text
stringlengths
256
2k
language
stringclasses
2 values
numbers: place value -------------------- Scenario: What is the millions digit of 2364349? Therefore: 2 Scenario: What is the ten thousands digit of 38569? Therefore: 3 Scenario: What is the thousands digit of 23448927? Therefore: 8 Scenario: What is the hundreds digit of 4050803? Therefore: 8 Scenario: What is the units digit of 4668129? Therefore: 9 Scenario: What is the ten millions digit of 572616249? Therefore: 7 Scenario: What is the hundred thousands digit of 4668569702? Therefore: 5 Scenario: What is the hundred thousands digit of 16348440? Therefore: 3 Scenario: What is the hundreds digit of 1647903? Therefore: 9 Scenario: What is the tens digit of 3254156706? Therefore: 0 Scenario: What is the units digit of 1801201? Therefore: 1 Scenario: What is the units digit of 7268162? Therefore: 2 Scenario: What is the thousands digit of 301353516? Therefore: 3 Scenario: What is the units digit of 176? Therefore: 6 Scenario: What is the hundreds digit of 794? Therefore: 7 Scenario: What is the units digit of 1370234? Therefore: 4 Scenario: What is the tens digit of 930968344? Therefore: 4 Scenario: What is the units digit of 107809? Therefore: 9 Scenario: What is the units digit of 218? Therefore: 8 Scenario: What is the ten thousands digit of 19079? Therefore: 1 Scenario: What is the hundreds digit of 2865? Therefore: 8 Scenario: What is the tens digit of 1041? Therefore: 4 Scenario: What is the thousands digit of 138339? Therefore: 8 Scenario: What is the ten millions digit of 163734356? Therefore: 6 Scenario: What is the ten thousands digit of 865586? Therefore: 6 Scenario: What is the tens digit of 2508778022? Therefore: 2 Scenario: What is the thousands digit of 679394? Therefore: 9 Scenario: What is the hundred thousands digit of 2207781460? Therefore: 7 Scenario: What is the thousands digit of 1931? Therefore: 1 Scenario: What is the units digit of 90181940? Therefore: 0 Scenario: What is the hundreds digit of 18870833? Therefore: 8 Scenario: What is the tens
english
probability: swr p sequence --------------------------- Step: Three letters picked without replacement from {d: 2, a: 1, c: 2}. What is prob of sequence adc? Answer: 1/15 Step: Calculate prob of sequence qffs when four letters picked without replacement from qssqqqfsfqsq. Answer: 2/495 Step: Four letters picked without replacement from nyyyyysdlylls. Give prob of sequence dyyl. Answer: 3/572 Step: Calculate prob of sequence iiii when four letters picked without replacement from iiiiciiiiic. Answer: 21/55 Step: Two letters picked without replacement from {l: 1, q: 1, k: 5, s: 3, e: 1, z: 4}. Give prob of sequence kz. Answer: 2/21 Step: Calculate prob of sequence oz when two letters picked without replacement from okpzzdpdozdokp. Answer: 9/182 Step: Three letters picked without replacement from jkkjkkkvjkvjj. Give prob of sequence kjj. Answer: 10/143 Step: Two letters picked without replacement from {z: 3, u: 5, p: 2}. What is prob of sequence zu? Answer: 1/6 Step: Four letters picked without replacement from {a: 11, x: 5}. What is prob of sequence xxax? Answer: 11/728 Step: Three letters picked without replacement from {k: 1, t: 11, w: 2}. Give prob of sequence tkt. Answer: 55/1092 Step: Three letters picked without replacement from {o: 1, e: 2, w: 1}. What is prob of sequence weo? Answer: 1/12 Step: What is prob of sequence pkk when three letters picked without replacement from {h: 3, p: 10, k: 2}? Answer: 2/273 Step: What is prob of sequence ycc when three letters picked without replacement from cycbybyccyyycbbyybbb? Answer: 4/171 Step: Calculate prob of sequence jeu when three letters picked without replacement from {h: 1, j: 1, u: 1, e: 1, o: 3}. Answer: 1/210 Step: Calculate prob of sequence pluu when four letters picked without replacement from lppuuelpuluplpu. Answer: 10/819 Step: Three letters picked without replacement from {z: 3, n: 5, j: 6, q: 3}. What is prob of sequence qzq? Answer: 3/680 Step: Calculate prob of sequence yz when two letters picked withou
english
probability: swr p level set ---------------------------- What if: Two letters picked without replacement from {k: 6, y: 4, u: 1, t: 5}. What is prob of picking 1 k and 1 u? Derivation: 1/20 What if: What is prob of picking 1 v and 1 d when two letters picked without replacement from {v: 1, q: 1, u: 3, d: 4, t: 4}? Derivation: 2/39 What if: What is prob of picking 1 r, 2 q, and 1 p when four letters picked without replacement from pprppaqarqqqqqqparqq? Derivation: 36/323 What if: What is prob of picking 2 i and 2 b when four letters picked without replacement from {i: 2, f: 2, e: 1, b: 4}? Derivation: 1/21 What if: What is prob of picking 2 t when two letters picked without replacement from iistiitit? Derivation: 1/12 What if: Three letters picked without replacement from ajjjajaajaajj. What is prob of picking 3 j? Derivation: 35/286 What if: Two letters picked without replacement from {v: 7, q: 6}. Give prob of picking 1 v and 1 q. Derivation: 7/13 What if: Two letters picked without replacement from {e: 3, w: 3, r: 11, n: 2}. What is prob of picking 2 w? Derivation: 1/57 What if: Four letters picked without replacement from {j: 2, y: 3, k: 6, g: 5, u: 2}. What is prob of picking 2 g, 1 j, and 1 k? Derivation: 2/51 What if: Calculate prob of picking 2 n when two letters picked without replacement from nnnnn. Derivation: 1 What if: Two letters picked without replacement from muua. What is prob of picking 1 m and 1 u? Derivation: 1/3 What if: Four letters picked without replacement from rzrozrokqkkzozqo. What is prob of picking 2 k and 2 r? Derivation: 9/1820 What if: What is prob of picking 1 n and 1 u when two letters picked without replacement from nnvvvnnvvbnunn? Derivation: 1/13 What if: What is prob of picking 1 h, 1 k, and 1 e when three letters picked without replacement from kkhokehkkhre? Derivation: 3/22 What if: What is prob of picking 1 i and 1 d when two letters picked without replacement from {d: 10, i: 10}? Derivation: 10/19 What if: Three letters pick
english
numbers: gcd ------------ Q/A: What is the greatest common divisor of 933420 and 195? Calculation: 15 Q/A: What is the highest common factor of 9 and 144? Calculation: 9 Q/A: What is the highest common divisor of 704 and 1276? Calculation: 44 Q/A: Calculate the greatest common divisor of 1 and 27. Calculation: 1 Q/A: What is the greatest common divisor of 232493 and 116? Calculation: 29 Q/A: What is the greatest common divisor of 54 and 69? Calculation: 3 Q/A: Calculate the highest common divisor of 283 and 814518431. Calculation: 283 Q/A: Calculate the highest common divisor of 6 and 194. Calculation: 2 Q/A: What is the greatest common factor of 700 and 550? Calculation: 50 Q/A: What is the greatest common factor of 4752 and 36204432? Calculation: 528 Q/A: Calculate the greatest common divisor of 81830 and 118. Calculation: 2 Q/A: Calculate the highest common divisor of 2366 and 98. Calculation: 14 Q/A: What is the highest common divisor of 560 and 7588? Calculation: 28 Q/A: What is the greatest common factor of 48 and 48? Calculation: 48 Q/A: What is the greatest common divisor of 108 and 120? Calculation: 12 Q/A: What is the highest common divisor of 68 and 170? Calculation: 34 Q/A: What is the highest common factor of 104 and 338? Calculation: 26 Q/A: What is the highest common divisor of 160023 and 738? Calculation: 123 Q/A: What is the highest common factor of 25139 and 5009219? Calculation: 1093 Q/A: What is the greatest common factor of 5367973 and 536? Calculation: 67 Q/A: Calculate the greatest common factor of 335 and 35045824. Calculation: 67 Q/A: What is the greatest common divisor of 22 and 110? Calculation: 22 Q/A: What is the greatest common factor of 105 and 6? Calculation: 3 Q/A: What is the highest common divisor of 23560448 and 256? Calculation: 256 Q/A: What is the highest common divisor of 3161 and 545? Calculation: 109 Q/A: What is the highest common divisor of 2419192 and 8? Calculation: 8 Q/A: What is the greatest common factor of 3285 and 1
english
measurement: time ----------------- Exercise: What is 525 minutes after 10:29 PM? Resolution: 7:14 AM Exercise: What is 49 minutes after 4:05 PM? Resolution: 4:54 PM Exercise: What is 14 minutes after 7:50 PM? Resolution: 8:04 PM Exercise: How many minutes are there between 12:31 AM and 8:44 AM? Resolution: 493 Exercise: How many minutes are there between 9:54 PM and 5:22 AM? Resolution: 448 Exercise: What is 715 minutes after 3:19 AM? Resolution: 3:14 PM Exercise: How many minutes are there between 4:20 PM and 3:24 AM? Resolution: 664 Exercise: How many minutes are there between 8:02 PM and 7:51 AM? Resolution: 709 Exercise: How many minutes are there between 1:38 PM and 12:05 AM? Resolution: 627 Exercise: How many minutes are there between 11:28 AM and 7:28 PM? Resolution: 480 Exercise: What is 685 minutes after 7:17 PM? Resolution: 6:42 AM Exercise: How many minutes are there between 10:18 AM and 7:51 PM? Resolution: 573 Exercise: How many minutes are there between 5:09 AM and 2:53 PM? Resolution: 584 Exercise: How many minutes are there between 11:52 PM and 8:05 AM? Resolution: 493 Exercise: How many minutes are there between 8:49 AM and 12:03 PM? Resolution: 194 Exercise: How many minutes are there between 3:36 PM and 4:28 PM? Resolution: 52 Exercise: How many minutes are there between 7:46 AM and 6:13 PM? Resolution: 627 Exercise: What is 126 minutes after 11:07 PM? Resolution: 1:13 AM Exercise: What is 266 minutes after 10:00 PM? Resolution: 2:26 AM Exercise: How many minutes are there between 1:24 PM and 11:05 PM? Resolution: 581 Exercise: What is 467 minutes before 3:36 AM? Resolution: 7:49 PM Exercise: What is 181 minutes after 12:10 AM? Resolution: 3:11 AM Exercise: What is 295 minutes after 11:06 PM? Resolution: 4:01 AM Exercise: How many minutes are there between 12:19 PM and 8:20 PM? Resolution: 481 Exercise: What is 630 minutes before 8:11 AM? Resolution: 9:41 PM Exercise: What is 387 minutes after 10:20 AM? Resolution: 4:47 PM Exercise: How many minu
english
numbers: is prime ----------------- Exercise: Is 9719 a composite number? Eval: False Exercise: Is 851406013 a prime number? Eval: True Exercise: Is 709035781 a prime number? Eval: True Exercise: Is 147165961 prime? Eval: True Exercise: Is 16406711 a composite number? Eval: False Exercise: Is 1732823 a composite number? Eval: True Exercise: Is 3649307 a prime number? Eval: True Exercise: Is 76753904041 prime? Eval: True Exercise: Is 18595121 a prime number? Eval: False Exercise: Is 2020037 a prime number? Eval: True Exercise: Is 15006071 composite? Eval: False Exercise: Is 5184103 prime? Eval: True Exercise: Is 14860159 composite? Eval: True Exercise: Is 6657437 a prime number? Eval: True Exercise: Is 2019461 a prime number? Eval: True Exercise: Is 3474656747 a composite number? Eval: False Exercise: Is 249500549 a composite number? Eval: False Exercise: Is 85081 a prime number? Eval: True Exercise: Is 493537 composite? Eval: True Exercise: Is 30485243 a composite number? Eval: True Exercise: Is 3742565 composite? Eval: True Exercise: Is 348709 composite? Eval: False Exercise: Is 13058597 prime? Eval: True Exercise: Is 498989 prime? Eval: True Exercise: Is 2237 prime? Eval: True Exercise: Is 40387 prime? Eval: True Exercise: Is 767218091 composite? Eval: False Exercise: Is 713599477 a prime number? Eval: True Exercise: Is 1021648441 a composite number? Eval: True Exercise: Is 7403 a prime number? Eval: False Exercise: Is 3827683833 composite? Eval: True Exercise: Is 2242417101 prime? Eval: False Exercise: Is 76461349 composite? Eval: False Exercise: Is 21709 a prime number? Eval: False Exercise: Is 101917 a composite number? Eval: False Exercise: Is 38371 composite? Eval: False Exercise: Is 93529 composite? Eval: False Exercise: Is 189854771 prime? Eval: False Exercise: Is 21173773657 prime? Eval: False Exercise: Is 18509 a prime number? Eval: False Exercise: Is 72809531 a composite number? Eval: True Exercise: Is 53183 composite? Eval: True Exercise: Is 23009219 pr
english
numbers: is prime ----------------- Situation: Is 243213617 a prime number? Finding: False Situation: Is 11737917949 composite? Finding: False Situation: Is 4763159 prime? Finding: True Situation: Is 4101966977 prime? Finding: False Situation: Is 38584724341 a composite number? Finding: True Situation: Is 254295823 a composite number? Finding: False Situation: Is 78922271 prime? Finding: False Situation: Is 9083 a prime number? Finding: False Situation: Is 8332529 composite? Finding: False Situation: Is 39299917 a prime number? Finding: True Situation: Is 135483 a composite number? Finding: True Situation: Is 72345587 composite? Finding: False Situation: Is 4703 a prime number? Finding: True Situation: Is 1195361 a composite number? Finding: False Situation: Is 5915872667 prime? Finding: False Situation: Is 169523 a prime number? Finding: True Situation: Is 46229 composite? Finding: False Situation: Is 222585173 a prime number? Finding: False Situation: Is 2692553483 a prime number? Finding: False Situation: Is 22670218507 a prime number? Finding: False Situation: Is 135870379 prime? Finding: True Situation: Is 45547048471 a composite number? Finding: True Situation: Is 943477999 composite? Finding: True Situation: Is 53657 prime? Finding: True Situation: Is 188213 a prime number? Finding: False Situation: Is 51134311 prime? Finding: True Situation: Is 21123757 prime? Finding: True Situation: Is 585811 a composite number? Finding: True Situation: Is 41304163 prime? Finding: True Situation: Is 8709829 a prime number? Finding: False Situation: Is 40737749 composite? Finding: True Situation: Is 913 composite? Finding: True Situation: Is 875204243 a prime number? Finding: True Situation: Is 5977583 prime? Finding: False Situation: Is 20423 composite? Finding: True Situation: Is 272775563 a prime number? Finding: True Situation: Is 351151 prime? Finding: True Situation: Is 33497681879 prime? Finding: True Situation: Is 72724891 prime? Finding: True Situation: Is 23834390
english
arithmetic: nearest integer root -------------------------------- Task: What is 4746495 to the power of 1/2, to the nearest integer? Fix: 2179 Task: What is 29695878 to the power of 1/3, to the nearest integer? Fix: 310 Task: What is the third root of 34800742 to the nearest integer? Fix: 326 Task: What is 496331 to the power of 1/2, to the nearest integer? Fix: 705 Task: What is the third root of 4212349629 to the nearest integer? Fix: 1615 Task: What is the square root of 3766103 to the nearest integer? Fix: 1941 Task: What is the cube root of 227920056 to the nearest integer? Fix: 611 Task: What is 89275595 to the power of 1/6, to the nearest integer? Fix: 21 Task: What is the square root of 38448 to the nearest integer? Fix: 196 Task: What is 2825999577 to the power of 1/2, to the nearest integer? Fix: 53160 Task: What is the sixth root of 1024152920 to the nearest integer? Fix: 32 Task: What is 322514 to the power of 1/5, to the nearest integer? Fix: 13 Task: What is 16878037 to the power of 1/2, to the nearest integer? Fix: 4108 Task: What is the third root of 19956 to the nearest integer? Fix: 27 Task: What is the third root of 3892283 to the nearest integer? Fix: 157 Task: What is the cube root of 500 to the nearest integer? Fix: 8 Task: What is the square root of 190217 to the nearest integer? Fix: 436 Task: What is the third root of 2357754 to the nearest integer? Fix: 133 Task: What is 936264 to the power of 1/9, to the nearest integer? Fix: 5 Task: What is 277603 to the power of 1/4, to the nearest integer? Fix: 23 Task: What is 1790084 to the power of 1/3, to the nearest integer? Fix: 121 Task: What is the fourth root of 95846 to the nearest integer? Fix: 18 Task: What is the third root of 1766 to the nearest integer? Fix: 12 Task: What is the ninth root of 1068312 to the nearest integer? Fix: 5 Task: What is the fourth root of 263675415 to the nearest integer? Fix: 127 Task: What is the cube root of 142174 to the nearest integer? Fix: 52 Task: What is
english
measurement: conversion ----------------------- Inquiry: What is 1/80 of a meter in micrometers? Explanation: 12500 Inquiry: How many months are there in eighty-seven fifths of a century? Explanation: 20880 Inquiry: Convert 2313161.7 hours to days. Explanation: 96381.7375 Inquiry: How many millilitres are there in 3/5 of a litre? Explanation: 600 Inquiry: Convert 0.8333527mg to grams. Explanation: 0.0008333527 Inquiry: Convert 0.6357437 kilometers to micrometers. Explanation: 635743700 Inquiry: How many millilitres are there in 21/2 of a litre? Explanation: 10500 Inquiry: How many months are there in eight thirds of a year? Explanation: 32 Inquiry: Convert 3966.888ug to kilograms. Explanation: 0.000003966888 Inquiry: What is nine tenths of a milligram in micrograms? Explanation: 900 Inquiry: How many nanograms are there in 0.5870169mg? Explanation: 587016.9 Inquiry: How many millilitres are there in 11/2 of a litre? Explanation: 5500 Inquiry: What is 70835.98l in millilitres? Explanation: 70835980 Inquiry: What is 409.7063 micrometers in meters? Explanation: 0.0004097063 Inquiry: How many micrometers are there in thirteen eighths of a centimeter? Explanation: 16250 Inquiry: How many nanograms are there in 69.6623 micrograms? Explanation: 69662.3 Inquiry: Convert 610080.5 decades to centuries. Explanation: 61008.05 Inquiry: What is 1.881613 weeks in days? Explanation: 13.171291 Inquiry: How many micrograms are there in 1/5 of a milligram? Explanation: 200 Inquiry: How many months are there in 26/5 of a decade? Explanation: 624 Inquiry: What is 9.425859t in micrograms? Explanation: 9425859000000 Inquiry: What is 32/7 of a week in days? Explanation: 32 Inquiry: What is 7.890296 weeks in nanoseconds? Explanation: 4772051020800000 Inquiry: How many centimeters are there in three fifths of a meter? Explanation: 60 Inquiry: How many kilograms are there in three eighths of a tonne? Explanation: 375 Inquiry: How many seconds are there in 21/5 of a hour? Explanation: 15120 In
english
numbers: div remainder ---------------------- Case: What is the remainder when 31099 is divided by 798? A: 775 Case: What is the remainder when 1148938 is divided by 2992? A: 10 Case: What is the remainder when 2107397 is divided by 1053698? A: 1 Case: Calculate the remainder when 149950018 is divided by 1005. A: 1003 Case: Calculate the remainder when 1897 is divided by 221. A: 129 Case: What is the remainder when 45462 is divided by 14967? A: 561 Case: What is the remainder when 1453421 is divided by 1890? A: 11 Case: What is the remainder when 8191 is divided by 139? A: 129 Case: Calculate the remainder when 14943 is divided by 35. A: 33 Case: What is the remainder when 40619 is divided by 33? A: 29 Case: What is the remainder when 5756132 is divided by 3453? A: 3434 Case: What is the remainder when 869 is divided by 235? A: 164 Case: Calculate the remainder when 1127152 is divided by 730. A: 32 Case: What is the remainder when 9155 is divided by 1282? A: 181 Case: Calculate the remainder when 147530 is divided by 366. A: 32 Case: What is the remainder when 7019 is divided by 60? A: 59 Case: Calculate the remainder when 283007980 is divided by 406. A: 402 Case: Calculate the remainder when 15429 is divided by 43. A: 35 Case: Calculate the remainder when 126 is divided by 17. A: 7 Case: Calculate the remainder when 680971 is divided by 6364. A: 23 Case: Calculate the remainder when 2387 is divided by 1177. A: 33 Case: What is the remainder when 434 is divided by 48? A: 2 Case: What is the remainder when 67583 is divided by 2842? A: 2217 Case: Calculate the remainder when 492 is divided by 50. A: 42 Case: What is the remainder when 75 is divided by 24? A: 3 Case: What is the remainder when 2526 is divided by 197? A: 162 Case: Calculate the remainder when 26411 is divided by 93. A: 92 Case: What is the remainder when 2505359 is divided by 390? A: 389 Case: What is the remainder when 788 is divided by 137? A: 103 Case: What is the remainder when 460745 is divided by
english
numbers: div remainder ---------------------- Inquiry: Calculate the remainder when 57885 is divided by 2388. Response: 573 Inquiry: Calculate the remainder when 1150 is divided by 271. Response: 66 Inquiry: Calculate the remainder when 7144 is divided by 723. Response: 637 Inquiry: What is the remainder when 1087682 is divided by 1087667? Response: 15 Inquiry: Calculate the remainder when 57 is divided by 32. Response: 25 Inquiry: Calculate the remainder when 66 is divided by 25. Response: 16 Inquiry: What is the remainder when 373449 is divided by 52? Response: 37 Inquiry: Calculate the remainder when 3620 is divided by 15. Response: 5 Inquiry: What is the remainder when 14282 is divided by 1019? Response: 16 Inquiry: What is the remainder when 1882 is divided by 70? Response: 62 Inquiry: What is the remainder when 160292 is divided by 822? Response: 2 Inquiry: Calculate the remainder when 115255 is divided by 546. Response: 49 Inquiry: Calculate the remainder when 314 is divided by 161. Response: 153 Inquiry: What is the remainder when 30884987 is divided by 1616? Response: 1611 Inquiry: Calculate the remainder when 309 is divided by 131. Response: 47 Inquiry: What is the remainder when 49158 is divided by 26? Response: 18 Inquiry: Calculate the remainder when 7369785 is divided by 41637. Response: 36 Inquiry: Calculate the remainder when 1473647 is divided by 210521. Response: 0 Inquiry: Calculate the remainder when 2368 is divided by 173. Response: 119 Inquiry: What is the remainder when 276 is divided by 23? Response: 0 Inquiry: Calculate the remainder when 6324 is divided by 57. Response: 54 Inquiry: Calculate the remainder when 245069 is divided by 70. Response: 69 Inquiry: Calculate the remainder when 10925 is divided by 29. Response: 21 Inquiry: What is the remainder when 19673 is divided by 19649? Response: 24 Inquiry: What is the remainder when 2723755 is divided by 1164? Response: 1159 Inquiry: Calculate the remainder when 104 is divided by 15. Response
english
probability: swr p level set ---------------------------- Item: Calculate prob of picking 2 h, 1 x, and 1 c when four letters picked without replacement from oogggccghgxgxogogo. Calculation: 0 Item: Two letters picked without replacement from lpwprrp. Give prob of picking 1 w and 1 r. Calculation: 2/21 Item: Two letters picked without replacement from {x: 1, f: 10, b: 1, y: 1}. Give prob of picking 2 b. Calculation: 0 Item: Two letters picked without replacement from {s: 6}. Give prob of picking 2 s. Calculation: 1 Item: Two letters picked without replacement from bhhmmhuhaaha. Give prob of picking 1 h and 1 a. Calculation: 5/22 Item: What is prob of picking 1 k and 3 e when four letters picked without replacement from {e: 7, k: 2}? Calculation: 5/9 Item: Three letters picked without replacement from uivhieeexhxhhihxhhh. What is prob of picking 1 e, 1 x, and 1 h? Calculation: 24/323 Item: Four letters picked without replacement from jeiiiieeiijijijee. Give prob of picking 2 e and 2 i. Calculation: 2/17 Item: Calculate prob of picking 1 s and 1 z when two letters picked without replacement from sszsisnsniisnxsssssk. Calculation: 11/190 Item: Two letters picked without replacement from kfwffwkwfkwfkk. What is prob of picking 2 k? Calculation: 10/91 Item: Calculate prob of picking 1 n and 3 g when four letters picked without replacement from {g: 8, n: 5}. Calculation: 56/143 Item: What is prob of picking 1 u and 1 s when two letters picked without replacement from ususuus? Calculation: 4/7 Item: Two letters picked without replacement from {h: 1, a: 3, r: 3, y: 1, w: 2, x: 1}. What is prob of picking 1 h and 1 w? Calculation: 2/55 Item: Two letters picked without replacement from eedtut. What is prob of picking 1 d and 1 u? Calculation: 1/15 Item: Two letters picked without replacement from kdlkdkkdllkdldlkz. Give prob of picking 2 d. Calculation: 5/68 Item: Calculate prob of picking 1 l and 1 v when two letters picked without replacement from vvvlvwvwvvwvw. Calculation
english
numbers: place value -------------------- Task: What is the ten millions digit of 1976718129? Hence: 7 Task: What is the ten thousands digit of 27712? Hence: 2 Task: What is the thousands digit of 253168479? Hence: 8 Task: What is the units digit of 26348313? Hence: 3 Task: What is the ten millions digit of 1392904523? Hence: 9 Task: What is the hundreds digit of 631? Hence: 6 Task: What is the hundreds digit of 179? Hence: 1 Task: What is the millions digit of 151099190? Hence: 1 Task: What is the ten millions digit of 554486282? Hence: 5 Task: What is the hundreds digit of 302778037? Hence: 0 Task: What is the units digit of 846599? Hence: 9 Task: What is the thousands digit of 2526? Hence: 2 Task: What is the thousands digit of 5632379? Hence: 2 Task: What is the hundreds digit of 409437? Hence: 4 Task: What is the units digit of 1221181? Hence: 1 Task: What is the thousands digit of 35719? Hence: 5 Task: What is the tens digit of 5496? Hence: 9 Task: What is the ten thousands digit of 403835? Hence: 0 Task: What is the thousands digit of 842472974? Hence: 2 Task: What is the tens digit of 112465? Hence: 6 Task: What is the thousands digit of 574268? Hence: 4 Task: What is the ten thousands digit of 30806950? Hence: 0 Task: What is the tens digit of 853? Hence: 5 Task: What is the hundreds digit of 88401? Hence: 4 Task: What is the millions digit of 41616850? Hence: 1 Task: What is the ten thousands digit of 24351889? Hence: 5 Task: What is the hundred thousands digit of 3094766? Hence: 0 Task: What is the ten millions digit of 2501539280? Hence: 0 Task: What is the thousands digit of 5678085? Hence: 8 Task: What is the tens digit of 74161? Hence: 6 Task: What is the hundred thousands digit of 47084672? Hence: 0 Task: What is the units digit of 4764? Hence: 4 Task: What is the thousands digit of 219942? Hence: 9 Task: What is the ten thousands digit of 11525? Hence: 1 Task: What is the thousands digit of 3703? Hence: 3 Task: What is the ten millions digit of 4044
