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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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 Finance/190419: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? 1 solutions Answer 142911 by stanbon(57984)   on 2009-04-09 19:49:33 (Show Source): You can put this solution on YOUR website!If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? -------------------------------- Sally DATA: time = 4 hrs/job ; rate = 1/4 job/hr -------------------------------------- John DATA: time = 6 hrs/job ; rate = 1/6 job/hr ------------------------------------- Together DATA: time = x hrs/job ; rate = 1/x job/hr ========================================= Equation: rate + rate = together rate 1/4 + 1/6 = 1/x 3x + 2x = 12 x = 12/5 = 2.4 hrs (time for them to do the job together) ========================================================= Cheers, Stan H. ---------------------
 Polynomials-and-rational-expressions/190417: How do you evaluate (3*10^4)(3*10^5)1 solutions Answer 142908 by stanbon(57984)   on 2009-04-09 19:28:05 (Show Source): You can put this solution on YOUR website!How do you evaluate (3*10^4)(3*10^5) -------------------------------------- = 3*3*10^4*10^5 --- = 9*10^9 = 9,000,000,000 =============== Cheers, Stan H.
 Exponential-and-logarithmic-functions/190411: Can you please help me with this problem: simplify: 3(5x^2)^(1/3) I tried to to distribute the (1/3) first and got 3(5^(1/3)*x^(2/3)) then I tried to distribute in the 3 and got 15^(1/3)*x^(2/3) but then I do not know what to do1 solutions Answer 142905 by stanbon(57984)   on 2009-04-09 19:22:43 (Show Source): You can put this solution on YOUR website!simplify: 3(5x^2)^(1/3) ---- There is no way to simplify what you have posted. Cheers, Stan H. --------------------
 Miscellaneous_Word_Problems/190229: Worker efficiency. In a study of worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled by the formula N(t)=3t^3+ 23^t2 + 8t. a) Rewrite the formula by factoring the right-hand side completely. b) Use the factored version of the formula to find N(3). 1 solutions Answer 142904 by stanbon(57984)   on 2009-04-09 19:09:18 (Show Source): You can put this solution on YOUR website!N(t)=3t^3 + 23^t2 - 8t. N(t) = t(3t^2 + 23t - 8) N(t) = t(3t^2 +24t-t-8) N(t) = t(3t(t+8) - (t+8)) N(t) = t(t+8)(3t-1) ================================ a) Rewrite the formula by factoring the right-hand side completely. b) Use the factored version of the formula to find N(3). N(3) = 3*11*8 = 264 ========================= Cheers, Stan H.
 Probability-and-statistics/190337: stanbon 21772 having trouble to figure out how you solved the question about the baseball player hits a homerun on the average of once every 12 times at bat= would you mind letting me what to due thanks 1 solutions Answer 142893 by stanbon(57984)   on 2009-04-09 17:52:48 (Show Source): You can put this solution on YOUR website!Hope the additional explanation is helpful. Let me know if there are statements you do not understand. --------------------------- A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions. --- If he bats 5 times in a game, what is the probability he will hit exactly one home run? It's binomial with n=5, p = 1/12, x = 1 If you use a TI calculator you get binompdf(5,12^-1,1) = 0.2942 -------- If you do not have a TI: P(x=1) = 5C1(1/12)^1(11/12)^4 = 5*(1/12)(0.70607) = 0.2942 ------------------------------------------ If he comes to bat 5 times, what is the probability he will hit at least one home run? P(at least one) = 1 - P(no home runs) = 1-binompdf(5,12^-1,0) = 0.3528 OR P(at least one) = 1-P(no home runs) = 1 - 5C0(1/12)^0(11/12)^5 = 1 - 1*1* = 1-0.6472 = 0.3528 ------------------------------------------ If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit? E(x) = np = 5(1/12) = 5/12 ============================================== Cheers, Stan H.
