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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Graphs/74585: Please help me understand this If points A,B, and C lie on a coordinate line and points A and B have coordinates 15 and 7 respectively, then which of the possible coodinates for point C satisfy(ies) d(A,C) < d(B,C) Thanks to anyone who takes the time to teach me this1 solutions Answer 53553 by stanbon(57224)   on 2007-03-15 18:36:13 (Show Source): You can put this solution on YOUR website!If "c" is the coordinate of C, then the coordinate value is between eleven and fifteen. Any of these coordinates will result in the distance from A to C is less than the distance from B to C. ----------- Cheers, Stan H.
 Probability-and-statistics/74581: Given a normal distribution with µ = 100 and σ = 10, if you select a sample of n = 25, what is the probability that X bar is a. less than 95? b. Between 95 amd 97.5? c. Above 102.2? d. There is a 65% chance that X bar is above what value? 1 solutions Answer 53552 by stanbon(57224)   on 2007-03-15 18:18:48 (Show Source): You can put this solution on YOUR website!Given a normal distribution with µ = 100 and sigma = 10, if you select a sample of n = 25, what is the probability that X bar is a. less than 95? z(95) = (95-100)/10/sqrt25) = -5/2 = -2.5 P(xbar<95)=P(z<-2.5)=0.006 ------------- b. Between 95 amd 97.5 z(95)=-2.5 ; z(97.5) = (97.5-100)/10/5=-2.5/2=-1.25 P(95 -------------- c. Above 102.2? z(102.2)=(102.2-100)/2=1.1 P(xbar>102.2)=P(z>1.1)=0.135666... --------------- d. There is a 65% chance that X bar is above what value? The corresponding z-value is z=-0.38532... Converting to raw score: -0.38532 = (xbar-100)/2; xbar=2*(-0.38532)+100 xbar=99.23 ------------- ====================== Cheers, Stan H.
 Miscellaneous_Word_Problems/74570: Hi. Im studing for a test and im having some problems. I was wondering if anyone can help me. I would really appreciate it. I have 4 questions. 1) Translate into algebraic expression. The Difference between five times the input and seve. 2) six times the input, added to 8 3) Solve the problem Write a symbolic rule that represents the relationship in which the output variable t is 5 more than 3.5 times the input variable r. What is the input corresponding to an output value of 26? 4) Write a symbolic rule that represents the relationship in which the output variable t is 7 more than 2.5 times the input variable r. What is the corrisponding to an input value of 8? 1 solutions Answer 53542 by stanbon(57224)   on 2007-03-15 16:29:58 (Show Source): You can put this solution on YOUR website!1) Translate into algebraic expression. The Difference between five times the input and seven. Let the input be "x": 5x-7 ------------- 2) six times the input, added to 8 6x+8 ----------------- 3) Solve the problem Write a symbolic rule that represents the relationship in which the output variable t is 5 more than 3.5 times the input variable r. t=3.5r+5 ---------- What is the input corresponding to an output value of 26? t=3.5*26 +5 t = 91+5 = 96 ----------------- 4) Write a symbolic rule that represents the relationship in which the output variable t is 7 more than 2.5 times the input variable r. t = 2.5r+7 ----------------- What is the corrisponding to an input value of 8? t = 2.5*8+7 t = 27 ----------------- Cheers, Stan H.
 Human-and-algebraic-language/74572: the sum of two consecutive integers is 145. what are the two integers?1 solutions Answer 53541 by stanbon(57224)   on 2007-03-15 16:21:08 (Show Source): You can put this solution on YOUR website!the sum of two consecutive integers is 145. what are the two integers? Let the two integers be x and x+1. EQUATION: x+x+1 = 145 2x=144 x=72 x+1 = 73 -------------- Cheers, Stan H.
