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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, >>Next

 Mixture_Word_Problems/630637: Andrew factored the expression -4x^3+2x^2+8x as -2x(4x^2-2x-8). But when Melissa applied the distributive law and multiplied out -2x(4x^2-2x-8), she got -8x^3+4x^2+16x; thus, Andrew's solution does not appear to check. Why is this? Please help Andrew to understand this better. EXPLAIN YOUR REASONING and correctly factor the orginal expression, if possible. If the expression is prime, so state. I have worked on this and I am totally messed up. Can you help? Thanks in advance...1 solutions Answer 397063 by stanbon(57203)   on 2012-07-21 20:06:02 (Show Source): You can put this solution on YOUR website!-4x^3+2x^2+8x ------ = -2x(2x^2 -x - 4) ========================= Cheers, Stan H. =============
 Polynomials-and-rational-expressions/630636: Factor the expression 4x^2- 20xy +25y^2 into a product of binomials. Please show your steps. When I worked it out .... I got a= 2 am I right? Thank you in advance...1 solutions Answer 397060 by stanbon(57203)   on 2012-07-21 20:00:35 (Show Source): You can put this solution on YOUR website!Factor the expression 4x^2- 20xy +25y^2 into a product of binomials. -------------- = (2x-5y)(2x-5y) =================== Cheers, Stan H. ===================
 Quadratic_Equations/630634: Carlos trows a rock from the pier. The height of the rock h(t) can be moxled by the function. h(t)=-5t^2+13t+6. When will the rock hit the water ? What is the maximum height of the rock ? 1 solutions Answer 397058 by stanbon(57203)   on 2012-07-21 19:53:03 (Show Source): You can put this solution on YOUR website!Carlos trows a rock from the pier. The height of the rock h(t) can be moxled by the function. h(t)=-5t^2+13t+6. When will the rock hit the water ? What is the maximum height of the rock ? ---- Its height is zero when the rock hits the water. ---- Solve -5t^2 + 13t + 6 = 0 Factor: -5t^2 + 15t-2t + 6 = 0 -5t(t-3)-2(t-3) = 0 (t-3)(-5t-2) = 0 t = 3 seconds (time at which the rock hits the water --- max height occurs when t = -b/(2a) = -13/(2*-5) = 13/10 = 1.3 --- Max height = h(1.3) = -5(1.3)^2 + 13(1.3) + 6 = -5*1.69 +16.9+6 = 14.49 ft =================================== Cheers, Stan H. ===================================
 Rational-functions/630631: Solve and check 3x^2+2x=161 solutions Answer 397057 by stanbon(57203)   on 2012-07-21 19:41:20 (Show Source): You can put this solution on YOUR website!Solve and check 3x^2+2x=16 ------ 3x^2+2x-16 = 0 3x^2+8x-6x-16 = 0 x(3x+8)-2(3x+8) = 0 (3x+8)(x-2) = 0 x = 2 or x = -8/3 ================== Cheers, Stan H.
 Rational-functions/630632: Find the maximum y value on the graph of y=f(x) f(x)=-x^2+8x+11 solutions Answer 397056 by stanbon(57203)   on 2012-07-21 19:36:26 (Show Source): You can put this solution on YOUR website!Find the maximum y value on the graph of y=f(x) f(x)=-x^2+8x+1 --- Max occures when x = -b/(2a) = -8/(2*-1) = 4 --- Max y-value = f(4) = -4^2+8*4+1 = -16 + 32 + 1 = 17 -------------------- Cheers, Stan H. =================
 Rational-functions/630633: Solve by completing the square what value should you add to each side of the equation x^2+18x=-91 solutions Answer 397053 by stanbon(57203)   on 2012-07-21 19:26:47 (Show Source): You can put this solution on YOUR website!Solve by completing the square what value should you add to each side of the equation x^2+18x=-9 --------------- x^2 + 18x + (18/2)^2 = -9 + (18/2)^2 ---- Answer: (18/2)^2 = 9^2 = 81 ------------------------------ Cheers, Stan H.
