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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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 Probability-and-statistics/130977: I need help with this question. Question: The temperature recorded by a certain thermometer when placed in boiling water (true temperature 100 degree C) is normally distributed with mean μ = 99.8 degree C and standard deviation σ = 0.1 degree C. [Please draw a density curve before you do any calculations.] 1). What is the probability that the thermometer reading is greater than 100 degree C? 2). What is the probability that the thermometer reading is exactly 100 degree C? 3). What is the probability that the thermometer reading is within ± 0.05 degree C? 1 solutions Answer 95747 by stanbon(57307)   on 2008-03-09 09:29:26 (Show Source): You can put this solution on YOUR website!The temperature recorded by a certain thermometer when placed in boiling water (true temperature 100 degree C) is normally distributed with mean μ = 99.8 degree C and standard deviation σ = 0.1 degree C. [Please draw a density curve before you do any calculations.] ------------ Draw a normal curve; put mean = 99.8. Calculate the z-value of the termperature in each of the problems using z(x) = (x-mu)/sigma ----------- 1). What is the probability that the thermometer reading is greater than 100 degree C? z(100) = (100-99.8)/0.1 = 0.02/0.1 = 0.2 P(z>0.2) = 0.4207 -------------------- 2). What is the probability that the thermometer reading is exactly 100 degree C? The probability of any particular value is zero -------------------------------------------------------- 3). What is the probability that the thermometer reading is within ± 0.05 degree C? I'll assume you mean within 0.05 degrees of the mean. Find the z-value of 99.8+0.05= 99.85 z(99.85) = (99.85-99.8)/0.1 = 0.5 --------- P(99.8-0.05 < temp < 99.5+0.05) = P(-0.5 < z < 0.5) = 0.3829 ============ Cheers, Stan H.
 Probability-and-statistics/131000: This question is from textbook Applied Statistics in Business and Economics 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, 461 solutions Answer 95746 by stanbon(57307)   on 2008-03-09 09:16:14 (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/131110: This is not a textbook question. A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medication, at least one person's infection will not improve. Thank you :)1 solutions Answer 95742 by stanbon(57307)   on 2008-03-09 08:51:47 (Show Source): You can put this solution on YOUR website!A medication is 75% effective against a bacterial infection. P(effective) = 0.75 ; P(not effective) = 0.25 -------------------- Find the probability that if 12 people take the medication, at least one person's infection will not improve: ------- P(at least one not effective) = 1 - P(none are not effective) = 1- P(all are effective) = 1 - (0.75)^12 = 0.968... =============== Cheers, Stan H.
 Probability-and-statistics/131111: Consider the distribution of Grades in Dr. Smith's class: Gender Grade Male Female A 18 12 B 30 30 C 53 27 D 12 8 F 7 3 120 80 If I select a student at random, what is the probability that: a. the student earned an A? b. the student earned at least a C? c. the student earned a D, given that it's a male student? Not a textbook question, thank you for any assistance :)1 solutions Answer 95741 by stanbon(57307)   on 2008-03-09 08:46:46 (Show Source): You can put this solution on YOUR website!Consider the distribution of Grades in Dr. Smith's class: Gender Grade Male Female A 18 12 B 30 30 C 53 27 D 12 8 F 7 3 120 80 If I select a student at random, what is the probability that: a. P(the student earned an A) = 30/200 = 3/20 b. P(the student earned at least a C) = (80+60+30)/200 = 17/20 c. P(the student earned a D, given that it's a male student) = 12/120 = 1/10 ================ Cheers, Stan H.
 Probability-and-statistics/131112: A package of 12 recordable CDs contains 3 which are defective. If 4 CDs are selected at random, find the probability that: a. No defective CDs are found. b. 1 of the 4 CDs is defective. c. 3 of the 4 CDs are defective. Not a text book question. Thank you for your help :) 1 solutions Answer 95739 by stanbon(57307)   on 2008-03-09 07:54:13 (Show Source): You can put this solution on YOUR website!A package of 12 recordable CDs contains 3 which are defective. If 4 CDs are selected at random, find the probability that: a. No defective CDs are found. b. 1 of the 4 CDs is defective. c. 3 of the 4 CDs are defective. ------------ P(defective)= 3/12 = 1/4; P(non defective)=3/4 ---------------------- a. P(No defective CDs are found)= (3/4)^4 b. P(1 of the 4 CDs is defective)= 4C1(1/4)(3/4)^3 = 0.421875... c. P(3 of the 4 CDs are defective)=4C3(1/4)^3(3/4)= 0.421875... -------------- Cheers, Stan H.
