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Recent problems solved by 'stanbon'

stanbon answered: 57894 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 , 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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Polynomials-and-rational-expressions/415753: Solve the logarithmic equation. Express irriational solutions in exact form and as a decimal rounded o 3 decimal places. log[base a]x+log[base a](x-2)=log [base a](x+4) 1 solutions Answer 291403 by stanbon(57967)   on 2011-03-01 10:51:08 (Show Source): You can put this solution on YOUR website! log[base a]x+log[base a](x-2)=log [base a](x+4) ---- loga[x(x-2)] = loga(x+4) ------ x^2-2x = x+4 x^2-3x-4 = 0 --- Factor: (x-4)(x+1) = 0 Positive solution: x = 4 ==================== Cheers, Stan H. ============

Inverses/415754: use multiplication principle to solve equation;n x 4/15= 12/15 1 solutions Answer 291401 by stanbon(57967)   on 2011-03-01 10:48:34 (Show Source): You can put this solution on YOUR website! use multiplication principle to solve equation; n x 4/15= 12/15 --- Multiply both sides by 15/4 to get: n = (12/15)(15/4) --- n = 3 ====================== Cheers, Stan H.

Numbers_Word_Problems/415761: How can we solve this word problems; The width of a rectangle is w cm and the length is 9 cm. The area of the rectangle is: Thanks.. 1 solutions Answer 291400 by stanbon(57967)   on 2011-03-01 10:46:34 (Show Source): You can put this solution on YOUR website! duplicate

Polynomials-and-rational-expressions/415755: 2log[base 3](x+4)-log[base 3]9=2 1 solutions Answer 291399 by stanbon(57967)   on 2011-03-01 10:45:47 (Show Source): You can put this solution on YOUR website! 2log[base 3](x+4)-log[base 3]9=2 ----- 2log3(x+4) - log3(9) = 2 --- log3[(x+4)^2/9] = 2 ---- (x+4)^2/9 = 3^2 (x+4)^2 = 81 --- x^2+8x+16-81 = 0 --- x^2 + 8x - 55 = 0 --- x = [-8 +- sqrt(64-4*-55)]/2 ---- x = [-8 +- sqrt(284)]/2 --- x = [-8 +- 2sqrt(71)]/2 --- x = -4+sqrt(71) or x = -4-sqrt(71) ================== Cheers, Stan H. ============

Numbers_Word_Problems/415760: Hi.. How can we solve; The width of a rectangle is w cm and the length is 9 cm. The area of the rectangle is: Thanks.. 1 solutions Answer 291397 by stanbon(57967)   on 2011-03-01 10:40:37 (Show Source): You can put this solution on YOUR website! How can we solve; The width of a rectangle is w cm and the length is 9 cm. The area of the rectangle is: --------- Area = width*length Area = w cm * 9 cm = 9w cm^2 ============================== Cheers, Stan H. =============

Numbers_Word_Problems/415758: Research showed that 0.283 of the employees were totally loyal. If the corporation had 6000 employees, how many of them were not loyal? 1 solutions Answer 291396 by stanbon(57967)   on 2011-03-01 10:39:05 (Show Source): You can put this solution on YOUR website! Research showed that 0.283 of the employees were totally loyal. If the corporation had 6000 employees, how many of them were not loyal? === loyal = 0.283*6000 = 1698 -------- Cheers, Stan H. ===========

Miscellaneous_Word_Problems/415756: If P is the measure of an angle, 180-P is the measure of the supplement of the angle. If the measure of an angle equals three times the measure of its supplement, what is the measure of the angle? 1 solutions Answer 291395 by stanbon(57967)   on 2011-03-01 10:36:20 (Show Source): You can put this solution on YOUR website! If P is the measure of an angle, 180-P is the measure of the supplement of the angle. If the measure of an angle equals three times the measure of its supplement, what is the measure of the angle? ----------- Equation: P = 3(180-P) P = 540-3P 4P = 540 P = 135 ----------------- Cheers, Stan H. ============