 Square-cubic-other-roots/630618: what is 3 inside the radical of 54 ?1 solutions Answer 397044 by stanbon(57203)   on 2012-07-21 18:15:35 (Show Source): You can put this solution on YOUR website!what is 3 inside the radical of 54 ? --- That "3" means cube root. ---- cbrt(54) = cbrt(27)*cbrt(2) = 3*cbrt(2) ============================================== Cheers, Stan H. =============================
 Quadratic_Equations/630611: what is the quadratic equation for the given solutions 7i and -7i1 solutions Answer 397043 by stanbon(57203)   on 2012-07-21 18:13:24 (Show Source): You can put this solution on YOUR website!what is the quadratic equation for the given solutions 7i and -7i ---- Ans: (x-7i)(x--7i) = x^2+7ix-7ix+49 = x^2+49 -------------------------------- Cheers, Stan H.
 Quadratic_Equations/630606: Hello I have couple questions. 1) what is the exact values of x^2+4x-20=0 and how can I find it 2)a floor measures 12m by 8m. a rug covers one-third of the floor.the uncovered part of the floor forms a uniform strip around the rag . how wide is the strip ? Thanks for helping1 solutions Answer 397041 by stanbon(57203)   on 2012-07-21 17:59:52 (Show Source): You can put this solution on YOUR website!1) what is the exact values of x^2+4x-20=0 and how can i find it? ---- Factor: x = [-4 +- sqrt(16-4*-20)]/2 x = [-4 +- sqrt(96)]/2 x = [-4 +- 4sqrt(6)]/2 x = -2 + 2sqrt(6) or x = -2 - 2sqrt(6) ------------------------------------------ 2)a floor measures 12m by 8m. a rug covers one-third of the floor.the uncovered part of the floor forms a uniform strip around the rug . how wide is the strip ? Draw a picture of a rectangle inside a rectangle. Area of the outer rectangle including the area of the inner: 12m x 8m = 96 m^2 Area outside the inner and inside the outer rectangle: (1/3)96 = 32 m^2 ------ Dimensions of that area: (12-2x)(8-2x) = 32 m&3 96-40x+4x^2 = 32 x^2 - 10x + 24 = 0 (x-6)(x-4) = 0 x = 4m (width of the strip) =========================================== Cheers, Stan H. ===============
 Exponential-and-logarithmic-functions/630604: 1 solutions Answer 397039 by stanbon(57203)   on 2012-07-21 17:40:08 (Show Source): You can put this solution on YOUR website!(log((z)))^2=log((z^2)) ----- = [log(z)]^2 - 2log(z) = 0 ---- Factor: log(z)[log(z)-2)] = 0 ---- log(z) = 0 or log(z) = 2 ---- z = 1 or z = 100 ======================= Cheers, Stan H. =============
 Exponential-and-logarithmic-functions/630605: 1 solutions Answer 397037 by stanbon(57203)   on 2012-07-21 17:35:05 (Show Source): You can put this solution on YOUR website!2^x*2^(x+1)=4^(x^2+x) ------------ 2^(2x+1) = 2^(2x^2+2x) ------ 2x+1 = 2x^2 + 2x 2x^2 = 1 x^2 = 1/2 x = sqrt(1/2) or x = -sqrt(1/2) ------------------------------- Cheers, Stan H. -------------------------------
 Exponential-and-logarithmic-functions/630595: Need help on Log equation: 1 solutions Answer 397036 by stanbon(57203)   on 2012-07-21 17:30:16 (Show Source): You can put this solution on YOUR website!4(1.02)^x=3(1.03)^x ----------- (1.02/1.03)^x = 3/4 ---- x*log[(1.02/1.03)] = log(3/4) ---- x*(-0.0042) = -1.2493 x = 29.3872 =============== Cheers, Stan H.
