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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

Finance/251753: snookers Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out three times as many units of plywood as lumber. it makes a profit of $20 on a unit of lumber and $50 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $17680? Snookers Lumber must produce and sell _ units of lumber and _ units of plywood to make a profit of $15680. A disc jockey must play 12 commercial spots during 1 hour of a radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 8 min, how many 30-second commercials were played that hour? How many 60-second commercials? 1 solutions Answer 183432 by stanbon(57203)   on 2009-12-20 17:30:46 (Show Source): You can put this solution on YOUR website! Snookers Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out three times as many units of plywood as lumber. it makes a profit of $20 on a unit of lumber and $50 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $15680? Snookers Lumber must produce and sell _ units of lumber and _ units of plywood to make a profit of $15680. ---- Value Equation: 20L + 50P = 17680 Quantity Eq:::: P = 3L --- Substitute for "P" and solve for "L": 20L + 50*3L = 15680 20L + 150L = 15680 70L = 15680 L = 224 (# of units of lumber produced and sold) --- P = 3L ; P = 3*224 = 672 (# of units of plywood produced and sold) ======================================================================= A disc jockey must play 12 commercial spots during 1 hour of a radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 8 min, how many 30-second commercials were played that hour? How many 60-second commercials? --- Equation: T + S = 12 30T + 60S = 8*60 seconds ------------------------------ T = 12-S Substitute for T and solve for "S": 30(12-S) + 60S = 8*60 30*12 - 30S + 60S = 8*60 30S = 480-360 30S = 120 S = 4 (# of sixty seconds commercials) ---- Since T = 12-S, T = 8 (@ of thirty second commercials) =========================== Cheers, Stan H.

Expressions-with-variables/251745: I would love some help with this problem. Jack can mow a lawn in 3 hours. Marilyn can mow the same lawn in 4 hours. How much time will it take if they do it together? Thank you so much for any help!!! 1 solutions Answer 183431 by stanbon(57203)   on 2009-12-20 17:05:59 (Show Source): You can put this solution on YOUR website! Jack can mow a lawn in 3 hours. Marilyn can mow the same lawn in 4 hours. How much time will it take if they do it together? ------------ Jack rate = 1/3 job/hr Marilyn rate = 1/4 job/hr Together rate = 1/x job/hr ---------------------------- Equation: rate + rate + together rate 1/3 + 1/4 = 1/x Multiply thru by 12x 4x + 3x = 12 7x = 12 x = 12/7 = 1 5/12 hrs (time needed for the job if they work together) x = 1 hr 25 minutes ======================== Cheers, Stan H.

Linear-systems/251743: 1. The question is Write a linear equation for the cost of EACH band 2. Find the number of tickets for which the cost of the two bands will be equal. Band A charges $600 to play for the entire evening. Band B charges $350 plus $1.25 for each ticket sold. 1 solutions Answer 183428 by stanbon(57203)   on 2009-12-20 16:21:13 (Show Source): You can put this solution on YOUR website! The question is Write a linear equation for the cost of EACH band Band A charges $600 to play for the entire evening. A(x) = $600 --- Band B charges $350 plus $1.25 for each ticket sold. B(x) = 350 + 1.25x where x is the number of tickets sold. ---- 2. Find the number of tickets for which the cost of the two bands will be equal. A(x) = B(x) 600 = 350 + 1.25x 1.25x = 250 x = 200 (# of tickets sold to make the costs equal) ================ Cheers, Stan H.

Probability-and-statistics/251649: a hypothesis will test that two population means are equal. a sample of 10 with a standard deviation of 3 is selected from the first population and a smaple of 3 is selected from the first population. the standard deviations are not equal. testing the claim at the .01 level, what is the critical value? Assume unequal standard deviations a. 2.845 b. 2.787 c. 2.807 d. 2.977 1 solutions Answer 183408 by stanbon(57203)   on 2009-12-20 13:40:55 (Show Source): You can put this solution on YOUR website! a hypothesis will test that two population means are equal. a sample of 10 with a standard deviation of 3 is selected from the first population and a sample of 3 is selected from the first population with standard deviation = 8. The standard deviations are not equal. Testing the claim at the .01 level, what is the critical value? Assume unequal standard deviations ============ df = n1+n2-2 = 10+3-2 = 11 --- Critical value for 2-tail test, when df=11 and alpha = 1% = invT(0.995,11) = 3.1058 ===================== That is not one of your listed answers but it is the critical value for your posted problem. --------------------- Cheers, Stan H. --------------- a. 2.845 b. 2.787 c. 2.807 d. 2.977

