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

Algebra ->  Probability-and-statistics -> Questions on Algebra: Probability and statistics answered by real tutors!      Log On


   



Tutors Answer Your Questions about Probability-and-statistics (FREE)


Question 108299: You roll a red number cube and a blue number cube. Find each probability. P(red and blue equal)
Click here to see answer by wgunther(43) About Me 

Question 108360: Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n=73 p=.7
Find the mean of the binomial distribution
mean=?

Click here to see answer by stanbon(75887) About Me 

Question 108363: Thirteen percent of people are left handed. You randomly select 8 persons and ask them if they are left-handed. Find the probability that (a) exactly 1 person are left handed (b) at least 1 persons are left handed, and (C) less than 1 are left handed.
Click here to see answer by stanbon(75887) About Me 

Question 108365: Suppose that twenty-eight percent of women consider themselves hockey fans. You randomly select 9 of the population and ask each if they are hockey fans. Construct a binomial distribution and use the distribution to find the mean, variance, and standard deviation of the binomial distribution.
Click here to see answer by stanbon(75887) About Me 

Question 108364: Suppose that 68% of married couples paid for their honeymoon themselves. You randomly select 6 couples and ask each if they paid for their honeymoon themselves. Find the probability that the number of couples who say they paid for their honeymoon themselves (A) exactly 4 couples, (B) more than 4 couples, and (C) at most 4 couples.
Click here to see answer by stanbon(75887) About Me 

Question 108362: You are taking a multiple-choice quiz that consists of 3 questions. Each question has 4 possible answers, only one of which is correct. To complete the quiz, you randomly guess the answer to each question. Find the probability of guessing (A) exactly 2 answers correctly, (B) at least 2 answers correctly, or (C) less than 2 answers correctly.
Click here to see answer by stanbon(75887) About Me 

Question 108462: On National Public Radio, the Weekend edition program on Sunday, September 7, 1991, the following probability problem was posed: Given a certain number of balls, of which some are blue, pick 5 at random. The probability that 5 are blue is 1/2. Determine the original number of balls and decide how many are blue.
Click here to see answer by checkley71(8403) About Me 

Question 108475: I am doing permutation problems using the formula nPr = n!/(n-r)!. The problem I am having difficulty with is 6Pn = 30. I can get it this far:
6! / (6-X)! = 30
6! / 30 = (6-X)!
24 = (6-X)! Then I can't figure out how to get X. Please help. Thanks.

Click here to see answer by stanbon(75887) About Me 

Question 108469: I am doing permutation problems using the formula nPr = n!/(n-r)!. The problem I am having difficulty with is nP3 = 24. I can get it this far:
n(n-1)(n-2)...2x1 / (n-3)(n-4)...2x1 = 24
n(n-1)(n-2) = 24 Then I'm not sure how to finish. Please help.

Click here to see answer by stanbon(75887) About Me 

Question 108467: Hi, can you help me with this question as i've been figuring out for long and still could not get the answer:
In the coming school holiday,the probability for Dave to visit his brother in Ireland is 3/5 and the probability of him going on island vacation is 2/3. Calculate the probability that Dave
a) will not visit his brother nor on an island vacation
b) will only do one activity.
Pls help me, i'm doing my o levels next week thanks

Click here to see answer by stanbon(75887) About Me 

Question 108600: a girl has 24 quarters and dimes. togther they had up to 3.60 how many quarters does she have?
Click here to see answer by elima(1433) About Me 
Question 108600: a girl has 24 quarters and dimes. togther they had up to 3.60 how many quarters does she have?
Click here to see answer by checkley71(8403) About Me 

Question 108786: Please help me with the following question: (It is not in the book, it is on a homework assignment.)
The lifetime of a popular dvd player is guaranteed to be 8 years. If the lives of this dvd players are normally distributed with a mean of 8.75 and a SD of .45 years, find the percentage of the DVD players that will not meet the guarantee.

Click here to see answer by Fombitz(32388) About Me 
Question 108786: Please help me with the following question: (It is not in the book, it is on a homework assignment.)
The lifetime of a popular dvd player is guaranteed to be 8 years. If the lives of this dvd players are normally distributed with a mean of 8.75 and a SD of .45 years, find the percentage of the DVD players that will not meet the guarantee.