english
measurement: time ----------------- Question: What is 231 minutes after 9:02 AM? Soln: 12:53 PM Question: How many minutes are there between 4:07 AM and 9:03 AM? Soln: 296 Question: How many minutes are there between 4:59 AM and 4:18 PM? Soln: 679 Question: What is 525 minutes before 4:51 PM? Soln: 8:06 AM Question: How many minutes are there between 2:15 PM and 12:26 AM? Soln: 611 Question: What is 25 minutes before 12:14 PM? Soln: 11:49 AM Question: How many minutes are there between 4:40 AM and 5:39 AM? Soln: 59 Question: What is 592 minutes after 12:06 AM? Soln: 9:58 AM Question: How many minutes are there between 3:23 PM and 2:44 AM? Soln: 681 Question: What is 327 minutes after 7:39 AM? Soln: 1:06 PM Question: What is 195 minutes after 1:01 PM? Soln: 4:16 PM Question: What is 92 minutes after 3:52 AM? Soln: 5:24 AM Question: How many minutes are there between 10:44 PM and 2:48 AM? Soln: 244 Question: What is 557 minutes after 2:47 AM? Soln: 12:04 PM Question: How many minutes are there between 5:12 PM and 6:59 PM? Soln: 107 Question: How many minutes are there between 5:37 AM and 1:13 PM? Soln: 456 Question: How many minutes are there between 10:24 PM and 6:11 AM? Soln: 467 Question: How many minutes are there between 1:36 PM and 5:45 PM? Soln: 249 Question: What is 345 minutes after 2:02 AM? Soln: 7:47 AM Question: What is 207 minutes after 7:19 AM? Soln: 10:46 AM Question: What is 488 minutes before 3:19 PM? Soln: 7:11 AM Question: How many minutes are there between 4:33 AM and 2:03 PM? Soln: 570 Question: How many minutes are there between 5:37 PM and 5:36 AM? Soln: 719 Question: What is 204 minutes after 7:53 PM? Soln: 11:17 PM Question: What is 657 minutes after 7:33 PM? Soln: 6:30 AM Question: How many minutes are there between 5:49 PM and 1:12 AM? Soln: 443 Question: How many minutes are there between 8:21 AM and 2:32 PM? Soln: 371 Question: What is 148 minutes before 4:17 PM? Soln: 1:49 PM Question: How many minutes are there between 1:29 PM and 12:30
english
probability: swr p sequence --------------------------- Subject: Four letters picked without replacement from xtxuxyxletxte. What is prob of sequence xxly? Response: 1/858 Subject: Two letters picked without replacement from rqrcwnkwc. What is prob of sequence kc? Response: 1/36 Subject: Three letters picked without replacement from woswahsh. Give prob of sequence whs. Response: 1/42 Subject: What is prob of sequence qxs when three letters picked without replacement from {x: 2, r: 6, p: 2, q: 1, s: 1}? Response: 1/660 Subject: Three letters picked without replacement from {x: 4, p: 4, g: 1, b: 6, o: 1, s: 2}. What is prob of sequence gsb? Response: 1/408 Subject: Calculate prob of sequence vo when two letters picked without replacement from {v: 1, t: 2, u: 1, o: 3, n: 3, b: 1}. Response: 3/110 Subject: Two letters picked without replacement from {o: 1, h: 1, w: 3}. What is prob of sequence ho? Response: 1/20 Subject: Calculate prob of sequence ppmp when four letters picked without replacement from {m: 3, p: 9}. Response: 7/55 Subject: Calculate prob of sequence xx when two letters picked without replacement from {x: 10}. Response: 1 Subject: Two letters picked without replacement from xkkkxxxx. What is prob of sequence kx? Response: 15/56 Subject: Three letters picked without replacement from {r: 7, g: 5}. What is prob of sequence grg? Response: 7/66 Subject: What is prob of sequence gggg when four letters picked without replacement from gwwwgwgwwgwgg? Response: 3/143 Subject: Calculate prob of sequence svwb when four letters picked without replacement from bsvwn. Response: 1/120 Subject: Calculate prob of sequence eo when two letters picked without replacement from {d: 1, o: 2, e: 4, q: 1, x: 10}. Response: 4/153 Subject: Calculate prob of sequence nna when three letters picked without replacement from {m: 7, k: 2, l: 2, a: 1, x: 2, n: 2}. Response: 1/1680 Subject: Three letters picked without replacement from {t: 3, o: 5, b: 3, i: 2, r: 2}. What is prob of sequenc
english
numbers: is prime ----------------- Situation: Is 334642201 a prime number? Compute: True Situation: Is 203057 a composite number? Compute: False Situation: Is 15643341853 a composite number? Compute: False Situation: Is 10583757683 composite? Compute: True Situation: Is 1830519409 a composite number? Compute: True Situation: Is 19788919 composite? Compute: True Situation: Is 5093999423 a prime number? Compute: True Situation: Is 394934473 a composite number? Compute: False Situation: Is 869203 a composite number? Compute: False Situation: Is 313843961 a prime number? Compute: True Situation: Is 1151 prime? Compute: True Situation: Is 35491 a composite number? Compute: False Situation: Is 1850440297 composite? Compute: False Situation: Is 4249 composite? Compute: True Situation: Is 157320673 composite? Compute: True Situation: Is 52517 composite? Compute: False Situation: Is 102259 composite? Compute: False Situation: Is 5366377 composite? Compute: False Situation: Is 325590313 composite? Compute: True Situation: Is 137894 a prime number? Compute: False Situation: Is 194991 composite? Compute: True Situation: Is 17532077263 a prime number? Compute: False Situation: Is 82765169 composite? Compute: False Situation: Is 3615049 a prime number? Compute: False Situation: Is 6697013 prime? Compute: False Situation: Is 73939 prime? Compute: True Situation: Is 464468863 composite? Compute: False Situation: Is 1732721554 prime? Compute: False Situation: Is 233663 prime? Compute: True Situation: Is 43997 prime? Compute: True Situation: Is 685397707 a composite number? Compute: False Situation: Is 47063 prime? Compute: False Situation: Is 102373 prime? Compute: False Situation: Is 50341 composite? Compute: False Situation: Is 90846131 composite? Compute: False Situation: Is 1878377 composite? Compute: True Situation: Is 19385083087 a composite number? Compute: True Situation: Is 38993 composite? Compute: False Situation: Is 239594 a prime number? Compute: False Situation: Is 20
english
numbers: div remainder ---------------------- Ask: Calculate the remainder when 782054 is divided by 5175. Clarification: 629 Ask: Calculate the remainder when 339 is divided by 23. Clarification: 17 Ask: Calculate the remainder when 2393647 is divided by 134. Clarification: 5 Ask: What is the remainder when 896 is divided by 21? Clarification: 14 Ask: Calculate the remainder when 1254 is divided by 14. Clarification: 8 Ask: Calculate the remainder when 115674 is divided by 239. Clarification: 237 Ask: Calculate the remainder when 201 is divided by 5. Clarification: 1 Ask: Calculate the remainder when 5039 is divided by 1259. Clarification: 3 Ask: What is the remainder when 140 is divided by 18? Clarification: 14 Ask: What is the remainder when 350 is divided by 32? Clarification: 30 Ask: Calculate the remainder when 26334 is divided by 941. Clarification: 927 Ask: What is the remainder when 3426 is divided by 126? Clarification: 24 Ask: Calculate the remainder when 66331 is divided by 8290. Clarification: 11 Ask: Calculate the remainder when 398 is divided by 57. Clarification: 56 Ask: Calculate the remainder when 6088146 is divided by 1009. Clarification: 849 Ask: Calculate the remainder when 26790 is divided by 406. Clarification: 400 Ask: Calculate the remainder when 686 is divided by 195. Clarification: 101 Ask: Calculate the remainder when 3242 is divided by 50. Clarification: 42 Ask: What is the remainder when 157 is divided by 34? Clarification: 21 Ask: What is the remainder when 128 is divided by 68? Clarification: 60 Ask: What is the remainder when 60118 is divided by 210? Clarification: 58 Ask: Calculate the remainder when 81234639 is divided by 96. Clarification: 15 Ask: Calculate the remainder when 156282 is divided by 13. Clarification: 9 Ask: What is the remainder when 8073 is divided by 5? Clarification: 3 Ask: What is the remainder when 11005 is divided by 3465? Clarification: 610 Ask: Calculate the remainder when 664942 is divided by 7312. Clarific
english
measurement: conversion ----------------------- Situation: Convert 62113.37 micrometers to kilometers. Explanation: 0.00006211337 Situation: How many minutes are there in 17.107338s? Explanation: 0.2851223 Situation: What is 7.28 litres in millilitres? Explanation: 7280 Situation: What is three fifths of a litre in millilitres? Explanation: 600 Situation: How many weeks are there in 15711.9858 seconds? Explanation: 0.0259788125 Situation: What is 27/2 of a gram in milligrams? Explanation: 13500 Situation: What is eleven quarters of a millennium in months? Explanation: 33000 Situation: What is 52/5 of a litre in millilitres? Explanation: 10400 Situation: How many millilitres are there in 29/2 of a litre? Explanation: 14500 Situation: What is 3/50 of a kilometer in centimeters? Explanation: 6000 Situation: How many centimeters are there in 8657.294m? Explanation: 865729.4 Situation: How many nanoseconds are there in thirteen quarters of a microsecond? Explanation: 3250 Situation: How many milliseconds are there in 3/25 of a second? Explanation: 120 Situation: What is 21/4 of a litre in millilitres? Explanation: 5250 Situation: What is 3/50 of a meter in centimeters? Explanation: 6 Situation: What is 29/3 of a decade in months? Explanation: 1160 Situation: Convert 703156.8ms to seconds. Explanation: 703.1568 Situation: Convert 45139.31 hours to nanoseconds. Explanation: 162501516000000000 Situation: Convert 8795.471 years to decades. Explanation: 879.5471 Situation: How many years are there in 0.264502 centuries? Explanation: 26.4502 Situation: What is 147.673kg in tonnes? Explanation: 0.147673 Situation: How many micrometers are there in 2684.42 nanometers? Explanation: 2.68442 Situation: How many years are there in 4928.55 months? Explanation: 410.7125 Situation: What is 4/3 of a week in hours? Explanation: 224 Situation: Convert 179.1356 milligrams to kilograms. Explanation: 0.0001791356 Situation: How many millennia are there in 101153.4 decades? Explanation: 1011.
english
numbers: gcd ------------ Request: Calculate the highest common factor of 1295 and 5. Thus: 5 Request: What is the highest common divisor of 603 and 18? Thus: 9 Request: Calculate the greatest common factor of 5969 and 47. Thus: 47 Request: What is the greatest common divisor of 248 and 352718? Thus: 62 Request: What is the highest common divisor of 219 and 504576? Thus: 219 Request: Calculate the greatest common divisor of 915 and 15. Thus: 15 Request: Calculate the greatest common factor of 39996 and 91834452. Thus: 3636 Request: Calculate the highest common divisor of 1386 and 66. Thus: 66 Request: Calculate the highest common divisor of 12415903 and 93. Thus: 31 Request: Calculate the highest common factor of 18998 and 90492902. Thus: 2714 Request: Calculate the greatest common divisor of 68324 and 464. Thus: 116 Request: Calculate the highest common factor of 1554 and 1281. Thus: 21 Request: Calculate the highest common divisor of 1360 and 92. Thus: 4 Request: What is the greatest common divisor of 41484 and 24? Thus: 12 Request: What is the highest common factor of 3941 and 118793? Thus: 563 Request: What is the greatest common divisor of 96 and 1282608? Thus: 48 Request: What is the highest common divisor of 139806 and 108? Thus: 54 Request: What is the highest common factor of 2771 and 17? Thus: 17 Request: What is the greatest common divisor of 225 and 27? Thus: 9 Request: Calculate the greatest common divisor of 870 and 4. Thus: 2 Request: What is the highest common factor of 164 and 4018? Thus: 82 Request: What is the highest common factor of 88974 and 80334? Thus: 18 Request: Calculate the highest common factor of 105 and 33. Thus: 3 Request: Calculate the highest common factor of 108 and 54. Thus: 54 Request: What is the highest common divisor of 384753 and 14127? Thus: 831 Request: What is the greatest common factor of 476812 and 40208? Thus: 28 Request: Calculate the highest common factor of 1001 and 113659. Thus: 91 Request: What is the highest commo
english
numbers: place value -------------------- Qn: What is the hundred thousands digit of 1258387816? Fix: 3 Qn: What is the thousands digit of 24759984? Fix: 9 Qn: What is the hundred thousands digit of 128093425? Fix: 0 Qn: What is the thousands digit of 27354? Fix: 7 Qn: What is the hundreds digit of 16201? Fix: 2 Qn: What is the units digit of 28068768? Fix: 8 Qn: What is the thousands digit of 118317? Fix: 8 Qn: What is the millions digit of 6233863? Fix: 6 Qn: What is the tens digit of 4846446246? Fix: 4 Qn: What is the tens digit of 708519612? Fix: 1 Qn: What is the tens digit of 20918? Fix: 1 Qn: What is the hundreds digit of 895992059? Fix: 0 Qn: What is the thousands digit of 957860484? Fix: 0 Qn: What is the ten thousands digit of 7181473? Fix: 8 Qn: What is the hundred thousands digit of 134404? Fix: 1 Qn: What is the ten millions digit of 1231580214? Fix: 3 Qn: What is the ten thousands digit of 332495? Fix: 3 Qn: What is the tens digit of 34100967? Fix: 6 Qn: What is the hundreds digit of 1231888856? Fix: 8 Qn: What is the tens digit of 906? Fix: 0 Qn: What is the hundreds digit of 349148? Fix: 1 Qn: What is the units digit of 3939460115? Fix: 5 Qn: What is the units digit of 874953? Fix: 3 Qn: What is the tens digit of 28230? Fix: 3 Qn: What is the hundred millions digit of 240641995? Fix: 2 Qn: What is the thousands digit of 4062629? Fix: 2 Qn: What is the units digit of 492? Fix: 2 Qn: What is the units digit of 36813? Fix: 3 Qn: What is the tens digit of 11255? Fix: 5 Qn: What is the thousands digit of 22051? Fix: 2 Qn: What is the tens digit of 7511443? Fix: 4 Qn: What is the tens digit of 1465883738? Fix: 3 Qn: What is the ten millions digit of 27317116? Fix: 2 Qn: What is the tens digit of 898080? Fix: 8 Qn: What is the hundreds digit of 705454? Fix: 4 Qn: What is the ten thousands digit of 3729230? Fix: 2 Qn: What is the hundreds digit of 4020451? Fix: 4 Qn: What is the ten thousands digit of 10866? Fix: 1 Qn: What is the tens digit of 1194? Fix: 9
english
numbers: is factor ------------------ Problem #: Does 45 divide 41596965? Resolution: True Problem #: Is 11251739 a multiple of 147? Resolution: False Problem #: Does 31 divide 771? Resolution: False Problem #: Does 62 divide 88983020? Resolution: True Problem #: Is 5457370 a multiple of 19? Resolution: True Problem #: Is 105 a multiple of 7? Resolution: True Problem #: Is 10 a factor of 9645349? Resolution: False Problem #: Is 82 a factor of 33368? Resolution: False Problem #: Is 143771 a multiple of 254? Resolution: False Problem #: Does 31 divide 31? Resolution: True Problem #: Is 114759 a multiple of 13? Resolution: False Problem #: Is 3 a factor of 316? Resolution: False Problem #: Does 107 divide 3017400? Resolution: True Problem #: Is 927 a multiple of 56? Resolution: False Problem #: Is 8 a factor of 171409816? Resolution: True Problem #: Is 2095747 a multiple of 273? Resolution: False Problem #: Is 6988230 a multiple of 37? Resolution: False Problem #: Is 407 a multiple of 18? Resolution: False Problem #: Is 1256328539 a multiple of 58? Resolution: False Problem #: Is 436 a factor of 116848? Resolution: True Problem #: Does 561 divide 785400? Resolution: True Problem #: Does 6 divide 8007048? Resolution: True Problem #: Is 325 a factor of 1290765? Resolution: False Problem #: Does 19 divide 577711811? Resolution: False Problem #: Does 964 divide 5281756? Resolution: True Problem #: Is 258 a multiple of 6? Resolution: True Problem #: Does 2 divide 1774183? Resolution: False Problem #: Does 41 divide 4462? Resolution: False Problem #: Does 34 divide 1700? Resolution: True Problem #: Does 43 divide 2365? Resolution: True Problem #: Does 9 divide 42615? Resolution: True Problem #: Is 11018376 a multiple of 391? Resolution: False Problem #: Does 105 divide 25525? Resolution: False Problem #: Is 4421544 a multiple of 24? Resolution: True Problem #: Is 16 a factor of 91081211? Resolution: False Problem #: Is 86 a factor of 34097? Resolution: False Problem #: Is 42
english
measurement: time ----------------- Problem: How many minutes are there between 1:29 PM and 6:12 PM? Sol: 283 Problem: How many minutes are there between 8:44 PM and 8:00 AM? Sol: 676 Problem: How many minutes are there between 1:53 PM and 9:47 PM? Sol: 474 Problem: How many minutes are there between 6:47 AM and 9:21 AM? Sol: 154 Problem: How many minutes are there between 12:43 PM and 6:08 PM? Sol: 325 Problem: What is 401 minutes after 12:20 AM? Sol: 7:01 AM Problem: What is 488 minutes before 4:23 PM? Sol: 8:15 AM Problem: How many minutes are there between 11:32 AM and 10:34 PM? Sol: 662 Problem: How many minutes are there between 3:15 PM and 6:19 PM? Sol: 184 Problem: What is 101 minutes before 4:52 AM? Sol: 3:11 AM Problem: How many minutes are there between 2:41 AM and 7:46 AM? Sol: 305 Problem: What is 681 minutes after 4:54 PM? Sol: 4:15 AM Problem: How many minutes are there between 12:31 AM and 5:53 AM? Sol: 322 Problem: What is 678 minutes before 1:56 AM? Sol: 2:38 PM Problem: What is 525 minutes before 10:01 AM? Sol: 1:16 AM Problem: How many minutes are there between 2:23 PM and 1:50 AM? Sol: 687 Problem: How many minutes are there between 3:17 AM and 4:55 AM? Sol: 98 Problem: What is 456 minutes after 11:08 PM? Sol: 6:44 AM Problem: What is 520 minutes before 11:40 AM? Sol: 3:00 AM Problem: How many minutes are there between 11:57 AM and 1:58 PM? Sol: 121 Problem: How many minutes are there between 7:23 AM and 10:10 AM? Sol: 167 Problem: How many minutes are there between 5:06 AM and 3:42 PM? Sol: 636 Problem: How many minutes are there between 1:11 AM and 6:03 AM? Sol: 292 Problem: How many minutes are there between 9:10 PM and 8:41 AM? Sol: 691 Problem: What is 14 minutes before 5:12 PM? Sol: 4:58 PM Problem: How many minutes are there between 6:13 AM and 7:24 AM? Sol: 71 Problem: What is 277 minutes after 11:42 AM? Sol: 4:19 PM Problem: How many minutes are there between 7:15 PM and 9:43 PM? Sol: 148 Problem: How many minutes are there between 10:0
english
numbers: gcd ------------ Q/A: What is the greatest common divisor of 168 and 15480? A: 24 Q/A: What is the highest common divisor of 117 and 54? A: 9 Q/A: What is the highest common divisor of 759 and 18469? A: 253 Q/A: What is the highest common factor of 132 and 75202842? A: 66 Q/A: What is the greatest common factor of 458656 and 32? A: 32 Q/A: What is the highest common factor of 489091527 and 2241? A: 2241 Q/A: What is the highest common divisor of 22 and 265765742? A: 22 Q/A: Calculate the greatest common factor of 282 and 36240102. A: 282 Q/A: What is the greatest common divisor of 45 and 11008485? A: 45 Q/A: What is the greatest common divisor of 1317404 and 638? A: 22 Q/A: What is the greatest common factor of 365432 and 68? A: 68 Q/A: Calculate the highest common factor of 66 and 4032171. A: 33 Q/A: What is the highest common factor of 5668432 and 5136? A: 1712 Q/A: What is the highest common divisor of 20979 and 1104873? A: 21 Q/A: What is the highest common divisor of 93951 and 3796? A: 949 Q/A: Calculate the highest common factor of 104 and 1144. A: 104 Q/A: What is the greatest common divisor of 69 and 552? A: 69 Q/A: What is the highest common divisor of 122915 and 465? A: 155 Q/A: What is the highest common divisor of 353513 and 337? A: 337 Q/A: What is the highest common divisor of 398 and 131513727? A: 199 Q/A: Calculate the highest common divisor of 20284 and 9020. A: 44 Q/A: Calculate the highest common factor of 85839 and 7545369. A: 1209 Q/A: What is the highest common factor of 57812 and 1940? A: 388 Q/A: Calculate the highest common factor of 958600 and 4200. A: 200 Q/A: Calculate the greatest common divisor of 2326 and 5337565240. A: 2326 Q/A: What is the highest common factor of 52389032 and 16? A: 8 Q/A: What is the highest common factor of 1048 and 56? A: 8 Q/A: What is the highest common divisor of 312463 and 1592293? A: 1153 Q/A: What is the greatest common divisor of 2166625 and 500? A: 125 Q/A: What is the greatest common divisor of
english
measurement: conversion ----------------------- Exercise: How many litres are there in 330.7517ml? Calculation: 0.3307517 Exercise: How many decades are there in 610.8714 centuries? Calculation: 6108.714 Exercise: How many nanometers are there in fourty-five halves of a micrometer? Calculation: 22500 Exercise: Convert 57.60711 centuries to months. Calculation: 69128.532 Exercise: How many milliseconds are there in 3.428573 nanoseconds? Calculation: 0.000003428573 Exercise: What is 7/8 of a kilogram in grams? Calculation: 875 Exercise: How many nanograms are there in twenty-one halves of a microgram? Calculation: 10500 Exercise: What is 3/10 of a litre in millilitres? Calculation: 300 Exercise: How many milligrams are there in 7032.697 tonnes? Calculation: 7032697000000 Exercise: Convert 125.9631 millimeters to centimeters. Calculation: 12.59631 Exercise: How many micrometers are there in fifty-three fifths of a millimeter? Calculation: 10600 Exercise: What is 9493.085 decades in years? Calculation: 94930.85 Exercise: How many months are there in 13/8 of a decade? Calculation: 195 Exercise: How many millilitres are there in thirty-one fifths of a litre? Calculation: 6200 Exercise: What is 3/8 of a kilometer in meters? Calculation: 375 Exercise: What is 34/5 of a litre in millilitres? Calculation: 6800 Exercise: Convert 7.633653 millimeters to kilometers. Calculation: 0.000007633653 Exercise: How many kilograms are there in 90.63774 tonnes? Calculation: 90637.74 Exercise: How many months are there in nine tenths of a millennium? Calculation: 10800 Exercise: How many grams are there in 3/50 of a kilogram? Calculation: 60 Exercise: How many millilitres are there in 1/4 of a litre? Calculation: 250 Exercise: How many millilitres are there in 8366.78 litres? Calculation: 8366780 Exercise: Convert 94581.61ml to litres. Calculation: 94.58161 Exercise: Convert 43.53317l to millilitres. Calculation: 43533.17 Exercise: How many micrograms are there in 102959.6ng? Calculation:
english
arithmetic: nearest integer root -------------------------------- Question: What is 1329647 to the power of 1/8, to the nearest integer? Final Answer: 6 Question: What is 2423 to the power of 1/7, to the nearest integer? Final Answer: 3 Question: What is the cube root of 2154182302 to the nearest integer? Final Answer: 1291 Question: What is 1115520030 to the power of 1/3, to the nearest integer? Final Answer: 1037 Question: What is 1601056640 to the power of 1/2, to the nearest integer? Final Answer: 40013 Question: What is 29442857 to the power of 1/2, to the nearest integer? Final Answer: 5426 Question: What is 3524530 to the power of 1/4, to the nearest integer? Final Answer: 43 Question: What is 3367 to the power of 1/4, to the nearest integer? Final Answer: 8 Question: What is the cube root of 1265 to the nearest integer? Final Answer: 11 Question: What is 80106 to the power of 1/10, to the nearest integer? Final Answer: 3 Question: What is the cube root of 2926876 to the nearest integer? Final Answer: 143 Question: What is the square root of 38461288 to the nearest integer? Final Answer: 6202 Question: What is the sixth root of 7373283 to the nearest integer? Final Answer: 14 Question: What is the square root of 2137 to the nearest integer? Final Answer: 46 Question: What is 2895060 to the power of 1/3, to the nearest integer? Final Answer: 143 Question: What is 24717912 to the power of 1/3, to the nearest integer? Final Answer: 291 Question: What is 7992148 to the power of 1/9, to the nearest integer? Final Answer: 6 Question: What is the square root of 136868 to the nearest integer? Final Answer: 370 Question: What is the square root of 60161 to the nearest integer? Final Answer: 245 Question: What is the square root of 592894638 to the nearest integer? Final Answer: 24349 Question: What is 146 to the power of 1/4, to the nearest integer? Final Answer: 3 Question: What is 5716 to the power of 1/3, to the nearest integer? Final Answer: 18 Question: What is t
english
