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Recent problems solved by 'stanbon'

stanbon answered: 57135 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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next

Mixture_Word_Problems/386077: a chemist needs 120 milliliters of a 50% solution but has only 48% and 60% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. 1 solutions Answer 272980 by stanbon(57203)   on 2010-12-14 14:06:22 (Show Source): You can put this solution on YOUR website! a chemist needs 120 milliliters of a 50% solution but has only 48% and 60% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. ----------------- Equations: Quantity: x + y = 120 ml Active::: 0.48x + 0.60y = 0.50*120 ------------------ Multiply thru 1st by 48 Multiply thru 2nd by 100 --------------------------- 48x + 48y = 48*120 48x + 60y = 50*120 ======================= 12y = 2*120 y = 20 ml (amt. of 60% solution needed in the mix) --- Since x + y = 120 , x = 100 ml (amt. of 48% solution needed in the mix) =================== Cheers, Stan H. ====================

Probability-and-statistics/386068: The lifetime of a Duracell AAA battery is normally distributed with a mean M=28.5 hours and standard deviation baby sigma= 5.3 hours. Compute z scores to determine for a battery selected at random, what is the probability is that the lifetime will be a.) 25 hours or less b.) 34 hours or more c.) between 25 hours and 34 hours. 1 solutions Answer 272979 by stanbon(57203)   on 2010-12-14 14:01:48 (Show Source): You can put this solution on YOUR website! The lifetime of a Duracell AAA battery is normally distributed with a mean M=28.5 hours and standard deviation baby sigma= 5.3 hours. Compute z scores to determine for a battery selected at random, what is the probability is that the lifetime will be a.) 25 hours or less z(25) = (25-28.5)/5.3 = -0.6604 P(x <= 25) = P(z <= -0.6604) = 0.2545 =================== Cheers, Stan H. b.) 34 hours or more Prob = 0.1497 c.) between 25 hours and 34 hours. Prob = 0.5960 ================= Cheers, Stan H. ===============

Probability-and-statistics/386073: A weighted coin is tossed four times. The probability for the number if heads observed is given below # heads Probability 0 .4096 1 .4096 2 .1536 3 .0256 4 .0016 What is the probability of getting at least ones head? 1 solutions Answer 272978 by stanbon(57203)   on 2010-12-14 13:54:22 (Show Source): You can put this solution on YOUR website! duplicate

Probability-and-statistics/386071: A veterinarian tells you that the mean life span of an Appaloosa horse is 19 years with a standard deviation of 2 years. Use Chebyshev's Theorem to find an interval A to B for the number of years in which at least 93.8% of the Appaloosa life spans will fall. 1 solutions Answer 272977 by stanbon(57203)   on 2010-12-14 13:46:44 (Show Source): You can put this solution on YOUR website! A veterinarian tells you that the mean life span of an Appaloosa horse is 19 years with a standard deviation of 2 years. Use Chebyshev's Theorem to find an interval A to B for the number of years in which at least 93.8% of the Appaloosa life spans will fall. ------------ 1-(1/4)^2 = 93.8% --- 4 std = 4*2 = 8 --- A = 19-8 B = 19+8 ---- Interval (11,27) ================== Cheers, Stan H. ==================

Probability-and-statistics/386070: Please help me with this homework problem: What is the standard error of mean for these three appraisal values: 215,195, and 160? I said 27.84 for my answer. I came up with this by take s/ the square root of n. Is this correct? 1 solutions Answer 272975 by stanbon(57203)   on 2010-12-14 13:41:33 (Show Source): You can put this solution on YOUR website! What is the standard error of mean for these three appraisal values: 215,195, and 160? I said 27.84 for my answer. I came up with this by take s/ the square root of n. --------------------------------- It's not the standard error of the set, it's the standard error of the mean of the set. It's 27.84/sqrt(3) = 16.07 === Cheers, Stan H.

Probability-and-statistics/386069: Sixty-two balls numbered from 1 to 62 are placed in an urn. One ball is randomly drawn from the urn. What is the probability that the number on the ball is greater than or equal to 24? 1 solutions Answer 272973 by stanbon(57203)   on 2010-12-14 13:36:58 (Show Source): You can put this solution on YOUR website! Sixty-two balls numbered from 1 to 62 are placed in an urn. One ball is randomly drawn from the urn. What is the probability that the number on the ball is greater than or equal to 24? ----------------- Ans: 18/62 = 9/31 Cheers, Stan H.