 Probability-and-statistics/131113: An instructor bases final grades on the following scale: Item Weight term papers 30% tests 20% homework 10% final exam 40% Find the final average of a student who earned the following scores: term paper 1- 85 term paper 2- 93 test 1- 80 test 2- 88 test 3- 92 homework total 95 final exam 81 When using weighted average how do you figure the term paper and test scores. I averaged each category (for papers and tests) and then did weighted average, is this correct?? My final answer was 85.93%. Thank you. This question not taken from a text. 1 solutions Answer 95737 by stanbon(57307)   on 2008-03-09 07:48:20 (Show Source): You can put this solution on YOUR website!An instructor bases final grades on the following scale: Item Weight term papers 30% tests 20% homework 10% final exam 40% Find the final average of a student who earned the following scores: term paper 1- 85 term paper 2- 93 test 1- 80 test 2- 88 test 3- 92 homework total 95 final exam 81 When using weighted average how do you figure the term paper and test scores. I averaged each category (for papers and tests) and then did weighted average, is this correct?? My final answer was 85.93%. ------------------ Add the three test scores; divide by 300 to get their average; multiply by 0.20 to properly weight their contribution to the final grade. -------------------- Add the term paper scores; divide by 200 to get their average; multiply by 0.30 to properly weight their contribution to the final grade. ================= Cheers, Stan H.
 Probability-and-statistics/131114: Please assist me with this question: A Web-base company has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using alpha=.025? Question is not from a book, it's an online course. Thank you in advance1 solutions Answer 95736 by stanbon(57307)   on 2008-03-09 07:35:51 (Show Source): You can put this solution on YOUR website!A Web-base company has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using alpha=.025? -------------------------------- Ho: p = 0.95 Ha: p > 0.95 --------------- z(485/500) = (0.97-0.95)/sqrt[0.95*0.05/500] = 2.0519... p-value= Prob(2.0519 Conclusion: Since p-value is less than alpha=0.025, Reject Ho. They are exceeding their goal. ============= Cheers, stan H.
 logarithm/131077: log64/log4, log64/log8, log64/log32 Decribe how to obtain the third answer in each row from the first two answers1 solutions Answer 95712 by stanbon(57307)   on 2008-03-08 21:09:22 (Show Source): You can put this solution on YOUR website!log64/log4, log64/log8, log64/log32 Decribe how to obtain the third answer in each row from the first two answers -------------------------- I don't know what you mean by that, but: log64/log4 = log(base4)64 = 3 -------------- log64/log8 = log(base8)64 = 2 -------------- log64/log32 = log(base2)64/log(base2)32 = 6/5 = 1.2 ========================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/131069: Hello members and tutors of algebra.com, I'm a high school student, in year 8 and am 13 years old. This question has propped up in my problem solving examination and I can never figure them out, particularly where there are multiple variables concerned. I have had a number of these, and I can remember it is possible to solve using diophantine equations. My teacher showed me a way to solve it that doesn't necessarily work for all of these types of problems and I'd like to know the alternative method. Here's the question and an explanation of how the answer would be obtained, is greatly appreciated: "A cabbage and a cauliflower cost \$3 in total, a cauliflower and a pumpkin cost \$4 in total and a pumpkin and a cabbage cost \$5 in total. Find the total cost of one of each vegetable." I'd like to know how you approach this problem and please teach me as I'd like to know. Thankyou very much, Jasmine 1 solutions Answer 95707 by stanbon(57307)   on 2008-03-08 20:54:06 (Show Source): You can put this solution on YOUR website!"A cabbage and a cauliflower cost \$3 in total, a cauliflower and a pumpkin cost \$4 in total and a pumpkin and a cabbage cost \$5 in total. Find the total cost of one of each vegetable." ------------------ This is one way to work the problem; I'm sure there are others. Let the cauliflower cost be "a" Let the pumpkin cost be "b" Let the cabbage cost be "c" -------------------------- Three equations a + 0b + c = 3 a + b + 0c = 4 0a + b + c = 5 --------------------- Subtract the 1st equation from the 2nd to get: a + 0b + c = 3 0 + b - c = 1 0 + b + c = 5 ------------------------ Subtract the 2nd equation from the 3rd to get: a + 0b + c = 3 0 + b - c = 1 0 + 0 + 2c = 4 ===================== Now: 1st: solve for c and get c = 2 (# of cabbages is 2) -------- 2nd: substitute into the 2nd equation to get: b-2 = 1 b = 3 (# of pumpkins is 3) -------- 3rd: substitute into the 1st equation to get: a + 0 + 2 = 3 a = 1 (# of cauliflower is 1) ============== Good wishes on your studies. Cheers, Stan H.