measurement: conversion ----------------------- Q=: How many weeks are there in 136.96879 days? Response: 19.56697 Q=: What is eleven halves of a millennium in months? Response: 66000 Q=: How many millennia are there in 0.3495618 centuries? Response: 0.03495618 Q=: Convert 0.0220463 millennia to decades. Response: 2.20463 Q=: How many micrograms are there in twenty-five halves of a milligram? Response: 12500 Q=: How many days are there in 2410.78707 seconds? Response: 0.027902628125 Q=: How many meters are there in 21/8 of a kilometer? Response: 2625 Q=: What is 72435.96 millilitres in litres? Response: 72.43596 Q=: What is 13065.06 minutes in seconds? Response: 783903.6 Q=: What is one tenth of a week in seconds? Response: 60480 Q=: How many minutes are there in three tenths of a day? Response: 432 Q=: How many millilitres are there in 18/5 of a litre? Response: 3600 Q=: How many milligrams are there in thirteen eighths of a gram? Response: 1625 Q=: What is 158406.6t in milligrams? Response: 158406600000000 Q=: What is 52/3 of a decade in months? Response: 2080 Q=: Convert 0.2036846m to kilometers. Response: 0.0002036846 Q=: How many milligrams are there in 21228.83g? Response: 21228830 Q=: What is 3.602018 tonnes in milligrams? Response: 3602018000 Q=: How many micrograms are there in 271.0228 tonnes? Response: 271022800000000 Q=: Convert 3990.439l to millilitres. Response: 3990439 Q=: Convert 0.304929 meters to centimeters. Response: 30.4929 Q=: How many meters are there in 449.7231mm? Response: 0.4497231 Q=: How many micrometers are there in one fifth of a millimeter? Response: 200 Q=: What is 4822.374 years in decades? Response: 482.2374 Q=: How many millimeters are there in eleven halves of a centimeter? Response: 55 Q=: How many milliseconds are there in one fifteenth of a minute? Response: 4000 Q=: How many tonnes are there in 426.7551mg? Response: 0.0000004267551 Q=: How many grams are there in 6/25 of a kilogram? Response: 240 Q=: What is six fifths of a c
english
numbers: is factor ------------------ Problem: Is 28815 a multiple of 255? Solution: True Problem: Does 4 divide 10733? Solution: False Problem: Is 570380 a multiple of 20? Solution: True Problem: Does 91 divide 28732249? Solution: True Problem: Is 462 a multiple of 33? Solution: True Problem: Does 4 divide 4248? Solution: True Problem: Does 12 divide 162624? Solution: True Problem: Does 8970 divide 1685027634? Solution: False Problem: Is 13410589 a multiple of 37? Solution: False Problem: Does 35 divide 35506030? Solution: True Problem: Is 5121 a multiple of 9? Solution: True Problem: Is 578195037 a multiple of 189? Solution: True Problem: Does 20 divide 30400? Solution: True Problem: Does 412 divide 570713834? Solution: False Problem: Is 862 a factor of 174476794? Solution: False Problem: Does 8 divide 1090? Solution: False Problem: Is 8 a factor of 180872? Solution: True Problem: Is 997 a multiple of 22? Solution: False Problem: Does 232 divide 94448360? Solution: True Problem: Is 1919 a factor of 610689127? Solution: True Problem: Does 158 divide 54820954? Solution: False Problem: Is 729 a multiple of 27? Solution: True Problem: Does 53 divide 591153692? Solution: False Problem: Is 195 a multiple of 49? Solution: False Problem: Is 2438 a factor of 1516121498? Solution: True Problem: Does 1572 divide 187486152? Solution: True Problem: Does 49 divide 261758? Solution: True Problem: Is 4 a factor of 64759? Solution: False Problem: Does 625 divide 7958750? Solution: True Problem: Is 512 a factor of 1856839? Solution: False Problem: Is 10560 a multiple of 15? Solution: True Problem: Is 51 a multiple of 13? Solution: False Problem: Is 5721926 a multiple of 277? Solution: False Problem: Does 16 divide 20474? Solution: False Problem: Is 6609704 a multiple of 620? Solution: False Problem: Does 255 divide 2894482? Solution: False Problem: Does 13 divide 1162? Solution: False Problem: Is 495 a factor of 1355113485? Solution: True Problem: Is 21948 a multiple of 93? Solutio
english
measurement: conversion ----------------------- Question: How many kilograms are there in three fifths of a tonne? A: 600 Question: What is one fifteenth of a century in months? A: 80 Question: Convert 41988.8 weeks to hours. A: 7054118.4 Question: What is 23/3 of a week in minutes? A: 77280 Question: How many millilitres are there in twenty-nine halves of a litre? A: 14500 Question: Convert 99927.49 millilitres to litres. A: 99.92749 Question: How many micrometers are there in 3/50 of a centimeter? A: 600 Question: What is eleven tenths of a centimeter in millimeters? A: 11 Question: What is one sixth of a century in months? A: 200 Question: How many decades are there in 6/5 of a century? A: 12 Question: What is five eighths of a microgram in nanograms? A: 625 Question: How many centimeters are there in 7/16 of a kilometer? A: 43750 Question: What is seven quarters of a year in months? A: 21 Question: Convert 3.465595kg to micrograms. A: 3465595000 Question: What is seven eighths of a day in hours? A: 21 Question: How many kilograms are there in 13/4 of a tonne? A: 3250 Question: What is 56.88577 nanograms in tonnes? A: 0.00000000000005688577 Question: How many centuries are there in 0.6133945 decades? A: 0.06133945 Question: Convert 1783.243 nanometers to millimeters. A: 0.001783243 Question: How many nanoseconds are there in sixty-one halves of a microsecond? A: 30500 Question: How many millilitres are there in twenty-five halves of a litre? A: 12500 Question: Convert 7.607836km to nanometers. A: 7607836000000 Question: How many days are there in 7.0584723ms? A: 0.00000008169528125 Question: What is 145728.1854us in weeks? A: 0.0000002409526875 Question: How many microseconds are there in one tenth of a millisecond? A: 100 Question: How many months are there in 1/16 of a century? A: 75 Question: What is seventy-five eighths of a litre in millilitres? A: 9375 Question: Convert 35.14799 micrometers to meters. A: 0.00003514799 Question: How many months are there in
english
probability: swr p sequence --------------------------- Problem: Three letters picked without replacement from zzzzzzkkzz. Give prob of sequence zkk. Workthrough: 1/45 Problem: Calculate prob of sequence hhww when four letters picked without replacement from {w: 5, h: 5}. Workthrough: 5/63 Problem: Two letters picked without replacement from {p: 4, s: 2, i: 4, l: 4}. Give prob of sequence pi. Workthrough: 8/91 Problem: Calculate prob of sequence ei when two letters picked without replacement from igiegxg. Workthrough: 1/21 Problem: What is prob of sequence xgx when three letters picked without replacement from {x: 3, g: 2, m: 2, q: 4, y: 1}? Workthrough: 1/110 Problem: Four letters picked without replacement from zzizzzcziczzz. Give prob of sequence zzzz. Workthrough: 126/715 Problem: Calculate prob of sequence qqaa when four letters picked without replacement from qqqqaqaqhaqaa. Workthrough: 7/143 Problem: What is prob of sequence oooe when four letters picked without replacement from {e: 11, o: 9}? Workthrough: 77/1615 Problem: Calculate prob of sequence ca when two letters picked without replacement from {n: 2, c: 1, q: 1, s: 1, x: 2, a: 7}. Workthrough: 1/26 Problem: Three letters picked without replacement from {h: 4, y: 3, x: 1}. What is prob of sequence hyh? Workthrough: 3/28 Problem: What is prob of sequence qee when three letters picked without replacement from {e: 11, d: 1, q: 7}? Workthrough: 385/2907 Problem: Calculate prob of sequence jo when two letters picked without replacement from {c: 2, a: 5, k: 5, o: 1, j: 3}. Workthrough: 1/80 Problem: What is prob of sequence pxpp when four letters picked without replacement from pxpxppppppppxppp? Workthrough: 33/280 Problem: Calculate prob of sequence tp when two letters picked without replacement from ojohjprrt. Workthrough: 1/72 Problem: What is prob of sequence xx when two letters picked without replacement from {x: 3, a: 1}? Workthrough: 1/2 Problem: What is prob of sequence pw when two letters picked with
english
measurement: time ----------------- Test item: How many minutes are there between 12:46 AM and 3:26 AM? Gives: 160 Test item: What is 457 minutes after 8:45 PM? Gives: 4:22 AM Test item: What is 581 minutes after 8:16 AM? Gives: 5:57 PM Test item: How many minutes are there between 2:00 PM and 11:51 PM? Gives: 591 Test item: What is 406 minutes after 10:50 PM? Gives: 5:36 AM Test item: What is 309 minutes after 5:00 AM? Gives: 10:09 AM Test item: How many minutes are there between 9:44 AM and 12:37 PM? Gives: 173 Test item: What is 599 minutes before 5:44 PM? Gives: 7:45 AM Test item: How many minutes are there between 5:45 AM and 8:13 AM? Gives: 148 Test item: How many minutes are there between 10:48 PM and 6:58 AM? Gives: 490 Test item: How many minutes are there between 3:02 AM and 2:46 PM? Gives: 704 Test item: How many minutes are there between 5:55 AM and 5:43 PM? Gives: 708 Test item: How many minutes are there between 12:46 AM and 7:45 AM? Gives: 419 Test item: What is 324 minutes after 11:45 AM? Gives: 5:09 PM Test item: How many minutes are there between 6:06 AM and 12:50 PM? Gives: 404 Test item: How many minutes are there between 9:30 PM and 11:45 PM? Gives: 135 Test item: What is 504 minutes after 8:55 PM? Gives: 5:19 AM Test item: How many minutes are there between 8:06 AM and 10:46 AM? Gives: 160 Test item: What is 643 minutes after 2:57 AM? Gives: 1:40 PM Test item: How many minutes are there between 12:44 PM and 8:17 PM? Gives: 453 Test item: What is 27 minutes before 3:45 PM? Gives: 3:18 PM Test item: What is 153 minutes after 12:12 AM? Gives: 2:45 AM Test item: How many minutes are there between 2:08 PM and 6:14 PM? Gives: 246 Test item: What is 492 minutes after 1:52 AM? Gives: 10:04 AM Test item: How many minutes are there between 11:09 PM and 12:31 AM? Gives: 82 Test item: How many minutes are there between 7:48 PM and 1:59 AM? Gives: 371 Test item: What is 568 minutes after 12:56 PM? Gives: 10:24 PM Test item: How many minutes are there betwee
english
arithmetic: nearest integer root -------------------------------- Example: What is the sixth root of 190888 to the nearest integer? Math A: 8 Example: What is 979 to the power of 1/10, to the nearest integer? Math A: 2 Example: What is the cube root of 1119 to the nearest integer? Math A: 10 Example: What is the third root of 396 to the nearest integer? Math A: 7 Example: What is the cube root of 36474 to the nearest integer? Math A: 33 Example: What is the square root of 1491310 to the nearest integer? Math A: 1221 Example: What is 434182 to the power of 1/10, to the nearest integer? Math A: 4 Example: What is 237202727 to the power of 1/3, to the nearest integer? Math A: 619 Example: What is the sixth root of 626894909 to the nearest integer? Math A: 29 Example: What is 17662158 to the power of 1/9, to the nearest integer? Math A: 6 Example: What is 229123 to the power of 1/2, to the nearest integer? Math A: 479 Example: What is the third root of 4222228 to the nearest integer? Math A: 162 Example: What is 5196 to the power of 1/5, to the nearest integer? Math A: 6 Example: What is 758522 to the power of 1/10, to the nearest integer? Math A: 4 Example: What is 49345 to the power of 1/3, to the nearest integer? Math A: 37 Example: What is 464684 to the power of 1/7, to the nearest integer? Math A: 6 Example: What is 7377555 to the power of 1/10, to the nearest integer? Math A: 5 Example: What is the third root of 16241053 to the nearest integer? Math A: 253 Example: What is 533712866 to the power of 1/2, to the nearest integer? Math A: 23102 Example: What is the ninth root of 164021842 to the nearest integer? Math A: 8 Example: What is the square root of 22320 to the nearest integer? Math A: 149 Example: What is 244122067 to the power of 1/2, to the nearest integer? Math A: 15624 Example: What is the cube root of 966943832 to the nearest integer? Math A: 989 Example: What is the square root of 6766 to the nearest integer? Math A: 82 Example: What is 11872662 to the
english
measurement: conversion ----------------------- Scenario: What is thirteen quarters of a millennium in years? A: 3250 Scenario: Convert 766.5156 millilitres to litres. A: 0.7665156 Scenario: Convert 86.33001 milligrams to kilograms. A: 0.00008633001 Scenario: Convert 9.09771 years to months. A: 109.17252 Scenario: Convert 476.3745 decades to millennia. A: 4.763745 Scenario: How many grams are there in 11/8 of a kilogram? A: 1375 Scenario: What is seven eighths of a microgram in nanograms? A: 875 Scenario: What is 3/10 of a century in decades? A: 3 Scenario: How many micrometers are there in one sixteenth of a meter? A: 62500 Scenario: What is 8518.319 millennia in years? A: 8518319 Scenario: How many milligrams are there in 0.0878953t? A: 87895300 Scenario: What is 610621.7mm in micrometers? A: 610621700 Scenario: What is 39040.17l in millilitres? A: 39040170 Scenario: What is 0.7824302cm in meters? A: 0.007824302 Scenario: Convert 10840.27 litres to millilitres. A: 10840270 Scenario: How many millilitres are there in three eighths of a litre? A: 375 Scenario: What is 6373.306nm in micrometers? A: 6.373306 Scenario: How many millilitres are there in eighteen fifths of a litre? A: 3600 Scenario: How many hours are there in 5739141.6 milliseconds? A: 1.594206 Scenario: How many micrometers are there in 6/5 of a centimeter? A: 12000 Scenario: How many millilitres are there in fifty-four fifths of a litre? A: 10800 Scenario: What is 8085.705 days in minutes? A: 11643415.2 Scenario: Convert 0.4758401 millilitres to litres. A: 0.0004758401 Scenario: How many micrograms are there in 1/4 of a milligram? A: 250 Scenario: How many decades are there in 2349597.6 months? A: 19579.98 Scenario: How many centuries are there in 4585.892 millennia? A: 45858.92 Scenario: How many nanograms are there in 23.79689 tonnes? A: 23796890000000000 Scenario: What is 17/4 of a meter in centimeters? A: 425 Scenario: How many millennia are there in 3207.406 years? A: 3.207406 Scenario: Convert 2
english
probability: swr p level set ---------------------------- Example: Three letters picked without replacement from vviiivrvvvvirr. What is prob of picking 1 v and 2 r? Thus: 3/52 Example: What is prob of picking 1 x, 2 v, and 1 t when four letters picked without replacement from {v: 6, c: 1, x: 1, t: 2, j: 3}? Thus: 6/143 Example: Calculate prob of picking 3 k and 1 g when four letters picked without replacement from {g: 2, k: 5}. Thus: 4/7 Example: Three letters picked without replacement from fxxxfxxf. What is prob of picking 2 x and 1 f? Thus: 15/28 Example: Four letters picked without replacement from {i: 11, u: 1, s: 2}. Give prob of picking 2 i and 2 s. Thus: 5/91 Example: Calculate prob of picking 1 m and 1 e when two letters picked without replacement from {i: 2, m: 2, h: 4, a: 8, s: 3, e: 1}. Thus: 1/95 Example: Two letters picked without replacement from {q: 1, i: 5, f: 3, a: 4, j: 1}. What is prob of picking 1 q and 1 a? Thus: 4/91 Example: Four letters picked without replacement from aaaaaaa. What is prob of picking 4 a? Thus: 1 Example: Four letters picked without replacement from {q: 2, u: 2, w: 1}. What is prob of picking 1 w, 1 q, and 2 u? Thus: 2/5 Example: Two letters picked without replacement from ddoglgggg. What is prob of picking 1 g and 1 o? Thus: 5/36 Example: What is prob of picking 2 j when two letters picked without replacement from jjjqjjjj? Thus: 3/4 Example: Two letters picked without replacement from {s: 4, v: 4, h: 2}. What is prob of picking 2 v? Thus: 2/15 Example: What is prob of picking 1 r and 1 e when two letters picked without replacement from {r: 5, q: 2, u: 5, e: 3}? Thus: 1/7 Example: Four letters picked without replacement from {t: 2, g: 1, k: 2, v: 2, r: 1}. What is prob of picking 1 k, 1 t, 1 v, and 1 g? Thus: 4/35 Example: What is prob of picking 1 x and 1 o when two letters picked without replacement from {l: 1, x: 7, o: 4, j: 2}? Thus: 4/13 Example: Calculate prob of picking 1 i and 3 j when four letters picked without r
english
probability: swr p sequence --------------------------- Query: Four letters picked without replacement from frmrmmjmrfmm. What is prob of sequence rjfm? Steps: 1/330 Query: Calculate prob of sequence fso when three letters picked without replacement from {t: 1, g: 1, o: 1, f: 1, s: 4}. Steps: 1/84 Query: Calculate prob of sequence byo when three letters picked without replacement from ylookyb. Steps: 2/105 Query: Calculate prob of sequence km when two letters picked without replacement from beekmtmmterkbk. Steps: 9/182 Query: Four letters picked without replacement from {s: 5, e: 2, i: 7}. Give prob of sequence isse. Steps: 5/429 Query: Calculate prob of sequence ownn when four letters picked without replacement from {z: 4, n: 9, e: 1, o: 1, t: 1, w: 1}. Steps: 3/2380 Query: What is prob of sequence gg when two letters picked without replacement from {g: 2, a: 6, y: 1, w: 1, f: 4, d: 4}? Steps: 1/153 Query: Two letters picked without replacement from {l: 3, r: 13}. Give prob of sequence ll. Steps: 1/40 Query: What is prob of sequence gg when two letters picked without replacement from {s: 5, c: 1, g: 2, b: 6, l: 3}? Steps: 1/136 Query: Calculate prob of sequence rmp when three letters picked without replacement from rmhpmpmibmrr. Steps: 1/55 Query: Calculate prob of sequence ccm when three letters picked without replacement from {s: 1, x: 2, m: 3, c: 3, e: 2, l: 1}. Steps: 3/220 Query: Calculate prob of sequence zo when two letters picked without replacement from ozrsoxrp. Steps: 1/28 Query: Calculate prob of sequence uv when two letters picked without replacement from zubvyzzybuzzbbbzu. Steps: 3/272 Query: Calculate prob of sequence aa when two letters picked without replacement from mazaa. Steps: 3/10 Query: Three letters picked without replacement from {z: 7, c: 1, j: 1, v: 2, q: 3}. What is prob of sequence cvq? Steps: 1/364 Query: What is prob of sequence eraa when four letters picked without replacement from {a: 4, r: 1, k: 1, q: 4, e: 5}? Steps: 1/546 Query:
english
numbers: is prime ----------------- Topic: Is 7723030277 composite? Therefore: False Topic: Is 210215 a composite number? Therefore: True Topic: Is 66799112447 prime? Therefore: True Topic: Is 32569 a prime number? Therefore: True Topic: Is 1740637 a prime number? Therefore: False Topic: Is 36777094 a composite number? Therefore: True Topic: Is 14961 composite? Therefore: True Topic: Is 84629 composite? Therefore: False Topic: Is 502297 composite? Therefore: True Topic: Is 5171 prime? Therefore: True Topic: Is 3461102 composite? Therefore: True Topic: Is 4854811 composite? Therefore: True Topic: Is 529 composite? Therefore: True Topic: Is 23188841111 a prime number? Therefore: True Topic: Is 12490923629 a prime number? Therefore: True Topic: Is 473868779 a composite number? Therefore: False Topic: Is 4041989 prime? Therefore: False Topic: Is 3407 a prime number? Therefore: True Topic: Is 57487 composite? Therefore: False Topic: Is 398144447 a prime number? Therefore: False Topic: Is 526387 prime? Therefore: True Topic: Is 493753061 a composite number? Therefore: False Topic: Is 281495 a prime number? Therefore: False Topic: Is 9793205417 prime? Therefore: True Topic: Is 99107891 prime? Therefore: True Topic: Is 18980797 composite? Therefore: True Topic: Is 31937693 a prime number? Therefore: True Topic: Is 4297897 a composite number? Therefore: False Topic: Is 22189 prime? Therefore: True Topic: Is 936391 prime? Therefore: True Topic: Is 11625709 prime? Therefore: False Topic: Is 186362521 a composite number? Therefore: True Topic: Is 1719724603 composite? Therefore: False Topic: Is 8172811 a composite number? Therefore: True Topic: Is 100161641 prime? Therefore: False Topic: Is 1181615 a composite number? Therefore: True Topic: Is 2894 composite? Therefore: True Topic: Is 70812151 prime? Therefore: True Topic: Is 2147419 a composite number? Therefore: False Topic: Is 9939 prime? Therefore: False Topic: Is 8055779 a prime number? Therefore: True Topic: Is 4621 a com
english
numbers: is factor ------------------ Let us solve: Is 80 a factor of 50349? Calculation: False Let us solve: Is 7 a factor of 161? Calculation: True Let us solve: Is 18898 a multiple of 22? Calculation: True Let us solve: Is 3736903 a multiple of 116? Calculation: False Let us solve: Is 12184625 a multiple of 25? Calculation: True Let us solve: Is 26632580 a multiple of 26? Calculation: True Let us solve: Does 11 divide 79771461? Calculation: True Let us solve: Is 79 a factor of 88322? Calculation: True Let us solve: Does 72 divide 198861? Calculation: False Let us solve: Does 692 divide 1864213400? Calculation: True Let us solve: Is 5 a factor of 496? Calculation: False Let us solve: Is 201 a factor of 1681365? Calculation: True Let us solve: Is 169 a factor of 104273? Calculation: True Let us solve: Is 736 a multiple of 16? Calculation: True Let us solve: Is 247 a factor of 22085? Calculation: False Let us solve: Does 6 divide 12762? Calculation: True Let us solve: Does 370 divide 1277240? Calculation: True Let us solve: Is 190276 a multiple of 65? Calculation: False Let us solve: Is 47545285 a multiple of 109? Calculation: False Let us solve: Is 204 a factor of 8806735? Calculation: False Let us solve: Does 121 divide 17061? Calculation: True Let us solve: Does 15 divide 8941? Calculation: False Let us solve: Is 80892 a multiple of 54? Calculation: True Let us solve: Is 1940 a factor of 201627128? Calculation: False Let us solve: Is 548 a factor of 9503964? Calculation: True Let us solve: Does 605 divide 68569490? Calculation: True Let us solve: Is 18 a factor of 5998? Calculation: False Let us solve: Does 36 divide 12066776? Calculation: False Let us solve: Does 339 divide 106213351? Calculation: False Let us solve: Does 204 divide 642565524? Calculation: True Let us solve: Does 1874 divide 440641116? Calculation: True Let us solve: Does 26 divide 65077? Calculation: False Let us solve: Does 72 divide 2592? Calculation: True Let us solve: Is 17 a factor of 1802
english
numbers: place value -------------------- Problem #: What is the hundred thousands digit of 5904431062? Reply: 4 Problem #: What is the hundred thousands digit of 290134? Reply: 2 Problem #: What is the units digit of 383698180? Reply: 0 Problem #: What is the units digit of 82661? Reply: 1 Problem #: What is the units digit of 6793? Reply: 3 Problem #: What is the hundred thousands digit of 158878476? Reply: 8 Problem #: What is the hundreds digit of 128794236? Reply: 2 Problem #: What is the tens digit of 1373? Reply: 7 Problem #: What is the tens digit of 18258? Reply: 5 Problem #: What is the thousands digit of 64535560? Reply: 5 Problem #: What is the millions digit of 6851390? Reply: 6 Problem #: What is the hundred thousands digit of 105523? Reply: 1 Problem #: What is the ten millions digit of 30547306? Reply: 3 Problem #: What is the hundreds digit of 9932? Reply: 9 Problem #: What is the hundred millions digit of 2081371893? Reply: 0 Problem #: What is the thousands digit of 11231310? Reply: 1 Problem #: What is the thousands digit of 1249? Reply: 1 Problem #: What is the units digit of 43090539? Reply: 9 Problem #: What is the ten thousands digit of 33427? Reply: 3 Problem #: What is the tens digit of 1006? Reply: 0 Problem #: What is the thousands digit of 3339640664? Reply: 0 Problem #: What is the units digit of 848931? Reply: 1 Problem #: What is the hundred millions digit of 3719259552? Reply: 7 Problem #: What is the units digit of 1278336711? Reply: 1 Problem #: What is the hundred thousands digit of 250762? Reply: 2 Problem #: What is the ten thousands digit of 1476966? Reply: 7 Problem #: What is the thousands digit of 73795? Reply: 3 Problem #: What is the ten thousands digit of 33579? Reply: 3 Problem #: What is the tens digit of 19704? Reply: 0 Problem #: What is the tens digit of 159? Reply: 5 Problem #: What is the units digit of 14278679? Reply: 9 Problem #: What is the ten millions digit of 3058721560? Reply: 5 Problem #: What is the ten t
english
numbers: gcd ------------ Problem: What is the greatest common factor of 468 and 684? Eval: 36 Problem: What is the greatest common divisor of 978397010 and 23260? Eval: 11630 Problem: What is the highest common factor of 25717026 and 986? Eval: 58 Problem: Calculate the greatest common factor of 6 and 3276. Eval: 6 Problem: Calculate the highest common divisor of 15600 and 295200. Eval: 1200 Problem: Calculate the greatest common factor of 880 and 5. Eval: 5 Problem: Calculate the greatest common factor of 14654519 and 11. Eval: 11 Problem: What is the greatest common divisor of 10951 and 564? Eval: 47 Problem: Calculate the greatest common factor of 255 and 2836395. Eval: 15 Problem: What is the highest common factor of 972 and 7804? Eval: 4 Problem: Calculate the greatest common factor of 66 and 77. Eval: 11 Problem: Calculate the highest common factor of 392 and 10633. Eval: 49 Problem: Calculate the highest common factor of 6150360 and 15807. Eval: 1437 Problem: Calculate the highest common divisor of 208547 and 347. Eval: 347 Problem: What is the greatest common divisor of 84 and 272664? Eval: 84 Problem: What is the highest common factor of 15943 and 959113? Eval: 149 Problem: Calculate the greatest common factor of 638 and 66. Eval: 22 Problem: Calculate the highest common divisor of 17471648 and 1904. Eval: 272 Problem: What is the greatest common divisor of 64 and 104? Eval: 8 Problem: Calculate the greatest common divisor of 344 and 88. Eval: 8 Problem: What is the highest common divisor of 14210 and 2320? Eval: 290 Problem: What is the highest common factor of 241230752 and 112? Eval: 112 Problem: Calculate the highest common factor of 4968 and 2323362204. Eval: 2484 Problem: Calculate the greatest common divisor of 23 and 161. Eval: 23 Problem: Calculate the greatest common divisor of 3885 and 26196. Eval: 111 Problem: What is the highest common factor of 3760 and 279923540? Eval: 940 Problem: Calculate the greatest common factor of 47118 and 6. Eval: 6
english