Miscellaneous_Word_Problems/386058: Frank can type a report in 3 hours and James takes 7 hours. How long will it take the two of them typing together? 1 solutions Answer 272972 by stanbon(57203)   on 2010-12-14 13:34:02 (Show Source): You can put this solution on YOUR website! Frank can type a report in 3 hours and James takes 7 hours. How long will it take the two of them typing together? ---------------------- Frank rate = 1/3 job/hr James rate = 1/7 job/hr Together rate = 1/x job/hr ------------------ Equation: rate + rate = together rate 1/3 + 1/7 = 1/x (7+3)/21 = 1/x x = 21/10 x = 2.1 hrs = 2 hr 6 minutes (time to do the job together0 ============= Cheers, Stan H.

Probability-and-statistics/386067: A statistical study is being conducted to determine if the population mean yield for all Arizona municipal bonds is greater than the national average. A random sample of size (n=16) is drawn from Arizona municipal bonds. What would be the critical value (a=.01) for this test? 1 solutions Answer 272970 by stanbon(57203)   on 2010-12-14 13:30:34 (Show Source): You can put this solution on YOUR website! A statistical study is being conducted to determine if the population mean yield for all Arizona municipal bonds is greater than the national average. A random sample of size (n=16) is drawn from Arizona municipal bonds. What would be the critical value (a=.01) for this test? ---------- It's a right-tail test with alpha = 1% --- invt(0.99 with df = 15) = 2.6025 ===================== Cheers, Stan H. ==========

logarithm/386066: find the indicated composite for the pair functions, (f0g)(x): f(x)=3x+7, g(x)=4x-1 1 solutions Answer 272969 by stanbon(57203)   on 2010-12-14 13:26:54 (Show Source): You can put this solution on YOUR website! find the indicated composite for the pair functions, (fog)(x): f(x)=3x+7, g(x)=4x-1 fog(x) = f[g(x)] = f[4x-1] = 3(4x-1)+7 = 12x+4 ========================================= Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/385957: I am trying to solve a system's problem. Walt has three investments totaling $110,000. These investments earn interest at 8%, 10% and 12% respectively. Walt's total income from these investments is $11,600. The income from the 12% investment exceeds the total income from the other two investments by $400. Find how much Walt has invested at 8%. Thanks so much for the help!! Denise 1 solutions Answer 272947 by stanbon(57203)   on 2010-12-14 09:14:53 (Show Source): You can put this solution on YOUR website! Walt has three investments totaling $110,000. These investments earn interest at 8%, 10% and 12% respectively. Walt's total income from these investments is $11,600. The income from the 12% investment exceeds the total income from the other two investments by $400. Find how much Walt has invested at 8%. --------------- Equations: x + y + z = 110,000 8x+10y+12z= 1160000 z = (x+y)+400 --------------------------- Rearrange: x + y + z = 110,000 8x+10y+12z= 1160000 x + y - z = -400 -------------------------- Use any method you know to get: x = 25200 y = 29600 z = 55200 ============== Cheers, Stan H.

percentage/385948: Solve. Please show the algebraic inequality you used and show all of your work. The Lido Company rents copy machines for a monthly charge of $300 + 10 cents per copy. The Lumsden Company rents copy machines for a monthly charge of $500 + 3 cents per copy. How many copies make the Lido Company more expensive than the Lumsden Company? 1 solutions Answer 272944 by stanbon(57203)   on 2010-12-14 08:45:15 (Show Source): You can put this solution on YOUR website! The Lido Company rents copy machines for a monthly charge of $300 + 10 cents per copy. The Lumsden Company rents copy machines for a monthly charge of $500 + 3 cents per copy. How many copies make the Lido Company more expensive than the Lumsden Company? --------------------------- Lido cost: L(x) = 300+0.10x --- Lums cost: M(x) = 500 + 0.03x ---------------------------------- Solve: L(x) > M(x) --- 300+0.10x > 500 + 0.03x 0.07x > 200 x > 2857.14 =============== Cheers, Stan H. ============

percentage/385942: Solve the following equation for m. Please show all of your work s= 4m-3n/21 1 solutions Answer 272943 by stanbon(57203)   on 2010-12-14 08:40:38 (Show Source): You can put this solution on YOUR website! s= (4m-3n)/21 --- 21s = 4m-3n ---- 21s+3n = 4m -------- m = (21s+3n)/4 ================== Cheers, Stan H.

