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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/320406: A quality engineer is investigating the effect of four assembly methods (A,B,C,D) on the assembly time for a colour television component. He selects four operators for the study so that he can also test if there will be variation based on the operators. Furthermore- he knows that each assembly method produces such fatigue that the time required for the last assembly may be greater than the time required for the first assembly. Hence he must also test the different orderes of the assembly. To account for all the sources he decides to use latin-square procedure and obtain the following results: Order of assembly Operator 1 2 3 4 Order 1 C=10 D=14 A=7 B=8 Order 2 B=7 C=18 D=11 A=8 Order 3 A=5 B=10 C=11 D=9 Order 4 D=10 A=10 B=12 C=14 PERFORM AN ANALYSIS OF VARIANCE PROCEDURE TO DETERMINE WHETHER THERE IS A SIGNIFICANT DIFFERENCE BETWEEN THE ASSEMBLY METHODS (use α = 0.05) 1 solutions Answer 229565 by stanbon(57222)   on 2010-07-07 18:39:36 (Show Source): You can put this solution on YOUR website!Order of assembly Operator 1 2 3 4 Order 1 C=10 D=14 A=7 B=8 Order 2 B=7 C=18 D=11 A=8 Order 3 A=5 B=10 C=11 D=9 Order 4 D=10 A=10 B=12 C=14 PERFORM AN ANALYSIS OF VARIANCE PROCEDURE TO DETERMINE WHETHER THERE IS A SIGNIFICANT DIFFERENCE BETWEEN THE ASSEMBLY METHODS (use α = 0.05) ----------------------------------------------- Ho: The means are all equal. Ha: At least one is different ---- I ran an ANOVA against the data and got the following: test statistic: F = 0.5502 p-value: 0.6576 -- Since the p-value is greater than 5%, fail to reject Ho. =============================================================== Cheers, Stan H.
 Probability-and-statistics/320366: 3. A dart hits a dartboard that is in the shape of a square with sides of 4 m. There are four congruent circles inside the square that are all touching. The shaded region is everything but the 4 circles. What is the probability that the dart will land in a circle? a. 21% b. 25% c. 50% d. 79%1 solutions Answer 229522 by stanbon(57222)   on 2010-07-07 15:53:30 (Show Source): You can put this solution on YOUR website!A dart hits a dartboard that is in the shape of a square with sides of 4 m. There are four congruent circles inside the square that are all touching. The shaded region is everything but the 4 circles. What is the probability that the dart will land in a circle? ----------------- Draw the pictures and you will see the diameter of each of the circles is 2 m; so each radius is 1m. So the area of each circle is pi sq meters. So the area of the four circles is 4pi sq meters. --- The area of the square is 16 sq meters. --------------- P(land in a circle) = 4pi/16pi = 1/4 = 25% ============================================= Cheers, Stan H. ================== a. 21% b. 25% c. 50% d. 79%
 Probability-and-statistics/320408: The lifetime of a certain brand of battery is known to have a standard deviation of hours. Suppose that a random sample of such batteries has a mean lifetime of hours. Based on this sample, find a confidence interval for the true mean lifetime of all batteries of this brand. Then complete the table below. 1 solutions Answer 229520 by stanbon(57222)   on 2010-07-07 15:33:23 (Show Source): You can put this solution on YOUR website!Numbers are misssing from your post. Cheers, stan H.
 Probability-and-statistics/320410: Suppose that % of the women who gave birth at a certain hospital last year were over years old, and that % were unmarried. If % of the women were over or unmarried (or both), what is the probability that a woman who gave birth at the hospital was both unmarried and over.1 solutions Answer 229519 by stanbon(57222)   on 2010-07-07 15:32:37 (Show Source): You can put this solution on YOUR website!Numbers are missing from your post. Cheers, Stan H.
 Probability-and-statistics/320420: On three tests, each graded on a scale of 0 to 100, Jim had an average score of 78. If Jim pulls his average up to 84 after taking two additional tests, what is the lowest possible score he could have received on one of the last two tests?1 solutions Answer 229518 by stanbon(57222)   on 2010-07-07 15:31:40 (Show Source): You can put this solution on YOUR website!On three tests, each graded on a scale of 0 to 100, Jim had an average score of 78. If Jim pulls his average up to 84 after taking two additional tests, what is the lowest possible score he could have received on one of the last two tests? ---------- To average 84 in five tests Jim would need 5*84 = 420 points. ----------------- After three tests Jim has 3*78 = 234 points. He needs 186 points in the remaining tests. If one of the tests is 100 the other could be 86 ================ Cheers, Stan H.