Probability-and-statistics/251724: Bob is planning to pack 6 shirts and 4 pairs of pants for a trip. If he has 11 shirts and 10 pairs of pants to choose from, in how many different ways can this be done? 1 solutions Answer 183407 by stanbon(57203)   on 2009-12-20 13:32:42 (Show Source): You can put this solution on YOUR website! Bob is planning to pack 6 shirts and 4 pairs of pants for a trip. If he has 11 shirts and 10 pairs of pants to choose from, in how many different ways can this be done? ----- Pick 6 shirts: 11C6 ways Pick 4 pair pants: 10C4 ---------------------------- Total ways: 462*210 = 97020 ways --- Cheers, Stan H.

Probability-and-statistics/251650: which of the following conditions must be met to conduct a test for the difference in two sample means? a. data must be at least of interval scale b. populations must be normal c. variance in the two populations must be equal d. a and b are correct e. a, b, and c are correct 1 solutions Answer 183406 by stanbon(57203)   on 2009-12-20 13:29:05 (Show Source): You can put this solution on YOUR website! Ans: d Cheers, Stan H.

Probability-and-statistics/251651: adinistering the same test to a group of 15 students and a sceond group of 15 students to see which group scpres higher is an example of a. a one sample test of means b. a two sample test of means c. a paired t-test d. a test of proportions 1 solutions Answer 183405 by stanbon(57203)   on 2009-12-20 13:27:24 (Show Source): You can put this solution on YOUR website! Ans: b Cheers, Stan H.

Probability-and-statistics/251652: if two samples, one of size 14 and the sceond of size 13, are used to test the difference between population means, how many dgrees of freedom are used to find the critical value? Assume the population standard deviations are equal a. 27 b. 26 c. 25 d. 14 e. 13 1 solutions Answer 183403 by stanbon(57203)   on 2009-12-20 13:25:57 (Show Source): You can put this solution on YOUR website! if two samples, one of size 14 and the sceond of size 13, are used to test the difference between population means, how many dgrees of freedom are used to find the critical value? Assume the population standard deviations are equal --- df = n1+n2-2 = 27-2 = 25 ============ Cheers, Stan H. a. 27 b. 26 c. 25 d. 14 e. 13

Travel_Word_Problems/251676: Two freight trains, 120 miles apart, start toward each other. Each train is traveling at a rate of 40 miles per hour. A carrier pigeon on the first train flies to the second train, then flies back to the first train, and continues to fly back and forth in this way from one train to the other at a constant rate of 60 mph until the trains meet. How many miles does the pigeon fly? a) 120 b) 110 c) 100 d) 90 e) none of these 1 solutions Answer 183367 by stanbon(57203)   on 2009-12-20 10:20:11 (Show Source): You can put this solution on YOUR website! Two freight trains, 120 miles apart, start toward each other. Each train is traveling at a rate of 40 miles per hour. A carrier pigeon on the first train flies to the second train, then flies back to the first train, and continues to fly back and forth in this way from one train to the other at a constant rate of 60 mph until the trains meet. How many miles does the pigeon fly? ------------------- 1st: Determine the time required till the trains meet. The closing speed is 40+40 = 80 mph --- distance / rate = time 120/80 = 1.5 hrs ----------------------- 2nd: Determine how far the pigeon can fly in that amount of time. Distance = rate*time Distance = 60 mph *1.5 hrs Distance = 90 miles (the pigeon flies 90 miles) ========================================================= a) 120 b) 110 c) 100 d) 90 e) none of these ========================================================= Cheers, Stan H.

Linear-systems/251683: how do I solve these problems: y = x - 600 = y = 1.25X + 350 = 1 solutions Answer 183364 by stanbon(57203)   on 2009-12-20 10:15:48 (Show Source): You can put this solution on YOUR website! how do I solve these problems: y = x - 600 = y = 1.25X + 350 = ---------------------- substitute to get: x-600 = 1.25x+350 0.25x = -950 x = -3000 ===================== Substitute to solve for "y": y = -3000-600 y = - 3600 ======================= Cheers, Stan H.

