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

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

Question 356933: A box contains eleven balls, numbered 1,2,3�.10,11,11. if 6 balls are drawn simultaneously at random, what is the probability that the sum of the numbers on the balls drawn is odd?
Click here to see answer by robertb(5830)

Question 356934: If the 3 digit positive integer n = ABC = AB + BA + AC + CA + BC + CB, compute the largest possible value for n. (Note: A, B, C are single digits from 0 to 9)
Click here to see answer by robertb(5830)

Question 356914: A jar contains 10 black marbles and 40 white marbles.
a. If you randomly select a marble from the jar, what is the probability that you will get a white marble?
b. If you are selecting a random sample of n = 3 marbles, and the first 2 marbles are both white, what is the probability that the third marble will be black?
Click here to see answer by edjones(8007)

Question 356899: When playing a game of cardwars with a friend, what are the odds that I play nine hands in a row without winning?
If you're not sure what cardwars are, it is a very simple game that involves 2 players drawing cards from a deck. If I draw a higher card I win, if I draw a lower card I lose. For this scenario, let's also assume that if 2 equal cards are drawn (ex: 2 Kings are drawn by him and me both) I lose as well. The only way I win is if I draw a higher card than my opponent.
So, what are the odds that I lose 9 hands in a row (I draw a lower or equal card nine straight times).
Thanks in advance for your help as I can not solve this problem on my own.
Click here to see answer by edjones(8007)

Question 357045: Vacation Sites A U.S. Travel Data Center's survey of 1500 adults found that 42% of respondents stated that they favor historical sites as vacations. Find the 95% confidence interval of the true proportion of all adults who favor visiting historical sites as vacations
Click here to see answer by stanbon(75887)

Question 357070: a box contains 17 large and 16 small marbles
each marble is either green or white
6 large marbles are green, 8 small marbles are white
if a marble is selected from the box what is the probability that it is large or green
Click here to see answer by stanbon(75887)

Question 357080: How do you know what formula to use for probability?
For example for the problem:
A Company had manufactures a batch of 400 backup power supply units for computers, 8 of them are defective. If 3 of the units are randomly selected for testing, what is the probability that the entire batch will be accepted?
What formula would i use to solve this? Thank you!
Click here to see answer by edjones(8007)

Question 357090: Following are the American College Test (ACT) scores attained by the 25 members of a local high school graduating class.
21 24 23 17 31 19 19 20 19 25 17 23 16
21 20 28 25 25 21 14 19 17 18 28 20

Find P5, P10, and P20 for the ACT scores.

Click here to see answer by stanbon(75887)

Question 357066: hey, I am stuck on this question.
A "true or false" test has five questions. construct a tree diagram to list all the possible answers.
is it asking me to use just these four possible outcomes - TFTFT, FTFTF, TTTTT,FFFFF- or am I suppose to try and get 32 possible outcomes for the tree diagram? and if so how do I draw a tree diagram with 32 outcomes?
thanks
Click here to see answer by jim_thompson5910(35256)

Question 357109: In each of the four examples listed below, one of the given variables is independent (x) and one of the given variables is dependent (y). Indicate in each case which variable is independent and which variable is dependent.
I. Cost to ship; Size of package
II. Geographic location; Average annual snowfall
III. Length of ride; Taxi fare
IV. DNA of offspring; DNA of parents

Click here to see answer by neatmath(302)

Question 357138: There are 9 apples in a bag; 5 are red and 4 are yellow. Two apples are selected at random, one after another with replacement, and the color of each is noted. Find the probablity that at least 1 is red?
Click here to see answer by stanbon(75887)

Question 357104: Find the range, standard deviation, and variance for the following sample data:
44, 2, 5, 16, 76, 17, 1, 95, 34, 40, 75, 46, 6, 6, 44, 94
Click here to see answer by Fombitz(32388)

Question 357303: A shipment of pins contains 25 good ones and 2 defective ones. At the receiving
department an inspector picks three pins at random and tests them. If any
defective pin is found among the three that are tested, the shipment would be
rejected. What is the probability that the shipment would be accepted ? To
increase the probability of acceptance to atleast 90%, it is decided to do one of the
following:
1. Add some good pins to the shipment
2. Remove some defective pins in the shipment
For each of the two options, find out exactly how many pins should be added or
removed.
Click here to see answer by edjones(8007)

Question 357342: Your school yearbook has an editor-in-chief and an assistant editor-in-chief. The staff of the yearbook has 15 students. In how many ways can students be chosen for these 2 positions?
Click here to see answer by checkley77(12844)

Question 357343: You must take 6 elective classes to meet your graduation requirements for college. There are 12 classes that you are interested in. In how many ways can you select you elective classes?
Click here to see answer by edjones(8007)

Question 357335: There are 6 artists each presenting 5 works of art in an art contest. The 4 works judged best will be displayed in a local gallery. In how many ways can these 4 works all be chosen from the same artist's collection?
Click here to see answer by edjones(8007)

Question 357376: The find the probability of the event. Drawing three queens in a row from a standard deck of cards when the drawn card is not returned to the deck each time?
Click here to see answer by edjones(8007)