Click here to see answer by edjones(8007) About Me 

Question 109439: two runners leave the same point,running in opposite directions .One runneer runs 1 mi/hr faster than the other does.After running for two hours the runneres are 50 miles apart.How fast does each run?
help asap please

Click here to see answer by scott8148(6628) About Me 

Question 109291: HI
THIS IS MY QUESTION THAT I NEED SOLVING
PETER AND LYN ARE CARRYING OUT AN EXPERIMENT TO ESTIMATE THE NUMBER OF DIFFERENT COLOURED BALLS IN A BAG.
*THEY TAKE IT IN TURNS TO DRAW A BALL FROM THE BAG
*THEY NOTE ITS COLOUR AND RECORD IT IN A TABLE
*THEY REPEAT THIS 10 TIMES
*THE BAG CONTAINS 20 BALLS IN TOTAL
HERE ARE THE RESULTS
BLUE 3
GREEN 2
RED 4
YELLOW 1
USE THE RESULTS TO ESTIMATE THE PROBABILITY OF DRAWING EACH COLOUR BALL FROM THE BAG?

Click here to see answer by stanbon(75887) About Me 

Question 108939: Boxes of maraconi are filled by machine and the net weight of a box has a normal distribution with mean 10oz and standard deviation 0.7oz
If 25 boxes are selected at random, what is the probability that the average of their weights is greater tna 10.35oz?

Click here to see answer by stanbon(75887) About Me 

Question 109584: P(A) = 0.30
P(B) = 0.40
P(C) = 0.10
P(AorD) = 0.50
P(A and D ) = 0.04
P(A and C) = 0.03
P(B/A) = 0.60
Determine :
P(AandB)
P(A/B)
P(D)
thank you

Click here to see answer by stanbon(75887) About Me 

Question 108125: The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cose is kep within budget and the campaign will increase sales is what?
Click here to see answer by stanbon(75887) About Me 

Question 109952: The ice cream parlor can make a sundae using any combination of 6 toppings and 4 different types of ice cream, as shown on the menu below.
Types of Ice Cream Sundae Toppings
vanilla hot fudge
chocolate hot caramel
strawberry cookie crumbs
coffee nuts
candy pieces
chocolate sprinkles
A. Anne wants a sundae with 2 different toppings on chocolate ice cream. How many different combinations of toppings for Anne’s sundae are possible? Show your work and explain why you did each step.
B. Will wants a sundae with 3 different toppings on any type of ice cream. How many different sundae combinations are possible? Show your work and explain why you did each step

Click here to see answer by stanbon(75887) About Me 

Question 110477: Coming out of the grocery store, Ebree has has eight coins, none of which is a half-dollar, that add up to $1.45. Unfortunately, on the way home she loses one of them. Which type of coin did she most likely use?
Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 110209: Rashawn bought a CD that cost $18.99 and paid $20.51, including sales tax. what was the rate of sales tax?
Click here to see answer by stanbon(75887) About Me 

Question 110337: Population: {0,1,2}, n=2
Find the
A. mean of the population
B. the SD of the population
C. the sampling distribution of the sample mean
d. the mean of the probability distribution of means
e. the SD of the probability distribution of means
I have tried to work this out several times, but my answers don't match the answers in the back of the book. However, my teacher says that a lot of the answers in the back of the book are wrong, so I really have no idea if I am working these questions out right or not. Please show me how to work this problem so I can have a better understanding of what I am doing. Thanks

Click here to see answer by stanbon(75887) About Me 

Question 111560: I have a problem regarding probability. Here it is...
It is known that 53% of graduating students are boys. Three grads are chosen at random. Given that at least two of the three grads are boys, determine the probability that all three of the grads are boys.
I believe the answer is either 0.14887 or 53%.
Thanks for any help.

Click here to see answer by edjones(8007) About Me 

Question 112034: It is known that 10% of all people are left handed. A sample of 10 students is selected at random. What is the probability that 2 of these 10 students is left handed? Find the probability that none of the students are left handed?
Here are my thought:
The events are mutually exclusive and follow normal distibution. If you have a sample size of ten and take the only left handed person out of the sample on the first selection, then there is zero probability that there are any remaining left handed people. The converse applies the the second part of the question.
So my answers are zero for the probability that two are left handed and zero for the probability that none are left handed.
Thanks for you help.
Cheers
CC

Click here to see answer by Edwin McCravy(20077) About Me 

Question 112078: Use the union rule to answer the question
If n(A)=5, n(B)=11, and n(A\cap B)=3,what is n(A\cup B)?

Click here to see answer by stanbon(75887) About Me 

Question 112267: You have three $1 bills, four $5, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random.Find p($10 then $1)
Click here to see answer by Edwin McCravy(20077) About Me 

Question 112391: Joe's Used Cars sold 50 Cars in 2002. In 2007, they sold 180 cars. Find the average rate of change in cars sold from 2002 to 2007.
- I guessed that this was a proportion. I subtracted the years to get 5, then I crossed multiplied to get an answer of 18. although I am not sure if that is correct.