 Rational-functions/74573: I don't know if this is in the correct area but, I will try anyways. I don't understand how to get Rational Zeros from this equation at all. The equation is 2x^3+4x^2-22x-24. 1 solutions Answer 53540 by stanbon(57224)   on 2007-03-15 16:13:01 (Show Source): You can put this solution on YOUR website!2x^3+4x^2-22x-24=0 x^3+2x^2-11x-12 = 0 Notice that f(-1)=0 so x=-1 is a zero. Use synthetic division to find the quotient after dividing by (x+1): -1....1....2....-11....-12 .......1....1.....-12..|..0 So, x^2+x-12 is the other factor after dividing: It factors into (x+4)(x-3) Therefore x=-4, and x=3 are also zeroes. ------------- Cheers, Stan H.
 Probability-and-statistics/74534: use this data. subject actually told the truth and polygraph indicated truth 65 subject actually told the truth and polygraph indicated lie 15 subject actually told a lie and polygraph indicated truth 3 subject actually told a lie and polygraph indicated lie 17 Q1. If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told a lie. Q2.If 1 of the 100 subjects is randomly selected, find the probability of getting someone for whom the polygraph test indicted that a lie was being told. Q3.If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told a lie or had the polygraph test indicated that a lie was being told. Q4.If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told the truth or had the polygraph test indicate that the truth was being told. Q5. If 2 diffrent subjects are randomly selected, find the probability that they both told the truth. Q6.If 2 different subjects are randomly selected, find the probability that they both had the polygraph test indicate that a lie was being told. Q7.If 1 subject is randomly selected, find the probability that he or she told the truth, given that the polygraph test indicated that a lie was being told. Q8. If 1 subject is randomly selected, find the probability that he or she has a polygraph test indication that a lie was being told, given that the subject actually told the truth. Thank you i look forward to your answers. 1 solutions Answer 53539 by stanbon(57224)   on 2007-03-15 16:00:36 (Show Source): You can put this solution on YOUR website!subject actually told the truth and polygraph indicated truth 65 subject actually told the truth and polygraph indicated lie 15 subject actually told a lie and polygraph indicated truth 3 subject actually told a lie and polygraph indicated lie 17 -------------------- Draw a "Contingency Table" with two rows: Poly said true;and Poly said lied two columns: Acutually told truth; Actually Lied ---------------------- Q1. If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told a lie. (3+17)/100 = 1/5 ------------------- Q2.If 1 of the 100 subjects is randomly selected, find the probability of getting someone for whom the polygraph test indicted that a lie was being told. (15+17)/100 = 32/100 -------------- Q3.If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told a lie or had the polygraph test indicated that a lie was being told. (20+3-17)/100 = 35/100 ------------------- Q4.If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told the truth or had the polygraph test indicate that the truth was being told. (80+68-65)/100 = 83/100 ----------- Q5. If 2 different subjects are randomly selected, find the probability that they both told the truth. 80C2/100C2 = 0.638... --------- Q6.If 2 different subjects are randomly selected, find the probability that they both had the polygraph test indicate that a lie was being told. 32C2/100C2 = 0.100... ----------- Q7.If 1 subject is randomly selected, find the probability that he or she told the truth, given that the polygraph test indicated that a lie was being told. P(told truth|poly said lied) = 15/32 To get this " look only at the "poly said lied" row which has a total of 32 Then find the intersecting box for "told the truth" = 15 ------------------------ Q8. If 1 subject is randomly selected, find the probability that he or she has a polygraph test indication that a lie was being told, given that the subject actually told the truth. P(Poly said lied | person told truth) Look at column for "told the truth" = 80 Find intersecting box "Poly said lied" = 15 P(...) = 15/80 ------------------- Cheers, Stan H.
 Square-cubic-other-roots/74554: Simplify. . The answer I got was . Thank you for checking this for me. 1 solutions Answer 53537 by stanbon(57224)   on 2007-03-15 13:18:34 (Show Source): You can put this solution on YOUR website!6sqrt(3)-sqrt(192) =6sqrt(3) - 8sqrt(3) = - 2sqrt(3) --------------- Cheers, Stan H.
 percentage/74562: what is 125%of 751 solutions Answer 53535 by stanbon(57224)   on 2007-03-15 13:10:18 (Show Source): You can put this solution on YOUR website!125% = 125/100 = 1.25 125%(75) = 1.25*75 = 93.75 ---------- Cheers, Stan H.
