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# Recent problems solved by 'stanbon'

stanbon answered: 57174 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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Probability-and-statistics/195196: Please help. On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons who score (a)340 (b) 310 and (c) 260. Give the raw scores for persons whose Z scores on the test are (d) 2.4 , (e) 1.5, (f) 0 and (g) -4.5.1 solutions Answer 146403 by stanbon(57242)   on 2009-05-06 21:18:35 (Show Source): You can put this solution on YOUR website!On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons who score (a)340 (b) 310 and (c) 260. These raw scores are converted with the formula z = (x - xbar)/sigma Ex: z(340) = (340-300)/20 = 40/20 = 2 ------------------------------------------------------- Give the raw scores for persons whose Z scores on the test are (d) 2.4 , (e) 1.5, (f) 0 and (g) -4.5. These z scores can be converted using x = z*sigma + xbar Ex: x(2.4) = 2.4*20 + 300 = 48 + 300 = 348 ======================================================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/195085: helloo sir, 1] A merchant sold his goods for Rs.75 at a profit per cent equal to its cost price .The cost price was ? waiting for yurs reply. thank u.1 solutions Answer 146322 by stanbon(57242)   on 2009-05-06 11:28:20 (Show Source): You can put this solution on YOUR website!hello sir, 1] A merchant sold his goods for Rs.75 at a profit per cent equal to its cost price. The cost price was ? waiting for your reply. ------------------------------- P = R - C 0.75C = 75 - C 1.75C = 75 Cost = 42.86 Rs ================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/195049: Respected sir, [1] The percent profit made when an article is sold for Rs.78 is twice as when it is sold for Rs. 69.The cost price of the article is ? plz solve my problem...1 solutions Answer 146307 by stanbon(57242)   on 2009-05-06 07:53:44 (Show Source): You can put this solution on YOUR website!The percent profit made when an article is sold for Rs.78 is twice as when it is sold for Rs. 69.The cost price of the article is ? ---------------- Profit = Revenue - Cost --------- Equations: 2p = 78 - C p = 69 - C ----------------- p = 9 ---- Substitute into p = 69 - C to get: 9 = 69 - C Cost = 60Rs ================== Cheers, Stan H.
 Probability-and-statistics/194561: . Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline that will have the best fuel economy. The four grades are: regular, below regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades and the miles per gallon recorded. At the 0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon for each fuel is the same. Kilometers per liter Regular Below Regular Premium Super Premium 39.31 36.69 38.99 40.04 39.87 40.00 40.02 39.89 39.87 41.01 39.99 39.93 1 solutions Answer 146306 by stanbon(57242)   on 2009-05-06 07:44:13 (Show Source): You can put this solution on YOUR website!Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline that will have the best fuel economy. The four grades are: regular, below regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades and the miles per gallon recorded. At the 0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon for each fuel is the same. Kilometers per liter Regular Below Regular Premium Super Premium 39.31 36.69 38.99 40.04 39.87 40.00 40.02 39.89 39.87 41.01 39.99 39.93 ----------------------------------- Ho: the means are all equal Ha: at least one of the means is not the same --------------- I ran an ANOVA Test on the columnar data and found F = 0.19135.... ------ By the way, the p-value was 89%. Gas grade made no difference. ============================== Cheers, Stan H.
 Probability-and-statistics/195010: Please help. A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. Corporations. The figures for the governors were 44, 36, 52 and 40 square feet. The figures for the CEOs were 32, 60 48 and 36 square feet. (a) Figure the mean and the standard deviation for the governors and for the CEOs. (b)Explain what you have done to a person who has never had a course in statistics (c) Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. Governors and large corporations’ CEOs in general.1 solutions Answer 146296 by stanbon(57242)   on 2009-05-05 22:29:21 (Show Source): You can put this solution on YOUR website!A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. Corporations. The figures for the governors were 44, 36, 52 and 40 square feet. The figures for the CEOs were 32, 60 48 and 36 square feet. ------------------------------------ (a) Figure the mean and the standard deviation for the governors and for the CEOs. Governors: x-bar = 43 : s = 6.83 CEO: x-bar = 44 ; s = 12.65 -------------------------------------- (b)Explain what you have done to a person who has never had a course in statistics I'll leave that to you. -------------------------------------- (c) Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. Governors and large corporations’ CEOs in general. Means are about the same. The range is twice as wide for CEO's, indicating some CEO have much larger desks and some have much smaller desks. ==================================================================== Cheers, Stan H.
