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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

 Probability-and-statistics/286222: After the first exam the professor reports to the class that the mean for the exam was 73, and the standard deviation was 7. If the bottom 10% of the class fail the exam, what score would earn a student a failing grade?1 solutions Answer 207545 by stanbon(57226)   on 2010-03-28 18:27:33 (Show Source): You can put this solution on YOUR website!After the first exam the professor reports to the class that the mean for the exam was 73, and the standard deviation was 7. If the bottom 10% of the class fail the exam, what score would earn a student a failing grade? -------------------- Find the z-value with a 10% left tail: invNorm(0.10) = -1.2816... ------------------- Find the score corresponding to that z-score: ------ x = zs+u x = -1.2816*7 + 73 x = 64.029 Scores below that fail. =============================== Cheers, Stan H.
 Triangles/286186: okay so in a right triangle the degree measures of the acute angles are in the ratio of 2:3. the degree measure of the smallest angle is___. please tell me how to solve this problem1 solutions Answer 207511 by stanbon(57226)   on 2010-03-28 16:41:36 (Show Source): You can put this solution on YOUR website! okay so in a right triangle the degree measures of the acute angles are in the ratio of 2:3. the degree measure of the smallest angle is___. please tell me how to solve this problem --------------- Those two acute angles are complementary; they add up to 90 degrees. --- 2:3 is the same as 2x to 3x ----------------------------- Equation: 2x + 3x = 90 degrees 5x = 90 degrees x = 18 degrees ---------------- The smaller angle is 2x = 2*18 = 36 degrees. =============================================== Cheers, Stan H.
 Graphs/286100: How do you graph a line symmetric to another line?1 solutions Answer 207509 by stanbon(57226)   on 2010-03-28 16:38:49 (Show Source): You can put this solution on YOUR website!How do you graph a line symmetric to another line? ------------- 1st: You need to identify an axis for the symmetry. 2nd: For two points of the given line, draw a line segment perpendicular to the axis of symmetry and an equal distance beyond it. Put a point at the end of that segment. 3rd: Draw a line thru those two end points. ----- Result: The resulting line will be symmetric to the given line with repect to the axis of symmetry. =============================== Cheers, Stan H. ===============================
 Probability-and-statistics/286164: A TV executive is interested in the popularity of a particular cable TV show. She has been told that a whopping of American households would be interested in tuning in to a new network version of the show. If this is correct, what is the probability that all of the households in her city being monitored by the TV industry would tune in to the new show? Assume that the households constitute a random sample of American households. Round your response to at least three decimal places. 1 solutions Answer 207506 by stanbon(57226)   on 2010-03-28 16:31:45 (Show Source): You can put this solution on YOUR website!Essential numbers are missing from your post. Cheers, Stan H.
 percentage/286118: linda bought a pair of trainers when there was 20% off the normal price. she paid £18.00 for them. what was the normal price for the trainers?1 solutions Answer 207461 by stanbon(57226)   on 2010-03-28 13:41:13 (Show Source): You can put this solution on YOUR website!linda bought a pair of trainers when there was 20% off the normal price. she paid £18.00 for them. what was the normal price for the trainers? ------------------ Let the normal price be "x": x - 0.20x = 18 --- 0.80x = 18 ---- x = 22.50 ============= Cheers, Stan H.
 Probability-and-statistics/286115: If a baseball player's batting average is 0.340 or 34%, find the probability that the player will have a bad season and only score at most 60 hits in 200 times at bat?1 solutions Answer 207459 by stanbon(57226)   on 2010-03-28 13:38:15 (Show Source): You can put this solution on YOUR website! If a baseball player's batting average is 0.340 or 34%, find the probability that the player will have a bad season and only score at most 60 hits in 200 times at bat? -------- Binomial Problem with n= 200 ; p = 0.34 ; x = 60 --------------------- P(x=60) = 200C60*(0.34)^60*(0.66)^140 = 0.02968... ----------------- Cheers, Stan H.
