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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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 Quadratic_Equations/139615: If the equation of a circle is x^2+y^2+3x-my+10=0 and the point (2,-5) lies on the circle, what is the value of m? I think it is -6???1 solutions Answer 101792 by stanbon(57967)   on 2008-05-01 19:49:03 (Show Source): You can put this solution on YOUR website!If the equation of a circle is x^2+y^2+3x-my+10=0 and the point (2,-5) lies on the circle, what is the value of m? I think it is -6??? -------------------------------------- 2^2+5^2+3*2+5m+10 = 0 4 + 25 + 6 + 5m + 10 = 0 5m = -45 m = -9 ============= Cheers, Stan H.
 Numbers_Word_Problems/139510: 3. An investor bought 500 shares of stock , some at \$ 3.50 per share and some at \$6.00 per share. If the total cost was \$ 2187.50, how many shares of each stock did the investor buy? (a) How will you set up the problem? (b) What is the equation in terms of the variables? (c) Which shares are more? 1 solutions Answer 101741 by stanbon(57967)   on 2008-05-01 13:11:53 (Show Source): You can put this solution on YOUR website!An investor bought 500 shares of stock , some at \$ 3.50 per share and some at \$6.00 per share. If the total cost was \$ 2187.50, how many shares of each stock did the investor buy? (a) How will you set up the problem? Let # of 3.50 shares be "x" ; value is 3.5x dollars # of 6.00 shares is "500-x" ; value is 6(500-x)=3000-6x dollars EQUATION: value = value = 2187.50 3.5x + 3000-6x = 2187.5 -2.5x = -812.5 x = 325 (# of 3.50 shares) 500-x = 175 (# of 6.00 shares) ---------------------------------------- (b) What is the equation in terms of the variables? (c) Which shares are more? ======================== Cheers, Stan H.
 Probability-and-statistics/139532: 2. In how many ways can you arrange six out of eight books on a shelf? (1 point)1 solutions Answer 101738 by stanbon(57967)   on 2008-05-01 13:06:16 (Show Source): You can put this solution on YOUR website!In how many ways can you arrange six out of eight books on a shelf? --------- 8P6 = 8!/(8-6)! = 8!/2! = 8*7*6*5*4*3 = 21160 ============== Cheers, Stan H.
 percentage/139541: x% of 25=15 help me solve this!1 solutions Answer 101736 by stanbon(57967)   on 2008-05-01 13:03:17 (Show Source): You can put this solution on YOUR website!x% of 25=15 ------ (x/100) = 15/25 x = 100(3/5) x = 100*0.6 x = 60 ============= Cheers, Stan H.
 Money_Word_Problems/139543: I know the formula for this type of problem, but I can't seem to turn it around to get the answer to this problem. What is the initial investment if you end up with \$30,000 after 18 years of instantaneous interest at 10%. Please help!1 solutions Answer 101734 by stanbon(57967)   on 2008-05-01 13:01:21 (Show Source): You can put this solution on YOUR website!What is the initial investment if you end up with \$30,000 after 18 years of instantaneous interest at 10%. ---------------- A(t) = Pe^(rt) 30000 = Pe^(0.10*18) 30000 = Pe^1.8 P = 30000/6.0496 P = \$4958.97 ================ Cheers, Stan H.
 Exponential-and-logarithmic-functions/139525: Suppose that x and y vary inversely and x=4 when y=7 Write the function that models the inverse variation a. y+1.75 b. y= 28/x c. y=11/x d. y=3/x1 solutions Answer 101708 by stanbon(57967)   on 2008-05-01 09:48:27 (Show Source): You can put this solution on YOUR website!Suppose that x and y vary inversely x = k/y ------------------- and x=4 when y=7 So, solve for "k": 4 = k/7 k=28 ----------- Now you know the equation is: x = 28/y or y = 28/x This is the function that models the inverse variation ------------------------- a. y+1.75 b. y= 28/x c. y=11/x d. y=3/x ------------- Answer: b =========================== Cheers, Stan H.
 Exponents/139526: x^3(2x^-2+4x) what is the method of answering the question above?1 solutions Answer 101707 by stanbon(57967)   on 2008-05-01 09:43:33 (Show Source): You can put this solution on YOUR website!x^3(2x^-2+4x) what is the method of answering the question above? -------------- It tells you to multiply x^3 and (2x^-2 + 4x) You use the distributive property and get: --------- x^3(2x^-2) + x^3*(4x) = 2x^(3-2) + 4x^(3+1) = 2x^1 + 4x^4 = 2x + 4x^4 ================== Cheers, Stan H.
