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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 , 57180..57209 , 57210..57239, >>Next

 Linear_Equations_And_Systems_Word_Problems/221832: Advance tickets to a show cost , and same-day tickets cost . The total number of tickets sold was for total receipts of . How many tickets of each type were sold? 1 solutions Answer 166255 by stanbon(57307)   on 2009-10-05 10:17:43 (Show Source): You can put this solution on YOUR website!The numbers do not appear in your post. Cheers, Stan H.
 Equations/221831: solve the following equation for A : 2A/3=8+4A1 solutions Answer 166254 by stanbon(57307)   on 2009-10-05 10:15:52 (Show Source): You can put this solution on YOUR website!solve the following equation for A : 2A/3=8+4A ------------------------------------- Multiply thru by 3 to get rid of the fraction. 2A = 24 + 12A 10A = -24 A = -12/5 --------------- Cheers, Stan H.
 Graphs/221830: How do you graph a piecewise-defined function that has the lines y = 2x+3 and y = 3-x?1 solutions Answer 166253 by stanbon(57307)   on 2009-10-05 10:12:46 (Show Source): You can put this solution on YOUR website!How do you graph a piecewise-defined function that has the lines y = 2x+3 and y = 3-x? ---------- Pieces of a piecewise-defined functions are always defined over a certain interval of "x". Your y=2x+3 must be defined over some interval; what is it. Similarly for the piece y = 3-x. ====================================== Cheers, Stan H.
 Travel_Word_Problems/221824: Two cars are traveling 225 miles apart. They start traveling torwards each other at the same time, but one car is going 5 miles an hour faster than the other. If it took 3 hours for the cars to pass each other, what was each car's rate?1 solutions Answer 166252 by stanbon(57307)   on 2009-10-05 10:08:31 (Show Source): You can put this solution on YOUR website!Two cars are traveling 225 miles apart. They start traveling towards each other at the same time, but one car is going 5 miles an hour faster than the other. If it took 3 hours for the cars to pass each other, what was each car's rate? -------------------------------- 1st car DATA: time = 3 hrs ; rate = x mph ; distance = t*r = 3x miles --------------------------------- 2nd car DATA: time = 3 hrs ; rate = x+5 mph ; distance = t*r = 3(x+5) miles --------------------------------- Equation: distance + distance = 225 3x + 3(x+5) = 225 6x + 15 = 225 6x = 210 x = 35 mph (rate of car one) x+5=40 mph (rate of car two) ============================= Cheers, Stan H.
 Probability-and-statistics/221801: Fsu wants to make an inference about the percentage of students at the school who perfer having a break between the last day of school and the start of exams to help reduce stress. a survery is taken of 1000 students. - it is known that the population proportion that favor a break between classes and final exams is 50%. let the random variable x be defined as the number of students that are in favor of a break between classes and final exams. state the distrubtion if x and compute the mean and variance of the distrubtion????1 solutions Answer 166251 by stanbon(57307)   on 2009-10-05 10:00:10 (Show Source): You can put this solution on YOUR website!The variable "x" is binomial. mean = np = 1000*0.5 = 500 standard deviation = sqrt(npq) = sqrt(1000*1/2*1/2) = sqrt(250) = 5sqrt(10) ============================================================================ Cheers, Stan H.
 Probability-and-statistics/221779: A climate researcher knows that it has previously been the case that the mean temperature in his city has been 23.9 °C. He suspects that this may no longer be the case and that the mean temperature may now have changed, and he suspects that is has risen in recent times. He collects sample data with the aim of conducting a hypothesis test to examine his suspicions. He will use a level of significance of 0.01 for the test. Select the correct null and alternate hypotheses for this test: a.)H0: μ ≠ 23.9 °C H1: μ = 23.9 °C b.)H0: μ ≤ 23.9 °C H1: μ > 23.9 °C c.)H0: μ = 23.9 °C H1: μ ≠ 23.9 °C d.)H0: μ > 23.9 °C H1: μ ≤ 23.9 °C1 solutions Answer 166250 by stanbon(57307)   on 2009-10-05 09:54:49 (Show Source): You can put this solution on YOUR website!Ans: b Cheers, Stan H.
