# Questions on Algebra: Probability and statistics answered by real tutors!

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 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Question 190013: the product of the numbers showing on the two dice is less than 10 Click here to see answer by Mathtut(3670)

 Question 190015: The number showing on the red die is greater than the number showing on the blue die. Click here to see answer by Mathtut(3670)

 Question 190016: Tow bags contain marbles. The first bag contains a red and a blue marble. The second bag contains a red, a blue, a yellow, and a green marble. One marble is drawn from each bag. a. specify the sample space. b. specify the event that at least one red marble is drawn. c. specify the event that neither marble drawn is blue. Click here to see answer by Mathtut(3670)

 Question 190017: A red, a blue, and a green die are tossed. Let (r,b,g) represent each outcome. a.how many elements are in the sample space? b. specify the event that all three dice show the same number c. specify the event that the sum of numbers showing on the red and blue dice is less than the number showing on the green die. Click here to see answer by stanbon(57307)

 Question 190008: In an intelligence test administration to 1000 student the average score is 42 and the standard deviation is 24. The score are normally distributed. 1. Number of student whose score exceed 58. 2. Number of student whose score lie between 30 & 66. 3. If 40% student have failed in this intelligence test what is the score below which they have failed. Given that p(0 Click here to see answer by stanbon(57307)

 Question 190018: In October 2004 the Boston Red Sox won the American League Championship playoff series 4 games to 3 after the New York Yankees had won the first 3 games. This was the first time in the history of Major League baseball that a team had come from a 3-0 deficit to win a 7-game playoff series. Suppose teams A and B are playing in a series where the winner must win 4 games. And suppose that the games form independent trials where in each game played the probability that A wins is 0.36 and the probability that B wins is 0.64. What is the probablity one of the teams wins the first 3 games but the other team wins the series? Click here to see answer by stanbon(57307)

 Question 189512: The Academy of Orthopedic surgeons states that 90% of U.S women wear shoes that are too small for their feet. A researcher wants to be 95% confident that this proportion is within 2% of the true proportion. How large a sample is necessary? Can you please show me how you get the answer? Thanks Click here to see answer by stanbon(57307)

 Question 190139: The bank is considering paying interest to customers carrying average daily balance in excess of a certain amount. If the bank does not want to pay interest to more than 5% of its customers, what is the minimum average daily balance it should be willing to pay interest on? Given that p(0 Click here to see answer by stanbon(57307)

 Question 189502: A physician's health study of the effectiveness of aspirin in the reduction of heart attacks was begun in 1982 and completed in 1987 (see C. Hennekens et al., "Findings from the Aspirin Component of the Ongoing Physician's Health Study," The New England Journal of Medicine 318 (January 28, 1988): 262-264). Of 11,037 male medical doctors in the United States who took one 325 mg buffered aspirin tablet every other day, 104 suffered heart attacks during the five-year period of the study. Of 11,034 male medical doctors in the United States who took a placebo (i.e., a pill that, unknown to the participants in the study, contained no active ingredients), 189 suffered heart attacks during the five-year period of the study. Is there evidence that the proportion having heart attacks is significantly lower for the male medical doctors in the United States who received the buffered aspirin every other day than for those who received a placebo? Does this lead you to believe that taking one buffered aspirin every other day is effective in reducing the incidence of heart attacks? Explain. Click here to see answer by stanbon(57307)

 Question 190164: Based on a sample of 3,000 people, the civilian unemployment rate in the United States was 5.5%. the 5.5% is referred to as a _________________. Click here to see answer by stanbon(57307)

 Question 190153: a computer password contains 4 digits followed by 2 letters. Find the number of password possibilities if the first digit cannot be 0 and repetition is permitted. Click here to see answer by stanbon(57307)

 Question 190152: you are taking a test that contains 5 multiple choice questions with 4 possible answers. you guess at all questions. find the probability that you guess exactly 2 questions correctly. Click here to see answer by stanbon(57307)

 Question 190151: at a local deli, 5 out of every 8 people order a turkey club. find the probability that exactly 2 of the next 5 people will order a turkey club. Click here to see answer by stanbon(57307)