 Probability-and-statistics/320472: In orange county, 12% of those eligible for jury duty are left-handed. Among 250 people selected for jury duty, 25 (or 10%) are lefties. Find the probability of getting at most 25 lefties assuming that they are chosen with a process designed to yeild a 12% rate of lefties. Can we conclude that this process of selecting jurors discriminates against lefties?1 solutions Answer 229517 by stanbon(57222)   on 2010-07-07 15:19:29 (Show Source): You can put this solution on YOUR website!In orange county, 12% of those eligible for jury duty are left-handed. -------------------------- Among 250 people selected for jury duty, 25 (or 10%) are lefties. -------------------------- Find the probability of getting at most 25 lefties assuming that they are chosen with a process designed to yield a 12% rate of lefties. --- Binomial with n = 250 and p = 0.12 P(0<= x <= 25) = binompdf(250,0.12,25) = 0.0509 ----------------------------- Can we conclude that this process of selecting jurors discriminates against lefties? It's lower than the rate of lefties in Orange County. ================== Cheers, Stan H.
 Probability-and-statistics/320483: a) Describe the two assumptions needed for the confidence interval statement to be valid b) For each assumption, give an example of what could go wrong if it were not satisfied c) How does the central limit theorem help satisfy one of these assumptions? 1 solutions Answer 229515 by stanbon(57222)   on 2010-07-07 14:49:56 (Show Source): You can put this solution on YOUR website!Those two assumptions depend on what text book you are using. You would have to post them so we could see how the Central Limit Theorem relates to them. cheers, Stan H.
 Probability-and-statistics/320494: I was wondering if I can get help answering this problem. I chose #1 Sex X Mean St Dev SE Mean F 116 1.95 1.51 0.14 M 59 2.37 1.87 0.24 (95% CI for mu(f) - mu(m):(-0.97,0.14) T-Test mu(f)=mu(m) (vs not =): T= -1.49 P=0.14 DF=97 For the variable "Time spent watching TV in Typical Day," the results of a two-sample t-procedure that compares a random sample of men and women at a college are shown above. What is the alternative hypothesis of the t-test? 1. μ1 − μ2 < 0 2. μ1 − μ2 = 0 3. μ1 − μ2 ≠ 0 4. μ1 − μ2 > Thanks, Kim1 solutions Answer 229514 by stanbon(57222)   on 2010-07-07 14:47:58 (Show Source): You can put this solution on YOUR website!I was wondering if I can get help answering this problem. I chose #1 Sex X Mean St Dev SE Mean F 116 1.95 1.51 0.14 M 59 2.37 1.87 0.24 (95% CI for mu(f) - mu(m):(-0.97,0.14) T-Test mu(f)=mu(m) (vs not =): T= -1.49 P=0.14 DF=97 For the variable "Time spent watching TV in Typical Day," the results of a two-sample t-procedure that compares a random sample of men and women at a college are shown above. What is the alternative hypothesis of the t-test? --------------------- Your problem statement says you are testing mu(f) = mu(m) (vs not =) ---------------------- Since Ho must ALWAYS include equality, the alternate hypotheses is mu(f)-mu(m) is not equal to 0 ========================================================== Cheers, Stan H. 1. μ1 − μ2 < 0 2. μ1 − μ2 = 0 3. μ1 − μ2 ≠ 0 4. μ1 − μ2 >
 Probability-and-statistics/320495: Hot Shot Battery manufactures batteries in batches of 15 with a defective rate of 10% a.What is the probability that exactly 2 will be defective? b.What is the probability that between 2 and 4 inclusive will be defective? c.What is the probability that no batteries will be defective? 0 d.Find the mean  e.Find the variance 2 1 solutions Answer 229513 by stanbon(57222)   on 2010-07-07 14:42:42 (Show Source): You can put this solution on YOUR website! Hot Shot Battery manufactures batteries in batches of 15 with a defective rate of 10% --- Binomial Problem with n= 15 and p = 0.10 ----------------------------------------------- a.What is the probability that exactly 2 will be defective? P(x+2) = 15C2*0.10^2*0.90^13 = binompdf(15,0.1,2) = 0.2669 ------------------------------------- b.What is the probability that between 2 and 4 inclusive will be defective? binomcdf(15,0.1,4)-binomcdf(15,0.1,1) = 0.4382 ------------------------------------ c.What is the probability that no batteries will be defective? P(x=0) = 15C0*0.1^0*0.9^15 = 0.9^15 = 0.2059 ------------------------------------ d.Find the mean ; mean of a binomial distribution = np np = 15*0.1 = 1.5 ------------------------------------ e.Find the variance variance = npq npq = 1.5*0.9 = 1.35 ===================== Cheers, Stan H.