probability: swr p sequence --------------------------- Problem: What is prob of sequence zc when two letters picked without replacement from zzc? Solution: 1/3 Problem: Two letters picked without replacement from cjjccjjcbcjjcccccjcj. Give prob of sequence jb. Solution: 2/95 Problem: Three letters picked without replacement from {e: 2, u: 1, j: 1, k: 1}. Give prob of sequence eku. Solution: 1/30 Problem: Two letters picked without replacement from {x: 4, w: 3, k: 6, a: 2, l: 2}. Give prob of sequence ww. Solution: 3/136 Problem: What is prob of sequence vz when two letters picked without replacement from {z: 1, y: 6, q: 2, v: 3}? Solution: 1/44 Problem: Calculate prob of sequence zzq when three letters picked without replacement from {q: 2, x: 1, z: 3, j: 3, b: 3, m: 1}. Solution: 1/143 Problem: Two letters picked without replacement from clvbvgbyggb. What is prob of sequence yg? Solution: 3/110 Problem: What is prob of sequence lua when three letters picked without replacement from brbbbwbbllaalula? Solution: 1/280 Problem: Two letters picked without replacement from hjjjjhhhjhjhjhhjhjj. Give prob of sequence jj. Solution: 5/19 Problem: What is prob of sequence mbap when four letters picked without replacement from {m: 1, i: 3, p: 2, b: 1, y: 1, a: 3}? Solution: 1/1320 Problem: Three letters picked without replacement from {d: 5, x: 3}. Give prob of sequence ddd. Solution: 5/28 Problem: Two letters picked without replacement from hhahahhhhhhhhhhhhh. Give prob of sequence ah. Solution: 16/153 Problem: What is prob of sequence oxqo when four letters picked without replacement from {q: 3, x: 4, j: 5, o: 1}? Solution: 0 Problem: Calculate prob of sequence rrrr when four letters picked without replacement from rrrrrrrrrr. Solution: 1 Problem: What is prob of sequence jq when two letters picked without replacement from {j: 3, l: 1, q: 10, p: 1, r: 4}? Solution: 5/57 Problem: What is prob of sequence is when two letters picked without replacement from sftifbbiifaffababfb
english
numbers: is prime ----------------- Subquestion: Is 51271327 a composite number? Derivation: True Subquestion: Is 12323 composite? Derivation: False Subquestion: Is 513866869 composite? Derivation: False Subquestion: Is 2515 composite? Derivation: True Subquestion: Is 728779 prime? Derivation: False Subquestion: Is 4175227 a prime number? Derivation: False Subquestion: Is 13450947623 a composite number? Derivation: True Subquestion: Is 5309 a prime number? Derivation: True Subquestion: Is 56299 a composite number? Derivation: False Subquestion: Is 7405 a composite number? Derivation: True Subquestion: Is 5155 composite? Derivation: True Subquestion: Is 2371 a composite number? Derivation: False Subquestion: Is 37264488973 composite? Derivation: False Subquestion: Is 8891 a composite number? Derivation: True Subquestion: Is 14996951 composite? Derivation: True Subquestion: Is 25493903 a prime number? Derivation: True Subquestion: Is 16601693521 a prime number? Derivation: False Subquestion: Is 17498801 a prime number? Derivation: True Subquestion: Is 124164841 composite? Derivation: False Subquestion: Is 135321149 composite? Derivation: False Subquestion: Is 12845025253 composite? Derivation: True Subquestion: Is 47296497 a composite number? Derivation: True Subquestion: Is 53953 composite? Derivation: True Subquestion: Is 21862213 composite? Derivation: True Subquestion: Is 187591 prime? Derivation: False Subquestion: Is 74929259 prime? Derivation: True Subquestion: Is 110963 prime? Derivation: False Subquestion: Is 473377 a composite number? Derivation: False Subquestion: Is 4247917 composite? Derivation: False Subquestion: Is 1520278619 a composite number? Derivation: True Subquestion: Is 1609968889 a prime number? Derivation: False Subquestion: Is 153257 prime? Derivation: False Subquestion: Is 70403677 a composite number? Derivation: True Subquestion: Is 80983117 a prime number? Derivation: True Subquestion: Is 3503 prime? Derivation: False Subquestion: Is 56618
english
numbers: div remainder ---------------------- Prompt: What is the remainder when 672 is divided by 330? = : 12 Prompt: What is the remainder when 9403 is divided by 19? = : 17 Prompt: Calculate the remainder when 78620 is divided by 63. = : 59 Prompt: Calculate the remainder when 7472140 is divided by 13586. = : 13426 Prompt: What is the remainder when 3675486 is divided by 33720? = : 6 Prompt: Calculate the remainder when 172709278 is divided by 40. = : 38 Prompt: Calculate the remainder when 1170 is divided by 200. = : 170 Prompt: What is the remainder when 24335 is divided by 78? = : 77 Prompt: Calculate the remainder when 33752588 is divided by 257. = : 7 Prompt: Calculate the remainder when 4268 is divided by 4257. = : 11 Prompt: Calculate the remainder when 11818528 is divided by 498. = : 490 Prompt: What is the remainder when 2059 is divided by 69? = : 58 Prompt: Calculate the remainder when 7385757 is divided by 3203. = : 2842 Prompt: What is the remainder when 6371 is divided by 1591? = : 7 Prompt: Calculate the remainder when 116 is divided by 7. = : 4 Prompt: What is the remainder when 25155 is divided by 70? = : 25 Prompt: What is the remainder when 49849382 is divided by 142? = : 140 Prompt: Calculate the remainder when 103798 is divided by 43. = : 39 Prompt: Calculate the remainder when 163 is divided by 29. = : 18 Prompt: Calculate the remainder when 428716060 is divided by 2039. = : 2037 Prompt: Calculate the remainder when 26441663 is divided by 93. = : 89 Prompt: What is the remainder when 228 is divided by 56? = : 4 Prompt: Calculate the remainder when 4040519 is divided by 1346832. = : 23 Prompt: What is the remainder when 1080 is divided by 57? = : 54 Prompt: What is the remainder when 11134 is divided by 192? = : 190 Prompt: Calculate the remainder when 844396 is divided by 753. = : 283 Prompt: What is the remainder when 252 is divided by 168? = : 84 Prompt: Calculate the remainder when 463 is divided by 30. = : 13 Prompt: What is the remainder
english
numbers: gcd ------------ Situation: Calculate the greatest common divisor of 27 and 801. Solution: 9 Situation: What is the highest common divisor of 312526 and 15043? Solution: 307 Situation: Calculate the highest common divisor of 501 and 321. Solution: 3 Situation: What is the greatest common factor of 2166 and 4? Solution: 2 Situation: Calculate the highest common divisor of 4680 and 1499607720. Solution: 4680 Situation: What is the greatest common divisor of 93526380 and 81? Solution: 27 Situation: Calculate the greatest common factor of 602 and 14. Solution: 14 Situation: What is the greatest common factor of 3525 and 1200? Solution: 75 Situation: What is the highest common divisor of 432 and 96? Solution: 48 Situation: What is the greatest common divisor of 242138 and 13066? Solution: 278 Situation: Calculate the greatest common divisor of 6810 and 15030. Solution: 30 Situation: Calculate the greatest common divisor of 406 and 2303. Solution: 7 Situation: Calculate the greatest common factor of 436 and 25556. Solution: 4 Situation: Calculate the greatest common factor of 1386800 and 3550. Solution: 50 Situation: What is the greatest common factor of 63 and 168? Solution: 21 Situation: What is the highest common divisor of 32 and 2448? Solution: 16 Situation: Calculate the greatest common divisor of 3861558 and 27. Solution: 9 Situation: What is the greatest common divisor of 228 and 62? Solution: 2 Situation: What is the greatest common divisor of 21 and 41376? Solution: 3 Situation: Calculate the greatest common factor of 806 and 99541. Solution: 403 Situation: What is the greatest common divisor of 16984 and 4268? Solution: 44 Situation: Calculate the greatest common factor of 1206 and 18. Solution: 18 Situation: Calculate the highest common factor of 7802 and 332. Solution: 166 Situation: Calculate the highest common factor of 135 and 999. Solution: 27 Situation: What is the highest common divisor of 1080 and 120? Solution: 120 Situation: What is the high
english
numbers: is factor ------------------ Scenario: Is 10 a factor of 2296? Steps: False Scenario: Does 13 divide 7852? Steps: True Scenario: Is 615454 a multiple of 83? Steps: False Scenario: Does 142 divide 19170? Steps: True Scenario: Is 14 a factor of 54414? Steps: False Scenario: Is 19362 a multiple of 14? Steps: True Scenario: Does 11 divide 3787? Steps: False Scenario: Is 746 a factor of 7967654? Steps: False Scenario: Does 278 divide 1112? Steps: True Scenario: Does 1423 divide 8819006? Steps: False Scenario: Is 3449547 a multiple of 81? Steps: True Scenario: Is 1754747 a multiple of 51? Steps: False Scenario: Is 56 a factor of 102? Steps: False Scenario: Is 42857956 a multiple of 175? Steps: False Scenario: Does 90 divide 298338120? Steps: True Scenario: Is 218082480 a multiple of 240? Steps: True Scenario: Is 59 a factor of 188859? Steps: True Scenario: Is 4 a factor of 4860? Steps: True Scenario: Is 82 a factor of 15277010? Steps: True Scenario: Is 136 a factor of 442544? Steps: True Scenario: Is 723 a multiple of 39? Steps: False Scenario: Does 35 divide 193? Steps: False Scenario: Is 321 a factor of 838408? Steps: False Scenario: Is 518 a multiple of 32? Steps: False Scenario: Is 2350 a multiple of 50? Steps: True Scenario: Does 467 divide 3169062? Steps: True Scenario: Does 22 divide 310? Steps: False Scenario: Is 8293 a factor of 356010598? Steps: False Scenario: Is 138451142 a multiple of 18? Steps: False Scenario: Does 18 divide 1782? Steps: True Scenario: Is 37344 a multiple of 8? Steps: True Scenario: Is 2923 a factor of 183444557? Steps: True Scenario: Is 7 a factor of 3777? Steps: False Scenario: Is 607 a factor of 13919117? Steps: True Scenario: Does 29 divide 5518? Steps: False Scenario: Is 393 a factor of 1835355? Steps: False Scenario: Is 13 a factor of 146442023? Steps: True Scenario: Does 16 divide 816? Steps: True Scenario: Does 14 divide 462? Steps: True Scenario: Is 85760894 a multiple of 75? Steps: False Scenario: Does 4205 divide 12267365
english
arithmetic: nearest integer root -------------------------------- Math Problem: What is 6380799 to the power of 1/6, to the nearest integer? Final Answer: 14 Math Problem: What is 83142407 to the power of 1/7, to the nearest integer? Final Answer: 14 Math Problem: What is 311486 to the power of 1/8, to the nearest integer? Final Answer: 5 Math Problem: What is 789550 to the power of 1/2, to the nearest integer? Final Answer: 889 Math Problem: What is 32579467 to the power of 1/8, to the nearest integer? Final Answer: 9 Math Problem: What is 1220109 to the power of 1/3, to the nearest integer? Final Answer: 107 Math Problem: What is 6424536 to the power of 1/3, to the nearest integer? Final Answer: 186 Math Problem: What is 1244055 to the power of 1/2, to the nearest integer? Final Answer: 1115 Math Problem: What is 861544 to the power of 1/4, to the nearest integer? Final Answer: 30 Math Problem: What is 5312 to the power of 1/3, to the nearest integer? Final Answer: 17 Math Problem: What is 1271 to the power of 1/9, to the nearest integer? Final Answer: 2 Math Problem: What is the sixth root of 632511644 to the nearest integer? Final Answer: 29 Math Problem: What is the square root of 6537 to the nearest integer? Final Answer: 81 Math Problem: What is the cube root of 4030171 to the nearest integer? Final Answer: 159 Math Problem: What is the square root of 1242 to the nearest integer? Final Answer: 35 Math Problem: What is the third root of 1776988 to the nearest integer? Final Answer: 121 Math Problem: What is 668095 to the power of 1/3, to the nearest integer? Final Answer: 87 Math Problem: What is the third root of 4604292681 to the nearest integer? Final Answer: 1664 Math Problem: What is the square root of 923097 to the nearest integer? Final Answer: 961 Math Problem: What is 1504 to the power of 1/8, to the nearest integer? Final Answer: 2 Math Problem: What is 27786488 to the power of 1/3, to the nearest integer? Final Answer: 303 Math Problem: What is the
english
numbers: place value -------------------- Step: What is the units digit of 3084045? Ans: 5 Step: What is the ten thousands digit of 38923? Ans: 3 Step: What is the millions digit of 121075779? Ans: 1 Step: What is the hundreds digit of 1837870809? Ans: 8 Step: What is the tens digit of 62361395? Ans: 9 Step: What is the hundreds digit of 8300? Ans: 3 Step: What is the tens digit of 282609? Ans: 0 Step: What is the thousands digit of 138903? Ans: 8 Step: What is the ten thousands digit of 189645? Ans: 8 Step: What is the thousands digit of 5625? Ans: 5 Step: What is the thousands digit of 58509? Ans: 8 Step: What is the hundred thousands digit of 1635523? Ans: 6 Step: What is the millions digit of 71064368? Ans: 1 Step: What is the tens digit of 308490942? Ans: 4 Step: What is the tens digit of 3058395? Ans: 9 Step: What is the hundred thousands digit of 246774? Ans: 2 Step: What is the thousands digit of 181750? Ans: 1 Step: What is the units digit of 6707? Ans: 7 Step: What is the hundreds digit of 1029320? Ans: 3 Step: What is the thousands digit of 66423? Ans: 6 Step: What is the units digit of 23387? Ans: 7 Step: What is the hundreds digit of 229310? Ans: 3 Step: What is the ten millions digit of 2680259265? Ans: 8 Step: What is the tens digit of 18175? Ans: 7 Step: What is the hundred thousands digit of 727703? Ans: 7 Step: What is the hundred millions digit of 1132828799? Ans: 1 Step: What is the hundreds digit of 788? Ans: 7 Step: What is the thousands digit of 37327? Ans: 7 Step: What is the hundred thousands digit of 39050898? Ans: 0 Step: What is the millions digit of 1496666? Ans: 1 Step: What is the thousands digit of 60745384? Ans: 5 Step: What is the tens digit of 11495435? Ans: 3 Step: What is the tens digit of 38720345? Ans: 4 Step: What is the hundreds digit of 1102763? Ans: 7 Step: What is the tens digit of 2585635? Ans: 3 Step: What is the ten millions digit of 18332552? Ans: 1 Step: What is the tens digit of 7338? Ans: 3 Step: What is the thousan
english
numbers: gcd ------------ Prompt: What is the highest common divisor of 285062 and 46? Response: 46 Prompt: What is the greatest common divisor of 40245 and 8? Response: 1 Prompt: Calculate the highest common factor of 147568498 and 55. Response: 11 Prompt: Calculate the highest common divisor of 25625 and 287. Response: 41 Prompt: What is the highest common divisor of 55437571 and 98? Response: 49 Prompt: What is the greatest common factor of 70 and 630? Response: 70 Prompt: What is the greatest common factor of 124 and 4898093? Response: 31 Prompt: Calculate the greatest common divisor of 329 and 2914. Response: 47 Prompt: Calculate the greatest common divisor of 86230 and 17190. Response: 10 Prompt: What is the highest common factor of 25098 and 2427456? Response: 282 Prompt: What is the highest common factor of 110 and 30? Response: 10 Prompt: Calculate the highest common factor of 20 and 44530. Response: 10 Prompt: What is the greatest common divisor of 4 and 81938? Response: 2 Prompt: What is the greatest common factor of 114 and 102? Response: 6 Prompt: What is the greatest common factor of 180 and 45? Response: 45 Prompt: Calculate the highest common factor of 527 and 39363619. Response: 17 Prompt: Calculate the greatest common factor of 75834 and 10890. Response: 198 Prompt: Calculate the greatest common divisor of 39886 and 147. Response: 49 Prompt: Calculate the highest common divisor of 267 and 445. Response: 89 Prompt: What is the highest common factor of 42 and 162? Response: 6 Prompt: Calculate the greatest common factor of 85400 and 41227704. Response: 3416 Prompt: Calculate the greatest common factor of 56 and 77396879. Response: 7 Prompt: What is the greatest common divisor of 855 and 273315? Response: 285 Prompt: What is the highest common factor of 79 and 711? Response: 79 Prompt: Calculate the highest common divisor of 17883 and 382131. Response: 9 Prompt: Calculate the highest common divisor of 49 and 1813. Response: 49 Prompt: Calculate the hi
english
numbers: place value -------------------- Math Q: What is the thousands digit of 3370653924? Gives: 3 Math Q: What is the tens digit of 549? Gives: 4 Math Q: What is the tens digit of 6390? Gives: 9 Math Q: What is the units digit of 63583320? Gives: 0 Math Q: What is the units digit of 1706102885? Gives: 5 Math Q: What is the hundreds digit of 665394? Gives: 3 Math Q: What is the tens digit of 71431? Gives: 3 Math Q: What is the thousands digit of 1381? Gives: 1 Math Q: What is the hundred thousands digit of 6500058? Gives: 5 Math Q: What is the ten millions digit of 2000519348? Gives: 0 Math Q: What is the hundreds digit of 491425862? Gives: 8 Math Q: What is the hundred thousands digit of 1237533? Gives: 2 Math Q: What is the thousands digit of 3978? Gives: 3 Math Q: What is the tens digit of 1373? Gives: 7 Math Q: What is the units digit of 77832? Gives: 2 Math Q: What is the ten millions digit of 33612116? Gives: 3 Math Q: What is the ten millions digit of 118837828? Gives: 1 Math Q: What is the hundreds digit of 12098483? Gives: 4 Math Q: What is the ten millions digit of 182628732? Gives: 8 Math Q: What is the ten millions digit of 5175638243? Gives: 7 Math Q: What is the tens digit of 9333994? Gives: 9 Math Q: What is the tens digit of 2632? Gives: 3 Math Q: What is the tens digit of 3172? Gives: 7 Math Q: What is the tens digit of 92325? Gives: 2 Math Q: What is the ten thousands digit of 138486? Gives: 3 Math Q: What is the hundred thousands digit of 7983492? Gives: 9 Math Q: What is the tens digit of 46901079? Gives: 7 Math Q: What is the tens digit of 126869? Gives: 6 Math Q: What is the ten thousands digit of 592097? Gives: 9 Math Q: What is the ten thousands digit of 29815689? Gives: 1 Math Q: What is the hundreds digit of 127294? Gives: 2 Math Q: What is the tens digit of 89203? Gives: 0 Math Q: What is the thousands digit of 2922582? Gives: 2 Math Q: What is the units digit of 3463964? Gives: 4 Math Q: What is the ten thousands digit of 32497? Gives:
english
numbers: place value -------------------- Exercise: What is the hundreds digit of 3102? Steps: 1 Exercise: What is the units digit of 47598? Steps: 8 Exercise: What is the units digit of 411? Steps: 1 Exercise: What is the millions digit of 19837879? Steps: 9 Exercise: What is the ten thousands digit of 74610? Steps: 7 Exercise: What is the hundred thousands digit of 918030? Steps: 9 Exercise: What is the ten thousands digit of 2162941? Steps: 6 Exercise: What is the hundred millions digit of 1059758445? Steps: 0 Exercise: What is the ten thousands digit of 44220772? Steps: 2 Exercise: What is the hundreds digit of 3836? Steps: 8 Exercise: What is the tens digit of 4193? Steps: 9 Exercise: What is the ten thousands digit of 54709871? Steps: 0 Exercise: What is the tens digit of 10203128? Steps: 2 Exercise: What is the thousands digit of 1281? Steps: 1 Exercise: What is the ten millions digit of 3192527434? Steps: 9 Exercise: What is the tens digit of 278? Steps: 7 Exercise: What is the ten thousands digit of 94010? Steps: 9 Exercise: What is the thousands digit of 26800? Steps: 6 Exercise: What is the units digit of 3231656478? Steps: 8 Exercise: What is the tens digit of 713534276? Steps: 7 Exercise: What is the tens digit of 74370? Steps: 7 Exercise: What is the thousands digit of 3995? Steps: 3 Exercise: What is the ten thousands digit of 1273963? Steps: 7 Exercise: What is the millions digit of 163300390? Steps: 3 Exercise: What is the ten thousands digit of 18612? Steps: 1 Exercise: What is the ten millions digit of 892564034? Steps: 9 Exercise: What is the thousands digit of 29555848? Steps: 5 Exercise: What is the tens digit of 49226054? Steps: 5 Exercise: What is the thousands digit of 47458839? Steps: 8 Exercise: What is the units digit of 3730044? Steps: 4 Exercise: What is the ten thousands digit of 882942? Steps: 8 Exercise: What is the tens digit of 364? Steps: 6 Exercise: What is the thousands digit of 190481523? Steps: 1 Exercise: What is the hundreds
english
numbers: gcd ------------ Exercise: Calculate the highest common divisor of 1170 and 2070. Sol: 90 Exercise: What is the greatest common divisor of 42436 and 309? Sol: 103 Exercise: What is the highest common divisor of 8157 and 6? Sol: 3 Exercise: Calculate the greatest common divisor of 414 and 46. Sol: 46 Exercise: What is the highest common factor of 951 and 6423? Sol: 3 Exercise: What is the highest common divisor of 16625 and 28875250? Sol: 2375 Exercise: What is the highest common divisor of 75818 and 1002? Sol: 334 Exercise: Calculate the greatest common factor of 16768224 and 20619. Sol: 711 Exercise: What is the greatest common factor of 106392 and 88? Sol: 88 Exercise: What is the greatest common divisor of 6 and 6? Sol: 6 Exercise: What is the greatest common divisor of 258 and 301? Sol: 43 Exercise: Calculate the highest common factor of 2169 and 450. Sol: 9 Exercise: What is the highest common factor of 4686 and 174234? Sol: 426 Exercise: Calculate the greatest common factor of 135930872 and 616. Sol: 616 Exercise: What is the greatest common divisor of 6 and 1866? Sol: 6 Exercise: What is the highest common factor of 2134 and 1552? Sol: 194 Exercise: What is the greatest common divisor of 121361 and 3092? Sol: 773 Exercise: Calculate the greatest common factor of 96 and 156. Sol: 12 Exercise: What is the highest common divisor of 2537 and 43? Sol: 43 Exercise: Calculate the greatest common factor of 481 and 2249. Sol: 13 Exercise: Calculate the highest common divisor of 33 and 7249. Sol: 11 Exercise: What is the greatest common divisor of 3987 and 4617? Sol: 9 Exercise: What is the highest common divisor of 100 and 590? Sol: 10 Exercise: What is the greatest common divisor of 38 and 59299? Sol: 19 Exercise: What is the highest common factor of 1924 and 20706569? Sol: 481 Exercise: Calculate the highest common factor of 918 and 1565496. Sol: 306 Exercise: Calculate the highest common factor of 180 and 3260. Sol: 20 Exercise: What is the greatest common
english
numbers: gcd ------------ Step: What is the highest common factor of 1431 and 10356147? Clarification: 1431 Step: What is the highest common divisor of 714 and 1734? Clarification: 102 Step: What is the highest common factor of 27 and 7389? Clarification: 9 Step: Calculate the greatest common divisor of 126065 and 1235. Clarification: 95 Step: What is the greatest common divisor of 2307942 and 936? Clarification: 234 Step: What is the greatest common factor of 15 and 6795? Clarification: 15 Step: What is the highest common factor of 5809647 and 32088? Clarification: 573 Step: Calculate the highest common divisor of 44038 and 5238. Clarification: 194 Step: What is the greatest common divisor of 763 and 274603? Clarification: 7 Step: What is the highest common factor of 20 and 39945970? Clarification: 10 Step: Calculate the highest common factor of 3230 and 133. Clarification: 19 Step: Calculate the highest common factor of 33 and 8827093. Clarification: 11 Step: What is the greatest common factor of 2139 and 2077? Clarification: 31 Step: Calculate the highest common factor of 21 and 483. Clarification: 21 Step: What is the highest common divisor of 12752335 and 45? Clarification: 5 Step: Calculate the highest common divisor of 9 and 201. Clarification: 3 Step: Calculate the highest common factor of 576 and 1488. Clarification: 48 Step: What is the highest common factor of 374 and 15521? Clarification: 187 Step: What is the highest common factor of 2428 and 1814126332? Clarification: 2428 Step: Calculate the highest common factor of 82 and 8938. Clarification: 82 Step: What is the greatest common factor of 13311 and 87? Clarification: 87 Step: What is the greatest common divisor of 138310168 and 12016? Clarification: 6008 Step: What is the greatest common factor of 3 and 7017? Clarification: 3 Step: Calculate the greatest common divisor of 1157870 and 357. Clarification: 119 Step: What is the greatest common factor of 21270128 and 578? Clarification: 34 Step: Calculat
english
arithmetic: nearest integer root -------------------------------- Issue: What is the square root of 13419758 to the nearest integer? Fix: 3663 Issue: What is 28591 to the power of 1/4, to the nearest integer? Fix: 13 Issue: What is 13295 to the power of 1/6, to the nearest integer? Fix: 5 Issue: What is 38765755 to the power of 1/3, to the nearest integer? Fix: 338 Issue: What is 45091613 to the power of 1/3, to the nearest integer? Fix: 356 Issue: What is the square root of 558986 to the nearest integer? Fix: 748 Issue: What is 3760568 to the power of 1/2, to the nearest integer? Fix: 1939 Issue: What is the cube root of 11778029 to the nearest integer? Fix: 228 Issue: What is the sixth root of 25653 to the nearest integer? Fix: 5 Issue: What is 606 to the power of 1/6, to the nearest integer? Fix: 3 Issue: What is the square root of 1675408 to the nearest integer? Fix: 1294 Issue: What is 7492625 to the power of 1/5, to the nearest integer? Fix: 24 Issue: What is the third root of 1298 to the nearest integer? Fix: 11 Issue: What is the sixth root of 2020551 to the nearest integer? Fix: 11 Issue: What is the fourth root of 424 to the nearest integer? Fix: 5 Issue: What is the sixth root of 26708 to the nearest integer? Fix: 5 Issue: What is the sixth root of 755690575 to the nearest integer? Fix: 30 Issue: What is the third root of 48679321 to the nearest integer? Fix: 365 Issue: What is the fifth root of 372860 to the nearest integer? Fix: 13 Issue: What is 471 to the power of 1/4, to the nearest integer? Fix: 5 Issue: What is the fifth root of 507548 to the nearest integer? Fix: 14 Issue: What is the third root of 1120935 to the nearest integer? Fix: 104 Issue: What is the fourth root of 570051 to the nearest integer? Fix: 27 Issue: What is the cube root of 156935 to the nearest integer? Fix: 54 Issue: What is the third root of 2041912 to the nearest integer? Fix: 127 Issue: What is 203280 to the power of 1/2, to the nearest integer? Fix: 451 Issue: What is 51276
