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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299, >>Next

Probability-and-statistics/483269: In a clinical trial 250 patients are randomly assigned to receive either a proposed stroke prevention medication ( ) or a placebo ( ) and are followed over the course of a 5-years study period. These results are given in the following table: Treatment Group Event Stroke No Stroke Total 12 108 120 28 102 130 Total 40 210 250 a. Estimate the risk of stroke comparing those on the medication to those on placebo and interpret the result. b. Interpret your result in part a. 1 solutions Answer 330744 by stanbon(57347)   on 2011-08-19 07:49:53 (Show Source): You can put this solution on YOUR website! In a clinical trial 250 patients are randomly assigned to receive either a proposed stroke prevention medication ( ) or a placebo ( ) and are followed over the course of a 5-years study period. These results are given in the following table: Treatment Group Event Stroke No Stroke Total ::::::12 108 120 ::::::28 102 130 Total 40 210 250 -------------------- I'll assume the "12" refers to the treatment group and the 28 is the not-treatment group. --- So p-hat = 12/120 = 0.10 for the treatment group and p-hat = 28/130 = 0.22 for the non-treatment group ---- Ho: p1-p2 = 0 H1: p1-p2 < 0 --- test stat: (0.10-0.22)/sqrt[(0.1*0.9/120)+(0.22*0.78/130)] = -2.6375 --- p-value = P(z < -2.6375) = 0.0042 ---------- Conclusion: Since the p-value is less than 1%, reject Ho at the 1% significance level. ================================================== a. Estimate the risk of stroke comparing those on the medication to those on placebo and interpret the result. b. Interpret your result in part a. The non-treatment group is twice as liable have a stroke. ============================================================ Cheers, Stan H.

Quadratic_Equations/483204: y^2+6y+34=0 solve by "completing the square" 1 solutions Answer 330690 by stanbon(57347)   on 2011-08-18 22:45:27 (Show Source): You can put this solution on YOUR website! y^2+6y+34=0 solve by "completing the square" --- y^2+6y + ? = -34 + ? --- y^2+6y+9 = -34+9 ---- (y+3)^2 = -25 ---- y + 3 = 5i or y+3 = -5i ----- y = -3+5i or y = -3-5i =========================== cheers, stan H.

Linear-equations/483193: y = 2x + 3 y = 2x + 5 You know by looking at these two problems that the slope is the same for each equation (y = mx + b - the slope is 2) and they have a different y-intercept. First - what is the y-intercept for each of these equations? Second - can you say anything about this system of equations - visualize the solution? 1 solutions Answer 330689 by stanbon(57347)   on 2011-08-18 22:42:07 (Show Source): You can put this solution on YOUR website! y = 2x + 3 y = 2x + 5 You know by looking at these two problems that the slope is the same for each equation (y = mx + b - the slope is 2) and they have a different y-intercept. --------------------------- First - what is the y-intercept for each of these equations? 1st: 3 2nd: 5 ------------------- Second - can you say anything about this system of equations - visualize the solution? The line are parallel. They have no common point. The system has no solution. ---------------------------- Cheers, Stan H.

Permutations/483194: Hi, here's the question, "how many ways can 3 student representatives be chosen from 100. Here's my work: 100C3 = 100•99•98•97! / 3! 97! But the answer didn't come out right 1 solutions Answer 330685 by stanbon(57347)   on 2011-08-18 22:34:48 (Show Source): You can put this solution on YOUR website! "how many ways can 3 student representatives be chosen from 100. Here's my work: 100C3 = 100•99•98•97! / 3! 97! But the answer didn't come out right ----- Cancel the 97! in the numerator and the denominator to get: (100*99*98)/(1*2*3) = 161,700 ========== Cheers, Stan H. ==========

logarithm/483161: 9=3^2 In a logarithmic form 1 solutions Answer 330683 by stanbon(57347)   on 2011-08-18 22:30:59 (Show Source): You can put this solution on YOUR website! 9=3^2 In a logarithmic form ------ "log" means power or exponent. ---- Your problem has exponent = 2, base = 3 and result = 9 --- So, log3(9) = 2 ================== Cheers, Stan H.

