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probability: swr p level set ---------------------------- Issue: Calculate prob of picking 1 g, 1 v, and 2 e when four letters picked without replacement from {v: 2, e: 3, f: 1, g: 4, u: 3, m: 2}. Interpretation: 8/455 Issue: Three letters picked without replacement from {z: 1, m: 8, p: 3, r: 1, i: 2, b: 2}. What is prob of picking 1 r and 2 b? Interpretation: 1/680 Issue: Calculate prob of picking 3 j and 1 n when four letters picked without replacement from jjjnjjjjjjjjjnjjnnjj. Interpretation: 448/969 Issue: What is prob of picking 1 c, 1 q, and 2 n when four letters picked without replacement from cqqccncnccnnqcqc? Interpretation: 48/455 Issue: Three letters picked without replacement from {x: 4, b: 4, i: 2}. Give prob of picking 3 b. Interpretation: 1/30 Issue: Four letters picked without replacement from vzyoolttovltovt. Give prob of picking 1 z, 1 y, and 2 l. Interpretation: 1/1365 Issue: What is prob of picking 3 x when three letters picked without replacement from xxxxx? Interpretation: 1 Issue: Calculate prob of picking 2 q and 2 r when four letters picked without replacement from qrqrrrrrr. Interpretation: 1/6 Issue: What is prob of picking 4 a when four letters picked without replacement from {e: 14, a: 5}? Interpretation: 5/3876 Issue: What is prob of picking 1 d and 2 c when three letters picked without replacement from ccddccddddcc? Interpretation: 9/22 Issue: Two letters picked without replacement from {j: 1, d: 3, n: 2, r: 10}. What is prob of picking 2 r? Interpretation: 3/8 Issue: Two letters picked without replacement from {n: 1, p: 1, e: 3, g: 3, d: 4, k: 3}. What is prob of picking 1 e and 1 p? Interpretation: 1/35 Issue: Three letters picked without replacement from hyllloyyyff. Give prob of picking 1 h and 2 l. Interpretation: 1/55 Issue: Two letters picked without replacement from pqpppppqp. What is prob of picking 2 q? Interpretation: 1/36 Issue: Calculate prob of picking 2 u when two letters picked without replacement from ullruuuuuruuuur.
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numbers: is prime ----------------- Conundrum: Is 1728871 a composite number? Derivation: False Conundrum: Is 708655 a composite number? Derivation: True Conundrum: Is 172097593 composite? Derivation: True Conundrum: Is 3779 composite? Derivation: False Conundrum: Is 9588091 prime? Derivation: True Conundrum: Is 3769211 composite? Derivation: True Conundrum: Is 120152426071 a prime number? Derivation: False Conundrum: Is 253 prime? Derivation: False Conundrum: Is 2103 a prime number? Derivation: False Conundrum: Is 3025793 prime? Derivation: True Conundrum: Is 11038466641 a prime number? Derivation: True Conundrum: Is 11822773 prime? Derivation: True Conundrum: Is 19862499 a prime number? Derivation: False Conundrum: Is 429411 composite? Derivation: True Conundrum: Is 270947 composite? Derivation: True Conundrum: Is 26626627 composite? Derivation: False Conundrum: Is 47148539 prime? Derivation: True Conundrum: Is 66220807 a prime number? Derivation: False Conundrum: Is 83813 prime? Derivation: True Conundrum: Is 48851 a prime number? Derivation: False Conundrum: Is 31121 a composite number? Derivation: False Conundrum: Is 44598919 composite? Derivation: True Conundrum: Is 90445 a composite number? Derivation: True Conundrum: Is 117989 composite? Derivation: False Conundrum: Is 994985 composite? Derivation: True Conundrum: Is 9520343 a prime number? Derivation: False Conundrum: Is 3067 prime? Derivation: True Conundrum: Is 1606487 composite? Derivation: False Conundrum: Is 123022327 a composite number? Derivation: False Conundrum: Is 61861 composite? Derivation: False Conundrum: Is 178085 a prime number? Derivation: False Conundrum: Is 48133 composite? Derivation: True Conundrum: Is 3550327 prime? Derivation: False Conundrum: Is 103321 a composite number? Derivation: True Conundrum: Is 1433356177 a composite number? Derivation: True Conundrum: Is 93284381 composite? Derivation: False Conundrum: Is 21313 a prime number? Derivation: True Conundrum: Is 95077938463 prime
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numbers: place value -------------------- Problem: What is the hundreds digit of 308389? Soln: 3 Problem: What is the hundred thousands digit of 303299? Soln: 3 Problem: What is the ten thousands digit of 28383? Soln: 2 Problem: What is the hundreds digit of 224? Soln: 2 Problem: What is the units digit of 284? Soln: 4 Problem: What is the thousands digit of 241796095? Soln: 6 Problem: What is the millions digit of 702817915? Soln: 2 Problem: What is the ten thousands digit of 19567? Soln: 1 Problem: What is the units digit of 5? Soln: 5 Problem: What is the units digit of 59286? Soln: 6 Problem: What is the thousands digit of 301178? Soln: 1 Problem: What is the millions digit of 1140656? Soln: 1 Problem: What is the ten thousands digit of 9015220? Soln: 1 