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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 , 57180..57209 , 57210..57239, >>Next

 Equations/393742: Find the value(s) of k for which the equation (x+2)(x+k)=-1 has equal roots.1 solutions Answer 279405 by stanbon(57286)   on 2011-01-12 12:33:32 (Show Source): You can put this solution on YOUR website!Find the value(s) of k for which the equation (x+2)(x+k)=-1 has equal roots. ------- x^2+(k+2)x+2k = -1 --- Has equal roots when the discriminant equals zero. --- (k+2)^2 -4*(2k) = 0 --- k^2+4k+4-8k = 0 --- k^2-4k+4 = 0 (k-2)^2 = 0 k = 2 ================ Cheers, Stan H.
 test/393745: 3b-5-10b-4 5g-3-5-5g Simplify each expression bt combining any like terms. 1 solutions Answer 279403 by stanbon(57286)   on 2011-01-12 12:29:31 (Show Source): You can put this solution on YOUR website!3b-5-10b-4 = -7b-9 =============== 5g-3-5-5g = -8 ================= Cheers, Stan H.
 Probability-and-statistics/393678: When betting on even in roulette, the winning numbers are even numbers from 2 to 36. There are 38 equally likely events in roulette. What is the probability of winning when betting on even?1 solutions Answer 279368 by stanbon(57286)   on 2011-01-12 10:08:38 (Show Source): You can put this solution on YOUR website!When betting on even in roulette, the winning numbers are even numbers from 2 to 36. There are 38 equally likely events in roulette. What is the probability of winning when betting on even? --- There are 18 even numbers P(even) = 18/38 = 9/19 =========== Cheers, Stan H.
 Trigonometry-basics/393683: how would I write four subtracted from a number multiplied by eight equals fifty six1 solutions Answer 279366 by stanbon(57286)   on 2011-01-12 10:05:50 (Show Source): You can put this solution on YOUR website!how would I write four subtracted from a number multiplied by eight equals fifty six --- Let the number be "x": Equation: 8x-4 = 56 8x = 60 x = 15/2 x = 7.5 =========== Cheers, Stan H.
 Mixture_Word_Problems/393674: hi again.. 1. A hospital needs to dilute a 50% boric acid solution to a 10% solution. If it needs 25 liters of the 10% solution, how much of the 50% solution and how much water should it use? 2. anabel has 25 ounces of a boric acid solution which she wishes to dilute to a 10% solution. how much of the 10% solution must be used? 1 solutions Answer 279364 by stanbon(57286)   on 2011-01-12 10:04:13 (Show Source): You can put this solution on YOUR website!1. A hospital needs to dilute a 50% boric acid solution to a 10% solution. If it needs 25 liters of the 10% solution, how much of the 50% solution and how much water should it use? ----------------------- Equation: boric + boric = boric 0.50x + 0*(25-x) = 0.10*25 --- Multiply thru by 100 to get: 50x = 10*25 x = 5 liters (amt. of 50% solution needed for the final mixture) 25-x = 20 liters (amt of water needed for the final mixture) ===================== 2. anabel has 25 ounces of a boric acid solution which she wishes to dilute to a 10% solution. how much of the 10% solution must be used? ------ If you start with 100% boric acid and then add a 10% solution you cannot end up with a 10% solution. -------------------------- Cheers, Stan H.
 Exponential-and-logarithmic-functions/393681: 1) 3√30x^15/120x^17y^-1 It is a cube root. 2)3√4√10=100^2x There's 10 inside of cube root and 4th root. 3)9√(2xy^4)^-12/(8x^12y)^2 It is a 9th root. Thank you so much!!!!!! I have a test on Friday and my teacher really can't teach :(1 solutions Answer 279363 by stanbon(57286)   on 2011-01-12 09:55:06 (Show Source): You can put this solution on YOUR website!1)3√30x^15/120x^17y^-1 It is a cube root. --- [cbrt(30x^15)]/[120x^17y^-1)] ---- [x^5*y*cbrt(30)]/[120x^17] ---- [y*cbrt(30)]/[24x^12] ========================== 2)3√4√10=100^2x There's 10 inside of cube root and 4th root. --- 10^(1/12) = [10^2]^(2x) --- 10^(1/12) = 10^(4x) --- 4x = 1/12 x = 1/48 ================== 3)9√(2xy^4)^-12/(8x^12y)^2 It is a 9th root. --- (2xy^4)^(-12/9) / (64x^24y^2) --- (2xy^4)^(-4/3) / (2^6*x^24y^2) [2^(-4/3)*x^(-4/3)*y^(-16/3)]/[2^6*x^24*y^2] --- = 1/[2^(22/3)*x^23*y^(22/3) === There are a number of forms the next step could take. I'll leave it to you. Sometimes the answer book will show one form and you have an equivalent other form. Try to determine whether the two forms are equivalent. If they are you have found the solution. ------ Cheers, Stan H.