Permutations/415616: how many permutations can be made from selecting 4 college courses out of 10 and i had some trouble understanding, four students can choose to write on one of 5 essay topics for their english class . how many different essays can the student write without repetition of the topics? how many different essays can the student write with repetition of the topics? 1 solutions Answer 291325 by stanbon(57967)   on 2011-02-28 22:36:03 (Show Source): You can put this solution on YOUR website! how many permutations can be made from selecting 4 college courses out of 10 10P4 = 10*9*8*7 = 5040 ------------------------------- four students can choose to write on one of 5 essay topics for their english class. how many different essays can the students write without repetition of the topics? -- Ans: 5*4*3*2 = 120 The assumption here is that order makes a difference. ------- how many different essays can the students write with repetition of the topics? 5^4 = 625 =============== Cheers, Stan H. ===========

Radicals/415615: Please help me solve this equation: 1 solutions Answer 291323 by stanbon(57967)   on 2011-02-28 22:26:36 (Show Source): You can put this solution on YOUR website! ( 2x+3 )^( 3/4 )- 3 = 5 --- (2x+3)^(3/4) = 8 --- (2x+3) = 8^(4/3) --- 2x+3 = 2^4 --- 2x+3 = 16 2x = 13 x = 6.5 ============= Cheers, Stan H. =============

Inequalities/415609: i have 3 problems to figure out. the first one is: 14-10+x<-x-8. i started to do 4+x<-x-8 then i was lost. 2. 1(1+7)-6(-7-x)<40-4 i got -1-7x+42-6x<40-4 then i did more and got -1+42-13<44, then 41-13x<44 and subtracted 41 from 41 and 44. im not sure if im right but that's how far i got. 3. -5(1-5x)+5(-8x-2)>-4x-8x. i haven't got to that one yet because i have been to frustrated with the other 2 problems. 1 solutions Answer 291322 by stanbon(57967)   on 2011-02-28 22:24:11 (Show Source): You can put this solution on YOUR website! the first one is: 14-10+x<-x-8. 4+x < -x-8 2x < -12 x < -6 ----------------- 2. 1(1+7)-6(-7-x)<40-4 1(8)+42+6x < 36 50 + 6x < 36 6x < -14 x < -7/3 -------------------- 3. -5(1-5x)+5(-8x-2)>-4x-8x --- -5+25x-40x-19 > -12x -15x-24 > -12x -24 > 3x x < -8 ==================== Cheers, Stan H. ====================

Equations/415607: Five times the difference of twice a number and seven is negative five. Find the number. 1 solutions Answer 291321 by stanbon(57967)   on 2011-02-28 22:16:16 (Show Source): You can put this solution on YOUR website! Five times the difference of twice a number and seven is negative five. Find the number. ------------------------ Equation: 5(2x-7) = -5 2x-7 = -1 2x = 6 x = 3 ============ Cheers, Stan H. ============

Travel_Word_Problems/415611: This problem seems to be straigt forward, i just cannot work it. I would appreciate the help. JCULP Bob walks 5 mph,then jogs 9 mph for one hour. The total distance is 6 miles. How far did he walk. 1 solutions Answer 291319 by stanbon(57967)   on 2011-02-28 22:13:53 (Show Source): You can put this solution on YOUR website! Bob walks 5 mph,then jogs 9 mph for one hour. The total distance is 6 miles. How far did he walk. -------------------- Walk DATA: rate = 5 mph ; time = x hrs ; distance = 5x miles -------- Jog DATA: rate = 9 mph ; time = 1-x hrs ; distance = 9(1-x) miles ----- Equation: distance + distance = 6 miles 5x + 9(1-x) = 6 5x + 9-9x = 6 -4x = -3 x = 3/4 hr. --- Walk distance: 5x = 5(3/4) = 15/4 = 3 3/4 miles =================================================== Cheers, Stan H. =============

