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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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 Linear_Equations_And_Systems_Word_Problems/183226: The difference of two numbers is 3. Their sum is 13. Find the numbers.1 solutions Answer 137570 by stanbon(57410)   on 2009-02-22 17:53:24 (Show Source): You can put this solution on YOUR website!The difference of two numbers is 3. Their sum is 13. Find the numbers. ---------- x - y = 3 x + y = 13 ------------- Add the two equations to get: 2x = 16 x = 8 ------------- Substitute into x + y = 13 to solve for "y": 8 + y = 13 y = 5 ------------------------ Solution : x = 8 and y = 5 ================================ Cheers, Stan H.
 Exponents/183219: (3z^4 - 8)^21 solutions Answer 137568 by stanbon(57410)   on 2009-02-22 17:48:50 (Show Source): You can put this solution on YOUR website! (17:21:47): (3z^4 - 8)^2 ---------------------- [17/(21/47)) / (3z^4 - 8)^2 = [(17*47)21] / (9z^8 - 2*8*3z^4 + 64) = [38.048] / [9z^8 - 48z^4 + 64] ======================================= Cheers, Stan H.
 Probability-and-statistics/183154: Hi, Can you please help me solve for this, Doane−Seward: Applied Statistics in Business and Economics, ch. 15: High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as “Low” (under 88 decibels), “Medium” (88 to 91 decibels), or “High” (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research question: At α = .05, is the cockpit noise level independent of flight phase? (Data are from Capt. Robert E. Hartl, retired.) Noise Level Climb Cruise Descent Row Total Low 6 2 6 14 Medium 18 3 8 29 High 1 3 14 18 Col Total 25 8 28 61 (This format is cramming the numbers together to make it easier to read - Noise Level: Low, Climb: 6, Cruise: 2, Descent: 6, Row Total: 14.) Thank you1 solutions Answer 137563 by stanbon(57410)   on 2009-02-22 17:23:14 (Show Source): You can put this solution on YOUR website!High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as “Low” (under 88 decibels), “Medium” (88 to 91 decibels), or “High” (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research question: At α = .05, is the cockpit noise level independent of flight phase Noise level climb cruise descent row total low 6 2 6 14 medium 18 3 8 29 high 1 3 14 18 col total 25 8 28 61 ------------------------- Ho: row and column factors are independent Ha: they are dependent ---- I ran a Chi-Sq. Test on the 3 by 3 array of data. Test Statistic: Chi-Sq. = 15.160 p-value: 0.004 df: (3-1)(3-1) = 4 ------- Conclusion: Since p-value is less than 5%, Reject Ho. The row and column factors are dependent. ============================================= Cheers, Stan H.
 Probability-and-statistics/183159: A bag contains 23 cubes, of which 13 are red. Three cubes are drawn simultaneously, without replacement. Let x be the number of red cubes drawn. Find the expected value of x.1 solutions Answer 137535 by stanbon(57410)   on 2009-02-22 14:30:52 (Show Source): You can put this solution on YOUR website!A bag contains 23 cubes, of which 13 are red. Three cubes are drawn simultaneously, without replacement. Let x be the number of red cubes drawn. Find the expected value of x. ---------------------- Random Variable Values: 0,1,2,3 This is the number of red balls drawn ------------------------------------------ Corresponding Probabilities: P(x=0) = 10C3/23C3 P(x=1) = [13C1*10C2]/23C3 P(x=2) = [13C2*10C1]/23C3 P(x=3) = 13C3/23C3 ------------------------------------------- To calculate the "expected value", Multiply each random variable value by its probability. Then add up the 4 products. That is the expected value of "x". -------------------------------------- [10C3/23C3]*0 = 0 [[13C1*10C2]/23C3]*1 = 0.3303 [[13C2*10C1]/23C3]*2 = 0.8807 [13C3/23C3]*3 = 0.4845 -------- Adding you get 0.3303+-8807+.4845 = 1.7 That is the expected value of "x". Cheers, Stan H.