Permutations/483173: 1.I make 5,000 more then 2 times Jack? How do I make this a algabraic equation? 1 solutions Answer 330681 by stanbon(57347)   on 2011-08-18 22:19:24 (Show Source): You can put this solution on YOUR website! I make 5,000 more then 2 times Jack? How do I make this a algabraic equation? ---- I = 2J + 5000 ======================= Cheers, Stan H.

Travel_Word_Problems/483190: Hello! Can anyone pls. answer this problem, it's all about distance/rate problem. I don't know how to start solving this problem. Pls. help me solve this. Problem: An automobile traveling at a certain rate can go from one province to another in 9 hours. If the rate were 12 kilometers per hour faster, the trip would require two hour less. What is the distance between provinces? Pls. do answer this problem. >>Thank You<< 1 solutions Answer 330679 by stanbon(57347)   on 2011-08-18 22:17:20 (Show Source): You can put this solution on YOUR website! An automobile traveling at a certain rate can go from one province to another in 9 hours. If the rate were 12 kilometers per hour faster, the trip would require two hour less. What is the distance between provinces? ----------------- 1st trip DATA: time = 9 hrs; rate = x kph ; distance = 9x km --------------- 2nd trip DATA: time = 7 hrs; rate = x+12 kph ; distance = 7(x+12) km -------------------- Equation: distance = distance 9x = 7(x+12) 9x = 7x + 84 --- 2x = 84 x = 42 ---- distance = 9*42 = 378 km ============================ Cheers, Stan H. =============

absolute-value/483180: 3|p-5|=2p 1 solutions Answer 330676 by stanbon(57347)   on 2011-08-18 22:11:22 (Show Source): You can put this solution on YOUR website! 3|p-5|=2p ----- |p-5| = (2/3)p --- p-5 = (2/3)p or p-5 = (-2/3)p ------ p = 5 + (2/3)p or p = 5+(-2/3)p (1/3)p = 5 or (5/3)p = 5 --- p = 15 or p = 3 =================== Cheers, Stan H.

Linear-equations/483185: the speed of an automobile in mph varies directly with its speed in kph. a speed of 64 mph is equivalent to a speed of 103 kph. write a linear equation that relates speed in miles per hour to speed in kph 1 solutions Answer 330674 by stanbon(57347)   on 2011-08-18 22:06:27 (Show Source): You can put this solution on YOUR website! the speed of an automobile in mph varies directly with its speed in kph. a speed of 64 mph is equivalent to a speed of 103 kph. write a linear equation that relates speed in miles per hour to speed in kph ---------------- mph = k*kph --- Solve for "k": 64 = k*103 k = 64/103 ---- mph = (64/103)kph ========================== Cheers, Stan H. ============

percentage/483186: find the number of residents in a city where 13% of the population, or 962 people, had influenza. 1 solutions Answer 330672 by stanbon(57347)   on 2011-08-18 22:02:39 (Show Source): You can put this solution on YOUR website! find the number of residents in a city where 13% of the population, or 962 people, had influenza. ----- Equation: 0.13x = 962 x = 962/0.13 x = 7400 (# of residents) ============================== Cheers, Stan H.

Numeric_Fractions/483148: Can some please help me!! Simplify by removing factors of 1. 1280u ^7 ^8/100u^2y^2 The simplified form is ___ 1 solutions Answer 330654 by stanbon(57347)   on 2011-08-18 20:58:10 (Show Source): You can put this solution on YOUR website! (1280u^7y^8) / (100u^2y^2) -------------------------------- = (1280/100)(u^7/u^2)(y^8/y^2) ----- = 12.8*u^5*y^6 ================== Cheers, Stan H. ============