Permutations/415610: in how many ways can 4 boys and 3 girls be seated in a row of 7 seats if end seats are to be occupied by boys 1 solutions Answer 291318 by stanbon(57967)   on 2011-02-28 22:08:21 (Show Source): You can put this solution on YOUR website! in how many ways can 4 boys and 3 girls be seated in a row of 7 seats if end seats are to be occupied by boys --- 4 ways to fill one of the end seats 3 ways to fill the other end seat. 4! = 24 ways to fill the remaining seats. ---- Total = 12*24 = 288 ways ============================ Cheers, Stan H. =============

Probability-and-statistics/415606: John claims he has ESP. An experiment is set up to determine the likelyhood of his claim. Jenny is placed in one classroom and John placed in another classroom across the hall. Jenny is asked to pick one of the integers 1, 2, 3, 4, 5 at random. In the other room, John identifies the number he believes was picked. The experiment was repeated 10 times. What is the probability of John randomly chooses the same number as Jenny out of the integers 1, 2, 3, 4, 5? Give your answer to 1 decimal place STUCK please Help! 1 solutions Answer 291316 by stanbon(57967)   on 2011-02-28 22:01:36 (Show Source): You can put this solution on YOUR website! What is the probability of John randomly chooses the same number as Jenny out of the integers 1, 2, 3, 4, 5? Give your answer to 1 decimal place ------ Jenny can pick any one of the 5 integers. --- Probability John will pick the same integer is 1/5 ==================== Cheers, Stan H. ============

Sequences-and-series/415604: what would be the next three numbers of this pattern -2,0,3,7,12 1 solutions Answer 291315 by stanbon(57967)   on 2011-02-28 21:58:28 (Show Source): You can put this solution on YOUR website! what would be the next three numbers of this pattern -2,0,3,7,12 ----- -2+2 = 0 0+3 = 3 3+4 = 7 7+5 = 12 ---- 12+6 = 18 18+7 = 25 25+8 = 33 33+9 = 42 ---------- Cheers, Stan H. ============

Triangles/415593: this is my problem: if the dimensions of a 3-4-5 right triangle is increased 50 percent by what percentage is the area incresed? how do i figure it out? 1 solutions Answer 291313 by stanbon(57967)   on 2011-02-28 21:42:31 (Show Source): You can put this solution on YOUR website! this is my problem: if the dimensions of a 3-4-5 right triangle is increased 50 percent by what percentage is the area incresed? --------------------- Area of the 3-4-5 is (1/2)*3*4 = 6 sq. units ---- New area: (3+1.5)(4+2) = 4.5*6 = 27 sq units --- %age ? Quantity increase 27-6 = 21 --- % increase: 21/6 = 7/2 = 3.5 = 350% ======================================= Cheers, Stan H. ============

Age_Word_Problems/415589: Mike is 6 years younger than Cassie. Twelve years ago, CCassie was twice as old as Mike was. How old is each now? Also, Shalane is 14 and her grandmother is 54. How many years ago was her grandmother 6 times as old as Shalane? If you could just help a bit, that would be great. Thankyou 1 solutions Answer 291312 by stanbon(57967)   on 2011-02-28 21:37:29 (Show Source): You can put this solution on YOUR website! Mike is 6 years younger than Cassie. Twelve years ago, Cassie was twice as old as Mike was. How old is each now? ---- m = c-6 (c-12) = 2(m-12) --- Substitute for "m" and solve for "c": c-12 = 2(c-6-12) c-12 = 2(c-18) c-12 = 2c-36 c = 24 (Cassie's age now) m = c-6 = 18 (Mikes age now) ================================= Also, Shalane is 14 and her grandmother is 54. How many years ago was her grandmother 6 times as old as Shalane? Shalane = 14 Grandma = 54 ---- Equation: (54-x) = 6(14-x) 54-x = 84 - 6x 5x = 30 x = 6 (# of years ago) ========================== Cheers, Stan H. =============