logarithm/385928: if b is 1.2 and t is 4. first make x the subject and work out its value in this equation b = log4x - 2log t 1 solutions Answer 272940 by stanbon(57203)   on 2010-12-14 08:36:57 (Show Source): You can put this solution on YOUR website! if b is 1.2 and t is 4. first make x the subject and work out its value in this equation ------------------------ b = log4x - 2log t --- 1.2 = log4(x) - 2log(4) --- 1.2 = log4(x) - log(16) ---- 1.2 = log4(x) - 1.2041 ---- log4(x) = 2.4041 --- x = 4^2.4041 --- x = 28.016.. =============== Cheers, Stan H. ============

Probability-and-statistics/385490: Consider the following contingency table of travelers on a cruise ship and their ages: Age 1st cruise 2nd cruise 3rd cruise 21 - 30 25 17 33 31 - 40 12 23 10 41 – 50 35 15 45 Total 72 55 88 A. If a person is selected at random, what is the probability it is his/her 2nd cruise? ____ B. If a person is selected at random, what is the probability the person is either in the age group 31-40 or 41-50? ____ C. If a person is selected at random, what is the probability the person is either 21-30 or on his/her 2nd cruise? _____ D. If two people are selected at random, what is the probability they are both on their 1st cruise? ____ If I get this answer correct, I will provide you with a DONATION. 1 solutions Answer 272937 by stanbon(57203)   on 2010-12-14 08:30:11 (Show Source): You can put this solution on YOUR website! Consider the following contingency table of travelers on a cruise ship and their ages: Age 1st cruise 2nd cruise 3rd cruise 21 - 30 25 17 33 31 - 40 12 23 10 41 – 50 35 15 45 Total 72 55 88 A. If a person is selected at random, what is the probability it is his/her 2nd cruise? (total of 2nd cruise column)/(grand total) B. If a person is selected at random, what is the probability the person is either in the age group 31-40 or 41-50? (sum of those rows)/grand total) C. If a person is selected at random, what is the probability the person is either 21-30 or on his/her 2nd cruise? (sum of 21-30 and 2nd - intersection of that row and column)/grand total D. If two people are selected at random, what is the probability they are both on their 1st cruise? 144C2/grandtotalC2 =================== Cheers, Stan H.

Sequences-and-series/385826: Find the next 3 numbers in the following pattern: 2/3, 2/5, 6/25, 18/125,... 1 solutions Answer 272884 by stanbon(57203)   on 2010-12-13 22:13:14 (Show Source): You can put this solution on YOUR website! Find the next 3 numbers in the following pattern: 2/3, 2/5, 6/25, 18/125,... --------------------- Find the pattern: The numerators are multiplied by 3 The denominators are multiplied by 5 --- 5th term: (3/5)(18/125) --- 6th term: (3/5)^2(18/125) ---- 7th term: (3/5)^3(18/125) ============================ Cheers, Stan H.

Inequalities/385819: 6. Write an inequality to describe all the points on the coordinate plane above y = -4. A. y < 4 B. y > -4 C. y > 4 D. y < -4 1 solutions Answer 272881 by stanbon(57203)   on 2010-12-13 21:56:32 (Show Source): You can put this solution on YOUR website! Write an inequality to describe all the points on the coordinate plane above y = -4. Ans: y > -4 ============= Cheers, Stan H.