 Probability-and-statistics/13912: This is my problem: Three boys and two girls want to be on the softball team. If the coach chooses two of them at random, what is the probability that: one boy and one girl will be chosen? two boys will be chosen? two girls will be chosen? I already submitted it to my teacher and got it wrong...help! Thank you!1 solutions Answer 53534 by stanbon(57224)   on 2007-03-15 13:08:14 (Show Source): You can put this solution on YOUR website!Three boys and two girls want to be on the softball team. If the coach chooses two of them at random, what is the probability that: two boys will be chosen? Choose 2 boys in 3C2=3 ways Choose 2 of any gender = 5C2=10 Therefore P(2 boys) = 3/10 ---------------- two girls will be chosen? Choose two girls in 2C2=1 way Choose 2 of any gender = 10 Therefore P(2 girls) = 1/10 ------------------- one boy and one girl will be chosen? P(one boy and one girl)= 1-[prob(2 boys)+2(girls)] = 1-((3/10)+(1/10))=6/10 -------------- Cheers, Stan H.
 Quadratic-relations-and-conic-sections/74533: This question is from textbook Algebra 2 Hi! I just submitted this problem, but I think I figured it out! Can someone tell me if this is correct? Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0). The length of the major axis would be 12 units. 2a=12. a=6. The length of the minor axis is 8 units. 2b=8. b=4. The equation for an ellipse is y^2/a^2 + x^2/b^2=1. So the answer would be y^2/36 + x^2/16=1. Can someone please tell me if I did this right?1 solutions Answer 53498 by stanbon(57224)   on 2007-03-15 09:04:59 (Show Source): You can put this solution on YOUR website!Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0). The length of the major axis would be 12 units. 2a=12. a=6. The length of the minor axis is 8 units. 2b=8. b=4. The equation for an ellipse is y^2/a^2 + x^2/b^2=1. So the answer would be y^2/36 + x^2/16=1. Can someone please tell me if I did this right? --------------- Your equation would cause the center to be at (0,0) If you plot the end points of the major and the minor axis you will see that the center is at (1,0). --------- Can you adjust your equation for that? ------------- Cheers, Stan H.
 Mixture_Word_Problems/74505: A tank holds 80 liters of a chemical solution. Currently the solution has a strength of 30%. How much of this solution must be drained and replaced with a 70% solution to get a strength of 40%?1 solutions Answer 53475 by stanbon(57224)   on 2007-03-14 23:12:54 (Show Source): You can put this solution on YOUR website!A tank holds 80 liters of a chemical solution. Currently the solution has a strength of 30%. How much of this solution must be drained and replaced with a 70% solution to get a strength of 40%? ------------- 30% solution DATA: Amt = 80 L ; amt of active ingredient = 0.3*80 = 24 L ---------- 70% solution DATA: Amt = x L ; amt of active ingredient = 0.7x L ------------- 40% remainder DATA: Amt = (80) L ; Amt of active ingredient = 0.4(80) = 32 L ------------------- EQUATION: active - active = active 24 + 0.7x = 32 0.7x = 8 x= 11.43 L ------------------- Cheers, Stan H.
 Quadratic-relations-and-conic-sections/74502: This question is from textbook Heath Algebra 2 An integrated Approach please help me find the vertex, focus and directrix of the parabola if the question is: (x - 1) + 8(y + 2)^2 = 01 solutions Answer 53472 by stanbon(57224)   on 2007-03-14 23:01:43 (Show Source): You can put this solution on YOUR website!find the vertex, focus and directrix of the parabola if the question is: (x - 1) + 8(y + 2)^2 = 0 (y+2)^2=(-1/8)(x-1) Vertex at (1,-2) The parabola opens downward: 4p=(-1/8) p= -1/32 The directrix is a horizontal line with equation y=-2+1/32 = -63/32 Focus (1,-2-1/32) = (1,65/32) -------------- Cheers, Stan H. -------------- Cheers, Stan H.