 Probability-and-statistics/221778: A teacher is interested in comparing the means scores on a mathematics and verbal test for two populations of students, population A and population B. In particular, the teacher suspects that the mean score for population A is higher than in population B. A random sample of 30 test scores from each population is collected. Sample A 83.5 66 92.5 61.5 62.5 94 71.5 68 97 66.5 93 71.5 63 90.5 69 93 95 66 74 92.5 85 66.5 86.5 65 73 66.5 88.5 69.5 80 69.5 Sample B 92 51.5 73 73 95 63 74 79 46.5 93.5 88 88 64.5 49.5 79 51.5 53 89.5 78.5 84.5 80 72.5 71 94.5 67 55 85.5 70 92 64.5 Conduct a one-tailed hypothesis test for equality of the populations means. You may find this Student's t distribution table useful. a)Calculate the test statistic. Give your answer to 3 decimal places. t =??? b)At a 95% confidence level, from the result of the test you can conclude that there is: 1.)significant evidence to conclude that the mean of population A is greater than the mean of population B 2.)significant evidence to conclude that the mean of population A is less than or equal to the mean of population B 3.)not enough evidence to conclude that the mean of population A is greater than the mean of population B 4.)not enough evidence to conclude that the mean of population A is less than or equal to than the mean of population B1 solutions Answer 166248 by stanbon(57307)   on 2009-10-05 08:26:28 (Show Source): You can put this solution on YOUR website!The most time consuming part of problems of this kind is calculating the same means and standard deviations. I think you should supply that data if you want help with the analytic part of the problem. Cheers, Stan H.
 Probability-and-statistics/221780: Heather is a student in a class that has been asked to conduct a hypothesis test for a population proportion. The null and alternative hypotheses are: H0: Pi symbol = 0.5 H1: Pi symbol ≠ 0.5 Heather is given a sample and calculates the test statistic. Using a level of significance of α = 0.05, she rejects the null hypothesis. Heather's friends, Alan and Bill, also use the sample to calculate a test statistic. However, they differ in the level of significance they use. Alan uses a level of significance of α = 0.1, while Bill uses α = 0.01. All three students perform their calculations correctly. For each of Heather's friends, select whether or not they reject the null hypothesis, or whether it is impossible to tell from the information given. Reject Retains Cannot tell a) Alan b) Bill 1 solutions Answer 166246 by stanbon(57307)   on 2009-10-05 08:12:27 (Show Source): You can put this solution on YOUR website!a) Alan If Ho is rejected at 5% it certainly will be rejected at 10% b) Bill If Ho is rejected at 5% is may or may not be rejected at 1% ========================= Cheers, Stan H.
 Probability-and-statistics/221781: Dr Carl is a mathematics and statistics lecturer. He is interested in studying a new approach at teaching mathematics and statistics in high school. Recently this new approach has been adopted. It was previously the case that the mean score for all high school students doing their end of year exam was 68, however, the population standard deviation is unknown. The scores of all students are approximately normally distributed. He thinks that, with this new teaching approach, the mean score may have increased. A random sample of 50 scores is gathered and the sample mean and standard deviation calculated. Dr Carl will conduct a hypothesis test using a level of significance of 0.05. Select the correct null and alternate hypotheses for this test: a.)H0: μ > 68 H1: μ ≤ 68 b.)H0: μ ≤ 68 H1: μ < 68 c.)H0: μ = 68 H1: μ ≠ 68 d.)H0: μ ≤ 68 H1: μ > 681 solutions Answer 166245 by stanbon(57307)   on 2009-10-05 08:00:30 (Show Source): You can put this solution on YOUR website!d --------------------- Cheers, Stan H.
 Probability-and-statistics/221782: In city A, it is known that the mean monthly energy usage per household has historically been 1,570 kilowatt-hours per month. The population standard deviation in monthly household energy use is not known. Recently, there has been a widespread government campaign using print, radio and television media aimed at encouraging household to be more energy efficient. As part of investigating the success of the campaign, research was commissioned to study the possible effect on average household energy usage. A sample of 56 randomly selected households had their monthly energy use measured for a period before and after the campaign. The researcher will use the before and after measurements, corresponding to each household, to test the hypothesis that the mean difference in household energy use before and after the campaign is more than zero. They will use a level of significance of 0.01. Select the correct null and alternate hypotheses for this test: 1.)H0: μd = 0 H1: μd ≠ 0 2.)H0: μd ≠ 0 H1: μd = 0 3.)H0: μd ≤ 0 H1: μd > 0 4.)H0: μbefore - μafter ≠ 0 H1: μbefore - μafter = 0 5.)H0: μbefore - μafter = 0 H1: μbefore - μafter ≠ 0 6.)H0: μd > 0 H1: μd ≤ 01 solutions Answer 166244 by stanbon(57307)   on 2009-10-05 07:52:00 (Show Source): You can put this solution on YOUR website!3.)H0: μd ≤ 0 H1: μd > 0 ----------------------- The data consists of 56 DEPENDENT pairs of data so ud is the appropriate measure for the test. ------------- Cheers, Stan H.