Problem: What is the ten thousands digit of 5255694? Soln: 5 Problem: What is the units digit of 10547? Soln: 7 Problem: What is the units digit of 91916125? Soln: 5 Problem: What is the ten thousands digit of 1693530477? Soln: 3 Problem: What is the ten thousands digit of 660180? Soln: 6 Problem: What is the thousands digit of 7009? Soln: 7 Problem: What is the ten thousands digit of 2183426? Soln: 8 Problem: What is the thousands digit of 5450? Soln: 5 Problem: What is the ten thousands digit of 1163446? Soln: 6 Problem: What is the hundred thousands digit of 209158? Soln: 2 Problem: What is the thousands digit of 1690266? Soln: 0 Problem: What is the ten thousands digit of 19131? Soln: 1 Problem: What is the ten thousands digit of 2250132? Soln: 5 Problem: What is the thousands digit of 461339381? Soln: 9 Problem: What is the millions digit of 295176178? Soln: 5 Problem: What is the hundred thousands digit of 655178? Soln: 6 Problem: What is the ten millions digit of 49793398? Soln: 4 Problem: What is the units digit of 87367172? Soln: 2 Problem: What is the units digit of 4133? Soln: 3 Problem: What is the tens digit of 1777500324? Soln: 2 Problem: What is the units digit of 63881? Soln: 1 Problem: What is th
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probability: swr p level set ---------------------------- Problem: Calculate prob of picking 4 b when four letters picked without replacement from {b: 4, a: 5, c: 1}. Conclusion: 1/210 Problem: What is prob of picking 2 u when two letters picked without replacement from uuucuuc? Conclusion: 10/21 Problem: Four letters picked without replacement from {i: 1, s: 7}. What is prob of picking 3 s and 1 i? Conclusion: 1/2 Problem: Three letters picked without replacement from trffftzttkttfdd. Give prob of picking 1 r and 2 d. Conclusion: 1/455 Problem: Two letters picked without replacement from {a: 5, i: 5, t: 8}. Give prob of picking 2 t. Conclusion: 28/153 Problem: Calculate prob of picking 2 a when two letters picked without replacement from {g: 3, a: 2, n: 3, t: 9, j: 2, x: 1}. Conclusion: 1/190 Problem: Calculate prob of picking 4 i when four letters picked without replacement from jiiijii. Conclusion: 1/7 Problem: What is prob of picking 1 a and 1 q when two letters picked without replacement from qnnfanqnfnqaraaarny? Conclusion: 5/57 Problem: Two letters picked without replacement from {a: 5, t: 2, v: 4, x: 4}. What is prob of picking 2 x? Conclusion: 2/35 Problem: Three letters picked without replacement from cqcc. What is prob of picking 1 q and 2 c? Conclusion: 3/4 Problem: Two letters picked without replacement from {g: 2, y: 8, n: 1, x: 5}. What is prob of picking 1 g and 1 n? Conclusion: 1/60 Problem: Three letters picked without replacement from issismssmm. Give prob of picking 1 m and 2 s. Conclusion: 1/4 Problem: Two letters picked without replacement from {w: 3, y: 10, b: 2}. What is prob of picking 2 b? Conclusion: 1/105 Problem: Two letters picked without replacement from {c: 1, o: 4, a: 2, b: 4}. Give prob of picking 1 o and 1 a. Conclusion: 8/55 Problem: Three letters picked without replacement from yuyyuymiiyyiyi. What is prob of picking 3 y? Conclusion: 5/52 Problem: Calculate prob of picking 1 q and 2 d when three letters picked without replacement
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numbers: is factor ------------------ Topic: Is 6 a factor of 58219? Outcome: False Topic: Is 928 a multiple of 41? Outcome: False Topic: Is 442343176 a multiple of 498? Outcome: False Topic: Is 5376 a factor of 613901568? Outcome: True Topic: Is 6 a factor of 2470? Outcome: False Topic: Is 389 a factor of 20890? Outcome: False Topic: Is 6 a factor of 8652? Outcome: True Topic: Is 9 a factor of 17368710? Outcome: False Topic: Is 275 a factor of 22550? Outcome: True Topic: Is 288 a multiple of 2? Outcome: True Topic: Is 307795978 a multiple of 14? Outcome: True Topic: Is 6 a factor of 959? Outcome: False Topic: Is 23 a factor of 1018? Outcome: False Topic: Does 13 divide 814195? Outcome: False Topic: Is 9 a factor of 414? Outcome: True Topic: Does 6 divide 332? Outcome: False Topic: Does 48 divide 2496? Outcome: True Topic: Is 1710 a multiple of 45? Outcome: True Topic: Is 2 a factor of 1711379? Outcome: False Topic: Is 17 a factor of 1343? Outcome: True Topic: Is 644 a multiple of 11? Outcome: False Topic: Does 48 divide 115525152? Outcome: True Topic: Does 9 divide 61897401? Outcome: True Topic: Is 127 a factor of 514999? Outcome: False Topic: Is 104191 a multiple of 25? Outcome: False Topic: Is 19 a factor of 11096? Outcome: True Topic: Does 176 divide 186736? Outcome: True Topic: Does 68 divide 1224? Outcome: True Topic: Does 4 divide 10835885? Outcome: False Topic: Is 79 a factor of 1078? Outcome: False Topic: Is 14 a factor of 87584? Outcome: True Topic: Is 656 a multiple of 82? Outcome: True Topic: Does 31 divide 21601792? Outcome: True Topic: Is 216767644 a multiple of 1278? Outcome: False Topic: Does 2 divide 48? Outcome: True Topic: Is 4159 a multiple of 15? Outcome: False Topic: Does 13 divide 9399? Outcome: True Topic: Is 628920 a multiple of 45? Outcome: True Topic: Is 37 a factor of 327? Outcome: False Topic: Is 45 a factor of 1102500? Outcome: True Topic: Does 2246 divide 129143874? Outcome: False Topic: Is 27 a factor of 806? Outcome: False Topic: Is