 Probability-and-statistics/14613: It has been estimated that eighty percent of people with coronoary disease have chest pain syptom and twenty-five percent of people without the disease have chest pain symptoms. A person visits a doctor with chest pain symptom, what are the probabilities of the following events? a) the person has coronary heart disease b)the person does not have coronary disease. I have just started my module on probability, I know this maybe pretty basic stuff, but would appreciate any help that will make it easier for me to understand the subject,thanks in advance.1 solutions Answer 53470 by stanbon(57224)   on 2007-03-14 22:47:52 (Show Source): You can put this solution on YOUR website!It has been estimated that eighty percent of people with coronoary disease have chest pain syptom and twenty-five percent of people without the disease have chest pain symptoms. A person visits a doctor with chest pain symptom, what are the probabilities of the following events? a) the person has coronary heart disease Looks like a Bayes Problem: Let "D" mean "has coronary disease"; Let "p" means "has pain". P(D|P) = P(D and P)/[P(P and D) + P(P and not D) = 0.80/(0.80 + 0.25) = 0.8/1.05 = 0.762 ------------------- b)the person does not have coronary disease. Also, looks like a Bayes Problem. P(not D |Pain) = P(not D and Pain)/[P(not D and Pain) + P(not D and not Pain) =0.25/[0.25+0.20) = 0.556 ------------- Cheers, Stan H.
 Probability-and-statistics/74469: A die is rolled twice What is the probabilty of both being a 6 1 solutions Answer 53461 by stanbon(57224)   on 2007-03-14 20:06:44 (Show Source): You can put this solution on YOUR website!The results of the two rolls are independent; that means what happens on the 1st roll has no effect on what happens on the 2nd roll. So Prob( 6 and then 6) = Prob 6 * Prob 6 = 1/6 *1/6 = 1/36 ------------ Cheers, Stan H.
 Probability-and-statistics/14625: First of all, thaks for helping in advance... Here's the problem Suppose there are 10 items on a true-false test. The person taking the test does not read the questions; he just answers each question randomly. What is the probability of his guessing all answers correctly? I ended up with 1/512...but I started this a while ago and now I've forgotten how I got to that. Any help would be great. Thanks, Liz1 solutions Answer 53415 by stanbon(57224)   on 2007-03-14 07:22:56 (Show Source): You can put this solution on YOUR website!The probability of getting one answer right is 1/2 The probability of getting two right is 1/2 *1/2 = 1/2^2=1/4 You multiply because the events are independent; what you do on one problem does not effect what you do on the next. The prob of get all 10 right is (1/2)^10 = 1/1024 -------- Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/74264: This question is from textbook intermediate algebra A manufacturer builds racing bikes and mountain bikes, with the per unit manufacturing costs shown in table . The company has bugeted \$15,900 for labor and \$13,075 for materials .How many bicycles of each type can be built? model cost of materials cost of labor racing \$55 \$60 mountain \$70 \$90 1 solutions Answer 53382 by stanbon(57224)   on 2007-03-13 21:02:58 (Show Source): You can put this solution on YOUR website!A manufacturer builds racing bikes and mountain bikes, with the per unit manufacturing costs shown in table . The company has bugeted \$15,900 for labor and \$13,075 for materials .How many bicycles of each type can be built? model cost of materials cost of labor racing \$55 \$60 