Mixture_Word_Problems/251686: A boy made 40 quarts of lemonade, which contained 20% lemon. How much water would he have to add to reduce it to 10% lemon? 1 solutions Answer 183362 by stanbon(57203)   on 2009-12-20 10:12:31 (Show Source): You can put this solution on YOUR website! A boy made 40 quarts of lemonade, which contained 20% lemon. How much water would he have to add to reduce it to 10% lemon? ----------------------------- Equation: lemon + lemon = lemon 0.20*40 + 0*x = 0.10(40+x) Multiply thru by 100 to get: 20*40 + 0 = 10*40 + 10x 10x = 10*40 x = 40 guarts (amt. of water needed for the mixture) ================== Cheers, Stan H.

Probability-and-statistics/251653: 20 randomly selected statistics students were given 15 multiple choice questions and 15 open ended questions all on the same material. the professor was interested in determining which type of questions the students scored higher. This experiment is an example of a. a one sample test of means b. a two sample test of means c. a paired t-test d. a test pf proportions 1 solutions Answer 183360 by stanbon(57203)   on 2009-12-20 10:08:43 (Show Source): You can put this solution on YOUR website! Ans: paired t-test Cheers, Stan H.

Probability-and-statistics/251654: if an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate? a. too many degrees of freedom b. no difference between the population means c. a difference at least one paor of population means d. none of the above 1 solutions Answer 183359 by stanbon(57203)   on 2009-12-20 10:06:00 (Show Source): You can put this solution on YOUR website! if an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate? a. too many degrees of freedom b. no difference between the population means c. a difference at least one pair of population means d. none of the above Ans: c ------------- Cheers, Stan H.

Probability-and-statistics/251685: how many samples of size 3 can be drawn from s={2,4,8,10,12,}, (a) with replacement, (b) without replacement 1 solutions Answer 183358 by stanbon(57203)   on 2009-12-20 10:03:56 (Show Source): You can put this solution on YOUR website! how many samples of size 3 can be drawn from s={2,4,8,10,12,}, (a) with replacement: 5^3 = 125 ------------------ (b) without replacement: 5P3 = 5*4*3 = 60 ------ Cheers, Stan H.

Probability-and-statistics/251655: a preliminary study of hourly wages paid to unskilled employees in three metropolitian areas was conducted. seven employees were included from area a, 9 from area b and 12 from area c. the test statistic was computed to be 4.91. What can we conclude at the .05 level? a. mean hourly wages of unskilled employees all areas are equal b. mean hourly wages in at least 2 metropolitian areas are different c. more degrees of freedom are needed d. none of these are correct 1 solutions Answer 183357 by stanbon(57203)   on 2009-12-20 09:59:05 (Show Source): You can put this solution on YOUR website! A preliminary study of hourly wages paid to unskilled employees in three metropolitian areas was conducted. seven employees were included from area a, 9 from area b and 12 from area c. ----- the test statistic was computed to be 4.91. What can we conclude at the .05 level? ---------- Determine the degrees of freedom of the test. c = number of categories = 3 n = number of subjects = 28 --- Then F(sub c-1,n-c) = F(2,25) = ? In F-chart df = 2 for numerator; df= 25 for denominator. F-chart value for right-tail test with alpha = 5% is 3.39 ---- Conclusion: Since the test stat is greater than the critical value reject Ho. Answer: b =============== Cheers, Stan H. =============== a. mean hourly wages of unskilled employees all areas are equal b. mean hourly wages in at least 2 metropolitian areas are different c. more degrees of freedom are needed d. none of these are correct

Probability-and-statistics/251656: what is our decision regarding the differences between the observed and expected frequencies if the critical value of cji-squared is 9.488 and the computed value is 6.079 a. the difference is probably due to sampling erroe; do not reject the null hypothesis b. not due to chance; reject the null hypothesis c. not due to chance ; do not reject the alternative hypothesis d. too close; reserve judgement 1 solutions Answer 183354 by stanbon(57203)   on 2009-12-20 09:36:39 (Show Source): You can put this solution on YOUR website! what is our decision regarding the differences between the observed and expected frequencies if the critical value of cji-squared is 9.488 and the computed value is 6.079 --- Since the computed value is less than the critical value do not reject Ho. Answer: c --- Cheers, Stan H. --- a. the difference is probably due to sampling erroe; do not reject the null hypothesis b. not due to chance; reject the null hypothesis c. not due to chance ; do not reject the alternative hypothesis d. too close; reserve judgement