 Rate-of-work-word-problems/393653: Three people can pick all the apples from five trees in five hours. How long will it take five people?1 solutions Answer 279354 by stanbon(57286)   on 2011-01-12 08:43:21 (Show Source): You can put this solution on YOUR website! Three people can pick all the apples from five trees in five hours. How long will it take five people? ----------------- time to pick all the apples is directly related to # of trees and inversely related to # of people. ---- time = kT/p --- Solve for "k" using "Three people can pick all the apples from five trees in five hours." 5 = k5/3 k = 3 --- Equation for this problem: time = 3T/p ---- Problem: How long will it take five people? t = 3*5/5 --- Ans: 3 hrs =============== Cheers, Stan H.
 Probability-and-statistics/393668: The probability that an employee at the company is over 30 years old is 0.7 if 15 employees are asked their age find the probability that A) 5 are over 30 years old B)at least 10 are over 30 years old C) fewer than 8 are over 30 D)mean E) variance F) standard deviation1 solutions Answer 279351 by stanbon(57286)   on 2011-01-12 08:33:30 (Show Source): You can put this solution on YOUR website!The probability that an employee at the company is over 30 years old is 0.7 If 15 employees are asked their age find the probability that A) 5 are over 30 years old P(x = 5) = binompdf(15,0.7,5) = 0.0030 --------------------- B)at least 10 are over 30 years old P(10<= x <=15) = 1-binomcdf(15,0.7,9) = 0.7216 --------------------- C) fewer than 8 are over 30 P(0<= x <=7) = binomcdf(15,0.7,7) = 0.0500 --- D)mean = np = 15*0.7 --- E) variance = npq = 15*0.7*0.3 --- F) standard deviation = sqrt(variance) ========================================= cheers, Stan H.
 Probability-and-statistics/393667: For a fair game what should be the charge to play if there is a .003 probability to win \$1,000, .007 probability to win \$100, and .99 probability of not winning anything1 solutions Answer 279349 by stanbon(57286)   on 2011-01-12 08:24:47 (Show Source): You can put this solution on YOUR website! For a fair game what should be the charge to play if there is a .003 probability to win \$1,000, .007 probability to win \$100, and .99 probability of not winning anything --- Let the charge be "x". ---- Winning values are: 1000-x ; 100-x ; -x --- Note: A fair game has an expected value of zero. ---- Equation: 0.003(1000-x)+0.007(100-x)+0.99(-x) = 0 ---- 3(1000-x) + 7(100-x) - 990x = 0 --- 3000-3x + 700-7x - 990x = 0 -1000x = -3700 x = \$3.70 (amount you should pay to play the game) ==================== Cheers, Stan H.
 Probability-and-statistics/393664: At a raffle, 100 tickets were sold at \$1.00 each for three prizes of \$25, \$10, and \$5. Find the expected value1 solutions Answer 279347 by stanbon(57286)   on 2011-01-12 08:18:27 (Show Source): You can put this solution on YOUR website!At a raffle, 100 tickets were sold at \$1.00 each for three prizes of \$25, \$10, and \$5. Find the expected value ---- Let x be expected winnings of the player. Values of x are 24,9,4,-1 dollars ------- Probabilities are (1/100),1/100,1/100,97/100 --- Expected winnings = [24 + 9 + 4 - 97]/100 = -60 cents ===================== Cheers, Stan H.