mountain \$70 \$90 -------------------- Let r be # of racing bikes and m be # of mountain bikes: 60r+90m = 15900 55r+70m = 13075 -------------- Rewrite to get smaller numbers: 2r + 3m = 530 11r+ 14m =2615 ---------- Multiply 1st by 11 and 2nd by 2 to get: 22r + 33m =11*530 22r + 28m =2*2615 ------------- Subtract 2nd from 1st to get: 5m = 600 m=120 (# of mountain bikes) Substitute in 2r+3m = 530 to solve for "r": 2r+3*120 = 530 2r = 170 r = 85 (# of racing bikes) -------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/74326: Can someone explain to me the steps so i can understand them.thanks ... Problem #1 Write in simplest form. (5)/(12) + (1)/(4) Problem #2 Multiply. (3x-27)/(x^2+5x) * (2x)/(9-x) this symbol "*" means multiply. Problem # 3 Divide (x^2-4y^2)/(8x^2-16y) divided by ((x^2+2xy)) 1 solutions Answer 53380 by stanbon(57224)   on 2007-03-13 20:51:59 (Show Source): You can put this solution on YOUR website!Can someone explain to me the steps so i can understand them.thanks ... Problem #1 Write in simplest form. (5)/(12) + (1)/(4) You can only add fractions if they have the same denominator. The "least common denominator" for your problem is 12. Rewrite each fraction with 12 as its denominator, as follows: 5/12 + 3/12 Now you can add the fractions: =8/12 Now you can reduce the fraction: =2/3 --------------- Problem #2 Multiply. (3x-27)/(x^2+5x) * (2x)/(9-x) this symbol "*" means multiply. To multiply fractions it sometimes helps to first factor the pieces: =(3(x-9)) / (x(x+5) * 2x / -(x-9) Since (x-9) is in the numerator and in the denominator, cancel it: 3/(x(x+5) * 2x / (-1) Since "x" is in the numerator and in the denominator, cancel it. 3/(x+5) *2/(-1) Multiply numerators then multiply denominators to get: = -6/(x+5) -------------------- Problem # 3 Divide (x^2-4y^2)/(8x^2-16y) divided by ((x^2+2xy)) To divide you have to invert the denominator and multiply: [(x-2y)(x+2y)/[8(x^2-2y)]/[x(x+2y)] Cancel the (x+2y) factor to get: (x-2y)/[8(x^2-2y)]/x =(x-2y)/8x(x^2-2y) ------------ Cheers, Stan H.
 Inequalities/74351: Could someone please help me with this? I tried to multiply both sides by 7, and I ended up with: Am I on the right track? Your help would be appreciated. A1 solutions Answer 53378 by stanbon(57224)   on 2007-03-13 20:36:50 (Show Source): You can put this solution on YOUR website! 2(n+1)/7 >= (n+4)/5 Multiply both sides by 35 to get: 10(n+1) >= 7(n+4) 10n+10 >= 7n+28 3n >= 18 n >= 6 ------------ Cheers, Stan H.
 logarithm/74352: I need to evaluate the following expressions: log of base 5 (0.008) and log of base 64 sqrt(4)1 solutions Answer 53376 by stanbon(57224)   on 2007-03-13 20:31:21 (Show Source): You can put this solution on YOUR website!I need to evaluate the following expressions: log of base 5 (0.008) =ln(0.008)/ln5 =-4.828313737.../1.609437912...= -3 ---------------- and log of base 64 sqrt(4) =ln(sqrt(4))/ln(64) =0.693147.../4.158883... = 0.1666666666667 --------- Cheers, Stan H.
 Trigonometry-basics/74356: Find the a(sub2) in the arithmetic sequence where a(sub5) = 42 and a(sub10) = 62.1 solutions Answer 53373 by stanbon(57224)   on 2007-03-13 20:24:53 (Show Source): You can put this solution on YOUR website!Find the a(sub2) in the arithmetic sequence where a(sub5) = 42 and a(sub10) = 62. -------------- a(10)= a(1)+9d = 62 a(5) = a(1)+4d = 42 Subtract a(5) from a(10) to get: 5d=20 d=4 If d=4 substitute into a(1)+9d=62 to solve for a(1) a(1)+9*4=62 a(1)+36=62 a(1) = 26 --------------- Now find a(2) a(2) = a(1) + (1)d a(2) = 26 + 4 a(2) = 30 ------------ Cheers, Stan H.