Click here to see answer by checkley71(8403) About Me 

Question 112901: This is a homework assignment not in the book. Ra226 has a half-life of1600 years. How many grams of Ra226 will be present after 2000 years if there are 20g present initially?
Click here to see answer by scott8148(6628) About Me 

Question 113054: natasha is going to order an ice cream cone with three different toppings. she can choose from the following toppings; crushed nuts; chocolate syrup; stawberry syrup; chocolate chips; M-and-Ms. in how many ways is it possible to make the selection?
Click here to see answer by solver91311(24713) About Me 

Question 113072: eric has 5 dog ands and 7 turtles. he is going to choose 4 dogs and 4 trtles to get groomed. how many ways is it possible to choose the 8 animals?
Click here to see answer by checkley71(8403) About Me 

Question 113193: Two fair dice are rolled. Determine the probability of getting a sum equal to eight.
Click here to see answer by stanbon(75887) About Me 

Question 113190: Consider a fair coin that is tossed 12 times. Determine the number of possible outcomes for this experiment.
Click here to see answer by stanbon(75887) About Me 

Question 113197: Consider an experiment with the following distribution of outcomes
x 1 2 3 4 5 6 7 8
P(x) .105 .285 .024 .082 .142 .251 .041 .060
determine the probability of the outcome of either 1 and 4 occurring
determine the probability of the outcome 6' (not 6) occurring
determine the probability of the outcome of NOT obtaining outcome 3 or 4

Click here to see answer by stanbon(75887) About Me 

Question 113194: In a bag with 100 marbles, 15 have only one red stripe, 26 have only one green stripe, 10 have only one blue stripe, 5 have one blue and one green stripe, 7 have one red and one green stripe. there are many that have no sripes. Determine the probability of randomly selecting a marble from the bag that has exactly one stripe; the probability of selecting one that has exactly two stripes; the probability of selcting one that has no stripes; and one with at least one red stripe.
Click here to see answer by solver91311(24713) About Me 

Question 113276: In a group of 100 students, 30 are HIstory majors, 6 of the History majors have a dual major in Business, in addition there are 45 Business majors, and there are 25 Engineering majors (none of which have dual majors and no student has a triple major. Many students have not declared a major. Determine the probability that a a student selected at random is either a business or engineering major.
***I am confused because I have a total of 100 students and some how I am coming up with a 51% probability that a random student selected is eiher business or engineering; however, I am not taking into consideration those who are NOT declared majors. How far off am I?

Click here to see answer by solver91311(24713) About Me 

Question 113279: THere are 10 pictures available to place on exhibit in a museum. How many arrangements (permutations) are possible if 7 pictures are selected at a time?
Click here to see answer by SHUgrad05(58) About Me 

Question 113277: Given a fair coin tossed 3 times. List the possible outcomes for this experiement. Determine the probability of obtaining at least two heads.
***my solution....
(tt, th, ht, hh) 1/4
(tt, th, ht, hh) 1/4
(tt, th, ht, hh) 1/4
_______________________
3/4

Click here to see answer by stanbon(75887) About Me 

Question 112895: I am having a rough time solving my problems on probability and standard deviation. One problem in particular, Mean is 12.29 and standard deviation is .09. The problem asks for the percentage of cans that contain less than 12 ounces. I'm really not sure even where to start with this one. Please help.
Shanen

Click here to see answer by stanbon(75887) About Me 

Question 114133: One colored chip-red,blue, or green- is selected ar random, and a die is rolled. Use the counting prnciple to determine the number of sample points in the sample space.
Click here to see answer by stanbon(75887) About Me 

Question 112276: On mornings when shool is in session in January, Sara notices that her school bus is late one-thrid of the time. What is the probability that during a 5-day school week in January her bus will be late at least three times?
Click here to see answer by stanbon(75887) About Me 

Question 114296: Draw and label a diagram for problem 1.Write answers as complete sentences
1. A rain gutter is made from sheets of aluminum that are 20 inches wide by turning up the edges to form right angles. A) Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow. B) What is the maximum cross-sectional area?

Click here to see answer by solver91311(24713) About Me 

Question 114284: Please help
Apply the Law of Large Numbers
1. Using a coin toss and fictitious data, explain how the following scenario is possible: As the number of trials increases, the differences between the number of actual and expected successes tends to grow, but the difference between the percentage of actual and expected successes tends to decrease.
2. Explain your answer to the following question: Is it true that if I flip a coin 1,000 times I will get heads 500 times?
3. Explain your answer to the following question: Is it true that if I get tails 3 times in a row that my chances of getting heads on my next toss is greater than 50%?

