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Let X be the circle with radius 2 centered at the origin (0,0) in the xy-plane. Let f(x,y) = x^2 + y^2.
Compute the cohomology group H^2(X) with coefficients in ℤ/4ℤ. | tiger_lab_math | [
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Consider the graph G with vertices 1, 2, 3, 4, 5 and edges {(1,2),(1,3),(2,4),(3,4),(4,5)}. Determine the automorphism group of G. How many automorphisms does G have? | tiger_lab_math | [
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Let $m$ be the product of all positive integers less than $4!$ which are invertible modulo $4!$. Find the remainder when $m$ is divided by $4!$.
(Here $n!$ denotes $1\times\cdots\times n$ for each positive integer $n$.) Let's write a program. | tiger_lab_math | [
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Harry has 50 books in his library. His sister Flora has twice as many books and their cousin Gary has half the books Harry has. How many books do the three of them own together? Please write a program to solve it | tiger_lab_math | [
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Determine the order of the element 5 in the multiplicative group of integers modulo 14 under multiplication. Answer Choices: (A) 1 (B) 2 (C) 3 (D) 6 | tiger_lab_math | [
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At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours? | tiger_lab_math | [
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Alex and Max are running a race against each other. At the beginning of the race they are even with each other for 200 feet. Then Alex gets ahead of Max by 300 feet. Then Max gets ahead of Alex by 170 feet. Alex gets a burst of speed and gets ahead of Max by 440 feet. If the road they're running on is 5000 feet long, h... | tiger_lab_math | [
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A tap can fill a tank in 10 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
Answer Choices: (A) 5hr 45min (B) 6hr 30min (C) 4hr (D) 3hr 25min (E) 2hr 10min | tiger_lab_math | [
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Jackson works 5 days a week going door-to-door collecting for charity. His goal is to raise $1000 for the week. He earned $300 on Monday and $40 on Tuesday. If he collects an average of $10 for every 4 houses he visits, how many houses will he have to visit on each of the remaining days of the week to meet his goal? | tiger_lab_math | [
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"statement 1": Sachi invested amount of more than 5000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum, "statement 2" :Sachi invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum, "options: " Entailment or contradiction or neutral? Let's program in ... | tiger_lab_math | [
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Before getting to work, Jess has a few errands to run. Jess has to walk 11 blocks to the store and 6 blocks to the gallery, before walking the final 8 blocks to arrive at work. If Jess has already walked 5 blocks, how many more blocks must she walk before arriving at work? Please respond by writing a program in Python. | tiger_lab_math | [
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800 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
Answer Choices: (A) 162 (B) 138 (C) 16 (D) 38 (E) 12 | tiger_lab_math | [
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If you roll one fair six-sided die, what is the probability that the number is even or greater than 3?
Answer Choices: (A) 1/2 (B) 1/3 (C) 2/3 (D) 3/4 (E) 5/6 | tiger_lab_math | [
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A hiker walked for 3 days. She walked 18 miles on the first day, walking 2 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. ... | tiger_lab_math | [
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A bus leaves Burbank at 9:00 a.m. traveling east at 50 miles per hour. At 1:00 p.m. a plane leaves Burbank traveling east at 300 miles per hour. At what time will the plane overtake the bus?
Answer Choices: (A) 12:45 p.m. (B) 1:10 p.m (C) 1:40 p.m (D) 1:48 p.m (E) 1:55 p.m | tiger_lab_math | [
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A retailer bought a hat at wholesale and marked it up 70% to its initial price of $34. By how many more dollars does he need to increase the price to achieve a 100% markup?
Answer Choices: (A) 2 (B) 4 (C) 6 (D) 8 (E) 10 | tiger_lab_math | [
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john bought 9.25 m of cloth for $ 416.25 . find the cost price per metre . Please write a program to solve it | tiger_lab_math | [
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Tim bought a new machine to help him picking apples from apple trees. If this new machine can pick 20 apples every 30 minutes and Tim wants to pick 500 apples today. How many hours he is going to take?
Answer Choices: (A) 10 (B) 12.5 (C) 15 (D) 17.5 (E) 20 | tiger_lab_math | [
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Every time she goes to the store, Felicity gets a lollipop. After she finishes them, she uses the sticks to build a fort. The fort needs 400 sticks to finish it. Her family goes to the store three times a week and she always goes. If the fort is 60% complete, how many weeks has Felicity been collecting lollipops for? | tiger_lab_math | [
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A battery company claims that their batteries have an average lifespan of 120 hours. A sample of 25 batteries was taken and the sample mean was found to be 115 hours with a standard deviation of 10 hours. What is the 95% confidence interval for the average lifespan of the batteries if we assume the lifespan follows a n... | tiger_lab_math | [
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If Mary has 5 apples and John has 3 apples, and you know for sure that they together have at least 6 apples, how many apples could they possibly have together in intuitionistic logic? | tiger_lab_math | [
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A fraction becomes 2/3 when 1 is added to both, its numerator and denominator.
And ,it becomes 1/2 when 1 is subtracted from both the numerator and denominator. Find the fraction.
Answer Choices: (A) 1/2 (B) 3/4 (C) 2/3 (D) 3/5 (E) 2/5 | tiger_lab_math | [
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What will come in place of the x in the following Number series? 612, 207, 72, 27, 12, x
Answer Choices: (A) 6 (B) 7 (C) 8 (D) 9 (E) 10 | tiger_lab_math | [
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Suppose we have a 5x5 grid that we want to fill with the numbers 1 to 5 such that no number is repeated in any row or column. How many different ways can we fill in the grid? | tiger_lab_math | [
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The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 65
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Ph... | tiger_lab_math | [
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Apple Infotech has 4 Senior Managing Directors and 5 Managing Directors. Each investment banking deal requires the guidance of two managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Apple Infotech possibly provide guidance for?
Answer Choices: (A... | tiger_lab_math | [
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Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what time R will the job be finished?