 Quadratic_Equations/131070: Can some one help me? Thank you Solve the formula for the given letter. Assume all variables represent non negatibve numbers. E=nc^2, for c1 solutions Answer 95705 by stanbon(57307)   on 2008-03-08 20:38:20 (Show Source): You can put this solution on YOUR website!Solve the formula for the given letter. Assume all variables represent non negative numbers. E=nc^2, for c -------------- c^2 = E/n c = sqrt(E/n) =============== Cheers, Stan H.
 Quadratic_Equations/131071: I am not sure of this answer. I think the answer has one real solution. Am I correct? x^2-3x+10=0 Does it have one real solution, two real solutions or two non-real solutions.1 solutions Answer 95704 by stanbon(57307)   on 2008-03-08 20:36:08 (Show Source): You can put this solution on YOUR website!I think the answer has one real solution. Am I correct? x^2-3x+10=0 ----------------- Look at the discriminant: b^2-4ac 3^2-4*1*10 = 9-40 = -31 Since the discriminant is negative there are no Real Number solutions. ==================== Cheers, Stan H.
 Probability-and-statistics/130980: At Ajax Spring Water, a 1/2 liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. (A) which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why? (B) Set up hypotheses and a twotailed decision rult for the correct mean using the 5 percent level of significance. (C) If a sample of 16 bottles shows a mean fill of 515 ml, does that contradict the hypothesis that the true mean is 520ml?1 solutions Answer 95703 by stanbon(57307)   on 2008-03-08 20:33:33 (Show Source): You can put this solution on YOUR website!At Ajax Spring Water, a 1/2 liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. ---------------------------- (A) which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why? The t-distribution which is suitable for small-sample testing. ---------------------------- (B) Set up hypotheses and a twotailed decision rule for the correct mean using the 5 percent level of significance. Ho: mu = 520 Ha: mu is not equal to 520 Critical values for alpha = 5% and 9 degrees of freedom : t = +-1.833 ---------------------------- (C) If a sample of 16 bottles shows a mean fill of 515 ml, does that contradict the hypothesis that the true mean is 520ml? Critical values for alpha=5% and 15 degrees of freedom : t= +-1.753 Test statistic: t(515)=(515-520)/[4/sqrt(16)]=-5*4/4 = -5 Conclusion: Since -5 < -1.753, reject Ho; this contradicts the hypothesis that the true mean is 520 ml. =============================== Cheers, Stan H. ----------------------------
 Percentage-and-ratio-word-problems/131067: Hi Tutors at algebra.com, I have this question and ts extremely difficult to work out. I'm not sure what year level it should be aimed at, so I'm not sure whether I'm expected to work it out. Your help and your guidance in solving this problem is very much needed and would be appreciated. Here is the question: "A person's wage increased by a% to \$250 per week. The wage prior to this increes in \$ was: a) 250 - (a/100 x 250) b) a/100 x 250 c) (100 + a)/100 x 250 d) 100/(100 + a) x 250 e) 250/a x 100 An explanation of how you got the answer and help on explaining it to me would be really, really appreciated