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Question 1182292: f(x)=3-2x
find the domain of f(x). Hint: you may want to use a calculator!
Click here to see answer by ikleyn(52776)

Question 1182255: Patsy Wong owns two computer service shops. This year the telephone bill for her Summit shop was $580 less than twice the telephone bill for her Norton shop. The total telephone expense for both shops was $2060. What was the cost of each shop's telephone service for the year?
Click here to see answer by josgarithmetic(39616)

Question 1182328: Show that
2
7
sin4 2𝜃 sin4 𝜃 = cos 12𝜃 − 4 cos 10𝜃 + 2 cos 8𝜃 + 12 cos 6𝜃 − 17 cos 4𝜃 − 8 cos 2𝜃 + 14
Sum the series
sin 𝜃 sin 2𝜃 + sin 2𝜃 sin 3𝜃 + sin 3𝜃 sin 4𝜃 + ⋯ upto n terms, 𝑛 ∈ ℕ
Solve the equation
(𝑧 + 1)
7 = 𝑧
7
[cos 7𝛼 + 𝑖 sin 7𝛼] .
Click here to see answer by ikleyn(52776)

Question 1182334: Consider the vector space ℝ3
and its subset 𝑆
𝑆 = {(𝑎, 𝑏, 𝑐) ∶ 3𝑎 − 4𝑏 + 𝑐 = 0, 𝑎 + 2𝑏 − 𝑐 = 0, 𝑎, 𝑏, 𝑐 ∈ ℝ}
Show that 𝑆 is a subset of ℝ3
and also find dim 𝑆 .
Determine whether or not the vectors (1, −3,2), (2,4,1) and (1,1,1) form a basis of ℝ3
Are the following sets linearly independent or linearly dependent?
𝐴 = {(3 − 𝑖, 2 + 2𝑖, 4), (2,2 + 4𝑖, 3), (1 − 𝑖, −2𝑖, 1)} ; 𝐵 = {(1,2,3), (1,3,2), (3,7,8)}
Click here to see answer by ikleyn(52776)

Question 1182333: Solve the system of equations:
3𝑥 + 4𝑦 − 6𝑧 + 𝑤 = 7
𝑥 − 2𝑦 + 3𝑧 − 2𝑤 = −1
𝑥 − 3𝑦 + 4𝑧 − 𝑤 = −2
5𝑥 − 𝑦 + 𝑧 − 2𝑤 = 4
Find the rank of the matrix
𝐴 = (
−2 −1 −3 −1
1 2 3 −1
1 0 1 1
0 1 1 −1
)
Verify that the matrix 𝐵 satisfies its own characteristic equation and hence find its inverse
𝐵 = (
12 −1 4
−1 12 −1
4 −1 12
)
Click here to see answer by ikleyn(52776)

Question 1182332: . Find the multiplicative inverses of the given elements if they exist:
[11]16 𝑖𝑛 ℤ16 𝑎𝑛𝑑 [38]83 𝑖𝑛 ℤ83 .
Let 𝑎 be a fixed element of a group 𝐺 and let
𝑁(𝑡) = {𝑥 ∈ 𝐺 ∶ 𝑥𝑡 = 𝑡𝑥}.
Show that 𝑁(𝑡) is a subgroup of 𝐺.
Find the order and inverse of the permutation
(
1 2 3
2 5 4
4 5 6
3 6 1
)
Click here to see answer by ikleyn(52776)

Question 1182331: In permutation group 𝑆6, if 𝛼 = (2 3 4) and 𝛽 = (2 5 6), then find a permutation 𝜙 such that
𝜙𝛼𝜙
−1 = 𝛽.
Let 𝑎 be a fixed element of a ring R, and let
𝐼𝑠 = {𝑥 ∈ 𝑅 ∶ 𝑠𝑥 = 0}.
Show that 𝐼𝑠
is a subring of 𝑅.
Show that ℤ8 = {0,1,2,3,4,5,6,7,8} is a commutative ring w.r.t. addition modulo 8 and
multiplication modulo 8.
Click here to see answer by ikleyn(52776)