 Linear-equations/320300: I want to see the steps in solving 2 math problems. Got them wrong on a quiz and have no idea what I am doing. 5x+6<88 2x+5=11 solutions Answer 229403 by stanbon(57222)   on 2010-07-06 20:55:06 (Show Source): You can put this solution on YOUR website!5x+6<88 5x < 82 x < 82/5 x < 16 2/5 ------------------ 2x+5=1 2x = -4 x = -2 ===================== Cheers, Stan H.
 Probability-and-statistics/320299: A drawer contains 4 red socks, 7 white socks, and 11 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is blue and the second sock is blue? 1 solutions Answer 229401 by stanbon(57222)   on 2010-07-06 20:52:11 (Show Source): You can put this solution on YOUR website!A drawer contains 4 red socks, 7 white socks, and 11 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is blue and the second sock is blue? ----------------------- P(blue on 1st draw) = 11/22 = 1/2 ---- Since the blue sock is replaced, P(blue on 2nd draw) = 11/22 = 1/2 --------------------------------- P(2 blue with replacement) = (1/2)(1/2) = 1/4 ================================================= Cheers, Stan H. ==========
 Equations/320298: Hello how are you I was working on this problem n-29=-53and i wanted to get an understanding on working the problem.......this is what i did 53-29=24 and then i add the neg sign b/c both numbers were neg. so my answer was n=-241 solutions Answer 229400 by stanbon(57222)   on 2010-07-06 20:48:58 (Show Source): You can put this solution on YOUR website!n-29=-53 ---- Add 29 to both sides to solve for "n": n-29+29 = -53+29 n = -24 =========== Cheers, Stan H. ===========
 Polynomials-and-rational-expressions/320291: Which of the following is FALSE about the normal distribution? A. The mean, median, and mode are equal. B. The normal curve never crosses the x-axis. C. The total area under the normal curve is equal to 1. D. The normal curve has inflection points on the x-axis. E. The graph of a normal distribution is called the normal curve. I was thinking E because through it was called an inflection points1 solutions Answer 229399 by stanbon(57222)   on 2010-07-06 20:46:28 (Show Source): You can put this solution on YOUR website!D --- Cheers, Stan H.
 Polynomials-and-rational-expressions/320292: The standard normal distribution always has a mean of 0 and a standard deviation of 1. is this statement true 1 solutions Answer 229396 by stanbon(57222)   on 2010-07-06 20:43:08 (Show Source): You can put this solution on YOUR website!True. That is what "standard" means. Cheers, Stan H.
 percentage/320269: Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the cost for such a station are \$2,500 for setup costs and \$3.00 to administer each test. a. Write an expression that gives the total cost to test x animals. b. You can find the average cost per animal by dividing total costs by number of animals. Write the expression that gives the average cost per animal. c.Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals. d.As the number of animals increases, what happens to the average cost to test the animals? Would the average cost ever fall below \$3.00? If so, identify a value that supports your answer.If not explain how you know. e. How many animals should be testes for the average cost to be \$5.00 per animal?1 solutions Answer 229392 by stanbon(57222)   on 2010-07-06 20:31:20 (Show Source): You can put this solution on YOUR website!Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the cost for such a station are \$2,500 for setup costs and \$3.00 to administer each test. a. Write an expression that gives the total cost to test x animals. C(x) = 2500 + 3x ------------------------------ b. You can find the average cost per animal by dividing total costs by number of animals. Write the expression that gives the average cost per animal. Ave = (2500+3x)/x ------------------------------ c.Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals. Ave(10) = (2530)/10 = \$253 Ave(100) = (2800)/100 = \$28 Ave(1000) = (5500)/1000 = \$5.50 ------------------------------ d.As the number of animals increases, what happens to the average cost to test the animals? Would the average cost ever fall below \$3.00? If so, identify a value that supports your answer.If not explain how you know. --- Horizontal asymptotte at Ave(x) = 3 =========================================== e. How many animals should be tested for the average cost to be \$5.00 per animal? Solve: 5 = (2500+3x)/x 5x = 2500+3x 2x = 2500 x = 1250 =============== Cheers, Stan H. ================
 Problems-with-consecutive-odd-even-integers/320283: The sum of three consecutive page numbers is 60. Find the numbers. I dont understand what they mean can u help? this problem was solved for me but i dont understand how the person got the number 57 or the answer 19 can someone walk me through this i am so lost i would like to be able to work this out thanks1 solutions Answer 229389 by stanbon(57222)   on 2010-07-06 20:10:45 (Show Source): You can put this solution on YOUR website!The sum of three consecutive page numbers is 60. Find the numbers. --- Let the 1st page be "x" Next page is "x+1" Next page is "x+2" ----------------------- Equation: x + x+1 + x+2 = 60 3x + 3 = 60 3x = 57 x = 19 x+1 = 20 x+2 = 21 ============ Cheers, Stan H.