 Angles/630560: You have a heptagon with the following measurements of 6 interior angles: 125º, 130º, 175º, 105º, 165º, 25º. What is the measure of the 7th angle? If it is not possible, write not possible and explain why it is not possible.1 solutions Answer 397011 by stanbon(57203)   on 2012-07-21 14:56:37 (Show Source): You can put this solution on YOUR website!You have a heptagon with the following measurements of 6 interior angles: 125º, 130º, 175º, 105º, 165º, 25º. What is the measure of the 7th angle? If it is not possible, write not possible and explain why it is not possible. --- sum of the interior angles of a heptagon = (7-2)*180 = 900 degrees ---- Sum of the six given angles: 725 ----- Measure of the 7th angle 900-725 = 175 degrees ===================== Cheers, Stan H. ---------------
 Equations/630579: add or subtract as indicated. simplify. show cancelling,factoring,and the steps for finding the lowest common denominator. assume that no denominator is 0. a/a^2-4 - 2/a^2-41 solutions Answer 397009 by stanbon(57203)   on 2012-07-21 14:42:10 (Show Source): You can put this solution on YOUR website!a/a^2-4 - 2/a^2-4 ---- Since the denominators are the same, combine the numerators over the common denominator: ---- = (a-2)/[(a-2)(a+2)] ---- Cancel the factor common to numerator and denominator to get: ----- = 1/(a+2) ============= Cheers, Stan H. ==============
 Probability-and-statistics/630356: If X is a normal random variable with standard deviation 3.50, and if the probability that X is more than 12.33 is .1271, then what is the mean of X?1 solutions Answer 397008 by stanbon(57203)   on 2012-07-21 14:39:30 (Show Source): You can put this solution on YOUR website!If X is a normal random variable with standard deviation 3.50, and if the probability that X is more than 12.33 is .1271, then what is the mean of X? ---- P(x > 12.33) = 0.1271 --- Find the z-value with a right tail of 0.1271 invNorm(1-0.1271) = 1.1402 --- Use z = (x-u)/s to find u. --- 1.1402 = (12.33-u)/3.50 -u = (1.1402*3.50) - 12.33 -u = -8.3393 ---- u = 8.3393 ========================== Cheers, Stan H. ===============
 Probability-and-statistics/630463: I am having a difficult time with this problem. With 71.1% of a town's population made up of college students, what is the probability that in a random sample of 150 people from the town, more than 50 are not college students?1 solutions Answer 397007 by stanbon(57203)   on 2012-07-21 14:33:39 (Show Source): You can put this solution on YOUR website!With 71.1% of a town's population made up of college students, what is the probability that in a random sample of 150 people from the town, more than 50 are not college students? ----- Binomial Problem withe n = 150 and P(not college) = 0.289 --- P(x > 50) = 1 - binomcdf(150,0.289,49) = 0.1345 ======================== Cheers, Stan H. ===============
 Probability-and-statistics/630473: I am looking for help regarding this problem please. A mail order company has an 8% success rate. If it mails advertisements to 600 people, find the probability of getting less than 40 sales.1 solutions Answer 397005 by stanbon(57203)   on 2012-07-21 14:29:28 (Show Source): You can put this solution on YOUR website!A mail order company has an 8% success rate. If it mails advertisements to 600 people, find the probability of getting less than 40 sales. ------- Binomial Problem with n = 600 and p(success) = 0.08 ---- P(0<= x <40) = binomcdf(600,0.08,39) = 0.0977 ========================== Cheers, Stan H.
 Probability-and-statistics/630558: Help, In your own line of work, give one example of a discrete and one example of a continuous random variable, and describe why each is continuous or discrete.1 solutions Answer 397004 by stanbon(57203)   on 2012-07-21 14:25:22 (Show Source): You can put this solution on YOUR website!In your own line of work, give one example of a discrete and one example of a continuous random variable, and describe why each is continuous or discrete. # of workers present is discrete. Time to complete a report is continuous. Cheers, Stan H.
 Probability-and-statistics/630574: A bag contains 8 white and 2 red marbles. A marble is removed at random, its color is noted and it is replaced back into the bag. The experiment is repeated 5 times in all. Describe the distribution followed by the number of red marbles removed.1 solutions Answer 397003 by stanbon(57203)   on 2012-07-21 14:23:06 (Show Source): You can put this solution on YOUR website!A bag contains 8 white and 2 red marbles. A marble is removed at random, its color is noted and it is replaced back into the bag. The experiment is repeated 5 times in all. Describe the distribution followed by the number of red marbles removed. ----- Binomial distribution with n = 5 and P(red) = 2/10 Let # of red be 0<= x <=5. and show P(x) for each x value. ------------------------ Cheers, Stan H.