 Quadratic_Equations/194982: I have four questions. 1) Find and label the vertex and the line of symetry f(x)=1/3x^2 2) Find the line of symetry f(x)=(x+2)^2 3) Nature of the solutions x^2-6=0 I say 2 real solutions am I correct? 4) Number of tickets sold each day is given by N(x)=-0.3x^2 +7.2x+14 where x is the number of days since the show was announced. When will the daily tickets sales peak? How many tickets will be sold on the first day? Thanks in advance 1 solutions Answer 146293 by stanbon(57242)   on 2009-05-05 21:52:49 (Show Source): You can put this solution on YOUR website!1) Find and label the vertex and the line of symetry f(x)=1/3x^2 x^2 = 3y (x-0)^2 = 3(y-0) Vertex is (0,0) Axis of symmetry is x = 0 ============================================== 2) Find the line of symetry f(x)=(x+2)^2 (x+2)^2 = y-0 Since vertex is (-2,0), the axis of symmetry is x = -2 ============================================== 3) Nature of the solutions x^2-6=0 I say 2 real solutions am I correct? x = sqrt(6) and x = -sqrt(6) Two Real Number solutions. ============================================== 4) Number of tickets sold each day is given by N(x)=-0.3x^2 +7.2x+14 where x is the number of days since the show was announced. When will the daily tickets sales peak? max occurs at x = -b/2a = -7.2(2*-0.3) = 12 Peak sales 12 days after the show was announced. ------------------------------------------------------- How many tickets will be sold on the first day? N(0) = 14 =============== Cheers, Stan H.
 Rational-functions/194984: please help me out........... -54=10-(m-10)^3/21 solutions Answer 146289 by stanbon(57242)   on 2009-05-05 21:42:55 (Show Source): You can put this solution on YOUR website!-54=10-(m-10)^3/2 --- (m - 10)^(3/2) = 64 --- Raise both sides to the 2/3 power to get: m - 10 = 64^(2/3) -------- Take the cube root of the right side: m-10 = 4^2 Square the right side m - 10 = 16 m = 26 ============ Cheers, Stan H.
 Rational-functions/195007: This question is from textbook Algebra 2 (x/x+1)/(x+(x/3) 1 solutions Answer 146285 by stanbon(57242)   on 2009-05-05 21:27:47 (Show Source): You can put this solution on YOUR website!(x/x+1)/(x+(x/3) --------- (x/(x+1)) / ((3x+x)/3} ------------- Invert the denominator and multiply: = (x/(x+1)) * (3/(4x)) ------------- Cancel the "x" that is common to numerator and denominator: ------------- = (3/4)(x+1) =============== Cheers, Stan H.
 Miscellaneous_Word_Problems/195012: Using mathematical calculations, explain why the speed of light ("c") is the absolute "speed limit" in the universe. Can't use imaginary clock!1 solutions Answer 146284 by stanbon(57242)   on 2009-05-05 21:22:27 (Show Source): You can put this solution on YOUR website!You will probably find a nice discussion of that fact using Google on the net. Cheers, Stan H.
 Probability-and-statistics/195013: eleven people are entered in a race. if there are no ties, in how many ways can the first two places come out?1 solutions Answer 146283 by stanbon(57242)   on 2009-05-05 21:20:44 (Show Source): You can put this solution on YOUR website!eleven people are entered in a race. if there are no ties, in how many ways can the first two places come out? ------------ # of ways to have the 1st place = 11 # of ways to have the 2nd place = 10 ----------- Total # of ways = 110 =========================== Cheers, Stan H.