Numeric_Fractions/483144: Can someone help me please solve?!! y^2-25/y ÷y-5/y+9 (Divide and simply)Type a fraction Leave answer in factor form 1 solutions Answer 330652 by stanbon(57347)   on 2011-08-18 20:54:12 (Show Source): You can put this solution on YOUR website! (y^2-25)/y ÷ (y-5)/(y+9) ------ Invert the denominator and multiply to get: (y^2-25)/y * (y+9)/(y-5) ---- Factor: [(y-5)(y+5)/y] ----- Cancel the common (y-5) factor: ---- = [(y+5)(y+9)]/y ==================== Cheers, Stan H. =============

Exponents/483145: The season attendance at your school's football games is 1000 people one year. The attendance doubles each year for the next 3 years. Write an expression with a power that shows the season attendance at the football games after 3 years. 1 solutions Answer 330648 by stanbon(57347)   on 2011-08-18 20:49:06 (Show Source): You can put this solution on YOUR website! The season attendance at your school's football games is 1000 people one year. The attendance doubles each year for the next 3 years. Write an expression with a power that shows the season attendance at the football games after 3 years. -------- 1st year: 1000 2nd year: 1000*2 3rd year: 1000*2^2 --- A(t) = 1000*2^x where t is the number of years. ============================================== Cheers, Stan H.

Numeric_Fractions/483146: What is the rational expression for this problem? Find all numbers for which the rational expression is -7/20x 1 solutions Answer 330646 by stanbon(57347)   on 2011-08-18 20:45:21 (Show Source): You can put this solution on YOUR website! duplicate

Numeric_Fractions/483147: What is the rational expression for this problem? Find all numbers for which the rational expression is undefined -7/20x 1 solutions Answer 330644 by stanbon(57347)   on 2011-08-18 20:44:31 (Show Source): You can put this solution on YOUR website! Find all numbers for which the rational expression is undefined -7/(20x) --- Undefined when x = 0. ================================ Cheers, Stan H. ============

Numbers_Word_Problems/483136: A super confusing word problem to an average math student. "A laboratory used 120 fence posts in an experiment comparing two types of paint. Six fewer than twice as many fence posts were painted with paint A as were painted with paint B. How many fence posts were painted with paint A? Paint B?" Would be glad to get your help! 1 solutions Answer 330642 by stanbon(57347)   on 2011-08-18 20:42:49 (Show Source): You can put this solution on YOUR website! A laboratory used 120 fence posts in an experiment comparing two types of paint. ------------ Six fewer than twice as many fence posts were painted with paint A as were painted with paint B. ----------------- How many fence posts were painted with paint A? Paint B?" ==== Equations: A + B = 120 posts A = 2B -6 ------------ Subtract for "A" and solve for "B": 2B-6 + B = 120 3B = 126 B = 42 (# of B-painted posts) ---- Solve for "A": A = 2B-6 A = 2*42-6 A = 84-6 A = 76 (# of A-painted posts) ============================== Cheers, Stan H. ==============

Probability-and-statistics/483100: Given a level of confidence of 95% and a population standard deviation of 9, answer the following: (A) What other information is necessary to find the sample size (n)? (B) Find the Maximum Error of Estimate (E) if n = 56. Show all your calculations. Show all work. Thank you so much 1 solutions Answer 330631 by stanbon(57347)   on 2011-08-18 20:12:44 (Show Source): You can put this solution on YOUR website! Given a level of confidence of 95% and a population standard deviation of 9, answer the following: (A) What other information is necessary to find the sample size (n)? n = [z*s/E]^2 Missing the maximum error. ================================= (B) Find the Maximum Error of Estimate (E) if n = 56. Show all your calculations. Show all work. ME = z*s/sqrt(n) ME = 1.96 = 2.3572 =================================== Cheers, Stan H.