 Equations/190302: hi. i need some help in performing this indicated operation and simplifying it: a^2 - a - 20/a^2 - 16 divided by a-5 thanks!1 solutions Answer 142839 by stanbon(57984)   on 2009-04-09 09:08:03 (Show Source): You can put this solution on YOUR website!a^2 - a - 20/a^2 - 16 divided by a-5 ------------- Factor where you can to get: = [(a-5)(a+4)]/[(a-4)(a+4)]/(a-5) Invert the denominator and multiply to get: = [(a-5)(a+4)]/[(a-4)(a+4)] Cancel factors that are common to a numerator and a denominator such as (a+4), (a-5) = [1/(a-4)] =============== Cheers, Stan H.
 Quadratic_Equations/190316: Prove the identity : sin theta tan theta + cos theta= sec theta1 solutions Answer 142838 by stanbon(57984)   on 2009-04-09 09:02:12 (Show Source): You can put this solution on YOUR website!Prove the identity : sin theta tan theta + cos theta= sec theta ----------- sin(sin/cos) + cos = sec Multiply thru by cos to get: sin^2 + cos^2 = 1 1 = 1 ============== Cheers, Stan H.
 Linear_Algebra/190317: This question is from textbook algebra and trigonometry structure and method book 2 The stretch on a wire under a given tension varies directly as the length of the wire and inversely as the square of its diameter. A wire having length 2m and diameter 1.5mm stretches 1.2 mm. If a second wire of the same material(and under the same tension) has length 3m and diameter 2.0mm, find the amount of stretch. Please help as i keep on messing the decimals up and can't seem to get the right answer. Please explain also. thank you!1 solutions Answer 142837 by stanbon(57984)   on 2009-04-09 08:58:17 (Show Source): You can put this solution on YOUR website!The stretch on a wire under a given tension varies directly as the length of the wire and inversely as the square of its diameter. stretch = k[L/d^2] ------------------------------ A wire having length 2m and diameter 1.5mm stretches 1.2 mm. 1.2 = k[2/1.5^2] 1.2 = k[8/9] k = (9/8)1.2 k = 27/20 So the equation for your problem is stretch = (27/20)[L/d^2] --------- If a second wire of the same material(and under the same tension) has length 3m and diameter 2.0mm, find the amount of stretch. stretch = (27/20)[3/2^2] = 1.0125 ===================================== Cheers, Stan H. -----------------------
 real-numbers/190315: why a2 + b2 cannot be factored.1 solutions Answer 142836 by stanbon(57984)   on 2009-04-09 08:51:45 (Show Source): You can put this solution on YOUR website!why a2 + b2 cannot be factored ------------ It can be factored, but not in the Real Number System. -------------- The factors are (a+bi)(a-bi) in the Complex Number System. -------- Cheers, Stan H.
 Probability-and-statistics/190311: A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions. If he bats 5 times in a game, what is the probability he will hit exactly one home run? If he comes to bat 5 times, what is the probability he will hit at least one home run? If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit? thanks for your help1 solutions Answer 142834 by stanbon(57984)   on 2009-04-09 08:10:29 (Show Source): You can put this solution on YOUR website!A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions. --- If he bats 5 times in a game, what is the probability he will hit exactly one home run? It's binomial with n=5, p = 1/12, x = 1 If you use a TI calculator you get binompdf(5,12^-1,1) = 0.2942 -------- If you do not have a TI: P(x=1) = 5C1(1/12)^1(11/12)^4 = 5*(1/12)(0.70607) = 0.2942 ------------------------------------------ If he comes to bat 5 times, what is the probability he will hit at least one home run? P(at least one) = 1 - P(no home runs) = 1-binompdf(5,12^-1,0) = 0.3528 OR P(at least one) = 1-P(no home runs) = 1 - 5C0(1/12)^0(11/12)^5 = 1 - 1*1* = 1-0.6472 = 0.3528 ------------------------------------------ If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit? E(x) = np = 5(1/12) = 5/12 ============================================== Cheers, Stan H.
