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Recent problems solved by 'stanbon'

stanbon answered: 57274 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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test/633773: Solve √(x+1)+5=x+4 1 solutions Answer 399113 by stanbon(57347)   on 2012-08-01 11:11:21 (Show Source): You can put this solution on YOUR website! Solve √(x+1)+5=x+4 ---- sqrt(x+1) = x-5 --- Square both sides to get: x+1 = x^2 - 10x +25 x^2 -11x + 24 = 0 --- Factor: x^2 - 3x - 8x + 24 = 0 x(x-3) - 8(x-3) = 0 ---- (x-3)(x-8) = 0 ---- x = 3 or x = 8 ================ Cheers, Stan H.

Age_Word_Problems/633774: A girl is ten years older than her brother, next year she will be twice as old as him, how old is the girl? 1 solutions Answer 399111 by stanbon(57347)   on 2012-08-01 11:08:21 (Show Source): You can put this solution on YOUR website! A girl is ten years older than her brother, next year she will be twice as old as him, how old is the girl? ------ Equations: g = b + 10 g+1 = 2(b+1) ---- Substitute for "g" and solve for "b": b+10+1 = 2b+2 b = 9 --- Solve for "g": g = b + 10 = 19 (girl's age now) ======= Cheers, Stan H. ============

Probability-and-statistics/633644: if my odds are 1 out of 4.63 how many tickets do i need to buy 1 solutions Answer 399091 by stanbon(57347)   on 2012-08-01 09:03:33 (Show Source): You can put this solution on YOUR website! if my odds are 1 out of 4.63 how many tickets do i need to buy --- P(you win) = 1/5.63 is approximately 18% P(you lose) is approximately 82% --- The more tickets you buy the better your chances of winning will be. Cheers, Stan H.

Probability-and-statistics/633743: The diameters of peaches in a certain orchard are normally distributed with a mean of 4.01 inches and a standard deviation of 0.44 inches. Show all work. (A) What percentage of the peaches in this orchard is larger than 3.94 inches? (B) A random sample of 100 peaches is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 3.94 inches? 1 solutions Answer 399089 by stanbon(57347)   on 2012-08-01 08:58:31 (Show Source): You can put this solution on YOUR website! The diameters of peaches in a certain orchard are normally distributed with a mean of 4.01 inches and a standard deviation of 0.44 inches. Show all work. ----------------------- (A) What percentage of the peaches in this orchard is larger than 3.94 inches? Find the z-value of 3.94 Find the probability of z being greater than that z-value. Ans: 0.5632 =========================== (B) A random sample of 100 peaches is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 3.94 inches? z(3.94) = (3.94-4.01)/[0.44/sqrt(100)] = -1.5910 P(x-bar > 3.94) = P(z > -1.5910) = 0.9442 ============ Cheers, Stan H. ============

Vectors/633726: The magnitude and directions of u and v are given. Find vector w's polar coordinates. u: magnitde 23, bearing 215° v: magnitude 14.5, bearing 105° w: u + v A:(22.7, 77°) B:(77, 22.7°) C:(22.6, 177.9°) D:(177.9, 22.6°) 1 solutions Answer 399086 by stanbon(57347)   on 2012-08-01 08:52:38 (Show Source): You can put this solution on YOUR website! The magnitude and directions of u and v are given. Find vector w's polar coordinates. u: magnitude 23, bearing 215° v: magnitude 14.5, bearing 105° w: u + v --- x ccordinate of u+v: 23cos(215)+14.5cos(105) = -22.59 y coordinate of u+v: 23sin(s15)+14.5sin(105) = 0.8136 --- magnitude of u+v: sqrt[(-22.59)^2+(0.8136)^2] = 22.60 direction of u+v: tan^-1(0.8136/(-22.59)) = -2.06 = 180-2.06 = 177.9 degrees ---- Ans: C ================== Cheers, Stan H. ============================ A:(22.7, 77°) B:(77, 22.7°) C:(22.6, 177.9°) D:(177.9, 22.6°)

test/633635: 3m 2-3m ------------ m2+m-2 1 solutions Answer 399039 by stanbon(57347)   on 2012-07-31 22:53:39 (Show Source): You can put this solution on YOUR website! 3m^2-3m ------------ m^2 + m-2 ========= [3x(m-1)] / [(m+2)(m-1)] ---- Cancel the common (m-1) factor: ---- = (3x)/(m+2) ============== Cheers, Stan H. ==============

Expressions-with-variables/633637: evaluate the expression x+19 1 solutions Answer 399038 by stanbon(57347)   on 2012-07-31 22:50:12 (Show Source): You can put this solution on YOUR website! evaluate the expression x+19 --- More information needed. Cheers, Stan H.