 Question 190148: A class contains 3 fresh, 4 soph, 6 juniors and 2 seniors. four students are selected at random, find the probability that... a. all four are juniors b. no fresh are selected c. 1 of each year is selected d.. 2 fresh and 2 juniors Click here to see answer by stanbon(57307)

 Question 190275: I would like to verify that i have the answered the problem below correctly, Thanks in advance for the help. During a certain week in the winter, the following minimum temperatures were recorded in an eastern city: 20, 28, 24, 28, 40, 39, and 31. Find the following: A. Median B. Standard Deviation The answers that I came up with are the following: A. Median = 28 B. Standard Deviation = 7.371114773221212 I greatly appreciate the help. Sam Click here to see answer by stanbon(57307)

 Question 190261: can someone please help..thanks Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. Let's suppose that for each game they play, the probability that the Bears win is 0.54 and the probability the Wildcats win is 0.46. What is the probability that the bears win the series in 3 games ? .1574 What is the probability that the wildcats win the series in 3 games? .0973 What is the probability that the bears win the series in 4 games? .216 What is the probability that the wildcats win the series in 4 games? .156 what is the probability that the bears win the series in 5 games? what is the probability that the wildcats win the series in 5 games? What is the probability that the bears win the series? what is the probability that the wildcats win the series ? Click here to see answer by stanbon(57307)

 Question 190292: I would like if possible for someone to verify the answers below are correct. Attached is the problem and the answers I came up with. It includes a diagram so hopefully you can understand it without confusion. Question: Assume it takes 1 minute to serve the first customer in line and that the customer leaves immediately. I will write the minute and the customers with arrived during that particular minute: Minute 1 - A, Minute 2 - B, Minute 3 - C, D, E, Minute 4 - F, Minute 5 - No one arrived. A. Draw a diagram showing the line during each of the first 5 minutes B. Find the mean of the number of people in line during the 5 minutes C. Find the mode of the number of people in line. The answers I came up with are: a. Here is the way my diagram should read. Then number is the minute and the letter is the customer or customers: 1st Minute - A 2nd Minute - B 3rd Minute - C,D,E 4th Minute - D,E,F 5th Minute - E,F b. Mean = 2 c. Mode= 1, 3 I hope you can understand this and many, many thanks in advance for your help. Sam Click here to see answer by solver91311(16877)

 Question 190311: A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions. If he bats 5 times in a game, what is the probability he will hit exactly one home run? If he comes to bat 5 times, what is the probability he will hit at least one home run? If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit? thanks for your help Click here to see answer by stanbon(57307)

 Question 190378: What is the mean, median and mode of the following distribution? Ages Number 40 up to 50 10 50 up to 60 28 60 up to 70 12 Click here to see answer by solver91311(16877)

 Question 190337: stanbon 21772 having trouble to figure out how you solved the question about the baseball player hits a homerun on the average of once every 12 times at bat= would you mind letting me what to due thanks Click here to see answer by stanbon(57307)

 Question 190443: In this question, answer to at least 3 decimal places accuracy. Data shows that 86% of all people are right handed. In a group of 10 people, what would be the expected value for the number of right handed people in the group? 8.6 What is the probability that exactly 8 of the people in the group are right handed? What is the probability that at least 8 of the people in the group are right handed? thanks bunches Click here to see answer by stanbon(57307)

 Question 190321: The U.S. Federal Aviation Administration reported that passenger revenues on international flights increased from \$528 million in 1981 to \$5,100 million in 2004. What is the geometric mean annual percent increase in international passenger revenues? Click here to see answer by nene189(2)

 Question 190465: Nonstandard dice can produce interesting distributions of outcomes. You have two balanced, six-sided dice. One is a standard dice, with faces having 1,2,3,4,5 and 6 spots. The other die has three faces with 0 spots and three faces with 6 spots. Find the probability distribution for the total number of spots Y on the up-faces when you roll these two dice. Click here to see answer by edjones(7569)

 Question 190466: A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the children in other group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age. Group n Mean s Breast-fed 23 13.3 1.7 Formula 19 12.4 1.8 a. Is there significant evidence that the mean hemoglobin level is higher among breastfed babies? State null hypothesis and alternate hypothesis and conduct a t-test. b. Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants. Click here to see answer by stanbon(57307)