 Probability-and-statistics/195014: in how many ways can you choose 4 cassettes from the 9 you own?1 solutions Answer 146282 by stanbon(57242)   on 2009-05-05 21:18:21 (Show Source): You can put this solution on YOUR website!in how many ways can you choose 4 cassettes from the 9 you own? ------------- 9C4 = (9*8*7*6)/(1*2*3*4) = 126 ============ Cheers, Stan H.
 expressions/195002: Simplify the expression by first factorising the numerator and the denominator 7x+14y _____________ 3x+6y+nx+2ny1 solutions Answer 146278 by stanbon(57242)   on 2009-05-05 20:55:21 (Show Source): You can put this solution on YOUR website!Simplify the expression by first factorising the numerator and the denominator (7x+14y) / (3x+6y+nx+2ny) --- (7(x+2y)) / (3(x+y) + n(x+2y)) ------ (7(x+2y)) / (3(x+y) + n(x+2y)) ------ Comment: No simplifying is possible because there is no factor common to the numerator and the denominator. ===================================================== Cheers, Stan H.
 Probability-and-statistics/195001: Find the number of permutations. 7P61 solutions Answer 146273 by stanbon(57242)   on 2009-05-05 20:47:17 (Show Source): You can put this solution on YOUR website!Find the number of permutations. 7P6 ------------------------------------------ 7P6 = 7!/(7-6)! = 7!/1! = 7*6*5*4*3*2 = 5040 =============================================== Cheers, Stan H.
 Probability-and-statistics/194999: Find the number of combinaTIONS? 7c51 solutions Answer 146271 by stanbon(57242)   on 2009-05-05 20:43:22 (Show Source): You can put this solution on YOUR website!Find the number of combinaTIONS? 7c5 7C5 = 7!/[(7-5)!*5!] = (7*6)/(1*2) = 7*3 = 21 ================ Cheers, Stan H.
 Unit_Conversion_Word_Problems/194993: The posted speed limit on many US highways is 65 miles per hour. What is this speed in feet per second? Please help???????1 solutions Answer 146269 by stanbon(57242)   on 2009-05-05 20:39:55 (Show Source): You can put this solution on YOUR website!The posted speed limit on many US highways is 65 miles per hour. What is this speed in feet per second? ------------------- 65 (miles/hour)(5280 ft./mile)(1 hour/3600 seconds) --- = (65*5280*1/1*1*3600)(feet/second) --- = (95.3333..) feet/second =================================== Cheers, Stan H.
 Equations/194994: The quotient of a number and 7 is 63?1 solutions Answer 146265 by stanbon(57242)   on 2009-05-05 20:26:49 (Show Source): You can put this solution on YOUR website!The quotient of a number and 7 is 63? --------------------- Equation: x/7 = 63 Multiply both sides by 7 to get: x = 7*63 x = 441 =========================== Cheers, Stan H.
 Probability-and-statistics/194987: six balls numbered from 1 to 6 are placed in a urn. if one ball is selected at random, find the probability that it is number 3. 1 solutions Answer 146263 by stanbon(57242)   on 2009-05-05 20:21:53 (Show Source): You can put this solution on YOUR website!six balls numbered from 1 to 6 are placed in a urn. if one ball is selected at random, find the probability that it is number 3. ---------------------- # of ways to succeed is 1 # of possible outcomes is 6 ----------- Probability of a "3" being drawn = 1/6 ========================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/194979: Hi, could you please help me with factoring? 4s^3+12s^2-64s-192= I am not sure what I am doing, but I am not coming up with the correct answer. Thanks1 solutions Answer 146260 by stanbon(57242)   on 2009-05-05 19:41:03 (Show Source): You can put this solution on YOUR website!please help me with factoring? 4s^3+12s^2-64s-192 Factor the 1st two and the last two terms separately to get: = 4s^2(s+3) - 64(s + 3) --- = (s+3)(4s^2- 64) --- = 4(s+3)(s^2 - 16) --- = 4(s+3)(s-4)(s+4) ======================= Cheers, Stan H.