Question 357338: An amusement park has 20 different rides. You want to ride at least 15 of them. How many different combinations are there to consider?
Click here to see answer by edjones(8007)

Question 357419: Here are the probabilities of the most popular colors for vehicles made in North America: Silver:.210, White: .156, Black: .112, Blue: .112, Red: .099, Green: .076, Other?
What is the probability that a randomly selected is the "Other" color?
A. 0.765
B. 0.235
C. Impossible to tell.
D. 0.221
Click here to see answer by edjones(8007)

Question 357436: Which of the following is not a valid probability value?
A. 0
B. 11/13
C. 0.57
D. 4/3
Click here to see answer by ewatrrr(24785)

Question 357438: The table below provides information about the students in an accounting class:
Male Female Total
Junior 11 18 29
Senior 8 6 14
Other 5 3 8
Total 24 27 51
If a student is selected at random from the class, what is the probability that the student is a senior male?
A. 8/51
B. 8/24
C. 8/14
D. 8/100
Click here to see answer by ewatrrr(24785)

Question 357481: The table below provides information about the students in an accounting class:
Male Female Total
Junior 11 18 29
Senior 8 6 14
Other 5 3 8
Total 24 27 51

If a student is selected at random from the class, what is the probability that the student is a senior given that the student is a female?
A. 6/51
B. 6/27
C. 6/14
D. 41/45
Click here to see answer by jim_thompson5910(35256)

Question 357550: How do you solve this question? The IQ scores of a distribution is subject to the normal distribution with the mean X=105 and standard deviation s= 15. What is the percentage (likelihood) that an IQ score is lower than 135?
Click here to see answer by stanbon(75887)

Question 357708: A recent study published in the Toronto Globe and Mail reveals that 25% of
mathematics degrees from Canadian universities and colleges are awarded to women.
If five recent graduates from Canadian universities and colleges are selected at
random, what is the probability that
a. At least one would be a woman.
b. None of them would be a woman.
Click here to see answer by robertb(5830)

Question 357731: As reported in Runner�s World magazine, the times of the finishers in the New York City 10K Run are normally distributed with a mean of 61.2 minutes and a standard deviation of 9.3 minutes.
a. A runner is selected at random. Find the probability that the runner�s finishing time was more than 75 minutes.

b. A runner is selected at random. Find the probability that the runner�s finishing time was between 60 and 63 minutes

c. Runners whose finishing times are in the top 5% are automatically invited to participate in next year�s race. What finishing time separates the top 5% from the others? Round answer to 1 decimal place.

Click here to see answer by stanbon(75887)

Question 357800: A die is cast repeatedly until a 6 falls uppermost. Let the random variable X denote the number of times the die is cast. What are the values that X may assume?
a){1, 2, 3, 4, 5, 6}
b) {0, 1, 2, 3,...}
c) {1, 2, 3,...}
d) {1, 2, 3,...150}
e) {0, 1, 2, 3,...150}
Click here to see answer by Fombitz(32388)

Question 357852: STATISTIC QUESTION:CONSIDERED A BINOMIAL RANDOM VARIABLE WHERE THENUMBER OF TRIALS IS 12 AND THE PROBABILITY OF SUCCESS ON EACH TRIAL IS 0.25 . FIND THE MEAN AND STANDARD DEVIATION OF THE RANDOM VARIABLE.
2.iF I GO INTO AN ICREAM PARLOR ,AND I HAVE THE CHOICE OF HAVING ONE OF 10 DIFFRENT FLAVORS , WITH ONE OF 5 TOPINGS AND ONE OF 3 DIFFRENT TYPES OF CONES, HOW MANY TIMES CAN I COME BACK TO THIS PLACE AND GET A DIFFRENT ICE CREAM CONE COMBINATION?
3THERE ARE 10 COLORED BALLS IN A BOX(5RED,3BLUE,2GREEN). WHAT IS THE PROBABILITY OF PICKING OUT THE RED BALL THEN A BLUE BALL (IF I DONOT REPLACE THE RED BALL)?
PLEASE I'M IN DESPREATE NEED OF HELP . THANK YOU IN ADVANCED.
Click here to see answer by ewatrrr(24785)

Question 357696: Find the probability of getting at least three defective items in a batch of ten items if the overall percentage of defects is 40%
Click here to see answer by Fombitz(32388)

Question 357893: You are given the following data. Number of Absences
Final
Grade

0
91

1
89

2
84

3
76

4
67

5
49

- Find the correlation coefficient for the data.
- Find the equation for the regression line for the data, and predict the final grade of a student who misses 3.5 days.
Click here to see answer by Fombitz(32388)

Question 357946: 3. Cans of regular Coke are labeled as containing 12.00 oz. Assume that the actual contents are normally distributed with a mean of 12.19 oz and a standard deviation of 0.11 oz.
a. What percentage of cans contain less than 12.10 oz ?

b. What amount of Coke separates the top 10% of the cans from the others?

c. To save some of the Coke in cans that are filled too much, the quality-control manager is instituting a plan to remove some of the Coke from cans that are in
the top 2%. What is the minimum amount of Coke in such cans that will be �reworked�?

d. What is the maximum amount of Coke in the cans that are in the bottom 15% ?