 Question 190142: I'm working on some multiple choice problems and I'm a little stumped on them. Here's what I've come up with, if someone could tell me if I've got them or if not what is right so I know. 1.A 2.B 3.D 4.B 5.B 6.D 7.D 8.D 9.C 10.A 11.A 12.B 13.D 14.A 15.C 16.D 17.D 18.D 19.C 20.A Here's the problems 1.In a one-tailed test A.The rejection region is in one of the tails. B.The rejection region is split between the tails. C.The p-value is always less than the significance level. D.The p-value is always more than the significance level. 2.To conduct a one sample test of means and use the z distribution as the test statistic A.We need to know the population standard deviation. B.We can use the sample standard deviation provided n is at least 30. C.We need n to be at least 5. D.Both a and b are correct. 3.Which of the following statements are correct when deciding whether to use the z or the t distribution A.Use z when the sample size is 30 or more. B.Use z when we have a normal population and know the standard deviation. C.Use t when the population is normal, the population standard deviation is not known, and n is less than 30. D.All of the above statements are correct. 4.Which of the following is not a requirement for the two-sample test of means for independent samples when both samples contain less than 30 observations? A.Normal populations B.Equal population standard deviations C.Equal sample sizes D.All of the above are required. 5.To conduct a test of means for two independent samples which of the following are always required? A.At least one of the samples must have 30 observations B.Both samples must have 30 observations C.n and n (1 - ) must be 5. D.None of the above. 6.The term MSE A.Is called the mean square error. B.Is found by SSE/(n - k). C.Is an estimate of the common population variance. D.All of the above. 7.Which of the following is not an assumption required for ANOVA? A.The populations are normally distributed B.The populations have equal standard deviations C.The samples are independent. D.None of the above. 8.Under which of the following conditions will the computed value of F be negative? A.When there is no difference in the treatment means B.When there is no difference in the block means C.When the SS total is larger than SST. D.F cannot be negative. 9.Suppose we conduct an ANOVA test of four treatment means and reject the null hypothesis. Construction of a confidence interval for the difference between the first and second sample mean revealed the interval to be 10 plus or minus 12. We conclude A.This pair of means differ. B.This pair of means does not differ. C.Because we do not know the units involved, we cannot draw any conclusion. D.Because we do not know the degrees of freedom, we cannot draw any conclusion. 10.In a two-way ANOVA the second source of variation is due to A.Random error. B.Blocks. C.Total variation D.None of the above 11.In a contingency table a sample of 400 people is classified by gender and hair color (4 groups: blond, brown, black, and red). How many degrees of freedom are there? A.3 B.8 C.399 D.None of the above. 12.For a 2 goodness-of-fit test A.There is only one degree of freedom. B.The rejection region is in the upper right tail. C.The scale of measurement is interval. D.We must assume a normal population. 13.To find the expected frequency in a contingency table A.Take the square root of the degrees of freedom. B.Multiple the row and column totals and divide by the grand total. C.Use the total number of observations minus one. D.None of these. 14.Suppose we are conducting a Chi-Square Goodness of Fit test of hypothesis to determine if a set of observations with 6 categories meets an expected set. How many degrees of freedom are there? A.5 B.97 C.3 D.None of these. 15.Under what conditions could the 2 distribution assume negative values? A.When the sample size is small. B.When the cell frequencies are all equal. C.When the degrees of freedom is 1. D.Never 16.A scatter diagram is a chart A.In which the dependent variable is scaled along the vertical axis. B.In which the independent variable is scaled along the horizontal axis. C.That portrays the relationship between two variables. D.All of the above. 17.In correlation analysis A.We consider several independent variables. B.We study the strength of the association between two variables. C.We consider the intercept with the Y-axis. D.None of the above. 18.The sample coefficient of correlation A.Has the same sign as the slope, i.e. b. B.Can range from -1.00 up to 1.00 C.Is also called Pearson's r. D.All of the above. 19.The coefficient of determination A.Is the square of the coefficient of correlation. B.Cannot be negative. C.Reports the percent of the variation in the dependent variable explained by the independent variable. D.All of the above. 20.Suppose we developed the following least squares regression equation: Y' = 3.5 +2.1 . Which of the following statement is correct? A.The dependent variable increases 2.1 for an increase of 1 in . B.The equation crosses the Y-axis at 3.5. C.If = 5, then Y' = 14. D.All of the above. Click here to see answer by stanbon(57307)