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probability: swr p sequence --------------------------- Part A: Three letters picked without replacement from {b: 1, u: 2, v: 1, r: 1}. Give prob of sequence vub. Workthrough: 1/30 Part A: What is prob of sequence xwoh when four letters picked without replacement from wxoxuuxwxohhxwxxx? Workthrough: 1/595 Part A: What is prob of sequence mjj when three letters picked without replacement from {m: 2, k: 2, j: 10}? Workthrough: 15/182 Part A: What is prob of sequence zzz when three letters picked without replacement from zzzzzzz? Workthrough: 1 Part A: Four letters picked without replacement from {u: 8, k: 1, b: 2, q: 2}. Give prob of sequence uquu. Workthrough: 28/715 Part A: What is prob of sequence xxx when three letters picked without replacement from {x: 3, g: 1}? Workthrough: 1/4 Part A: Two letters picked without replacement from pvugmmypmmgymgmgmuyy. What is prob of sequence gm? Workthrough: 7/95 Part A: Two letters picked without replacement from {f: 1, j: 2, e: 2, n: 1, d: 2, l: 4}. Give prob of sequence ee. Workthrough: 1/66 Part A: Two letters picked without replacement from {q: 2, i: 1, n: 1, s: 1}. What is prob of sequence qn? Workthrough: 1/10 Part A: Three letters picked without replacement from bsl. Give prob of sequence bsl. Workthrough: 1/6 Part A: Three letters picked without replacement from {t: 5}. What is prob of sequence ttt? Workthrough: 1 Part A: Two letters picked without replacement from xxqxxxqxxxxq. Give prob of sequence qx. Workthrough: 9/44 Part A: What is prob of sequence ja when two letters picked without replacement from zjaaz? Workthrough: 1/10 Part A: What is prob of sequence uyy when three letters picked without replacement from {u: 2, o: 12, y: 5}? Workthrough: 20/2907 Part A: Calculate prob of sequence cc when two letters picked without replacement from bjcjbcjjj. Workthrough: 1/36 Part A: Two letters picked without replacement from wzpzlzzzlhhhl. Give prob of sequence zh. Workthrough: 5/52 Part A: What is prob of sequence zcz wh
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numbers: div remainder ---------------------- Given: Calculate the remainder when 29142 is divided by 8. Sol: 6 Given: What is the remainder when 8772251 is divided by 2193011? Sol: 207 Given: Calculate the remainder when 2572 is divided by 853. Sol: 13 Given: What is the remainder when 118 is divided by 17? Sol: 16 Given: Calculate the remainder when 38279 is divided by 4736. Sol: 391 Given: What is the remainder when 263 is divided by 56? Sol: 39 Given: Calculate the remainder when 9295 is divided by 56. Sol: 55 Given: What is the remainder when 237 is divided by 97? Sol: 43 Given: What is the remainder when 55161 is divided by 320? Sol: 121 Given: Calculate the remainder when 1152 is divided by 563. Sol: 26 Given: What is the remainder when 85622 is divided by 590? Sol: 72 Given: What is the remainder when 358 is divided by 37? Sol: 25 Given: Calculate the remainder when 2837504 is divided by 145. Sol: 144 Given: What is the remainder when 6151 is divided by 27? Sol: 22 Given: Calculate the remainder when 2674269 is divided by 10. Sol: 9 Given: Calculate the remainder when 91 is divided by 19. Sol: 15 Given: Calculate the remainder when 67692 is divided by 26. Sol: 14 Given: Calculate the remainder when 54015 is divided by 17984. Sol: 63 Given: What is the remainder when 2151177 is divided by 38? Sol: 35 Given: Calculate the remainder when 784896 is divided by 111993. Sol: 945 Given: Calculate the remainder when 9718 is divided by 187. Sol: 181 Given: Calculate the remainder when 105524 is divided by 10512. Sol: 404 Given: What is the remainder when 233 is divided by 5? Sol: 3 Given: What is the remainder when 317 is divided by 51? Sol: 11 Given: Calculate the remainder when 12888 is divided by 22. Sol: 18 Given: Calculate the remainder when 3552346 is divided by 1115. Sol: 1071 Given: Calculate the remainder when 75112 is divided by 117. Sol: 115 Given: Calculate the remainder when 36360 is divided by 93. Sol: 90 Given: Calculate the remainder when 14855 is divi