 Number-Line/221679: Where is -3/2 on a number line?1 solutions Answer 166211 by stanbon(57307)   on 2009-10-04 21:38:37 (Show Source): You can put this solution on YOUR website!Where is -3/2 on a number line? Half-way between -2/2 and -4/2 Same as half-way between -1 and -2. ==================================== Cheers, Stan H.
 Probability-and-statistics/221674: The new Twinkle bulb has a standard deviation 34 hours. A random sample of 77 light bulbs is selected from inventory. The sample mean was found to be 492 hours. Find the margin of error E for a 90% confidence interval. Round your answer to the nearest hundredths. Then I have to construct a 90% confidence interval for the mean life. I know how to do that part I just can't figure out the first part. The sqrt gets me. 1 solutions Answer 166210 by stanbon(57307)   on 2009-10-04 21:37:01 (Show Source): You can put this solution on YOUR website!The new Twinkle bulb has a standard deviation 34 hours. A random sample of 77 light bulbs is selected from inventory. The sample mean was found to be 492 hours. Find the margin of error E for a 90% confidence interval. Round your answer to the nearest hundredths. Then I have to construct a 90% confidence interval for the mean life. I know how to do that part I just can't figure out the first part. The sqrt gets me. --------------------------------------- invT(0.05,76) = -1.6652 ------------ E = 1.6652[34/sqrt(77)] = 6.4519 ------------------------------------------- 90% CI: 492 - 6.4519 < u < 492 + 6.4519 ================================================= Cheers, Stan H.
 Permutations/221650: This problem stumps me..can u please explain how to work it?? The producer of All Things Considered, a radio-news program on NPR, has 4 in-depth and 8 short news stories for broadcast during the next two hours. The producer must arrange the in-depth and short stories by starting with an in-depth story followed by two short stories, and then another in-depth story and two short stories until all 12 stories have been aired. How many arrangements for the broadcast are possible?1 solutions Answer 166209 by stanbon(57307)   on 2009-10-04 21:29:47 (Show Source): You can put this solution on YOUR website!The producer of All Things Considered, a radio-news program on NPR, has 4 in-depth and 8 short news stories for broadcast during the next two hours. The producer must arrange the in-depth and short stories by starting with an in-depth story followed by two short stories, and then another in-depth story and two short stories until all 12 stories have been aired. How many arrangements for the broadcast are possible? -------------------------------------- 1st segment: 4 ways 2nd/3rd segment: 8*7 ways 4th segment: 3 ways 5th/6th segment: 6*5 ways 7th: 2 ways 8th/9th segment: 4*3 ways 10th: 1 way 11th/12th: segment: 2*1 ------------------------------- Total # of ways: 4!*8! = 967680 ======================================== Cheers, Stan H.
 Probability-and-statistics/221659: 2. How many 4-character license plates are possible with 2 letters from the alphabet followed by 2 digits, if repetitions are allowed? if repetitions are not allowed?1 solutions Answer 166205 by stanbon(57307)   on 2009-10-04 21:16:13 (Show Source): You can put this solution on YOUR website!How many 4-character license plates are possible with 2 letters from the alphabet followed by 2 digits, if repetitions are allowed? if repetitions are not allowed? ---------------------- Repetitions allowed: 26^2*10^2 = 67600 ---------------------------- Not allowed: 26*25*10*9 = 58500 ------------------------------ Cheers, Stan H.
 Quadratic_Equations/221658: Hi, I am having a problem with a question that reads the following: Use the quadratic formula to solve the equation for x in terms of y. 8x^2-8xy=6(1-y^2)=0 Thanks in advance.1 solutions Answer 166203 by stanbon(57307)   on 2009-10-04 21:12:20 (Show Source): You can put this solution on YOUR website!Too many equal signs. Cheers, Stan H.
 absolute-value/221656: Hi, I have an absolute value problem. I tried solving it like a regular equation, but when I check it it is wrong. The problem is 6|5x+45|-113=7. Thanks in advance.1 solutions Answer 166200 by stanbon(57307)   on 2009-10-04 21:09:26 (Show Source): You can put this solution on YOUR website!6|5x+45|-113=7 6|5x+45| = 120 |5x+45| = 20 5x+45 = 20 or 5x+45 = -20 5x = -25 or 5x = -65 x = -5 or x = -13 ------------------------- Cheers, Stan H.