 Travel_Word_Problems/286107: A car traveled 175 miles at a certain speed. If the speed had been 20 mph faster, the trip could of been made in one less hour. Find the speed of the car. I have both the distances as 175 i have one rate as r and the other rate as r+20 then the car with the rate of r and have as t time and the car with the rate of r+20 i have the time a t-1 is this right?1 solutions Answer 207458 by stanbon(57226)   on 2010-03-28 13:34:09 (Show Source): You can put this solution on YOUR website! A car traveled 175 miles at a certain speed. If the speed had been 20 mph faster, the trip could of been made in one less hour. Find the speed of the car. --- Slower speed DATA: distance = 175 miles ; rate = r mph ; time = 175/r hrs. ---------------------------------------------- Faster speed DATA: distance = 175 miles ; rate = r+20 mph ; time = 175/(r+20) hrs ---------------------------------------------- Equation: slow time - fast time = 1 hr 175/r - 175/(r+20) = 1 --- Multiply thru by r(r+20): 175(r+20) - 175r = r(r+20) 175*20 = r^2 + 20r -------------------------- r^2 + 20r - 175*20 = 0 --- (r+70)(r-50) = 0 Positive solution rate = 50 mph (slower rate) r+20 = 70 mph (faster rate) ================================ Cheers, Stan H. ================================ I have both the distances as 175 i have one rate as r and the other rate as r+20 then the car with the rate of r and have as t time and the car with the rate of r+20 i have the time a t-1 is this right?
 Equations/286104: ok my teacher gave us words problmes to do and im stuck. Here is the problem: Bill is 3 times as old as Peter. Six years from now, Bill will be twice as old as Peter will be then. Find their present ages. Im stuck on what the formula is. 1 solutions Answer 207454 by stanbon(57226)   on 2010-03-28 13:19:00 (Show Source): You can put this solution on YOUR website!Bill is 3 times as old as Peter. b = 3p ------------------- Six years from now, Bill will be twice as old as Peter will be then. (b+6) = 2(p+6) --------------------------- Substitute for "b" and solve for "p": (3p+6) = 2(p+6) 3p+6 = 2p+12 p = 6 (peter's age now) --- Since b = 3p, b = 18 (bill'e age now) ============================= Cheers, Stan H. Find their present ages.
 Probability-and-statistics/286095: You want to prove that a population mean is not 7. Data is ratio and a large sample size will be used (n = 225). When the sample is done the sample mean is computed to be 7.2 and the sample standard deviation is 1.5. Test the hypothesis using an alpha of 5%. Use formal hypothesis testing and compute the p-value. 1 solutions Answer 207453 by stanbon(57226)   on 2010-03-28 13:14:25 (Show Source): You can put this solution on YOUR website!You want to prove that a population mean is not 7. Data is ratio and a large sample size will be used (n = 225). When the sample is done the sample mean is computed to be 7.2 and the sample standard deviation is 1.5. Test the hypothesis using an alpha of 5%. Use formal hypothesis testing and compute the p-value. ----- Ho: u = 7 Ha: u is not 7 (claim) ------------------------------- t(7.2) = (7.2-7)/1.5 = 0.1333... --- p-value = 2*P(t > 0.13333.. with df = 224) = 2*tcdf(0.13333..,100,224) = 0.8940 ---- Wow! Fail to reject Ho; that p-value is much larger than the p-value. ================================================= Cheers, Stan H. =================================================
 Triangles/286027: A triangle has three angles with measurements A, B, and C such that A = x^2 + 49, B = x + 2, and C = x + 130. Assume all angles are measured in degrees. Find x. A. x = 0 B. x = 1 C. x = 180 D. x = −1 E. None of these. 1 solutions Answer 207422 by stanbon(57226)   on 2010-03-28 09:52:28 (Show Source): You can put this solution on YOUR website! A triangle has three angles with measurements A, B, and C such that A = x^2 + 49, B = x + 2, and C = x + 130. Assume all angles are measured in degrees. Find x. --------------------- Equation: A + B + C = 180 degrees (x^2+49) + (x+2) + (x+130) = 180 --- x^2 + 2x + 181 = 180 --- x^2 + 2x + 1 = 0 (x+1)^2 = 0 x = -1 ----- A = x^2+49 = 50 degrees B = x+2 = 1 degree C = x + 130 = 129 degrees ============================ Cheers, Stan H. ============================ A. x = 0 B. x = 1 C. x = 180 D. x = −1 E. None of these.