Answer Choice... | tiger_lab_math | [
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Big Joe is the tallest player on the basketball team. He is one foot taller than Ben, who is one foot taller than Larry, who is one foot taller than Frank, who is half a foot taller than Pepe. If Pepe is 4 feet six inches tall, how tall is Big Joe, in feet? | tiger_lab_math | [
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Two trains 120 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Answer Choices: (A) 10.9 (B) 10.7 (C) 10.3 (D) 10.08 (E) 10.2 | tiger_lab_math | [
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Theon's ship can move 15 nautical miles per hour while Yara's ship can move 30 nautical miles per hour. If their destination is 90 nautical miles away, how many hours ahead will Yara be ahead of Theon? Let's program in Python in the response. | tiger_lab_math | [
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What is the present worth of Rs. 143 due in 2 years at 5% simple interest per annum?
Answer Choices: (A) 288 (B) 266 (C) 120 (D) 277 (E) 130 | tiger_lab_math | [
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-0.03762851655483246,
0.044139157980680466,
-0.01780937984585762,
-0.005201057996600866,
0.052010614424943924,
0.03778904303908348,
-0.00020741358457598835,
0.022885216400027275,
0.03229139745235443,
-0.02509205788373947,
-0... | 0.793042 | 0.831726 | -0.038684 |
If three coins are tossed at the same time, what is the probability of getting two tails and one head? Express your answer as a common fraction. Let's write a program. | tiger_lab_math | [
0.01528295036405325,
0.01984504796564579,
-0.02484087273478508,
-0.034908927977085114,
0.042706191539764404,
-0.01363006979227066,
-0.0276405718177557,
0.054578009992837906,
0.022287918254733086,
-0.021676447242498398,
0.026241160929203033,
0.029538758099079132,
-0.020308397710323334,
-0.0... | 0.827028 | 0.829852 | -0.002825 |
Find the face value of 8 in 8213456
Answer Choices: (A) 8000 (B) 80 (C) 8 (D) 800 (E) 80000 | tiger_lab_math | [
0.01649806834757328,
0.021854648366570473,
-0.02076958678662777,
-0.02073829434812069,
0.029203373938798904,
-0.03159531578421593,
-0.008634188212454319,
0.05166567862033844,
0.052421048283576965,
0.00040138582699000835,
0.028313035145401955,
0.041100069880485535,
-0.03682541102170944,
-0.... | 0.787614 | 0.825292 | -0.037678 |
Find the unknown term 8,8,6,X,-4, -12
Answer Choices: (A) 2 (B) 4 (C) 6 (D) 8 (E) 9 | tiger_lab_math | [
0.03145430237054825,
0.011158371344208717,
-0.02904244139790535,
-0.024474162608385086,
0.05010329931974411,
-0.023039037361741066,
-0.023672103881835938,
0.049701157957315445,
0.03900090605020523,
-0.00737876957282424,
0.013073666952550411,
0.050503406673669815,
-0.03720901906490326,
-0.0... | 0.812419 | 0.850353 | -0.037934 |
Betty and Dora started making some cupcakes at the same time. Betty makes 10 cupcakes every hour and Dora makes 8 every hour. If Betty took a two-hour break, what is the difference between the number of cupcakes they made after 5 hours? Let's write a Python program to solve it. | tiger_lab_math | [
0.0065694465301930904,
0.024611596018075943,
-0.023060273379087448,
-0.01210090797394514,
0.019065141677856445,
-0.004596693441271782,
-0.04099768027663231,
0.06524936854839325,
0.04040606692433357,
-0.021476948633790016,
0.01872582919895649,
0.015031607821583748,
-0.031021971255540848,
-0... | 0.815879 | 0.823486 | -0.007607 |
Let X be a topological space and let A be a non-empty, connected subset of X. Suppose there exist open sets U and V in X such that A is a subset of both U and V, and A ∩ U and A ∩ V are disconnected.
What is the smallest possible number of connected components of (U ∩ V)? | tiger_lab_math | [
0.02189258672297001,
0.017507655546069145,
-0.04304305091500282,
-0.015854166820645332,
0.035753034055233,
0.010255793109536171,
-0.02270389348268509,
0.05151260271668434,
0.04630346968770027,
-0.0028810855001211166,
0.03544136881828308,
0.031239844858646393,
-0.02117101661860943,
-0.01396... | 0.833871 | 0.819377 | 0.014494 |
Let $a_1,$ $a_2,$ $\dots,$ $a_{12}$ be positive real numbers such that $a_1 + a_2 + \dots + a_{12} = 1.$ Find the minimum value of
\[\frac{1}{a_1} + \frac{1}{a_2} + \dots + \frac{1}{a_{12}}.\] | tiger_lab_math | [
0.020914636552333832,
0.03317141905426979,
-0.03526009991765022,
-0.039559345692396164,
0.04565662518143654,
-0.010212922468781471,
-0.013939699158072472,
0.055795926600694656,
0.04391278699040413,
-0.023397846147418022,
-0.003390450496226549,
0.012395424768328667,
-0.030438806861639023,
-... | 0.846773 | 0.830993 | 0.01578 |
X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 28 days. How long will Y take to complete the work?
Answer Choices: (A) 10 (B) 12 (C) 15 (D) 18 (E) 35 | tiger_lab_math | [
0.019266100600361824,
0.023772096261382103,
-0.017996689304709435,
-0.02152293547987938,
0.0401623472571373,
-0.04146362841129303,
-0.034690406173467636,
0.07127673178911209,
0.044865306466817856,
-0.018648475408554077,
0.01852315105497837,
0.05318555235862732,
-0.022781571373343468,
-0.02... | 0.790308 | 0.82767 | -0.037361 |
A mass-spring-damper system with mass 0.5 kg, spring constant 100 N/m and damping coefficient 2 Ns/m is given by the differential equation:
$$mx'' + bx' + kx = 0$$
Using the Fourier transform, determine the stability of the system. If the system is unstable, find a value of the damping coefficient such that the syste... | tiger_lab_math | [
0.04538087174296379,
0.01742640882730484,
-0.04167759791016579,
-0.044139306992292404,
0.05594508349895477,
-0.04207468032836914,
-0.015421923249959946,
0.08839796483516693,
0.03995455428957939,
-0.007538094185292721,
0.009710400365293026,
0.03570180386304855,
-0.04846850410103798,
-0.0334... | 0.805632 | 0.807479 | -0.001847 |
What is $\frac{1}{4}\%$ of 120? Express your answer as a decimal. | tiger_lab_math | [
0.025544771924614906,
0.011384883895516396,
-0.03308954834938049,
-0.052764859050512314,
0.03603464365005493,
-0.04273785650730133,
-0.000521030742675066,
0.05647013708949089,
0.06214689463376999,
-0.010971522890031338,
0.020709501579403877,
0.04539387300610542,
-0.023315390571951866,
-0.0... | 0.801434 | 0.835859 | -0.034425 |
We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $397. How many math books did we buy?