 test/393661: The total outing cost for a group of people amounted to Php. 8000. When an additional 4 persons decided to join the outing, the cost per person decreased by Php. 100. How many people actually joined the outing? (Show Your Solution)1 solutions Answer 279345 by stanbon(57286)   on 2011-01-12 08:13:16 (Show Source): You can put this solution on YOUR website!The total outing cost for a group of people amounted to Php. 8000. ------------ Original DATA: Let number in the group be "x". Average cost per person is 8000/x Php. ----------------------------- When an additional 4 persons decided to join the outing, the cost per person decreased by Php. 100. New DATA: Number in the group is "x+4". Average cost perperson is 8000/(x+4) Php. -------------- How many people actually joined the outing? Equation: original average - new average = 100 Php 8000/x - 8000/(x+4) = 100 --- Divide thru by 100 to get: 80/x - 80/(x+4) = 1 ----------------------- Multiply thru by x(x+4) to get: 80(x+4) - 80x = x(x+4) 80*4 = x^2+4x --- x^2+4x-320 = 0 (x-16)(x+20) = 0 --- Positive solution: x = 16 (original # of people in the group) =============== Cheers, Stan H.
 Mixture_Word_Problems/393546: a spice mixture is 25% thyme. How many grams of thyme must be added to a 12 g. of mixture to increase the thyme content to 40%?1 solutions Answer 279279 by stanbon(57286)   on 2011-01-11 21:54:41 (Show Source): You can put this solution on YOUR website!duplicate
 Equations/393543: 10= c/3 - 4 + c/61 solutions Answer 279278 by stanbon(57286)   on 2011-01-11 21:53:58 (Show Source): You can put this solution on YOUR website!10= c/3 - 4 + c/6 --- Multiply thru by 6 to get: 60 = 2c - 40 + c ================ 100 = 3c c = 33 1/3 ================= cheers, Stan H.
 Miscellaneous_Word_Problems/393545: write a situation that can be represented by 6n+41 solutions Answer 279276 by stanbon(57286)   on 2011-01-11 21:52:17 (Show Source): You can put this solution on YOUR website!write a situation that can be represented by 6n+4 --- The national debt is 4 billion more than six times its 1990 level. ======================= cheers, Stan H.
 Miscellaneous_Word_Problems/393544: How many pints of a 9% cleaning solution must be mixed with 4 pints of a 15% cleaning solution to give a 12% solution?1 solutions Answer 279275 by stanbon(57286)   on 2011-01-11 21:49:13 (Show Source): You can put this solution on YOUR website!How many pints of a 9% cleaning solution must be mixed with 4 pints of a 15% cleaning solution to give a 12% solution? ----------- Equations: active + active = active 0.09x + 0.15*4 = 0.12(x+4) --- Multiply thru by 100 to get: 9x + 15*4 = 12x + 12*4 ---- -3x = -3*4 x = 4 pints (amt of 9% solution needed in the mix) --- Cheers, Stan H.
 Mixture_Word_Problems/393541: a spice mixture is 25% thyme.How many grams of thyme must be added to a 12 g. of mixture to increase the thyme content to 40%?1 solutions Answer 279273 by stanbon(57286)   on 2011-01-11 21:45:35 (Show Source): You can put this solution on YOUR website!a spice mixture is 25% thyme.How many grams of thyme must be added to a 12 g. of mixture to increase the thyme content to 40%? --------------- Equation: thyme + thyme = thyme 0.25x + 1.0(12-x) = 0.40*12 --- Multiply thru by 100 to get: 25x + 100*12-100x = 40*12 -75x = -60*12 x = 9.6 g (amt of 25% mixture needed in the final mix) 12-x = 2.4 g (amt of pure thyme needed in the final mix) =============== Cheers, Stan H.
 Permutations/393533: 3 cards are chosen at random from a standard 52-card deck. What is the probability that they form a pair? (A 3-card hand is a pair if two of the cards match in rand but the third card is different.)1 solutions Answer 279271 by stanbon(57286)   on 2011-01-11 21:39:10 (Show Source): You can put this solution on YOUR website!3 cards are chosen at random from a standard 52-card deck. What is the probability that they form a pair? (A 3-card hand is a pair if two of the cards match in rand but the third card is different.) --- Pick a type of card: 13 ways Pick a pair of that type: 4C2 = 6 ways ---- Pick a 3rd card that is not that type: 48 ways ---- P(event as described) = [13*6*48]/52C3 = 3744/22100 = 0.1694 ================= Cheers, Stan H.
