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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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 Exponential-and-logarithmic-functions/437414: Sorry should have been an equal sign e^(x^2+7x)=(1/e^12) 1 solutions Answer 302594 by stanbon(57967)   on 2011-04-18 15:10:25 (Show Source): You can put this solution on YOUR website! Sorry should have been an equal sign e^(x^2+7x)=(1/e^12) ------------ Cross-multiply: e(x^2+7x+12) = 1 ---- Take the natural log x^2+7x+12 = 0 (x+3)(x+4) = 0 x = -3 or x = -4 =================== Cheers, Stan H.
 test/437408: Factor this equation 9c^3-12c^2+18c-24 1 solutions Answer 302590 by stanbon(57967)   on 2011-04-18 15:05:30 (Show Source): You can put this solution on YOUR website!Factor this equation 9c^3-12c^2+18c-24 ------------------- = 3(3c^3-4c^2+6c-8) ---------------------------- factor the 1st 2 and the last 2 terms separately: = 3(c^2(3c-4)+6(3c-4) ------------------------ = 3(3c-4)(c^2+6) ====================== Cheers, Stan H. ===========
 Linear-equations/437402: Write an equation of the line containing the given point and perpendicular to the given line. (0,9) 4x+7y=21 solutions Answer 302588 by stanbon(57967)   on 2011-04-18 14:59:15 (Show Source): You can put this solution on YOUR website!Write an equation of the line containing the given point and perpendicular to the given line. (0,9) 4x+7y=2 --- Find the slope of the given line: y = (-4/7)x+(2/7) slope = -4/7 ---------------------- Any perpendicular line must have slope = 7/4 ------- y-intercept is 9 ----- Required equation is y = (7/4)x+9 ===================================== Cheers, Stan H. ===========
 Quadratic_Equations/437405: HOW DO YOU REWRITE AN EQUATION BY COMPLETING THE SQUARE THEN SOLVE THE EQUATION? 1 solutions Answer 302587 by stanbon(57967)   on 2011-04-18 14:56:01 (Show Source): You can put this solution on YOUR website!Please post a few of your problems.
 Exponential-and-logarithmic-functions/437404: Please help: e^(x^2+7x)/(1/e^12)1 solutions Answer 302585 by stanbon(57967)   on 2011-04-18 14:55:03 (Show Source): You can put this solution on YOUR website!e^(x^2+7x)/(1/e^12) ---- Invert the denominator and multiply to get: = e^(x^2+7x+12) ================== Cheers, Stan H. ============
 Triangles/437293: Find each base angle of isosceles triangle ABC if it is 12 degrees more than the vertex angle.1 solutions Answer 302468 by stanbon(57967)   on 2011-04-18 10:07:53 (Show Source): You can put this solution on YOUR website!Find each base angle of isosceles triangle ABC if it is 12 degrees more than the vertex angle. --- Let the vertex angle be "x". Then each base angle is "x+12". Equation: x + 2(x+12) = 180 3x = 156 x = 52 degrees Each base angle is x+12 = 64 degrees. Cheers, Stan H.
 test/437296: How many solutions does 5x^2-2x+3 have?1 solutions Answer 302466 by stanbon(57967)   on 2011-04-18 10:05:02 (Show Source): You can put this solution on YOUR website!All quadratic equations have 2 solutions. Sometimes the 2 solutions are the same. sometimes they are real numbers sometimes they are complex numbers. --------------------- Use the quadratic equation to find the solutions. x = [-b +- sqrt(b^2-4ac)]/(2a) --------------------------------- Cheers, Stan H. ==========
 Probability-and-statistics/437265: Bill runs a bicycle repair shop. During the summer months the number of jobs per week follows a normal distribution with mean 45 and deviation 9. For a week chosen at random find the probability that he will have 52 or more jobs. Travis took a standardized test to try to get credit for first-year Spanish. His standardized score was 1.86. The mean score for the exam was 100 with standard deviation 11.2. Compute Travis raw (actual) score. the language department requires a raw score of 125 to get credit for this class. Will Travis get credit for this course based on his exam? Explain.1 solutions Answer 302443 by stanbon(57967)   on 2011-04-18 08:38:18 (Show Source): You can put this solution on YOUR website!Bill runs a bicycle repair shop. During the summer months the number of jobs per week follows a normal distribution with mean 45 and deviation 9. For a week chosen at random find the probability that he will have 52 or more jobs. ------------------- z(52) = (52-45)/9 = 7/9 --- P(x>= 52) = P(z>= 7/9) = normalcdf(7/9,100) = 0.2184 =========== Travis took a standardized test to try to get credit for first-year Spanish. His standardized score was 1.86. The mean score for the exam was 100 with standard deviation 11.2. Compute Travis raw (actual) score. --- x = zs+u raw score = 1.86*11.2+100 = 120.83 =========================================== the language department requires a raw score of 125 to get credit for this class. Will Travis get credit for this course based on his exam? Explain. --- No, his score is 120.83. ============================ cheers, Stan H. =============================