 Unit_Conversion_Word_Problems/221654: I have another problem that i do not understand. Help please! 5w2-18w+9 of course the 2 after the w is supposed to be a little tiny 2 a bit above the w. Thank you for your help. 1 solutions Answer 166198 by stanbon(57307)   on 2009-10-04 21:06:45 (Show Source): You can put this solution on YOUR website!5w2-18w+9 -------------- AC = 5*9 = 45 B = -18 ------------------- The numbers you want are -15 and -3 ------------------- Rewrite: 5w^2 - 15w -3w + 9 --- Factor 1st two and last two: 5w(w-3) - 3(5w-3) --- Final Answer: (w-3)(5w-3) ============================ Cheers, Stan H.
 Unit_Conversion_Word_Problems/221647: HI everyone long time no see. I am currently having problems with factoring at school. Here is the problem i have to factor W2+10w+16 of course the 2 after the W is to the power of type of 2. How is this done? Why is there a capital W and a little one too w? Please help me figure this one out please and thanks.1 solutions Answer 166196 by stanbon(57307)   on 2009-10-04 21:03:41 (Show Source): You can put this solution on YOUR website!factor W^2+10w+16 --------- The capital W and the small w have no particular meaning. ---------------------- To factor, think of two numbers whose product is 16 and whose sum is 10. --- The numbers are 8 and 2. So replace 10w by 8w + 2w to get: w^2 + 8w + 2w + 16 --- Factor the 1st two and the last two terms separately to get: w(w+8) +2(w+8) --- Factor again to get the final answer: (w+8)(w+2) ------------------ This procedure is called the AC Method. =========================================== Cheers, Stan H.
 Polygons/221630: Please help! How do you figure out the number of sides in a regular polygon if you only know the measure of the interior angles? THANKS! Need my tomorrow morning please!1 solutions Answer 166194 by stanbon(57307)   on 2009-10-04 20:57:11 (Show Source): You can put this solution on YOUR website!Please help! How do you figure out the number of sides in a regular polygon if you only know the measure of the interior angles? THANKS! Need my tomorrow morning please! -------------------------- Let's say the angle is 120 degrees. ------------ Then its corresponding exterior angle is 180-120 = 60 degrees ------------ That means every exterior angle is 60 degrees. -------------- Important point: The sum of ALL the exterior angles is ALWAYS 360 degrees. --- # of exterior angles is 360/60 = 6 ---- Therefore # of sides is 6. ============================== Cheers, Stan H.
 Mixture_Word_Problems/221639: Mary bought two computers, one desktop and one laptop. Before finance charges, the laptop cost more than the desktop. Mary paid for the computers using two different financing plans. For the desktop the interest rate was per year, and for the laptop it was per year. The total finance charges for one year were . How much did the desktop computer cost before finance charges? 1 solutions Answer 166191 by stanbon(57307)   on 2009-10-04 20:51:09 (Show Source): You can put this solution on YOUR website!Numbers are missing from your post. Cheers, Stan H.
 Exponential-and-logarithmic-functions/221643: I need a little help on where to continue on this problem x^4 - 81 I got down to (x^2-9(x^2+9) Where do I go from there?1 solutions Answer 166190 by stanbon(57307)   on 2009-10-04 20:49:52 (Show Source): You can put this solution on YOUR website!x^4 - 81 I got down to (x^2-9)(x^2+9) --- Factor again to get: = (x-3)(x+3)(x^2+9) =========================== Cheers, Stan H.
 Linear-equations/221640: how do you solve for x and check the solution to the equation, -0.3 + x-5(x + 1/10)= -0.8 + 5(-x+0.1)1 solutions Answer 166188 by stanbon(57307)   on 2009-10-04 20:47:45 (Show Source): You can put this solution on YOUR website!how do you solve for x and check the solution to the equation, -0.3 + x-5(x + 1/10)= -0.8 + 5(-x+0.1) --- Multiply thru by 10 to get rid of some of the decimals: -3 + 10x - 50(x + (1/10)) = -8 +50(-x + 0.1) ---- Modify: -3 + 10x - 50x - 5 = -8 - 50x + 5 ------------- Combine: -8 - 40x = -3 - 50x ----------------- Add 50x to both sides; Add 8 to both sides: 10x = 5 x = 1/2 ------------------- Checking: Substitute for "x" in the original equation to see if you get a true statement. ===================================== Cheers, Stan H.