english
probability: swr p level set ---------------------------- Statement: Two letters picked without replacement from xkkkkqxqqrkqxkqqx. What is prob of picking 2 k? Soln: 15/136 Statement: Two letters picked without replacement from {c: 1, h: 19}. What is prob of picking 1 c and 1 h? Soln: 1/10 Statement: Calculate prob of picking 2 l when two letters picked without replacement from qqcqqllqqq. Soln: 1/45 Statement: What is prob of picking 1 l and 2 k when three letters picked without replacement from {n: 2, b: 3, k: 8, l: 3}? Soln: 3/20 Statement: Two letters picked without replacement from eielelnnelelleeni. Give prob of picking 2 l. Soln: 5/68 Statement: What is prob of picking 1 p and 2 e when three letters picked without replacement from {l: 4, m: 5, e: 6, x: 1, p: 4}? Soln: 1/19 Statement: Three letters picked without replacement from {w: 11, j: 5, g: 1, n: 2}. What is prob of picking 1 n and 2 j? Soln: 20/969 Statement: Three letters picked without replacement from {d: 1, b: 6, s: 1, q: 3, z: 4}. What is prob of picking 2 z and 1 q? Soln: 18/455 Statement: Four letters picked without replacement from {s: 2, b: 4, e: 10}. What is prob of picking 1 e and 3 b? Soln: 2/91 Statement: Calculate prob of picking 2 n when two letters picked without replacement from nnq. Soln: 1/3 Statement: What is prob of picking 1 f and 1 x when two letters picked without replacement from jfjfjxffjffmf? Soln: 7/78 Statement: Two letters picked without replacement from {h: 1, w: 1, t: 2, q: 3}. Give prob of picking 1 t and 1 h. Soln: 2/21 Statement: Two letters picked without replacement from gvvxxjxglg. Give prob of picking 1 j and 1 l. Soln: 1/45 Statement: Three letters picked without replacement from {z: 3, y: 3, b: 7, n: 2}. What is prob of picking 1 n and 2 b? Soln: 6/65 Statement: Three letters picked without replacement from ssvvfvssisisssfsii. Give prob of picking 1 i, 1 f, and 1 v. Soln: 1/34 Statement: Two letters picked without replacement from ojjajjjoaqqqjaq. What is prob o
english
probability: swr p level set ---------------------------- Step: Two letters picked without replacement from phlbwlhwwyllwwlphbw. Give prob of picking 1 y and 1 p. Finding: 2/171 Step: Three letters picked without replacement from duqjjfddjjduddjdjjqd. Give prob of picking 1 u and 2 q. Finding: 1/570 Step: Calculate prob of picking 1 i, 1 f, and 2 p when four letters picked without replacement from fhfiphphhhhhh. Finding: 2/715 Step: Four letters picked without replacement from vzzzavazzzzaazzzaaz. Give prob of picking 1 a, 2 v, and 1 z. Finding: 11/646 Step: What is prob of picking 1 w, 1 r, and 2 a when four letters picked without replacement from {w: 1, a: 2, r: 9, t: 3, l: 3}? Finding: 1/340 Step: Four letters picked without replacement from hwhwdadadwmdaddh. What is prob of picking 2 h, 1 a, and 1 d? Finding: 27/910 Step: Four letters picked without replacement from {z: 7, x: 3, p: 1, h: 1, a: 1}. What is prob of picking 1 p and 3 z? Finding: 7/143 Step: What is prob of picking 2 d when two letters picked without replacement from jsdjssjsjjssjssjsjj? Finding: 0 Step: Four letters picked without replacement from bhblbbbbhjbj. What is prob of picking 2 b and 2 h? Finding: 7/165 Step: Two letters picked without replacement from jawab. Give prob of picking 1 w and 1 j. Finding: 1/10 Step: What is prob of picking 1 k and 1 u when two letters picked without replacement from {u: 6, l: 10, n: 2, k: 2}? Finding: 6/95 Step: Two letters picked without replacement from {p: 1, e: 2, d: 1, n: 1, c: 1, z: 2}. Give prob of picking 1 c and 1 n. Finding: 1/28 Step: Two letters picked without replacement from {z: 2, i: 1, g: 3, o: 6, h: 1, y: 2}. What is prob of picking 2 g? Finding: 1/35 Step: What is prob of picking 4 u when four letters picked without replacement from {l: 5, u: 4, i: 2}? Finding: 1/330 Step: Calculate prob of picking 2 e when two letters picked without replacement from bkkkqjqbjjjjeje. Finding: 1/105 Step: What is prob of picking 1 t, 1 j, and 1 n when three le
english
numbers: div remainder ---------------------- Exercise: Calculate the remainder when 975 is divided by 19. Workthrough: 6 Exercise: Calculate the remainder when 56645 is divided by 73. Workthrough: 70 Exercise: What is the remainder when 84550 is divided by 158? Workthrough: 20 Exercise: What is the remainder when 1471 is divided by 5? Workthrough: 1 Exercise: Calculate the remainder when 114882 is divided by 894. Workthrough: 450 Exercise: What is the remainder when 3508170 is divided by 289? Workthrough: 288 Exercise: What is the remainder when 68 is divided by 9? Workthrough: 5 Exercise: What is the remainder when 54401 is divided by 144? Workthrough: 113 Exercise: Calculate the remainder when 398 is divided by 53. Workthrough: 27 Exercise: What is the remainder when 15255 is divided by 372? Workthrough: 3 Exercise: Calculate the remainder when 8773 is divided by 515. Workthrough: 18 Exercise: Calculate the remainder when 277 is divided by 54. Workthrough: 7 Exercise: What is the remainder when 22942 is divided by 4587? Workthrough: 7 Exercise: Calculate the remainder when 252 is divided by 5. Workthrough: 2 Exercise: Calculate the remainder when 1847 is divided by 50. Workthrough: 47 Exercise: Calculate the remainder when 5609 is divided by 1293. Workthrough: 437 Exercise: Calculate the remainder when 153617 is divided by 543. Workthrough: 491 Exercise: Calculate the remainder when 116223 is divided by 115796. Workthrough: 427 Exercise: What is the remainder when 64089 is divided by 10676? Workthrough: 33 Exercise: Calculate the remainder when 11317 is divided by 3126. Workthrough: 1939 Exercise: What is the remainder when 12779650 is divided by 107? Workthrough: 105 Exercise: What is the remainder when 204 is divided by 54? Workthrough: 42 Exercise: Calculate the remainder when 15999 is divided by 1333. Workthrough: 3 Exercise: Calculate the remainder when 25634 is divided by 1068. Workthrough: 2 Exercise: Calculate the remainder when 152812 is divided by 21797
english
probability: swr p sequence --------------------------- Ask: What is prob of sequence zzz when three letters picked without replacement from kzzzzzzzzzzzzzzzkzz? Yields: 40/57 Ask: What is prob of sequence vo when two letters picked without replacement from mmjvaajjjajo? Yields: 1/132 Ask: What is prob of sequence hh when two letters picked without replacement from {h: 11, e: 6, i: 1}? Yields: 55/153 Ask: What is prob of sequence qdq when three letters picked without replacement from qgqqgqdqdgqqggq? Yields: 8/195 Ask: What is prob of sequence uz when two letters picked without replacement from {u: 9, z: 3}? Yields: 9/44 Ask: Two letters picked without replacement from {o: 3, p: 4, s: 1, d: 2}. What is prob of sequence od? Yields: 1/15 Ask: Calculate prob of sequence tma when three letters picked without replacement from mamathaoaoaao. Yields: 1/143 Ask: Two letters picked without replacement from {c: 2, a: 3, w: 6, u: 2}. Give prob of sequence ca. Yields: 1/26 Ask: Three letters picked without replacement from {m: 1, y: 1, t: 1, r: 2, i: 2}. What is prob of sequence yri? Yields: 2/105 Ask: Four letters picked without replacement from kzskhhkyk. What is prob of sequence skyk? Yields: 1/252 Ask: Calculate prob of sequence aaaq when four letters picked without replacement from aqaaqaaaaaa. Yields: 7/55 Ask: What is prob of sequence av when two letters picked without replacement from {v: 2, a: 3}? Yields: 3/10 Ask: Four letters picked without replacement from idcwlgwc. What is prob of sequence dclg? Yields: 1/840 Ask: Four letters picked without replacement from inhhkiknthnhin. Give prob of sequence hkhn. Yields: 4/1001 Ask: Four letters picked without replacement from {p: 2, l: 1, c: 1, u: 1, t: 2, j: 1}. Give prob of sequence upjt. Yields: 1/420 Ask: Three letters picked without replacement from gtggtfaaasn. What is prob of sequence tft? Yields: 1/495 Ask: What is prob of sequence crh when three letters picked without replacement from chrrrrqrrrhrcrrqrqqr? Yields: 2/
english
numbers: place value -------------------- Exercise: What is the units digit of 88591? Ans: 1 Exercise: What is the hundred thousands digit of 13939657? Ans: 9 Exercise: What is the tens digit of 33675416? Ans: 1 Exercise: What is the hundreds digit of 955? Ans: 9 Exercise: What is the ten thousands digit of 179197? Ans: 7 Exercise: What is the units digit of 2062659? Ans: 9 Exercise: What is the hundred thousands digit of 2140576? Ans: 1 Exercise: What is the tens digit of 734479? Ans: 7 Exercise: What is the units digit of 4368? Ans: 8 Exercise: What is the hundreds digit of 1050921? Ans: 9 Exercise: What is the tens digit of 421640? Ans: 4 Exercise: What is the hundreds digit of 626256787? Ans: 7 Exercise: What is the tens digit of 819? Ans: 1 Exercise: What is the thousands digit of 20759? Ans: 0 Exercise: What is the ten millions digit of 2473139357? Ans: 7 Exercise: What is the units digit of 418122? Ans: 2 Exercise: What is the thousands digit of 485263? Ans: 5 Exercise: What is the hundred thousands digit of 2902366? Ans: 9 Exercise: What is the hundreds digit of 3272? Ans: 2 Exercise: What is the units digit of 5107? Ans: 7 Exercise: What is the hundred thousands digit of 4283550050? Ans: 5 Exercise: What is the ten millions digit of 15821954? Ans: 1 Exercise: What is the ten thousands digit of 73112? Ans: 7 Exercise: What is the thousands digit of 2221759? Ans: 1 Exercise: What is the units digit of 10622? Ans: 2 Exercise: What is the tens digit of 17373884? Ans: 8 Exercise: What is the tens digit of 774? Ans: 7 Exercise: What is the hundred millions digit of 3663988167? Ans: 6 Exercise: What is the thousands digit of 33169504? Ans: 9 Exercise: What is the ten thousands digit of 89013? Ans: 8 Exercise: What is the units digit of 1595? Ans: 5 Exercise: What is the ten thousands digit of 8004932? Ans: 0 Exercise: What is the tens digit of 70197137? Ans: 3 Exercise: What is the hundreds digit of 125483515? Ans: 5 Exercise: What is the units digit of 5502? Ans:
english
numbers: lcm ------------ Problem Statement: What is the common denominator of -145/108 and -59/120? Ans: 1080 Problem Statement: Calculate the lowest common multiple of 398193 and 663655. Ans: 1990965 Problem Statement: Find the common denominator of -12/55 and 67/154825. Ans: 154825 Problem Statement: Calculate the lowest common multiple of 10944 and 57. Ans: 10944 Problem Statement: Find the common denominator of -167/3666 and -127/1416. Ans: 865176 Problem Statement: Calculate the smallest common multiple of 52008 and 55. Ans: 260040 Problem Statement: What is the lowest common multiple of 40 and 168? Ans: 840 Problem Statement: What is the least common multiple of 5 and 176828? Ans: 884140 Problem Statement: Find the common denominator of 47/4 and -119/10536. Ans: 10536 Problem Statement: What is the least common multiple of 2050614 and 11164454? Ans: 100480086 Problem Statement: Calculate the least common multiple of 1237605 and 255. Ans: 21039285 Problem Statement: What is the least common multiple of 216 and 39? Ans: 2808 Problem Statement: Calculate the common denominator of 57/22 and 45/2654. Ans: 29194 Problem Statement: Find the common denominator of 81/660538 and 17/772970. Ans: 36329590 Problem Statement: Calculate the lowest common multiple of 6 and 48. Ans: 48 Problem Statement: Find the common denominator of -53/435721 and -17/154364067. Ans: 1698004737 Problem Statement: Find the common denominator of -133/324 and 49/15. Ans: 1620 Problem Statement: Find the common denominator of -33/37519 and -4/306773. Ans: 5215141 Problem Statement: Calculate the lowest common multiple of 143 and 2803. Ans: 400829 Problem Statement: Calculate the least common multiple of 114 and 24. Ans: 456 Problem Statement: Find the common denominator of 6/5 and -23/441. Ans: 2205 Problem Statement: Calculate the least common multiple of 1268752 and 6. Ans: 3806256 Problem Statement: What is the least common multiple of 360 and 3398550? Ans: 40782600 Problem Statement: What i
english
probability: swr p sequence --------------------------- Given: Calculate prob of sequence qqw when three letters picked without replacement from qqgsbqasbaqaqqaaqsqw. Workthrough: 7/855 Given: Calculate prob of sequence yy when two letters picked without replacement from {x: 5, y: 9}. Workthrough: 36/91 Given: Two letters picked without replacement from {o: 5, j: 1, u: 1, m: 2}. Give prob of sequence oo. Workthrough: 5/18 Given: Four letters picked without replacement from aafarakaaakafarfqrak. Give prob of sequence fqka. Workthrough: 1/1292 Given: Calculate prob of sequence tt when two letters picked without replacement from {m: 9, r: 1, t: 9}. Workthrough: 4/19 Given: What is prob of sequence qb when two letters picked without replacement from {f: 5, b: 1, d: 1, s: 4, t: 1, q: 1}? Workthrough: 1/156 Given: Two letters picked without replacement from vbbbbbbb. What is prob of sequence bb? Workthrough: 3/4 Given: Three letters picked without replacement from chchzccccc. Give prob of sequence hhc. Workthrough: 7/360 Given: Four letters picked without replacement from jjjjjj. What is prob of sequence jjjj? Workthrough: 1 Given: Two letters picked without replacement from {y: 1, t: 2, u: 1, q: 2, x: 2}. Give prob of sequence qu. Workthrough: 1/28 Given: What is prob of sequence yyy when three letters picked without replacement from iyfaqfyqafahfhyh? Workthrough: 1/560 Given: Two letters picked without replacement from kkkhkzkhkzkkhhzzhhk. What is prob of sequence kz? Workthrough: 2/19 Given: Two letters picked without replacement from pplllplplglppppw. Give prob of sequence ll. Workthrough: 1/8 Given: Calculate prob of sequence fl when two letters picked without replacement from {h: 2, f: 1, l: 1}. Workthrough: 1/12 Given: Four letters picked without replacement from {s: 8, u: 2, r: 1, b: 3, n: 1, k: 1}. What is prob of sequence bbnk? Workthrough: 1/7280 Given: Calculate prob of sequence cw when two letters picked without replacement from ciwic. Workthrough: 1/10 Given
english
numbers: is prime ----------------- Exercise: Is 9246773 a composite number? Yields: True Exercise: Is 402821891 composite? Yields: True Exercise: Is 917751707 a prime number? Yields: True Exercise: Is 984513 a composite number? Yields: True Exercise: Is 167507 a composite number? Yields: True Exercise: Is 3087329303 a prime number? Yields: True Exercise: Is 50055139891 a composite number? Yields: False Exercise: Is 1096483 a composite number? Yields: True Exercise: Is 32804719 a composite number? Yields: True Exercise: Is 30742387 a prime number? Yields: False Exercise: Is 186474373 a composite number? Yields: False Exercise: Is 1870814357 composite? Yields: False Exercise: Is 696551 a prime number? Yields: False Exercise: Is 783982679 a composite number? Yields: True Exercise: Is 3193177 a composite number? Yields: True Exercise: Is 15630239 a prime number? Yields: False Exercise: Is 828049 a composite number? Yields: True Exercise: Is 4049 composite? Yields: False Exercise: Is 1390704307 prime? Yields: True Exercise: Is 220596107 prime? Yields: True Exercise: Is 2160959 a prime number? Yields: False Exercise: Is 23999722193 composite? Yields: False Exercise: Is 918805 a prime number? Yields: False Exercise: Is 3955561 a prime number? Yields: True Exercise: Is 8884604249 a prime number? Yields: True Exercise: Is 579263 prime? Yields: True Exercise: Is 7583 composite? Yields: False Exercise: Is 1264789 a composite number? Yields: True Exercise: Is 851066429 a composite number? Yields: False Exercise: Is 45839 a composite number? Yields: True Exercise: Is 229784731 composite? Yields: True Exercise: Is 369406183 composite? Yields: False Exercise: Is 45794429 composite? Yields: False Exercise: Is 74401841 composite? Yields: True Exercise: Is 743549 prime? Yields: True Exercise: Is 1775219 composite? Yields: False Exercise: Is 794351 a composite number? Yields: True Exercise: Is 115294389809 a prime number? Yields: False Exercise: Is 217009005607 a composite number? Yi
english
probability: swr p sequence --------------------------- Q-: Calculate prob of sequence grie when four letters picked without replacement from {r: 1, e: 1, i: 1, w: 1, g: 1}. Conclusion: 1/120 Q-: Three letters picked without replacement from hjhhjhhhhhhhhj. What is prob of sequence jhh? Conclusion: 55/364 Q-: Four letters picked without replacement from {b: 3, d: 3}. What is prob of sequence dbdd? Conclusion: 1/20 Q-: Three letters picked without replacement from caccaaa. What is prob of sequence ccc? Conclusion: 1/35 Q-: What is prob of sequence xs when two letters picked without replacement from {s: 5, a: 10, j: 4, x: 1}? Conclusion: 1/76 Q-: What is prob of sequence ycy when three letters picked without replacement from {r: 2, y: 4, c: 2, l: 6, i: 1}? Conclusion: 4/455 Q-: Calculate prob of sequence afk when three letters picked without replacement from {k: 1, j: 3, y: 1, f: 1, i: 2, a: 5}. Conclusion: 5/1716 Q-: Two letters picked without replacement from vvhg. What is prob of sequence gh? Conclusion: 1/12 Q-: Calculate prob of sequence bzz when three letters picked without replacement from {b: 3, z: 4}. Conclusion: 6/35 Q-: Calculate prob of sequence opdt when four letters picked without replacement from ojjjptdtppjb. Conclusion: 1/1980 Q-: Two letters picked without replacement from {y: 1, u: 1, p: 1}. Give prob of sequence pu. Conclusion: 1/6 Q-: What is prob of sequence ooo when three letters picked without replacement from ooooooo? Conclusion: 1 Q-: What is prob of sequence iiz when three letters picked without replacement from {x: 8, n: 2, p: 1, z: 2, i: 7}? Conclusion: 7/570 Q-: Two letters picked without replacement from fbfbuuff. Give prob of sequence uu. Conclusion: 1/28 Q-: Two letters picked without replacement from pymmppyyypmyy. What is prob of sequence mp? Conclusion: 1/13 Q-: What is prob of sequence nwwf when four letters picked without replacement from nmmnwmmmwnqmmqfnnm? Conclusion: 1/7344 Q-: Three letters picked without replacement from hhpu
english
numbers: place value -------------------- Prompt: What is the units digit of 17966443? Therefore: 3 Prompt: What is the units digit of 30368? Therefore: 8 Prompt: What is the tens digit of 557? Therefore: 5 Prompt: What is the tens digit of 1381656? Therefore: 5 Prompt: What is the hundred thousands digit of 407218? Therefore: 4 Prompt: What is the hundreds digit of 9528? Therefore: 5 Prompt: What is the tens digit of 500? Therefore: 0 Prompt: What is the thousands digit of 21528? Therefore: 1 Prompt: What is the thousands digit of 8870? Therefore: 8 Prompt: What is the tens digit of 511? Therefore: 1 Prompt: What is the thousands digit of 5971258? Therefore: 1 Prompt: What is the millions digit of 240264120? Therefore: 0 Prompt: What is the ten millions digit of 544073494? Therefore: 4 Prompt: What is the ten millions digit of 36572085? Therefore: 3 Prompt: What is the tens digit of 75? Therefore: 7 Prompt: What is the hundreds digit of 332? Therefore: 3 Prompt: What is the hundreds digit of 797? Therefore: 7 Prompt: What is the millions digit of 7561041? Therefore: 7 Prompt: What is the units digit of 158864? Therefore: 4 Prompt: What is the ten thousands digit of 134717? Therefore: 3 Prompt: What is the units digit of 3341? Therefore: 1 Prompt: What is the ten millions digit of 11880010? Therefore: 1 Prompt: What is the hundred thousands digit of 261848? Therefore: 2 Prompt: What is the hundred millions digit of 1690773529? Therefore: 6 Prompt: What is the millions digit of 68089560? Therefore: 8 Prompt: What is the millions digit of 742604995? Therefore: 2 Prompt: What is the thousands digit of 35707? Therefore: 5 Prompt: What is the ten thousands digit of 358887? Therefore: 5 Prompt: What is the units digit of 67340? Therefore: 0 Prompt: What is the hundred millions digit of 196730542? Therefore: 1 Prompt: What is the hundreds digit of 2856? Therefore: 8 Prompt: What is the units digit of 1668520332? Therefore: 2 Prompt: What is the thousands digit of 10997? Th
english
numbers: place value -------------------- Math Q: What is the thousands digit of 12291443? Response: 1 Math Q: What is the hundreds digit of 765? Response: 7 Math Q: What is the units digit of 166? Response: 6 Math Q: What is the ten thousands digit of 38568132? Response: 6 Math Q: What is the millions digit of 2129389? Response: 2 Math Q: What is the millions digit of 15721727? Response: 5 Math Q: What is the tens digit of 16351148? Response: 4 Math Q: What is the ten millions digit of 297072695? Response: 9 Math Q: What is the ten millions digit of 27865519? Response: 2 Math Q: What is the hundreds digit of 5206? Response: 2 Math Q: What is the thousands digit of 4736? Response: 4 Math Q: What is the units digit of 5045? Response: 5 Math Q: What is the thousands digit of 13391? Response: 3 Math Q: What is the thousands digit of 667047? Response: 7 Math Q: What is the hundred thousands digit of 338433? Response: 3 Math Q: What is the hundred thousands digit of 1172997? Response: 1 Math Q: What is the ten millions digit of 2639518992? Response: 3 Math Q: What is the tens digit of 1657? Response: 5 Math Q: What is the ten thousands digit of 8231093? Response: 3 Math Q: What is the hundreds digit of 19453387? Response: 3 Math Q: What is the hundreds digit of 5438360? Response: 3 Math Q: What is the thousands digit of 3838? Response: 3 Math Q: What is the thousands digit of 7720? Response: 7 Math Q: What is the ten thousands digit of 200855375? Response: 5 Math Q: What is the ten thousands digit of 687266? Response: 8 Math Q: What is the thousands digit of 147987? Response: 7 Math Q: What is the thousands digit of 60121? Response: 0 Math Q: What is the units digit of 25841? Response: 1 Math Q: What is the units digit of 92855246? Response: 6 Math Q: What is the units digit of 6893? Response: 3 Math Q: What is the ten thousands digit of 830870? Response: 3 Math Q: What is the tens digit of 42261? Response: 6 Math Q: What is the ten millions digit of 95398152? Response:
english
numbers: is prime ----------------- Let us solve: Is 791443799 a composite number? A: False Let us solve: Is 20089737193 a composite number? A: False Let us solve: Is 93564581161 a prime number? A: True Let us solve: Is 157016031 composite? A: True Let us solve: Is 325709 composite? A: False Let us solve: Is 6671 a composite number? A: True Let us solve: Is 1881251 composite? A: True Let us solve: Is 493 a composite number? A: True Let us solve: Is 152335 a composite number? A: True Let us solve: Is 207923 prime? A: True Let us solve: Is 11372203 composite? A: True Let us solve: Is 46571 prime? A: False Let us solve: Is 1839833 prime? A: True Let us solve: Is 25819 composite? A: False Let us solve: Is 393257 a prime number? A: True Let us solve: Is 72057 a prime number? A: False Let us solve: Is 2261267 a composite number? A: False Let us solve: Is 14699 a prime number? A: True Let us solve: Is 190415 prime? A: False Let us solve: Is 7889767297 a composite number? A: False Let us solve: Is 30161 a composite number? A: False Let us solve: Is 259729541 a composite number? A: True Let us solve: Is 7517363 a composite number? A: True Let us solve: Is 744565 a prime number? A: False Let us solve: Is 5961536551 prime? A: False Let us solve: Is 60209 a prime number? A: True Let us solve: Is 61402087 composite? A: True Let us solve: Is 20070235 a composite number? A: True Let us solve: Is 102836087 a prime number? A: False Let us solve: Is 182323 composite? A: True Let us solve: Is 102471823 prime? A: True Let us solve: Is 113453 a prime number? A: True Let us solve: Is 18152953079 a prime number? A: True Let us solve: Is 291911 a composite number? A: True Let us solve: Is 14309 composite? A: True Let us solve: Is 92585 composite? A: True Let us solve: Is 416071 prime? A: True Let us solve: Is 5415855331 prime? A: True Let us solve: Is 161081 prime? A: False Let us solve: Is 30541 prime? A: False Let us solve: Is 1943747843 a composite number? A: True Let us solve: Is 19841
english
arithmetic: nearest integer root -------------------------------- Problem Statement: What is 305847804 to the power of 1/3, to the nearest integer? Workthrough: 674 Problem Statement: What is 665651162 to the power of 1/9, to the nearest integer? Workthrough: 10 Problem Statement: What is the square root of 5771524 to the nearest integer? Workthrough: 2402 Problem Statement: What is 555313 to the power of 1/3, to the nearest integer? Workthrough: 82 Problem Statement: What is the third root of 1461041 to the nearest integer? Workthrough: 113 Problem Statement: What is the third root of 603578644 to the nearest integer? Workthrough: 845 Problem Statement: What is 1369566513 to the power of 1/2, to the nearest integer? Workthrough: 37008 Problem Statement: What is 2032656441 to the power of 1/6, to the nearest integer? Workthrough: 36 Problem Statement: What is the sixth root of 343428015 to the nearest integer? Workthrough: 26 Problem Statement: What is the square root of 63613 to the nearest integer? Workthrough: 252 Problem Statement: What is the square root of 10218521 to the nearest integer? Workthrough: 3197 Problem Statement: What is 387118408 to the power of 1/2, to the nearest integer? Workthrough: 19675 Problem Statement: What is the fifth root of 1619772 to the nearest integer? Workthrough: 17 Problem Statement: What is 330250 to the power of 1/2, to the nearest integer? Workthrough: 575 Problem Statement: What is the fourth root of 879106 to the nearest integer? Workthrough: 31 Problem Statement: What is the square root of 11199486 to the nearest integer? Workthrough: 3347 Problem Statement: What is the seventh root of 36833209 to the nearest integer? Workthrough: 12 Problem Statement: What is 50885 to the power of 1/3, to the nearest integer? Workthrough: 37 Problem Statement: What is 723862803 to the power of 1/9, to the nearest integer? Workthrough: 10 Problem Statement: What is the third root of 21223598 to the nearest integer? Workthrough: 277 Problem