 Miscellaneous_Word_Problems/182992: Complete the magic square below. This box has a total 9 blocks 3 on top and 3 down each row. On the first row and inthe last box 21 goes in there. On the second row in the middle box 19 goes in there. On the last row, in the first box 17 gowes in there and in the last box 26 goes in there. 1 solutions Answer 137523 by stanbon(57410)   on 2009-02-22 11:32:20 (Show Source): You can put this solution on YOUR website!Use Google to get information on solving Magic Squares. Cheers, Stan H.
 Money_Word_Problems/183125: This question is from textbook Mr.adams will be serving 20 people at a barbeque. He plans to make two hamburgers for each person. Mr. Adams spent \$27.00 at the store on meat, which sells for \$2.25 per pound. If Mr.Adams wants to make all the hamburgers the same size, what will be the size, in pounds of each hamburger?1 solutions Answer 137519 by stanbon(57410)   on 2009-02-22 10:55:06 (Show Source): You can put this solution on YOUR website!Mr.adams will be serving 20 people at a barbeque. He plans to make two hamburgers for each person. Mr. Adams spent \$27.00 at the store on meat, which sells for \$2.25 per pound. If Mr.Adams wants to make all the hamburgers the same size, what will be the size, in pounds of each hamburger? ------------ # of people: 20 # of hamburgers: 40 # of pounds of hamburger: 27/2.25 = 12 weight of each hamburger: 40/12 = 0.3 lbs ---------------------------------------------- Cheers, Stan H.
 Rational-functions/183000: Difference Quotient A. Given the function g(x) - x^2 - 3x + 5, find the difference quotient g(x+h) - g(x)/h. B. Given the function f(x) = -x^2 + 2x -3, find the difference quotient.. 1 solutions Answer 137518 by stanbon(57410)   on 2009-02-22 10:49:05 (Show Source): You can put this solution on YOUR website!Difference Quotient A. Given the function g(x) - x^2 - 3x + 5, find the difference quotient g(x+h) - g(x)/h. --------------- g(x+h) = (x+h)^2 - 3(x+h) + 5 g(x+h) = x^2 + 2hx + h^2 - 3x - 3h + 5 Now subtract g(x) from f(x+h) to get: g(x+h)-g(x) = 2hx + h^2 - 3h Now divide by "h": [g(x+h)-g(x)]/h = 2x + h - 3 =================================== B. Given the function f(x) = -x^2 + 2x -3, find the difference quotient.. f(x+h) = -(x+h)^2 + 2(x+h) - 3 f(x+h) = -(x^2 + 2hx + h^2) + 2x + 2h -3 f(x+h) = -x^2 - 2hx - h^2 + 2x + 2h - 3 Now subtract f(x) from f(x+h) to get f(x+h)-f(x) = -2hx - h^2 + 2h Now divide by "h" [f(x+h)-fIx)]/h = -2x - h + 2 ==================================== Cheers, Stan H.
 Mixture_Word_Problems/183089: 1.moonshine has 50 liters of a 70% alcohol solution.how many liters of pure alcohol must be added to obtain an 80% alcohol solution 2.how many kg of pure salt must be added to 20 kg of a 10% salt solution to obtain a 25% salt solution 3. how much pure acid must be added to 6 ml of a 5% acid solution to produce a 40% acid solution? 1 solutions Answer 137510 by stanbon(57410)   on 2009-02-22 09:17:29 (Show Source): You can put this solution on YOUR website!1.moonshine has 50 liters of a 70% alcohol solution. How many liters of pure alcohol must be added to obtain an 80% alcohol solution? --- Equation: active + active = active 0.70*50 + 1.00x = 0.80(50+x) solve for "x" -------------------- 2.how many kg of pure salt must be added to 20 kg of a 10% salt solution to obtain a 25% salt solution --- Equation: active + active = active 0.10*20 + 1.00x = 0.25(20+x) solve for "x" --------------------- 3. how much pure acid must be added to 6 ml of a 5% acid solution to produce a 40% acid solution? --- Equation: active + active = active 0.05*6 + 1.00x = 0.40(6+x) solve for "x" ====================== Cheers, Stan H.