and would make me happy indeed. Could you also tell me what the wage just prior to this increase in dollars is as well as the equation as above. Thanks, Jasmine (year 8 student, 13 years old) 1 solutions Answer 95702 by stanbon(57307)   on 2008-03-08 19:28:40 (Show Source): You can put this solution on YOUR website!"A person's wage increased by a% to \$250 per week. The wage prior to this increase in \$ was: a) 250 - (a/100 x 250) b) a/100 x 250 c) (100 + a)/100 x 250 d) 100/(100 + a) x 250 e) 250/a x 100 --------------------------- Let "x" be the person's wage prior to the increase. EQUATION: Person's wage after the increase = x + (a/100)x 250 = x + (a/100)x ----------------------- Solve for "x": x[1+(a/100)] = 250 x[100+a]/100 = 250 x = 250*100/[100+a] x = [100/(100+a)]*250 --------------------- Answer: "d" -------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/131064: Can you help me with this problem? The product of two consecutive integers is 360. Find the integers. I got to (x-18)(x+20)=0, but then I got confused Thanks!1 solutions Answer 95700 by stanbon(57307)   on 2008-03-08 19:02:35 (Show Source): You can put this solution on YOUR website!The product of two consecutive integers is 360. Find the integers. -------------------- I think you need consecutive EVEN integers. --------------------- 1st: 2x 2nd: 2x+2 ------------ EQUATION: 2x*(2x+2) = 360 4x^2+4x-360 = 0 x^2 + x -90 = 0 x = [-1 +- sqrt(1-4*-90)]/2 x = [-1 +- sqrt(361)]/2 x = [-1 +- 19]/2 x = [18/2] or [-20/2] x = 9 or -10 --------------- 2x = 18 and 2x+2 = 20 OR 2x -20 and 2x+2 = -18 ========================= Cheers, Stan H.
 Functions/131065: Hello, I am having a hard time understanding the concept of even and odd Trigonometric Functions and have come to a problem I just do not understand how to solve. The problem is: Use the even-odd properties to find the exact value of the expression. It may be helpful to draw the unit circle graph. I can input this into a calculator to get the answer, but I need to learn and understand for future studies. sin(-pi) Any help or explanation in layman's terms would be appreciated. Thanks so much! 1 solutions Answer 95693 by stanbon(57307)   on 2008-03-08 18:06:03 (Show Source): You can put this solution on YOUR website!sin(-pi) ------------ Draw the unit circle on a coordinate system. Four points on the circle: At 0 radians you have (1,0) At pi/2 you have (0,1) At pi you have (-1,0) At (3/2)pi you have (0,-1) ------------------------------- The point (-1,0) is at pi radians and at -pi radians. ---------------------------- The y-value for each of these points (and all other points on the circle, is the sine of the corresponding angle. ----------------------------- So, sin(-pi) = 0 ====================== Cheers, Stan H.
 Polynomials-and-rational-expressions/131066: Please help! Factor completely. 3(x-2)^2-3(x-2)-6 Thank you!1 solutions Answer 95691 by stanbon(57307)   on 2008-03-08 17:58:11 (Show Source): You can put this solution on YOUR website!Factor completely. 3(x-2)^2-3(x-2)-6 Let w= x-2 ------------ Substitute to get: 3w^2 -3w -6 3(w^2-w-2) 3(w-2)(w+1) --------------- Substitute to get: 3(x-2-2)(x-2+1) 3(x-4)(x-1) ================= Cheers, Stan H.