Question 1182330: Show that
2
7
sin4 2𝜃 sin4 𝜃 = cos 12𝜃 − 4 cos 10𝜃 + 2 cos 8𝜃 + 12 cos 6𝜃 − 17 cos 4𝜃 − 8 cos 2𝜃 + 14
Sum the series
sin 𝜃 sin 2𝜃 + sin 2𝜃 sin 3𝜃 + sin 3𝜃 sin 4𝜃 + ⋯ upto n terms, 𝑛 ∈ ℕ
Solve the equation
(𝑧 + 1)
7 = 𝑧
7
[cos 7𝛼 + 𝑖 sin 7𝛼] .
Click here to see answer by ikleyn(52776)

Question 1182329: Find the multiplicative inverses of the given elements if they exist:
[11]16 𝑖𝑛 ℤ16 𝑎𝑛𝑑 [38]83 𝑖𝑛 ℤ83 .
Let 𝑎 be a fixed element of a group 𝐺 and let
𝑁(𝑡) = {𝑥 ∈ 𝐺 ∶ 𝑥𝑡 = 𝑡𝑥}.
Show that 𝑁(𝑡) is a subgroup of 𝐺.
Find the order and inverse of the permutation
(
1 2 3
2 5 4
4 5 6
3 6 1
) .
Click here to see answer by ikleyn(52776)

Question 1182356: (a) Sketch the line with slope
5
4
that passes through the point
(−3, 2).
b) Find an equation for this line.
Click here to see answer by MathLover1(20849)

Question 1182355: The given equation involves a power of the variable. Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
(x − 1)2 = 6
Click here to see answer by MathLover1(20849)

Question 1182353: Find an equation of the line that satisfies the given conditions.
Through
(−7, 2);
slope undefined
Click here to see answer by ikleyn(52776)

Question 1182354: Find the slope of the line through P and Q.
P(−9, 1), Q(7, −4)
Click here to see answer by ikleyn(52776)

Question 1182300: Using the fact that lim x-->0 (sinx/x)=1 to find lim x-->0 ((1-cosx)/xsinx)) .
Click here to see answer by Edwin McCravy(20054)

Question 1182391: Solve the equation for the indicated variable. (Enter your answers as a comma-separated list.)
PV = nRT;
for n
Click here to see answer by josgarithmetic(39616)

Question 1182390: Solve the equation for the indicated variable. (Enter your answers as a comma-separated list.)
wd = rTH; for H
Click here to see answer by josgarithmetic(39616)

Question 1182397: (a) Sketch the line with slope
5
4
that passes through the point
(−3, 2).
Click here to see answer by Alan3354(69443)

Question 1182445: Give complete computation/solutions and 6 steps in solving.
1.A firm that manufactures tires
2. A cigarette manufacturer claims that
3. A manufacturer packs sugar
Click here to see answer by ikleyn(52776)

Question 1182250: Tasha Spellman owns two small appliance parts shops. This year the telephone bill for her Hesperia shop was $630 less than twice the telephone bill for her Diamond Springs shop. The total telephone expense for both shops was $1989. What was the cost of each shop's telephone service for the year?
Click here to see answer by Solver92311(821)

Question 1181790: ou deposit P200 in an account earning 5% compound interest for 3 years. Find the future value and the interest earned for each of the following compounding frequencies. Use the Bankers' Rule for daily compounding.

Frequency Future Value Interest Earned
Annually:
Semiannually:
Quarterly:
Monthly:
Daily:
Click here to see answer by Boreal(15235)

Question 1182522: It is estimated that the annual cost of driving a certain new car is given by the formula
C = 0.35m + 2700
where m represents the number of miles driven per year and C is the cost in dollars. Jane has purchased such a car and decides to budget between $6900 and $8300 for next year's driving costs. What is the corresponding range of miles that she can drive her new car?
Jane can drive a minimum of
miles and a maximum of miles

Click here to see answer by josgarithmetic(39616)

Question 1182531: The ratio of Geoff’s allowance to Ken’s allowance is 7:11. If Ken gives Geoff $84, they will have the same amount of money. How much do they have altogether?