 Travel_Word_Problems/630566: If a car traveled 80 miles between 2pm and 4pm. Is it true thst there must have been a time which its instantaneous speed was exactly 40 miles per hour? Justify your answer with an appropriate theorem or a counterexample if false. 1 solutions Answer 397002 by stanbon(57203)   on 2012-07-21 14:20:27 (Show Source): You can put this solution on YOUR website!If a car traveled 80 miles between 2pm and 4pm. Is it true thst there must have been a time which its instantaneous speed was exactly 40 miles per hour? Justify your answer with an appropriate theorem or a counterexample if false. --- His average speed was 40. Either he maintained 40 for 2 hours, or he went slower for a time, then faster for a time. --- In either case there was an instant when his speed was 40 mph. ============== Cheers, Stan H.
 Equations/630572: simplify each expression show cancelling and factoring (x+2)^2 / x^2+3x+21 solutions Answer 397001 by stanbon(57203)   on 2012-07-21 14:17:13 (Show Source): You can put this solution on YOUR website!simplify each expression show cancelling and factoring (x+2)^2 / (x^2+3x+2) ----- = (x+2)^2 / [(x+2)(x+1)] ----- = (x+2)/(x+1) -------------- Cheers, Stan H. ==============
 Polynomials-and-rational-expressions/630567: (3a^-4b^5)^-2/(9a^4b^-5)^-1 Simplify please. Would it cancel out to 0?1 solutions Answer 397000 by stanbon(57203)   on 2012-07-21 14:14:01 (Show Source): You can put this solution on YOUR website! (3a^-4b^5)^-2/(9a^4b^-5)^-1 Simplify please. ---- Work inside each parenthesis: (3b^5/a^4)^-2 / (9a^4/b^5)^-1 ---- Work with the exponent of each parenthesis: = (a^8/9b^10)/(b^5/9a^4) ---- Invert the denominator and multiply: = 9a^12/9b^15 ---- Simplify: = a^12/b^15 ============== Cheers, Stan H. ==============
 Trigonometry-basics/630569: Let (-5,-7) be a point on the terminal side of theta. Find the exact values of cos theta, csc theta, tan theta1 solutions Answer 396995 by stanbon(57203)   on 2012-07-21 14:03:57 (Show Source): You can put this solution on YOUR website! Let (-5,-7) be a point on the terminal side of theta. Find the exact values of cos theta, csc theta, tan theta --- In 3rd Quadrant you have x = -5, y = -7: Then r = sqrt(5^2+7^2) = sqrt(60) = 2sqrt(15) ----- sin = y/r = -7/(2sqrt(15)) cos = x/r = -5/(2sqrt(15)) tan = -7/-5 = 7/5 ----------------- csc, sec, and ctn are the inverse. ============ Cheers, Stan H.
 Angles/630408: three angles of hexagon are 60,100and 120 . find the other three angles if they are ratio of 1:4:51 solutions Answer 396896 by stanbon(57203)   on 2012-07-20 19:22:38 (Show Source): You can put this solution on YOUR website!three angles of hexagon are 60,100and 120 . find the other three angles if they are ratio of 1:4:5 ----- The sum of the interior angles of a hexagon is (6-2)*180 = 4*180 = 720 degrees ------------------- The 3 angles you know have a sum of 280 degrees. The other 3 angles must have a sum of 720-280 = 440 degrees ----- Equation: x + 4x + 5x = 440 10x = 440 x = 44 degrees 4x = 176 degrees 5x = 220 degrees ----------------------- Cheers, Stan H.
 Equations/630421: Can you solve this with your work : 1x+2x+3x+4x+5x+6x+..........+98x+99x+100x=50x+10000 P.s. can you show all your work1 solutions Answer 396895 by stanbon(57203)   on 2012-07-20 19:13:12 (Show Source): You can put this solution on YOUR website!Can you solve this with your work : 1x+2x+3x+4x+5x+6x+..........+98x+99x+100x=50x+10000 ------ 1x+100x = 101x 2x+99x = 101x 3x+98x = 101x .... ... The left side adds up to (100/2)(1+100)x = 50*101x = 5050x --------------------- Equation: 5050x = 50x + 10000 5000x = 10,000 x = 2 ================ Cheers, Stan H.