 Polynomials-and-rational-expressions/183060: I need help with this problem find the quotient and remainder for this division (a3-3a2+4a-4):(9-2)1 solutions Answer 137509 by stanbon(57410)   on 2009-02-22 09:10:29 (Show Source): You can put this solution on YOUR website!You have a typo in your posted problem. Cheers, Stan H.
 Equations/183120: Is x=y^4+5 a function?1 solutions Answer 137508 by stanbon(57410)   on 2009-02-22 09:08:54 (Show Source): You can put this solution on YOUR website!Is x=y^4+5 a function? -------- Solve for "y": y = (x-5)^(1/4) ----------------- Example: If you let x = 21 you get y = (21-5)^(1/4) y = 16^(1/4) y = 2 or y = -2 --------------------- Since there are two y-values for a single value of "x" x = y^4+5 is not a function. ==================================== Cheers, Stan H.
 Proportions/183090: identify the amount,base,and p value of 25% of 400cars is 100 cars 45 of 50 children is 90% in a recent survey38% ofUnited States say that gas prices have affected the type 0f vehecle they will buy. In a sample of 500 people who are in the market for a new vehcle,how many would you expect to be influenced by gas prices? Yellowstone National Park has 3366mi.2 of undevelopedland. If this represents 99% of the totalarea,fine the total area of the park? As of the2002--2003 football season,Peyton Manning had completed 1357 passes out of 2226 attempts. Find his completion percetage to the nearest tenth of a percent.1 solutions Answer 137506 by stanbon(57410)   on 2009-02-22 09:04:05 (Show Source): You can put this solution on YOUR website!identify the amount,base,and p value of 25% of 400cars is 100 cars amount: 100 base: 400 p-value: 25 or maybe 25% (depends on what your text says) ------------------------------- 45 of 50 children is 90% mount: 45 base: 50 p-value: 90 or 90% ------------------------------- in a recent survey38% ofUnited States say that gas prices have affected the type 0f vehecle they will buy. In a sample of 500 people who are in the market for a new vehcle,how many would you expect to be influenced by gas prices? --- 18% of 500 = 90 people ------------------- Yellowstone National Park has 3366mi.2 of undevelopedland. If this represents 99% of the total area, ,find the total area of the park? --- 0.99*(total area) = 3366 sq mi total area = 3366/0.99 = 3400 sq. mi. -------------------------------- As of the 2002--2003 football season, Peyton Manning had completed 1357 passes out of 2226 attempts. Find his completion percentage to the nearest tenth of a percent. 1357/2226 = 0.60961 = 61% ================================ Cheers, Stan H.
 Linear_Algebra/183119: This question is from textbook Contemporary Linear Algebra 17. In each part, sketch the vector u + v+ w, and express it in component form. (What am I doing wrong? I got the coordinate points of each initial point of the vectors and head of each vector, then I applied the formula and I am not getting the same answer as the book which is (-2,5). The head point for u is (5,-5), v is (-5,-3), and W is (-2,5). The coordinates for the initial points are u = (0,0), v = (5,-5), and w is (-5,-3). Initial points: u= (0,0) V= (5, -5), w = (-5,-3) Terminal Points u= (5,-5), v= (-5,-3) and w= (-2,5) 1 solutions Answer 137505 by stanbon(57410)   on 2009-02-22 08:52:10 (Show Source): You can put this solution on YOUR website!17. In each part, sketch the vector u + v+ w, and express it in component form. (What am I doing wrong? I got the coordinate points of each initial point of the vectors and head of each vector, then I applied the formula and I am not getting the same answer as the book which is (-2,5). The head point for u is (5,-5), v is (-5,-3), and W is (-2,5). The coordinates for the initial points are u = (0,0), v = (5,-5), and w is (-5,-3). Initial points: u= (0,0) V= (5, -5), w = (-5,-3) Terminal Points u= (5,-5), v= (-5,-3) and w= (-2,5) -------------- The answer book is wrong: x-coordinate = 5+-5+-2 = -2 y-coordinate = -5+-3+5 = -3 ----------- Cheers, Stan H.
