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

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Question 75220: 1. In the contest of Serach for Most Outstanding Teacher, 3 candidates are teaching Mathematics, 2 are teaching English, 2 are teaching Science and 1 is teaching in Filipino. What is the probability that the winner is teaching:
a. Mathematibs
b. Science
c. Filipino
d. Any subject except English
e. any subject except math
2. If the probabilities are 0.40, 0.55 and 0.3 that student will get a failing grade either in Accountancy or Marketing, or in both, what is the probability that he fail at least one of these subjects?

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Question 75427: Q. M&M candies:Are 10% blue?
According to a consumer affairs representative from Mars(the candy company, not the planet), 10% of all M&M plain candies are blue. Data set 19 in Appendix B shows that among 100 M&Ms chosen, 5 are blue. Estimate the probability of randomly selecting 100 M&Ms and getting 5 or fewer that are blue. Assume that the company's 10% blue rate is correct. Based on the result, is it unusual to get 5 or fewer blue M&Ms when 100 are randomly selected?

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Question 75466: Q1. A final exam in math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test score is greater than 78.
Q2.For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n = 16 and p = 0.5
Q3. This is the same as question 1, but find the probability that the mean of their test scores is LESS than 70
Q4. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. With n = 20 and p = 0.06, estimate p (fewer than 8).

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Question 75493: Q1. if Z is a standard normal variable, find the probability. P(-0.73 Q2. express the confidence interval in the form of +/-E, -0.052 Q3. find the critical value Z(alpha/2) that corresponds to a degree of confidence of 91%
Q4. find the minimum sample size you should use to assure that your estimate of P will be within the required margin of error around the population P. Margin of error:0.04 confidence level:94% P and q unknown.

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Question 75535: Four letters and envelopes are addressed to four different people. If the letters are randomly inserted into the envelopes, what is the probability that(a) exactly one is inserted and (b) at least one is inserted in the correct envelope
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Question 75536: Help me please....
A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames:
a. None will need adjustment.
b. At least one will need adjustment.
c. More than two will need adjustment.
Thank You!

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Question 75539: The Director of Emergency Medicine at Big Mountain Medical Services is studying patient waiting time. Waiting time is defined as the time from when a patient enters the facility until seen by a physician. The study indicates the waiting time follows a normal distribution with a mean of 22 minutes and a standard deviation of 8 minutes.
a. What fraction of the patients is seen in between 15 and 22 minutes?
b. What fraction is seen in less than 15 minutes?
c. What fraction is seen in more than 15 minutes but less than 32 minutes?
d. What fraction is seen in more than 25 minutes but less than 32 minutes?
e. Five percent of the patients are seen in how many minutes or less? That is, how quickly are 5 percent of the patients seen?
Thank You

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Question 75537: In a recent study 90 percent of the homes in the United States were found to have color TVs. In a sample of nine homes, what is the probability that:
a. All nine have color TVs?
b. Less than five have color TVs?
c. More than five have color TVs?
d. At least seven homes have color TVs?

Thank You

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Question 75094: Q. what is meant by the sampling distridution of the mean?
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Question 75557: FINDING SAMPLE SIZE.
Q1. margin of error:$125, confidence level:95%,standard deviation=$500

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Question 48934: how many numbers of five different digits, each number to contain 3 odd and 2 even digits, can be formed from the digits 1,2,3,4,5,6,7,8 and 9?Thanks!
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Question 75159: There are 75 people present to vote new members into their organization. There are 12 candidates and only 6 candidates can be voted in to become members of the organization. In order to become part of the organization, you must receive 75% of the vote amongst the 75 people that are voting. These 75 people can vote for up to 6 candidates during each voting session. Is it possible for all 6 candidates to get 75% of the vote if voters are selecting anywhere between 1 to 6 candidates on each ballot? If so, how many times must the group vote in order to select 6 people to meet the 75% requirement?
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Question 75072: 1 The hospital records show that the mean weight of newly born baby is 7 lbs, with the standard deviation of 0.75 lbs. A researcher takes a sample of 55 newly born babies and found to have a mean weight of 6.73 lbs. Test the claim at 0.05 level of significance.(use z-test)
2 To compare freshmen’s knowledge of mathematics in two departments of the College of Computer of the Manuel S. Enverga University Foundation, a certain professor in business mathematics got a sample of economics and accountancy students and gave them special examination. A sample of 25 economics major students had a mean score of 85.85 with standard deviation of 7.5. A sample of 29 accounting major students had a mean score of 90.5 with a standard deviation of 10.3. Is there a significant difference between the two sample means? Use 0.01 level of significance.(use t-test)
3 In the contest of Search for Most Outstanding Teacher, 3 candidates are teaching Mathematics, 2 are teaching English, 2 are teaching Science and 1 teaching Filipino. What is the probability that the winner is teaching:
a.Mathematics
b.Science
c.Filipino
d.Any subject except English
e.Any subject except Math
4) If the probabilities are 0.40, 0.55 and 0.3 that student will get a failing grade either in Accountancy or Marketing, or in both, what is the probability that he fail at least one of these subjects?