Probability-and-statistics/483101: A sample of 102 golfers showed that their average score on a particular golf course was 88.55 with a standard deviation of 4.27. Answer each of the following (show all work and state the final answer to at least two decimal places.): (A) Find the 95% confidence interval of the mean score for all 102 golfers. (B) Find the 95% confidence interval of the mean score for all golfers if this is a sample of 135 golfers instead of a sample of 102. (C) Which confidence interval is smaller and why Thank you very much! 1 solutions Answer 330629 by stanbon(57347)   on 2011-08-18 20:05:37 (Show Source): You can put this solution on YOUR website! A sample of 102 golfers showed that their average score on a particular golf course was 88.55 with a standard deviation of 4.27. ----------------------- Answer each of the following (show all work and state the final answer to at least two decimal places.): ----------------------- (A) Find the 95% confidence interval of the mean score for all 102 golfers. x-bar = 88.55 ME = 1.96*4.25/sqrt(102) = 0.8248 -- 95% CI: 88.55-0.8248 < u < 88.55+0.8248 ============================================== (B) Find the 95% confidence interval of the mean score for all golfers if this is a sample of 135 golfers instead of a sample of 102. --- Same procedure but put 135 in place of 102 in the calculation. --------------------- (C) Which confidence interval is smaller and why The Confidence Interval is always twice as wide as the margin of error. And ME = z*s/sqrt(n) shows that ME and n are indirectly related. So, ME gets wider as sample size gets smaller. ---- Your sample size got larger (from 102 up to 135, so ME became smaller. So the CI became narrower for n = 135 then it was for n = 102. ========================= Cheers, Stan H.

Probability-and-statistics/483103: The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.93 inches and a standard deviation of 0.59 inches. Show all work. (A) What percentage of the grapefruits in this orchard is larger than 5.88 inches? (B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.88 inches? Thanks much 1 solutions Answer 330625 by stanbon(57347)   on 2011-08-18 19:56:35 (Show Source): You can put this solution on YOUR website! The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.93 inches and a standard deviation of 0.59 inches. Show all work. (A) What percentage of the grapefruits in this orchard is larger than 5.88 inches? ---- z(5.88) = (5.88-5.93)/0.59 = -0.0847 P(x > 5.88) = P(z > -0.0847) = 0.5338 =========================================== (B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.88 inches? z(5.88) = (5.88-5.93)/[0.59/sqrt(100)] = -0.8475 P(x-bar > 5.88) = P(z > -0.8475) = 0.8016 ============================================ Cheers, Stan H.

Probability-and-statistics/482894: If, in a sample of n=25 selected from a normal populatin, X=53 and S=10, what are the critical values of t level of significance, a, is 0.01, the null hypothesis, Ho, is u=50, and the alternative hypothesis, H1, is u not equal to 50? Critical value of t are +/-: round four decimal places. 1 solutions Answer 330616 by stanbon(57347)   on 2011-08-18 18:36:42 (Show Source): You can put this solution on YOUR website! If, in a sample of n=25 selected from a normal populatin, X=53 and S=10, what are the critical values of t level of significance, a, is 0.01, the null hypothesis, Ho, is u=50, and the alternative hypothesis, H1, is u not equal to 50? ----- The H1 implies this is a 2-tail test. So each tail has 0.005 of the t-values. --------------------------------------------------- InvT(0.005 when df = 24) = 2.7969 Critical value of t are +/-2.7969 -------- Cheers, Stan H.

Probability-and-statistics/482938: True or False: . The critical value of t required to reject a null hypothesis at a given type 1-level is larger for a two- tailed test than for a one-tailed test. 1 solutions Answer 330613 by stanbon(57347)   on 2011-08-18 18:26:02 (Show Source): You can put this solution on YOUR website! True or False: -------------------- The critical value of t required to reject a null hypothesis at a given type 1-level is larger for a two- tailed test than for a one-tailed test. ----------- Ans: True ================= Cheers, Stan H.

Probability-and-statistics/483075: Two numbered cubes are rolled, the first cube shows a 4 what is the probability of getting a product of less than 20. 1 solutions Answer 330609 by stanbon(57347)   on 2011-08-18 18:11:48 (Show Source): You can put this solution on YOUR website! Two numbered cubes are rolled, the first cube shows a 4 what is the probability of getting a product of less than 20. ---------------------------- Products involving "4": 4,8,12,16,20,24 ---- P(product less than 20) = 4/6 = 2/3 ================== Cheers, Stan H.