 Probability-and-statistics/183099: This question is from textbook Study Guide: Review 13. The 10-number math team randomly selects 4 representatives to send to a meet. What is the probability that the 4 members chosen are the 4 with the lowest math grades? 14. A 5-digit code is given to all cashiers at a store to let them log onto the cash register. What is the probability that an employee receives a code with all 5 numbers the same? Explain why the events are independent and find the probability. 25. rolling "doubles" 3 times in a row when rolling 2 number cubes 26. selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red and 15 blue pens with replacement Could you explain how to solve it? Thank you for your help.1 solutions Answer 137504 by stanbon(57410)   on 2009-02-22 08:40:27 (Show Source): You can put this solution on YOUR website!13. The 10-number math team randomly selects 4 representatives to send to a meet. What is the probability that the 4 members chosen are the 4 with the lowest math grades? --- There are 10C4 = 210 sets of 4 There is only one set that has the 4 lowest math grades P(4 lowest) = 1/210 ==================================== 14. A 5-digit code is given to all cashiers at a store to let them log onto the cash register. What is the probability that an employee receives a code with all 5 numbers the same? --- Since repetition is allowed in the code there are 5^10 different codes. There are 10 codes that have all digits the same: 00000,11111,...,99999 P(all digits are the same = 10/10^5 = 1/10^4 = 1/10,000 ===================================== Explain why the events are independent and find the probability The events are independent because once you have selected a digit, that digit is replaced for the next selection. No selection depends on the previous selection. ------------------------------------------ 25. rolling "doubles" 3 times in a row when rolling 2 number cubes P(doubles on one pair of dice) = 6/36 = 1/6 P(doubles on three separage rolls) = (1/6)^3 = 1/216 ============================================= 26. selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red and 15 blue pens with replacement --- Number of red/blue pairs = 10*15 = 150 Number of unrestricted pairs: 25C2 = 300 P(red/blue pair) = 150/300 = 1/2 =================================== Cheers, Stan H.
 Radicals/183088: Explain and Simply the rational expression: 9x-2 ---- 2-9x a) 1 b) 9x-2 c) -1 d)0 e) 2x-91 solutions Answer 137468 by stanbon(57410)   on 2009-02-21 22:08:41 (Show Source): You can put this solution on YOUR website! Explain and Simplify the rational expression: 9x-2 ---- 2-9x ==================== (9x-2) / (-(9x-2) Cancel the common facor of 9x-2 to get: = 1/-1 = -1 =========================================== Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/183077: The sum of two consecutive odd interger is 29 more than the next odd interger. Find the three intergers in increasing order.1 solutions Answer 137467 by stanbon(57410)   on 2009-02-21 22:04:24 (Show Source): You can put this solution on YOUR website!The sum of two consecutive odd interger is 29 more than the next odd interger. Find the three intergers in increasing order. ------------------------- 1st: 2x-1 2nd: 2x+1 3rd: 2x+3 ------------------- Equation: 1st + 2nd = 3rd + 29 2x-1 + 2x+1 = 2x+3 + 29 2x = 32 x = 16 ------------ 1st: 2x-1 = 31 2nd: 33 3rd: 35 ========================== Cheers, Stan H.