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Question 75597: A certain 18-hole golf course has par-3, par-4, and par-5 holes, and there are twice as many par-4 as par-5 holes. How many holes of each type are there if a golfer has a par on every hole for a score of 70?
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Question 75610: Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish-speaking American. Of the first 12 potential jurors, only 2 are Spanish-speaking Americans, and 10 are not. The defendant’s lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. What do you think?
Thank You

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Question 74947: A producer of materials that are used in Laboratories has a sampling problem. One important category of his products is of two types; alpha and beta. Beta type is relatively new and is both costly and perishable, so it’s important to produce it in small it in qualities closely in line with market demand. Laboratory technology and preferences seem to have been changing rapidly in favour of beta type, so past sales records offer very little basis for forecasting. The manufacture’s current guess is that 60 % of the combines sales of the two products next year maybe of beta type but is going to confirm his hypothesis by having sales representative call on a sample of buyers to learn how much alpha and beta they intend to buy.
How large a sample size would they call if he the manager decided that tolerable error in estimating error in estimating the population proportion is not to be greater than 2 % at confidence level of 99 % .

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Question 74945: CBA Bank is studying the use of automatic teller machines. Of interest is whether young adults (under 25 yrs) use the machine more than senior. To investigate further, sample of customers under 25 yrs of age an customers over 60 yrs of age were selected.
The number of ATM transactions last month was determined for each selected individual and the results are shown below.

Age Number of transactions
Under 25 10 10 11 15 7 11 10 9
Over 60 4 4 7 7 4 5 1 7 10 5

At the 0.01 significant level. Can bank management conclude that younger customers use the ATM more?

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Question 74940: Mr. jones is opposed to national health isurance. He argues that it would be too costly to implement, particularly since the existence of such systems would, among other effects, tend to encourage people to spend more times in hospitals. Mr >jones believes that, length of stays in hospitals is dependent on the types of health isurance that people have. He asked the head of R & D department to check this out – who duly collected data on a random sample of 600 hospitals stays. the data is summarized below :
Days is hospitals

<5 days 5-10 days >10 days
Fraction of costs <25% 40 75 65
covered by insurance 25-50% 30 45 75
>50 % 40 100 190
Prepare a statistical analysis to determine whether Mr. Jones’s concern is supported by empirical evidence. You may use 5 % level of significance

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Question 74936: use this data
3.647 3.638 3.635 3.645 3.521 3.617 3.666
3.588 3.545 3.590 3.621 3.532 3.511 3.516
3.531 3.678 3.643 3.583 3.723 3.673 3.588
3.600 3.611 3.580 3.667 3.506 3.632 3.450
3.660 3.569 3.573 3.526 3.494 3.601 3.604
3.407 3.522 3.598 3.585 3.577 3.522 3.464
3.604 3.508 3.718 3.635 3.643 3.507 3.687
3.582 3.622 3.654 3.482 3.494 3.475 3.492
3.542 3.625 3.688 3.468 3.639 3.582 3.491
3.535 3.548 3.671 3.665 3.726 3.576 3.725
Q. TESTING FOR NORMALITY. Do those weights appear to come from a population that has a normal distribution? Explain.