 Graphs/221636: Graph the following and put your answer in set builder notation and interval notation. 3 > z - 11 solutions Answer 166185 by stanbon(57307)   on 2009-10-04 20:39:56 (Show Source): You can put this solution on YOUR website!Graph the following and put your answer in set builder notation and interval notation. 3 > z - 1 --------------- Solve for "z": z < 4 ---------------- Set builder notation: {z | z<4} ----------------- Draw a Number line. Mark a point "4" and draw a circle around the point. Draw an arrow starting from that point and extending to the left. ======================== Cheers, Stan H.
 Sequences-and-series/221632: "write and solve an equation to find the nth term of each aritmetic sequence" 3,7,11,15, . . . n=8 10,5,0,-5, . . . n=21 34,49,64,79, . . . n=200 1 solutions Answer 166182 by stanbon(57307)   on 2009-10-04 20:37:04 (Show Source): You can put this solution on YOUR website!"write and solve an equation to find the nth term of each arithmetic sequence" --- Every arithmetic sequence has this form: a(n)= a(1)+(n-1)d -------------------------------- 3,7,11,15, . . . n=8 a(8) = 3 + 7*4 = 31 -------------------------- 10,5,0,-5, . . . n=21 a(21) = 10 +(20)*-5 = 10-100 = -90 ------------------------------------- 34,49,64,79, . . . n=200 a(200) = 34 + (199)*15 = 3019 ============================================ Cheers, Stan H.
 Polynomials-and-rational-expressions/221614: u^3-8v^31 solutions Answer 166179 by stanbon(57307)   on 2009-10-04 20:30:56 (Show Source): You can put this solution on YOUR website!u^3-8v^3 ---- Factor as the difference of cubes: u^3 - (2v)^3 --- = (u-2v)(u^2 + u(2v) + (2v)^2) --- = (u - 2v)(u^2 +2uv + 4v^2) ============================== Cheers, Stan H.
 Linear-equations/221598: what is the equation of a line that is perpendicular to the graph of 3y-4x= -21, and goes through the point (-1,0).How do i write the answer in slope-intercept and standard form?1 solutions Answer 166164 by stanbon(57307)   on 2009-10-04 19:59:50 (Show Source): You can put this solution on YOUR website!what is the equation of a line that is perpendicular to the graph of 3y-4x= -21, and goes through the point (-1,0).How do i write the answer in slope-intercept and standard form? ----------------------------------------- Given line: 3y-4x = -21 y = (4/3)x - 7 slope = 4/3 ---------------------- Perpendicular Line? slope = -3/4 Find intercept if y = 0 when x = -1. y = mx + b 0 = (-3/4)(-1) + b b = -3/4 ----------------- Equation: y = (-3/4)x - 3/4 ------------------------ Standard Form: (3/4)x + y = -3/4 Multiply thru by 4 to get: 3x + 4y = -3 ====================== Cheers, Stan H. ================== ===============================================================
 Miscellaneous_Word_Problems/221589: A tree grows 1/2 inch per year. The tree is currently 50 feet tall; how long will it take to grow to 60 feet? Answers must be shown as a one variable algebraic equation with 'x' equaling the same value on each side of the equation. I believe the correct answer is 240 years, but I don't know how to show the work in the proper way. 1 solutions Answer 166161 by stanbon(57307)   on 2009-10-04 19:42:40 (Show Source): You can put this solution on YOUR website!A tree grows 1/2 inch per year. The tree is currently 50 feet tall; how long will it take to grow to 60 feet? Answers must be shown as a one variable algebraic equation with 'x' equaling the same value on each side of the equation. I believe the correct answer is 240 years, but I don't know how to show the work in the proper way. ----------------------------------------------- Slope is always the amount y grows when x increases by one. --- slope = 1/2 inch per year ----- intercept is always the value of y at zero, or at the "beginning". ------------- intercept = 50 feet = 600 inches =================================================================== height = (1/2)t+600 ----- How long to get to a height of 60 ft. or 720 inches --- (1/2)t + 600 = 720 (1/2)t = 120 t = 240 years ======================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/221560: Hello my name is Wanda, I have been trying to solve this by using the substitution system. The question is: A class of Math A 30 