 Sequences-and-series/320277: What is the fifth term of the sequence whose first term is a1 = 8 and whose nth term is an = 3an-1 + 7?1 solutions Answer 229388 by stanbon(57222)   on 2010-07-06 20:07:48 (Show Source): You can put this solution on YOUR website!What is the fifth term of the sequence whose first term is a1 = 8 and whose nth term is an = 3a(n-1) + 7? ------ a(5) = 3*a(4) + 7 ------ a(1) = 8 a(2) = 3*a(2) + 7 = 24+7 = 31 a(3) = 3*a(2) + 7 = 93+7 = 100 a(4) = 3*a(3) + 7 = 300+7= 307 a(5) = 3*a(4) + 7 = 921+7 = 928 ==================================== Cheers, Stan H.
 Expressions-with-variables/320278: Write an equivalent expression using radical notation for(16a^6)^3/41 solutions Answer 229387 by stanbon(57222)   on 2010-07-06 19:57:52 (Show Source): You can put this solution on YOUR website!Write an equivalent expression using radical notation for(16a^6)^3/4 ------- 4th root of (16a^6) cubed ================================= Cheers, Stan H.
 Inequalities/320279: Domain D = {5, 2, -4} F (X) = X2 to the second power + 3x + 1 Evaluate the equation of a nonlinear function with two inputs Please help!!!!! I do not understand 1 solutions Answer 229386 by stanbon(57222)   on 2010-07-06 19:54:40 (Show Source): You can put this solution on YOUR website!Domain D = {5, 2, -4} F(X) = X^2 + 3x + 1 Evaluate the equation of a nonlinear function with two inputs ------------------ F(5) = 5^2 + 3*5 + 1 = 41 ------------ F(-4) = (-4)^2 +3(-4) + 1 = 16 -12 +1 = 5 ========================================== Cheers, Stan H. ===============
 percentage/320272: To estimate animal population, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat(in acres) polled. a.Write an equation using only one variable that could be used to solve for the constat of variation k. b.A biologist counted 12 white tail deer in a 100 acre parcel of land in a nature preserve.Find the constant of variation k. c.If the entire nature preserve is 2,500 acres, then what is the total white tail deer population in the preserve? Describe the answer?Thanks1 solutions Answer 229385 by stanbon(57222)   on 2010-07-06 19:51:03 (Show Source): You can put this solution on YOUR website!To estimate animal population, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat(in acres) polled. ---- a.Write an equation using only one variable that could be used to solve for the constat of variation k. --- T = ka ------ b.A biologist counted 12 white tail deer in a 100 acre parcel of land in a nature preserve.Find the constant of variation k. 12 = k*100 k = 12/100 = 0.12 -------------------------- c.If the entire nature preserve is 2,500 acres, then what is the total white tail deer population in the preserve? Describe the answer?Thanks --- T = 0.12*2500 T = 300 deer ============================= Cheers, Stan H. =============================
 Probability-and-statistics/320191: In a group of 100 batteries, 30 are dead. if you choose 5 how many would you expect to work?1 solutions Answer 229366 by stanbon(57222)   on 2010-07-06 17:49:12 (Show Source): You can put this solution on YOUR website!In a group of 100 batteries, 30 are dead. if you choose 5 how many would you expect to work? -------------- P(good battery) = 70/100 = 0.7 ---- Expected number of good in 5 = 5*0.7 = 3.5 ======================= Cheers, Stan H.