 Linear-equations/183078: Bobbi leaves biloxi, MS for Keokuk, Iowa at 6:00am, traveling at 50mph. two hours later, Pat leaves Keokuk, Iowa for Biloxi Traveling at 65 mph. These two city's are 560 miles apart; and they will travel the same highway. when they meet who will have traveled the farther and by how much?1 solutions Answer 137464 by stanbon(57410)   on 2009-02-21 21:56:32 (Show Source): You can put this solution on YOUR website!Bobbi leaves biloxi, MS for Keokuk, Iowa at 6:00am, traveling at 50mph. two hours later, Pat leaves Keokuk, Iowa for Biloxi Traveling at 65 mph. These two city's are 560 miles apart; and they will travel the same highway. when they meet who will have traveled the farther and by how much? -------------------------------------------- Bobbi DATA: rate = 50 mph ; time = x hrs ; distance = rt = 50x miles --------------------------------------------- Pat DATA: rate = 65 mph ; time = x-2 hrs ; distance = rt = 65(x-2) ------------------------------------------------ EQuation: distance + distance = 560 50x + 65(x-2) = 560 115x - 130 = 560 115x = 690 x = 6 hrs (Bobbi time) x-2 = 4 hrs (Pat time) -------------------- Bobbi distance = 50x = 50*6 = 300 miles -------- Pat distance = 65*(x-2) = 65*4 = 260 miles ======================================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/183081: Could you help me by showing how to divide this polynomial? (3x^3-9x-3)/(3x-3)1 solutions Answer 137458 by stanbon(57410)   on 2009-02-21 21:08:14 (Show Source): You can put this solution on YOUR website!divide this polynomial? (3x^3-9x-3)/(3x-3) ---------------------- Common Factor: [3(x^3-3x-1)] / [3(x-1)] Cancel the common factor of "3": [x^3- 3x -1] / [x-1] ------------------------ Use synthetic division: 1)....1....0....-3....-1 .......1....1....-2...|-3 Quotient: x^2+x-2 Remainder: -3 ========================== Cheers, Stan H.
 Graphs/183082: The body mass index, I, can be used to determine an individual's risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by the formula, or model, I = 700w/H^2, where W = weight, in pound's, and H = height, in inches. Jerome is 75 inches tall. What weights will keep his body mass index between 25 and 33? Jerome's body mass index will fall between 25 and 33 for the set of all weights such that ____< W < ____. (round to the nearest whole number as needed)1 solutions Answer 137453 by stanbon(57410)   on 2009-02-21 20:10:59 (Show Source): You can put this solution on YOUR website!The body mass index, I, can be used to determine an individual's risk for heart disease. An index less than 25 indicates a low risk. ------------------------------ The body mass index is given by the formula, or model, I = 700w/H^2, where W = weight, in pound's, and H = height, in inches. ------------------------------ Jerome is 75 inches tall. What weights will keep his body mass index between 25 and 33? --- 25 < I < 33 25 < 700w/H^2 < 33 H = 75 so you get: 25 < 700 w/75^2 < 33 25*75^2 < 700 w < 33*75^2 (25*75^2)/700 < w < (33*75^2)/700 200.893 lbs. < weight < 265.179 lbs. ======================================== Stan H. Jerome's body mass index will fall between 25 and 33 for the set of all weights such that ____< W < ____. (round to the nearest whole number as needed)
 Proportions/183008: Darla bicycled at an average rate of 15 miles per hour in a 60 kilometer race. Determine the lenght of time in hours that it took her to complete the race.(hint: 1.6 kilometers= 1 mile) please help1 solutions Answer 137452 by stanbon(57410)   on 2009-02-21 19:59:13 (Show Source): You can put this solution on YOUR website!Darla bicycled at an average rate of 15 miles per hour in a 60 kilometer race. Determine the lenght of time in hours that it took her to complete the race.(hint: 1.6 kilometers= 1 mile) ----------------------------------- DATA: rate = 15 mph = (15*1.6) = 24 km/h ---------------------------------- distance = 60 km ------------------------ time = distance / rate = 60/24 = 2.5 hrs. ================================================ Cheers, Stan H.