Rate-of-work-word-problems/415587: A filler pipe can fill a tank in 10 hours, while an outlet pipe can empty the tank in 15 hours. How long will it take to fill the empty tank with both pipes operating? I have tried 1/10 - 1/15 = 1/t then with a common factor 3/30-2/30=1/t now I am at a loss for what to do. 1 solutions Answer 291311 by stanbon(57967)   on 2011-02-28 21:31:42 (Show Source): You can put this solution on YOUR website! A filler pipe can fill a tank in 10 hours, while an outlet pipe can empty the tank in 15 hours. How long will it take to fill the empty tank with both pipes operating? ----- Equation: rate - rate = together rate ----- I have tried 1/10 - 1/15 = 1/t Multiply thru by 150t to get: 15t - 10t = 150 5t = 150 t = 30 hrs. ============= Cheers, Stan H. =============

Equations/415582: I am trying to find the equation for the following: where x=1,2,3,4 and y=6,8,12,20 ie when x=1 y=6 when x=2 y=8 I can't figure out the pattern Thanks for looking at this. D. 1 solutions Answer 291310 by stanbon(57967)   on 2011-02-28 21:28:11 (Show Source): You can put this solution on YOUR website! find the equation for the following: where x=1,2,3,4 and y=6,8,12,20 ie when x=1 y=6 when x=2 y=8 ------------------- Quadratic Equation: y = 1.5x^2 - 2.9x + 7.5 --------------------- OR Cubic Equation: y = (1/3)x^3 - x^2 + (8/3)x +4 ================================= Cheers, Stan H. ========================

Probability-and-statistics/415372: How many ways can 12 jurors be chosen from 20 male and 30 female potential jurors: a) no restriction is made. b) there must be an equal number of men and women 1 solutions Answer 291302 by stanbon(57967)   on 2011-02-28 20:32:52 (Show Source): You can put this solution on YOUR website! How many ways can 12 jurors be chosen from 20 male and 30 female potential jurors: a) no restriction is made::: 50C12 = 1.213997x10^11 -------------------------------------------------------- b) there must be an equal number of men and women (20C6)*(30C6) = 38760*593775 = 2.301472x10^10 ------- Cheers, Stan H. =========

Probability-and-statistics/415534: Charles has eight different winter scarves, and he wears three at a time. How many different ways can Charles wear three scarves? 1 solutions Answer 291301 by stanbon(57967)   on 2011-02-28 20:26:23 (Show Source): You can put this solution on YOUR website! Charles has eight different winter scarves, and he wears three at a time. How many different ways can Charles wear three scarves? --- 8C3 = (8*7*6)/(1*2*3) = 56 ============================= Cheers, Stan H. =========

Probability-and-statistics/415541: How do you solve inclusive events and mutually exclusive events dealing with probability? 1 solutions Answer 291300 by stanbon(57967)   on 2011-02-28 20:24:49 (Show Source): You can put this solution on YOUR website! How do you solve inclusive events and mutually exclusive events dealing with probability? ---- Exclusive events are events that cannot happen simultaneously. You cannot have hht and hth when you throw a coin 3 times. So the probability of hht or hth = (1/8)+(1/8) = 1/4 ------- Inclusive events are events that can happen simultaneouly. You can simultaneously draw a face card and a club from a deck of cards. So P(face or club) = 12/52 + 13/52 - 4/52 = 21/52 ======================= Cheers, Stan H. ===========

Travel_Word_Problems/415536: A walker travels 3.6 miles in the same time that a jogger travels 6 miles. If the walkers speed is 2 miles per hour less then the joggers, find the speed of the walker and the speed of the jogger. I know that its r=t/d and that walker= 3.6, jogger 6 ? -2miles Thank you 1 solutions Answer 291298 by stanbon(57967)   on 2011-02-28 20:17:17 (Show Source): You can put this solution on YOUR website! A walker travels 3.6 miles in the same time that a jogger travels 6 miles. If the walkers speed is 2 miles per hour less then the joggers, find the speed of the walker and the speed of the jogger. ---- Walker DATA: distance = 3.6 miles ; rate = x mph ; time = d/r = 3.6/x hrs. -------------------- Jogger DATA: distance = 6 miles ; rate = x+2 mph ; time = d/r = 6/(x+2) hrs. -------------------- Equation: time = time 3.6/x = 6/(x+2) --- 3.6x + 7.2 = 6x 2.4x = 7.2 x = 3 mph (walker speed) x+2 = 5 mph (jogger speed) ============================== Cheers, Stan H. ===========

Polynomials-and-rational-expressions/415535: -sqrt(36) + -sqrt(500) express in terms of i. a + bi form 1 solutions Answer 291297 by stanbon(57967)   on 2011-02-28 20:11:56 (Show Source): You can put this solution on YOUR website! -sqrt(36) + -sqrt(500) -------- -6 -10sqrt(5) ================= Cheers, Stan H.