 Linear_Equations_And_Systems_Word_Problems/286043: The sales representative informs you that there are two floor plans still available, and that there are a total of 63 houses available. The sales representative later indicates that there are six times as many homes available with the second floor plan than the first. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2. (I keep finding myself struggling with these I really have no idea where to start. Thanks in advance for helping me, I really appreciate it, more than you'll ever know!!)1 solutions Answer 207419 by stanbon(57226)   on 2010-03-28 09:38:50 (Show Source): You can put this solution on YOUR website!The sales representative informs you that there are two floor plans still available, and that there are a total of 63 houses available. The sales representative later indicates that there are six times as many homes available with the second floor plan than the first. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2. (I keep finding myself struggling with these I really have no idea where to start. Thanks in advance for helping me, I really appreciate it, more than you'll ever know!!) ---------------------------------- Quantity Equation: x + y = 63 Quantity Equation: y = 6x ================================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/286044: The sales representative here tells you they also have two floor plans available, but they only have 42 homes available. The representative tells you that floor plan #1 sells for \$100,000 and floor plan #2 sells for \$150,000. She also mentions that all the available houses combined are worth \$6 million. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2. ( I think the equations would be x + 100,000 = 6,000,000 and y + 150,000 =6,000,000 But im second guessing myself.) 1 solutions Answer 207418 by stanbon(57226)   on 2010-03-28 09:36:25 (Show Source): You can put this solution on YOUR website!The sales representative here tells you they also have two floor plans available, but they only have 42 homes available. The representative tells you that floor plan #1 sells for \$100,000 and floor plan #2 sells for \$150,000. She also mentions that all the available houses combined are worth \$6 million. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2. ( I think the equations would be x + 100,000 = 6,000,000 and y + 150,000 =6,000,000 But im second guessing myself.) ------------------------------------------------- Quantity Equation: x + y = 42 Value equation:100,000x + 150,000y = 6,000,000 ------------------------------------------------------ Cheers, Stan H.
 Square-cubic-other-roots/286045: Simplify each expresion. Rationalize all denominators. Assume that all variables are positive of the equation sqrt(20) – 3sqrt(5) + sqrt(45)1 solutions Answer 207417 by stanbon(57226)   on 2010-03-28 09:33:46 (Show Source): You can put this solution on YOUR website! Assume that all variables are positive of the equation sqrt(20) – 3sqrt(5) + sqrt(45) ------------------------------------ Rewrite as: sqrt(4*5) - 3*sqrt(5) + sqrt(9*5) --- = 2sqrt(5) - 3sqrt(5) + 3sqrt(5) --- = (2-3+3)sqrt(5) --- = 2sqrt(5) =================== Cheers, Stan H. ===================
 Number-Line/286049: 3x-y=3 with x-0 and y-6 My answer is 3, I don't get why answer is -1, can you give me steps1 solutions Answer 207416 by stanbon(57226)   on 2010-03-28 09:30:59 (Show Source): You can put this solution on YOUR website!3x-y=3 with x-0 and y-6 My answer is 3, I don't get why answer is -1, can you give me steps -------------------------------- Note: What do you mean by "x-0" and "y-6"?? How did you get an answer of "3"?? Cheers, Stan H.
 Probability-and-statistics/286006: a box contains 6 red,4 white and 5 black balls .A person draws 4 balls from the box at random. find the probability among the balls drawn there is at least one ball of each color1 solutions Answer 207414 by stanbon(57226)   on 2010-03-28 09:27:45 (Show Source): You can put this solution on YOUR website!A box contains 6 red, 4 white and 5 black balls. A person draws 4 balls from the box at random. A find the probability among the balls drawn there is at least one ball of each color ------- Ans: 1 - P(no red or no white or no black) --- = 1 - [P(no red)+P(no white)+P(no black)] --- = 1 - [9C4 + 11C4 + 10C4]/15C4 --- = 1 - 666/1365 --- = 0.5121.... Cheers, Stan H.