 Trigonometry-basics/74358: Given that n^2 + n = 2k, how can (n+1)^2 + (n+1) be written as a multiple of 2?1 solutions Answer 53370 by stanbon(57224)   on 2007-03-13 20:19:06 (Show Source): You can put this solution on YOUR website!Given that n^2 + n = 2k, n(n+1)=2k how can (n+1)^2 + (n+1) be written as a multiple of 2? -------------- (n+1)^2 + (n+1) =(n+1)[n+1+1 =n(n+1+1)+(n+1+1) =n(n+1) +n +n+2 =n(n+1) +2(n+1) =2k +2(n+1) =2[k+n+1] which is a multiply of 2 ------------ Cheers, Stan H.
 logarithm/74363: This question is from textbook Demana Waits Foley Kennedy Precalculus log7X The exercise asks, write the espression using only natural logarithms. The other problems I worked X was given a value. What is X in this problem.1 solutions Answer 53366 by stanbon(57224)   on 2007-03-13 20:11:43 (Show Source): You can put this solution on YOUR website!log7X The exercise asks, write the espression using only natural logarithms. -------------- I'm going to assume you means log(base7)x If that is correct it can be written as [lnx]/[ln7] ---------------- Cheers, Stan H.
 Linear-equations/74366: Solve this problem using the substitution method 4x - y = -3 y - 3 = 4x1 solutions Answer 53364 by stanbon(57224)   on 2007-03-13 20:08:48 (Show Source): You can put this solution on YOUR website!Solve this problem using the substitution method 4x - y = -3 y - 3 = 4x ------------- Solve the 2nd equation for y: y=4x+3 Substitute that into the 1st equation to solve for "x": 4x-(4x+3)=-3 4x-4x-3=-3 -3=-3 This means the two equations are dependent which means one is a multiple of the other. It also means that every point on the line y=4x+3 is a solution for the system of equations. ------------------ Cheers, Stan H.
 Polynomials-and-rational-expressions/74365: can someone check this for me? (x-10)(x+9) =x^2-1x-901 solutions Answer 53362 by stanbon(57224)   on 2007-03-13 20:04:41 (Show Source): You can put this solution on YOUR website!It's correct. Cheers, Stan H.
 Probability-and-statistics/14857: Dave, Talor and lindsay created their own board game. one of the players tosses two coins. Dave moves one space if the result is 2 heads. Taylor moves one espace if the result is 2 tails. Lindsay moves one espace if the result is 1 heald and 1 tail. does each of the players have an equal chance of winning the games ? *if you think the players have equal chances, find the probability that each of the players will win. explaine how you know your answer is correct. *if you think the players do not have equal chances, explain in detail why you think they do not. lpese help I don`t understand very vell the probability1 solutions Answer 53360 by stanbon(57224)   on 2007-03-13 20:03:36 (Show Source): You can put this solution on YOUR website!Dave moves one space if the result is 2 heads. Taylor moves one espace if the result is 2 tails. Lindsay moves one espace if the result is 1 heald and 1 tail. does each of the players have an equal chance of winning the games ? ------------- The probability of throwing two heads is (1/2)(1/2)=1/4 The probability of throwing two tails is (1/2)(1/2)=1/4 The probability of throwing a head and a tail is 2(1/2)(1/2)=2/4 = 1/2 ------------------- Lindsay has twice as good a chance of winning as Dave or Taylor. --------- Cheers, Stan H.