Answer Choices: (A) 47 (B) 53 (C) 56 (D) 61 (E) 64 | tiger_lab_math | [
0.039156392216682434,
-0.009482728317379951,
-0.029078328981995583,
-0.03302503377199173,
0.046461205929517746,
-0.03686746582388878,
-0.038901835680007935,
0.03541949391365051,
0.06241234764456749,
-0.03166589513421059,
0.004072976298630238,
0.015453411266207695,
-0.05781887099146843,
-0.... | 0.802634 | 0.826417 | -0.023783 |
8597 - ? = 7429 - 4358
Answer Choices: (A) 5526 (B) 5536 (C) 5556 (D) 5576 (E) 5586 Let's program in Python in the response. | tiger_lab_math | [
-0.008455980569124222,
0.02272414229810238,
-0.023459702730178833,
-0.0391276478767395,
0.038290102034807205,
-0.02456100657582283,
-0.026851683855056763,
0.04644561558961868,
0.049144547432661057,
-0.012858029454946518,
0.024994714185595512,
0.021387405693531036,
-0.032035477459430695,
-0... | 0.802173 | 0.846119 | -0.043946 |
A sum of 13,400 amounts to 14,400 in 2 years at the rate of simple interest. What is the rate of interest?
Answer Choices: (A) 2% (B) 1% (C) 6% (D) 4% (E) 8% | tiger_lab_math | [
0.012412020936608315,
0.01899748481810093,
-0.038078319281339645,
-0.026974117383360863,
0.047575902193784714,
-0.026957131922245026,
-0.016350721940398216,
0.05718879774212837,
0.030812587589025497,
-0.0021528578363358974,
0.029795899987220764,
0.009907440282404423,
-0.02592521905899048,
... | 0.789384 | 0.822525 | -0.033141 |
find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 14 cm . Please write a program to solve it | tiger_lab_math | [
0.021047033369541168,
0.03076249547302723,
-0.054492462426424026,
-0.04387950897216797,
0.0430024079978466,
-0.014893597923219204,
-0.030383769422769547,
0.05465251952409744,
0.04872182011604309,
-0.006594971287995577,
0.030772659927606583,
0.04412879794836044,
-0.018406637012958527,
0.000... | 0.82874 | 0.832001 | -0.003261 |
What is the volume of a Menger sponge with a side length of 4 units after removing the central cubes from each face of the original cube? | tiger_lab_math | [
0.020314263179898262,
0.024109505116939545,
-0.049138668924570084,
-0.037114813923835754,
0.02196611277759075,
-0.03032873198390007,
-0.05441534146666527,
0.01765727438032627,
0.037797942757606506,
-0.01407400518655777,
0.019948653876781464,
0.021803805604577065,
-0.015457408502697945,
-0.... | 0.799923 | 0.814272 | -0.01435 |
Debora has 12 more dresses than Melissa. Melissa has half the number of dresses Emily has. If Emily has 16 dresses, how many dresses do the three of them have in total? | tiger_lab_math | [
0.004341662395745516,
-0.0027848840691149235,
-0.05086054280400276,
-0.039300594478845596,
0.03806843236088753,
-0.027117939665913582,
-0.03326011076569557,
0.05626028776168823,
0.026146918535232544,
-0.00793742947280407,
0.0062544215470552444,
0.03233266621828079,
-0.03317687660455704,
-0... | 0.793793 | 0.815603 | -0.02181 |
What is the value of the Lorenz-Stenflo system's "x" variable at time t=30 when the initial conditions are
x(0) = 0.7, y(0) = 1.2, and z(0) = 2.5 with parameters σ = 10, β = 8/3, and ρ = 28? | tiger_lab_math | [
-0.0061426665633916855,
0.0218291487544775,
-0.06610607355833054,
-0.0411609522998333,
0.039182037115097046,
-0.009933517314493656,
-0.03298621252179146,
0.06554214656352997,
0.0367208756506443,
-0.049858689308166504,
0.00847648922353983,
0.02726796455681324,
-0.02913309819996357,
-0.03125... | 0.796435 | 0.820432 | -0.023998 |
A student needs to arrange a 5-member committee using 9 available members. However, two of the members refuse to serve together on the same committee. How many possible ways can the committee be formed using the inclusion-exclusion principle? | tiger_lab_math | [
0.014927336014807224,
0.004296240396797657,
-0.03775247558951378,
-0.019415443763136864,
0.02620689570903778,
-0.042897507548332214,
-0.019952867180109024,
0.04269036278128624,
0.033195316791534424,
-0.012522796168923378,
0.016453348100185394,
0.026173027232289314,
-0.04018916189670563,
-0... | 0.813476 | 0.812443 | 0.001034 |
what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 4 if each digit can be used only once in each number ? Let's program in Python in the response. | tiger_lab_math | [
0.0075159878470003605,
0.015012659132480621,
-0.03097706288099289,
-0.029742708429694176,
0.045924652367830276,
-0.01972389779984951,
-0.0273667611181736,
0.029926571995019913,
0.027383575215935707,
-0.008173963986337185,
0.02174563519656658,
0.050173237919807434,
-0.03979617729783058,
-0.... | 0.809123 | 0.820374 | -0.011252 |
Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers?