 Sequences-and-series/183079: inductive reasoning to determine the next three numbers in the pattern: 3, 12, 26, 45, 1 solutions Answer 137451 by stanbon(57410)   on 2009-02-21 19:45:42 (Show Source): You can put this solution on YOUR website!inductive reasoning to determine the next three numbers in the pattern: 3, 12, 26, 45, ------------ Quadratic function: f(n) = (5/2)n^2 + (3/2)n -1 ----------------- Next three numbers f(5) = 69 f(6) = 98 f(7) = 132 ================ Cheers, Stan H.
 Probability-and-statistics/183061: bob and fred play the following game. Bob rolls a single die. if the result is the number 1,2,3,4,5 bob must pay fred the number of dollars indicated by the number rolled. if a 6 is rolled fred must pay bob \$57 dollars. find freds expectation? 1 solutions Answer 137449 by stanbon(57410)   on 2009-02-21 19:28:43 (Show Source): You can put this solution on YOUR website!bob and fred play the following game. Bob rolls a single die. if the result is the number 1,2,3,4,5 bob must pay fred the number of dollars indicated by the number rolled. if a 6 is rolled fred must pay bob \$57 dollars. find freds expectation? --------------------------------- Random variable values: 1,2,3,4,5,-57 corresponding probabilities are each 1/6 ------------------------------------------- Expected "winnings": (1/6)(1+2+3+4+5-57) = (1/6)(-42) = -\$7.00 =============================================================== Cheers, Stan H.
 Trigonometry-basics/183067: This question is from textbook Find all solutions to the equation. Use a lowercase n to denote an arbitrary integer; separate your answers with commas; use the most compact expressions possible. -sqrt(3) + 2 sin (x) = 0 Any help is greatly appreciated! I am really struggling just to start these problems. I received 4Pi/3 + n*Pi as an answer but the system said it was wrong.1 solutions Answer 137447 by stanbon(57410)   on 2009-02-21 18:45:53 (Show Source): You can put this solution on YOUR website!-sqrt(3) + 2 sin (x) = 0 ------------------- 2sin(x) = sqrt(3) sin(x) = (1/2)sqrt(3) Take the inverse sin to get x = pi/3 or x = (2/3)pi ============================= Cheers, Stan H.
 Vectors/183074: When is it not appropriate to use the Product Rule? Give Examples please. 1 solutions Answer 137446 by stanbon(57410)   on 2009-02-21 18:33:15 (Show Source): You can put this solution on YOUR website!For what? =========================== Cheers, Stan H.
 Trigonometry-basics/183065: This question is from textbook Find all solutions to the equation. Use a lower-case n to denote an arbitrary integer; separate your answers with commas; use the most compact expressions possible. sin(4x - Pi/3) = sqrt(3)/2 Any help is greatly appreciated! I am really struggling just to get these problems started. The answer I received for this one is 2Pi/3 + 3+Pi*n but the system said that answer was wrong.1 solutions Answer 137445 by stanbon(57410)   on 2009-02-21 18:31:52 (Show Source): You can put this solution on YOUR website!sin(4x - Pi/3) = sqrt(3)/2 ------------------------- Take the inverse sin of both sides to get: 4x-(pi/3) = pi/3 4x = (2/3)pi x = (1/6)pi or (5/6)pi ======================== Cheers, Stan H.