 Linear-equations/131057: I am having problems setting up and solving the following word problem, can you help? 1. An art dealer sold 2 artworks for \$1520 thereby making a profit of 25% on the first work and 10% on the other, whereas if he had approached any exhibition he would have sold them together for \$1535 with a profit of 10% on the first and 25% on the other art work. Find the actual cost of each artwork.1 solutions Answer 95689 by stanbon(57307)   on 2008-03-08 17:51:09 (Show Source): You can put this solution on YOUR website!An art dealer sold 2 artworks for \$1520 thereby making a profit of 25% on the first work and 10% on the other, whereas if he had approached any exhibition he would have sold them together for \$1535 with a profit of 10% on the first and 25% on the other art work. Find the actual cost of each artwork. ----------------------------------- Let price on 1st artwork be "x"; Let price on 2nd artwork be "y". -------------------------- EQUATIONS: 0.25x + 0.10y = 1520 0.10x + 0.25y = 1535 ------------------------------------------- Rearrange: 25x + 10y = 152000 10x + 25y = 153500 ----------------------- Multiply 1st by 25 and 2nd by 10 to get: 250x + 100y = 152000*10 250x + 625y = 153500*25 ----------------------------- Subtract 1st from 2nd to get: 625y = 2317500 y = \$3708 ------------- Substitute to solve for "x": 250x + 100(3708) = 1520000 250x = 1149200 x = \$4596.80 ---------------- Cheers, Stan H.
 Exponential-and-logarithmic-functions/131041: I missed lecture on Chapter 13.2 and 13.3 because I had to work and I am struggling trying to understand what it is they want me to do and how to work it. Problem is # 8 in section 13.2 Graph y=3^ ^ is x other problems listed are y= (1/3) ^ with ^ being x. I m not understanding how or what format is used in drawing out the box and where the numbers come from. Please help. 1 solutions Answer 95682 by stanbon(57307)   on 2008-03-08 17:10:40 (Show Source): You can put this solution on YOUR website!Graph y=3^ ^ is x other problems listed are y= (1/3) ^ with ^ being x. ------------------- y = 3^x Exponential equation curving upward. Points: (-1,1/3), (0,1), (1,3), (2,9) etc ------------------------------ y = (1/3)^x Exponental equation---decreasing Points: (-1,3),(0,1),(1,1/3), (2,1/9) ================== Cheers, Stan H.
 Linear_Algebra/131059: Can you help set up and solve the following problem? 1. A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased by 75%. Find the number of boys and girls involved inthe projuect initially.1 solutions Answer 95679 by stanbon(57307)   on 2008-03-08 16:54:30 (Show Source): You can put this solution on YOUR website!A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased by 75%. Find the number of boys and girls involved inthe project initially. --------------- Let initial number of students be "x". # of boys is 0.6x # of girls is 0.4x -------------------------- Adjusted numbers: boys = 0.6x+6 girls = 0.4x-6 ------------------------- EQUATION: 0.6x+0.75*0.6x = 0.6x+6 1.75(0.6x)= 0.6x+6 1.05x= 0.6x+6 0.45x = 6 x = 13 1/3 ---------------- This cannot be a reasonable answer for the problem. ----------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/131047: Given f(x)=2x-1 and g(x)= -1-2x determine the value of (fg)(-2) determine the value of (g and f)(-2)1 solutions Answer 95675 by stanbon(57307)   on 2008-03-08 16:30:19 (Show Source): You can put this solution on YOUR website!Given f(x)=2x-1 and g(x)= -1-2x determine the value of (fg)(-2) = f[g(-2)]=f[-1-2*-2]=f[3]=2*3-1=5 determine the value of (g and f)(-2) Comment: I don't know what you mean by "g and f" Do you mean addition whitch is (g+f)x ? ============== Cheers, Stan H.