Click here to see answer by heidi(17) About Me 

Question 114309: 3. A piece of cardboard measuring 10 inches by 15 inches is to be made into a box with an open top by cutting equal-sized squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches.
a) Draw a diagram



b) What are the restrictions on x?
c) Determine a function V that gives the volume of the box.

d) Draw a graph the function and find the value of x that produces the maximum volume. What is the maximum volume of the box?




e) When will the volume of the box be greater than 80 cu inches?

Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 114579: A fruit bowl has 7 apples and 4 oranges. If one piece of fruit is selected at random and then a second piece of fruit is selected ar random, what are the chances that both pieces of fruit will be apples (this is without replacement)?
Click here to see answer by checkley71(8403) About Me 

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, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580, 41581..41625, 41626..41670, 41671..41715, 41716..41760, 41761..41805, 41806..41850, 41851..41895, 41896..41940, 41941..41985, 41986..42030, 42031..42075, 42076..42120, 42121..42165, 42166..42210, 42211..42255, 42256..42300, 42301..42345, 42346..42390, 42391..42435, 42436..42480, 42481..42525, 42526..42570, 42571..42615, 42616..42660, 42661..42705, 42706..42750, 42751..42795, 42796..42840, 42841..42885, 42886..42930, 42931..42975, 42976..43020, 43021..43065, 43066..43110, 43111..43155, 43156..43200, 43201..43245, 43246..43290, 43291..43335, 43336..43380, 43381..43425, 43426..43470, 43471..43515, 43516..43560, 43561..43605, 43606..43650, 43651..43695, 43696..43740, 43741..43785, 43786..43830, 43831..43875, 43876..43920, 43921..43965, 43966..44010, 44011..44055, 44056..44100, 44101..44145, 44146..44190, 44191..44235, 44236..44280, 44281..44325, 44326..44370, 44371..44415, 44416..44460, 44461..44505, 44506..44550, 44551..44595, 44596..44640, 44641..44685, 44686..44730, 44731..44775, 44776..44820, 44821..44865, 44866..44910, 44911..44955, 44956..45000, 45001..45045, 45046..45090, 45091..45135, 45136..45180, 45181..45225, 45226..45270, 45271..45315, 45316..45360, 45361..45405, 45406..45450, 45451..45495, 45496..45540, 45541..45585, 45586..45630, 45631..45675, 45676..45720, 45721..45765, 45766..45810, 45811..45855, 45856..45900, 45901..45945, 45946..45990, 45991..46035, 46036..46080, 46081..46125, 46126..46170, 46171..46215, 46216..46260, 46261..46305, 46306..46350, 46351..46395, 46396..46440, 46441..46485, 46486..46530, 46531..46575, 46576..46620, 46621..46665, 46666..46710, 46711..46755, 46756..46800, 46801..46845, 46846..46890, 46891..46935, 46936..46980, 46981..47025, 47026..47070, 47071..47115, 47116..47160, 47161..47205, 47206..47250, 47251..47295, 47296..47340, 47341..47385, 47386..47430, 47431..47475, 47476..47520, 47521..47565, 47566..47610, 47611..47655, 47656..47700, 47701..47745, 47746..47790, 47791..47835, 47836..47880, 47881..47925, 47926..47970, 47971..48015, 48016..48060, 48061..48105, 48106..48150, 48151..48195, 48196..48240, 48241..48285, 48286..48330, 48331..48375, 48376..48420, 48421..48465, 48466..48510, 48511..48555, 48556..48600, 48601..48645, 48646..48690, 48691..48735, 48736..48780, 48781..48825, 48826..48870, 48871..48915, 48916..48960, 48961..49005, 49006..49050, 49051..49095, 49096..49140, 49141..49185, 49186..49230, 49231..49275, 49276..49320, 49321..49365, 49366..49410, 49411..49455, 49456..49500, 49501..49545, 49546..49590, 49591..49635, 49636..49680, 49681..49725, 49726..49770, 49771..49815, 49816..49860, 49861..49905, 49906..49950, 49951..49995, 49996..50040, 50041..50085, 50086..50130, 50131..50175, 50176..50220, 50221..50265, 50266..50310, 50311..50355, 50356..50400, 50401..50445, 50446..50490, 50491..50535, 50536..50580, 50581..50625, 50626..50670, 50671..50715, 50716..50760, 50761..50805, 50806..50850, 50851..50895, 50896..50940, 50941..50985, 50986..51030, 51031..51075, 51076..51120, 51121..51165, 51166..51210, 51211..51255, 51256..51300, 51301..51345, 51346..51390, 51391..51435, 51436..51480, 51481..51525