 Probability-and-statistics/139426: 1. What is the difference between strong negative and strong positive r? What does the correlation tell you? 2. During the years 1790 to 1820, the correlation between the number of churches built in New England and barrels of Rum imported into the region was a perfect 1.0. What does this tell you  that church building causes rum drinking, that rum drinking causes church building, or something else? If something else, what? 1 solutions Answer 101706 by stanbon(57967)   on 2008-05-01 09:40:22 (Show Source): You can put this solution on YOUR website!1. What is the difference between strong negative and strong positive r? What does the correlation tell you? strong negative: as x increases, y decreases strong positive: as x increases, y increases ---------------------------- 2. During the years 1790 to 1820, the correlation between the number of churches built in New England and barrels of Rum imported into the region was a perfect 1.0. What does this tell you  that church building causes rum drinking, that rum drinking causes church building, or something else? If something else, what? It only tells you as one increases the other increases. It does not say anything about one causing or being caused by the other. ================== Cheers, Stan H.
 Equations/139516: 3/x+3/y divided by 3/x-3/y1 solutions Answer 101703 by stanbon(57967)   on 2008-05-01 08:02:41 (Show Source): You can put this solution on YOUR website!3/x+3/y divided by 3/x-3/y (3x+3y)/xy / (3y-3x)/xy Concel the xy denominators: = [3(x+y)]/[3(y-x)] Cancel the 3 factor in numerator and denominator. = (x+y)/(y-x) ================= Cheers, Stan H.
 Numbers_Word_Problems/139514: Sprint has a long distance phone plan that charges a monthly fee of \$9.99 plus \$0.03 per minute. (a) Write down the equation for monthly bill as a function of minutes used. (b) Identify dependent and independent variables. (c) Graph the function. (d) What is the monthly bill if 255 minutes are used for long distance phone calls? (e) How many minutes were used for long distance if the long distance phone bill was \$ 40.50? 1 solutions Answer 101702 by stanbon(57967)   on 2008-05-01 07:56:10 (Show Source): You can put this solution on YOUR website!Sprint has a long distance phone plan that charges a monthly fee of \$9.99 plus \$0.03 per minute. (a) Write down the equation for monthly bill as a function of minutes used. Bill(x) = 9.99 + 0.03x -------------------- (b) Identify dependent and independent variables. independent: minutes dependent: bill ----------------------- (c) Graph the function. ----------------------- (d) What is the monthly bill if 255 minutes are used for long distance phone calls? bill(255) = 9.99+0.03*255=17.64 ---------------------- (e) How many minutes were used for long distance if the long distance phone bill was \$ 40.50? 40.50 = 9.99 + 0.03x 0.03x = 40.50- 9.99 x = 1017 minutes ====================== Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/139498: This question is from textbook beginning algebra please help me to solve this word problem: if x is the first of four consecutive even integers, write their sum as an algebraic expression in x.1 solutions Answer 101700 by stanbon(57967)   on 2008-05-01 07:48:08 (Show Source): You can put this solution on YOUR website!1st: x 2nd: x+2 3rd: x+4 4th: x+6 ---------- Sum: x + x+2 + x+4 + x+6 = 4x + 12 ================ Cheers, Stan H.
 Quadratic_Equations/139496: complete the square, and find the roots of the quadratic equation Tutor plz help ? x2 + 16x = 0 1 solutions Answer 101699 by stanbon(57967)   on 2008-05-01 07:20:24 (Show Source): You can put this solution on YOUR website!x^2 + 16x = 0 x^2 + 16x + (16/2)^2 = 0 + (16/2)^2 x^2 + 16x + 64 = 64 Factor: (x+8)^2 = 64 Take the square root of both sides: x+8 = +8 or x+8 = -8 x = 0 or x = -16 ====================== Cheers, Stan H.