Divisibility_and_Prime_Numbers/251681: Find the sum of all the integers divisible by 7 between 32 and 5000. a) 1,514,285 b) 1,515,285 c) 1,615,185 d) 1,786,715 e) none of these 1 solutions Answer 183352 by stanbon(57203)   on 2009-12-20 09:32:13 (Show Source): You can put this solution on YOUR website! Find the sum of all the integers divisible by 7 between 32 and 5000. --- It would be an arithmetic series with: a(1) = 35 = 5*7 a(n) = 4998 = 714*7 So n = (714-5)+1 = 710 ---- Formula: S(n) = (n/2)(a(1)+a(n)) S(708) = (710/2)(35 + 4998) = 1,786,715 ============= Cheers, Stan H. a) 1,514,285 b) 1,515,285 c) 1,615,185 d) 1,786,715 e) none of these -----------

Probability-and-statistics/251657: for a junit change in the first independent variable with other things being held constant, what change can be expected in the dependent variable in the multiple regression equation Y= 5.2 + 6.3X1-7.1X2 a. -7.1 b. +6.3 c. +5.2 d. +4.4 1 solutions Answer 183350 by stanbon(57203)   on 2009-12-20 09:18:24 (Show Source): You can put this solution on YOUR website! for a junit change in the first independent variable with other things being held constant, what change can be expected in the dependent variable in the multiple regression equation Y= 5.2 + 6.3X1-7.1X2 --- If X1 increases by one, y increases by 6.3. Cheers, Stan H. a. -7.1 b. +6.3 c. +5.2 d. +4.4

Probability-and-statistics/251672: You know that houses in your school district sell for a mean of $350,000 with a standard deviation of $50,000. Assume they follow a normal distribution. You are looking for a new home in your school district, and want to spend between $280,000 and $340,000. What percentage of homes are within your budget? 1 solutions Answer 183348 by stanbon(57203)   on 2009-12-20 09:16:01 (Show Source): You can put this solution on YOUR website! You know that houses in your school district sell for a mean of $350,000 with a standard deviation of $50,000. Assume they follow a normal distribution. You are looking for a new home in your school district, and want to spend between $280,000 and $340,000. What percentage of homes are within your budget? ---------------- Find the z-score of 280000 and 340000 The P(280,000< x < 340000) = P(z is between those z-scores you found) --- I got Prob = 0.34 using a TI calculator and the command normalcdf(280000,340000,350000,50000). =============== Cheers, Stan H.

Linear-systems/251638: I don't under stand how come i have to put 3x to the right and divide by 2 on this question, (3x + 2y = 6) and i really just don't understand how to do these 1 solutions Answer 183323 by stanbon(57203)   on 2009-12-19 22:48:31 (Show Source): You can put this solution on YOUR website! I don't under stand how come i have to put 3x to the right and divide by 2 on this question, (3x + 2y = 6) and i really just don't understand how to do these ------------ If you want to write the equation in slope-intercept form you have to isolate "Y" on one side of the equal sign. --------------------- Start: 3x + 2y = 6 Subtract 3x from both sides to get: 2y = -3x+6 Divide both sides by 2 to isolate "y": y = (-3/2)x+3 ================== Cheers, Stan H.

logarithm/251637: log (225x2) = 3.456 1 solutions Answer 183322 by stanbon(57203)   on 2009-12-19 22:45:09 (Show Source): You can put this solution on YOUR website! log (225x2) = 3.456 --- log(225x^2) = 3.456 225x^2 = 10^3.456 225x^2 = 2857.5905 x^2 = 12.7004 x = 3.5638 or x = -3.5648 ============================= Cheers, Stan H.