 Probability-and-statistics/437263: use the given sample statistic to test teh claim about the difference between 2 Population means U1 and U2. at the given level of significance alfa. samples are random /independent. the populations are normally distributed. claim: U1=U2 i dont understand?? alfa: .05 x1: 300 S1: 26 N1: 19 x2: 290 S2: 22 N2: 121 solutions Answer 302442 by stanbon(57967)   on 2011-04-18 08:32:47 (Show Source): You can put this solution on YOUR website! use the given sample statistic to test the claim about the difference between 2 Population means U1 and U2. at the given level of significance alfa. samples are random /independent. the populations are normally distributed. Ho: u1-u2 = 0 (claim) Ha: u1-u2 is not 0 ================================ claim: U1=U2 i dont understand?? alfa: .05 x1: 300 S1: 26 N1: 19 x2: 290 S2: 22 N2: 12 --- I ran a 2-Sample T-test on a TI calculator and got the following: test stat: t= 1.1477 p-value = 0.2614 df = 26.41 ---- Conclusion: Since the p-value is greater than 5%, fail to reject Ho. The claim is supported by the test results. =============================================== cheers, Stan H.
 logarithm/437250: find value of log8 25 if log 2= 0.30101 solutions Answer 302436 by stanbon(57967)   on 2011-04-18 07:36:47 (Show Source): You can put this solution on YOUR website! find value of log8 25 if log 2= 0.3010 --- log8(25) = log(25)/log(8) --- = [log(100/2^2)]/[3*log(2)] ----- = [log100-2log(2)]/[0.9030] --- = [2-0.6020]/0.9030 === = 1.5482 ============== Cheers, Stan H.
 Probability-and-statistics/437035: twenty percent of the employees of a large company are female. find the probability that in a random sample of 15 employees, at least two are female. 1 solutions Answer 302428 by stanbon(57967)   on 2011-04-18 06:55:43 (Show Source): You can put this solution on YOUR website! twenty percent of the employees of a large company are female. find the probability that in a random sample of 15 employees, at least two are female. --- Binomial Problem with n = 15 and p = 0.2 --- P(x>=2) = 1-P(0<= x<=1) = 1 - binomcdf(15,0.2,1) = 0.8329 =============== Cheers, Stan H.
 Probability-and-statistics/437125: the final exam in a math coures consists of 40 multiple-choise question. each question has 4 possible answers, and only 1 of them is correct. an unprepared student makes random guesses for all of the answers. find the mean and standard deviation for the number of correct anwers for such student.1 solutions Answer 302427 by stanbon(57967)   on 2011-04-18 06:52:35 (Show Source): You can put this solution on YOUR website! the final exam in a math course consists of 40 multiple-choise question. each question has 4 possible answers, and only 1 of them is correct. an unprepared student makes random guesses for all of the answers. find the mean and standard deviation for the number of correct anwers for such student. ---------------------- Binomial Problem with n=40 and p = 1/4 ---- mean = np = (1/4)(40) = 10 std = sqrt[npq] = sqrt[10*(3/4)] = 2.7386 ==================== Cheers, Stan H.
 Probability-and-statistics/437155: A spinner is divided in half with one half A and the other B. what is the probability that a spinner spun eight times will land on B at least four times?1 solutions Answer 302426 by stanbon(57967)   on 2011-04-18 06:49:12 (Show Source): You can put this solution on YOUR website!duplicate
 Probability-and-statistics/437144: You have sampled 25 students to find the mean SAT scores at Morris Knolls High School. A 95% confidence interval for the mean SAT score is 900 to 1100. Which of the following statement gives a valid interpretation of this interval? A. 95% of the 25 students have a mean score between 900 and 1100. B. 95% of the population of all students at Morris Knolls have a score between 900 and 1,100. C. If this procedure were repeated many times, 95% of the resulting confidence intervals would contain the true mean SAT score at Morris Knolls. D. If this procedure were repeated many times, 95% of the sample means would be between 900 and 1100. E. If 100 samples were taken and a 95% confidence interval was computed, 5 of them would be in the interval from 900 to 1100.1 solutions Answer 302425 by stanbon(57967)   on 2011-04-18 06:48:26 (Show Source): You can put this solution on YOUR website!A spinner is divided in half with one half A and the other B. what is the probability that a spinner spun eight times will land on B at least four times? ------------------- Binomial Problem with n=8 and p= 1/2 --- P(x>=4) = 1-P(0<= x<=3) = 1-binomcdf(8,1/2,3) = 0.6367 ======================= cheers, Stan H.