 Probability-and-statistics/139502: A local company wanted to predict the weekly sales based on the weekly newspaper advertising dollars. The model that result is: ลท= 1.1 + 1.7x, where the dependent variable is the amount of sales, in thousands of dollars, realized during the week and the independent variable is the amount spent on newspaper advertising, in hundreds of dollars, during the week. Interpret the meaning of the values 1.1 and 1.7 in the context of the problem. 1 solutions Answer 101698 by stanbon(57967)   on 2008-05-01 07:15:45 (Show Source): You can put this solution on YOUR website!The model that result is: ลท= 1.1 + 1.7x, where the dependent variable is the amount of sales, in thousands of dollars, realized during the week and the independent variable is the amount spent on newspaper advertising, in hundreds of dollars, during the week. Interpret the meaning of the values 1.1 and 1.7 in the context of the problem. -------------- If money spent on advertising is zero the amount of sales is 1.1 thousand dollars. ----------- For each 100 dollar increase of spending on advertising the sales increase by 1.7 thousand dollars. ------------- Cheers, Stan H.
 Probability-and-statistics/139505: I need help with this one! IQ scores have a normal distribution with a mean of 100 and a standard deviation of 15. Out of a student body of 1800 students, how many would you expect expect to have an IQ above 109? My answer is: 1800 - 100 = 1700 / 15 = 113.33331 solutions Answer 101697 by stanbon(57967)   on 2008-05-01 07:10:38 (Show Source): You can put this solution on YOUR website!IQ scores have a normal distribution with a mean of 100 and a standard deviation of 15. Out of a student body of 1800 students, how many would you expect expect to have an IQ above 109? ------------------------------- 1st: Find the z-score for 109 z(109) = (109-100)/15 = 0.6 2nd: Find the probability above IQ=109. P(x>109) = P(z>0.6) = 0.2743 3rd: Find that percent of 1800 0.2743*1800 = 493 when rounded down ==================== Cheers, Stan H.
 Expressions-with-variables/139468: 1/3x + 2/3 = y 5/7x - y - 2 = 0 This is supposed to be solved with substitution or elimination. Thanks.1 solutions Answer 101684 by stanbon(57967)   on 2008-04-30 23:12:10 (Show Source): You can put this solution on YOUR website!1/3x + 2/3 = y 5/7x - y - 2 = 0 This is supposed to be solved with substitution or elimination --------------------- Multiply thru 1st equation by 3 ; Multiply thru 2nd equation by 7: ---------------------- x - y = -2 5x -7y = 14 ------------------ Multiply the 1st equation by 5 to get: 5x - 5y = -10 5x - 7y = 14 --------------- Subtract 2nd equation from 1st to get; 2y = -24 y = -12 ------------------ Substitute into x-y=-2 to solve for "x": x--12 = -2 x +12 = -2 x = -14 ---------------------- Check answer in 5x-7y = 14 5*-14 -7*-12 = 14 -70 + 84 = 14 14 = 14 ------------------ Final Answer: x = -14 ; y = -12 ==================================== Cheers, Stan H.
 Numbers_Word_Problems/139476: Could you help me from here; The value of a two digit number is twice as large as the sum of its digits. If the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find the original number. t = tens digit u = units digit 10t+u = original number 10u+t = the number named when the digits were reversed 10u+t = 9-5(10t+u) 1 solutions Answer 101683 by stanbon(57967)   on 2008-04-30 23:05:08 (Show Source): You can put this solution on YOUR website!The value of a two digit number is twice as large as the sum of its digits. If the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find the original number. t = tens digit u = units digit 10t+u = original number 10u+t = the number named when the digits were reversed 10u+t = 9-5(10t+u) ------------------ EQUATION: 10t + u = 2(t + u) 10u + t = 5(10t+u)-9 ------------------------- Rearrange the equations: 8t -u = 0 49t - 5u = 9 ------------------ solve by substitution: 49t - 5(8t) = 9 9t = 9 t = 1 ---------- Substitute to solve for "u": u = 8t so u = 8 ------------------- Original Number 18 ======================= Cheers, Stan H.
 Money_Word_Problems/139477: Two girls went to the store for rice and sugar. One girl bought 3 kilograms of sugar and 2 kilograms of rice for \$3.25. The other girl bought 2 kilograms of rice for \$2.50. Find the price per kilogram for both the sugar and rice. 1 solutions Answer 101682 by stanbon(57967)   on 2008-04-30 22:59:46 (Show Source): You can put this solution on YOUR website!Two girls went to the store for rice and sugar. One girl bought 3 kilograms of sugar and 2 kilograms of rice for \$3.25. The other girl bought 2 kilograms of rice for \$2.50. Find the price per kilogram for both the sugar and rice. -------------- 3s + 2r = 325 cents 2r = 250 cents ------------------ r = 125 cents (rice is \$1.25 per kg) Substitute to solve for s: 3s + 250 = 325 3s = 75 s = 25 cents (sugar is \$0.25 per kg) ================ Cheers, Stan H.