 Probability-and-statistics/320243: A researcher studying stress in interested in the blood pressure measurements of CEOs for major corporations. He believes that the mean systolic blood pressure of CEOs of major corporations is less than 123 mm Hg,which is the value reported in a possibly outdated journal article. He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 124 mm Hg and the standar deviation of the sample t be 15 mm Hg.Based on this information: What is the null hypothesis and the alternate hypothesis that should be used for this test? In the context of the test, what is a Type II error? Suppose the research decides to reject the hypothesis, What sort of error might he be making?1 solutions Answer 229363 by stanbon(57222)   on 2010-07-06 17:45:32 (Show Source): You can put this solution on YOUR website!A researcher studying stress in interested in the blood pressure measurements of CEOs for major corporations. He believes that the mean systolic blood pressure of CEOs of major corporations is less than 123 mm Hg,which is the value reported in a possibly outdated journal article. ----------------------------- He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of ?? CEOs of major corporations and finds the mean of the sample to be 124 mm Hg and the standard deviation of the sample t be 15 mm Hg.Based on this information: -------------------- What is the null hypothesis and the alternate hypothesis that should be used for this test? --- Ho: u = >= 123 Ha: u < 123 (researcher claim) --- Note: You have listed the sample mean but not the sample size. ======================================== Cheers, Stan H. ================== In the context of the test, what is a Type II error? Suppose the research decides to reject the hypothesis, What sort of error might he be making?
 Probability-and-statistics/320192: In a group of 100 batteries, 30 are dead. Use your calculator to find the probability that if you pick 20 batteries, more than 2 will be dead.1 solutions Answer 229361 by stanbon(57222)   on 2010-07-06 17:37:30 (Show Source): You can put this solution on YOUR website!In a group of 100 batteries, 30 are dead. Use your calculator to find the probability that if you pick 20 batteries, more than 2 will be dead. --- P(a single battery is dead) = 0.3 ------ P(3<= x <=30) = 1 - P(0<= x <=2) = 1 - binomcdf(20,0.3,2) = 0.9645 ==================== Cheers, Stan H. ====================
 Probability-and-statistics/320238: A popular manufacturer of men's jeans would like to estimate the population mean of 32" length jeans. The population standard deviation is known to be 0.65". Determine the sample size needed to hold the maximum error of the estimate to 0.5 with a confidence of 98%.1 solutions Answer 229360 by stanbon(57222)   on 2010-07-06 17:30:02 (Show Source): You can put this solution on YOUR website!A popular manufacturer of men's jeans would like to estimate the population mean of 32" length jeans. -------------------------- The population standard deviation is known to be 0.65". Determine the sample size needed to hold the maximum error of the estimate to 0.5 with a confidence of 98%. ---------------------- n = [z*s/E]^2 --- n = [2.3263*0.65/0.5]^2 = 9.14 Round up to n = 10 ================================= Cheers, Stan H.
 Radicals/320226: Use prime factorization to simplify the radical 32z51 solutions Answer 229351 by stanbon(57222)   on 2010-07-06 16:36:54 (Show Source): You can put this solution on YOUR website! Use prime factorization to simplify the radical 32z5 ------------------------- = 2^5*z^5 --- = (2z)^5 ================= cheers, Stan H.