 Probability-and-statistics/190261: can someone please help..thanks Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. Let's suppose that for each game they play, the probability that the Bears win is 0.54 and the probability the Wildcats win is 0.46. What is the probability that the bears win the series in 3 games ? .1574 What is the probability that the wildcats win the series in 3 games? .0973 What is the probability that the bears win the series in 4 games? .216 What is the probability that the wildcats win the series in 4 games? .156 what is the probability that the bears win the series in 5 games? what is the probability that the wildcats win the series in 5 games? What is the probability that the bears win the series? what is the probability that the wildcats win the series ?1 solutions Answer 142799 by stanbon(57984)   on 2009-04-08 23:02:09 (Show Source): You can put this solution on YOUR website!Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. Let's suppose that for each game they play, the probability that the Bears win is 0.54 and the probability the Wildcats win is 0.46. What is the probability that the bears win the series in 3 games ? .1575 What is the probability that the wildcats win the series in 3 games? .0973 What is the probability that the bears win the series in 4 games? .216 Patterns are LWWW, WLWW, WWLW Each has probability (0.54^3)(0.46)= 0.07243 But all three are mutually exclusive so the probability = 3(0.07243) = 0.2173 ---------------------------- What is the probability that the wildcats win the series in 4 games? .156 Prob = 3*0.46^3*0.54 = 0.1577 --------------------------------------------- what is the probability that the bears win the series in 5 games? # of patterns: 5C2 - 1= 10-1 = 9 Probability of each pattern = (0.54)^3(0.46)^2 = 0.03332 Ans: 9*0.3332 = 0.2999 --------------------------------------------- what is the probability that the wildcats win the series in 5 games? Ans: 9*(0.46)^3(0.54)^2 = 0.2747 ----------------------------------------------- What is the probability that the bears win the series? They could win it in 4, or 5, or 6, or 7 games. Figure each probability and add them. ------------------------------------------ what is the probability that the wildcats win the series ? Same process as with the bears winning. =========================================================== Cheers, Stan H.
 Probability-and-statistics/190275: I would like to verify that i have the answered the problem below correctly, Thanks in advance for the help. During a certain week in the winter, the following minimum temperatures were recorded in an eastern city: 20, 28, 24, 28, 40, 39, and 31. Find the following: A. Median B. Standard Deviation The answers that I came up with are the following: A. Median = 28 B. Standard Deviation = 7.371114773221212 I greatly appreciate the help. Sam1 solutions Answer 142797 by stanbon(57984)   on 2009-04-08 22:25:09 (Show Source): You can put this solution on YOUR website!Median and standard deviation are correct. Cheers, Stan H.
 Proportions/190276: To determine the number of bass in a lake, a conservationist catches 54 bass, tags them, and returns them to the lake. Later, 32 are observed and 8 are tagged. Estimate how many bass are in the lake.1 solutions Answer 142796 by stanbon(57984)   on 2009-04-08 22:20:43 (Show Source): You can put this solution on YOUR website!To determine the number of bass in a lake, a conservationist catches 54 bass, tags them, and returns them to the lake. Later, 32 are observed and 8 are tagged. Estimate how many bass are in the lake. ----------------------------------------------- [pop #/caught & tagged] = [caught including tagged]/[# tagged that were caught] ---------------------------- pop count/54 = 32/8 --- population count = 54[32/8) = 54*4 = 216 ---------------------------------------------- Cheers, Stan H.
 Probability-and-statistics/190148: A class contains 3 fresh, 4 soph, 6 juniors and 2 seniors. four students are selected at random, find the probability that... a. all four are juniors b. no fresh are selected c. 1 of each year is selected d.. 2 fresh and 2 juniors1 solutions Answer 142794 by stanbon(57984)   on 2009-04-08 22:08:03 (Show Source): You can put this solution on YOUR website!A class contains 3 fresh, 4 soph, 6 juniors and 2 seniors. four students are selected at random, find the probability that... a. P(all four are juniors) = 6C4/15C4 = 15/1365 = 0.01099.. ------------------------------------------------------------ b. P(no fresh are selected) = 12C4/15C4 = 495/1365 ------------------------------------------------------------- c. P(1 of each year is selected) = (3+4+6+2)/1365 = 15/1365 ------------------------------------------------------------ d.. P(2 fresh and 2 juniors) = [3C2 + 6C2]/15C4 = (3 + 15)/1365 = 18/1365 ------------------------------------------------------------- Cheers, Stan H.