 Question 189500: An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was \$275.66 with a standard deviation of \$78.11. (a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than \$250 out-of-pocket? State your hypotheses and decision rule. (b) Is this a close decision? Click here to see answer by stanbon(57307)

 Question 190740: Question 1 You want to prove that a population mean is not 7. Data is ratio and a large sample size will be used (n = 225). When the sample is done the sample mean is computed to be 7.2 and the sample standard deviation is 1.5. Test the hypothesis using an alpha of 5%. Use formal hypothesis testing and compute the p-value. Question 2 An associate asks for your help in deciphering the following Anova table, indicating that a test of means was performed on the average age of people at three different locations. Unfortunately the person leaves before you can get any further explanation or detail, but you know the results must be presented before senior staff within twenty minutes! Use the formal 5-step hypothesis testing model to describe the test, the results and interpret the results in conversational English. ANOVA Source of Variation SS df MS F P-value F crit Between Groups 700.0 2 350.0 4.00 0.0288 3.32 Within Groups 2625.0 30 87.5 Total 3325.0 32 Click here to see answer by stanbon(57307)

 Question 190784: in a group of 21 people, seven own an ITouch phone. If 9 people are selected at random what is the probability that 5 own an ITouch Click here to see answer by stanbon(57307)

 Question 190794: There are 8 physics textbooks, 7 us history textbooks, 4 calculus textbooks, and 3 resource books on a shelf. Assuming the books in each category are DISTINCT how many ways can they be arranged if books of the same kind must be together? Click here to see answer by solver91311(16877)

 Question 190805: At Nick and Francine's wedding reception, the wedding party were asked to dance during one song. Each person on the dance floor had to dance with every other person. If there were 18 people on the dance floor, how many "Dancing partners" were there? Click here to see answer by solver91311(16877)

 Question 190798: There are 8 physics textbooks, 7 us history textbooks, 4 calculus textbooks, and 3 resource books on a shelf. Assuming the books in each category are DISTINCT how many ways can they be arranged if books of the same kind must be together? Click here to see answer by stanbon(57307)

 Question 190814: The probability that a trainee will remain with a company is 0.6. The probability that an employee earns more than Rs.10, 000 per year is 0.5. The probability that an employee is a trainee who remained with the company or who earns more than Rs.10, 000 per year is 0.7. What is the probability that an employee earns more than Rs.10, 000 per year given that he is a trainee who stayed with the company. Click here to see answer by stanbon(57307)

 Question 190792: There are 8 Physics books, 4 calculus books, 7 us history textbooks, and 3 resource books on a shelf. Assuming the books in each category are NOT DISTINCT how many ways can they be arranged on the shelf? Click here to see answer by stanbon(57307)

 Question 190874: if automobile license plates consist of two letters followed by four digits, how many different possible license plates are possible if letters and numbers can repeated? Click here to see answer by checkley75(3666)

 Question 190938: if all the students in the class scored 100 percent on an exam, what is the standard deviation? tell why you answered the way you did? Can you show me how to answer this thank you. Click here to see answer by stanbon(57307)

 Question 190959: NEED HELP ASAP ON THIS!!! PLEASE PLEASE?? THANK YOU SO MUCH!! A U.S. dime is supposed to weigh 2.268 grams. A random sample of 15 circulated dimes showed a mean weight of 2.256 grams with a standard deviation of .026 grams. Using α = .05, is the mean weight of all circulated dimes lower than the specification? Explain your decision. Hypothesis Test: Mean vs. Hypothesized Value 2.26800 hypothesized value 2.25600 mean Sample data 0.02600 std. dev. 0.00671 std. error 15 n 14 df -1.79 t .0478 p-value (one-tailed, lower) 2.24160 confidence interval 95.% lower 2.27040 confidence interval 95.% upper 0.01440 half-width Click here to see answer by stanbon(57307)