 Probability-and-statistics/437158: The average price for a new car is \$16,000 and the standard deviation is \$1,500. What is the z score for a car price (x) = \$19,0001 solutions Answer 302424 by stanbon(57967)   on 2011-04-18 06:45:39 (Show Source): You can put this solution on YOUR website!The average price for a new car is \$16,000 and the standard deviation is \$1,500. What is the z score for a car price (x) = \$19,000 ------------------ z(19000) = (19000-16000)/1500 = 2 ====================================== Cheers, Stan H.
 Probability-and-statistics/437179: there are 8 green. 10 rf and 12 yellow balls in a basket if we pick a ball at random that is the probabitity that the ball is not gree and red1 solutions Answer 302423 by stanbon(57967)   on 2011-04-18 06:44:04 (Show Source): You can put this solution on YOUR website!there are 8 green. 10 rf and 12 yellow balls in a basket if we pick a ball at random that is the probabitity that the ball is not gree and red ---- I guess that means the ball is yellow. P(yellow) = 12/30 ===================== Cheers, Stan H.
 Probability-and-statistics/437210: Household income does not tend to follow a normal distribution in a particular state, yet average income is approximately \$45,000/year in this state, with a standard deviation of about \$9000. Within what income range would approximately 75% of the household incomes lie within this state? having trouble forming the right way to put the information in an equation.1 solutions Answer 302422 by stanbon(57967)   on 2011-04-18 06:42:03 (Show Source): You can put this solution on YOUR website!Household income does not tend to follow a normal distribution in a particular state, yet average income is approximately \$45,000/year in this state, with a standard deviation of about \$9000. Within what income range would approximately 75% of the household incomes lie within this state? having trouble forming the right way to put the information in an equation. --------------------- Draw the picture centering 75% on a mean of 45000 ---- The lower limit will have a left-tail of 0.5000-(1/2)0.75 = 0.1250 Find the z-value with a left-tail of 0.1250 invNorm(0.1250) = -1.1503 --- Find the corresponding x-value: x = zs+u x = -1.1503*9000+45000 = \$34646.86 ============================================= Cheers, Stan H.
 Probability-and-statistics/437211: Scores on the Stanford-Binet Intelligence scale have a mean of 100 and a standard deviation of 16, and are presumed to be normally distributed. A person who scores 68 on this scale has what percentile rank within the population? Show all work as to how this is obtained.1 solutions Answer 302421 by stanbon(57967)   on 2011-04-18 06:35:49 (Show Source): You can put this solution on YOUR website! Scores on the Stanford-Binet Intelligence scale have a mean of 100 and a standard deviation of 16, and are presumed to be normally distributed. A person who scores 68 on this scale has what percentile rank within the population? Show all work as to how this is obtained. ---- z(68) = (68-100)/16 = -2.5 --- Find the p-value or left-tail of z= -2.5: normalcdf(-100,-2.5) = 0.00621 ---- %ile score of raw score 68 is 0.621%ile ================================= Cheers, Stan H.
 Probability-and-statistics/437220: 2 Infant mortality rates (IMR) (i.e. the probability of a child dying before the age of one year) vary by race. In 2001 in the USA the IMR for Caucasians was 0.0057 and for African Americans it was 0.0133. Suppose three Caucasian children are selected at random. a. What is the probability all three will live past the age of one year? b. What is the probability that at least one will die within one year? c. Repeat part a and b for three randomly selected African American children 1 solutions Answer 302420 by stanbon(57967)   on 2011-04-18 06:29:55 (Show Source): You can put this solution on YOUR website!2 Infant mortality rates (IMR) (i.e. the probability of a child dying before the age of one year) vary by race. In 2001 in the USA the IMR for Caucasians was 0.0057 and for African Americans it was 0.0133. Suppose three Caucasian children are selected at random. a. What is the probability all three will live past the age of one year? Ans: (1-0.0057)^3 ----------------------------------- b. What is the probability that at least one will die within one year? Ans: 1-(1-0.0057)^3 ------------------------------------ c. Repeat part a and b for three randomly selected African American children Ans: (1-0.0133)^3 and 1-(1-0.0133)^3 ========================== Cheers, Stan H.