 Probability-and-statistics/285981: in Rivendell memorial hospital the time to complete surgery in a routine tubal ligation without complication is normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. The next procedure has been scheduled in the same operating room 60 minutes after the beginning of a tubal ligation procedure. Allowing 20 minutes to vacate and prepare the operating room between procedures, what is the probability that the next procedure will have to be delayed?1 solutions Answer 207386 by stanbon(57226)   on 2010-03-27 22:55:04 (Show Source): You can put this solution on YOUR website!in Rivendell memorial hospital the time to complete surgery in a routine tubal ligation without complication is normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. The next procedure has been scheduled in the same operating room 60 minutes after the beginning of a tubal ligation procedure. Allowing 20 minutes to vacate and prepare the operating room between procedures, what is the probability that the next procedure will have to be delayed? -------------------- If tubal ligation takes > 40 min (procedure delayed) ------------------------------------ z(40) = (40-30)/8 = 5/4 ------ P(procedure delayed) = P(x>40) = P(z> 5/4) = normalcdf(5/4,100) = 0.1056 ================================= Cheers, Stan H.
 Probability-and-statistics/285982: passengers using new york's metrocard system must swipe the card at a rate between 10 and 40 inches per second, or else the card must be re-swiped through the card reader. Research shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second. Determine: a. mean swipe rate - i got 27.5 b. standard deviation of the swipe rate - i got 12.99 c. 1st quartile d. third quartile e. what percentage of subway riders must re-swipe the card because they were outside the acceptable range? Not sure about quartiles and e., and hope a. and b. are correct1 solutions Answer 207384 by stanbon(57226)   on 2010-03-27 22:19:50 (Show Source): You can put this solution on YOUR website!passengers using new york's metrocard system must swipe the card at a rate between 10 and 40 inches per second, or else the card must be re-swiped through the card reader. --- Draw a picture of the uniform distribution. Base has width 50-5 = 45 Therefore height = 1/45 ------------------------------- Research shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second. Determine: a. mean swipe rate - (50-5)/2 = 27.5 -------------------------------------------- b. standard deviation of the swipe rate - i got 12.99 Note: I'm not sure how you got 12.99. The formula I find is sqrt[[(50-5)+1]^2 -1]/12] = sqrt[[46^2-1]/12] = 13.28 --------------------------------------------- c. 1st quartile Point with left tail = 0.25 base(1/45) = 0.25 base = 45*0.25 base = 11.25 But base starts at 5 so the 1st quartile value is 5+11.25 = 16.25 ------------------------------- d. third quartile Point with left tail of 0.75 base(1/45) = 0.75 base = 45*0.75 base = 33.75 But base starts at 5 so the 3rd quartile value is 5+33.75 = 38.75 ------------------------------- e. what percentage of subway riders must re-swipe the card because they were outside the acceptable range? Ans: 1 - P(10<= x <=40) = 1 - (30/45) = 1 - 2/3 = 1/3 = 33.33% --------------------------------- Cheers, Stan H.
 Probability-and-statistics/285933: Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why? Correct? Regular Cola Diet Cola Row Total Yes, got it right 7 7 14 No, got it wrong 12 20 32 ============================================= Col Total 19 27 46 1 solutions Answer 207360 by stanbon(57226)   on 2010-03-27 20:38:21 (Show Source): You can put this solution on YOUR website!Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why? Yes got it right - 7, 7, 14 no got it wrong - 12, 20, 32 total - 19, 27, 46 ----------------- Chi-Sq Test: Ho: the columns are homogeneous Ha; the columns are not homogeneous Using a TI-calculator Chi-Sq Test I get: Test statistic: Chi-Sq = 0.62768.... p-value = 0.428.. -------- Conclusion: Reject Ho; The columns are not homogeneous ======================================= Two-tailed sample z test: Ho: mu1 = mu2 Ha: mu1 is not equal to mu2 Critical value for 2-tailed test and alpha=5%: +-1.96 -------- x1-bar = 19/2= 9.5 x2-bar = 27/2= 13.5 sigma1^2 =7.77817^2 = 60.5 n1=19 sigma2^2 =9.1924^2=84.5 n2=27 --------------- z(9.5-13.5)/sqrt[(60.5/19) + (84.5)/27] = -1.59 p-value = 2P(-10 < z <-1.59) = 0.1118... -------- Conclusion: Since p-value > alpha, Fail to Reject Ho. The columns are homogeneous. ----------------------------- As you see, the test results are not the same. I'll leave the discussion of the final questions to you. ----------------------------- Cheers, Stan H.