Probability-and-statistics/482955: Can someone please help me, I submitted a question and ot no answer. A machine puts plastic into sheets that are 30 feet(360 inches)long. Assume that the population of lengths is normally distrubuted. Complete parts (a) and (b) a) The company wants to estimate the mean length the machine is cutting the plastic within 0.25 inc. Determine the minimum sample sia required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 0.50 inch. n= b) Repeat part (a) using an error tolerance of 0.125 inc. n= Which error tolerane requires a larger sample size? Explain. A The tolerance E= 0.125 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired acuracy. B. The tolerance E=0.25 inch requires a larger sample size. As erro size increases a larger sample must be taken to ensure the desired accuracy. C. The tolerance E=0.25 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy. D. The tolerance E = 0.125 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy. 1 solutions Answer 330606 by stanbon(57347)   on 2011-08-18 18:05:56 (Show Source): You can put this solution on YOUR website! A machine puts plastic into sheets that are 30 feet(360 inches)long. Assume that the population of lengths is normally distrubuted. Complete parts (a) and (b) ---------------------- a) The company wants to estimate the mean length the machine is cutting the plastic within 0.25 inc. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 0.50 inch. -------------- n= [z*s/E]^2 n = [1.96*0.50/0.25]^2 n = 16 when rounded up ================================= b) Repeat part (a) using an error tolerance of 0.125 inc. n= {1.96*0.50/0.125]^2 n = 62 when rounded up ============================= Which error tolerance requires a larger sample size? Explain. A The tolerance E= 0.125 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired acuracy. B. The tolerance E=0.25 inch requires a larger sample size. As erro size increases a larger sample must be taken to ensure the desired accuracy. C. The tolerance E=0.25 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy. D. The tolerance E = 0.125 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy. 0 solutions ============= Answer: D ; Error size and sample size are indirectly related. As the amount of allowed error decreases the sample size must rise. ================================== Cheers, Stan H. ================

Probability-and-statistics/482987: Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish speaking American. of the first 12 potential jurors, only 2 are Spanish speaking Americans, and 10 are not. The defendant's lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. What do you think? I am having trouble with this problem could someone please help me out the only thing the teacher told me was that this problem is binomial and I have been wrecking my brain trying to figure this answer out. Thank you for your help. 1 solutions Answer 330604 by stanbon(57347)   on 2011-08-18 17:50:45 (Show Source): You can put this solution on YOUR website! Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish speaking American. of the first 12 potential jurors, only 2 are Spanish speaking Americans, and 10 are not. The defendant's lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. What do you think? --- Binomial Problem with n = 12 and p = 0.30 --- P(x=2) = 12C2(0.30)^2(0.70)^10 = 0.1678 = 16.78% =================== Cheers, Stan H.

Probability-and-statistics/482947: Okay so I just looked over what is needed with the 5 step hypothesis test and we need step 5. So step 5 is take a sample and arrive at a decision. The mean of wins is 81 the alpha level is 95% and there are 33 teams. I know there is a formula to plug all this information in but I can't find it. 1 solutions Answer 330602 by stanbon(57347)   on 2011-08-18 17:44:58 (Show Source): You can put this solution on YOUR website! Please post the whole problem statement. Cheers, Stan H.

logarithm/482940: Find the inverse of the function f(x)= -2log3(x-1)+4 The '3' is the base of the logarithm. The coefficient and the '+4' part are throwing me off so if you could show me how to do it with or without the answer I'd appreciate it 1 solutions Answer 330508 by stanbon(57347)   on 2011-08-17 21:48:40 (Show Source): You can put this solution on YOUR website! Find the inverse of the function f(x)= -2log3(x-1)+4 ---- 1st: Interchange x and y x = -2log3(y-1) + 4 ---- 2nd: Solve for "y": -2log3(y-1) = x-4 --- divide by -2 to get: log3(y-1) = (4-x)/2 --- y-1 = 3^(4-x)/2 ---- y = 3^[(4-x)/2] +1 ---- That is the inverse function. ============================== Cheers, Stan H.