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numbers: place value -------------------- Problem: What is the hundreds digit of 1560596048? Resolution: 0 Problem: What is the tens digit of 10386? Resolution: 8 Problem: What is the tens digit of 515745? Resolution: 4 Problem: What is the units digit of 3375268? Resolution: 8 Problem: What is the hundreds digit of 17948? Resolution: 9 Problem: What is the thousands digit of 486105492? Resolution: 5 Problem: What is the units digit of 53219088? Resolution: 8 Problem: What is the units digit of 26923884? Resolution: 4 Problem: What is the tens digit of 1280312129? Resolution: 2 Problem: What is the units digit of 26370087? Resolution: 7 Problem: What is the tens digit of 33842? Resolution: 4 Problem: What is the units digit of 3029? Resolution: 9 Problem: What is the units digit of 102023782? Resolution: 2 Problem: What is the tens digit of 227076? Resolution: 7 Problem: What is the hundred millions digit of 140675190? Resolution: 1 Problem: What is the units digit of 865? Resolution: 5 Problem: What is the millions digit of 124610149? Resolution: 4 Problem: What is the tens digit of 2983? Resolution: 8 Problem: What is the ten thousands digit of 24176? Resolution: 2 Problem: What is the hundreds digit of 51510005? Resolution: 0 Problem: What is the hundreds digit of 7982230? Resolution: 2 Problem: What is the hundreds digit of 101499? Resolution: 4 Problem: What is the tens digit of 15958? Resolution: 5 Problem: What is the thousands digit of 1468? Resolution: 1 Problem: What is the ten thousands digit of 8795994? Resolution: 9 Problem: What is the millions digit of 667141524? Resolution: 7 Problem: What is the hundred millions digit of 2541919259? Resolution: 5 Problem: What is the thousands digit of 6116869? Resolution: 6 Problem: What is the hundred thousands digit of 3676835? Resolution: 6 Problem: What is the units digit of 114511? Resolution: 1 Problem: What is the thousands digit of 4073452? Resolution: 3 Problem: What is the tens digit of 115? Resolution: 1
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numbers: gcd ------------ Inquiry: Calculate the highest common divisor of 63859 and 133. Therefore: 19 Inquiry: What is the greatest common factor of 48 and 6? Therefore: 6 Inquiry: Calculate the highest common factor of 18 and 27009. Therefore: 9 Inquiry: Calculate the greatest common factor of 10005 and 2415. Therefore: 345 Inquiry: What is the greatest common divisor of 115 and 2962745? Therefore: 115 Inquiry: Calculate the greatest common divisor of 100 and 160. Therefore: 20 Inquiry: Calculate the highest common divisor of 228 and 168. Therefore: 12 Inquiry: What is the highest common divisor of 33 and 275? Therefore: 11 Inquiry: What is the greatest common divisor of 1280 and 119896960? Therefore: 640 Inquiry: What is the highest common factor of 20538 and 252? Therefore: 126 Inquiry: Calculate the greatest common factor of 469 and 14. Therefore: 7 Inquiry: Calculate the highest common factor of 1519219 and 299. Therefore: 299 Inquiry: Calculate the greatest common divisor of 10335 and 120. Therefore: 15 Inquiry: What is the greatest common divisor of 32 and 1000? Therefore: 8 Inquiry: Calculate the greatest common factor of 1904 and 4. Therefore: 4 Inquiry: Calculate the greatest common divisor of 690 and 60578550. Therefore: 690 Inquiry: What is the highest common divisor of 27 and 63? Therefore: 9 Inquiry: What is the greatest common factor of 410 and 13598921? Therefore: 41 Inquiry: Calculate the greatest common divisor of 5733 and 4446. Therefore: 117 Inquiry: What is the greatest common divisor of 640 and 10? Therefore: 10 Inquiry: What is the highest common factor of 621 and 407727? Therefore: 27 Inquiry: Calculate the greatest common factor of 4147 and 203. Therefore: 29 Inquiry: Calculate the greatest common factor of 808106 and 130. Therefore: 26 Inquiry: Calculate the highest common factor of 32890 and 18200130. Therefore: 2990 Inquiry: Calculate the highest common divisor of 22592 and 64. Therefore: 64 Inquiry: Calculate the greatest common diviso
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numbers: gcd ------------ Q=: Calculate the greatest common divisor of 70 and 1022. Fix: 14 Q=: Calculate the highest common divisor of 252 and 868. Fix: 28 Q=: What is the greatest common factor of 1045 and 2? Fix: 1 Q=: What is the greatest common factor of 1146550 and 69? Fix: 23 Q=: What is the greatest common factor of 3 and 30098? Fix: 1 Q=: Calculate the highest common factor of 2133266 and 249. Fix: 83 Q=: What is the greatest common factor of 2392 and 181064? Fix: 104 Q=: Calculate the greatest common divisor of 174 and 19401. Fix: 87 Q=: Calculate the highest common factor of 437 and 5153541. Fix: 437 Q=: Calculate the greatest common factor of 87 and 145. Fix: 29 Q=: What is the greatest common divisor of 3796 and 50943269? Fix: 949 Q=: Calculate the highest common factor of 65 and 91. Fix: 13 Q=: Calculate the highest common divisor of 298 and 16592938. Fix: 298 Q=: Calculate the highest common factor of 103953 and 687. Fix: 3 Q=: Calculate the highest common factor of 864 and 64. Fix: 32 Q=: Calculate the greatest common factor of 111930 and 974715. Fix: 105 Q=: What is the greatest common divisor of 967234 and 2252? Fix: 1126 Q=: Calculate the