 Probability-and-statistics/130993: This is not in a text book - can you help? A new model of digital camera is marketed in three major department store chains. THe number of cameras sold every month at each three store chains is listed below: Target - 177, 200, 191, 188 KMart - 164, 144, 170, 151 WalMart - 180, 213, 198, 204 At 0.05 level of significance is there a difference in the mean numbers of cameras sold at the three stores? a. state null and alternative hypothesis b. compute SS total, SST, SSE c. Develop ANOVA table d. what is the decision regarding the null hypothesis, is there a difference in the mean numbers od cameras sold at the three stores?1 solutions Answer 95672 by stanbon(57307)   on 2008-03-08 16:23:06 (Show Source): You can put this solution on YOUR website!A new model of digital camera is marketed in three major department store chains. THe number of cameras sold every month at each three store chains is listed below: Target - 177, 200, 191, 188 KMart - 164, 144, 170, 151 WalMart - 180, 213, 198, 204 At 0.05 level of significance is there a difference in the mean numbers of cameras sold at the three stores? a. state null and alternative hypothesis Ho: the means are the same Ha: at least one of the means is different ---------------------- b. compute SS total = Summation(x-xbarbar)^2= 3767.16667 SST = Summation n(subi)(x-bar-xbarbar)^2 SSE = Summation(ni-1)(si)^2 ------------------------------- c. Develop ANOVA table For each data element the expected value is (row total/grand total)*(columun total) d. what is the decision regarding the null hypothesis, is there a difference in the mean numbers od cameras sold at the three stores? Test statistic: F = 13.2907 p-value = 0.002058... Conclusion: Reject Ho: at least one of the means is different. =============== Cheers, Stan H.
 Probability-and-statistics/131012: This question is from textbook Statistics Find the mean, varience, and standard deviation for each of the following values of n and p when the conditions for the binomial distribution are met n= 300 p= 0.3 and n= 50 p= 2/51 solutions Answer 95638 by stanbon(57307)   on 2008-03-08 11:24:54 (Show Source): You can put this solution on YOUR website!mean = np variance = npq standard deviation = sqrt(npq) =============== Cheers, Stan H.
 Probability-and-statistics/131006: Please help me. I am not understanding this question. In a 3-digit lottery, each of the 3 digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency of occurrence of each digit for 90 consecutive daily 3-digit drawings. Perform the chi-squared test for a uniform distributions. At = .05, can you reject the hypothesis that the digits are from a uniform population? Digit No. of Occurrences 0 33 1 17 2 25 3 30 4 31 5 28 6 24 7 25 8 32 9 25 Total 270 Thank you for your help.1 solutions Answer 95632 by stanbon(57307)   on 2008-03-08 10:46:17 (Show Source): You can put this solution on YOUR website!In a 3-digit lottery, each of the 3 digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency of occurrence of each digit for 90 consecutive daily 3-digit drawings. Perform the chi-squared test for a uniform distributions. At alpha= .05, can you reject the hypothesis that the digits are from a uniform population? Digit No. of Occurrences 0 33 1 17 2 25 3 30 4 31 5 28 6 24 7 25 8 32 9 25 Total 270 1 solutions -------------------------------------------------------------------------------- Answer 95630 by stanbon(14224) on 2008-03-08 10:02:34 (Show Source): You can put this solution on YOUR website! In a 3-digit lottery, each of the 3 digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency of occurrence of each digit for 90 consecutive daily 3-digit drawings. Perform the chi-squared test for a uniform distributions. At alpha= .05, can you reject the hypothesis that the digits are from a uniform population? Digit No. of Occurrences 0 33 1 17 2 25 3 30 4 31 5 28 6 24 7 25 8 32 9 25 Total 270 -------------------------------- You would expect each digit to occur (1/10)*270 = 27 times ---------- Subtract that "expected" number from each listed No.of Occurrences to generate a "difference column" : Entries would be 5,-10,-2,3, etc. ------- Generate a "difference squared column": entries would be 25,100,4,9, etc --------- Divide each of those elements by 27: entries would be 25/27,100/27,4/27,9/27.. ---------- Add all those numbers to get a Chi-Sq number for your problem: Chi-Sq = 7.7037... ------------- Ho: all the digit proportions are the same Ha: at least one of the proportions is different ---------- Critical value for right-tail test with alpha=5% is Chi-sq = 16.919 based on df=9. ----------- Test statistic: Chi-sq = 7.7037 ----------------- Conclusion: Since the test statistic is less than the critical value Fail to reject Ho. The test shows no significant evidence that the proportion of digits is usual. ========== Cheers, Stan H.