Quadratic_Equations/633631: Equations of quadratic form 4x to the 4th power-10xsquare plus 9=0 I'm not sure whata numbers to factor 1 solutions Answer 399037 by stanbon(57347)   on 2012-07-31 22:48:08 (Show Source): You can put this solution on YOUR website! 4x to the 4th power-10xsquare plus 9=0 I'm not sure whata numbers to factor ----- 4x^4 - 10x^2 + 9 = 0 ---- Use the Quadratic Formula: x^2 = [10 +- sqrt(100-4*4*9)]/(2*4) --- x^2 = [10 +- sqrt(-17)]/8 --- Solve for "x": ===== Cheers, Stan H. ======

Travel_Word_Problems/633628: Write an equation or inequality: The distance d to school is 1 1/2 miles more than the distance p to the park. 1 solutions Answer 399034 by stanbon(57347)   on 2012-07-31 22:24:14 (Show Source): You can put this solution on YOUR website! Write an equation or inequality: The distance d to school is 1 1/2 miles more than the distance p to the park.Write an equation or inequality: The distance d to school is 1 1/2 miles more than the distance p to the park. -------------- d = p + 3/2 ---- Cheers, Stan H. ======

Word_Problems_With_Coins/633622: In a race, the first price will be $5 greater than the second and the second will be $4 greater than the third. the total prize of money is $52. Find each prize? 1 solutions Answer 399032 by stanbon(57347)   on 2012-07-31 22:13:30 (Show Source): You can put this solution on YOUR website! In a race, the first price will be $5 greater than the second and the second will be $4 greater than the third. the total prize of money is $52. Find each prize? ----- f = s + 5 s = t + 4 f + s + t = 52 ---- Substitute for "f" and for "t" to get: s+5 + s + s-4 = 52 3s + 1 = 52 3s = 51 s = 17 (2nd prize value) ---- f = s + 5 = 22 (value of 1st prize) t = s -4 = 13 (value of 3rd prize) ==================== Cheers, Stan H. ===========

Signed-numbers/633623: I haven't been in school for over 30 years. I am studying the compass test but find that I am having some difficulty remembering algebra. for example : which of the following is a factor of x^2 -5x -6. I'm not clear on the x. What do you do to find what x is? Thanks. If i can get an understanding of that it might help me. 1 solutions Answer 399024 by stanbon(57347)   on 2012-07-31 22:01:18 (Show Source): You can put this solution on YOUR website! which of the following is a factor of x^2 -5x -6 ------- Factored Form: = (x-6)(x+1) ================ Cheers, Stan H.

test/633610: Simplify (5/x)+(1/2x)(/)(4/3x)(-)(3/4x) 1 solutions Answer 399022 by stanbon(57347)   on 2012-07-31 21:56:37 (Show Source): You can put this solution on YOUR website! Simplify (5/x)+(1/2x)(/)(4/3x)(-)(3/4x) -------- (10x+x)/(2x^2) / (16x-9x)/(12x^2) ----- (11/2x) / (7/12x) ---- (11/2x)*(12x/7) ---- = 66/7 ============================ Cheers, Stan H.

logarithm/633478: logbase3(logbaseX(logbase416))=-1 I thought perhaps I must simply just add (which multiplies) so i took it out of the brackets. I was getting logbase3 +logbaseX +logbase4 4^2 <-fours cancel out right? Then I got logbase3 +logbase X +2=-1 then log base3 +log base X=-3 Then I am lost. Please help? 1 solutions Answer 398928 by stanbon(57347)   on 2012-07-31 12:47:39 (Show Source): You can put this solution on YOUR website! logbase3(logbaseX(logbase4(16))=-1 ------- log3(logx(log4(16)) = -1 ---- Work from right to left: --- = log3(logx(2)) = -1 --- logx(2) = 3^-1 ---- logx(2) = 1/3 --- 2 = x^(1/3) x = 2^3 = 8 ================== Cheers, Stan H.