 Money_Word_Problems/183070: This question is from textbook College Algebra a Graphing Approach 1.6 #84 Consumre Awareness. The suggested trtail price of a new car is p dollars. The dealership advertised a factory rebate of \$1200 and an 8% discount. a. Write a function R in terms of p giving the cost of the car after receiving the rebate from the factory. b. Write a function S in terms of p giving the cost of the car after receiving the dealership discount. c. Form the composite functions (R o S)(p) and (S o R)(p) and intercept each. d. Find (R o S)(18,400) and (S o R)(18,400. Which yields the lower cost for the car? Explain1 solutions Answer 137444 by stanbon(57410)   on 2009-02-21 18:22:51 (Show Source): You can put this solution on YOUR website!The suggested trtail price of a new car is p dollars. The dealership advertised a factory rebate of \$1200 and an 8% dealership discount. ------------------------------------- a. Write a function R in terms of p giving the cost of the car after receiving the rebate from the factory. --- R(p) = p - 1200 ============================================ b. Write a function S in terms of p giving the cost of the car after receiving the dealership discount. --- S(p) = p - 0.08p = 0.92p ============================================= c. Form the composite functions (R o S)(p) and (S o R)(p) and interpret each. RoS = R[S(p)] = R[0.92p] = (0.92p)-1200 Interpretation: The 8% discount is applied 1st, then the 1200 rebate. -------------------------------------------------- d. Find (R o S)(18,400) and (S o R)(18,400. Which yields the lower cost for the car? Explain --- Don't recognize that notation. ================================== Cheers, Stan H.
 Trigonometry-basics/183068: This question is from textbook Find all solutions to the equation. Use a lower-case n to denote an arbitrary integer; separate your answers with commas; use the most compact expressions possible. (cos(x) - 1) sin(x) = 0 Any help is greatly appreciated! I am really struggling just to start these problems. I received 0 + 2Pi as an answer for this but the system said it was wrong.1 solutions Answer 137440 by stanbon(57410)   on 2009-02-21 18:03:20 (Show Source): You can put this solution on YOUR website!(cos(x) - 1) sin(x) = 0 ------- You are given the factors. One of them must be zero since the product is zero. -------------- cos(x)-1 = 0 or sin(x) = 0 cos(x) = 1 or sin(x) = 0 x = pi/2 or (3/2)pi or x = 0 or pi ======================================= Cheers, Stan H.
 Vectors/183055: Find the point(s) where the tangent to the curve is horizontal for: y=2(x-29)(x+1) 1 solutions Answer 137429 by stanbon(57410)   on 2009-02-21 16:49:27 (Show Source): You can put this solution on YOUR website!Find the point(s) where the tangent to the curve is horizontal for: y=2(x-29)(x+1) --------------------- Take the derivative to get: y' = 2[(x-29)*1 + (x+1)*1] y' = 2[2x-28) --------- Let y' = 0 and solve for x: 2[2x-28]= 0 x = 14 ------------------- The slope is zero when x = 14 ------------------------------ f(14) = 2(14-29)(14+1) = 2(-15)(15) = -450 ================================= Ans: (14,-450) ====================== Cheers, Stan H.
 Square-cubic-other-roots/183053: This question is from textbook Algebra 2 using syntheetic substitution find f(-3) if f(x)=4x^3-3x^2-21 solutions Answer 137428 by stanbon(57410)   on 2009-02-21 16:44:50 (Show Source): You can put this solution on YOUR website!using synthetic substitution find f(-3) if f(x)=4x^3-3x^2-2 ---------------- -3)....4....-3....0....-2 .........4....-15..45...|,,-137 ====================================== f(-3) = -137 ====================================== Cheers, Stan H.
 Probability-and-statistics/183051: the odds aganist muffy beating her friend in a round of golf are 1:8 find the probability muffy will lose?1 solutions Answer 137427 by stanbon(57410)   on 2009-02-21 16:41:07 (Show Source): You can put this solution on YOUR website!the odds aganist muffy beating her friend in a round of golf are 1:8 find the probability muffy will lose? ----------------- odds against A = P(not A)/P(A) --------------------- Your Problem: odds against win = 1:8 = P(not win)/P(win) = [1/9]/[8/9] --- P(not win) = 1/9 ====================== Cheers, Stan H.