52:57 (Show Source): You can put this solution on YOUR website!A long distance trucker traveled 180 miles in one direction during a snow storm. -------------------- The return trip in rainy weather was accomplished at double speed and took 3 hours less time. Find the speed going? --- Going DATA: distance = 120 miles ; rate = x mph ; time = d/r = 180/x hrs =================== Return DATA: distance = 120 miles ; rate = 2x mph ; time = 120/(2x) = 60/x hrs =================== Equation: time - time = 3 hrs 180/x - 60/x = 3 hrs ---- 180 - 60 = 3x 3x = 120 x = 40 mph (the "Going" rate) ================================= Cheers, Stan H. The speed going was ____mph
 Probability-and-statistics/488402: essay show all work, a community 5k run will award \$50 to the winner, 35 people enter the race, and they each pay an entry fee of \$20. assuming they are all equally likely to win, what is a fair price for the competition? round to the nearest cent. thank you ahead of time for your help. 1 solutions Answer 333421 by stanbon(57274)   on 2011-08-30 19:33:01 (Show Source): You can put this solution on YOUR website!essay show all work, a community 5k run will award \$50 to the winner, 35 people enter the race, and they each pay an entry fee of \$20. assuming they are all equally likely to win, what is a fair price for the competition? round to the nearest cent. ----------------------- Probability of winning: 1/35 --- Let cost to participate be "x". Random winnings: 50-x ; -x ---- Expected winnings = (1/35)(50-x) + (34/35)(-x) ---- A fair price means the expected winnings is zero. ----- Solve: (1/35)(50-x) + (34/35)(-x) = 0 --- Multiply thru by 35 to get: 50-x -35x = 0 36x = 50 x = \$1.39 (that is the "fair" price for entering the race) ================== Cheers, Stan H.
 Probability-and-statistics/488449: I would be very delighted if you could help with my probability question, In a business's survey of 500 customers ,of their 240,000 costomers, how many unsatisfied customers should the business expect for their to be? ___________________________________ Pleased Satisfied Unsatisfied ----------------------------------- 126 339 35 ___________________________________ What is the probability of the customer being unsatisfied? I already knopw that I have to put the numbe of unsatisfid customers over the number of customers surveyed total. I found out that that would be a fraction of 35/500 and when simplified is 7/100. (I divided by 5). Although I do not know how to set 7/100 up as a proportion.1 solutions Answer 333412 by stanbon(57274)   on 2011-08-30 19:11:02 (Show Source): You can put this solution on YOUR website!In a business's survey of 500 customers ,of their 240,000 costomers, how many unsatisfied customers should the business expect for their to be? ___________________________________ Pleased Satisfied Unsatisfied ----------------------------------- 126 339 35 ___________________________________ What is the probability of the customer being unsatisfied? Ans: 35/500 = 7/100 ---------------------- I already know that I have to put the number of unsatisfid customers over the number of customers surveyed total. I found out that that would be a fraction of 35/500 and when simplified is 7/100. (I divided by 5). --- Proportion: Although I do not know how to set 7/100 up as a proportion. x/240,000 = 7/100 ---- x = (7/100)240,000 x = 16,800 =================== Cheers, Stan H.
 Probability-and-statistics/488543: (A) Find the binomial probability P(x = 4), where n = 12 and p = 0.70. (B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation. (C) How would you find the normal approximation to the binomial probability P(x = 4) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.1 solutions Answer 333407 by stanbon(57274)   on 2011-08-30 18:46:20 (Show Source): You can put this solution on YOUR website!(A) Find the binomial probability P(x = 4), where n = 12 and p = 0.70. --- P(x = 4) = 12C4*(0.7)^4*(0.6)^8 ------------------------------------------ (B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation. P(0<= x <=4) = normalcdf(12,0.7,4) ------------------------------------------ (C) How would you find the normal approximation to the binomial probability P(x = 4) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations. u = np = 12*0.7 = 8.4 --- std = sqrt(npq) = sqrt(8.4*0.6) = 2.245 ======================================== P(x = 4) in binomial -- - P(3.5 < x < 4.5) in normal --- Find the z-value of 3.5 and of 4.5 Find the probability z is between those two z-values. =============== Cheers, Stan H. ===============
 Probability-and-statistics/488573: Sam has 5different cards in a paper bag. The cards are numbered 1to 5. What is the chance of drawing out the cards in numerical order; for example 1, 2,3,4,5?1 solutions Answer 333404 by stanbon(57274)   on 2011-08-30 18:39:25 (Show Source): You can put this solution on YOUR website!The cards are numbered 1to 5. What is the chance of drawing out the cards in numerical order; for example 1, 2,3,4,5? ---- # of ways to select that order: 1 # of ways to select in random order: 5! = 120 ---- P(selecting in that order) = 1/120 ====================================== Cheers, Stan H.
 Probability-and-statistics/488561: How many ways can 6 students from a class of 22 be selected to go on a trip?1 solutions Answer 333401 by stanbon(57274)   on 2011-08-30 18:36:11 (Show Source): You can put this solution on YOUR website!How many ways can 6 students from a class of 22 be selected to go on a trip? --- 22C6 = 74,613 ================== Cheers, Stan H.
 Probability-and-statistics/488548: Find the value of z such that approximately 27.64% of the distribution lies between it and the mean. 1 solutions Answer 333399 by stanbon(57274)   on 2011-08-30 18:22:06 (Show Source): You can put this solution on YOUR website!Find the value of z such that approximately 27.64% of the distribution lies between it and the mean. -------------- left tail = 0.5000-0.2764 = 0.2236 --- z-value = invNorm(0.2236) = -0.7601 ============= Also, by symmetry, z = +0.7601 ==================== Cheers, Stan H.