Equations/415533: (5-i)/(3-i) * (2+i)/(3+i) 1 solutions Answer 291295 by stanbon(57967)   on 2011-02-28 20:10:37 (Show Source): You can put this solution on YOUR website! (5-i)/(3-i) * (2+i)/(3+i) === = [(5-i)(2+i)]/[9+1] --- = [10+3i+1]/10 --- = [11+3i]/10 =============== Cheers, Stan H. =========

Equations/415532: please help me solve this problem step by step (2x^-3)^2*(0.2x)2 1 solutions Answer 291294 by stanbon(57967)   on 2011-02-28 20:08:21 (Show Source): You can put this solution on YOUR website! (2x^-3)^2*(0.2x)2 ---- (4x^-6)*(0.4x) ---- 1.6x^-5 --- = 1.6/x^5 ========== Cheers, Stan H. ==========

Probability-and-statistics/415448: Suppose Q and R are independent events. Find P(Q and R). P(Q)=4/5 , P(R)= 4/11 I'm pretty sure you would just multiply 4/5*4/11, so it would be 16/55. I just wanted to make sure though. Thanks :) 1 solutions Answer 291293 by stanbon(57967)   on 2011-02-28 20:05:06 (Show Source): You can put this solution on YOUR website! If they are independent events, you are correct. Cheers, Stan H.

Probability-and-statistics/415466: A bag contains 1 green, 4 red, and 5 yellow balls. Two balls are selected at random. Find the probability. P(2 red and 1 yellow) 1 solutions Answer 291284 by stanbon(57967)   on 2011-02-28 19:34:24 (Show Source): You can put this solution on YOUR website! A bag contains 1 green, 4 red, and 5 yellow balls. Two balls are selected at random. Find the probability. P(2 red and 1 yellow) = [4C2*5C1]/52C3 = [6*5]/52C3 = 0.001357 ------------------ Cheers, Stan H. =============

Probability-and-statistics/415495: using a spinner 1-8 and you spin it 10 times how many even-numbered outcomes are possible? 1 solutions Answer 291283 by stanbon(57967)   on 2011-02-28 19:29:07 (Show Source): You can put this solution on YOUR website! 4 on each spin a total of 10*4 = 40 ============================ Cheers, Stan H. -----------

Probability-and-statistics/415497: in how many ways can a student work 6 out of 10 questions on an exam? 1 solutions Answer 291282 by stanbon(57967)   on 2011-02-28 19:27:35 (Show Source): You can put this solution on YOUR website! in how many ways can a student work 6 out of 10 questions on an exam? ------- 10C6 = 10!/[4!*6!] = (10*9*8*7)/(1*2*3*4) = 210 ======================== Cheers, Stan H. ===========

Mixture_Word_Problems/415490: Please help me solve this problem: A collection of 102 nickels, dimes, and quarters is worth $13.60. There are 14 more nickels than dimes. How many quarters are there? 1 solutions Answer 291280 by stanbon(57967)   on 2011-02-28 19:20:42 (Show Source): You can put this solution on YOUR website! A collection of 102 nickels, dimes, and quarters is worth $13.60. There are 14 more nickels than dimes. How many quarters are there? --------------- Equations: Quantity: n + d + q = 102 Quantity: n = d+14 Value:: 5n +10d+25q = 1360 cents ------------------------------------- Rearrange: n + d + q = 102 n - d + 0 = 14 5n+10d+25q= 1360 ----------------- Use any method you know to get: q = 36 ============== Cheers, Stan H.