Answer Choices: (A) 7 hours and 30 minutes. (B) 8 hours and 30 minutes. (C) 9 hours and 30 minutes. (D) 3 hours and 30 minutes. (E) 4 hrs and 30 min | tiger_lab_math | [
0.029001876711845398,
0.03404365852475166,
-0.03106478415429592,
-0.025873083621263504,
0.030467180535197258,
-0.037700165063142776,
-0.057201892137527466,
0.05312463268637657,
0.042905043810606,
-0.008553680963814259,
0.03160438314080238,
0.04167334735393524,
-0.010042974725365639,
-0.022... | 0.780851 | 0.810968 | -0.030118 |
Carla has some marbles. Carla bought 489.0 marbles. Now Calra has 2778.0 marbles all together. How many did Carla start with. Please respond by writing a program in Python. | tiger_lab_math | [
-0.010269266553223133,
0.0396629273891449,
-0.042314305901527405,
-0.04155528545379639,
0.05173468962311745,
-0.009258556179702282,
-0.03590777888894081,
0.059235285967588425,
0.0230697188526392,
-0.024671100080013275,
0.019061122089624405,
0.02814413420855999,
-0.046228084713220596,
-0.02... | 0.802584 | 0.821288 | -0.018704 |
Find the integer that is closest to $1000\sum_{n=3}^{10000}\frac1{n^2-4}$. Let's write a Python program. | tiger_lab_math | [
0.009142358787357807,
0.03930361941456795,
-0.031617671251297,
-0.01856016367673874,
0.03210294619202614,
-0.0319078303873539,
-0.024288080632686615,
0.02833567000925541,
0.036435820162296295,
-0.008046183735132217,
0.028313057497143745,
0.03642003983259201,
-0.01726459711790085,
-0.008805... | 0.821146 | 0.828614 | -0.007467 |
William earned $3,200 per month as a
teacher for the ten months from September
to June. Then he took a job as a barista at a
local café, where he earned $2,000 per
month during July and August. What was
his average monthly pay for the 12 months?
Answer Choices: (A) $2,400 (B) $2,800 (C) $2,600 (D) $3,000 (E) $2,500 | tiger_lab_math | [
0.047929853200912476,
0.017911668866872787,
-0.0327175073325634,
-0.03498045727610588,
0.019954001531004906,
-0.04674793779850006,
-0.038899704813957214,
0.0650649443268776,
0.02394675649702549,
0.0005694004939869046,
0.03589101880788803,
0.008667701855301857,
-0.03975348174571991,
-0.0236... | 0.778459 | 0.807611 | -0.029152 |
Find the period and amplitude of the function f(x) = 3sin(2x + π/4) - 2cos(3x - π/3). | tiger_lab_math | [
0.02979726903140545,
0.022513242438435555,
-0.038222044706344604,
-0.04742932319641113,
0.030966099351644516,
-0.03678645193576813,
-0.02039526216685772,
0.07174122333526611,
0.02945534698665142,
0.021275484934449196,
0.04235024377703667,
0.044757068157196045,
-0.03211322799324989,
-0.0319... | 0.819101 | 0.836297 | -0.017196 |
What is the treewidth of the graph given below?
```
A
/ \
B C
/ \ \
D E F
\
G
```
Hint: To determine the treewidth of a graph, find the minimum width of a tree decomposition. The width of a tree decomposition is the size of the largest set of vertices in any bag minus one. | tiger_lab_math | [
0.01697222702205181,
0.004498287104070187,
-0.037762533873319626,
-0.027576595544815063,
0.04292736202478409,
-0.0395425520837307,
-0.015407707542181015,
0.057400140911340714,
0.028856545686721802,
-0.003519343910738826,
0.028511302545666695,
0.010018473491072655,
-0.012874886393547058,
-0... | 0.790266 | 0.800279 | -0.010013 |
Let's consider the 3-dimensional manifold given by the equation x^2 + y^2 - z^2 = 1. Find the Riemann curvature tensor at the point P(1, 0, 0). | tiger_lab_math | [
0.008269091136753559,
0.03262219578027725,
-0.02324768528342247,
-0.05316374450922012,
0.03476780280470848,
-0.00024261235375888646,
-0.00623172614723444,
0.05156688392162323,
0.024725310504436493,
-0.01894342340528965,
0.005003403872251511,
0.027098003774881363,
-0.04516234248876572,
-0.0... | 0.824216 | 0.812423 | 0.011793 |
Aaron wants to purchase a guitar under a payment plan of $100.00 per month for 12 months. His father has agreed to lend him the entire amount for the guitar, plus a one-time 10% interest fee for the entire loan. With interest, how much money will Aaron owe his dad? | tiger_lab_math | [
0.04379148408770561,
0.026421530172228813,
-0.0581822395324707,
-0.03265772759914398,
0.019249387085437775,
-0.023939482867717743,
0.004945084452629089,
0.045721784234046936,
0.013656696304678917,
0.0001568486331962049,
0.018418213352560997,
0.012515542097389698,
-0.05738147720694542,
-0.0... | 0.780013 | 0.794927 | -0.014914 |
Erwan went on shopping. He purchased a pair of shoes at $200 but discounted 30%, and two shirts at $80 each. Upon checkout, the cashier said that there is an additional 5% discount. How much did he spend after all the discounts? | tiger_lab_math | [
0.02113710530102253,
0.019596869125962257,
-0.05524961277842522,
-0.028818340972065926,
0.031026756390929222,
-0.010865144431591034,
-0.02253458835184574,
0.042144518345594406,
0.03783416375517845,
-0.004521121736615896,
0.032840240746736526,
0.05159403756260872,
-0.06827747821807861,
-0.0... | 0.787348 | 0.808049 | -0.020701 |
Cindy can jump rope for 12 minutes before tripping up on the ropes. Betsy can jump rope half as long as Cindy before tripping up, while Tina can jump three times as long as Betsy. How many more minutes can Tina jump rope than Cindy? | tiger_lab_math | [
0.0023506954312324524,
0.018904076889157295,
-0.037410054355859756,
-0.020388297736644745,
0.03800166770815849,
-0.0334625169634819,
-0.029482048004865646,
0.06318903714418411,
0.04456619173288345,
-0.017519494518637657,
0.014837989583611488,
0.03095783293247223,
-0.028929315507411957,
-0.... | 0.792997 | 0.805805 | -0.012809 |
How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
Answer Choices: (A) 16.7 (B) 16.8 (C) 16.5 (D) 16.1 (E) 16.2 | tiger_lab_math | [
0.029636027291417122,
-0.004887749440968037,
-0.022225745022296906,
-0.048528965562582016,
0.04964694008231163,
-0.057869914919137955,
-0.04410003498196602,
0.052886538207530975,
0.02856116183102131,
-0.027402769774198532,
0.02417183481156826,
0.021625271067023277,
-0.015959013253450394,
-... | 0.792102 | 0.826702 | -0.0346 |
The perimeter of a rectangle is 56 meters. The ratio of its length to its width is 4:3. What is the length in meters of a diagonal of the rectangle? | tiger_lab_math | [
0.02771434746682644,
0.020362572744488716,
-0.03598850220441818,
-0.05575569346547127,
0.018763083964586258,
-0.02118539996445179,
-0.034743282943964005,
0.04818624630570412,
0.04029299318790436,
-0.005261740647256374,
0.03210200369358063,
0.02968929335474968,
-0.028447730466723442,
-0.015... | 0.813881 | 0.828012 | -0.014131 |
Here's a precise numerical problem about solving an optimization problem using particle swarm optimization:
A company has a production line with three machines. Each machine can produce a certain number of units of a product per hour, but also has a cost associated with running it. The hourly cost of machine 1 is $10,... | tiger_lab_math | [
0.005883038975298405,
0.003699753200635314,
-0.04315710440278053,
-0.020109696313738823,
0.025258444249629974,
-0.013057222589850426,
-0.04144039750099182,
0.056404344737529755,
0.03176562115550041,
0.0000029219468160590623,
0.012608434073626995,
0.017292838543653488,
-0.004547488410025835,
... | 0.809065 | 0.796399 | 0.012667 |
If x and y are two different prime numbers, which of the following cannot be true?