students contains twice as many girls as boys. Last Friday, when two of the boys were absent and all the girls were there, the number of girls tripled the number of boys. How many boys and how many girls are in the class? These are the two equations I came up with. But I just can't make it work. 2G = B 3G = B - 2 I'd appreciate your help. 1 solutions Answer 166159 by stanbon(57307)   on 2009-10-04 19:32:41 (Show Source): You can put this solution on YOUR website!The question is: A class of Math A30 students contains twice as many girls as boys. Last Friday, Equation: g = 2b -------------------------------- when two of the boys were absent and all the girls were there, the number of girls tripled the number of boys. Equation: g = 3(b-2) How many boys and how many girls are in the class? Substitute for "g" and solve for "b": 2b = 3b-6 b = 6 (# of boys before 2 were absent) --- Since g = 3(b-2), g = 3(6-2) = 12 (# of girls) ================================================== Cheers, Stan H. ----------------------------------------------
 Matrices-and-determiminant/221565: A bus leaves a depot traveling at 40 mi/hr.. An hour later a car leaves the station at 60 m/hr. Sketch d=fn(t) diagram When (t) and where (d) do they meet?1 solutions Answer 166145 by stanbon(57307)   on 2009-10-04 19:01:56 (Show Source): You can put this solution on YOUR website!A bus leaves a depot traveling at 40 mi/hr.. An hour later a car leaves the station at 60 m/hr. Sketch d=fn(t) diagram When (t) and where (d) do they meet? ------------------ Bus DATA: rate = 40 mph ; time = t hrs. ; distance = 40t miles ----------------------- Car DATA: rate = 60 mph ; time = (t-1) hrs; distance = 60(t-1) miles ------------------------- Equations: Bus:::: d = 40t Car;;;; d = 60(t-1) -------------------------- ----------------------------- They meet at t = 3 hrs. and d = 120 miles ================================================ Cheers, Stan H.
 Numbers_Word_Problems/221548: How many different pairs of letters from the English alphabet are possible?1 solutions Answer 166143 by stanbon(57307)   on 2009-10-04 18:55:10 (Show Source): You can put this solution on YOUR website!Ans: 26C2 = (26*25)/(1*2) = 13*25 = 325 ========================================== ANOTHER WAY TO DO IT: Choose the 1st letter: 26 ways Choose the 2nd letter: 25 ways ------ 26*25 gives you the total number of pairs you could form but it includes a/b and b/a which are really just one pair. So you divide by 2 to get the number of unique pairs. You get: (26*25)/(2) = 325 unique pairs. ---------------------- Cheers, Stan H.
 Linear-systems/221527: Can someone explain to me how to maximize by the simplex method? I get confused after the second step. Here is the problem, Maximize P=0.3x ++ 0.4y Subject to: 4x + 8y equals or less than 1600 12x+8y equal or less than 1920 x equal to or greater than 0; y equal to or greater than 0 Please help me. I know how to do the first step of charting but the second step on confuses me? How do I decide which negative should be the pivot point?1 solutions Answer 166141 by stanbon(57307)   on 2009-10-04 18:32:09 (Show Source): You can put this solution on YOUR website!Here is the problem, Maximize P=0.3x ++ 0.4y Subject to: 4x + 8y equals or less than 1600 12x+8y equal or less than 1920 x equal to or greater than 0; y equal to or greater than 0 Please help me. I know how to do the first step of charting but the second step on confuses me? How do I decide which negative should be the pivot point? ------------------------------------------ Solve each of the inequalities for "y" y <=(-1/2)x + 200 y <= (-3/2)x + 240 --------------------------- Plot those boundary lines and the intersecting solution regions. -------------------------- Find the corners of the solution region:(0,0),(0,200),(40,180),(160.0) ---------------------- Check each of those number pairs in P=0.3x + 0.4y to determine which pair give you the maximum "p" value. (0,0) gives P = 0 (0,200) gives p = 0 + 0.4*200 = 80 (40,180) gives p = 0.3*40 + 0.4*180 = 84 (150,0) gives p = 0.3*150 + 0 = 45 -------------------------------------------- So (40,180) gives the maximum Profit. =============================================== Cheers, Stan H.