 Quadratic_Equations/194973: How would you us e the quadratic equation to answer: 4z^2+z-6=0 Thank you1 solutions Answer 146257 by stanbon(57242)   on 2009-05-05 19:34:38 (Show Source): You can put this solution on YOUR website!How would you us e the quadratic equation to answer: 4z^2+z-6=0 ----------------- ForM x = [-b +- sqrt(b^2 - 4ac)]/(2a) ---------------------- Your Problem: a = 4 ; b = 1 ; c = -6 ---------------------------- z = [-1 +- sqrt(1 -4*4*-6)]/(2*4) --- z = [-1 +- sqrt(1+ 96)]/8 z = [-1 +- sqrt(97)]/8 z = [-1 + sqrt(97)]/8 or z = [-1 - sqrt(97)]/8 =================================================== Cheers, Stan H.
 test/194975: This question is from textbook CPM ALGEBRA VOLUME 2 UNITS 7-13 A).(FIND SLOPE LINE OF (10,2) AND (2,24)1 solutions Answer 146254 by stanbon(57242)   on 2009-05-05 19:13:37 (Show Source): You can put this solution on YOUR website!FIND SLOPE LINE OF (10,2) AND (2,24) --- slope = (24-2)/(2-10) slope = 22/-8 = -11/4 ---------------------------- Cheers, Stan H.
 Probability-and-statistics/194586: An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was \$275.66 with a standard deviation of \$78.11. (a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than \$250 out-of-pocket? State your hypotheses and decision rule. (b) Is this a close decision?1 solutions Answer 146253 by stanbon(57242)   on 2009-05-05 19:09:19 (Show Source): You can put this solution on YOUR website!An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was \$275.66 with a standard deviation of \$78.11. (a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than \$250 out-of-pocket? State your hypotheses and decision rule. ---------------- Ho: u <= 250 Ha: u > 250.11 --- test statistic: t(275.66) = (275.66-250)/[78.11/sqrt(25)] = 1.6426 --- p-value = P(t > 1.6426 with df = 24) = 0.0568 ----------------- Conclusion: Since the p-value is greater than 5%, fail to reject Ho. -------------------- (b) Is this a close decision? Yes as the p-value is not much greater than 5%. ------------------------------- Cheers, Stan H.
 Probability-and-statistics/194912: 0 260 356 403 536 0 268 369 428 536 268 396 359 536 162 338 403 536 536 130 (a) Construct a 95 percent confidence interval for the true mean. (b) Why might normality be an issue here? (c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence? (d) If this is not a reasonable requirement, suggest one that is. 1 solutions Answer 146248 by stanbon(57242)   on 2009-05-05 18:54:37 (Show Source): You can put this solution on YOUR website!260 356 403 536 0 268 369 428 536 268 396 359 536 162 338 403 536 536 130 ------------ Hopefully you can find the mean (x-bar) and the standard deviation (s), which is needed to calculate the standard error (E). Do that first then attack the questions below. -------------- (a) Construct a 95 percent confidence interval for the true mean. x-bar-E < u < x-bar+E ---------------------------------- (b) Why might normality be an issue here? I'll leave that to you. ---------------------------------- (c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence? Since E = zs/sqrt(n) sqrt(n) = zs/E then n = [zs/E]^2 --- For a 95% C.I., z = 1.96 You have figured out the sample standard deviation You are told that E = 10 So n = [1.96*s/10]^2 ----------------------------------- (d) If this is not a reasonable requirement, suggest one that is. If "n" seems too large you could reduce the confidence requirement, or increase the size of the error limit. ============================================= Get back to me if you need further help. ============================================= Cheers, Stan H.