 Probability-and-statistics/437222: An IQ test is approximately normally distributed witha mean of 100 and standard deviation of 15. What is the probability that a randomly chosen individual has an IQ score of 110 or higher?1 solutions Answer 302419 by stanbon(57967)   on 2011-04-18 06:26:15 (Show Source): You can put this solution on YOUR website!An IQ test is approximately normally distributed witha mean of 100 and standard deviation of 15. What is the probability that a randomly chosen individual has an IQ score of 110 or higher? -------------- z(110) = (110-100)/15 = 2/3 ---- P(x>= 110) = P(z >= (2/3)) = normalcdf(2/3,100) = 0.2525 ==================== Cheers, Stan H. ====================
 Geometry_Word_Problems/437232: A kite is tethered to a stake in the ground by a string 40 ft. long, which makes an angle of 60 degrees with the ground.if the kite fell vertically to the ground, how far away from the stake would the kite land?1 solutions Answer 302418 by stanbon(57967)   on 2011-04-18 06:22:03 (Show Source): You can put this solution on YOUR website!A kite is tethered to a stake in the ground by a string 40 ft. long, which makes an angle of 60 degrees with the ground.if the kite fell vertically to the ground, how far away from the stake would the kite land? ---------------- Draw the picture. You have a rt. triangle with hypotenuse = 40ft and base angle of 60 degrees. --- Find the base: x = r*cos(60) x = 40*(1/2) x = 20ft. ============== Cheers, Stan H.
 Triangles/437245: Geometry 10 std trangles property1 solutions Answer 302417 by stanbon(57967)   on 2011-04-18 06:17:28 (Show Source): You can put this solution on YOUR website!Insufficient information.
 Coordinate-system/437241: The measurements from an experiment were recorded in the following table: x(seconds) (0), (10), (20), (30), (40), (50) y(metres) (1500), (1200), (900), (600), (300), (0) Using suitable scales, draw a graph to illustrate the results of the experiment. Use your graph to answer the following questions: a) Find the value of y when x is i) 5, ii) 18, iii) 25, iv) 45, v) 47. b) Find the value of x when y is i) 1455, ii) 990, iii) 480, iv) 390, v) 270.1 solutions Answer 302416 by stanbon(57967)   on 2011-04-18 06:16:15 (Show Source): You can put this solution on YOUR website!The measurements from an experiment were recorded in the following table: x(seconds) (0), (10), (20), (30), (40), (50) y(metres) (1500), (1200), (900), (600), (300), (0) Using suitable scales, draw a graph to illustrate the results of the experiment. Use your graph to answer the following questions: --- Equation: y = -30x+1500 a) Find the value of y when x is i) 5, ii) 18, iii) 25, iv) 45, v) 47. f(5) = -30*5+1500 = 1350 f(18) = -30*18+1500 = 960 etc. ------------------------------------------- b) Find the value of x when y is i) 1455, ii) 990, iii) 480, iv) 390, v) 270. 1455 = -30x+1500 -45 = -30x x = 1.5 ------------------ 990 = -30x+1500 -30x = -510 x = 17 etc. =============== Graph: ================ Cheers, Stan H.
 Miscellaneous_Word_Problems/437244: Your boss has asked you to come up with a price model for one of the cell phone models that your company produces. In the model, costs and length of service are directly related. You are also asked to examine the profit formula based on selling a certain number of the phones to determine profitability based on how many are sold. Suppose a cell phone service costs \$45 per month, along with a \$60 activation fee. Write a cost equation that relates the number of months of service and the total cost for that time of service. (Hint: Let t = the number of months of service and c = the total cost.) Use the cost equation to determine the number of months of service for a cost of \$1,185. 1 solutions Answer 302415 by stanbon(57967)   on 2011-04-18 06:06:53 (Show Source): You can put this solution on YOUR website!Suppose a cell phone service costs \$45 per month, along with a \$60 activation fee. --------------------------------------- Write a cost equation that relates the number of months of service and the total cost for that time of service. (Hint: Let t = the number of months of service and c = the total cost.) --- Ans: C(x) = 60 + 45x where x is # of months of service. ----------------------------------------------------------------- Use the cost equation to determine the number of months of service for a cost of \$1,185. --- 1185 = 60 + 45x 45x = 1125 x = 25 months. =================== Cheers, Stan H.