Answer Choices: (A) xy is odd. (B) x + y is even. (C) x + y is odd (D) xy is even (E) x/y is an integer | tiger_lab_math | [
0.030551770702004433,
0.01774008199572563,
-0.014940607361495495,
-0.031171323731541634,
0.03499387577176094,
-0.03066049888730049,
-0.004299010615795851,
0.07446184009313583,
0.059678733348846436,
-0.035809438675642014,
0.02759171836078167,
0.027397267520427704,
-0.033485859632492065,
-0.... | 0.818586 | 0.831733 | -0.013147 |
elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 7 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ? Let's write a program. | tiger_lab_math | [
0.03409521281719208,
0.03699611872434616,
-0.021415548399090767,
-0.0002889355819206685,
0.015808703377842903,
-0.033114489167928696,
-0.033038973808288574,
0.056513600051403046,
0.030684851109981537,
-0.017203928902745247,
0.0038595024961978197,
0.041772618889808655,
-0.030117304995656013,
... | 0.790514 | 0.800601 | -0.010087 |
In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
Answer Choices: (A) 8 (B) 12 (C) 6 (D) 14 (E) None of these Let's write a Python program. | tiger_lab_math | [
0.027156008407473564,
0.011277692392468452,
-0.018846971914172173,
-0.043366678059101105,
0.05774477869272232,
-0.017891807481646538,
-0.027551939710974693,
0.03968651220202446,
0.042069919407367706,
-0.0380503386259079,
0.026045681908726692,
0.030018499121069908,
-0.03373292461037636,
-0.... | 0.806477 | 0.826294 | -0.019817 |
A rectangular pyramid has a base with a length of 6 cm and a width of 5 cm. Its height is 9 cm. What is the volume of the pyramid? | tiger_lab_math | [
0.011932142078876495,
0.021929727867245674,
-0.036884013563394547,
-0.0348176583647728,
0.041640497744083405,
-0.04620972275733948,
-0.022108308970928192,
0.034395981580019,
0.03721518814563751,
-0.02160470187664032,
0.024024618789553642,
0.04412704333662987,
-0.021786252036690712,
-0.0095... | 0.796763 | 0.807951 | -0.011187 |
elena ’ s bread recipe calls for 5 ounces of butter for each 7 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ? Let's write a program. | tiger_lab_math | [
0.03279581665992737,
0.03694725036621094,
-0.019345207139849663,
0.000005877408966625808,
0.017687426880002022,
-0.03460831195116043,
-0.0331362709403038,
0.057976726442575455,
0.03418121859431267,
-0.016377389430999756,
0.0012463777093216777,
0.03826535493135452,
-0.027785463258624077,
-0... | 0.789729 | 0.800489 | -0.01076 |
Find the area of a parallelogram with base 30 cm and height 12 cm?
Answer Choices: (A) 290 cm2 (B) 360 cm2 (C) 270 cm2 (D) 280 cm2 (E) 260 cm2 | tiger_lab_math | [
0.022733118385076523,
0.015581679530441761,
-0.03668913617730141,
-0.040445730090141296,
0.04063672944903374,
-0.03554743155837059,
-0.0157613568007946,
0.058167342096567154,
0.03289259597659111,
-0.019246941432356834,
0.01606583036482334,
0.06212431192398071,
-0.026340553537011147,
-0.026... | 0.814452 | 0.834361 | -0.019909 |
If a basket is capable of holding 40 fruit altogether, and there are 3 times as many apples as oranges, how many oranges are there? | tiger_lab_math | [
0.014624441973865032,
0.017405515536665916,
-0.03356959670782089,
-0.020931659266352654,
0.028499318286776543,
-0.035941753536462784,
-0.020794017240405083,
0.04041346162557602,
0.02466318942606449,
-0.032842718064785004,
0.0035431731957942247,
0.0262125376611948,
-0.04510914906859398,
-0.... | 0.806547 | 0.821471 | -0.014924 |
Carla works at a food bank and she currently has stocked up 2000 cans of food. One day, 500 people showed up and took 1 can of food each. Carla had to then restock 1500 more cans to keep up with demand. The next day, 1000 people showed up and took 2 cans of food each. Carla restocked again with 3000 cans of food this t... | tiger_lab_math | [
0.01887623220682144,
0.018530668690800667,
-0.049073684960603714,
-0.03182053565979004,
0.025548798963427544,
-0.02359873056411743,
-0.04039769247174263,
0.07260946929454803,
0.00601092167198658,
-0.0046783797442913055,
0.015916703268885612,
0.016477741301059723,
-0.048040010035037994,
-0.... | 0.807176 | 0.814505 | -0.007328 |
A factory produces two products A and B. Each unit of product A requires 3 hours of processing and generates a profit of $10 while each unit of product B requires 5 hours of processing and generates a profit of $15. The factory has a maximum of 80 hours of processing time available per day. How many units of each produ... | tiger_lab_math | [
0.0044443560764193535,
0.004717422649264336,
-0.05449274182319641,
0.011325889267027378,
0.0012532516848295927,
-0.021382715553045273,
-0.05531918257474899,
0.07706943154335022,
0.03910446912050247,
-0.012229083105921745,
-0.006838931702077389,
0.033713627606630325,
-0.007195689715445042,
... | 0.809845 | 0.803746 | 0.006099 |
In base $b$, there are exactly one hundred three-digit numbers whose digits are all distinct. (That's "one hundred" in the ordinary sense, $100_{10}$.)