 percentage/190267: If a product normally retails for \$40.00 and we give you a \$10 discount, what percentage discount do you receive? 1 solutions Answer 142786 by stanbon(57984)   on 2009-04-08 21:09:40 (Show Source): You can put this solution on YOUR website!If a product normally retails for \$40.00 and we give you a \$10 discount, what percentage discount do you receive? ------------- Amount of discount = \$10 Percent of discount:10/40 = 1/4 = 25% ------------------------------------------ Cheers, Stan H.
 Geometry_Word_Problems/190270: The rate, given that the distance is 200 ft and the time is x+3 seconds 1 solutions Answer 142785 by stanbon(57984)   on 2009-04-08 21:00:56 (Show Source): You can put this solution on YOUR website!The rate, given that the distance is 200 ft and the time is x+3 seconds ------------------- rate = distance/time rate = 200/(x+3) ft per second ===================================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/190268: This question is from textbook I would like to know how to factor this polynomial. 45y^2-18y^3+9y^41 solutions Answer 142783 by stanbon(57984)   on 2009-04-08 20:54:34 (Show Source): You can put this solution on YOUR website!factor this polynomial. 45y^2-18y^3+9y^4 Common Factor: 9y^2 = 9y^2(5 -2y + y^2) ----------------------- Cheers, Stan H.
 expressions/190269: How do you write this mathematical expression using parentheses and brackets. "Subtract 6 from 16. Divide this difference by 5. Multiply this quotient by 8." 1 solutions Answer 142782 by stanbon(57984)   on 2009-04-08 20:47:13 (Show Source): You can put this solution on YOUR website!How do you write this mathematical expression using parentheses and brackets. "Subtract 6 from 16. Divide this difference by 5. Multiply this quotient by 8." ------------------------------------------- [(16-6)/5]*8 =========================== Cheers, Stan H.
 Trigonometry-basics/190262: How do you solve the following trig equation and sketch a unit circle? Equation: cosx=/21 solutions Answer 142779 by stanbon(57984)   on 2009-04-08 20:34:44 (Show Source): You can put this solution on YOUR website!How do you solve the following trig equation and sketch a unit circle? Equation: cosx= sqrt[(3)]/2. Take the inverse cosine or arccos to get: x = arccos[(sqrt(3))/2] = 60 degrees or pi/3 ================================================ You sketch a unit circle by drawing a circle and letting the radius be "1". ------------------------- Cheers, Stan H.
 Probability-and-statistics/190151: at a local deli, 5 out of every 8 people order a turkey club. find the probability that exactly 2 of the next 5 people will order a turkey club.1 solutions Answer 142774 by stanbon(57984)   on 2009-04-08 20:05:04 (Show Source): You can put this solution on YOUR website!at a local deli, 5 out of every 8 people order a turkey club. find the probability that exactly 2 of the next 5 people will order a turkey club. --- Binomial Problem with n = 5, p = 5/8, x = 2 --- P(x=2) = 5C2(5/8)^2(3/8)^3 = 0.2060 ======================================== Cheers, Stan H.
 Reduction-of-unit-multipliers/190169: directions: convert the following units to the indicated units 1) 20 liters/ hour to milliliters/minute. 2) 80 mAs to Amp Hours1 solutions Answer 142740 by stanbon(57984)   on 2009-04-08 14:05:53 (Show Source): You can put this solution on YOUR website!convert the following units to the indicated units 1) 20 liters/ hour to milliliters/minute. --- (20 L/hr)(1000mL/L)(60 min/hr) = [(20*1000*60)]/[1*1*1] (mL/minute) = 1,200,000 (mL/minute) ================================ 2) 80 mAs to Amp Hours (80 mA sec)(Amp/1000 mA)(hr/3600 sec) = [80*1*1]/[1*1000*3600)(Amp hrs) = 80/3600000 Amp hrs = 0.00002222.. Amp hrs ============================ Cheers, Stan H.