highest common factor of 66600 and 75. Fix: 75 Q=: Calculate the highest common divisor of 9 and 18. Fix: 9 Q=: Calculate the highest common factor of 17355 and 141375. Fix: 195 Q=: What is the highest common factor of 90 and 38? Fix: 2 Q=: What is the greatest common divisor of 78 and 1898? Fix: 26 Q=: Calculate the greatest common divisor of 84 and 308. Fix: 28 Q=: What is the highest common divisor of 1493 and 41835353? Fix: 1493 Q=: Calculate the highest common factor of 12 and 7518. Fix: 6 Q=: Calculate the greatest common divisor of 76 and 625727. Fix: 19 Q=: Calculate the highest common factor of 4026 and 132. Fix: 66 Q=: What is the highest common divisor of 924 and 588? Fix: 84 Q=: Calculate the greatest common factor of 7868 and 58. Fix: 2 Q=: What is the highest common divisor of 405 and 401355? Fix: 4
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numbers: is prime ----------------- Test item: Is 313820461 composite? Conclusion: True Test item: Is 512711 prime? Conclusion: True Test item: Is 1167651229 prime? Conclusion: True Test item: Is 174169 composite? Conclusion: False Test item: Is 2427179 a composite number? Conclusion: False Test item: Is 67999 a composite number? Conclusion: True Test item: Is 137140021 composite? Conclusion: False Test item: Is 11597625111 a prime number? Conclusion: False Test item: Is 34733156401 a prime number? Conclusion: False Test item: Is 83651349 a composite number? Conclusion: True Test item: Is 15832331701 prime? Conclusion: False Test item: Is 2859479 a prime number? Conclusion: False Test item: Is 497719 prime? Conclusion: True Test item: Is 582229 a prime number? Conclusion: False Test item: Is 136269821 prime? Conclusion: True Test item: Is 104624537 a composite number? Conclusion: False Test item: Is 245381107 prime? Conclusion: True Test item: Is 1999667 composite? Conclusion: False Test item: Is 1179806 a prime number? Conclusion: False Test item: Is 6726811687 composite? Conclusion: True Test item: Is 243723713809 composite? Conclusion: False Test item: Is 17674759 a composite number? Conclusion: False Test item: Is 14713051 a composite number? Conclusion: False Test item: Is 77830723 composite? Conclusion: False Test item: Is 73020547 composite? Conclusion: False Test item: Is 12451 composite? Conclusion: False Test item: Is 2118217 a prime number? Conclusion: False Test item: Is 55135 a prime number? Conclusion: False Test item: Is 16072429357 a composite number? Conclusion: True Test item: Is 17454661 prime? Conclusion: False Test item: Is 178681 prime? Conclusion: True Test item: Is 1559411 a composite number? Conclusion: True Test item: Is 58943 a prime number? Conclusion: True Test item: Is 4682258377 a composite number? Conclusion: False Test item: Is 5951 a composite number? Conclusion: True Test item: Is 47246 a prime number? Conclusion: False Test item:
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numbers: place value -------------------- Exercise: What is the hundred thousands digit of 55233592? Response: 2 Exercise: What is the millions digit of 5894558? Response: 5 Exercise: What is the ten thousands digit of 11286? Response: 1 Exercise: What is the thousands digit of 3498? Response: 3 Exercise: What is the hundred thousands digit of 506928512? Response: 9 Exercise: What is the hundreds digit of 595103? Response: 1 Exercise: What is the ten millions digit of 559689678? Response: 5 Exercise: What is the hundreds digit of 3624? Response: 6 Exercise: What is the thousands digit of 4291278? Response: 1 Exercise: What is the units digit of 29456851? Response: 1 Exercise: What is the tens digit of 67833741? Response: 4 Exercise: What is the hundreds digit of 681986329? Response: 3 Exercise: What is the thousands digit of 4738? Response: 4 Exercise: What is the thousands digit of 1938? Response: 1 Exercise: What is the tens digit of 158068? Response: 6 Exercise: What is the units digit of 10117761? Response: 1 Exercise: What is the hundred thousands digit of 2740226? Response: 7 Exercise: What is the tens digit of 6110? Response: 1 Exercise: What is the tens digit of 3125027? Response: 2 Exercise: What is the ten thousands digit of 19171? Response: 1 Exercise: What is the hundred thousands digit of 267868? Response: 2 Exercise: What is the hundred thousands digit of 912560? Response: 9 Exercise: What is the thousands digit of 118267309? Response: 7 Exercise: What is the hundreds digit of 12406? Response: 4 Exercise: What is the hundreds digit of 59589438? Response: 4 Exercise: What is the units digit of 486334? Response: 4 Exercise: What is the millions digit of 94386102? Response: 4 Exercise: What is the units digit of 3536077? Response: 7 Exercise: What is the hundreds digit of 319268? Response: 2 Exercise: What is the ten thousands digit of 37490? Response: 3 Exercise: What is the units digit of 582? Response: 2 Exercise: What is the hundreds digit of 228883?