Click here to see answer by stanbon(75887)

Question 357977: Suppose you have 8 pairs of shoes and they are all mixed up in your closet. If you randomly pick two shoes in the dark, what is the probability that they are the same pair of shoes? Note: Since you are choosing them randomly, you simply reach down in the dark and pick two shoes without feeling around for the same style or shape.

Click here to see answer by sudhanshu_kmr(1152)

Question 357981: The probability that a student is late for statistics class is .2. There are 30 classes during the semster.
A. Find the probability that the student will be late exactly 5 times.

B. Find the probability that he will be late fewer than 3 times.
C. Find the average number of times he will be late.
D. Find the standard deviation of the number of times he will be late.
Click here to see answer by ewatrrr(24785)

Question 357978: n one version of the game Keno, the house has a pot containing 80 balls, numbered 1 through 80. A player buys a ticket for $1 and marks one number on it (from 1 through 80). The house then selects 20 of the 80 numbers at random. If the number selected by the player is among the 20 selected by the house (the management), the player is paid $3.20. Find the expected net winnings for this game.

Click here to see answer by solver91311(24713)

Question 358041: When a polling firm places 5 calls and the probability that a call reaches a live person is .2, what is the probability that none of the calls reach a live person?
Click here to see answer by Fombitz(32388)

Question 358096: There are 14 students in a class that has just completed an exam. The exam grades ranged from 55 to 100. If you choose 3 students from the class, what is the probability that the sum of their exam scores is less than 100?
Click here to see answer by solver91311(24713)

Question 358105: If the mean and standard deviation of serum iron values for healthy men are 116 and 14 micrograms per 100 mL, respectively, find the probability that a random sample of 58 healthy men will yield a mean of at most 120 micrograms per 100 mL.

I know that N = 58...I think...and I don't know if this makes sense but is 14/sqrt(58) on the right track?
If you could please help, that would be extremely appreciated, I am just completely lost! THANK YOU SO MUCH!
Click here to see answer by jrfrunner(365)

Question 358146: A special investigation is conducted to study the blood pressure of people with glaucoma. In the study, 21 people with glaucoma are recruited with a mean systolic blood pressure of 140 mm Hg and a standard deviation of 25 mm Hg. Construct a 95% confidence interval for the mean systolic blood pressure among people with glaucoma.
Since the work I did is so extensive I'll just tell you what I got...
the formula I used, with the numbers plugged in, was:
140 + or - (1.725)(25/sqrt(21)) and I got the interval of 130.59, 149.41...If this is correct please let me know!
THANK YOU!!
Click here to see answer by jrfrunner(365)

Question 358173: Using the digits 0,1,2,3,4 and 5, how many 5 digit odd numbers are possible if repetition is no allowed?
Click here to see answer by Edwin McCravy(20054)

Question 296751: the marketing department of a nationally known cereal maker plans to conduct a national survey to find out whether or not consumers of flake cereals can distinguish one of their favorite flake cereals. To test the questionnaire and procedure to be used, eight persons were asked to cooperate in an experiment. Five very small bowls of lake cereals were placed in front of a person. The bowls were labeled a, b, c, d, and e. the person was informed that only one bowl contained his or her favorite flake cereal. Suppose that the eight persons in the experiment were unable to identify their favorite cereal and just guessed which bowl it was in. what is the probability that one of the eight guessed correctly?

Click here to see answer by missashf(1)

Question 358279: A recent study reports that 2.5% of elementary children are allergic to peanuts. A random sample of 200 elementary school children is collected to test this.

Compute the probability that proportion of children in the sample of 200 who are allergic to peanuts is 3% or less. ( < .03).
Click here to see answer by stanbon(75887)

Question 358274: The marketing department of a nationally known cereal maker plans to conduct a national survey to find out whether or not consumers of flake cereals can distinguish one of their favorite flake cereals. To test the questionnaire and procedure to be used, eight persons were asked to cooperate in an experiment. Five very small bowls of flake cereals were placed in front of a person. The bowls were labeled A, B, C, D and E. The person was informed that only one bowl contained his or her favorite flake cereal. Suppose that the eight persons in the experiment were unable to identify their favorite cereal and just guessed which bowl it was in. What is the probability that none of the eight guessed correctly?

Click here to see answer by Edwin McCravy(20054)

Question 358276: The fuel economy of a particular car model is normally distributed with a mean of 25 mpg and a standard deviation of 1.25 mpg. A random sample of 10 cars is selected.

Compute the standard error, standard deviation of the mean , for the sample of 10 cars.
Click here to see answer by stanbon(75887)

Question 358400: A bag contains 5 red marbles, 6 green marbles, and 9 blue marbles. Suppose 3 marbles are chosen without replacement. What is the probability of choosing a red, a blue, and a red in that order?:
Click here to see answer by robertb(5830)

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, 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