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Question 74935: The govenment is in the process of formulating a poverty reductiong policy and wants an estimate of the proportion of the population living below the poverty line . It wants the estimate to be within 4 % of the true population . assuming a 97.14 % confidense level . determine the appropriate sample size to use for the study .
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Question 74934: A market research agency takes a sample of 1000 people and finds that 200 know of brand X . After an advertising campaighn a further sample of 1091 people are taken and its found that 240 people are aware of brand X . Its required to know if there has been an increase having awareness of brand X at 5 % level of significance .
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Question 74933: A sales clerk in a departmental store claims that 60 % of the shoppers entering the store leave without making a purchase . A random sample of 50 shoppers showed that 35 of them left without buying anything . Are these sample results consistent with the claims of the sales clerk ? test at signifincance level of 0.01 .
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Question 75681: In a large consignment of mangoes 2% are rotten. What is the probability that a carton of 96 mangoes will contain less than two rotten mangoes?
You are doing a great job. Keep it up. Thanking you in anticipation.

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Question 75690: Find the mean.
1, 2, 9, 10, 13

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Question 75810: Question 2
A researcher with the Ministry of Transport and Communication recently hypothesized that there are three times as many traffic accidents on Saturdays and on Sundays each as on any other day of the week. From the records of the state, 110 accidents are chosen randomly and their distribution according to the days of the week is found to be as follows:
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
15 9 10 8 11 30 27

Using suitable method, test the researchers claim at 5% level of significance
Prepare a statistical analysis to determine whether there is any relationship between the category of cash flow and the company’s operating leverage. Use the 1% level of significance.
NOTE : DO NOT USE A T- CALCULATOR . SHOW ALL YOUR WORKINGS .

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Question 75992: Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability of two or three of the balls are white.
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Question 75989: Juan Salvador just completed a study of the life expectancy of 100 light bulbs and discovered that the mean time that they lasted before burning out was 1,900 hours. If the standard deviation was 150 hours, the empirical rule allows Juan to conclude that approximately 68 of the bulbs burned out between _________ and _________ hours.
a. 1,750, 2,050
b. 1,800, 1,900.
c. 1,600, 2,200.
d. 1,450, 2,350.
Thank You!

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Question 75985: Help I am confused
Approximately 25% of the population belongs to a health maintenance organization (HMO). Assume that for a randomly selected group of 20 adults, the number belonging to an HMO has a binomial distribution.

7. The probability of finding exactly 5 in the 20 who belong to an HMO is:
a. 0.2023
b. 0.1567
c. 0.1750
d. 0.2345

The probability of finding at least one in the 20 who belongs to an HMO is:
a. 0.7500
b. 0.8012
c. 0.9056
d. 0.9968

Thank You

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Question 75984: Help please...
A recent election return indicated that 55% voted for a proposal, 40% voted against it, and 5% abstained. What is the probability that a voter either abstained or voted against the proposal?
a. 5%
b. 40%
c. 45%
d. 55%
Thank You!

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Question 75987: James Johnson, manager of quality control at Creative Auto Corp., just received a report from the assembly plant. The latest shipment of 200 lug bolts used to attach the wheels showed a mean diameter of 18.01 mm and a median of 17.92 mm. Therefore, James can conclude that the distribution of the diameters of the lug bolts
a. is perfectly symmetric.
b. is skewed left.
c. is skewed right.
d. has a range of 0.09 mm.
Thank You

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Question 76076: an someone help me show step by step the correct ansers to these questions i did incorrectly on my test Thankyou. It will be greatly appreciated. Step by Step answers Thankyou
1. The mean height of women in the U.S.(ages 20-29) is 64. inches and the standard deviation is 2.75 inches. If a women is selected at random, what is the probability that she will have a height between 61.23 and 65.99 inches?
Show standard normal graph and label z-scores.
b. If 8 women are selected at random what is the probability that they will have a mean height of between 65. and 66.56 inches? Show graph.


2. Assume each student chooses exactly 1 major.
27.70% Education, 11.11%english, 6.37%Math, 54.81%ISM.
A. If 8 students are randomly selected, what is the probability that exactly 6 of them will NOT be ISM majors?
B. If 8 students are randomly selected, what is the probability that exactly 7 of them will be ISM or English majors?