 Probability-and-statistics/139471: need help with these problems. a. What is the F critical value to be used at the 0.05 level of significance with 7 numerator degrees of freedom and 12 denominator degrees of freedom? b. What is the chi-square critical value with 12 degrees of freedom for a 0.05 probability? c. What is the exact probability of a value that fits a chi-square distribution with 17 degrees of freedom being higher than 30.995? d. I have a sample of 13 units and I want to run a hypothesis test comparing the average to a set value. The hypothesis test uses an alpha of 0.05. What critical value would be used to compare the test statistic against? 1 solutions Answer 101681 by stanbon(57967)   on 2008-04-30 22:41:56 (Show Source): You can put this solution on YOUR website!a. What is the F critical value to be used at the 0.05 level of significance with 7 numerator degrees of freedom and 12 denominator degrees of freedom? 3.5747 You can find these values by using Google; look for statistics F distribution ------------------------------- b. What is the chi-square critical value with 12 degrees of freedom for a 0.05 probability? You didn't say if it is a one tail or two tail test. If 2-tail you get 4.4004 and 23.337 If 1-tail you get either 5.226 or 21.026 ------------------------------------- c. What is the exact probability of a value that fits a chi-square distribution with 17 degrees of freedom being higher than 30.995?0 Ch-Sq(30.995,100,17) = 0.01999... ------------------------- d. I have a sample of 13 units and I want to run a hypothesis test comparing the average to a set value. The hypothesis test uses an alpha of 0.05. What critical value would be used to compare the test statistic against? --------------- Ho: u = set value Ha: u is not equal to set value Crit value for 2-tail test with alpha = 5% and df = 12: t = +/- 2.179 ================= Cheers, Stan H.
 Probability-and-statistics/139460: Stan, please explain the characteristics of a Chi-Square Goodness of Fit hypothesis test as well as the Chi-Square test for independence. Please provide an example of using one of these hypothesis test. Please be specifc providing the steps to the hypothesis test in your exmaple. 1 solutions Answer 101679 by stanbon(57967)   on 2008-04-30 22:25:37 (Show Source): You can put this solution on YOUR website!explain the characteristics of a Chi-Square Goodness of Fit hypothesis test as well as the Chi-Square test for independence. Please provide an example of using one of these hypothesis test. Please be specifc providing the steps to the hypothesis test in your exmaple. -------------------- These are large topics. You would have to see a text on statistics or use Google to get all of what you are looking for. But here is a little of it. ---------------- Goodness of Fit with a simplified example: 30 horse races are run with horses in 3 lanes. # of wins from lane one = 8 # of wins from lane two = 12 # of wins from lane three = 10 --------------------------------- Ho: It makes no difference which lane the horse starts in. Ha: It makes a difference. --------------- Comment: If it makes no difference there should be 10 wins from each position. --------------- Run a Chi-Sq on a 2 x 3 Matrix: row 1: 8....12....10 row 2: 10...10....10 ----------------------- Chi-Sq results: Test statistic: Chi-Sq = 0.404040404... p-value: 0.81707 df=2 ----------- Conclusion: Since p-value is greater than 5%, Fail to reject Ho. It makes no difference which lane the horse starts in. ================================================== Ch-Sq Test for Independence You have three horses, A, B, C and you have three lanes on the track 1,2.3. You keep track of how many wins each horse has on each track. ----------------- ------------------A..........B........C row 1.............2..........4........3 row 2.............3..........5........1 row 3.............4..........2........5 --------------------------- Ho: Horses and lanes are independent Ha: They are dependent Run a Chi-Sq on the 3 x 3 Matrix and get the following ------------ Test Statistic: Chi-Sq = 0.213447... p-value = 0.37789.. df=4 ------------ Conclusion: Since p-value is greater than 5%, Fail to reject Ho. Horses and lanes are independent. ================================= Hope that helps. ======================= Cheers, Stan H.