What is $b$? | tiger_lab_math | [
0.036969490349292755,
0.01018365565687418,
-0.05055852606892586,
-0.02669120952486992,
0.039831630885601044,
-0.043010663241147995,
-0.006153732538223267,
0.03713966906070709,
0.04851061850786209,
-0.022577673196792603,
0.023652827367186546,
0.04031098261475563,
-0.037560734897851944,
-0.0... | 0.831511 | 0.836083 | -0.004572 |
a light flashes every 20 seconds, how many times will it flash in ? of an hour?
Answer Choices: (A) 550 (B) 600 (C) 650 (D) 180 (E) 750 Let's write a Python program. | tiger_lab_math | [
0.007564936764538288,
0.02798129990696907,
-0.024149606004357338,
-0.02261420525610447,
0.02597152069211006,
-0.05452161654829979,
-0.03551088646054268,
0.055543817579746246,
0.05084573104977608,
-0.00502989673987031,
0.020091570913791656,
0.019342489540576935,
-0.020874926820397377,
-0.02... | 0.783423 | 0.812383 | -0.02896 |
For a periodic function f(x) defined on the interval [-π, π] with the Fourier series expansion
> f(x) = a0 + Σ(n=1 to ∞) [an cos(nx) + bn sin(nx)]
If the Fourier coefficients are given by:
> an = 0 for all n ≥ 0
> bn = (2(1-(-1)^n))/(nπ) for all n ≥ 1
Determine the convergence of the Fourier Series for the function... | tiger_lab_math | [
0.014432779513299465,
0.034949060529470444,
-0.05472690239548683,
-0.031345147639513016,
0.02384919300675392,
-0.026994112879037857,
-0.004704863298684359,
0.04871693626046181,
0.036910321563482285,
0.027603423222899437,
0.021843601018190384,
0.02277275174856186,
-0.038023412227630615,
-0.... | 0.81984 | 0.81341 | 0.006429 |
You have 5 sticks of lengths 10, 30, 40, 50, and 60 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is
Answer Choices: (A) 3 (B) 4 (C) 7 (D) 10 (E) 12 | tiger_lab_math | [
0.018937963992357254,
0.0020490512251853943,
-0.013813327066600323,
-0.0182819701731205,
0.03638366237282753,
-0.028913429006934166,
-0.024113746359944344,
0.05903319641947746,
0.0203697569668293,
-0.017251906916499138,
0.028980061411857605,
0.03977862000465393,
-0.053094472736120224,
-0.0... | 0.820625 | 0.828548 | -0.007923 |
Three consecutive even numbers are such that thrice the first number exceeds double the third number by seven. What is the third number?
Answer Choices: (A) 19 (B) 21 (C) 23 (D) 25 (E) 27 | tiger_lab_math | [
0.03022008202970028,
0.00272896746173501,
-0.028989676386117935,
-0.05473903566598892,
0.04688834771513939,
-0.02988874353468418,
-0.02325461246073246,
0.04865588620305061,
0.04026307538151741,
-0.025871125981211662,
0.02435331605374813,
0.047039780765771866,
-0.06642653048038483,
-0.02397... | 0.829266 | 0.844133 | -0.014867 |
A sporting goods store sold 60 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $204, what is the fewest number of $4 Frisbees that could have been sold?
Answer Choices: (A) 24 (B) 12 (C) 8 (D) 4 (E) 2 Let's write a Python program. | tiger_lab_math | [
0.012462489306926727,
0.01844988390803337,
-0.02874097041785717,
-0.021298645064234734,
0.04702972620725632,
-0.03831688314676285,
-0.045715779066085815,
0.04328767955303192,
0.051389697939157486,
0.007627757731825113,
0.021380523219704628,
0.030948404222726822,
-0.029336124658584595,
-0.0... | 0.812373 | 0.830912 | -0.018538 |
A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?