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Question 76117: Given: X = 100
The St Dev (sigma sign) is = 7
What is the probability that an item will be below 91 P(X < 91)
What is the probability that an item will be above 111 P(X > 111)
The probability that an item will be between 90 and 100 P(90 < X < 100)

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Question 75809: Question 1
Consider the following results from a survey of small businesses:
SECTOR
Retail Manufact. Financial Services
Mean number of Employees 4.1 11.7 7.2
Standard deviation 3.3 3.9 3.7
No. of businesses with cash flow problems 17 32 11
No. with no cash flow problems 13 18 9
Total number in sample 30 50 20
In connection with the above data, answer the following questions:
(a) Does the proportion of businesses having cash flow problems vary from one sector to another?
(b) Is there a significant difference between the average number of employees in the retail and manufacturing sectors?
(c) Given that it is quite a small sample, what would you expect the average number of employees over all small businesses in the manufacturing sector to be?
(d) In a survey of retail businesses done last year, about 50% admitted to having cash flow problems. Has this proportion increased significantly?

NOTE : DO NOT USE A T- CALCULATOR . SHOW ALL YOUR MANUAL WORKINGS .

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Question 76181: From a class of girls and boys, the probability that one student chosen at random will be a girl is 1/3. If four boys leave the class, the probability that a student chosen at random will be a girl is 2/5. How many boys and girls are there in the class before the four boys leave?
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Question 76132: 300 pennies are tossed into the air. Determine the probability of:
1) P(125 is less than or = X less than or = 170 tails)
2) If your co worker is willing to wager 10.00 on this, should I take the wager and why?

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Question 76131: Trudy Jones recently completed her certification examination and learned that her z-score was –2.5. The examining board also informed her that a failure to pass would be all scores that were 1 or more standard deviations below the mean and that those with scores higher than 2 standard deviations above the mean would receive a special commendation award. Trudy can, therefore, conclude that she
a. failed the exam.
b. passed the exam.
c. passed the exam and will receive a special commendation award.
d. passed the exam, but no commendation award is forthcoming.
Thank You

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Question 76130: The standard normal table shows an area value of 0.1 for a z-score of 0.25 and an area value of 0.35 for a z-score of 1.04. What percentage of the observations of a random variable that is normally distributed will fall between 0.25 standard deviations below the mean and 1.04 standard deviations above the mean?
a. 25%
b. 35%
c. 45%
d. 55%
Thank You!

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Question 76183: How do I work:

x^2-1/x / x+1/3

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Question 76129: At the start of the 1999 NCAA men’s basketball tournament, 64 teams were invited to compete for the national championship. Below is the number of victories that a sample of 26 of these teams had obtained during the regular season:
32 12 28 22 20 25 22 20 22 22 19 19 26
19 21 23 27 21 21 22 23 27 22 24 26 23
1. What is the sample mean number of regular season victories?
a. 9.0
b. 12.1
c. 22.6
d. 23.6

What is the sample median number of regular season victories?
a. 20
b. 21
c. 22
d. 23

What is the sample standard deviation of regular season victories?
a. 0.80
b. 3.81
c. 16.67
d. 22.12

Thank You!

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Question 76064: Can someone help solve the questions that i screwed up on, on my last test. please show step by step procedure to solving these problems. ThankYou Please Help.

1. If the mean height of a women in the U.S.(20-29) is 64.0 and the standard deviation is 2.8.... What is the height that seperates the bottom 20% of women from the top 80% of women? (show standard normal graph with z-scores).
2. A random sample of 41 men were measured in height. If the mean height was 69.6 with a standard deviation of 2.426 find the 99% confidence interval for the population mean. Assume that the population standard deviation is unknown. Also assume the heights are approximately normally distributed. Round off your final answer to 2 decimal places.
3. Suppose a probability experiment consists of tossing a fair coin 200 times. Assume that heads or tails are equally likely to occur on any 1 toss. What is the probablity that the number of tails is at least 96. Round your final answer to 3 significant digits. Sketch the standard normal graph.
4. A book of 350 pages contains 525 random misprint error(s). What is the probability of exactly 2 error(s) on a randomly selected page? (Round probability to 3 decimal places. Round the meaan=((#errors)+(#pages)) to the nearest thousandth.)
b. What is the probability of no more than 3 error(s) on any one page?

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Question 76806: How many different 6-player starting squads can be formed from a volleyball team of 11 players?
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Question 76806: How many different 6-player starting squads can be formed from a volleyball team of 11 players?
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Question 76804: Yow are required to solve any five of the six problems on an algebra quiz. How many different selections are possible?

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Question 76805: How many different 5-card hands can be dealt from a standard deck of 52 cards?
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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