 Quadratic_Equations/139356: if i have a parabola with a vertex of (4,10) and x-intercepts of 0 and 8, how do i establish the quadratic equation. i came up with y=(x-4)squared + 10. Ho do you establish the "a" of ax squared + bx + c1 solutions Answer 101592 by stanbon(57967)   on 2008-04-30 11:28:55 (Show Source): You can put this solution on YOUR website!if i have a parabola with a vertex of (4,10) and x-intercepts of 0 and 8, how do i establish the quadratic equation. i came up with y=(x-4)squared + 10. Ho do you establish the "a" of ax squared + bx + c ---------------------- y = a(x-h)^2 + k Vertex = (h,k) = (4,10) so h=4 and k=10 Substitute to get: y = a(x-4)^2 + 10 -------------------- Now use either the point (0,0) or the point (8,0) to find "a": Using 0,0 you get 0 = a*16 + 10 a = -10/16 = -5/8 ----------------------- EQUATION: y = (-5/8)(x-4)^2 + 10 ============================= Cheers, Stan H.
 Polynomials-and-rational-expressions/139348: sqrt sign 54w small 16 at top of w over 150z small 4 at top of z.please show me how to simplify this . i really value your help.thanks1 solutions Answer 101591 by stanbon(57967)   on 2008-04-30 11:23:52 (Show Source): You can put this solution on YOUR website!sqrt sign 54w small 16 at top of w over 150z small 4 at top of z --------- sqrt(54w^16/150z^4) -------------------------- Separate the radicand into two factors. Make the 1st factor be a perfect square. -------------------------- sqrt[(9w^16/25z^4)(6/6)] -------------------------- Take the square root of the perfect square out of the radical. -------------------------- =(3w^8)/(5z^2) That is the final answer because the 6's cancel. ================== Cheers, Stan H.
 Probability-and-statistics/139353: having problems figuring this out. help please A regular ANOVA will be used to compare 3 groups, called A, B, and C. What is the correct null hypothesis for ANOVA? a.. Ho: μA= μB= μC b. Ho: μA≠ μB≠ μC c. Ho: μA<μB<μC d. Ho: μA=μB or μA=μC 1 solutions Answer 101590 by stanbon(57967)   on 2008-04-30 11:14:34 (Show Source): You can put this solution on YOUR website!Ans: a ------------ Equality must ALWAYS be part of Ho. If it is not, you could not calculate the test statistic. Cheers, Stan H.
 Travel_Word_Problems/139334: I need to solve this with either the elimination or substitution method. Thank you. It takes Boat A 3 hours longer to travel 50kms than it takes Boat B to travel 60kms. Boat A travels one third the speed of Boat B. What is the speed of each boat. Thanks.1 solutions Answer 101588 by stanbon(57967)   on 2008-04-30 09:35:40 (Show Source): You can put this solution on YOUR website!solve this with either the elimination or substitution method. Thank you. It takes Boat A 3 hours longer to travel 50kms than it takes Boat B to travel 60kms. Boat A travels one third the speed of Boat B. What is the speed of each boat. ---------------------- A-Boat DATA: distance 50 km ; Rate = x kph ; time = 50/x ----------------------- B-Boat DATA: distance = 60 km ; rate = 3x kph ; time = 60/(3x) ---------------------------------- EQUATION: time A - time B = 3 50/x - 60/(3x) = 3 Multiply thru by 3x to get 150 - 60 = 9x 90 = 9x x = 10 kph (speed of A-Boat) 3x = 30 kph (speed of B-Boat) ========================== Cheers, Stan H.
 Polynomials-and-rational-expressions/139335: Please help me.find each sum or difference 6 sqrt sign 49a and small 9 at top ofa -5 sqrt sign 36b and small 2 at top of b thank you i appreciate your help1 solutions Answer 101587 by stanbon(57967)   on 2008-04-30 09:28:10 (Show Source): You can put this solution on YOUR website!6 sqrt sign 49a and small 9 at top ofa -5 sqrt sign 36b and small 2 at top of b ------------ 6sqrt(49a^9) - 5sqrt(36b^2) = 6sqrt(49a^8)sqrt(a) - 5*6b = 6*7a^4*sqrt(a) - 30b = 42a^4(sqrt(a)) - 30b ============================== Cheers, Stan H.