english
numbers: gcd ------------ Inquiry: Calculate the greatest common divisor of 120 and 24612360. Eval: 120 Inquiry: What is the greatest common factor of 418 and 88? Eval: 22 Inquiry: What is the greatest common divisor of 16354 and 30715328? Eval: 1258 Inquiry: Calculate the highest common factor of 3753 and 5421. Eval: 417 Inquiry: Calculate the greatest common divisor of 138 and 87207. Eval: 3 Inquiry: What is the greatest common factor of 392238 and 613998? Eval: 1386 Inquiry: Calculate the highest common factor of 16875 and 13743. Eval: 27 Inquiry: What is the highest common divisor of 3874 and 13? Eval: 13 Inquiry: What is the greatest common divisor of 63342 and 1458? Eval: 162 Inquiry: Calculate the greatest common divisor of 103059957 and 858. Eval: 429 Inquiry: Calculate the greatest common divisor of 1587 and 23. Eval: 23 Inquiry: Calculate the greatest common factor of 28 and 1106. Eval: 14 Inquiry: Calculate the highest common divisor of 324 and 4. Eval: 4 Inquiry: What is the greatest common factor of 11650 and 100? Eval: 50 Inquiry: What is the highest common divisor of 18 and 78? Eval: 6 Inquiry: What is the highest common factor of 2188 and 16? Eval: 4 Inquiry: What is the highest common divisor of 20 and 14? Eval: 2 Inquiry: What is the greatest common factor of 16 and 1841264? Eval: 16 Inquiry: Calculate the highest common divisor of 61 and 1433383612. Eval: 61 Inquiry: Calculate the greatest common factor of 97227 and 1404. Eval: 351 Inquiry: What is the highest common divisor of 756 and 131040? Eval: 252 Inquiry: Calculate the greatest common factor of 47759 and 9617. Eval: 163 Inquiry: What is the highest common divisor of 472 and 5? Eval: 1 Inquiry: What is the greatest common divisor of 3198 and 10136061? Eval: 1599 Inquiry: What is the highest common divisor of 18240 and 3135? Eval: 285 Inquiry: What is the greatest common factor of 660734 and 248? Eval: 62 Inquiry: Calculate the greatest common divisor of 8991016 and 41768. Eval: 1816 Inquiry:
english
probability: swr p level set ---------------------------- Let us solve: What is prob of picking 2 e, 1 r, and 1 o when four letters picked without replacement from {e: 2, o: 6, r: 4}? Derivation: 8/165 Let us solve: Two letters picked without replacement from cyyccyycycd. What is prob of picking 2 d? Derivation: 0 Let us solve: Two letters picked without replacement from njqnnljnqjjljjlqjqq. Give prob of picking 2 n. Derivation: 2/57 Let us solve: Two letters picked without replacement from {j: 4, a: 8, e: 8}. Give prob of picking 1 j and 1 e. Derivation: 16/95 Let us solve: Two letters picked without replacement from {h: 2, j: 3, s: 2, r: 4, y: 1}. What is prob of picking 1 s and 1 j? Derivation: 1/11 Let us solve: Two letters picked without replacement from nznznzzz. Give prob of picking 2 z. Derivation: 5/14 Let us solve: Two letters picked without replacement from jqjkjqjqqddjrrj. What is prob of picking 1 d and 1 r? Derivation: 4/105 Let us solve: Calculate prob of picking 2 d and 1 j when three letters picked without replacement from {d: 2, j: 9, l: 6}. Derivation: 9/680 Let us solve: Three letters picked without replacement from ybubbbbygggbdgdd. Give prob of picking 1 g, 1 y, and 1 d. Derivation: 3/70 Let us solve: Two letters picked without replacement from muxmxuxmuxu. What is prob of picking 1 x and 1 u? Derivation: 16/55 Let us solve: Calculate prob of picking 1 e, 1 l, and 1 c when three letters picked without replacement from cmzcrlrzzemzzl. Derivation: 1/91 Let us solve: Three letters picked without replacement from {a: 2, r: 1, s: 6, j: 4, c: 4}. Give prob of picking 1 j and 2 s. Derivation: 3/34 Let us solve: What is prob of picking 3 m and 1 s when four letters picked without replacement from {m: 13, s: 6}? Derivation: 143/323 Let us solve: What is prob of picking 1 m, 1 b, 1 g, and 1 t when four letters picked without replacement from {b: 1, r: 2, t: 3, m: 1, g: 3, u: 7}? Derivation: 9/2380 Let us solve: Three letters picked without replacement fr
english
numbers: place value -------------------- Problem: What is the units digit of 2888? Result: 8 Problem: What is the tens digit of 1561? Result: 6 Problem: What is the hundreds digit of 388468473? Result: 4 Problem: What is the ten thousands digit of 78083? Result: 7 Problem: What is the units digit of 396142? Result: 2 Problem: What is the hundreds digit of 2841? Result: 8 Problem: What is the units digit of 31970? Result: 0 Problem: What is the ten thousands digit of 10990? Result: 1 Problem: What is the tens digit of 1149358? Result: 5 Problem: What is the hundred thousands digit of 3686144875? Result: 1 Problem: What is the hundred thousands digit of 9242387? Result: 2 Problem: What is the millions digit of 36592803? Result: 6 Problem: What is the thousands digit of 21143? Result: 1 Problem: What is the hundreds digit of 60327? Result: 3 Problem: What is the thousands digit of 2926562? Result: 6 Problem: What is the hundred thousands digit of 24790383? Result: 7 Problem: What is the hundreds digit of 815722? Result: 7 Problem: What is the hundred thousands digit of 134176? Result: 1 Problem: What is the ten thousands digit of 27326? Result: 2 Problem: What is the hundred thousands digit of 498699? Result: 4 Problem: What is the hundred thousands digit of 19006187? Result: 0 Problem: What is the millions digit of 2341863? Result: 2 Problem: What is the units digit of 261? Result: 1 Problem: What is the hundreds digit of 628088? Result: 0 Problem: What is the tens digit of 739? Result: 3 Problem: What is the ten thousands digit of 485959076? Result: 5 Problem: What is the thousands digit of 1408? Result: 1 Problem: What is the ten millions digit of 880505614? Result: 8 Problem: What is the units digit of 53690? Result: 0 Problem: What is the ten millions digit of 16677145? Result: 1 Problem: What is the millions digit of 2314134? Result: 2 Problem: What is the ten thousands digit of 2338997? Result: 3 Problem: What is the ten thousands digit of 28434? Result: 2 Prob
english
measurement: time ----------------- Challenge: What is 546 minutes after 12:25 AM? Sol: 9:31 AM Challenge: What is 428 minutes after 6:52 PM? Sol: 2:00 AM Challenge: What is 634 minutes before 6:17 PM? Sol: 7:43 AM Challenge: What is 152 minutes after 2:55 AM? Sol: 5:27 AM Challenge: What is 360 minutes before 6:37 PM? Sol: 12:37 PM Challenge: What is 423 minutes before 3:58 PM? Sol: 8:55 AM Challenge: What is 121 minutes after 11:42 PM? Sol: 1:43 AM Challenge: What is 517 minutes after 11:06 AM? Sol: 7:43 PM Challenge: How many minutes are there between 7:51 AM and 8:02 AM? Sol: 11 Challenge: What is 6 minutes after 11:14 AM? Sol: 11:20 AM Challenge: What is 130 minutes after 7:26 AM? Sol: 9:36 AM Challenge: What is 398 minutes before 4:12 PM? Sol: 9:34 AM Challenge: How many minutes are there between 12:04 PM and 5:14 PM? Sol: 310 Challenge: What is 69 minutes before 9:41 PM? Sol: 8:32 PM Challenge: How many minutes are there between 4:01 AM and 11:49 AM? Sol: 468 Challenge: What is 252 minutes before 1:13 PM? Sol: 9:01 AM Challenge: How many minutes are there between 6:51 PM and 4:42 AM? Sol: 591 Challenge: How many minutes are there between 2:58 AM and 4:45 AM? Sol: 107 Challenge: What is 235 minutes after 12:42 PM? Sol: 4:37 PM Challenge: What is 709 minutes before 4:14 AM? Sol: 4:25 PM Challenge: How many minutes are there between 8:01 PM and 1:03 AM? Sol: 302 Challenge: What is 360 minutes after 2:15 PM? Sol: 8:15 PM Challenge: How many minutes are there between 1:07 PM and 12:35 AM? Sol: 688 Challenge: How many minutes are there between 2:52 PM and 4:28 PM? Sol: 96 Challenge: How many minutes are there between 2:31 AM and 8:42 AM? Sol: 371 Challenge: How many minutes are there between 5:05 PM and 2:35 AM? Sol: 570 Challenge: What is 76 minutes after 3:21 PM? Sol: 4:37 PM Challenge: What is 121 minutes after 1:39 PM? Sol: 3:40 PM Challenge: What is 556 minutes after 3:54 PM? Sol: 1:10 AM Challenge: What is 690 minutes before 4:56 AM? Sol: 5:26 PM Challenge: W
english
numbers: is prime ----------------- Part A: Is 25969 prime? Compute: True Part A: Is 29737789787 a composite number? Compute: False Part A: Is 53843681 composite? Compute: False Part A: Is 240900353 a composite number? Compute: True Part A: Is 5237138059 composite? Compute: False Part A: Is 20165274611 a prime number? Compute: False Part A: Is 2203 a composite number? Compute: False Part A: Is 4383517 composite? Compute: True Part A: Is 9127 a composite number? Compute: False Part A: Is 36721 prime? Compute: True Part A: Is 788153 a prime number? Compute: True Part A: Is 168311111 prime? Compute: True Part A: Is 117847 prime? Compute: False Part A: Is 20056589549 a prime number? Compute: False Part A: Is 20442511 prime? Compute: True Part A: Is 31333411 a composite number? Compute: False Part A: Is 379092277 prime? Compute: False Part A: Is 32565430357 composite? Compute: True Part A: Is 308571127 composite? Compute: True Part A: Is 78635 a composite number? Compute: True Part A: Is 79637 a prime number? Compute: False Part A: Is 494704061 prime? Compute: True Part A: Is 112963 a composite number? Compute: True Part A: Is 1866814067 a composite number? Compute: True Part A: Is 39059 composite? Compute: True Part A: Is 373727 a prime number? Compute: False Part A: Is 1002403 a composite number? Compute: False Part A: Is 120355346911 a composite number? Compute: False Part A: Is 29791063 a composite number? Compute: True Part A: Is 1309881189 a composite number? Compute: True Part A: Is 163846403 composite? Compute: True Part A: Is 179143 composite? Compute: False Part A: Is 126854411 prime? Compute: True Part A: Is 17083337 composite? Compute: True Part A: Is 23938105 composite? Compute: True Part A: Is 296941 a prime number? Compute: True Part A: Is 12887818699 a prime number? Compute: False Part A: Is 705093293 a prime number? Compute: False Part A: Is 96137 prime? Compute: True Part A: Is 28591 a prime number? Compute: True Part A: Is 49800449 prime? Compute: True
english
arithmetic: nearest integer root -------------------------------- Puzzle: What is 38 to the power of 1/3, to the nearest integer? Math A: 3 Puzzle: What is 3000573494 to the power of 1/2, to the nearest integer? Math A: 54777 Puzzle: What is the square root of 24420 to the nearest integer? Math A: 156 Puzzle: What is the ninth root of 16810 to the nearest integer? Math A: 3 Puzzle: What is the fourth root of 944170115 to the nearest integer? Math A: 175 Puzzle: What is 1492089 to the power of 1/5, to the nearest integer? Math A: 17 Puzzle: What is the square root of 37945198 to the nearest integer? Math A: 6160 Puzzle: What is 5162 to the power of 1/7, to the nearest integer? Math A: 3 Puzzle: What is 253 to the power of 1/7, to the nearest integer? Math A: 2 Puzzle: What is the third root of 11655 to the nearest integer? Math A: 23 Puzzle: What is the square root of 17764 to the nearest integer? Math A: 133 Puzzle: What is the fourth root of 197550 to the nearest integer? Math A: 21 Puzzle: What is 122 to the power of 1/2, to the nearest integer? Math A: 11 Puzzle: What is the tenth root of 74545731 to the nearest integer? Math A: 6 Puzzle: What is 264694 to the power of 1/3, to the nearest integer? Math A: 64 Puzzle: What is the seventh root of 220670238 to the nearest integer? Math A: 16 Puzzle: What is the ninth root of 1187 to the nearest integer? Math A: 2 Puzzle: What is 68915204 to the power of 1/2, to the nearest integer? Math A: 8302 Puzzle: What is 4881 to the power of 1/2, to the nearest integer? Math A: 70 Puzzle: What is the seventh root of 7093 to the nearest integer? Math A: 4 Puzzle: What is 4617 to the power of 1/3, to the nearest integer? Math A: 17 Puzzle: What is the square root of 4548091640 to the nearest integer? Math A: 67440 Puzzle: What is the square root of 14368 to the nearest integer? Math A: 120 Puzzle: What is the tenth root of 923451382 to the nearest integer? Math A: 8 Puzzle: What is the square root of 1700552 to the nearest intege
english
numbers: is factor ------------------ Statement: Is 31 a factor of 23188? Eval: True Statement: Is 17 a factor of 24304? Eval: False Statement: Does 3061 divide 864084976? Eval: False Statement: Does 1243 divide 4739681685? Eval: False Statement: Does 45 divide 52977330? Eval: True Statement: Does 26 divide 4031528? Eval: False Statement: Is 13 a factor of 73127? Eval: False Statement: Is 4030859692 a multiple of 62? Eval: True Statement: Is 168 a multiple of 42? Eval: True Statement: Is 50516 a multiple of 159? Eval: False Statement: Is 389113 a multiple of 11? Eval: False Statement: Is 1595950 a multiple of 2705? Eval: True Statement: Is 3278 a multiple of 11? Eval: True Statement: Is 78889980 a multiple of 65? Eval: True Statement: Does 11 divide 1428263? Eval: False Statement: Is 1517 a multiple of 41? Eval: True Statement: Does 59 divide 388763? Eval: False Statement: Does 10 divide 320? Eval: True Statement: Does 7 divide 1170? Eval: False Statement: Is 1016429660 a multiple of 8585? Eval: True Statement: Is 6127970 a multiple of 49? Eval: False Statement: Does 54 divide 16956? Eval: True Statement: Does 19 divide 99275? Eval: True Statement: Is 242729 a multiple of 388? Eval: False Statement: Does 661 divide 11228407? Eval: True Statement: Is 4979350 a multiple of 50? Eval: True Statement: Does 22 divide 24919048? Eval: True Statement: Is 295554 a multiple of 113? Eval: False Statement: Is 35 a factor of 6426910? Eval: True Statement: Does 8 divide 6448? Eval: True Statement: Is 38 a factor of 988? Eval: True Statement: Does 55 divide 1314? Eval: False Statement: Does 27 divide 13743? Eval: True Statement: Is 52 a factor of 2028? Eval: True Statement: Does 7 divide 25251? Eval: False Statement: Does 48 divide 25611? Eval: False Statement: Is 31061808 a multiple of 912? Eval: True Statement: Is 21 a factor of 67875? Eval: False Statement: Is 21 a factor of 4044201? Eval: True Statement: Does 20 divide 260? Eval: True Statement: Is 67477 a multiple of 8? Eval:
english
numbers: is factor ------------------ Example: Does 27 divide 45511335? Clarification: True Example: Is 841770 a multiple of 10? Clarification: True Example: Is 4 a factor of 6967520? Clarification: True Example: Does 26 divide 39235144? Clarification: True Example: Does 230 divide 817022? Clarification: False Example: Is 79 a factor of 119970142? Clarification: False Example: Does 31 divide 57839583? Clarification: True Example: Does 4 divide 74373? Clarification: False Example: Does 24 divide 881964681? Clarification: False Example: Does 105 divide 191114769? Clarification: False Example: Does 3 divide 333? Clarification: True Example: Is 10200 a multiple of 136? Clarification: True Example: Does 10 divide 660? Clarification: True Example: Does 24 divide 32736? Clarification: True Example: Is 9 a factor of 275869? Clarification: False Example: Is 17 a factor of 748102? Clarification: True Example: Is 210 a multiple of 21? Clarification: True Example: Does 66 divide 132? Clarification: True Example: Is 7 a factor of 711? Clarification: False Example: Is 384 a multiple of 22? Clarification: False Example: Is 6 a factor of 160290? Clarification: True Example: Is 16 a factor of 242? Clarification: False Example: Is 1158 a multiple of 14? Clarification: False Example: Is 50329768 a multiple of 1544? Clarification: True Example: Is 3754047 a multiple of 847? Clarification: False Example: Does 13 divide 1189397? Clarification: False Example: Is 3 a factor of 1588839? Clarification: True Example: Is 285 a factor of 2621281? Clarification: False Example: Is 71 a factor of 149362558? Clarification: True Example: Does 19 divide 2047517? Clarification: False Example: Does 112 divide 78512? Clarification: True Example: Does 605 divide 7357105? Clarification: False Example: Is 11 a factor of 3705889? Clarification: True Example: Does 18 divide 74525? Clarification: False Example: Does 37 divide 16771829? Clarification: False Example: Is 57 a factor of 1619427? Clarification: Tr
english
numbers: is prime ----------------- Conundrum: Is 892516517 a composite number? Response: True Conundrum: Is 113316719 a composite number? Response: False Conundrum: Is 189525863 prime? Response: False Conundrum: Is 19219205 prime? Response: False Conundrum: Is 1120786 a prime number? Response: False Conundrum: Is 20693 a composite number? Response: False Conundrum: Is 137947213 prime? Response: True Conundrum: Is 320123 composite? Response: True Conundrum: Is 4441 composite? Response: False Conundrum: Is 2045047 a composite number? Response: False Conundrum: Is 1494557 prime? Response: True Conundrum: Is 361723 a prime number? Response: True Conundrum: Is 20653 a composite number? Response: True Conundrum: Is 44553202 a composite number? Response: True Conundrum: Is 291773389 prime? Response: True Conundrum: Is 82699 composite? Response: False Conundrum: Is 116117 composite? Response: True Conundrum: Is 83117 a composite number? Response: False Conundrum: Is 10352864111 composite? Response: True Conundrum: Is 655519867 prime? Response: True Conundrum: Is 7321 a prime number? Response: True Conundrum: Is 162769 composite? Response: True Conundrum: Is 1184371 a composite number? Response: True Conundrum: Is 4369 a composite number? Response: True Conundrum: Is 214543967 a composite number? Response: True Conundrum: Is 60471071 a composite number? Response: True Conundrum: Is 27358 prime? Response: False Conundrum: Is 640861 prime? Response: False Conundrum: Is 4035761317 a prime number? Response: False Conundrum: Is 13397 composite? Response: False Conundrum: Is 2271 a composite number? Response: True Conundrum: Is 102656651 a composite number? Response: False Conundrum: Is 36796213 prime? Response: True Conundrum: Is 2069534 a prime number? Response: False Conundrum: Is 5532377701 a prime number? Response: True Conundrum: Is 91250181227 a composite number? Response: False Conundrum: Is 730694249 a composite number? Response: False Conundrum: Is 447 prime? Response:
english
numbers: gcd ------------ Example: What is the highest common factor of 108 and 53793? Steps: 9 Example: Calculate the highest common divisor of 4008430146 and 2478. Steps: 2478 Example: Calculate the highest common divisor of 70 and 407918. Steps: 14 Example: What is the highest common divisor of 48 and 492? Steps: 12 Example: What is the greatest common divisor of 3612945 and 145635? Steps: 1995 Example: What is the greatest common divisor of 224945 and 35? Steps: 35 Example: Calculate the greatest common factor of 210 and 24185. Steps: 35 Example: Calculate the greatest common divisor of 20 and 116. Steps: 4 Example: What is the highest common factor of 10090 and 17610? Steps: 10 Example: Calculate the highest common factor of 312 and 5976. Steps: 24 Example: What is the highest common divisor of 14759383 and 17? Steps: 17 Example: Calculate the greatest common divisor of 44310 and 15. Steps: 15 Example: What is the highest common divisor of 2743 and 416? Steps: 13 Example: What is the highest common divisor of 1059 and 6? Steps: 3 Example: Calculate the greatest common divisor of 9 and 18999. Steps: 9 Example: What is the greatest common factor of 20644984 and 424? Steps: 424 Example: Calculate the highest common factor of 9 and 27476487. Steps: 9 Example: What is the greatest common factor of 82426275 and 171? Steps: 171 Example: Calculate the greatest common factor of 497673 and 69696. Steps: 1089 Example: What is the highest common factor of 191081792 and 5888? Steps: 1472 Example: What is the highest common divisor of 2444 and 4? Steps: 4 Example: What is the highest common factor of 960 and 15? Steps: 15 Example: What is the greatest common factor of 30 and 14580? Steps: 30 Example: Calculate the greatest common divisor of 126 and 5436. Steps: 18 Example: What is the greatest common factor of 759 and 69? Steps: 69 Example: What is the greatest common factor of 627 and 1539? Steps: 57 Example: What is the highest common divisor of 4082 and 338? Steps: 26 Exa
english
probability: swr p level set ---------------------------- What if: What is prob of picking 1 y, 1 o, and 2 f when four letters picked without replacement from qyhqmffmo? β†’: 1/126 What if: What is prob of picking 1 m and 1 g when two letters picked without replacement from {u: 4, m: 1, y: 2, k: 3, v: 2, g: 2}? β†’: 2/91 What if: Three letters picked without replacement from {o: 3, r: 3, n: 3, k: 2, p: 3}. What is prob of picking 1 p and 2 k? β†’: 3/364 What if: Calculate prob of picking 2 y and 1 c when three letters picked without replacement from {s: 1, y: 6, f: 4, c: 1, e: 6}. β†’: 5/272 What if: Two letters picked without replacement from {o: 2, t: 3, u: 2, h: 1, q: 4, x: 2}. What is prob of picking 1 x and 1 q? β†’: 8/91 What if: What is prob of picking 1 j, 1 v, and 1 h when three letters picked without replacement from {h: 2, m: 1, j: 5, t: 2, z: 4, v: 1}? β†’: 2/91 What if: Two letters picked without replacement from aaaaa. What is prob of picking 2 a? β†’: 1 What if: Calculate prob of picking 1 b and 1 s when two letters picked without replacement from {s: 7, i: 1, b: 2}. β†’: 14/45 What if: Two letters picked without replacement from kcckllkl. Give prob of picking 1 l and 1 k. β†’: 9/28 What if: Three letters picked without replacement from {a: 6, h: 1, z: 3, f: 4}. Give prob of picking 1 a, 1 f, and 1 z. β†’: 18/91 What if: Three letters picked without replacement from jtujpuupu. What is prob of picking 2 u and 1 t? β†’: 1/14 What if: What is prob of picking 3 h when three letters picked without replacement from {w: 1, h: 17}? β†’: 5/6 What if: Calculate prob of picking 1 o and 2 l when three letters picked without replacement from ykkolcwwkkyoklcokkk. β†’: 1/323 What if: Calculate prob of picking 1 h and 1 k when two letters picked without replacement from djjkjjdjdrjrjdirikhj. β†’: 1/95 What if: Calculate prob of picking 1 x and 1 a when two letters picked without replacement from {p: 4, f: 1, d: 2, a: 2, x: 1}. β†’: 2/45 What if: Calculate prob of picking 1 m, 1 a, and 1 g when th
english
numbers: is prime ----------------- Case: Is 1312345994 composite? Derivation: True Case: Is 3209675927 a prime number? Derivation: True Case: Is 1843365169 composite? Derivation: False Case: Is 11281 a composite number? Derivation: True Case: Is 80737 a prime number? Derivation: True Case: Is 748650349 prime? Derivation: True Case: Is 95423039 composite? Derivation: True Case: Is 10073676289 composite? Derivation: False Case: Is 180750347 prime? Derivation: True Case: Is 2602837 composite? Derivation: True Case: Is 43560483671 prime? Derivation: False Case: Is 10709 composite? Derivation: False Case: Is 803178533 prime? Derivation: True Case: Is 6821896307 prime? Derivation: True Case: Is 28757 composite? Derivation: True Case: Is 119701 prime? Derivation: True Case: Is 21695101 composite? Derivation: True Case: Is 60493 prime? Derivation: True Case: Is 31298467699 a composite number? Derivation: False Case: Is 4193099 prime? Derivation: False Case: Is 15631535 a prime number? Derivation: False Case: Is 26341969631 prime? Derivation: True Case: Is 491 a composite number? Derivation: False Case: Is 618521 a composite number? Derivation: False Case: Is 699553 a prime number? Derivation: False Case: Is 8641 composite? Derivation: False Case: Is 451650623 prime? Derivation: False Case: Is 31725668177 a prime number? Derivation: False Case: Is 6060772919 a prime number? Derivation: False Case: Is 9259531 prime? Derivation: True Case: Is 4040064013 a prime number? Derivation: True Case: Is 390763283 a prime number? Derivation: True Case: Is 10730370197 a prime number? Derivation: False Case: Is 3035761 a composite number? Derivation: False Case: Is 27791 prime? Derivation: True Case: Is 343517 composite? Derivation: False Case: Is 2705225209 composite? Derivation: False Case: Is 31307 prime? Derivation: True Case: Is 8011 a composite number? Derivation: False Case: Is 55951537 a prime number? Derivation: True Case: Is 402029207 a composite number? Derivation: True Case:
english