Percentage-and-ratio-word-problems/251501: The ratio of the number of boys to the number of girls in a room is 5:7. When 24 more boys enter, the ratio is reversed. How many girls are in the room? a) 29 b) 32 c) 35 d) 36 e) none of these 1 solutions Answer 183312 by stanbon(57203)   on 2009-12-19 22:00:22 (Show Source): You can put this solution on YOUR website! The ratio of the number of boys to the number of girls in a room is 5:7. 5:7 is the same as 5x:7x where 5x is the # of boys and 7x is the number of girls. --------------------------------- When 24 more boys enter, the ratio is reversed. # of boys = 5x+24 # of girls is still 7x Ratio is 7:5 --- Equation: (5x+24)/(7x) = 7/5 Cross-multiply: 25x+120 = 49x 24x = 120 x = 5 --- How many girls are in the room? 7x = 35 (# of girls in the room) Cheers, Stan H. a) 29 b) 32 c) 35 d) 36 e) none of these

Quadratic-relations-and-conic-sections/251606: what is the intercepts, axis of symmetry and vertex of y=3x^2+12x+16 1 solutions Answer 183311 by stanbon(57203)   on 2009-12-19 21:49:40 (Show Source): You can put this solution on YOUR website! what is the intercepts, axis of symmetry and vertex of y=3x^2+12x+16 ----------- y-intercept: Let x = 0, then y = 16 ------------ x-intercepts: Solve 3x^2+12x+16 = 0 x = [-12 +- sqrt(144 - 4*3*16)]/6 --- x = [-12 +- sqrt(-48)]/6 Since the discriminant is negative there are no x-intercepts. ------------ Vertex occurs where x = -b/2a = -12/(2*3) = -2 f(-2) = 3(4)+12(-2)+16 = 28-24 = 4 --- Vertex (-2,4) --- Axis of symmetry is x=-b/2a = -2 -------------------------------------- ========================================= Cheers, Stan H.

Probability-and-statistics/251621: if the 1% level of signisicanc e is used and the computed value of z is +6.00, what is our decision? a. do not reject HO b. Reject HO c. Reject H1 d. none of the above 1 solutions Answer 183308 by stanbon(57203)   on 2009-12-19 21:34:33 (Show Source): You can put this solution on YOUR website! if the 1% level of signisicanc e is used and the computed value of z is +6.00, what is our decision? Reject HO. That test result is 6 sigmas above the hypothesized mean. That choice of mean is very, very shaky. Reject it. ===================================================== Cheers, Stan H. a. do not reject HO b. Reject HO c. Reject H1 d. none of the above

Probability-and-statistics/251620: mileage test are conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was found to be 50,000 miles with a standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires? a. 50,000 b. 3,500 c. 50,000/100 d. 3,500/100 1 solutions Answer 183306 by stanbon(57203)   on 2009-12-19 21:30:46 (Show Source): You can put this solution on YOUR website! mileage test are conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was found to be 50,000 miles with a standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires? ----------- The best point estimate is the sample mean: 50,000 ====================================== Cheers, Stan H. a. 50,000 b. 3,500 c. 50,000/100 d. 3,500/100

Numbers_Word_Problems/251617: (3x-2y)sq. 1 solutions Answer 183305 by stanbon(57203)   on 2009-12-19 21:27:57 (Show Source): You can put this solution on YOUR website! (3x-2y)sq. (3x-2y)^2 = (3x)^2-2(3x)(2y)+(2y)^2 --- = 9x^2 - 12xy + 4y^2 ======================== Cheers, Stan H.

Probability-and-statistics/251598: The number of dry cleaning orders picked up at Sunny Fresh Dry Cleaners was sampled over 4 hour periods. Compute the sample mean, median, mode, and midrange. Compute the 1st and 3rd quartiles and interpret their meanings. I have the answers for mode, median, midrange, mean and the quartiles. I do not understand about interpreting their meanings. Mean: 51.6 or 52 Median: 58 Mode: 61 Midrange: 46 Q1: 43.5 Q3: 61 Please help me interpret their meanings, as I have no idea what that means. 1 solutions Answer 183300 by stanbon(57203)   on 2009-12-19 21:01:05 (Show Source): You can put this solution on YOUR website! Plot those figures on a horizontal line. Try to draw a density curve over the line that reflects the meaning of some of those values.. --------------------- The data is skewed left and is heavily weighted at the right. Shows the majority of the pick-ups are iin the 4th timing segment which is toward the end of the business day. Cheers, Stan H.