Quadratic_Equations/633466: sketch graph of quadratic function f(x)=x^2-2x-3 1 solutions Answer 398925 by stanbon(57347)   on 2012-07-31 12:42:23 (Show Source): You can put this solution on YOUR website! sketch graph of quadratic function f(x)=x^2-2x-3 ----- ------ Cheers, Stan H. ==========

Probability-and-statistics/633435: Television viewers often express doubts about the validity of certain commercials. In a attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 1% of the true population proportion? Use the appropriate table in your book. 1 solutions Answer 398898 by stanbon(57347)   on 2012-07-31 10:29:13 (Show Source): You can put this solution on YOUR website! Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 1% of the true population proportion? ----- Since E = z*sqrt(pq/n) ---- n = [z/E]^2*pq -------------------- Your Problem: n = [1.96/0.01]^2*0.4*0.6 ----- n = 9220 when rounded up ============ Cheers, Stan H.

test/633440: Statistics and probablity 1 solutions Answer 398897 by stanbon(57347)   on 2012-07-31 10:23:18 (Show Source): You can put this solution on YOUR website!

test/633442: Statistics and probablity 1 solutions Answer 398896 by stanbon(57347)   on 2012-07-31 10:22:14 (Show Source): You can put this solution on YOUR website!

Graphs/633443: I am trying graph functions and I get a good graph but it doesn't match any that I am supposed to "pick from" The first one is f(x)= -2x+4 I used -2 as x and came out with 8 for Y also (-1,6), (0,4), (1,2) and (2,0)I made a chart but since it doesn't match with the answers I am stumped. What is the difference between graphing equations and graphing functions? 1 solutions Answer 398895 by stanbon(57347)   on 2012-07-31 10:21:40 (Show Source): You can put this solution on YOUR website! I am trying graph functions and I get a good graph but it doesn't match any that I am supposed to "pick from" The first one is f(x)= -2x+4 I used -2 as x and came out with 8 for Y also (-1,6), (0,4), (1,2) and (2,0)------- If x = -2, y = -2*-2+4 = 8 If x = -1, y = -2*-1+4 = 6 If x = 0, y = -2*0+4 = 4 If x = 1, y = -2*1+4 = 2 If x = 2, y = -2*2+4 = 0 ----- Your points are correct. Plot them and draw a line thru them to get: Cheers, Stan H. =============

test/633444: 1+2=? 1 solutions Answer 398894 by stanbon(57347)   on 2012-07-31 10:17:51 (Show Source): You can put this solution on YOUR website!

test/633445: 1+2=? 1 solutions Answer 398893 by stanbon(57347)   on 2012-07-31 10:17:08 (Show Source): You can put this solution on YOUR website! Ans: 3

Triangles/633441: A ski run must not exceed a slope of -3/5 due to safety concerns. What is the maximum elevation drop (in yards) if the run is to be 4000 yards long? 1 solutions Answer 398891 by stanbon(57347)   on 2012-07-31 10:16:11 (Show Source): You can put this solution on YOUR website! A ski run must not exceed a slope of -3/5 due to safety concerns. What is the maximum elevation drop (in yards) if the run is to be 4000 yards long? ----- Draw the picture. You have a right triangle with hypotenuse = 4000 yds. slope = -3/5 = -0.6 yds This means the skier decends 3 yds for each horizontal advance of 5 yds. ---- Let vertical change be 3x; then horizontal change is 5x. --- (3x)^2 + (5x)^2 = 4000^2 --- 34x^2 = 4000^2 --- x = sqrt[4000^2/34] ---- x = 4000/sqrt(34) ------ Total vertical change = 3x = 12000/sqrt(34) = 2058 yds ===================== Cheers, Stan H. =====================

Probability-and-statistics/633319: in the past year, 13% of business have eliminated jobs. if 5 business are selected at random, find the probability that at least 3 have estimated jobs during the last year. 1 solutions Answer 398811 by stanbon(57347)   on 2012-07-30 20:13:25 (Show Source): You can put this solution on YOUR website! in the past year, 13% of business have eliminated jobs. if 5 business are selected at random, find the probability that at least 3 have estimated jobs during the last year. --- Binomial Problem with n = 5 and p(have eliminated jobs) = 0.13 ----- P(3<= x <=5) = 1 - P(0<= x <- 2) = 1 - binomcdf(5,0..13,2) = 0.01790 ============ Cheers, Stan H. ==============

Probability-and-statistics/633326: Use a z-table to find the specified area. Between the mean and 1.64 deviations from the mean. 1 solutions Answer 398808 by stanbon(57347)   on 2012-07-30 20:07:09 (Show Source): You can put this solution on YOUR website! Use a z-table to find the specified area. Between the mean and 1.64 deviations from the mean. ------- Area between 0 and 1.64 = 0.4495 ---- Area to right + area to left of the mean = 2*0.4495 = 0.8990 ======================= Cheers, Stan H.