 Travel_Word_Problems/630341: carlos maneuvered his way through the first 80 miles in 5 hours.then he doubled his speed for the last part of the trip.if the total trip was 400 miles,how many hours did it take carlos to maneuver the last part?1 solutions Answer 396863 by stanbon(57203)   on 2012-07-20 14:56:49 (Show Source): You can put this solution on YOUR website!carlos maneuvered his way through the first 80 miles in 5 hours.then he doubled his speed for the last part of the trip.if the total trip was 400 miles,how many hours did it take carlos to maneuver the last part? ------- 1st Part DATA: distance = 80 miles ; time = 5 hrs ; rate = 80/5 = 16 mph -------- 2nd Part DATA: distance = 400-80 = 320 miles ; rate = 2*16 = 32 mph ----- Equation: 2nd Part time = distance/rate = 320/32 = 10 hrs ================================================== Cheers, Stan H. ==============
 Surface-area/630333: I have been asked to test a piece of material that is 1/2" thick by 1" wide in a continuos length. The instruction states that specimen shall be 1/2" in thickness and 4 square inches in area. I would assume that the length needed should be 4". I have been told that it is 2" because both the top and bottom surfaces count. Is this true?1 solutions Answer 396861 by stanbon(57203)   on 2012-07-20 14:50:11 (Show Source): You can put this solution on YOUR website!I have been asked to test a piece of material that is 1/2" thick by 1" wide in a continuos length. The instruction states that specimen shall be 1/2" in thickness and 4 square inches in area. I would assume that the length needed should be 4". I have been told that it is 2" because both the top and bottom surfaces count. Is this true? -------- top + bottom area = 2(1" * 2") = 4 in^2 ---- Side area = 2((1/2)" * 1") + 2((1/2)" * 2") = 2[(1/2)+1) = 3 in^2 ----------------------- Cheers, Stan H. =================
 Probability-and-statistics/630222: A committee of 4 women and 3 men need to select a chair person and a secretary. If every person is equally likely to be chosen, what is the probability that : a) both positions are filled by women? b) both positions are filled by men? c) the chairperson is female and the secretary is male? 1 solutions Answer 396798 by stanbon(57203)   on 2012-07-20 10:02:27 (Show Source): You can put this solution on YOUR website!A committee of 4 women and 3 men need to select a chair person and a secretary. If every person is equally likely to be chosen, what is the probability that : a) both positions are filled by women? Ans: 4C2/7C2 = 6/21 = 2/7 ------------------ b) both positions are filled by men? Ans: 3C2/7C2 = 3/21 = 1/7 ------------------------------- c) the chairperson is female and the secretary is male? # of ways to succeed: 4*3 = 12 # of possible outcomes: 7*6 Prob = 12/42 = 6/21 = 2/7 ------------------------------ Cheers, Stan H.
 Probability-and-statistics/630248: Can someone kindly tell me if my answer is correct? Thank you. A research center estimates that at least 35% of U.S. adults eat breakfast every day. In a random sample of 300 U.S. adults, 38% say they eat breakfast every day. At α = 0.05, conclude a hypothesis test for the population proportion, p. My answer for Z = 1.09 Fail to reject the claim because there is not enough evidence to reject the claim.1 solutions Answer 396794 by stanbon(57203)   on 2012-07-20 09:37:54 (Show Source): You can put this solution on YOUR website!Your z is correct Your conclusion is correct. ============= Cheers, Stan H.
 Mixture_Word_Problems/630249: sana purchases 3 lbs of mixed nuts and 89 cents per pound . hina purchases 2 lbs of peanuts at 49 cents per pound. what is the average price per pound for the mixture of both purchases ?1 solutions Answer 396792 by stanbon(57203)   on 2012-07-20 09:20:39 (Show Source): You can put this solution on YOUR website!sana purchases 3 lbs of mixed nuts and 89 cents per pound . hina purchases 2 lbs of peanuts at 49 cents per pound. what is the average price per pound for the mixture of both purchases ? -------- Average = value/weight ----- Value = 3*89 + 2*49 = 365 cents Weight = 3 + 2 = 5 lbs --- Average = 365/5 = 73 cents per pound ========== Cheers, Stan H.
 Linear-equations/630250: write a solution as an order pair s= -1 y= -51 solutions Answer 396791 by stanbon(57203)   on 2012-07-20 09:12:21 (Show Source): You can put this solution on YOUR website!write a solution as an order pair s= -1 y= -5 --- Ans: (-1,-5) ============= Cheers, Stan H. =============