 Permutations/393530: Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that (a) they all come up heads? (b) the penny and nickel both come up heads? (c) the penny and dime both come up the same? (d) at least 15 cents wort of coins come up heads?1 solutions Answer 279270 by stanbon(57286)   on 2011-01-11 21:33:57 (Show Source): You can put this solution on YOUR website! Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that (a) they all come up heads?:::: (1/2)^4 = 1/16 -------------------------------------- (b) the penny and nickel both come up heads? (1/2)(1/2)*1*1 = 1/4 --------------------------------------- (c) the penny and dime both come up the same? 2*(1/4)(1/4)*1*1 = 1/8 --------------------------------------- (d) at least 15 cents worth of coins come up heads? I'll leave that to you. Take a look at the 16 points in the sample space and see how many combinations of coins has value 15 cents or greater. ----------------------- Cheers, Stan H.
 Money_Word_Problems/393524: Computer A can do a job in 4 hours. Computer B can do the same job in 2 hours. How long will it take them to complete the job working together?1 solutions Answer 279267 by stanbon(57286)   on 2011-01-11 21:28:48 (Show Source): You can put this solution on YOUR website!Computer A can do a job in 4 hours. Computer B can do the same job in 2 hours. How long will it take them to complete the job working together? ------------- A rate = 1/4 job/hr B rate = 1/2 job/hr --- Together rate: 1/x job/hr ----------------------------- Equation: rate + rate = together rate 1/4 + 1/2 = 1/x --- Multiply thru by 4x to get: x + 2x = 4 3x = 4 x = 4/3 = 1hr and 20 min (time to do the job together) ==================== Cheers, Stan H. ===============
 Average/393529: State is 0.1 is written in scientific notation. If not, write it in scientific notation. 1 solutions Answer 279265 by stanbon(57286)   on 2011-01-11 21:25:44 (Show Source): You can put this solution on YOUR website!State if 0.1 is written in scientific notation. No If not, write it in scientific notation. 1.0x10^-1 ============ Cheers, Stan H.
 Matrices-and-determiminant/393527: 2a-3b=-8 4a+3b=-34 I am supposed to be using either substitution, elimination, or inverse matrices to solve. Thanks in advance for your time and help!1 solutions Answer 279264 by stanbon(57286)   on 2011-01-11 21:23:41 (Show Source): You can put this solution on YOUR website!2a-3b=-8 4a+3b=-34 ----------- Add to eliminate the b-terms: --- 6a = -42 --- a = -7 --- Solve for "b": 2a-3b=-8 2(-7)-3b = -8 -14-3b = -8 Add 14 to both sides to get: -3b = 6 b = -2 ============== cheers, Stan H.
 Percentage-and-ratio-word-problems/393477: Hello i have a geometry promblem: The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 cm.1 solutions Answer 279244 by stanbon(57286)   on 2011-01-11 20:20:11 (Show Source): You can put this solution on YOUR website!Hello i have a geometry promblem: The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 cm. -------------- 3:5:7 is the same as 3x:5x:7x --- Equation: 3x+5x+7x = 450 15x = 450 x = 30 --- 3x = 90 5x = 150 7x = 210 ============= Cheers, Stan H.
 decimal-numbers/393478: Please help me solve this problem: What decimal is equal to 2/5? Please show work. My step son is just starting... Thanks!!1 solutions Answer 279242 by stanbon(57286)   on 2011-01-11 20:18:15 (Show Source): You can put this solution on YOUR website!What decimal is equal to 2/5? --- You have to show your step son how to divide a larger number into a smaller number. --- 5)2 --- = 5)2.000 --- = 0.4 ================== Cheers, Stan H.