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numbers: place value -------------------- Problem #: What is the thousands digit of 19449520? Sol: 9 Problem #: What is the hundreds digit of 2514? Sol: 5 Problem #: What is the ten thousands digit of 22930? Sol: 2 Problem #: What is the thousands digit of 346736? Sol: 6 Problem #: What is the thousands digit of 27702656? Sol: 2 Problem #: What is the hundreds digit of 570419819? Sol: 8 Problem #: What is the hundreds digit of 35601? Sol: 6 Problem #: What is the thousands digit of 125641? Sol: 5 Problem #: What is the tens digit of 969223? Sol: 2 Problem #: What is the millions digit of 3539828218? Sol: 9 Problem #: What is the hundred thousands digit of 18860473? Sol: 8 Problem #: What is the tens digit of 3695? Sol: 9 Problem #: What is the units digit of 1717? Sol: 7 Problem #: What is the tens digit of 1654735? Sol: 3 Problem #: What is the ten thousands digit of 8072783? Sol: 7 Problem #: What is the hundreds digit of 753? Sol: 7 Problem #: What is the thousands digit of 985535? Sol: 5 Problem #: What is the thousands digit of 4297? Sol: 4 Problem #: What is the ten thousands digit of 20190? Sol: 2 Problem #: What is the tens digit of 20704883? Sol: 8 Problem #: What is the tens digit of 145989? Sol: 8 Problem #: What is the thousands digit of 55196? Sol: 5 Problem #: What is the tens digit of 382173? Sol: 7 Problem #: What is the hundreds digit of 1314530? Sol: 5 Problem #: What is the tens digit of 141741? Sol: 4 Problem #: What is the hundreds digit of 47452? Sol: 4 Problem #: What is the units digit of 336025? Sol: 5 Problem #: What is the units digit of 12589? Sol: 9 Problem #: What is the millions digit of 3513052699? Sol: 3 Problem #: What is the hundred thousands digit of 3704982180? Sol: 9 Problem #: What is the ten thousands digit of 726648? Sol: 2 Problem #: What is the thousands digit of 1480? Sol: 1 Problem #: What is the ten thousands digit of 9655098? Sol: 5 Problem #: What is the thousands digit of 8975? Sol: 8 Problem #: What is the ten millio
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numbers: gcd ------------ Request: What is the highest common factor of 192 and 2806712? Yields: 8 Request: Calculate the greatest common factor of 300795 and 165. Yields: 165 Request: What is the greatest common divisor of 17 and 125273? Yields: 17 Request: What is the highest common divisor of 923 and 13? Yields: 13 Request: What is the greatest common divisor of 3238284 and 7980? Yields: 1596 Request: Calculate the greatest common divisor of 1394081 and 158652. Yields: 1469 Request: Calculate the greatest common divisor of 30 and 285. Yields: 15 Request: Calculate the greatest common factor of 351923 and 654511. Yields: 3289 Request: Calculate the greatest common factor of 16 and 464. Yields: 16 Request: What is the greatest common divisor of 4878 and 608? Yields: 2 Request: Calculate the highest common divisor of 6455 and 12176712. Yields: 1291 Request: What is the greatest common factor of 999 and 879633? Yields: 27 Request: What is the greatest common factor of 50808 and 212868? Yields: 876 Request: What is the greatest common divisor of 532 and 84? Yields: 28 Request: What is the highest common factor of 24 and 95244? Yields: 12 Request: Calculate the highest common divisor of 4417 and 205075. Yields: 631 Request: What is the highest common factor of 12050 and 30? Yields: 10 Request: Calculate the highest common divisor of 22353032 and 1413. Yields: 157 Request: Calculate the highest common factor of 28428 and 552. Yields: 276 Request: Calculate the greatest common divisor of 9775 and 1105. Yields: 85 Request: What is the highest common divisor of 820 and 8036? Yields: 164 Request: What is the greatest common divisor of 1701411 and 316455? Yields: 3723 Request: What is the highest common divisor of 39055991 and 65? Yields: 13 Request: What is the highest common factor of 349360 and 939840? Yields: 880 Request: Calculate the greatest common factor of 11532 and 279. Yields: 93 Request: What is the highest common divisor of 10794994 and 882? Yields: 98 Request:
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numbers: div remainder ---------------------- Topic: Calculate the remainder when 215 is divided by 18. Answer: 17 Topic: Calculate the remainder when 19907 is divided by 343. Answer: 13 Topic: Calculate the remainder when 874 is divided by 58. Answer: 4 Topic: Calculate the remainder when 38450 is divided by 575. Answer: 500 Topic: What is the remainder when 5338 is divided by 734? Answer: 200 Topic: Calculate the remainder when 10710 is divided by 3570. Answer: 0 Topic: Calculate the remainder when 4060 is divided by 895. Answer: 480 Topic: What is the remainder when 1077 is divided by 49? Answer: 48 Topic: What is the remainder when 378 is divided by 279? Answer: 99 Topic: Calculate the remainder when 13782108 is divided by 25. Answer: 8 Topic: What is the remainder when 35374 is divided by 16? Answer: 14 Topic: What is the remainder when 182 is divided by 58? Answer: 8 Topic: What is the remainder when 51 is divided by 14? Answer: 9 Topic: What is the remainder when 514147 is divided by 17? Answer: 16 Topic: Calculate the remainder when 10698 is divided by 3561. Answer: 15 Topic: What is the remainder when 50580 is divided by 219? Answer: 210 Topic: Calculate the remainder when 21551 is divided by 400. Answer: 351 Topic: Calculate the remainder when 90 is divided by 82. Answer: 8 Topic: Calculate the remainder when 1019 is divided by 51. Answer: 50 Topic: Calculate the remainder when 371 is divided by 185. Answer: 1 Topic: What is the remainder when 11484103 is divided by 11484075? Answer: 28 Topic: What is the remainder when 3447284 is divided by 820? Answer: 4 Topic: Calculate the remainder when 267026 is divided by 39. Answer: 32 Topic: What is the remainder when 16120 is divided by 503? Answer: 24 Topic: What is the remainder when 462034 is divided by 215? Answer: 214 Topic: What is the remainder when 46811366 is divided by 526? Answer: 522 Topic: Calculate the remainder when 195757 is divided by 39151. Answer: 2 Topic: What is the remainder when 1306 is div