 Money_Word_Problems/320229: Lee invests \$10,000 in stocks and bonds. The stocks return 15% a year and the bonds return 10% a year. If the total return on the investment after one year is \$1,100, how much did Lee invest each in stocks and bonds?1 solutions Answer 229346 by stanbon(57222)   on 2010-07-06 16:33:05 (Show Source): You can put this solution on YOUR website!Lee invests \$10,000 in stocks and bonds. The stocks return 15% a year and the bonds return 10% a year. If the total return on the investment after one year is \$1,100, how much did Lee invest each in stocks and bonds? -------------- Quantity Equation: s + b = 10,000 Interest Equation:0.15s + 0.10b = 1100 ------------------------------------------------ Multiply thru 1st by 15; Multiply thru 2nd by 100: ------------------------------- 15s + 15b = 15*10,000 15s + 10b = 110000 ---------------------------- Subtract 2nd from 1st and solve for "b": 5b = 40,000 b = \$8000 (amt. invested in bonds) --- Since s + b = 10,000, s = \$2000 (amt. invested in stocks) ================================= Cheers, Stan H. ===============
 Expressions-with-variables/320219: Solve by substitution method 7x+8y=36 X=60-8y Thank you1 solutions Answer 229335 by stanbon(57222)   on 2010-07-06 16:11:54 (Show Source): You can put this solution on YOUR website!Solve by substitution method 7x+8y=36 X=60-8y ----- Substitute for "x" and solve for "Y": 7(60-8y) + 8y = 36 --- 7*60 - 56y + 8y = 36 -48 = -384 ------- y = 8 --- Since x = 60-8y, x = 60-8*8 = -4 ============================ Cheers, Stan H. ============================
 Equations/320216: Solve using multiplication principle -3/4x=-5/6 It makes no sense to me! Thank you1 solutions Answer 229324 by stanbon(57222)   on 2010-07-06 16:01:41 (Show Source): You can put this solution on YOUR website!Solve using multiplication principle (-3/4)x=(-5/6) --- Multiply both sides by -4/3 to get: ----- x = (-4/3)(-5/6) --- x = 20/18 --- x = 10/9 =============== Cheers, Stan H. ============
 Quadratic_Equations/320183: Please explain how I may obtain the needed answer. I have (x+3)^2=-25 I thought (X+3)*(x+3)=X^2+6x+9= -25 and moved into quadratic form by adding 25 to both sides. like so, x^2+6x+34=0 then solve for X. At this point I usually give the brain a break and solve using the TI89. Problem is that it keeps telling me false instead of the needed, {-3+5i,-3-5i} Can anyone tell me where I went wrong? Thanks1 solutions Answer 229289 by stanbon(57222)   on 2010-07-06 14:07:55 (Show Source): You can put this solution on YOUR website!The sum of squares factors as follows: a^2 + b^2 = (a+bi)(a-bi) ================================= (x+3)^2=-25 --- (x+3)^2 + 25 = 0 Factor: [x+3+5i][x+3-5i] = 0 x = -3-5i or x = -3+5i ======================== Not sure what your TI89 is doing. ======================== Cheers, Stan H. ============
 Linear-equations/320184: I have a question that is a T/F question. Can anyone explain? Thanks in advance for your wisdom! The equations y = 3x – 6 and y = 2x + 4 are independent. True or false and why.1 solutions Answer 229288 by stanbon(57222)   on 2010-07-06 14:04:05 (Show Source): You can put this solution on YOUR website!Yes, they are independent because the lines do not have the same slope and therefore are not parallel and are not dependent. ========================== Cheers, Stan H. =========== dependent: one is a multiple of the other independent: intersect at one point because slopes differ. inconsistent: parallel lines consistent: not parallel ==================
 Probability-and-statistics/320119: A leasing firm claims that the mean number of miles driven annually, , in its leased cars is less than miles. A random sample of cars leased from this firm had a mean of annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is miles. Assume that the population is normally distributed. Is there support for the firm's claim at the level of significance? Perform a one-tailed test. Then fill in the table below. What is the null hypothesis? What is the alternative hypothesis? What is the type of test statistic (Z, T, Chi Square). If T what is the degree of freedom? What is the value of the test statistic (round at least 3 decimal places) What is the critical value at the 0.05 level of significance (round at least 3 decimal places) Can we support the leasing firms claim that the mean number of miles driven annually is less than 13280 miles? 1 solutions Answer 229287 by stanbon(57222)   on 2010-07-06 13:58:50 (Show Source): You can put this solution on YOUR website!A leasing firm claims that the mean number of miles driven annually, , in its leased cars is less than miles. A random sample of cars leased from this firm had a mean of annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is miles. Assume that the population is normally distributed. Is there support for the firm's claim at the level of significance? Perform a one-tailed test. Then fill in the table below. What is the null hypothesis? What is the alternative hypothesis? What is the type of test statistic (Z, T, Chi Square). If T what is the degree of freedom? What is the value of the test statistic (round at least 3 decimal places) What is the critical value at the 0.05 level of significance (round at least 3 decimal places) Can we support the leasing firms claim that the mean number of miles driven annually is less than 13280 miles? ===================================== Read your posted problem. Notice that there are numbers missing from the text. I asked the site manager to look at what appears to be dropped numbers. Here is his feedback: "As far as I can tell, the numbers really are missing and there is no indication that they exist but in some unreadable format." ---- If you are using a non-standard way of posting your numbers, you might want to change that. ========================================= Cheers, Stan H. ======================