Miscellaneous_Word_Problems/251609: Help please. Thanks 1. The space in a landfill decreases with time as given by the function f(t)=270-70 log5(4t+1). Where t is measured in years. How much space is left when t =1? 1 solutions Answer 183296 by stanbon(57203)   on 2009-12-19 20:22:20 (Show Source): You can put this solution on YOUR website! The space in a landfill decreases with time as given by the function f(t)=270-70 log5(4t+1). Where t is measured in years. How much space is left when t =1? ------------------------- f(t) = 270 - 70*log5(4t+1) --- f(1) = 270 - 70*log5(5) f(1) = 270 - 70*1 f(1) = 200 cu units =================== Cheers, Stan H.

Travel_Word_Problems/251611: On a farm there are horses and chickens. There are total of 40 heads and 146 legs. How many horses are on the farm?" the horses have 3 legs that is all I got I cant help my kid he has this on a test I need to be able to show him how to solve it the numbes can change but they always have 3 legs 1 solutions Answer 183293 by stanbon(57203)   on 2009-12-19 20:18:42 (Show Source): You can put this solution on YOUR website! On a farm there are horses and chickens. There are total of 40 heads and 146 legs. How many horses are on the farm? ---------------- If horses have only three legs you get the following. If there are "h" horses the number of heads is h; the number of legs is 3h. --- If there are "c" chickens the number of heads is c; the number of legs is 2c. -------------------- Equations: Heads: h + c = 40 Legs::3h + 2c = 146 ---------------------------- Solve the 1st equation for "h": h = 40-c --- Substitute that into the Legs equation and solve for "c": 3(40-c)+2c = 146 120-3c + 2c = 146 -c = 26 c = -26 (# of chickens is -26) I guess that makes as much sense as saying the horses have 3 legs. --- Since h = 40-c, h = 40--26 = 66 (# of horses is 66) ==================================================== Cheers, Stan H.

Linear-systems/251603: i need to solve this problem by a system of 3 equations: A piggy bank contains 40 coins consisting of nickels, dimes, and quarters. the sum of the number of dimes and quarters is 10 coins less than the number of nickels. if the number of quarters and nickels were reversed, with the same amount of dimes, the value of the coins would be $7.50. find the number of each type of coin that is in the piggy bank. i tried these three equations with no luck: n+d+q=40 d+q=n-10 10d+25q+5n=750 1 solutions Answer 183292 by stanbon(57203)   on 2009-12-19 20:11:38 (Show Source): You can put this solution on YOUR website! i need to solve this problem by a system of 3 equations: A piggy bank contains 40 coins consisting of nickels, dimes, and quarters. the sum of the number of dimes and quarters is 10 coins less than the number of nickels. if the number of quarters and nickels were reversed, with the same amount of dimes, the value of the coins would be $7.50. find the number of each type of coin that is in the piggy bank. i tried these three equations with no luck: n+d+q=40 d+q=n-10 10d+25q+5n=750 -------------------------- Change your 3rd equation to 25n + 10d + 5q = 750 ---- Gather the equations: n + d + q = 40 n - d - q = 10 25n+10d +5q = 750 ------------------------- I used a matrix method and got: n = 25 (# of nickels) d = 10 (# of dimes) q = 5 (# of quarters) ============================ Cheers, Stan H.

Linear-systems/251605: I need to solve this problem with a system of three equations for age: The sum of the ages of three brothers, Andre, Brad, and Carlos is 48. In ten years, twice Brad's age will be 3 years less than the sum of his brothers ages. Six years ago, Carlos' age was four years younger than the sum of his brothers ages. How old are the brothers now? i failed with these equations: a+b+c=48 b+10=(a+c)-7 c-6=(b+a)-6 1 solutions Answer 183290 by stanbon(57203)   on 2009-12-19 19:57:15 (Show Source): You can put this solution on YOUR website! i need to solve this problem with a system of three equations for age: The sum of the ages of three brothers, Andre, Brad, and Carlos is 48. a + b + c = 48 --- In ten years, twice Brad's age will be 3 years less than the sum of his brothers ages. six years ago, 2(b+10) = (a-6) + (c-6)-3 2b+20 = a+c-15 a - 2b +c = 35 --- Carlos's age was four years younger than the sum of his brothers ages. c = a + b - 4 a + b - c = 4 ------------------------ how old are the brothers now? --------- Gather the equations: a + b + c = 48 a - 2b + c = 35 a + b - c = 4 ---------------------------- I used a matrix method and got: a = 21 2/3 b = 4 1/3 c = 22 ============= Cheers, Stan H.