 Probability-and-statistics/285960: The average stock price for companies making up the S&P 500 is \$30, and the standard deviation is \$8.20. Assume the stock prices are normally distributed. a) What is the probability a company will have a stock price of at least \$40? b) What is the probability a company will have a stock price no higher than \$20? c) How high does a stock price have to be to put a company in the top 10%? I'm sure I could work through a and b if I knew how to set up the equation? I'm really struggling to understand my current stats teacher, our whole class is. I just don't know where to start when it says "at least" or "no higher than" I don't know what number to use.....and letter c has me at a total loss. Thank you so much in advance for your help! If possible, can you show the equations you use so I have a starting point for future problems - and could show the rest of my class? Thanks again!!1 solutions Answer 207357 by stanbon(57226)   on 2010-03-27 20:29:52 (Show Source): You can put this solution on YOUR website!The average stock price for companies making up the S&P 500 is \$30, and the standard deviation is \$8.20. Assume the stock prices are normally distributed. a) What is the probability a company will have a stock price of at least \$40? Find the z-score of 40. Formula: z(x) = (x-u)/s z(40) = (40-30)/8.2 = 1.2195 Note: That means 40 is 1.2195 standard deviations above the mean. ----------------------------- Having converted 40 to a z-score you find the area to the right of 1.2195 under the standard curve. P(x> 40) = P(z> 1.2195) You have to use technology or a z-chart to find the area to the right of 1.2195. I use a TI84 calculator and get normalcdf(1.2195,100) = 0.1113.. -------------------------------------------------------------------- b) What is the probability a company will have a stock price no higher than \$20? z(20) = (20-30)/8.2 = -1.2295 Note: Here you are finding the area to the left of -1.2295. Because of symmetry the answer is the same as for "a". --------------------------------------------------------------------- c) How high does a stock price have to be to put a company in the top 10%? Find the z-score that has a right tail of 10%. I use the TI to get invNorm(0.90) = 1.28155.. Use the formula x = zs + u x = 1.28155*8.2 + 30 x = \$40.51 Stock prices above \$40.51 are in the top 10% of the stock prices. ---------------------------------------------------------------- Cheers, Stan H. ================================== I'm sure I could work through a and b if I knew how to set up the equation? I'm really struggling to understand my current stats teacher, our whole class is. I just don't know where to start when it says "at least" or "no higher than" I don't know what number to use.....and letter c has me at a total loss. Thank you so much in advance for your help! If possible, can you show the equations you use so I have a starting point for future problems - and could show the rest of my class? Thanks again!!
 Probability-and-statistics/285957: In 2004 the General social survey asked respondents to estimate how many hours and minutes they spent using the internet. The following table shows summary statistics for this measure comparing the responses for men and women. Use hypothesis testing procedures to determine if there is a statistically significant gender difference in internet use. Be certain to interpret the results. Use alpha=0.01 and 2 tail. Men: mean: 8.8, sd: 11.0, n: 793 Women: mean: 6.3, sd: 9.9, n: 908 1 solutions Answer 207353 by stanbon(57226)   on 2010-03-27 20:04:59 (Show Source): You can put this solution on YOUR website! Use hypothesis testing procedures to determine if there is a statistically significant gender difference in internet use. Be certain to interpret the results. Use alpha=0.01 and 2 tail. Men: mean: 8.8, sd: 11.0, n: 793 Women: mean: 6.3, sd: 9.9, n: 908 -------------- Ho: umen-uwomen = 0 Ha: umen-uwomen is not zero ------------------------------------- I ran a 2-Sample Ttest and got the following: test statistic: t = 4.898 p-value = 0.0000010659.. df = (794+907) = 1701 ======= Conclusion: Since the p-value is less than 1%, reject Ho. There is a gender difference in internet use. ================================================= Cheers, Stan H.