 Finance/194956: How to do calculation 223.13 = x + 5%. What is x? I don't know how to do this.1 solutions Answer 146236 by stanbon(57242)   on 2009-05-05 17:53:54 (Show Source): You can put this solution on YOUR website!223.13 = x + 5%. What is x 223.13 = x + 0.05 x = 223.13 - 0.05 x = 223.08 =============== Cheers, Stan H.
 Probability-and-statistics/194889: Five cards are drawn from a deck without replacement. The number of aces is counted. Find the expected number of aces.1 solutions Answer 146235 by stanbon(57242)   on 2009-05-05 17:45:06 (Show Source): You can put this solution on YOUR website!Five cards are drawn from a deck without replacement. The number of aces is counted. Find the expected number of aces. ------------------ The random varible, X, is a count of the number of acces drawn. Values of the random variable are 0, 1, 2, 3, 4 --------------------------------------------------- The corresponding probabilities are: P(X = 0) = 49C5/52C5 ---------- P(X = 1) = [4C1*48C4]/52C5 ---------- P(X = 2) = (4C2*48C3)/52C5 ---------- P(X = 3) = (4C3*48C2)/52C5 ------------- P(x = 4) = (4C4*48C1)/52C5 -------------- To find the expected number of aces drawn, multiply each X value by its corresponding probability ; then add the four products. =========================================== Cheers, Stan H.
 Probability-and-statistics/194890: The following time series data represent the quarterly amounts spent on advertising (in millions of dollars) by a large toy company (read across): Quarter 1 Quarter 2 Quarter 3 Quarter 4 14.8 14.8 12.6 13.0 15.8 15.1 13.3 14.9 13.3 16.3 16.6 15.7 16.6 14.3 18.3 14.4 17.9 16.2 16.6 16.9 17.7 16.5 19.4 This series of data begins in Quarter 1 of 1996 (i.e., time t=1 corresponds to the first quarter of 1996). Using regression analysis, a linear trend line of the form Tt=13.44 + 0.19t was fit to the data. Using this information, generate a forecast for the total yearly amount of money that will be spent on advertising in 2009. 1 solutions Answer 146200 by stanbon(57242)   on 2009-05-05 13:53:16 (Show Source): You can put this solution on YOUR website!The following time series data represent the quarterly amounts spent on advertising (in millions of dollars) by a large toy company (read across): Quarter 1 Quarter 2 Quarter 3 Quarter 4 14.8 14.8 12.6 13.0 15.8 15.1 13.3 14.9 13.3 16.3 16.6 15.7 16.6 14.3 18.3 14.4 17.9 16.2 16.6 16.9 17.7 16.5 19.4 This series of data begins in Quarter 1 of 1996 (i.e., time t=1 corresponds to the first quarter of 1996). Using regression analysis, a linear trend line of the form Tt=13.44 + 0.19t was fit to the data. Using this information, generate a forecast for the total yearly amount of money that will be spent on advertising in 2009. ----------- The "t" values for 1997 would be 5,6,7,9 Because 1997 is 1 year after 1996 ---------- 2009 is 13 years after 1996 so the "t" values would be 1+13*4 = 53, 54, 55,56 --------------- Then: T(53) = 13.44 + 0.19*53 = 23.51 T(54) = 23.51 + 0.19 = 23.7 T(55) = 23.7 + 0.19 = 23.89 t(56) = 23.89 + 0.19 = 24.08 ------------------------------ Add those up to get the money spent for the year. =================================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/194810: The average hourly wage of employees of a certain company is \$9.83. Assume the variable is normally distributed. If the standard deviation is \$4.58, find the probability that a randomly selected employee earns less than \$5.43. 1 solutions Answer 146144 by stanbon(57242)   on 2009-05-04 23:29:21 (Show Source): You can put this solution on YOUR website!The average hourly wage of employees of a certain company is \$9.83. Assume the variable is normally distributed. If the standard deviation is \$4.58, find the probability that a randomly selected employee earns less than \$5.43. --------------------------------- Find the z-value of 5.43 ----- z(5.43) = (5.43-9.83)/4.58 = -0.9607 ----------------------------------- P(x < 5.43) = P(z < 0.9607) = 0.1684 ========================================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/194795: two teachers are going to a conference for a fewdays.Mrs.Jerrerson plane on spending \$502 on 14 meals and 4 nights in a hotel. Mrs.Lloyd plans on spending \$370 on 10 meals and 3 nights in a hotel. How much are they planning on spending pre meal and pre night for a hotel1 solutions Answer 146143 by stanbon(57242)   on 2009-05-04 23:23:13 (Show Source): You can put this solution on YOUR website!two teachers are going to a conference for a fewdays.Mrs.Jerrerson plane on spending \$502 on 14 meals and 4 nights in a hotel. Mrs.Lloyd plans on spending \$370 on 10 meals and 3 nights in a hotel. How much are they planning on spending pre meal and pre night for a hotel ----------------------- Equations: 4n + 14m = 502 3n + 10m = 370 ----------------- Solve the system by any means you know to get: n = \$80 (price per night for a hotel room) m = \$13 (price per meal) =============================== Cheers, Stan H.