 Question 190974: CAN you HELP ASAP thank you sooooooooo very much Now suppose that Jacob is a basketball player who averages scoring 1.65 points whenever he has a one-and-one free throw situation. Let's use that information to calculate what his free-throw shooting percentage is. Let's use the symbols p and E to represent what we're talking about: p = success probability whenever Jacob shoots a free throw E = expected value for number of points scored in a one-and-one situation In Takeisha's case, we knew that p = 0.74, and we used that information to solve for E. In Jacob's case we know that E = 1.65, and we want to solve for p. To do this, use exactly the same procedure that you did with Takeisha, except instead of working with the number 0.74, simply use the symbol p. This should lead you to an equation involving p and E. Since you know the value of E in Jacob's case, plug in that value and solve for p. (It's a quadratic equation, so you'll need to use the quadratic formula.) Jacob's success probability when shooting free throws Click here to see answer by stanbon(57307)

 Question 190981: A random sample of 100 students at southern university was collected. The mean age was found to be 24.2 years, with a standard deviation of 3.4 years A) what percent of students are over 27.6 years old b)what percent of the students are between 20.8 and 24.2 years old c) If a student is selected at random from southern univesity, what is the probability that he or she will be over 20.8 years old I could use some help Click here to see answer by stanbon(57307)

 Question 191043: I started most of the work but I am not sure if I am doing it right. Please help. Hypothesis Testing for Mean (Small Samples) 3. Metro Bank claims that the mean wait time for a teller during peak hours is less than 4 minutes. A random sample of 20 wait times has a mean of 2.6 minutes with a sample standard deviation of 2.1 minutes. a. Use the critical value z0 method from the normal distribution to test for the population mean . Test the company’s claim at the level of significance  = 0.05. xbar = 2.6 µ = 4 s = 2.1 n = 20 d.f = n – 1 = 20 – 1 = 19 To find the critical value, use table 5 in Appendix B with d.f. = 19 and 0.05 in the “One Tail, ” column. Because the test is a left-tailed test, the critical value is negative. So t0 = -1.729 1. H0 : u >= 4 minutes Ha : u < 4 minutes 2. level of significance = 0.05 3. Test statistics: t = xbar - µ / s/√n (2.6-4)/[2.1/sqrt(20)] = -2.9814 4. P-value or critical z0 or t0. 5. Rejection Region: t < -1.729 6. Decision: Since -2.9814 is in the reject interval, Reject Ho. 7. Interpretation: The mean time is not <= 4 minutes b. Use the critical value z0 method from the normal distribution to test for the population mean. Test the company’s claim at the level of significance  = 0.01. xbar = 2.6 µ = 4 s = 2.1 n = 20 d.f = n – 1 = 20 – 1 = 19 To find the critical value, use table 5 in Appendix B with d.f. = 19 and 0.01 in the “One Tail, level of significance ” column. Because the test is a left-tailed test, the critical value is negative. So t0 = 2.539 1. H0 : u >= 4 minutes 2. Ha : u < 4 minutes 3. level of significance = 0.01 4. Test statistics: 5. P-value or critical z0 or t0. 6. Rejection Region: 7. Decision: 8. Interpretation: Hypothesis Testing for Proportions. 4. In a recent poll, it was found that 43% of registered U.S. voters would vote for the incumbent president. If 100 registered voters were sampled randomly, it was found that 35% would vote of the incumbent. Test the claim that the actual proportion is 43%. 1. H0 : Ha : 2. level of significance = 3. Test statistics: 4. P-value or critical z0 or t0. 5. Rejection Region: 6. Decision: 7. Interpretation: Click here to see answer by stanbon(57307)