Probability-and-statistics/633328: Given the mean equal to 26 and the standard deviation equal to 3, what is the chance that a value of X greater than 18 will occur? 1 solutions Answer 398807 by stanbon(57347)   on 2012-07-30 20:02:54 (Show Source): You can put this solution on YOUR website! Given the mean equal to 26 and the standard deviation equal to 3, what is the chance that a value of X greater than 18 will occur? --------- z(18) = (18-26)/3 = -8/3 ---- P(x > 18) = P(z > -8/3) = normalcdf(-8/3,100) = 0.9962 ============================= Cheers, Stan H.

Number-Line/633312: how do I graph the set of all negative even integers on a number line? 1 solutions Answer 398806 by stanbon(57347)   on 2012-07-30 19:58:50 (Show Source): You can put this solution on YOUR website! Draw a number line. Pick a point to be zero. Determine a unit by picking a point to the right as +1 and a point the same distance to the left of zero as -1. Contine unit distances to the left as -2,-3,-4,etc. --- The graph you want is a set of black dots at -2,-4,-6 etc. =========================== Cheers, Stan H.

Quadratic_Equations/633321: I think this is using the pythagorean theorem and I get really confused... A mason wants to be sure he has a right angle corner of a building's foundation. He marks a point 3 ft from the corner along one wall and another point 4ft from the corner along the other wall. If the corner is a right angle, what should the distance be between the two marked points?? I did the a^2 + b^2 = c^2 formula and plugged in 3^2 + b^2 = 4^2 and got an -7 as an answer. I know a negative # can't be it so that's where I need assistance. Thanks in advance. 1 solutions Answer 398805 by stanbon(57347)   on 2012-07-30 19:47:49 (Show Source): You can put this solution on YOUR website! A mason wants to be sure he has a right angle corner of a building's foundation. He marks a point 3 ft from the corner along one wall and another point 4ft from the corner along the other wall. If the corner is a right angle, what should the distance be between the two marked points?? ---- "c" is the hypotenuse. --- a^2 + b^2 = c^2 3^2 + 4^2 = c^2 9 + 16 = c^2 c^2 = 25 c = 5 ft, ------------------------- Cheers, Stan H. ===============

Probability-and-statistics/633313: What is the probability of getting at least 3 tails when tossing a coin 6 times? 1 solutions Answer 398796 by stanbon(57347)   on 2012-07-30 18:56:37 (Show Source): You can put this solution on YOUR website! answered

logarithm/633311: 5^2x+4*5^x-5=0 1 solutions Answer 398795 by stanbon(57347)   on 2012-07-30 18:54:41 (Show Source): You can put this solution on YOUR website! 5^2x+4*5^x-5=0 ----- (5^x)^2 + 4(5^x) - 5 = 0 --- Factor: [(5^x)+5] = 0 --- 5^x = -5 or 5^x = 1 ---- Note: 5^x cannot be -5 ---- Solve: 5^x = 1 --- x = 0 ============= Cheers, Stan H.

Probability-and-statistics/633310: What is the probability of getting at least 3 tails when tossing a coin 6 times. 1 solutions Answer 398792 by stanbon(57347)   on 2012-07-30 18:45:24 (Show Source): You can put this solution on YOUR website! What is the probability of getting at least 3 tails when tossing a coin 6 times. ------ P(3<= x <=6) = 1 - binomcdf(6,1/2,2) = 0.6563 ------ Cheers, Stan H.

Quadratic_Equations/633202: A small leak will fill an empty boat in 5 hours. The boat's bilge pump will empty a full boat in 3 hours. If the boat were half full and leaking, how long would it take the pump to empty the boat? 1 solutions Answer 398757 by stanbon(57347)   on 2012-07-30 15:51:32 (Show Source): You can put this solution on YOUR website! A small leak will fill an empty boat in 5 hours. The boat's bilge pump will empty a full boat in 3 hours. If the boat were half full and leaking, how long would it take the pump to empty the boat? --------------------------------------------- Fill rate = 1/5 job/hr --- Empty rate = 1/3 job/hr --- Together rate = 1/5 - 1/3 = (3-5)/15 = -2/15 job/hr. --- Time to empty a full boat = 15/2 = 7 1/2 hrs ----- Time to empty (1/2) boat = 15/4 = 3 3/4 hrs = 3 hr 45 minutes ====================== Cheers, Stan H.

�t�e�s�t/633236: Find all solutions of the equation. Check your solutions in the original equation. (If there is no solution, enter NO SOLUTION.) (x + 8)^3/2 = 27 1 solutions Answer 398755 by stanbon(57347)   on 2012-07-30 15:39:05 (Show Source): You can put this solution on YOUR website! (x + 8)^3/2 = 27 ----- Raise each side to the 2/3 power to get: x + 8 = 27^(2/3) --- x + 8 = 9 --- x = 1 ============== Cheers, Stan H. ==============