 Probability-and-statistics/139333: The questions is: There are 700 students that watch TV. 45% are men. If the confidence interval is 95% what is the true proportion of men that watch tv. What is the correct formula?1 solutions Answer 101586 by stanbon(57967)   on 2008-04-30 09:18:13 (Show Source): You can put this solution on YOUR website!There are 700 students that watch TV. 45% are men. If the confidence interval is 95% what is the true proportion of men that watch tv. -------- p-hat = 0.45 n=700 z* = 1.96 ---------------- 0.45-1.96[0.45*0.55/Sqrt(700)] < p < 0.45+1.96[0.45*0.55/sqrt(700)] ================= Cheers, Stan H.
 real-numbers/139311: Could I please have some help solving this problem. Thank you. x varies directly with y and inversely with z. x=0.25 when y=10 and z=20. find x when y=20 and z=10. Thank you...1 solutions Answer 101585 by stanbon(57967)   on 2008-04-30 08:52:40 (Show Source): You can put this solution on YOUR website!x varies directly with y and inversely with z. x = ky/z ------------------ x=0.25 when y=10 and z=20 Use this information to find "k": 0.25 = k*10/20 k = 0.125 --------------------- Now you have the equation: x = 0.125y/z ------------------- Use that equation to answer the next part of the problem: find x when y=20 and z=10. ----------------------------------- x = 0.125*20/10 x = 0.25 ================ Cheers, Stan H.
 Exponential-and-logarithmic-functions/139320: solve for b. log( b, 9 )=2/31 solutions Answer 101584 by stanbon(57967)   on 2008-04-30 08:34:59 (Show Source): You can put this solution on YOUR website!solve for b. log( b, 9 )=2/3 ------------------ Exponential Form: b^(2/3) = 9 Raise both sides to the (3/2) power to get: b = 9^(3/2) = 3^3 = 27 ============================ Cheers, Stan H.
 Probability-and-statistics/139332: Need help with problem..... The x and the y variable in the table below are correlated. Determine the R value, and then determine the regression equation. Also calculate the Sum of Squares Error (SSE). X 16.66 20.70 24.33 21.27 20.01 27.44 16.84 22.27 14.20 17.74 Y 28.34 37.38 45.52 39.70 39.72 55.54 30.40 38.26 25.68 33.51 1 solutions Answer 101583 by stanbon(57967)   on 2008-04-30 08:30:56 (Show Source): You can put this solution on YOUR website!I ran a Linear Regression test on the data and got R^2 = 0.9506... I ran an ANOVA test and got SSE = 831.01429 Thank the Lord for calculators. ---------- Cheers, Stan H.
 Probability-and-statistics/139126: In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p?1 solutions Answer 101582 by stanbon(57967)   on 2008-04-30 08:21:04 (Show Source): You can put this solution on YOUR website!a) I ran a 1-PropZInt test on a TI calculator to get the following interval 0.01238 < p < 0.0139 ------------------------- b) While p is small, the population is very large so np and nq > 5 is a reasonable assumption. Cheers, Stan H.
 Probability-and-statistics/139310: I need desperate help on this problem.... A manager hopes to improve the sales figures for 10 employees by sending them to a motivational seminar. To test the effectiveness of this seminar, the manager compares the sales figures for each salesperson for the month immediately prior to the seminar and the month immediately following it. Employee Homer Bart Lisa Marge Maggie Ned Milhouse Willie Stu Gill Before 19 6 9 5 9 8 11 11 11 7 After 12 18 12 7 14 17 9 17 12 7 Run a statistical hypothesis test and determine if the seminar significantly improved sales figures for the company. 1 solutions Answer 101581 by stanbon(57967)   on 2008-04-30 07:38:58 (Show Source): You can put this solution on YOUR website!A manager hopes to improve the sales figures for 10 employees by sending them to a motivational seminar. To test the effectiveness of this seminar, the manager compares the sales figures for each salesperson for the month immediately prior to the seminar and the month immediately following it. Employee Homer Bart Lisa Marge Maggie Ned Milhouse Willie Stu Gill Before 19 6 9 5 9 8 11 11 11 7 After 12 18 12 7 14 17 9 17 12 7 Run a statistical hypothesis test and determine if the seminar significantly improved sales figures for the company. -------------------- You have before and after data for 10 employees. These are dependent data pairs. -------------- Find the list of data differences (after-before). Find the sum of those differences. Find the mean(ud) and standard deviation(sd) of the set of differences. ------ Ho: ud = 0 Ha: ud > 0 --------------- Run a T-test on the sample mean (ud) Critical value for one-tail t-test with alpha=5% and df=9: t=1.833 test statistic: t(2.9) = (2.9-0)/[5.466/sqrt(10)]= 1.6778 ------------------ Conclusion: Since test statistic is not in the rejection interval, Fail to reject Ho. The seminar is not increase sales. ======================= Cheers, Stan H.