real-numbers/482900: find a real number between each pair of numbers 4 2/5 and 4 3/5 1 solutions Answer 330505 by stanbon(57347)   on 2011-08-17 21:36:29 (Show Source): You can put this solution on YOUR website! find a real number between each pair of numbers 4 2/5 and 4 3/5 ---- The average is between. ---- [(22/5)+(23/5)]/2 ---- = (45/5)/2 --- = 9/2 --- = 4 1/2 =========================================== Cheers, Stan h. =================

Polynomials-and-rational-expressions/482922: I need some help with this problem.... Thanks Factor by grouping 21x^3 - 15x^2 + 56x-40= and this one please... x^3 +4x^2-2x-8= thanks for all your help...I am just stuck on these few problems... 1 solutions Answer 330491 by stanbon(57347)   on 2011-08-17 20:58:28 (Show Source): You can put this solution on YOUR website! Factor by grouping 21x^3 - 15x^2 + 56x-40 ---- 3x^2(7x-5) + 8(7x-5) ---- = (7x-5)(3x^2+8) ========================== and this one please... x^3 +4x^2-2x-8 ---- x^2(x+4)-2(x+4) ---- (x+4)(x^2-2) ================= cheers, Stan H. =

Permutations/482920: A SKYDIVING CLUB HAS 30 MEMBERS.THE CLUB MEMBERS JUMP IN PAIRS.HOW MANY DIFFERENT PAIRS OF SKYDIVERS ARE POSSIBLE. 1 solutions Answer 330490 by stanbon(57347)   on 2011-08-17 20:52:33 (Show Source): You can put this solution on YOUR website! A SKYDIVING CLUB HAS 30 MEMBERS.THE CLUB MEMBERS JUMP IN PAIRS.HOW MANY DIFFERENT PAIRS OF SKYDIVERS ARE POSSIBLE. ---- Ans: 30C2 = (30*29)/(1*2) = 15*29 = 425 pairs Cheers, Stan H.

Probability-and-statistics/482907: Please Help me: Household income does not tend to follow a normal distribution in a particular state, yet average income is approximately $45,000/year in this state, with a standard deviation of about $9000. Approximately what percentage of household incomes in this state is between $27,000 to $63,000/year? Show all work as to how this is obtained. 1 solutions Answer 330489 by stanbon(57347)   on 2011-08-17 20:49:11 (Show Source): You can put this solution on YOUR website! Household income does not tend to follow a normal distribution in a particular state, yet average income is approximately $45,000/year in this state, with a standard deviation of about $9000. Approximately what percentage of household incomes in this state is between $27,000 to $63,000/year? Show all work as to how this is obtained. -------------------------- (27000-45000)/9000 = -2 --- (63000-45000)/9000 = 2 ----- Using Chebychev's approximation, (1-(1/2)^2)% = 0.75% of the households will fall in that range. =============================== Cheers, Stan H.

Distributive-associative-commutative-properties/482901: My son and I have been working on his homework for a few hours now. I can solve the problem, but I can't show the work on how to solve it how it is 'suppose to be' done. The problem is 7-2n/7+2n=1/18. I know that I can use a 'reverse system to solve for the right side of the = sign, but I've been out of school too long to explain to him the correct way to solve it nor explain how to show the work. Please help me explain this to him 1 solutions Answer 330487 by stanbon(57347)   on 2011-08-17 20:42:17 (Show Source): You can put this solution on YOUR website! (7-2n)/(7+2n) =1/18 --- Cross-multiply to get: 18(7-2n) = 7+2n ---- Distribute on the left side to get: 18*7 - 36n = 7+2n ---- Get the variable terms on one side; the numbers on the other: 2n+36n = 18*7-7 --- 38n = 17*7 n = (119/38) ================== Cheers, Stan H.