Click here to see answer by ikleyn(52776)

Question 1182623: please help me solve
3/2+x=2
Click here to see answer by MathLover1(20849)

Question 1182622: please help me solve

5x+y=2
Click here to see answer by MathLover1(20849)

Question 1182622: please help me solve

5x+y=2
Click here to see answer by ikleyn(52776)

Question 1182622: please help me solve

5x+y=2
Click here to see answer by greenestamps(13198)

Question 1182634: A recommendation for wheelchair ramps is that the rise-to-run ratio be no greater than 1:12. This ensures that the ramps are navigable by people in wheelchairs. If a business needs to install a concrete ramp to the entrance of their building, which is 12 inches off the ground, how long should the ramp be and how far out horizontally on the ground will it protrude from the building? Give answers in feet and inches, such as 5 feet, 4 inches. What percent grade is the ramp?
Click here to see answer by ikleyn(52776)

Question 1182668: In one class students play basketball, students play soccer and students play volleyball. students play soccer and volleyball, students play basketball and volleyball and students play basketball and soccer. students play all three sports. How many students is in the class if every student plays at least one sport?

Click here to see answer by greenestamps(13198)

Question 1182759: The function y = ax^3 + bx^2 + cx + d has a maximum turning point at (−2, 27) and a minimum turning point at (1, 0).
Find the values of a, b, c and d.
Click here to see answer by Solver92311(821)

Question 1182780: Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?

Click here to see answer by greenestamps(13198)

Question 1182790: a) Write a quadratic equation that can be solved by factoring and does not require the use of the quadratic formula.

b) Write a quadratic equation that cannot be solved by factoring and then solve it using the quadratic formula.
Click here to see answer by josgarithmetic(39616)

Question 1182789: For each formula, solve for the variable specified.
a) D = RT for T.

b) A = P + Prt for r.

c) S = 4r2 for r.
Click here to see answer by josgarithmetic(39616)

Question 1182788: For each problem, use meaningful variables to write a linear function to model the situation. Then interpret the slope and y-intercept in words. Identify which variable would be on the horizontal axis and which one would be on the vertical axis.
a) Model the cost if you buy an iPod for $200 and download songs for $1.29 each.

b) Model the weekly salary a salesman earns if his salary is a combination of his base salary and commissions on his sales. His base weekly salary is $500 and he makes $50 for each sale.
Click here to see answer by Theo(13342)

Question 1182829: One month Amanda rented 2 movies and 5 video games for a total of $33 . The next month she rented 8 movies and 3 video games for a total of $30 . Find the rental cost for each movie and each video game.

Click here to see answer by josgarithmetic(39616)

Question 1182934: a) Do all lines have a y-intercept? Why or why not?

b) What kinds of lines are not functions?

Click here to see answer by josgarithmetic(39616)

Question 1182935: Assuming that the data in the following table follows a linear pattern, complete the table and write the equation of the line that passes through the points.
X -1 0 1 2 3 4
Y -26 -8

Click here to see answer by josgarithmetic(39616)

Question 1182936: Complete each table assuming the type of change indicated. Then use the table to write the function.
a) Linear Change
X Y
-3 12
-2
-1 3
0
1
2
b) Exponential Change
X Y
-3 12
-2
-1 3
0
1
2

Click here to see answer by josgarithmetic(39616)

Question 1182928: Imagine that the price per gallon of gas with a $7 car wash is $3.19 and the price without the car wash is $3.39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?
Click here to see answer by Theo(13342)

Question 1182948: please help me solve
given that log 10 2x- log 10 (x-4)=1
find the value of x
Click here to see answer by robertb(5830)

Question 1182950: please help me solve

Click here to see answer by mananth(16946)

Question 1182950: please help me solve

Click here to see answer by ikleyn(52776)

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