 Percentage-and-ratio-word-problems/190177: 4z2+13z+3 Factor each polynomial the 2 is z to the 2nd power1 solutions Answer 142738 by stanbon(57984)   on 2009-04-08 13:56:36 (Show Source): You can put this solution on YOUR website!4z2+13z+3 Factor each polynomial Rewrite: 4z^2 + 12z + z + 3 Factor the 1st two and the last two terms separately ---- 4z(z+3) + (z+3) Factor again: (z+3)(4z+1) ============== Cheers, Stan H.
 Probability-and-statistics/190152: you are taking a test that contains 5 multiple choice questions with 4 possible answers. you guess at all questions. find the probability that you guess exactly 2 questions correctly.1 solutions Answer 142734 by stanbon(57984)   on 2009-04-08 13:54:01 (Show Source): You can put this solution on YOUR website!you are taking a test that contains 5 multiple choice questions with 4 possible answers. you guess at all questions. find the probability that you guess exactly 2 questions ------------------------------ Binomial problem with n=5, p = 1/4, x = 2 P(x=2) = 5C2(1/4)^2(3/4)^3 = 10*(27/4^5) = 0.2637 ==================================== Cheers, Stan H.
 Probability-and-statistics/190153: a computer password contains 4 digits followed by 2 letters. Find the number of password possibilities if the first digit cannot be 0 and repetition is permitted.1 solutions Answer 142731 by stanbon(57984)   on 2009-04-08 13:49:30 (Show Source): You can put this solution on YOUR website!a computer password contains 4 digits followed by 2 letters. Find the number of password possibilities if the first digit cannot be 0 and repetition is permitted. -------- 1st digit....9 ways 2nd digit....10 ways 3rd digit....10 ways 4th digit....10 ways 1st letter...26 ways 2nd letter...26 ways ------------------------ Total # of ways: 9*10^3*26^2 = 6,084,000 ways ================================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/190173: Factor each polynomial pq+6p2-q2 The 2's are a power so its p to the 2nd power1 solutions Answer 142727 by stanbon(57984)   on 2009-04-08 13:44:52 (Show Source): You can put this solution on YOUR website!Factor each polynomial pq+6p2-q2 Rearrange: 6p^2 + pq - q^2 Factor: (3p-1)(2p+1) =============== Cheers, Stan H.
 Miscellaneous_Word_Problems/190167: Hello, the question below has me stumped. It is from a homework handout so I do not have a textbook ISBN--sorry. Thanks in advance for your help. Two pipes can be used to fill a tank. The smaller diameter pipe takes 4 hours longer to fill the tank than the larger diameter pipe. If both pipes are used together, it takes 10 hours to fill the tank. How long would it take each pipe working alone to fill the tank? Round to the nearest tenth of an hour.1 solutions Answer 142726 by stanbon(57984)   on 2009-04-08 13:42:27 (Show Source): You can put this solution on YOUR website!Two pipes can be used to fill a tank. The smaller diameter pipe takes 4 hours longer to fill the tank than the larger diameter pipe. If both pipes are used together, it takes 10 hours to fill the tank. How long would it take each pipe working alone to fill the tank? Round to the nearest tenth of an hour. ----------------------------------- Smaller pipe DATA: time = x+4 hrs/job ; rate = 1/(x+4) job/hr ----------------------- Larger pipe DATA: time = x hrs/job ; rate = 1/4x job/hr ----------------------- Together DATA: time = 10 hrs/job ; rate = 1/10 job/hr ------------------------- Equation: rate + rate = together rate 1/(x+4) + 1/x = 1/10 Multiply thru by 10x*(x+4) to get: 10x + 10(x+4) = x(x+4) 20x + 40 = x^2 + 4x x^2 - 16x - 40 = 0 x = [16 +- sqrt(16^2-4*1*-40)]/2 Positive answer: x = [16 + sqrt(416)]/2 x = 18.2 hrs. (time for the larger pipe to do the job) x+4 = 22.2 hrs. (time for the smaller pipe to do the job.) ====================================== Cheers, Stan H.