 Probability-and-statistics/285901: A corporate CEO reviews the earnings of three divisions over the last eighteen months. Each division reports its earnings quarterly. Based on the earnings below, is there sufficient evidence to conclude, at the 99% level of confidence, that one of these divisions is more profitable than the others? Division I Division II Division III 42 40 7 39 32 1 32 27 11 1 11 15 49 25 16 54 23 8 · State the null and alternate hypotheses · Calculate the sums of squares SS(total), SS(factor), and SS(error) · Calculate the degrees of freedom df(total), df(factor), and df(error) · Calculate the mean square for factor, and the mean square for error · Calculate the F-statistic · Determine the critical value(s) · State your decision: Should the null hypothesis be rejected? 1 solutions Answer 207301 by stanbon(57226)   on 2010-03-27 15:49:05 (Show Source): You can put this solution on YOUR website!A corporate CEO reviews the earnings of three divisions over the last eighteen months. Each division reports its earnings quarterly. Based on the earnings below, is there sufficient evidence to conclude, at the 99% level of confidence, that one of these divisions is more profitable than the others? Division I Division II Division III 42 40 7 39 32 1 32 27 11 1 11 15 49 25 16 54 23 8 · State the null and alternate hypotheses Ho: the means are equal Ha: at least one of the means is different ------------------------- I ran ANOVA on the three data sets and got the following: test stat: F = 6.72531057.. p-value: 0.00082.. Factor: df=2 SS: 2153.44 MS: 1076.72 --- Error: df=15 SS: 2401.5 MS: 160.1 Sxp=12.6531... · Calculate the sums of squares SS(total), SS(factor), and SS(error) · Calculate the degrees of freedom df(total), df(factor), and df(error) · Calculate the mean square for factor, and the mean square for error · Calculate the F-statistic · Determine the critical value(s) · State your decision: Should the null hypothesis be rejected? Since the p-value is less than 1% reject Ho at the 99% significanc level. ======================= Cheers, Stan H.
 Trigonometry-basics/285881: Find Theta in degrees, for given trig. function sin(0)=0.6527 Could someone help me with this and if I was using a calculator, how would I solve this? Thanks, Nathalie1 solutions Answer 207300 by stanbon(57226)   on 2010-03-27 14:22:18 (Show Source): You can put this solution on YOUR website!Find Theta in degrees, for given trig. function sin(theta)=0.6527 -------------------------- sin^-1(0.6527) = 40.745... degrees ------------------------------ I am using a TI calculator. --- The "sin^-1" symbol is above the "sin" button. --- Press "2nd"; then press "sin". On your screen you should see sin^-1( ----- Enter 0.6527) and hit the Enter button. --- You should see 40.74548098 if you are in the degree Mode. ---- If you see 0.7111427985 you r calculator is in the radian Mode. ----- To change the Mode hit the "Mode" button and select degree. ====================== Cheers, Stan H.
 Probability-and-statistics/285878: A gas station manager thinks the average motorist changes their oil less than the recommended two times per year. In a survey 15 car owners were asked how many times they changed their oil in the past year. Here are the results: 1 1 2 1 2 2 0 1 0 1 2 3 1 3 0 The value of the test statistic is equal to _____________ ? Answer between two and four decimals Thank you for any help that you can provide!1 solutions Answer 207299 by stanbon(57226)   on 2010-03-27 14:14:59 (Show Source): You can put this solution on YOUR website!A gas station manager thinks the average motorist changes their oil less than the recommended two times per year. In a survey 15 car owners were asked how many times they changed their oil in the past year. Here are the results: 1 1 2 1 2 2 0 1 0 1 2 3 1 3 0 --- sample mean = (sum of the data)/15 = 20/15 = 4/3 sample standard deviation: 0.976 --------------------- test statistic = t(4/3) = (4/3 - 2)/[0.976/sqrt(15)] = -0.0882 The value of the test statistic is equal to -0.0882 Answer between two and four decimals =========================================== Cheers, Stan H.