Probability-and-statistics/385745: A set of final examination grades in an introductory statistics course was founded to be normally distributed with a mean of 73 and a standard deviation of 8. a. what is the probability of getting at most a grade of 91 on the exam? b. what percentage of students scored between 65 and 85? c. what percentage of students scored between81 and 89? d. what is the final exam grade in only 5% of the students taking the test scored higher? e. If the professor "curves"( gives A`s to the top 10% of the class regardless of the score), are you better off with a grade of 81on this exam or a grade of 68 on a different exam where the mean is 62 and the standard deviation is 3? show statistically and explain Include a normal distribution curve 1 solutions Answer 272880 by stanbon(57203)   on 2010-12-13 21:47:16 (Show Source): You can put this solution on YOUR website! A set of final examination grades in an introductory statistics course was founded to be normally distributed with a mean of 73 and a standard deviation of 8. a. what is the probability of getting at most a grade of 91 on the exam? --- z(91) = (91-73)/8 = 2.25 P(x <= 91) = P(z < 2.25) = 0.9878 ------------------------------------------------------- b. what percentage of students scored between 65 and 85? P(65 < x < 85) = 0.7745 ---------------------------------- c. what percentage of students scored between81 and 89? P(81< x <89) = 0.1359 ------------------------ d. what is the final exam grade if only 5% of the students taking the test scored higher? Find the z-value with a right tail of 5%: z = 1.645 Find the corresponding exam score: x = zs+u x = 1.645*8+73 x = 86.16 ============= e. If the professor "curves"( gives A`s to the top 10% of the class regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam where the mean is 62 and the standard deviation is 3? show statistically and explain Include a normal distribution curve I'll leave that to you. cheers, Stan H.

Mixture_Word_Problems/385787: how many pounds of 40 cent nuts and how many pounds of 25 cent nuts must you a dealer use to produce a misture of 90 pounds to sell at 31 cents per pound? 1 solutions Answer 272878 by stanbon(57203)   on 2010-12-13 21:17:26 (Show Source): You can put this solution on YOUR website! how many pounds of 40 cent nuts and how many pounds of 25 cent nuts must you a dealer use to produce a misture of 90 pounds to sell at 31 cents per pound? --------- Equations: Quantity: x + y = 90 lbs Value:::40x + 25y = 31*90 cents ---------------------------------- Multiply Quantity by 40 ---- 40x + 40y = 40*90 --- Subtract from Value and solve for "y": -15y = -9*90 y = 54 lbs (amt. of 25 cent nuts needed in the mixture) --- Since x+y = 90, x = 36 lbs (amt. of 40 cent nuts needed in the mixture) ------ Cheers, Stan H.

percentage/385788: what percentage of 600 is 750. 1 solutions Answer 272876 by stanbon(57203)   on 2010-12-13 20:55:43 (Show Source): You can put this solution on YOUR website! what percentage of 600 is 750 ---- x/100 = 750/600 --- x = 100(750/600) --- x = 750/6 --- x = 125% ============== Cheers, Stan H.

Linear-equations/385783: find the intercepts then use them to graph the equation: 1.1x-1.9y=4.18 1 solutions Answer 272875 by stanbon(57203)   on 2010-12-13 20:52:20 (Show Source): You can put this solution on YOUR website! find the intercepts then use them to graph the equation: 1.1x-1.9y=4.18 --- Multiply thru by 100 to get rid of the decimals. ---- 110x - 190y = 418 --- x-intercept = ? Let y = 0, then x = 418/110 = 3.8 ---- y-intercept = ? Let x = 0, then y = 418/-190 = -2.2 ======================= Plot (0,-2.2) and (3.8,0) and draw a line thru them to get: ========================== Cheers, Stan H. =========

logarithm/385774: Rewrite the expression as a single logarithm: log(3,5) + 5log(3,2) 1 solutions Answer 272873 by stanbon(57203)   on 2010-12-13 20:44:56 (Show Source): You can put this solution on YOUR website! Rewrite the expression as a single logarithm: log(3,5) + 5log(3,2) ---- log3(6)+5log3(2) -------- = log3(6)+log3(2^5) --- = log3(6)+log3(32) --- = log3[6*32] --- = log3[192] =============== Cheers, Stan H.

Percentage-and-ratio-word-problems/385766: Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in 1 year, then how much did she invest in each fund? 1 solutions Answer 272869 by stanbon(57203)   on 2010-12-13 20:39:19 (Show Source): You can put this solution on YOUR website! Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. ------------------------- She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in 1 year, then how much did she invest in each fund? ----- Equations: Quantity Eq::: x + y = 30000 Interest Eq::: 0.16x+0.25y = 6060 --- Multiply the Quantity Eq. by 16 Multiply the Interest Eq. by 100 ---------------------------- 16x + 16y = 16*30000 16x + 25y = 606000 ------------------------ Subtract and solve for "y": 9y = 126000 ---- y = $14000 (amt. invested at 25% --- Since x+y= 30000, x = $16000 (amt. invested at 16%) ============== Cheers, Stan H. -------

percentage/385768: roger has completed 78% of his 200 page thesis.how many pages has he written 1 solutions Answer 272862 by stanbon(57203)   on 2010-12-13 20:18:21 (Show Source): You can put this solution on YOUR website! roger has completed 78% of his 200 page thesis.how many pages has he written ---- # of pages = 0.78*200 = 156 ============= Cheers, Stan H.