numbers: place value -------------------- Example: What is the thousands digit of 1104806893? Therefore: 6 Example: What is the tens digit of 24037? Therefore: 3 Example: What is the tens digit of 1181880614? Therefore: 1 Example: What is the hundreds digit of 75080? Therefore: 0 Example: What is the hundreds digit of 1550065067? Therefore: 0 Example: What is the hundreds digit of 160771310? Therefore: 3 Example: What is the hundreds digit of 389262196? Therefore: 1 Example: What is the tens digit of 214533? Therefore: 3 Example: What is the thousands digit of 2072? Therefore: 2 Example: What is the millions digit of 12750777? Therefore: 2 Example: What is the tens digit of 1180985? Therefore: 8 Example: What is the hundreds digit of 518595013? Therefore: 0 Example: What is the ten thousands digit of 8214142? Therefore: 1 Example: What is the thousands digit of 3940? Therefore: 3 Example: What is the hundreds digit of 1473525? Therefore: 5 Example: What is the hundred thousands digit of 1009417? Therefore: 0 Example: What is the units digit of 3697? Therefore: 7 Example: What is the units digit of 32360? Therefore: 0 Example: What is the ten millions digit of 10296370? Therefore: 1 Example: What is the tens digit of 3169494377? Therefore: 7 Example: What is the hundreds digit of 87899? Therefore: 8 Example: What is the hundreds digit of 1990? Therefore: 9 Example: What is the hundred millions digit of 438199532? Therefore: 4 Example: What is the hundred thousands digit of 397729727? Therefore: 7 Example: What is the hundreds digit of 370009591? Therefore: 5 Example: What is the ten thousands digit of 131632? Therefore: 3 Example: What is the hundred thousands digit of 3299527? Therefore: 2 Example: What is the thousands digit of 114644973? Therefore: 4 Example: What is the units digit of 455169675? Therefore: 5 Example: What is the hundreds digit of 132735? Therefore: 7 Example: What is the thousands digit of 53158? Therefore: 3 Example: What is the millions digit o
english
numbers: div remainder ---------------------- Given: What is the remainder when 202796 is divided by 259? Outcome: 258 Given: What is the remainder when 18612528 is divided by 1511? Outcome: 30 Given: Calculate the remainder when 95 is divided by 19. Outcome: 0 Given: What is the remainder when 1620 is divided by 772? Outcome: 76 Given: What is the remainder when 270670 is divided by 11263? Outcome: 358 Given: What is the remainder when 19322 is divided by 1486? Outcome: 4 Given: What is the remainder when 7507 is divided by 764? Outcome: 631 Given: Calculate the remainder when 4059514 is divided by 148. Outcome: 22 Given: Calculate the remainder when 379 is divided by 16. Outcome: 11 Given: What is the remainder when 218226 is divided by 109109? Outcome: 8 Given: Calculate the remainder when 759 is divided by 314. Outcome: 131 Given: Calculate the remainder when 20381346 is divided by 7912. Outcome: 34 Given: What is the remainder when 2299601 is divided by 121? Outcome: 117 Given: Calculate the remainder when 310 is divided by 13. Outcome: 11 Given: What is the remainder when 245022 is divided by 27? Outcome: 24 Given: What is the remainder when 1451012 is divided by 131908? Outcome: 24 Given: Calculate the remainder when 627815 is divided by 41847. Outcome: 110 Given: Calculate the remainder when 664976 is divided by 2692. Outcome: 52 Given: Calculate the remainder when 271491 is divided by 271386. Outcome: 105 Given: What is the remainder when 160397 is divided by 14566? Outcome: 171 Given: What is the remainder when 21360 is divided by 308? Outcome: 108 Given: Calculate the remainder when 685 is divided by 334. Outcome: 17 Given: What is the remainder when 370756 is divided by 620? Outcome: 616 Given: What is the remainder when 1970384490 is divided by 3427? Outcome: 3424 Given: What is the remainder when 16584 is divided by 5524? Outcome: 12 Given: What is the remainder when 1051 is divided by 12? Outcome: 7 Given: Calculate the remainder when 5519 is divided
english
numbers: is prime ----------------- Problem: Is 18806 a composite number? Solution: True Problem: Is 7331 composite? Solution: False Problem: Is 4192527263 a prime number? Solution: False Problem: Is 48847 a composite number? Solution: False Problem: Is 134303 prime? Solution: False Problem: Is 26588203 prime? Solution: False Problem: Is 2414021 a composite number? Solution: False Problem: Is 1249851761 prime? Solution: False Problem: Is 35860200577 prime? Solution: False Problem: Is 118019279947 composite? Solution: True Problem: Is 103733033 composite? Solution: True Problem: Is 16753405597 composite? Solution: True Problem: Is 26203319 a composite number? Solution: False Problem: Is 9600047 a prime number? Solution: True Problem: Is 3251 a prime number? Solution: True Problem: Is 8870179 a prime number? Solution: True Problem: Is 1735637 a prime number? Solution: False Problem: Is 4634367 a composite number? Solution: True Problem: Is 37239599 composite? Solution: True Problem: Is 1840867 a composite number? Solution: True Problem: Is 4117 a prime number? Solution: False Problem: Is 46337 a prime number? Solution: True Problem: Is 3746329 composite? Solution: False Problem: Is 876479 a composite number? Solution: False Problem: Is 1009 composite? Solution: False Problem: Is 1282571 a composite number? Solution: False Problem: Is 85439 a composite number? Solution: False Problem: Is 10435 composite? Solution: True Problem: Is 78806381 a composite number? Solution: False Problem: Is 1572739 a prime number? Solution: False Problem: Is 14923 a prime number? Solution: True Problem: Is 18961009 a composite number? Solution: False Problem: Is 71658200099 a composite number? Solution: False Problem: Is 167683 a composite number? Solution: False Problem: Is 86797643 composite? Solution: True Problem: Is 11196569611 a prime number? Solution: True Problem: Is 2533963 a composite number? Solution: False Problem: Is 3390494669 composite? Solution: True Problem: Is 11182 a pri
english
probability: swr p sequence --------------------------- Ask: Three letters picked without replacement from {p: 1, a: 1, i: 1, z: 1, h: 1, x: 2}. What is prob of sequence azi? Math A: 1/210 Ask: What is prob of sequence qqf when three letters picked without replacement from {n: 5, f: 3, q: 3, h: 1}? Math A: 3/220 Ask: Two letters picked without replacement from bbllolobbobll. What is prob of sequence bl? Math A: 25/156 Ask: Calculate prob of sequence cuc when three letters picked without replacement from {c: 2, u: 4, s: 1}. Math A: 4/105 Ask: What is prob of sequence gip when three letters picked without replacement from {t: 5, g: 3, d: 1, e: 1, i: 2, p: 1}? Math A: 1/286 Ask: Calculate prob of sequence uz when two letters picked without replacement from uuuudduddudzdudr. Math A: 7/240 Ask: Two letters picked without replacement from dbsgk. Give prob of sequence db. Math A: 1/20 Ask: What is prob of sequence iih when three letters picked without replacement from hhiithit? Math A: 3/56 Ask: What is prob of sequence tfto when four letters picked without replacement from ohothohfpphoft? Math A: 2/3003 Ask: Calculate prob of sequence jja when three letters picked without replacement from {q: 4, j: 3, l: 6, y: 2, a: 2}. Math A: 1/340 Ask: What is prob of sequence bjbr when four letters picked without replacement from jfrfbfbbjjb? Math A: 1/220 Ask: Four letters picked without replacement from uxuuxupxlxixxpluu. Give prob of sequence pilu. Math A: 1/2380 Ask: Two letters picked without replacement from jregd. Give prob of sequence dj. Math A: 1/20 Ask: Calculate prob of sequence evtf when four letters picked without replacement from thfnevh. Math A: 1/840 Ask: What is prob of sequence pou when three letters picked without replacement from {u: 5, p: 1, o: 7}? Math A: 35/1716 Ask: Three letters picked without replacement from {o: 2, s: 1, y: 4}. Give prob of sequence osy. Math A: 4/105 Ask: Two letters picked without replacement from xoikaxpaixkxxixioa. What is prob of seque
english
probability: swr p level set ---------------------------- Prompt: Three letters picked without replacement from {y: 15, f: 4}. Give prob of picking 3 y. Answer: 455/969 Prompt: Two letters picked without replacement from {o: 2, j: 5}. Give prob of picking 2 o. Answer: 1/21 Prompt: Calculate prob of picking 4 i when four letters picked without replacement from {i: 12, d: 3, l: 1}. Answer: 99/364 Prompt: Calculate prob of picking 2 i and 1 r when three letters picked without replacement from riizzbz. Answer: 1/35 Prompt: Two letters picked without replacement from apncpaaiapjaija. What is prob of picking 1 a and 1 n? Answer: 2/35 Prompt: Calculate prob of picking 2 b when two letters picked without replacement from qqqbqqb. Answer: 1/21 Prompt: Calculate prob of picking 1 r, 2 b, and 1 d when four letters picked without replacement from {r: 1, j: 1, b: 2, d: 1}. Answer: 1/5 Prompt: What is prob of picking 2 n and 1 g when three letters picked without replacement from ganadddaandaannddnan? Answer: 1/76 Prompt: What is prob of picking 2 j and 1 n when three letters picked without replacement from jjjnjjnnnj? Answer: 1/2 Prompt: What is prob of picking 1 l and 2 q when three letters picked without replacement from {l: 2, v: 10, q: 6}? Answer: 5/136 Prompt: What is prob of picking 2 k and 2 g when four letters picked without replacement from {g: 2, k: 6}? Answer: 3/14 Prompt: Two letters picked without replacement from dddddvdddbd. What is prob of picking 1 d and 1 v? Answer: 9/55 Prompt: Two letters picked without replacement from exexteexexxegxe. Give prob of picking 2 x. Answer: 1/7 Prompt: Two letters picked without replacement from {n: 1, t: 3, m: 1, p: 4, i: 7, r: 2}. What is prob of picking 1 i and 1 r? Answer: 14/153 Prompt: What is prob of picking 1 i and 1 h when two letters picked without replacement from {a: 1, i: 1, f: 1, h: 1, d: 4}? Answer: 1/28 Prompt: Three letters picked without replacement from llblzbb. What is prob of picking 1 l and 2 b? Answer: 9/35
english
numbers: is prime ----------------- Math Q: Is 20520611 composite? Thus: True Math Q: Is 4677179 prime? Thus: False Math Q: Is 5579190013 a prime number? Thus: True Math Q: Is 31168218703 prime? Thus: True Math Q: Is 2829383 a composite number? Thus: False Math Q: Is 2933016917 composite? Thus: False Math Q: Is 15307 composite? Thus: False Math Q: Is 63914 composite? Thus: True Math Q: Is 7279 a composite number? Thus: True Math Q: Is 5630006861 a prime number? Thus: False Math Q: Is 20269 prime? Thus: True Math Q: Is 566413 composite? Thus: False Math Q: Is 119159 prime? Thus: True Math Q: Is 7533968261 composite? Thus: True Math Q: Is 9917 composite? Thus: True Math Q: Is 16758799 a composite number? Thus: True Math Q: Is 3589 composite? Thus: True Math Q: Is 468297131 prime? Thus: False Math Q: Is 321359 composite? Thus: False Math Q: Is 184391215 composite? Thus: True Math Q: Is 4111 prime? Thus: True Math Q: Is 42118 a composite number? Thus: True Math Q: Is 4575241 a prime number? Thus: False Math Q: Is 1420703 prime? Thus: False Math Q: Is 15779 prime? Thus: False Math Q: Is 8097501119 a prime number? Thus: True Math Q: Is 19154194187 composite? Thus: True Math Q: Is 4831 a composite number? Thus: False Math Q: Is 350737061 a prime number? Thus: True Math Q: Is 690103 a composite number? Thus: False Math Q: Is 5855 a composite number? Thus: True Math Q: Is 301461302 a composite number? Thus: True Math Q: Is 33157453 prime? Thus: False Math Q: Is 11299 a composite number? Thus: False Math Q: Is 19279379 a composite number? Thus: True Math Q: Is 7452145 a prime number? Thus: False Math Q: Is 38036898569 prime? Thus: True Math Q: Is 59395186 a prime number? Thus: False Math Q: Is 169488577 a composite number? Thus: True Math Q: Is 42589 a prime number? Thus: True Math Q: Is 737629 a composite number? Thus: False Math Q: Is 1531163 composite? Thus: True Math Q: Is 18299 a prime number? Thus: False Math Q: Is 1317134611 prime? Thus: False Math Q: Is 89369773 prime
english
probability: swr p level set ---------------------------- Question: Two letters picked without replacement from ararrsrasrrrssssa. What is prob of picking 1 a and 1 s? Answer: 3/17 Question: What is prob of picking 1 o and 1 j when two letters picked without replacement from {x: 2, z: 2, o: 3, j: 2}? Answer: 1/6 Question: Calculate prob of picking 1 m and 1 u when two letters picked without replacement from {r: 4, m: 4, y: 3, n: 2, u: 3, p: 1}. Answer: 3/34 Question: What is prob of picking 1 s and 1 h when two letters picked without replacement from {h: 6, s: 12}? Answer: 8/17 Question: Four letters picked without replacement from {k: 9, s: 3}. What is prob of picking 1 s and 3 k? Answer: 28/55 Question: Calculate prob of picking 2 r when two letters picked without replacement from ooooroooorrorg. Answer: 6/91 Question: Three letters picked without replacement from {g: 2, e: 1, i: 1}. Give prob of picking 1 e and 2 i. Answer: 0 Question: Four letters picked without replacement from {i: 1, y: 2, g: 1, u: 1}. Give prob of picking 1 u, 1 y, 1 g, and 1 i. Answer: 2/5 Question: Three letters picked without replacement from {x: 9}. Give prob of picking 3 x. Answer: 1 Question: Calculate prob of picking 1 t and 1 k when two letters picked without replacement from {g: 1, k: 1, t: 1}. Answer: 1/3 Question: What is prob of picking 2 j when two letters picked without replacement from {a: 2, j: 4, f: 2}? Answer: 3/14 Question: Three letters picked without replacement from {o: 2, r: 9}. Give prob of picking 1 r and 2 o. Answer: 3/55 Question: Calculate prob of picking 1 r and 1 f when two letters picked without replacement from {r: 1, d: 1, f: 1, j: 1, a: 1}. Answer: 1/10 Question: Calculate prob of picking 1 r and 1 p when two letters picked without replacement from pcr. Answer: 1/3 Question: Three letters picked without replacement from tyytbllyybyymccltm. Give prob of picking 1 c and 2 l. Answer: 1/136 Question: Calculate prob of picking 2 c when two letters picked without r
english
probability: swr p level set ---------------------------- Statement: Calculate prob of picking 3 k and 1 u when four letters picked without replacement from {p: 5, k: 7, u: 7}. Key: 245/3876 Statement: Four letters picked without replacement from {c: 1, o: 1, x: 2}. What is prob of picking 2 o, 1 x, and 1 c? Key: 0 Statement: Three letters picked without replacement from alltsyta. Give prob of picking 1 t, 1 a, and 1 y. Key: 1/14 Statement: What is prob of picking 1 z and 1 u when two letters picked without replacement from iuzhuuuue? Key: 5/36 Statement: Three letters picked without replacement from {i: 7, p: 3, q: 3}. Give prob of picking 1 p and 2 i. Key: 63/286 Statement: Two letters picked without replacement from {i: 16, b: 2}. What is prob of picking 1 b and 1 i? Key: 32/153 Statement: Three letters picked without replacement from mckimcccmwkkkw. What is prob of picking 2 m and 1 c? Key: 3/91 Statement: Four letters picked without replacement from sjjjjjsj. Give prob of picking 4 j. Key: 3/14 Statement: Calculate prob of picking 1 p, 1 o, and 2 v when four letters picked without replacement from {o: 3, v: 7, p: 3}. Key: 189/715 Statement: Calculate prob of picking 2 r when two letters picked without replacement from hrhhoohooorohhoirour. Key: 3/95 Statement: Calculate prob of picking 2 b when two letters picked without replacement from {b: 4, a: 7}. Key: 6/55 Statement: Four letters picked without replacement from {b: 1, q: 17}. What is prob of picking 4 q? Key: 7/9 Statement: Calculate prob of picking 2 n when two letters picked without replacement from {f: 5, y: 2, h: 1, p: 3, n: 8}. Key: 28/171 Statement: Four letters picked without replacement from rrnnerrneerrre. Give prob of picking 2 r and 2 n. Key: 9/143 Statement: What is prob of picking 2 n and 1 q when three letters picked without replacement from {h: 11, q: 1, v: 3, n: 5}? Key: 1/114 Statement: Two letters picked without replacement from zmzmwmzmwemwzm. Give prob of picking 1 m and 1 z. Key: 24/91
english
numbers: is prime ----------------- Let: Is 3641494487 a composite number? Interpretation: False Let: Is 4682280991 composite? Interpretation: True Let: Is 316718543 a composite number? Interpretation: True Let: Is 66379367 composite? Interpretation: False Let: Is 1779952781 a composite number? Interpretation: True Let: Is 65951 a composite number? Interpretation: False Let: Is 308129 composite? Interpretation: False Let: Is 41227831 a composite number? Interpretation: True Let: Is 46678 a composite number? Interpretation: True Let: Is 259923323 prime? Interpretation: False Let: Is 2569099179 composite? Interpretation: True Let: Is 9490142801 composite? Interpretation: True Let: Is 1556101 prime? Interpretation: False Let: Is 941 a prime number? Interpretation: True Let: Is 17270926411 composite? Interpretation: False Let: Is 317153 a prime number? Interpretation: False Let: Is 17389679465 composite? Interpretation: True Let: Is 14977297669 prime? Interpretation: True Let: Is 298929 composite? Interpretation: True Let: Is 117563 composite? Interpretation: False Let: Is 14163143 composite? Interpretation: False Let: Is 187723 a prime number? Interpretation: False Let: Is 6911 composite? Interpretation: False Let: Is 168673 composite? Interpretation: False Let: Is 31122439 composite? Interpretation: True Let: Is 2394641329 prime? Interpretation: True Let: Is 6999084669 a prime number? Interpretation: False Let: Is 7466372345 a prime number? Interpretation: False Let: Is 8479756823 prime? Interpretation: True Let: Is 177551131 a composite number? Interpretation: False Let: Is 143158009 a prime number? Interpretation: True Let: Is 1361 prime? Interpretation: True Let: Is 490201 prime? Interpretation: True Let: Is 13618117186 a prime number? Interpretation: False Let: Is 19407 prime? Interpretation: False Let: Is 1594365257 prime? Interpretation: False Let: Is 24017630663 a prime number? Interpretation: False Let: Is 37537 a prime number? Interpretation: True Let: Is 126
english
numbers: place value -------------------- Statement: What is the millions digit of 1948689173? Eval: 8 Statement: What is the hundreds digit of 3006? Eval: 0 Statement: What is the units digit of 2053313? Eval: 3 Statement: What is the tens digit of 7914539? Eval: 3 Statement: What is the hundreds digit of 3452? Eval: 4 Statement: What is the units digit of 9646? Eval: 6 Statement: What is the units digit of 10139202? Eval: 2 Statement: What is the hundreds digit of 17366285? Eval: 2 Statement: What is the units digit of 145? Eval: 5 Statement: What is the units digit of 85778547? Eval: 7 Statement: What is the hundred millions digit of 8108655019? Eval: 1 Statement: What is the tens digit of 3202? Eval: 0 Statement: What is the hundreds digit of 561922? Eval: 9 Statement: What is the tens digit of 22505? Eval: 0 Statement: What is the thousands digit of 1061421? Eval: 1 Statement: What is the tens digit of 2059? Eval: 5 Statement: What is the units digit of 316? Eval: 6 Statement: What is the units digit of 10895043? Eval: 3 Statement: What is the ten thousands digit of 77164? Eval: 7 Statement: What is the billions digit of 1007824124? Eval: 1 Statement: What is the millions digit of 14017189? Eval: 4 Statement: What is the hundred thousands digit of 146655044? Eval: 6 Statement: What is the hundreds digit of 245883492? Eval: 4 Statement: What is the ten millions digit of 152715083? Eval: 5 Statement: What is the thousands digit of 2636? Eval: 2 Statement: What is the tens digit of 354? Eval: 5 Statement: What is the ten millions digit of 127702390? Eval: 2 Statement: What is the units digit of 147129? Eval: 9 Statement: What is the tens digit of 35603083? Eval: 8 Statement: What is the tens digit of 773725119? Eval: 1 Statement: What is the tens digit of 1514? Eval: 1 Statement: What is the units digit of 68263661? Eval: 1 Statement: What is the tens digit of 1578? Eval: 7 Statement: What is the hundreds digit of 379867809? Eval: 8 Statement: What is the thousand
english
probability: swr p level set ---------------------------- Q/A: What is prob of picking 2 m when two letters picked without replacement from {k: 5, m: 5}? Eval: 2/9 Q/A: Calculate prob of picking 3 z and 1 w when four letters picked without replacement from {m: 1, z: 3, y: 1, d: 3, w: 3}. Eval: 1/110 Q/A: Four letters picked without replacement from dglglddljdlugglu. What is prob of picking 1 l, 1 j, and 2 g? Eval: 3/182 Q/A: Two letters picked without replacement from yybyyssyeyysysebyby. Give prob of picking 1 b and 1 s. Eval: 4/57 Q/A: Calculate prob of picking 1 m, 1 v, and 1 f when three letters picked without replacement from vfvxvxsvvmsxmfm. Eval: 6/91 Q/A: Calculate prob of picking 2 l and 1 d when three letters picked without replacement from kytdldoolodoo. Eval: 3/286 Q/A: Four letters picked without replacement from {s: 4, j: 2}. What is prob of picking 1 j and 3 s? Eval: 8/15 Q/A: Calculate prob of picking 2 d when two letters picked without replacement from {o: 3, d: 2}. Eval: 1/10 Q/A: What is prob of picking 1 c and 1 f when two letters picked without replacement from rrfrrfrcfbccrr? Eval: 9/91 Q/A: Calculate prob of picking 1 p and 1 b when two letters picked without replacement from {f: 3, m: 3, p: 1, b: 7}. Eval: 1/13 Q/A: What is prob of picking 3 o and 1 k when four letters picked without replacement from kkokkkkookoo? Eval: 14/99 Q/A: What is prob of picking 1 v and 1 m when two letters picked without replacement from {a: 2, m: 4, g: 9, v: 1}? Eval: 1/30 Q/A: Two letters picked without replacement from qqmqqqqcqqbqqqq. Give prob of picking 2 q. Eval: 22/35 Q/A: Four letters picked without replacement from {t: 5, b: 1, o: 4}. What is prob of picking 2 t and 2 o? Eval: 2/7 Q/A: What is prob of picking 2 s when two letters picked without replacement from ssssgggsgssssg? Eval: 36/91 Q/A: Three letters picked without replacement from {y: 3, b: 1, p: 2, c: 3, t: 10}. Give prob of picking 1 y, 1 c, and 1 p. Eval: 6/323 Q/A: What is prob of picking 2 s a
english
probability: swr p level set ---------------------------- Task: What is prob of picking 4 n when four letters picked without replacement from {w: 4, n: 7}? Outcome: 7/66 Task: What is prob of picking 1 y, 1 j, and 1 x when three letters picked without replacement from xjjqyxxqbjyj? Outcome: 6/55 Task: Four letters picked without replacement from {a: 7, b: 6}. Give prob of picking 2 b and 2 a. Outcome: 63/143 Task: Three letters picked without replacement from ertrhtw. What is prob of picking 2 r and 1 w? Outcome: 1/35 Task: Calculate prob of picking 1 y and 1 c when two letters picked without replacement from {g: 4, l: 1, s: 1, c: 2, y: 2}. Outcome: 4/45 Task: Two letters picked without replacement from vvv. Give prob of picking 2 v. Outcome: 1 Task: What is prob of picking 1 q, 1 f, and 2 d when four letters picked without replacement from qfdqhppdqffq? Outcome: 4/165 Task: Three letters picked without replacement from vllvvl. What is prob of picking 3 v? Outcome: 1/20 Task: What is prob of picking 1 b and 3 t when four letters picked without replacement from {f: 5, t: 7, b: 8}? Outcome: 56/969 Task: Four letters picked without replacement from {n: 2, b: 4, v: 4, a: 5}. What is prob of picking 4 v? Outcome: 1/1365 Task: Calculate prob of picking 2 k when two letters picked without replacement from kllkklkllllkknklkn. Outcome: 28/153 Task: What is prob of picking 3 h and 1 z when four letters picked without replacement from ozzzxhzhohxzzozhz? Outcome: 8/595 Task: Three letters picked without replacement from {g: 2, f: 10}. Give prob of picking 1 g and 2 f. Outcome: 9/22 Task: Three letters picked without replacement from {d: 7, k: 9}. Give prob of picking 3 d. Outcome: 1/16 Task: Three letters picked without replacement from cafcffaraaaa. Give prob of picking 1 r and 2 f. Outcome: 3/220 Task: Two letters picked without replacement from rawhu. Give prob of picking 1 a and 1 r. Outcome: 1/10 Task: What is prob of picking 1 r, 1 h, and 1 d when three letters picked wit
english
numbers: is factor ------------------ Question: Is 22 a factor of 35869? Math A: False Question: Is 45109337 a multiple of 13? Math A: True Question: Does 2 divide 14993? Math A: False Question: Does 13 divide 33566? Math A: True Question: Does 3364 divide 426349639? Math A: False Question: Is 77627 a multiple of 87? Math A: False Question: Is 152298726 a multiple of 165? Math A: False Question: Does 42 divide 5347227? Math A: False Question: Is 30 a factor of 451710? Math A: True Question: Is 165 a factor of 148830? Math A: True Question: Does 216 divide 43206518? Math A: False Question: Does 112 divide 89040? Math A: True Question: Is 43364338 a multiple of 667? Math A: True Question: Is 5576107068 a multiple of 9? Math A: True Question: Does 135 divide 5940? Math A: True Question: Does 3 divide 202? Math A: False Question: Is 47776652 a multiple of 408? Math A: False Question: Is 106 a factor of 525742? Math A: False Question: Does 12 divide 829318932? Math A: True Question: Does 41 divide 53773? Math A: False Question: Is 1184 a multiple of 32? Math A: True Question: Is 37 a factor of 3044? Math A: False Question: Does 303 divide 867186? Math A: True Question: Is 26938845 a multiple of 279? Math A: True Question: Does 94 divide 22654? Math A: True Question: Is 32 a factor of 450? Math A: False Question: Is 64 a factor of 1354? Math A: False Question: Does 174 divide 50808? Math A: True Question: Is 10734987 a multiple of 101? Math A: True Question: Is 11 a factor of 863623848? Math A: False Question: Is 199 a factor of 39800? Math A: True Question: Does 15 divide 4470? Math A: True Question: Is 65701 a multiple of 136? Math A: False Question: Is 1481172928 a multiple of 16? Math A: True Question: Is 7524841 a multiple of 23? Math A: True Question: Does 42 divide 374? Math A: False Question: Is 14 a factor of 383382828? Math A: False Question: Is 20870 a multiple of 35? Math A: False Question: Is 6 a factor of 822? Math A: True Question: Is 167 a factor of 2455?