 Reduction-of-unit-multipliers/194807: It says perform the following unit conversions. 3 3/4yd.=____in. The only thing so far that I come up with is:15/4=3.75 I cannot figure out what to do next. Please help. Thanks, Kathy Price1 solutions Answer 146139 by stanbon(57242)   on 2009-05-04 23:16:13 (Show Source): You can put this solution on YOUR website!It says perform the following unit conversions. 3 3/4yd.=____in. ------------- [(15/4)yd] * [36 in/1 yd] Note: 36 in / 1 yd is the "unit converter" in this case. It converts yds to inches. --- = [(15*36)/(4*1)] in = 15*9 in = 135 inches ============================ Cheers, Stan H.
 Linear-equations/194797: Solve the following linear using the Addition Method. Describe in words the steps you will take to do that. 3x + 4y = -6 5x + 6y = -21/21 solutions Answer 146135 by stanbon(57242)   on 2009-05-04 23:12:05 (Show Source): You can put this solution on YOUR website!3x + 4y = -6 5x + 6y = -21/2 -------------------- Multiply thru the 1st equation by 5 ; Multiply thru the 2nd equation by -3. ------------------------------ 15x + 20y = -30 -15x - 18y = 63/2 ----------------------- Add so you can solve for "y": 2y = 3/2 y = 3/4 -------------- Substitute in 3x + 4y = -6 to solve for "x": 3x + 4(3/4) = -6 3x + 3 = -6 3x = -9 x = -3 ------------------------------- Cheers, Stan H.
 Trigonometry-basics/194801: I'm trying to plot points on a graph. the problem is y=3sec4x. I have all the points but one. I'm stuck at 5 pi/2. I have no idea how to find this on the unit circle. Explain plz?1 solutions Answer 146131 by stanbon(57242)   on 2009-05-04 23:02:41 (Show Source): You can put this solution on YOUR website!I'm trying to plot points on a graph. the problem is y=3sec4x. I have all the points but one. I'm stuck at 5 pi/2. I have no idea how to find this on the unit circle. Explain plz? ------------------------------- Try cos(5pi/2) which is the same as cos(pi/2) = 0 ----------- Since sec is the inverse of cos, sec(5pi/2) is undefined. --------------- Cheers, Stan H.
 Graphs/194806: What is the 14th term in an arithmetic sequence in which the first term is 100 and the common difference is -4 ?1 solutions Answer 146128 by stanbon(57242)   on 2009-05-04 22:56:44 (Show Source): You can put this solution on YOUR website!What is the 14th term in an arithmetic sequence in which the first term is 100 and the common difference is -4 ? --------------- a(14) = 100 + (14-1)(-4) a(14) = 100 + 13*-4 a(14) = 100 - 52 a(14) = 48 =============== Cheers, Stan H.