 Probability-and-statistics/14994: Hi could you please help me with this problem: A certain drug has an 80% success rate in relieving the symptoms of migraine. In a group of 12 patients what is the probability that; 6 are helped by the drug At least i is helped by the drug No more than 2 are still suffering the effects of migraine Thanks1 solutions Answer 53283 by stanbon(57224)   on 2007-03-13 10:09:58 (Show Source): You can put this solution on YOUR website!A certain drug has an 80% success rate in relieving the symptoms of migraine. In a group of 12 patients what is the probability that; 6 are helped by the drug At least i is helped by the drug No more than 2 are still suffering the effects of migraine ----------- These are all binomial because people are either helped or are not helped. In a group of 12 patients what is the probability that; 6 are helped by the drug n=12 ; p=0.80 ; x=6 Using a TI calculator use binompdf(12,0.8,6) to get 0.055 --------------- At least ? is helped by the drug Use [1-binomcdf(12,0.8,?-1)] ---------------- No more than 2 are still suffering the effects of migraine Use binomcdf(12,0.8,2)=4.526 x 10^-6 = 0.000004526 --------- If you don't have a TI or are allowed to use a calculator let me know. --------- Cheers, Stan H
 Inverses/74287: g(x)=x=5;h(x)=x-5 , are these functions inverse if so, why?1 solutions Answer 53281 by stanbon(57224)   on 2007-03-13 09:58:09 (Show Source): You can put this solution on YOUR website!Functions are "inverse" if one UNDOES what the other DOES. Mathematically that means: f and g are inverse of one another if f(g(x))=x and g(f(x))=x So, let's try it: --------------- g(x)=x=5;h(x)=x-5 , are these functions inverse if so, why? ------ g(f(x))=g(x-5) = (x-5)-5 = x-10 Right away you know they are not inverse because the result was not "x". If you had tried f(g(x)) first you would have gotten the following: f(g(x))=f(x-5)=(x-5)-5 = x-10 Again, you did not get "x" as a result and that shows you they are not inverse. Hope this helps. Cheers, Stan H.
 Polynomials-and-rational-expressions/74278: can you check my answer? 7x^2+6x from 9x^2-3 9x^2-3 7x^2-6 =2x^2-3 9x^2-3 7x^2+6 =2x^--3 1 solutions Answer 53280 by stanbon(57224)   on 2007-03-13 09:49:04 (Show Source): You can put this solution on YOUR website!can you check my answer? 7x^2+6x from 9x^2-3 9x^2-3 7x^2-6 ---------------- =2x^2+3 You subtracted 7 from 9 and got 2 correctly. You should subtract -6 from -3 and get +3 The Rule is : "change the sign of the -6 to +6 and then add" to get +3 --------- Cheers, Stan H.
 Miscellaneous_Word_Problems/74283: 1 solutions Answer 53278 by stanbon(57224)   on 2007-03-13 09:42:14 (Show Source): You can put this solution on YOUR website!A container must hold 400 cubic inches of sand. Accurately sketch and label the dimensions of a rectangular prism, shere,and cylinder which will each hold 400 cubic inches of sand with the least amount of wasted space. Show the calculation that verifty that each container will hold 400 cubic inches. ------------ Use the formulas: Prism: lwh=400 cu in Let l=8;w=5;h=10 ---------- Sphere: (4/3)(pi)r^3=400 cu in r^3 = (3/4)(400)(pi)= 300pi Take the cube root to get: r=9.804 inches diameter = 2r=19.61 in -------------- Cylinder: (pi)r^2h=400 cu in r^2=400/(pi)h Let h=10 then r^2 = 40/(pi) Take the square root of 40/(pi) to get: r= 3.56 inches ------------ Cheers, Stan H.
 Miscellaneous_Word_Problems/74280: I need some help with this problem. The speed of a mototboat in still water is 15 mi/hr. If it takes the motorboat the same time to go 15 mi upstream the river as it takes to go 30 mi downstream, what is the speed of the current? Thank You!1 solutions Answer 53276 by stanbon(57224)   on 2007-03-13 09:19:50 (Show Source): You can put this solution on YOUR website!The speed of a mototboat in still water is 15 mi/hr. If it takes the motorboat the same time to go 15 mi upstream the river as it takes to go 30 mi downstream, what is the speed of the current? -------------- Let the rate of the current be "x": Upstream DATA: Distance = 15 mi ; rate = 15-x ; time = d/r = 15(15-x) mph ----------- Downstream DATA: Distance = 30 mi ; rate = 15+x ; time = d/r = 30/(15+x) mph ------------- EQUATION: time up = time down 15/(15-x) = 30/(15+x) Divide both sides by 15 to get: 1/(15-x) = 2/(15+x) 15+x = 2(15-x) 15+x = 30-2x 3x=15 x=5 mph The speed of the current is 5 mph --------------- Cheers, Stan H.