Answer Choices: (A) 120 metres (B) 180 metres (C) 324 metres (D) 250 metres (E) 150 metres | tiger_lab_math | [
0.01782769337296486,
0.01065698079764843,
-0.0203966423869133,
-0.04085209593176842,
0.04177161306142807,
-0.048499152064323425,
-0.030814278870821,
0.05018387734889984,
0.03554760292172432,
-0.03650838881731033,
0.014890667051076889,
0.01289279479533434,
-0.018917899578809738,
-0.02068369... | 0.797381 | 0.823613 | -0.026231 |
Consider $x(t)$ to be given as, $$ x(t)=\cos (1000 \pi t) $$ . Let the sampling frequency be $2000 \mathrm{~Hz}$. Does aliasing occur? | tiger_lab_math | [
0.021111121401190758,
0.0323762521147728,
-0.056309573352336884,
-0.0034693642519414425,
0.01858946494758129,
-0.036937881261110306,
-0.015509589575231075,
0.06869383901357651,
0.02739262767136097,
-0.016136184334754944,
0.029946252703666687,
0.017015043646097183,
-0.017986709251999855,
-0... | 0.81659 | 0.818189 | -0.001598 |
The expression (12.86 × 12.86 + 12.86 × p + 0.14 × 0.14) will be a perfect square for p equal to
Answer Choices: (A) 0.28 (B) 0.26 (C) 1 (D) 0 (E) 2 | tiger_lab_math | [
0.024610459804534912,
0.03560469672083855,
-0.028722574934363365,
-0.04393267631530762,
0.06226259469985962,
-0.03952423855662346,
-0.015390726737678051,
0.060064125806093216,
0.045530419796705246,
0.0005784502136521041,
0.016105160117149353,
0.03743567690253258,
-0.01584055833518505,
-0.0... | 0.823312 | 0.839874 | -0.016561 |
bella is taking a trip in her car from new york ( point a ) chicago , illinois ( point b ) . she is traveling at an average speed of 50 miles per hour , if the total distance from point a to point b is 790 miles , in approximately how long will bella reach her destination ? Let's write a Python program to solve it. | tiger_lab_math | [
0.006657320540398359,
0.015884440392255783,
-0.04391574487090111,
-0.018383866176009178,
0.01567876525223255,
-0.024291515350341797,
-0.05401404947042465,
0.044837210327386856,
0.05019797757267952,
-0.022771360352635384,
0.023678403347730637,
0.019693337380886078,
-0.01094401441514492,
-0.... | 0.793333 | 0.805186 | -0.011854 |
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
Answer Choices: (A) 17 min (B) 10 min (C) 15 min (D) 47 min (E) 55 min | tiger_lab_math | [
0.033089421689510345,
0.01352835912257433,
-0.016671696677803993,
-0.032497186213731766,
0.032864440232515335,
-0.049621935933828354,
-0.0363047793507576,
0.05369191616773605,
0.03392717242240906,
-0.01852243021130562,
0.028020888566970825,
0.02504267729818821,
-0.013737574219703674,
-0.02... | 0.793929 | 0.827227 | -0.033298 |
A travel agent reports that 70% of their customers book a flight and hotel package for their trips. If the agent has 400 customers this month, how many customers are likely to book a flight and hotel package for their trip? | tiger_lab_math | [
0.040248844772577286,
0.0042935810051858425,
-0.05446518585085869,
-0.05556725710630417,
0.03768967092037201,
-0.028638625517487526,
-0.02634129859507084,
0.025661736726760864,
0.040487561374902725,
-0.0054743532091379166,
0.006882518995553255,
0.042462561279535294,
-0.0180111825466156,
-0... | 0.784761 | 0.797916 | -0.013155 |
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 45kg. What is the weight of the new person?
Answer Choices: (A) 75 Kg (B) 65 Kg (C) 85 Kg (D) 80 Kg (E) 60 KG | tiger_lab_math | [
0.03539740666747093,
0.025343183428049088,
-0.018087290227413177,
-0.05136876180768013,
0.03589130938053131,
-0.04665001481771469,
-0.017412148416042328,
0.051692862063646317,
0.04424739629030228,
-0.03622061386704445,
0.020062724128365517,
0.005392172839492559,
-0.050608884543180466,
-0.0... | 0.789262 | 0.819312 | -0.03005 |
Walking with 4/5 of my usual speed, I arrive at the bus stop 7 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?
Answer Choices: (A) 12 (B) 16 (C) 20 (D) 24 (E) 28 | tiger_lab_math | [
0.03661295771598816,
0.022494902834296227,
-0.016701120883226395,
-0.024648120626807213,
0.03442557156085968,
-0.03141050413250923,
-0.043460581451654434,
0.053216323256492615,
0.04791279137134552,
-0.00439071049913764,
0.01223928015679121,
0.03904079645872116,
-0.04165969789028168,
-0.022... | 0.802507 | 0.840643 | -0.038137 |
To make pizza dough, Luca mixes 50 mL of milk for every 250 mL of flour. How many mL of milk does he mix with 750 mL of flour? Let's write a program. | tiger_lab_math | [
0.02371250092983246,
0.029045861214399338,
-0.024342652410268784,
-0.02696567215025425,
0.02627072110772133,
-0.02250378578901291,
-0.03799702972173691,
0.04057465121150017,
0.039147816598415375,
-0.02505480870604515,
0.011783197522163391,
0.04206657037138939,
-0.027630193158984184,
-0.020... | 0.794652 | 0.811592 | -0.01694 |
For integers $a$, $b$, $c$, and $d$, $(x^2+ax+b)(x^2+cx+d)=x^4+x^3-2x^2+17x-5$. What is the value of $a+b+c+d$? | tiger_lab_math | [
0.033741340041160583,
0.03637872636318207,
-0.061941858381032944,
-0.047807276248931885,
0.035226572304964066,
-0.03235889971256256,
0.005693135317414999,
0.0646800622344017,
0.06174711138010025,
-0.03133327141404152,
0.01127015333622694,
0.031092870980501175,
-0.0406571663916111,
-0.04733... | 0.844928 | 0.846491 | -0.001562 |
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train ?
Answer Choices: (A) 48 km/hr (B) 54 km/hr (C) 66 km/hr (D) 82 km/hr (E) 89 km/hr | tiger_lab_math | [
0.027047311887145042,
0.004551602993160486,
-0.021162141114473343,
-0.03259776532649994,
0.036734867841005325,
-0.02873154915869236,
-0.042300909757614136,
0.06404875963926315,
0.05041811242699623,
-0.035293906927108765,
0.017024416476488113,
-0.00219716620631516,
-0.023571131750941277,
-0... | 0.790288 | 0.822359 | -0.032071 |
a and b together can plough a field in 10 hours but by himself a requires 15 hours . how long would b take to plough the same field ? Let's write a program. | tiger_lab_math | [
0.018565969541668892,
0.023675333708524704,
-0.042652565985918045,
-0.022718513384461403,
0.025826212018728256,
-0.03718586638569832,
-0.03693604841828346,
0.06333644688129425,
0.04374757036566734,
-0.029172930866479874,
0.003916138783097267,
0.03680532053112984,
-0.02735138311982155,
-0.0... | 0.816087 | 0.830326 | -0.014239 |
When x + p is divided by p , the quotient is n and there is no remainder. Which of the following must be the value of x?
Answer Choices: (A) p (n - 1) (B) n (p − 1) (C) p (n + 1) + 2n (D) p (n - 1) + 2n (E) n (p + 1) (p − 1) | tiger_lab_math | [
0.0403585210442543,
0.0034283255226910114,
-0.030220597982406616,
-0.01762082800269127,
0.027952665463089943,
-0.03248508274555206,
0.013331325724720955,
0.06994569301605225,
0.037732966244220734,
-0.028068652376532555,
0.02730092592537403,
0.04207161068916321,
-0.03198165073990822,
-0.036... | 0.824055 | 0.833582 | -0.009527 |
Two athletes starting from same place walk in the same direction at a rate of 8 km/hr and 6 km/hr. What time will they take to be 10 km apart ?