 Inequalities/488542: Solve the inequality 8a-15>731 solutions Answer 333398 by stanbon(57274)   on 2011-08-30 18:17:32 (Show Source): You can put this solution on YOUR website!Solve the inequality 8a-15>73 --------------------- 8a-15>73 --- 8a > 88 --- a > 11 ============ Cheers, Stan H.
 test/488534: Please explain with detail what is extraneous solution also how do you solve: |-4x|=321 solutions Answer 333397 by stanbon(57274)   on 2011-08-30 18:13:50 (Show Source): You can put this solution on YOUR website!Please explain with detail what is extraneous solution also how do you solve: |-4x|=32 ---- Note: |-4x| = |4x| ---- Equation: |4x| = 32 4x = 32 or 4x = -32 x = 8 or x = -8 ----------------------- Cheers, Stan H. =========
 Probability-and-statistics/488453: A set of 50 data values has a mean of 41 and a variance of 36. I. Find the standard score (z) for a data value = 24. II. Find the probability of a data value > 24. 1 solutions Answer 333396 by stanbon(57274)   on 2011-08-30 18:10:08 (Show Source): You can put this solution on YOUR website!A set of 50 data values has a mean of 41 and a variance of 36. Note: the standard deviation = sqrt(36) = 6 I. Find the standard score (z) for a data value = 24. z(24) = (24-41)/6 = -2.8333 ================================== II. Find the probability of a data value > 24. P(x > 24) = P(z > -2.8333) = 0.9977 ================================== Cheers, Stan H.
 Probability-and-statistics/488457: Need Help!!!!The diameters of oranges in a certain orchard are normally distributed with a mean of 4.85 inches and a standard deviation of 0.40 inches. Show all work. (A) What percentage of the oranges in this orchard have diameters less than 6.3 inches? (B) What percentage of the oranges in this orchard are larger than 4.95 inches? 1 solutions Answer 333395 by stanbon(57274)   on 2011-08-30 18:04:37 (Show Source): You can put this solution on YOUR website!Need Help!!!!The diameters of oranges in a certain orchard are normally distributed with a mean of 4.85 inches and a standard deviation of 0.40 inches. Show all work. (A) What percentage of the oranges in this orchard have diameters less than 6.3 inches? z(6.3) = (6.3-4.85)/0.4 = 3.625 P(x < 6.3) = P(z < 3.625) = 0.9999 ========================================== (B) What percentage of the oranges in this orchard are larger than 4.95 inches? z(4.95) = (4.95-4.85)/0.4 = 0.25 P(x > 4.95) = P(z > 0.25) = 0.4013 ========================================== Cheers, Stan H.
 Probability-and-statistics/488501: There are 52 color cards. 13 red, 13 blue, 13 yellow, and 13 green. Each color has cards numbered from 0 to 12. What is the probability of a card being drawn at random that is red?1 solutions Answer 333394 by stanbon(57274)   on 2011-08-30 17:43:00 (Show Source): You can put this solution on YOUR website!There are 52 color cards. 13 red, 13 blue, 13 yellow, and 13 green. Each color has cards numbered from 0 to 12. What is the probability of a card being drawn at random that is red? --- P(red) = 13/52 = 1/4 ========================== Cheers, Stan H. ===============
 Travel_Word_Problems/488492: suppose you have entered a 155 mile biathlon that consists of a bicycle race and a running race. during your run your velocity is 10 miles per hour and during your bicycle race your velocity is 29 miles per hour. you finish the race in 6 hours. what is the distance of your run? what is the distance of your bicycle race? 155-d/29 155(10)/291 solutions Answer 333392 by stanbon(57274)   on 2011-08-30 17:32:11 (Show Source): You can put this solution on YOUR website! suppose you have entered a 155 mile biathlon that consists of a bicycle race and a running race. during your run your velocity is 10 miles per hour and during your bicycle race your velocity is 29 miles per hour. you finish the race in 6 hours. what is the distance of your run? what is the distance of your bicycle race? ---- run distance: 10x where x is the number of hours you run ---- bike distance: 29(6-x) ---- Equation: distance + distance = 155 miles 10x + 29(6-x) = 155 10x + 29*6 - 29x = 155 -19x = 155 - 29*6 -19x = -19 x = 1 (# of hrs you run) 6-x = 5 (# of hrs you bike) =============================== Cheers, Stan H. ==========
 Divisibility_and_Prime_Numbers/488489: i am number that is divisible by ,2,3,4 and 5 and less than 70 who am i 1 solutions Answer 333391 by stanbon(57274)   on 2011-08-30 17:25:28 (Show Source): You can put this solution on YOUR website! i am number that is divisible by ,2,3,4 and 5 and less than 70 who am i ---- Divisibility by 4 implies divisibility by 2 --- # = 3*4*5 = 60 ================ Cheers, Stan H.
 Exponents/488485: What is the correct steps to simplify this problem? (x^3/5)^7 1 solutions Answer 333390 by stanbon(57274)   on 2011-08-30 17:23:05 (Show Source): You can put this solution on YOUR website!What is the correct steps to simplify this problem? (x^3/5)^7 ----- Multiply the exponents to get: x ^(21/5) =========== Cheers, Stan H.