 Exponents/437240: x^4/3-5x^2/3+4=0 The answer the book gave is x=1 or x=+-8 Mustn't it be x=+-1 or x=+-8? When is it +- and when is it only 8. 1 solutions Answer 302414 by stanbon(57967)   on 2011-04-18 06:03:03 (Show Source): You can put this solution on YOUR website!x^4/3-5x^2/3+4=0 The answer the book gave is x=1 or x=+-8 Mustn't it be x=+-1 or x=+-8? When is it +- and when is it only 8. ----- Your problem is a quadratic form: [x^(2/3)]^2 - 5x^(2/3) + 4 = 0 ---- Let w = x^(2/3) ---- w^2 - 5w + 4 = 0 Factor: (w-4)(w-1) = 0 w = 4 or w = 1 ==================== Solve for "x": When x^(2/3) = 4 x = 4^(3/2) x = 8 ---- When x^(2/3) = 1 x = 1^(3/2) x = 1 =================== Your problem could be treated as a 4th degree equation: x^4/3-5x^2/3+4=0 ---- [x^(1/3)]^4-5[x^(1/3)]^2+4 = 0 Let w = x^(1/3) --- w^4 - 5w^2 + 4 = 0 Factor: (w^2-4)(w^2-1) = 0 ---- w = +-2 or w = +-1 ---- Solve for "x": x^(1/3) = 2 then x = 8 x^(1/3) = -2 then x = -8 x^(1/3) = 1 then x = 1 x^(1/3) = -1 then x = -1 ==================================== Cheers, Stan H. ===================
 Quadratic-relations-and-conic-sections/437242: what is the rectangular equivalent of a parametric curve....x=t/5-1 and y=t-211 solutions Answer 302413 by stanbon(57967)   on 2011-04-18 05:57:25 (Show Source): You can put this solution on YOUR website!what is the rectangular equivalent of a parametric curve.... x= (t/5)-1 and y=t-21 -------------------- Solve each equation for "t": t/5 = x+1 t = 5x+5 --------------- t = y+21 ------------------ Equation: 5x+5 = y+21 y = 5x-16 ================= Cheers, Stan H
 Quadratic_Equations/437139: x2+81=01 solutions Answer 302352 by stanbon(57967)   on 2011-04-17 21:12:08 (Show Source): You can put this solution on YOUR website!x^2+81=0 ------ Factor: (x+9i)(x-9i) = 0 x = -9i or x = +9i ====================== Cheers, Stan H. ===============
 Probability-and-statistics/437142: A 90% confidence interval for a population mean is determined to be 800 to 900. If the confidence is increased to 95% confidence while the sample statistics and sample size remain the same, the confidence interval for mui A. becomes narrower B. becomes .05 C. does not change D. becomes wider E. becomes .0251 solutions Answer 302351 by stanbon(57967)   on 2011-04-17 21:09:40 (Show Source): You can put this solution on YOUR website!A 90% confidence interval for a population mean is determined to be 800 to 900. If the confidence is increased to 95% confidence while the sample statistics and sample size remain the same, the confidence interval for mui ------------------------ If confidence is increased from 90 to 95, z increases, so ME increases, so the CI becomes wider. ---------------------------------------------- Cheers, Stan H. A. becomes narrower B. becomes .05 C. does not change D. becomes wider E. becomes .025
 Probability-and-statistics/437140: The level of significance is always A. the maximum allowable probability of type II error B. the maximum allowable probability of type I error C. the same as the confidence D. the same as the p-value E. 1 - P(type II error)1 solutions Answer 302349 by stanbon(57967)   on 2011-04-17 21:06:01 (Show Source): You can put this solution on YOUR website!The level of significance is always A. the maximum allowable probability of type II error B. the maximum allowable probability of type I error C. the same as the confidence D. the same as the p-value E. 1 - P(type II error) ================= I think B and E mean the same and are both true. Cheers, Stan H.
 Linear-equations/437141: How do I find the slope and the y-intercept of this problems: 10x=9y+811 solutions Answer 302347 by stanbon(57967)   on 2011-04-17 21:02:34 (Show Source): You can put this solution on YOUR website!find the slope and the y-intercept of this problems: 10x=9y+81 ----- 9y = 10x -81 y = (10/9)x - (9) ------ slope = 10/9 y-int = -9 ================== Cheers, Stan H.