Answer Choices: (A) 10 hours (B) 15 hours (C) 5 hours (D) 4 hours (E) None of these | tiger_lab_math | [
0.03726128116250038,
0.020170362666249275,
-0.03277859836816788,
-0.010777964256703854,
0.024525301530957222,
-0.02436322718858719,
-0.041339144110679626,
0.051348306238651276,
0.05407818406820297,
-0.047540731728076935,
0.01629522070288658,
0.03303639590740204,
-0.022378703579306602,
-0.0... | 0.792647 | 0.823647 | -0.031 |
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 9 o'clock in the morning?
Answer Choices: (A) 30 (B) 60 (C) 90 (D) 120 (E) 150 | tiger_lab_math | [
0.022496478632092476,
0.00022946493118070066,
-0.010765965096652508,
-0.016806738451123238,
0.02068822644650936,
-0.042234867811203,
-0.02885383926331997,
0.049507755786180496,
0.031162915751338005,
-0.03950687497854233,
0.008347147144377232,
0.04317079111933708,
-0.042735591530799866,
-0.... | 0.797363 | 0.825472 | -0.028109 |
If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms W in the sequence are smaller than the average?
Answer Choices: (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 | tiger_lab_math | [
0.00007119720248738304,
0.008503171615302563,
-0.024388227611780167,
-0.054989878088235855,
0.05308649316430092,
-0.0164774339646101,
-0.05686069279909134,
0.05420563369989395,
0.017042815685272217,
-0.01990385912358761,
0.002728762337937951,
0.035495128482580185,
-0.04981915280222893,
-0.... | 0.819466 | 0.842299 | -0.022833 |
Jimmy's father receives 20 emails a day. Halfway through April, he subscribed to a news channel that sent 5 more emails per day to his email. What's the total number of emails Jimmy's father had at the end of the month? | tiger_lab_math | [
0.006519356742501259,
0.0008177303825505078,
-0.04335017129778862,
-0.046738870441913605,
0.03192104399204254,
-0.03307971730828285,
-0.024020424112677574,
0.05053379386663437,
0.02410556748509407,
-0.0173794012516737,
0.014269215054810047,
0.03380192071199417,
-0.05250898376107216,
-0.016... | 0.794183 | 0.811358 | -0.017175 |
There are four members in one household. Each member consumes 3 slices of bread during breakfast and 2 slices of bread for snacks. A loaf of bread has 12 slices. How many days will five loaves of bread last in this family? Let's write a Python program to solve it. | tiger_lab_math | [
0.021021796390414238,
0.02604091726243496,
-0.05113345384597778,
-0.03236109018325806,
0.03407975658774376,
-0.028112521395087242,
-0.018859723582863808,
0.05161797255277634,
0.034206099808216095,
-0.029243865981698036,
0.00758097879588604,
0.02426285296678543,
-0.03437873348593712,
-0.016... | 0.805553 | 0.814836 | -0.009283 |
Kylie makes 10 beaded necklaces on Monday and 2 beaded necklaces on Tuesday. Then Kylie makes 5 beaded bracelets and 7 beaded earrings on Wednesday. 20 beads are needed to make one beaded necklace. 10 beads are needed to make one beaded bracelet. 5 beads are needed to make one beaded earring. How many beads does Kylie ... | tiger_lab_math | [
0.023722855374217033,
0.0393579937517643,
-0.06124689429998398,
-0.03156917914748192,
0.03957752883434296,
-0.05341120809316635,
-0.04143519699573517,
0.04820217564702034,
0.010307703167200089,
-0.006624667439609766,
0.00822066143155098,
0.03416093811392784,
-0.021929103881120682,
-0.01610... | 0.805249 | 0.813489 | -0.008241 |
Find the missing value : 8597 - ? = 7429 - 4358
Answer Choices: (A) 5526 (B) 5426 (C) 5326 (D) 5226 (E) None of them | tiger_lab_math | [
0.004541133064776659,
0.015851136296987534,
-0.02151554450392723,
-0.030452534556388855,
0.03991587832570076,
-0.029946820810437202,
-0.012817180715501308,
0.04573166370391846,
0.036963801831007004,
-0.02834397181868553,
0.02866475284099579,
0.03026648424565792,
-0.025161992758512497,
-0.0... | 0.806083 | 0.850322 | -0.044238 |
Let M be a smooth manifold defined by the equation x^2 + y^2 + z^2 = 1 in R^3, and let V be the vector field defined by V = x^2 i + y^2 j + z^2 k. Determine the Lie derivative of V with respect to the vector field X = x ∂/∂y - y ∂/∂x at the point (1/2, √3/2, 0). | tiger_lab_math | [
0.022766606882214546,
0.03175835311412811,
-0.041428498923778534,
-0.060937825590372086,
0.042604196816682816,
-0.008897015824913979,
-0.02510412409901619,
0.06145116686820984,
0.02771172672510147,
-0.01406060066074133,
0.004131022375077009,
0.02560407854616642,
-0.044961173087358475,
-0.0... | 0.814165 | 0.809013 | 0.005152 |
A sinusoidal wave has an equation of y = 4cos(2x - pi/3). Determine the phase shift of the wave. | tiger_lab_math | [
0.018295355141162872,
0.03576996177434921,
-0.04633307456970215,
-0.03527919948101044,
0.034043267369270325,
-0.03455240651965141,
-0.0369621105492115,
0.08332468569278717,
0.04898904263973236,
0.004092099145054817,
0.04301966354250908,
0.01588897593319416,
-0.028437834233045578,
-0.019997... | 0.808682 | 0.825666 | -0.016984 |
Find the range of the function
\[k(x) = \frac{2x + 7}{x - 3}.\] | tiger_lab_math | [
0.037821654230356216,
0.04483943060040474,
-0.03777742758393288,
-0.049206335097551346,
0.027174167335033417,
-0.018446583300828934,
-0.02072937600314617,
0.0657224953174591,
0.04224667698144913,
-0.025374392047524452,
0.025211092084646225,
0.0486670583486557,
-0.02022787183523178,
-0.0116... | 0.811084 | 0.828944 | -0.017859 |
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