 Probability-and-statistics/131008: 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? (Data are from Flying 120, no. 11 [November 1993], p. 31.) 1 solutions Answer 95631 by stanbon(57307)   on 2008-03-08 10:20:02 (Show Source): You can put this solution on YOUR website!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. p-hat = 1143/86991 = 0.0131... E = 1.96*sqrt[0.0131*0.9869/86991] = 7.556x10^-4 C.I. (p-hat-E,p-hat+E) = (0.0131,0.0131) -------------------------- (b) Why is the normality assumption not a problem, despite the very small value of p? n is so large pn and qn both are greater than 5 --------------------- (Data are from Flying 120, no. 11 [November 1993], p. 31.) =============== Cheers, Stan H.
 Probability-and-statistics/130986: Please help me. I am lost with this question. Thank you for your help In a 3-digit lottery, each of the 3 digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency of occurrence of each digit for 90 consecutive daily 3-digit drawings. Perform the chi-squared test for a uniform distributions. At alpha= .05, can you reject the hypothesis that the digits are from a uniform population? Digit No. of Occurrences 0 33 1 17 2 25 3 30 4 31 5 28 6 24 7 25 8 32 9 25 Total 270 1 solutions Answer 95630 by stanbon(57307)   on 2008-03-08 10:02:34 (Show Source): You can put this solution on YOUR website!In a 3-digit lottery, each of the 3 digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency of occurrence of each digit for 90 consecutive daily 3-digit drawings. Perform the chi-squared test for a uniform distributions. At alpha= .05, can you reject the hypothesis that the digits are from a uniform population? Digit No. of Occurrences 0 33 1 17 2 25 3 30 4 31 5 28 6 24 7 25 8 32 9 25 Total 270 -------------------------------- You would expect each digit to occur (1/10)*270 = 27 times ---------- Subtract that "expected" number from each listed No.of Occurrences to generate a "difference column" : Entries would be 5,-10,-2,3, etc. ------- Generate a "difference squared column": entries would be 25,100,4,9, etc --------- Divide each of those elements by 27: entries would be 25/27,100/27,4/27,9/27.. ---------- Add all those numbers to get a Chi-Sq number for your problem: Chi-Sq = 7.7037... ------------- Ho: all the digit proportions are the same Ha: at least one of the proportions is different ---------- Critical value for right-tail test with alpha=5% is Chi-sq = 16.919 based on df=9. ----------- Test statistic: Chi-sq = 7.7037 ----------------- Conclusion: Since the test statistic is less than the critical value Fail to reject Ho. The test shows no significant evidence that the proportion of digits is usual. ========== Cheers, Stan H.
 Probability-and-statistics/130994: This is not in a textbook, can you help? Two banks in the Greensboro NC area compete for credit card customers. In order to select the better bank, we want to test whether there is a difference in the proportion of times a customer is able to reach the customer service representative in less than 2 minutes. We have called the first bank 500 times and were able to speak to the customer service rep on 455 occasions. Then we attempted to call the second bank and were able to speak to service rep 344 of 400 trials. At the 0.05 significance level is there a difference in percentages of success between these two banks?1 solutions Answer 95629 by stanbon(57307)   on 2008-03-08 09:21:14 (Show Source): You can put this solution on YOUR website!test whether there is a difference in the proportion of times a customer is able to reach the customer service representative in less than 2 minutes. We have called the first bank 500 times and were able to speak to the customer service rep on 455 occasions. Then we attempted to call the second bank and were able to speak to service rep 344 of 400 trials. At the 0.05 significance level is there a difference in percentages of success between these two banks? ------------- Ho: p1 - p2 = 0 Ha: p1 - p2 is not zero ------------------------ p1-hat = 455/500 = 0.91 p2-hat = 344/400 = 0.86 ------------------------ Critical value for 2-tail test and alpha=5%: +-1.96 -------------------------- Test statistic: Pooling the data you get p-bar = (455+344)/(500+400)= 0.88777 z(0.91-0.86)= (0.05/sqrt[(0.888*0.112/500 + (0.888*0.112/400)] = 2.3634.. p-value = 2*P(2.3634 ----------------- Conclusion: Since p-value is less than 5%, reject Ho. There is significant statistical evidence that there is a difference between the two proportions. ===================== Cheers, Stan H. ---------------
 Linear-equations/130965: Bob has \$40 to spend on popcorn and pop. The equation 5x + 2y=40 describes the number of popcorns x and small drinks y she can buy. Graph this function and find its intercepts. The graph is set up with numbers 2-20 on each axis.1 solutions Answer 95588 by stanbon(57307)   on 2008-03-07 19:04:13 (Show Source): You can put this solution on YOUR website!Bob has \$40 to spend on popcorn and pop. The equation 5x + 2y=40 describes the number of popcorns x and small drinks y she can buy. Graph this function and find its intercepts. The graph is set up with numbers 2-20 on each axis. --------------------- 5x + 2y = 40 Intercepts: x-intercept: Let y = 0, then x = 8 Point (8,0) ---------------- y-intercept: Let x=0, then y = 20 Point (0,20) ----------------- ================================ Cheers, Stan H.