 logarithm/285873: log square root X=log(x-6)1 solutions Answer 207297 by stanbon(57226)   on 2010-03-27 14:07:07 (Show Source): You can put this solution on YOUR website!log square root X=log(x-6) log(x^(1/2)) = log(x-6) x^(1/2) = x-6 x = (x^2-12x+36) x^2-13x+36 = 0 Factor: (x-9)(x-4) = 0 x = 9 or x = 4 --- Only x = 9 is a true solution because log(4-6) does not exist. ----------------------- Cheers, Stan H. ---
 Linear_Equations_And_Systems_Word_Problems/285877: Aldo runs 4 miles in 30 minutes. At the same rate, how many miles would he run in 48 minutes. 1 solutions Answer 207296 by stanbon(57226)   on 2010-03-27 14:01:26 (Show Source): You can put this solution on YOUR website!Aldo runs 4 miles in 30 minutes. At the same rate, how many miles would he run in 48 minutes. --- miles/time = miles/time miles/48 min = 4 mi/30 min ---- miles = 48(2/15) miles = 96/15 miles = 6.4 miles ========================== Cheers, Stan H.
 Expressions-with-variables/285874: A man caught 100 fish and he tagged them and threw them back in the lake. He later caught 75 fish and of them 12 had tags. What is the population of the fish in the lake?1 solutions Answer 207295 by stanbon(57226)   on 2010-03-27 13:58:33 (Show Source): You can put this solution on YOUR website! A man caught 100 fish and he tagged them and threw them back in the lake. He later caught 75 fish and of them 12 had tags. What is the population of the fish in the lake? ----- population count/caught & tagged = total # caught/ # tagged ------------------------------------------------------------ population count/100 = 75/12 --- population count = 100(75/12) --- pop count = 625 =========================== Cheers, Stan H.
 Linear-equations/285870: Could You Graph y=-5x^2-51 solutions Answer 207294 by stanbon(57226)   on 2010-03-27 13:52:42 (Show Source): You can put this solution on YOUR website!Could You Graph y=-5x^2-5 --- (-3,-50) (-2,-25) (-1,-10) (0,-5) (1,-10) (2,-25) (3,-50) =================== ================ Cheers, Stan H. ================
 Inequalities/285867: One side of a triangle is 2 cm shorter than the base. The other side is 3 cm longer than the base. What lengths of the base will allow the perimeter to be greater than 19 cm? Show your work and explain your answer. 1 solutions Answer 207293 by stanbon(57226)   on 2010-03-27 13:22:38 (Show Source): You can put this solution on YOUR website!One side of a triangle is 2 cm shorter than the base. The other side is 3 cm longer than the base. What lengths of the base will allow the perimeter to be greater than 19 cm? Show your work and explain your answer. ------------------- Draw the triangle. Let the base be "x": Let a shorter side be "x-2" Let the 3rd side be "x+3". ------------------------------ Perimeter = 19 = x + x-2+x+3 19 = 3x+1 3x = 18 x = 6 cm (base) x-2 = 4 cm (shorter side) x+3 = 9 cm (longer side) ============================= Cheers, Stan H.
 Polynomials-and-rational-expressions/285869: factor yz + uy + 8z + 8u1 solutions Answer 207292 by stanbon(57226)   on 2010-03-27 13:17:15 (Show Source): You can put this solution on YOUR website!factor yz + uy + 8z + 8u --- y(z+u)+8(z+u) --- = (z+u)(y+8) =============== Cheers, Stan H.
 Trigonometry-basics/285364: what is the domain and range of y=csc x in interval notation or inequalities?1 solutions Answer 207291 by stanbon(57226)   on 2010-03-27 13:15:21 (Show Source): You can put this solution on YOUR website!what is the domain and range of y=csc x in interval notation or inequalities? --- y = 1/sin(x) --- Domain All Real Numbers except x = +-n(pi) where n = 0,1,2) ---------------- Range: = (-inf,-1]U[1,+inf) ============================== Cheers, Stan H.
 Linear-equations/285866: Factor 25y^2 - 91 solutions Answer 207290 by stanbon(57226)   on 2010-03-27 13:02:52 (Show Source): You can put this solution on YOUR website!Factor 25y^2 - 9 ---------- (5y-3)(5y+3) ================ Cheers, Stan H.