english
arithmetic: nearest integer root -------------------------------- Request: What is the third root of 6937 to the nearest integer? β†’: 19 Request: What is the seventh root of 595003152 to the nearest integer? β†’: 18 Request: What is 4271 to the power of 1/3, to the nearest integer? β†’: 16 Request: What is the square root of 1204565811 to the nearest integer? β†’: 34707 Request: What is the seventh root of 49609 to the nearest integer? β†’: 5 Request: What is the square root of 4801 to the nearest integer? β†’: 69 Request: What is 149479 to the power of 1/3, to the nearest integer? β†’: 53 Request: What is the third root of 47233461 to the nearest integer? β†’: 361 Request: What is the cube root of 72257057 to the nearest integer? β†’: 417 Request: What is the tenth root of 699685013 to the nearest integer? β†’: 8 Request: What is the seventh root of 15914685 to the nearest integer? β†’: 11 Request: What is 1510858749 to the power of 1/2, to the nearest integer? β†’: 38870 Request: What is 1287369 to the power of 1/2, to the nearest integer? β†’: 1135 Request: What is 564139 to the power of 1/5, to the nearest integer? β†’: 14 Request: What is 218813 to the power of 1/2, to the nearest integer? β†’: 468 Request: What is the square root of 87707 to the nearest integer? β†’: 296 Request: What is 230168899 to the power of 1/7, to the nearest integer? β†’: 16 Request: What is the third root of 8851649 to the nearest integer? β†’: 207 Request: What is the ninth root of 105785174 to the nearest integer? β†’: 8 Request: What is 55528 to the power of 1/9, to the nearest integer? β†’: 3 Request: What is 119369 to the power of 1/4, to the nearest integer? β†’: 19 Request: What is the third root of 7635 to the nearest integer? β†’: 20 Request: What is the square root of 5119682180 to the nearest integer? β†’: 71552 Request: What is the third root of 1160781002 to the nearest integer? β†’: 1051 Request: What is the cube root of 349 to the nearest integer? β†’: 7 Request: What is 3508 to the power of 1/2, to the nearest intege
english
measurement: time ----------------- Exercise: What is 90 minutes after 3:49 AM? Fix: 5:19 AM Exercise: How many minutes are there between 9:01 AM and 7:37 PM? Fix: 636 Exercise: What is 328 minutes after 7:25 AM? Fix: 12:53 PM Exercise: What is 324 minutes before 11:25 PM? Fix: 6:01 PM Exercise: How many minutes are there between 12:57 AM and 10:16 AM? Fix: 559 Exercise: How many minutes are there between 12:36 PM and 12:19 AM? Fix: 703 Exercise: How many minutes are there between 4:03 AM and 4:38 AM? Fix: 35 Exercise: What is 292 minutes after 5:53 AM? Fix: 10:45 AM Exercise: What is 126 minutes after 3:13 AM? Fix: 5:19 AM Exercise: How many minutes are there between 12:14 AM and 9:09 AM? Fix: 535 Exercise: How many minutes are there between 1:18 PM and 12:15 AM? Fix: 657 Exercise: What is 67 minutes before 5:04 PM? Fix: 3:57 PM Exercise: What is 655 minutes after 12:37 AM? Fix: 11:32 AM Exercise: What is 317 minutes before 5:10 AM? Fix: 11:53 PM Exercise: How many minutes are there between 5:27 PM and 2:45 AM? Fix: 558 Exercise: How many minutes are there between 2:19 PM and 7:46 PM? Fix: 327 Exercise: How many minutes are there between 7:51 PM and 4:03 AM? Fix: 492 Exercise: What is 709 minutes before 12:13 AM? Fix: 12:24 PM Exercise: How many minutes are there between 7:38 PM and 2:41 AM? Fix: 423 Exercise: How many minutes are there between 10:06 PM and 12:56 AM? Fix: 170 Exercise: What is 132 minutes after 11:39 AM? Fix: 1:51 PM Exercise: How many minutes are there between 11:11 PM and 11:15 PM? Fix: 4 Exercise: How many minutes are there between 12:12 PM and 8:52 PM? Fix: 520 Exercise: How many minutes are there between 10:21 PM and 9:46 AM? Fix: 685 Exercise: How many minutes are there between 12:47 AM and 6:04 AM? Fix: 317 Exercise: What is 56 minutes before 2:19 PM? Fix: 1:23 PM Exercise: What is 156 minutes after 6:42 PM? Fix: 9:18 PM Exercise: How many minutes are there between 3:05 AM and 6:00 AM? Fix: 175 Exercise: How many minutes are there between 7:
english
measurement: time ----------------- Case: How many minutes are there between 11:22 PM and 7:09 AM? Soln: 467 Case: What is 473 minutes before 5:33 AM? Soln: 9:40 PM Case: What is 355 minutes before 1:01 AM? Soln: 7:06 PM Case: How many minutes are there between 11:47 PM and 2:23 AM? Soln: 156 Case: How many minutes are there between 3:51 PM and 1:34 AM? Soln: 583 Case: What is 265 minutes after 12:43 AM? Soln: 5:08 AM Case: What is 705 minutes after 6:57 AM? Soln: 6:42 PM Case: How many minutes are there between 2:17 AM and 2:07 PM? Soln: 710 Case: How many minutes are there between 2:07 AM and 1:04 PM? Soln: 657 Case: What is 324 minutes after 10:49 AM? Soln: 4:13 PM Case: What is 592 minutes before 10:25 PM? Soln: 12:33 PM Case: How many minutes are there between 11:30 PM and 7:55 AM? Soln: 505 Case: How many minutes are there between 4:50 PM and 2:07 AM? Soln: 557 Case: How many minutes are there between 1:17 AM and 11:42 AM? Soln: 625 Case: What is 360 minutes before 8:45 PM? Soln: 2:45 PM Case: What is 573 minutes after 7:09 AM? Soln: 4:42 PM Case: How many minutes are there between 2:53 PM and 8:38 PM? Soln: 345 Case: How many minutes are there between 11:41 AM and 6:20 PM? Soln: 399 Case: How many minutes are there between 11:26 AM and 6:05 PM? Soln: 399 Case: What is 535 minutes before 6:23 AM? Soln: 9:28 PM Case: What is 616 minutes before 10:21 PM? Soln: 12:05 PM Case: What is 706 minutes after 8:09 AM? Soln: 7:55 PM Case: What is 416 minutes after 10:25 PM? Soln: 5:21 AM Case: What is 110 minutes after 5:13 PM? Soln: 7:03 PM Case: How many minutes are there between 11:13 PM and 4:02 AM? Soln: 289 Case: How many minutes are there between 1:11 PM and 3:08 PM? Soln: 117 Case: How many minutes are there between 3:17 AM and 9:43 AM? Soln: 386 Case: How many minutes are there between 10:42 PM and 8:18 AM? Soln: 576 Case: How many minutes are there between 9:14 PM and 6:38 AM? Soln: 564 Case: How many minutes are there between 2:56 PM and 7:35 PM? Soln: 279 Case
english
probability: swr p level set ---------------------------- Math Problem: Calculate prob of picking 4 u when four letters picked without replacement from {u: 5}. Resolution: 1 Math Problem: What is prob of picking 1 d and 2 n when three letters picked without replacement from {o: 2, d: 7, n: 2}? Resolution: 7/165 Math Problem: What is prob of picking 2 r and 1 s when three letters picked without replacement from {i: 2, s: 3, r: 5}? Resolution: 1/4 Math Problem: What is prob of picking 1 i and 2 y when three letters picked without replacement from cicicyykciiiykiiici? Resolution: 9/323 Math Problem: What is prob of picking 1 f and 1 q when two letters picked without replacement from tqttqrftftrfttt? Resolution: 2/35 Math Problem: Four letters picked without replacement from {h: 2, z: 4, y: 3}. What is prob of picking 2 y and 2 z? Resolution: 1/7 Math Problem: What is prob of picking 1 o and 1 d when two letters picked without replacement from {d: 2, o: 2, g: 4, t: 1, h: 3, b: 3}? Resolution: 4/105 Math Problem: Calculate prob of picking 2 o when two letters picked without replacement from {o: 3, b: 1, w: 1, a: 5}. Resolution: 1/15 Math Problem: Calculate prob of picking 1 p and 1 b when two letters picked without replacement from {b: 9, p: 1, a: 1, l: 2}. Resolution: 3/26 Math Problem: Four letters picked without replacement from {l: 3, s: 4, j: 2, c: 2}. Give prob of picking 2 c and 2 l. Resolution: 1/110 Math Problem: Three letters picked without replacement from zozzzzzzzzeozzezzpz. What is prob of picking 1 o and 2 e? Resolution: 2/969 Math Problem: What is prob of picking 2 c and 1 g when three letters picked without replacement from {x: 1, z: 3, g: 1, p: 3, h: 1, c: 2}? Resolution: 1/165 Math Problem: What is prob of picking 1 h and 1 q when two letters picked without replacement from khhhhhhhhhhkqq? Resolution: 20/91 Math Problem: Three letters picked without replacement from {f: 5}. Give prob of picking 3 f. Resolution: 1 Math Problem: Four letters picked witho
english
probability: swr p level set ---------------------------- Problem: Calculate prob of picking 2 e and 1 y when three letters picked without replacement from eeyyeeyeymekys. Soln: 75/364 Problem: What is prob of picking 1 d and 3 i when four letters picked without replacement from iibdiddd? Soln: 2/35 Problem: Four letters picked without replacement from {r: 14, j: 4}. Give prob of picking 3 r and 1 j. Soln: 364/765 Problem: What is prob of picking 2 z and 1 u when three letters picked without replacement from {u: 2, j: 5, d: 1, p: 8, z: 3}? Soln: 2/323 Problem: Two letters picked without replacement from cxoopoiooupp. What is prob of picking 1 c and 1 p? Soln: 1/22 Problem: Two letters picked without replacement from {h: 2, z: 3, j: 1, o: 4}. Give prob of picking 2 z. Soln: 1/15 Problem: Calculate prob of picking 2 w when two letters picked without replacement from wxwwwwwwwwwwwww. Soln: 13/15 Problem: Two letters picked without replacement from {f: 7, p: 1, z: 1, s: 2, i: 5, v: 1}. What is prob of picking 1 z and 1 f? Soln: 7/136 Problem: Calculate prob of picking 4 q when four letters picked without replacement from pqqqpqrpjppuqqja. Soln: 3/364 Problem: Two letters picked without replacement from {d: 1, l: 1, g: 1, i: 1, t: 1}. What is prob of picking 1 i and 1 g? Soln: 1/10 Problem: Two letters picked without replacement from {n: 1, p: 1, d: 1, m: 4, o: 5, b: 1}. What is prob of picking 1 m and 1 n? Soln: 2/39 Problem: Four letters picked without replacement from {d: 2, j: 3, i: 3, a: 1, u: 1}. What is prob of picking 3 j and 1 d? Soln: 1/105 Problem: Three letters picked without replacement from fhfffhhffhrffrff. Give prob of picking 3 h. Soln: 1/140 Problem: What is prob of picking 2 h, 1 k, and 1 g when four letters picked without replacement from hkhghkkghhhk? Soln: 8/33 Problem: What is prob of picking 3 t and 1 j when four letters picked without replacement from {j: 3, b: 1, t: 4, a: 4, l: 2, n: 3}? Soln: 3/595 Problem: Three letters picked without replacem
english
probability: swr p sequence --------------------------- Problem Statement: Three letters picked without replacement from {i: 4, e: 10}. Give prob of sequence eee. Steps: 30/91 Problem Statement: What is prob of sequence xy when two letters picked without replacement from bfablxy? Steps: 1/42 Problem Statement: Three letters picked without replacement from zgzzgzzgzgyggg. Give prob of sequence yzz. Steps: 5/364 Problem Statement: Three letters picked without replacement from ttrzzrtrtt. Give prob of sequence ztt. Steps: 1/18 Problem Statement: What is prob of sequence sf when two letters picked without replacement from {f: 10, s: 4}? Steps: 20/91 Problem Statement: What is prob of sequence pppl when four letters picked without replacement from pljlppp? Steps: 2/35 Problem Statement: Two letters picked without replacement from rrrrrvvamrmrmvvrrrr. Give prob of sequence rv. Steps: 22/171 Problem Statement: Three letters picked without replacement from mggeggggggeegggggmm. Give prob of sequence eee. Steps: 1/969 Problem Statement: What is prob of sequence ng when two letters picked without replacement from {c: 4, j: 5, g: 5, t: 1, n: 4}? Steps: 10/171 Problem Statement: What is prob of sequence zkkv when four letters picked without replacement from {z: 2, o: 1, k: 3, v: 1}? Steps: 1/70 Problem Statement: Calculate prob of sequence mmc when three letters picked without replacement from mtmmtmmctt. Steps: 1/36 Problem Statement: What is prob of sequence eee when three letters picked without replacement from {s: 4, k: 1, e: 3, o: 2, d: 1}? Steps: 1/165 Problem Statement: Calculate prob of sequence nw when two letters picked without replacement from dddkddwdwddnkkdirrw. Steps: 1/114 Problem Statement: Two letters picked without replacement from dcdcj. What is prob of sequence dc? Steps: 1/5 Problem Statement: Four letters picked without replacement from giiiuiiiig. What is prob of sequence giug? Steps: 1/360 Problem Statement: Two letters picked without replacement from {j:
english
numbers: div remainder ---------------------- Q.: Calculate the remainder when 525770 is divided by 3266. Key: 3210 Q.: What is the remainder when 1577504 is divided by 47? Key: 43 Q.: What is the remainder when 1289992 is divided by 651? Key: 361 Q.: Calculate the remainder when 48508 is divided by 147. Key: 145 Q.: Calculate the remainder when 4886 is divided by 136. Key: 126 Q.: What is the remainder when 9223029 is divided by 13? Key: 10 Q.: What is the remainder when 2359 is divided by 64? Key: 55 Q.: What is the remainder when 1696 is divided by 1685? Key: 11 Q.: Calculate the remainder when 120 is divided by 62. Key: 58 Q.: What is the remainder when 1314361 is divided by 290? Key: 81 Q.: What is the remainder when 240 is divided by 46? Key: 10 Q.: What is the remainder when 12094 is divided by 8? Key: 6 Q.: What is the remainder when 576562 is divided by 1343? Key: 415 Q.: Calculate the remainder when 93807 is divided by 164. Key: 163 Q.: What is the remainder when 468 is divided by 164? Key: 140 Q.: What is the remainder when 2493 is divided by 232? Key: 173 Q.: Calculate the remainder when 46631 is divided by 348. Key: 347 Q.: Calculate the remainder when 339320 is divided by 716. Key: 652 Q.: What is the remainder when 177067 is divided by 233? Key: 220 Q.: Calculate the remainder when 56 is divided by 11. Key: 1 Q.: What is the remainder when 4981283 is divided by 87? Key: 11 Q.: What is the remainder when 52 is divided by 10? Key: 2 Q.: Calculate the remainder when 35572 is divided by 98. Key: 96 Q.: Calculate the remainder when 5475388 is divided by 5475388. Key: 0 Q.: Calculate the remainder when 712071 is divided by 1846. Key: 1361 Q.: Calculate the remainder when 39577 is divided by 39. Key: 31 Q.: What is the remainder when 540260 is divided by 28428? Key: 128 Q.: What is the remainder when 98979 is divided by 14? Key: 13 Q.: What is the remainder when 145260 is divided by 112? Key: 108 Q.: Calculate the remainder when 386535 is divided by 69. Key:
english
measurement: time ----------------- Issue: How many minutes are there between 2:10 AM and 11:55 AM? Yields: 585 Issue: What is 172 minutes after 11:44 PM? Yields: 2:36 AM Issue: How many minutes are there between 5:08 AM and 1:13 PM? Yields: 485 Issue: How many minutes are there between 5:52 PM and 10:50 PM? Yields: 298 Issue: How many minutes are there between 4:15 PM and 6:37 PM? Yields: 142 Issue: What is 345 minutes before 3:06 PM? Yields: 9:21 AM Issue: What is 209 minutes after 10:35 AM? Yields: 2:04 PM Issue: What is 607 minutes after 1:35 AM? Yields: 11:42 AM Issue: What is 6 minutes after 2:53 PM? Yields: 2:59 PM Issue: What is 266 minutes after 12:18 AM? Yields: 4:44 AM Issue: What is 360 minutes before 12:51 PM? Yields: 6:51 AM Issue: How many minutes are there between 11:50 AM and 11:18 PM? Yields: 688 Issue: How many minutes are there between 3:38 PM and 7:07 PM? Yields: 209 Issue: What is 293 minutes after 9:25 AM? Yields: 2:18 PM Issue: What is 283 minutes before 5:17 PM? Yields: 12:34 PM Issue: How many minutes are there between 7:29 PM and 9:29 PM? Yields: 120 Issue: How many minutes are there between 5:19 AM and 3:46 PM? Yields: 627 Issue: How many minutes are there between 4:28 PM and 4:18 AM? Yields: 710 Issue: What is 428 minutes after 12:45 PM? Yields: 7:53 PM Issue: What is 490 minutes before 2:41 PM? Yields: 6:31 AM Issue: How many minutes are there between 11:36 AM and 8:34 PM? Yields: 538 Issue: What is 597 minutes after 1:44 PM? Yields: 11:41 PM Issue: How many minutes are there between 10:24 PM and 9:21 AM? Yields: 657 Issue: How many minutes are there between 7:34 AM and 12:08 PM? Yields: 274 Issue: What is 323 minutes before 2:25 PM? Yields: 9:02 AM Issue: How many minutes are there between 11:47 PM and 11:14 AM? Yields: 687 Issue: How many minutes are there between 6:43 PM and 8:43 PM? Yields: 120 Issue: How many minutes are there between 6:54 PM and 8:26 PM? Yields: 92 Issue: How many minutes are there between 9:51 PM and 6:19 AM? Yie
english
numbers: is factor ------------------ Math Problem: Does 245 divide 8115150? Result: False Math Problem: Is 94 a factor of 135078? Result: True Math Problem: Is 27966552 a multiple of 1847? Result: False Math Problem: Does 4 divide 1112611070? Result: False Math Problem: Is 5 a factor of 2070? Result: True Math Problem: Is 1900 a multiple of 25? Result: True Math Problem: Is 357121830 a multiple of 10? Result: True Math Problem: Does 8 divide 255912? Result: True Math Problem: Does 17 divide 135191? Result: False Math Problem: Is 251622 a multiple of 18? Result: True Math Problem: Is 11 a factor of 1216390? Result: False Math Problem: Is 204484 a multiple of 268? Result: True Math Problem: Is 641708 a multiple of 57? Result: False Math Problem: Does 74 divide 8421348? Result: True Math Problem: Is 347671 a multiple of 35? Result: False Math Problem: Is 327160 a multiple of 7? Result: False Math Problem: Does 28 divide 406476? Result: True Math Problem: Is 718 a multiple of 12? Result: False Math Problem: Does 426 divide 5666226? Result: True Math Problem: Is 608 a factor of 112639944? Result: False Math Problem: Is 479 a factor of 340722280? Result: True Math Problem: Does 9 divide 19230193? Result: False Math Problem: Is 8096 a multiple of 16? Result: True Math Problem: Is 8413117 a multiple of 13? Result: False Math Problem: Does 8498 divide 860923882? Result: True Math Problem: Is 180 a factor of 847? Result: False Math Problem: Is 36671535 a multiple of 327? Result: False Math Problem: Is 619 a factor of 16654814? Result: True Math Problem: Does 20 divide 18413440? Result: True Math Problem: Is 28 a factor of 23501? Result: False Math Problem: Is 182 a factor of 182730? Result: False Math Problem: Does 198 divide 6310668? Result: False Math Problem: Is 28 a factor of 61250874? Result: False Math Problem: Is 31 a factor of 3691? Result: False Math Problem: Is 3 a factor of 5163? Result: True Math Problem: Does 42 divide 11634? Result: True Math Problem: Is 119400
english
arithmetic: nearest integer root -------------------------------- Q: What is the third root of 190885290 to the nearest integer? Hence: 576 Q: What is the square root of 38136118 to the nearest integer? Hence: 6175 Q: What is the eighth root of 698338658 to the nearest integer? Hence: 13 Q: What is the third root of 1173186369 to the nearest integer? Hence: 1055 Q: What is the third root of 6574256971 to the nearest integer? Hence: 1873 Q: What is the cube root of 1223960 to the nearest integer? Hence: 107 Q: What is 83447237 to the power of 1/9, to the nearest integer? Hence: 8 Q: What is the third root of 335463869 to the nearest integer? Hence: 695 Q: What is 9572 to the power of 1/3, to the nearest integer? Hence: 21 Q: What is the sixth root of 55665868 to the nearest integer? Hence: 20 Q: What is 171163 to the power of 1/6, to the nearest integer? Hence: 7 Q: What is the cube root of 1470557 to the nearest integer? Hence: 114 Q: What is the seventh root of 5194012 to the nearest integer? Hence: 9 Q: What is 3793 to the power of 1/3, to the nearest integer? Hence: 16 Q: What is the eighth root of 23522 to the nearest integer? Hence: 4 Q: What is 631523410 to the power of 1/2, to the nearest integer? Hence: 25130 Q: What is the fifth root of 337195 to the nearest integer? Hence: 13 Q: What is 306287466 to the power of 1/8, to the nearest integer? Hence: 12 Q: What is 391478 to the power of 1/10, to the nearest integer? Hence: 4 Q: What is 220402 to the power of 1/2, to the nearest integer? Hence: 469 Q: What is the ninth root of 75946 to the nearest integer? Hence: 3 Q: What is 7936 to the power of 1/4, to the nearest integer? Hence: 9 Q: What is 794435 to the power of 1/4, to the nearest integer? Hence: 30 Q: What is the fourth root of 2438426 to the nearest integer? Hence: 40 Q: What is the cube root of 2782976 to the nearest integer? Hence: 141 Q: What is the square root of 7835 to the nearest integer? Hence: 89 Q: What is the cube root of 312846 to the neare
english
measurement: time ----------------- Q/A: What is 331 minutes before 1:48 PM? Derivation: 8:17 AM Q/A: How many minutes are there between 12:05 PM and 7:30 PM? Derivation: 445 Q/A: How many minutes are there between 9:32 AM and 2:41 PM? Derivation: 309 Q/A: How many minutes are there between 4:01 PM and 12:17 AM? Derivation: 496 Q/A: How many minutes are there between 4:56 PM and 3:27 AM? Derivation: 631 Q/A: What is 468 minutes after 8:18 AM? Derivation: 4:06 PM Q/A: What is 680 minutes after 11:24 AM? Derivation: 10:44 PM Q/A: What is 472 minutes after 12:44 AM? Derivation: 8:36 AM Q/A: What is 457 minutes before 10:03 AM? Derivation: 2:26 AM Q/A: How many minutes are there between 4:24 PM and 12:01 AM? Derivation: 457 Q/A: What is 328 minutes after 7:58 PM? Derivation: 1:26 AM Q/A: What is 11 minutes after 1:39 AM? Derivation: 1:50 AM Q/A: What is 244 minutes before 3:35 AM? Derivation: 11:31 PM Q/A: How many minutes are there between 5:15 AM and 10:25 AM? Derivation: 310 Q/A: How many minutes are there between 11:54 PM and 9:38 AM? Derivation: 584 Q/A: How many minutes are there between 5:39 PM and 10:39 PM? Derivation: 300 Q/A: What is 91 minutes before 5:03 PM? Derivation: 3:32 PM Q/A: How many minutes are there between 10:45 AM and 4:51 PM? Derivation: 366 Q/A: How many minutes are there between 2:08 PM and 1:11 AM? Derivation: 663 Q/A: What is 277 minutes before 11:29 AM? Derivation: 6:52 AM Q/A: What is 103 minutes after 7:26 PM? Derivation: 9:09 PM Q/A: How many minutes are there between 3:08 AM and 5:54 AM? Derivation: 166 Q/A: What is 657 minutes before 9:00 AM? Derivation: 10:03 PM Q/A: How many minutes are there between 6:13 AM and 11:54 AM? Derivation: 341 Q/A: How many minutes are there between 8:24 PM and 3:14 AM? Derivation: 410 Q/A: What is 158 minutes after 6:40 PM? Derivation: 9:18 PM Q/A: What is 689 minutes after 10:54 AM? Derivation: 10:23 PM Q/A: How many minutes are there between 10:39 AM and 10:53 AM? Derivation: 14 Q/A: What is 265 minutes
english