 Question 191017: Not sure on how to complete the following. I think I did the first one right. Introduction to Hypothesis Testing State the claim mathematically. Then write the null and alternative hypothesis. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. a. In a recent poll, it was found that 43% of registered U.S. voters would vote for the incumbent president. If 100 registered voters were sampled randomly, it was found that 35% would vote of the incumbent. Test the claim that the actual proportion is 43%. Answer: claim: The claim “that 43% of registered U.S voters would vote for the incumbent president” H0: p = 43 Ha: p not equal to 43 Test: Because Ha contains the not eual to 43, the testis a two-tailed hypothesis test. b. Convicted murderers receive a sentence of an average of 18.7 years in prison. A criminologist wants to perform a hypothesis test to determine whether the mean sentence by one particular judge differs from 18.7 years. Answer: claim: the mean sentence by one particular judge differs from 18.7 years H0: Ha: Test: Click here to see answer by stanbon(57307)

 Question 191029: Did I do this right? Hypothesis Testing for the Mean (Large Samples) Convicted murderers receive a sentence of an average of 18.7 years in prison. A criminologist wants to perform a hypothesis test to determine whether the mean sentence by one particular judge differs from 18.7 years. A random sample of 40 cases from the court files from this judge is taken. It is found that sample mean is 17.2 years. Assume that the population standard deviation is 7.4 years. Test at the 0.05 significance level. Solution: Criminologist wants to perform a hypothesis test to determine whether the mean sentence by one particular judge differs from 18.7 years 1. H0: µ = 18.7 Ha: µ ≠18.7 2. significance level = 0.05 3. Test statistics: The test is two-tailed z = xbar - µ / ơ/√n = (17.2-18.7)/[7.4/sqrt(40)] = -1.2820 4. P-value or critical z0 or t0. The critical values are – z0 = -1.96 and z0 = 1.96 5. Rejection Region: z < -1.96 and z > 1.96 6. Decision: since test statistic is not in the reject interval, Fail to reject Ho. 7. Interpretation: The test does not provide strong evidence for rejecting the belief the average sentence is 18.7 b. Use the P-value method. 1. H0: µ = 18.7 Ha: µ ≠18.7 2. significance level = 0.05 3. Test statistics: z = xbar - µ / ơ/√n = (17.2-18.7)/[7.4/sqrt(40)] = -1.2820 4. P-value or critical z0 or t0. In Table 4, the area corresponding to z = -1.2820 is 0.1003. Because the test is a two-tailed test, the P-value is equal to twice the area to the left of z = 0.2820 P = 2(0.1003) = 0.2006 5. Rejection Region: ? 6. Decision: Since p-value is greater than 0.05 fail to reject Ho. 7. Interpretation: The test does not provide strong evidence for rejecting the belief the average sentence is 18.7 Click here to see answer by stanbon(57307)

 Question 191001: b) The odds against student X solving a Business statistics problem are 8 to 6, and odds in favour of student Y solving the problem are 14 to 16. 1. What is the chance that the problem will be solved if they both try independent of each other? 2. What is the probability that none of them is able to solve the problem? Question 2: Marks: 1+3+2+3+1= 10 For the frequency distribution given below: Length of Service No of employees 7.5-7.9 6 8.0-8.4 22 8.5-8.9 36 9.0-9.4 18 9.5-9.9 14 10.0-10.4 4 Calculate (i) Mean (ii) Standard deviation (iii) Co-efficient of Variation (iv) Mean Deviation (from median) (v) Range Question 3: Marks: 2+2=4 a) How many distinct four-digit numbers can be performed from the following integers 1, 2, 3,4,5,6 if each integer is used only once? b) What would be the shape and name of the frequency distribution if 1. mean=median=mode 2. mean>median>mode Question 4: Marks: 2+6=8 a) Describe the situation in which two variables are perfect positively correlated? b) The cost of output at a factory is thought to depend on the number of units produced. Data have been collected for the number of units produced each month in the last six months, and the associated costs, as follows; Output (‘000s of units) X Cost (\$’000) Y 2 9 3 11 1 7 4 13 3 11 5 15 Calculate the correlation coefficient and comment on your result. Click here to see answer by stanbon(57307)

 Question 191344: There are 10 houses in your neighborhood having a yard sale. You want to go to at least 5 of the houses having a yard sale. How many different combinations of yard sales can you attend? My answer choices are: A) 386 B) 638 C) 848 D) 1,286 E) 9,858,240 Click here to see answer by solver91311(16877)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240