 Age_Word_Problems/393476: What is Henry’s age when told that he is 5 times as old as his son, but will in 4 years time be only 3 times as old?1 solutions Answer 279241 by stanbon(57286)   on 2011-01-11 20:15:45 (Show Source): You can put this solution on YOUR website!What is Henry’s age when told that he is 5 times as old as his son, but will in 4 years time be only 3 times as old? --------------------- Equations: h = 5s h+4 = 3(s+4) --- Substitute for "h" and solve for "s": 5s+4 = 3s+12 2s = 8 s = 4 (Son's age now) --- Solve for "h": h = 5s h = 5*4 = 20 (Henry's age now) ============================= Cheers, Stan H. ===========
 Travel_Word_Problems/393475: Car One leaves on time and travels at 50 mph. Car Two leaves one hour later and travels at 75 mph. For how long does each car travel before the second car catches up to the first?1 solutions Answer 279239 by stanbon(57286)   on 2011-01-11 20:12:10 (Show Source): You can put this solution on YOUR website!Car One leaves on time and travels at 50 mph. Car Two leaves one hour later and travels at 75 mph. For how long does each car travel before the second car catches up to the first? -------------- First car DATA: rate = 50 mph ; time = x hrs ; distance = rt = 50x miles -------------------------------- Second car DATA: rate = 75 mph ; time = x-1 hrs ; distance = rt = 75(x-1) miles -------------- Equation: distance = distance 50x = 75(x-1) 50x = 75x-75 -25x = -75 x = 3 hrs (1st car time) --- x-1 = 2 hrs (2nd car time) ============================== cheers, Stan H.
 Polynomials-and-rational-expressions/393473: factor 3x^2+14x+151 solutions Answer 279237 by stanbon(57286)   on 2011-01-11 20:08:21 (Show Source): You can put this solution on YOUR website!factor 3x^2+14x+15 --- 3x^2+5x+9x+15 --- x(3x+5)+3(3x+5) --- (3x+5)(x+3) =============== Cheers, Stan H.
 Distributive-associative-commutative-properties/393472: How do you foil 2x^2+x-31 solutions Answer 279236 by stanbon(57286)   on 2011-01-11 20:05:39 (Show Source): You can put this solution on YOUR website!How do you foil 2x^2+x-3 ---------- 2x^2+3x-2x-3 --- x(2x+3)-(2x+3) --- (2x+3)(x-1) =============== This is called inverse FOIL. Cheers, Stan H.
 Expressions-with-variables/393433: two cars leave town at the same time going in opposite directions. one car travels 44mi/h and the other travels 55mi/h. in how many hours will they be 297 miles apart?1 solutions Answer 279220 by stanbon(57286)   on 2011-01-11 19:32:22 (Show Source): You can put this solution on YOUR website!two cars leave town at the same time going in opposite directions. one car travels 44mi/h and the other travels 55mi/h. in how many hours will they be 297 miles apart? --- They are separating at the rate of 44+55 = 99 mph --- time = distance/rate tim = 297/99 = 3 hrs ================================ Cheers, Stan H.
 test/393436: Negative times positive equals?1 solutions Answer 279217 by stanbon(57286)   on 2011-01-11 19:28:23 (Show Source): You can put this solution on YOUR website!Negative
 Exponents-negative-and-fractional/393432: I need help solving the below problem 4{3[5(y − 3) + 9] + 2(y + 8)}1 solutions Answer 279216 by stanbon(57286)   on 2011-01-11 19:27:47 (Show Source): You can put this solution on YOUR website!4{3[5(y − 3) + 9] + 2(y + 8)} --- Working from the inside to the outside: 4{3[5(y − 3) + 9] + 2(y + 8)} --- = 4{3{5y-15)+9] + 2y+16} --- = 4{15y-45+9]+ 2y+16} --- = 4{17y-20} --- = 68y-80 ============== Cheers, Stan H.
 Linear-systems/393431: how do i write an equation of a line when i am given the point and the slope?1 solutions Answer 279213 by stanbon(57286)   on 2011-01-11 19:22:24 (Show Source): You can put this solution on YOUR website!how do i write an equation of a line when i am given the point and the slope? --- One way to do it. -- If the point is (a,b) and the slope is m the equation is: y-b = m(x-a) ==================== Cheers, Stan H.