 Linear-equations/130963: The question was graph 6x-5y=-30. Well my teacher told me to create a function so I did but I dont know how to solve it my function for my x values were 1 and 2 but Im still confused????1 solutions Answer 95586 by stanbon(57307)   on 2008-03-07 18:58:12 (Show Source): You can put this solution on YOUR website!The question was graph 6x-5y=-30. ---------------------------- Solve for "y": 5y = 6x+30 y = (6/5)x + 6 -------------- Find and plot two points: If x = 0, y = 6 giving you point (0,6) If x = 5, y = 12 giving you point (5,12) ---------------- Plot the two points and draw a line thru them. ======================= Cheers, Stan H.
 Proportions/130961: The problem reads as follows: Ideally, a school district would like the boy/girl ratio in each classroom to be essentially the same as the ratio of boys to girls in the whole class. Suppose an incoming fifth grade class is made up of 123 boys and 87 girls. Assuming there are 7 classrooms, how many boys and girls will ideally be in each room? I am puzzled on how to complete this one, any help would be greatly appreciated.1 solutions Answer 95584 by stanbon(57307)   on 2008-03-07 18:53:07 (Show Source): You can put this solution on YOUR website!Ideally, a school district would like the boy/girl ratio in each classroom to be essentially the same as the ratio of boys to girls in the whole class. Suppose an incoming fifth grade class is made up of 123 boys and 87 girls. Assuming there are 7 classrooms, how many boys and girls will ideally be in each room? ------------------ Total number of 5th grade students = 123+87 = 210 The percentage of boys is 0.5857... Assuming the 7 classes are 7 classes of 5th graders, there are 30 students in each room. EQUATION: Let "x" be the number of boys in each room: x = 0.5857*30 = 17.57 (number of boys in each class) 30-x = 12.43 (number of girls in each class) ------------------ Rounding off: 18 boys in each class 12 girls in each class ================================ Cheers, Stan H
 Finance/130943: This question is from textbook algebra I need help! Please help In the period of a year, an investor lost twince as much as he gained. If he originally had \$10,000 and now has \$8000, what amount did he gain and what did he lose? Please and Thank You=)1 solutions Answer 95580 by stanbon(57307)   on 2008-03-07 18:23:15 (Show Source): You can put this solution on YOUR website!In the period of a year, an investor lost twince as much as he gained. If he originally had \$10,000 and now has \$8000, what amount did he gain and what did he lose? ------------ Let his gain be "x" dollars; His loss is "2x" dollars --------------- x - 2x = -2000 -x = -2000 x = 2000 (his gain) 2x = 4000 (his loss) ========================= Cheers, Stan H.
 Square-cubic-other-roots/130960: This question is from textbook Introductory Algebra Between what two consecutive integers is the square root of 78?1 solutions Answer 95577 by stanbon(57307)   on 2008-03-07 18:15:48 (Show Source): You can put this solution on YOUR website!Between what two consecutive integers is the square root of 78? ---------- 8^2 = 64 and 9^2=81 78 is between 64 and 81 So, sqrt78 is between 8 and 9 =============================== Cheers, Stan H.