test/385756: 8y over 4 equals 2y 1 solutions Answer 272861 by stanbon(57203)   on 2010-12-13 20:15:59 (Show Source): You can put this solution on YOUR website! 8y over 4 equals 2y ---- (8y)/4 = 2y That is true for all Real Numbers. It is an identity. Cheers, Stan H.

Probability-and-statistics/385634: a coin is flipped five times. find the number of possible sets of heads and tails that have each of the follwing a. 0 heads b. 2 heads 1 solutions Answer 272829 by stanbon(57203)   on 2010-12-13 18:55:04 (Show Source): You can put this solution on YOUR website! a coin is flipped five times. find the number of possible sets of heads and tails that have each of the follwing --- Binomial Problem with n = 5 and p = 1/2 ---- a. P(0 heads) = (1/2)^5 = 1/32 ------ b. P(2 heads) = 5C2(1/2)^5 = 10/32 5/16 ============== Cheers, Stan H.

Exponents/385695: -3x over 8 times 16x over 9 1 solutions Answer 272823 by stanbon(57203)   on 2010-12-13 18:39:04 (Show Source): You can put this solution on YOUR website! -3x over 8 times 16x over 9 -------- [-3x/8] --- Cancel any factor that is common to a numerator and a denominator. ---- = [-x/1] ---- = -(2/3)x^2 ============ Cheers, Stan H.

logarithm/385685: ln(2x-1)=8 1 solutions Answer 272819 by stanbon(57203)   on 2010-12-13 18:33:44 (Show Source): You can put this solution on YOUR website! ln(2x-1)=8 ----- 2x-1 = e^8 2x = e^(8) +1 2x = 2981.96 ---- x = 1490.98 ====================== Cheers, Stan H.

logarithm/385687: ln2+lnx=5 1 solutions Answer 272814 by stanbon(57203)   on 2010-12-13 18:27:11 (Show Source): You can put this solution on YOUR website! ln2+lnx=5 ---- ln[2x] = 5 --- 2x = e^5 --- 2x = 148.41 --- x = 74.205 =============== Cheers, Stan H.

logarithm/385683: log3x+log9=0 1 solutions Answer 272812 by stanbon(57203)   on 2010-12-13 18:23:57 (Show Source): You can put this solution on YOUR website! log3x+log9=0 ---- log[9*3x] = 0 ---- 27x = 10^0 --- 27x = 1 x = 1/27 ========== Cheers, Stan H.

Quadratic_Equations/385671: Twelve less than the square root of a number is the same as 4 times the number. Find the number 1 solutions Answer 272810 by stanbon(57203)   on 2010-12-13 18:19:07 (Show Source): You can put this solution on YOUR website! Twelve less than the square root of a number is the same as 4 times the number. Find the number ------------------ Equation: sqrt(x) - 12 = 4x --------- Rearrange: sqrt(x) = 4x+12 --- Square both sides to get: x = 16x^2 + 96x + 144 ---- 16x^2 + 95x + 144 = 0 -------- Positive solution: There is no positive soltion. ========================= Cheers, Stan H.

Travel_Word_Problems/385663: if i average 20 miles per hour on the way to a show and 30 miles per hour on the way back what was the average speed for the whole trip? 1 solutions Answer 272803 by stanbon(57203)   on 2010-12-13 18:10:24 (Show Source): You can put this solution on YOUR website! If i average 20 miles per hour on the way to a show and 30 miles per hour on the way back what was the average speed for the whole trip? ---- To the show: rate = 20 mph ; distance = x miles ; time = x/20 hrs. ------------------- From the show: rate = 30 mph ; distance = x miles ; time = x/30 hrs. ---- Average for the whole trip = total distance/ total time = (2x)/[x/20 + x/30] --- = (2x)/[(30x+20x)/600] --- = (2x)/[50x/600] --- = 2x[600/50x] = 2[12] = 24 mph ========== Cheers, Stan H.