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numbers: round number --------------------- Math Problem: Round 0.0003122 to four dps. Clarification: 0.0003 Math Problem: Round 1196247.517 to the nearest ten thousand. Clarification: 1200000 Math Problem: Round -2.789892501 to three dps. Clarification: -2.79 Math Problem: Round 0.03008624 to three dps. Clarification: 0.03 Math Problem: Round 0.019622 to three dps. Clarification: 0.02 Math Problem: Round 0.000000096184725 to seven decimal places. Clarification: 0.0000001 Math Problem: Round -66336.45167 to the nearest 10000. Clarification: -70000 Math Problem: Round -260980900 to the nearest one hundred thousand. Clarification: -261000000 Math Problem: What is 1983 rounded to the nearest one hundred? Clarification: 2000 Math Problem: Round 0.00827 to three dps. Clarification: 0.008 Math Problem: What is 120.5686 rounded to the nearest integer? Clarification: 121 Math Problem: Round -1584397.62 to the nearest one hundred thousand. Clarification: -1600000 Math Problem: What is -0.001190809 rounded to six dps? Clarification: -0.001191 Math Problem: Round 1.551107 to two dps. Clarification: 1.55 Math Problem: Round -0.0000113774 to 7 dps. Clarification: -0.0000114 Math Problem: Round -3600000 to the nearest one million. Clarification: -4000000 Math Problem: Round -3630710 to the nearest one million. Clarification: -4000000 Math Problem: What is -300.5325 rounded to the nearest 100? Clarification: -300 Math Problem: Round 0.058739194 to 4 decimal places. Clarification: 0.0587 Math Problem: What is 3.022969 rounded to two decimal places? Clarification: 3.02 Math Problem: What is -59392070 rounded to the nearest 100000? Clarification: -59400000 Math Problem: What is -0.00541365165 rounded to three decimal places? Clarification: -0.005 Math Problem: What is 0.0011231 rounded to 5 decimal places? Clarification: 0.00112 Math Problem: What is -1.1498 rounded to 1 decimal place? Clarification: -1.1 Math Problem: Round 10.9465446 to 2 dps. Clarification: 10.95 Math Problem: Rou
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numbers: is factor ------------------ Inquiry: Does 11 divide 4400? Calculation: True Inquiry: Is 4752 a multiple of 36? Calculation: True Inquiry: Is 815689361 a multiple of 696? Calculation: False Inquiry: Is 17 a factor of 1893630? Calculation: True Inquiry: Is 4 a factor of 464960630? Calculation: False Inquiry: Is 1989 a factor of 313713036? Calculation: True Inquiry: Does 7 divide 1548? Calculation: False Inquiry: Is 75 a factor of 18042? Calculation: False Inquiry: Is 51920 a multiple of 25? Calculation: False Inquiry: Does 944 divide 6497552? Calculation: True Inquiry: Does 63 divide 32157? Calculation: False Inquiry: Does 42 divide 286? Calculation: False Inquiry: Is 56 a factor of 9921912? Calculation: True Inquiry: Is 115 a factor of 69646? Calculation: False Inquiry: Is 18224 a multiple of 134? Calculation: True Inquiry: Is 22 a factor of 35486? Calculation: True Inquiry: Is 4653160 a multiple of 7? Calculation: False Inquiry: Does 49 divide 122078373? Calculation: False Inquiry: Is 6992 a multiple of 152? Calculation: True Inquiry: Does 4845 divide 1713865455? Calculation: True Inquiry: Is 1138 a factor of 148069614? Calculation: False Inquiry: Is 775 a multiple of 2? Calculation: False Inquiry: Is 135 a factor of 26760032? Calculation: False Inquiry: Is 7372 a multiple of 38? Calculation: True Inquiry: Is 5 a factor of 45596160? Calculation: True Inquiry: Is 4770 a multiple of 159? Calculation: True Inquiry: Is 21369478 a multiple of 62? Calculation: True Inquiry: Does 2 divide 102? Calculation: True Inquiry: Is 86 a factor of 3842? Calculation: False Inquiry: Is 1760122 a multiple of 14? Calculation: True Inquiry: Does 585 divide 1158591? Calculation: False Inquiry: Is 7 a factor of 23427? Calculation: False Inquiry: Is 4 a factor of 896? Calculation: True Inquiry: Does 15 divide 7170? Calculation: True Inquiry: Is 228 a factor of 125974? Calculation: False Inquiry: Is 70 a factor of 683866236? Calculation: False Inquiry: Is 115907 a multiple of 11? C
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probability: swr p level set ---------------------------- Problem: Two letters picked without replacement from jvjvvjvvvvvvvvjvjv. What is prob of picking 2 v? Steps: 26/51 Problem: What is prob of picking 1 g and 1 s when two letters picked without replacement from ghcghshhghgcgchh? Steps: 1/24 Problem: What is prob of picking 1 p and 3 l when four letters picked without replacement from {d: 4, p: 1, l: 3}? Steps: 1/70 Problem: Two letters picked without replacement from hhhpuhsg. Give prob of picking 1 g and 1 p. Steps: 1/28 Problem: Calculate prob of picking 2 z when two letters picked without replacement from {h: 2, s: 4, z: 2}. Steps: 1/28 Problem: Calculate prob of picking 2 h when two letters picked without replacement from hnhnhh. Steps: 2/5 Problem: What is prob of picking 2 x and 1 c when three letters picked without replacement from qcqeeeeqeeexneccxxx? Steps: 6/323 Problem: Two letters picked without replacement from {p: 2, d: 18}. What is prob of picking 2 d? Steps: 153/190 Problem: Calculate prob of picking 2 r and 1 m when three letters picked without replacement from mrvbmrmrrrrmrrmvvrrr. Steps: 55/228 Problem: What is prob of picking 2 r when two letters picked without replacement from {q: 6, r: 3, l: 1, u: 2, i: 4}? Steps: 1/40 Problem: Two letters picked without replacement from ccccggc. Give prob of picking 1 c and 1 g. Steps: 10/21 Problem: Two letters picked without replacement from saimpvm. Give prob of picking 2 m. Steps: 1/21 Problem: Calculate prob of picking 1 y and 2 n when three letters picked without replacement from {z: 3, y: 1, i: 6, c: 7, n: 2}. Steps: 1/969 Problem: Three letters picked without replacement from {p: 3, i: 6, v: 2, z: 1, e: 3}. Give prob of picking 1 z and 2 v. Steps: 1/455 Problem: What is prob of picking 2 m and 1 x when three letters picked without replacement from xmmmxmwx? Steps: 9/28 Problem: Four letters picked without replacement from {t: 2, z: 1, e: 2, o: 1, y: 2}. What is prob of picking 2 t and 2 e? Steps:
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probability: swr p sequence --------------------------- Question: Calculate prob of sequence fx when two letters picked without replacement from {x: 18, f: 2}. Gives: 9/95 Question: Four letters picked without replacement from {j: 3, s: 2, c: 2, l: 3, m: 5}. What is prob of sequence mllj? Gives: 1/364 Question: Two letters picked without replacement from qqqqffjqqqfqjqfqifq. What is prob of sequence fi? Gives: 5/342 Question: Calculate prob of sequence tbji when four letters picked without replacement from {e: 2, t: 1, j: 1, v: 1, b: 1, i: 1}. Gives: 1/840 Question: Calculate prob of sequence xv when two letters picked without replacement from aqdvaxxxdvxqdxdxqaqa. Gives: 3/95 Question: Calculate prob of sequence ztt when three letters picked without replacement from txjtjtjhtjjhztjtttjt. Gives: 1/95 Question: Two letters picked without replacement from {n: 2, s: 2, m: 2, f: 2, a: 5, z: 5}. Give prob of sequence sn. Gives: 2/153 Question: Calculate prob of sequence wsta when four letters picked without replacement from tawsqcw. Gives: 1/420 Question: What is prob of sequence yyy when three letters picked without replacement from mqmqyyyqy? Gives: 1/21 Question: Calculate prob of sequence mmm when three letters picked without replacement from ssmssssmssmsssss. Gives: 1/560 Question: What is prob of sequence qqx when three letters picked without replacement from xxxxxxxxqq? Gives: 1/45 Question: Three letters picked without replacement from lllllllllllllrllrl. What is prob of sequence llr? Gives: 5/51 Question: Two letters picked without replacement from bkkbkwbbbbddwbb. Give prob of sequence kd. Gives: 1/35 Question: Three letters picked without replacement from {g: 5, b: 1, o: 1, l: 1, x: 6}. Give prob of sequence xbx. Gives: 5/364 Question: Calculate prob of sequence rrrd when four letters picked without replacement from rdddibvibrirfbd. Gives: 1/1365 Question: Calculate prob of sequence uku when three letters picked without replacement from {k: 1, u: 2}. Gives: 1/
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arithmetic: nearest integer root -------------------------------- Task: What is the third root of 391024 to the nearest integer? Math A: 73 Task: What is the fifth root of 220049448 to the nearest integer? Math A: 47 Task: What is 944560 to the power of 1/2, to the nearest integer? Math A: 972 Task: What is 196610578 to the power of 1/9, to the nearest integer? Math A: 8 Task: What is 27145 to the power of 1/3, to the nearest integer? Math A: 30 Task: What is the eighth root of 51766 to the nearest integer? Math A: 4 Task: What is the cube root of 575002 to the nearest integer? Math A: 83 Task: What is the fourth root of 1658021 to the nearest integer? Math A: 36 Task: What is the third root of 92623069 to the nearest integer? Math A: 452 Task: What is 2087 to the power of 1/3, to the nearest integer? Math A: 13 Task: What is the third root of 283532 to the nearest integer? Math A: 66 Task: What is the cube root of 13271 to the nearest integer? Math A: 24 Task: What is 316609 to the power of 1/9, to the nearest integer? Math A: 4 Task: What is the cube root of 330201 to the nearest integer? Math A: 69 Task: What is 346 to the power of 1/9, to the nearest integer? Math A: 2 Task: What is the third root of 36439 to the nearest integer? Math A: 33 Task: What is the third root of 326211 to the nearest integer? Math A: 69 Task: What is 153904 to the power of 1/2, to the nearest integer? Math A: 392 Task: What is 1177 to the power of 1/7, to the nearest integer? Math A: 3 Task: What is 3664051 to the power of 1/3, to the nearest integer? Math A: 154 Task: What is 26621406 to the power of 1/2, to the nearest integer? Math A: 5160 Task: What is the third root of 4161870 to the nearest integer? Math A: 161 Task: What is the cube root of 1079898640 to the nearest integer? Math A: 1026 Task: What is 5965302 to the power of 1/9, to the nearest integer? Math A: 6 Task: What is 20584028 to the power of 1/3, to the nearest integer? Math A: 274 Task: What is the cube root of 16387
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numbers: is factor ------------------ Example: Does 94 divide 60254? Solution: True Example: Is 190137 a multiple of 183? Solution: True Example: Is 137 a factor of 4980307? Solution: False Example: Does 6 divide 4194816? Solution: True Example: Does 4 divide 28357? Solution: False Example: Does 631 divide 291748? Solution: False Example: Is 28975488 a multiple of 384? Solution: True Example: Does 22 divide 272? Solution: False Example: Is 3666126 a multiple of 9? Solution: False Example: Does 443 divide 129390222? Solution: False Example: Is 275 a factor of 3328281? Solution: False Example: Is 159 a factor of 26553? Solution: True Example: Does 18 divide 5393897? Solution: False Example: Is 1585035363 a multiple of 2871? Solution: False Example: Is 1082 a factor of 7894428? Solution: False Example: Is 12 a factor of 886001? Solution: False Example: Does 1238 divide 1928582925? Solution: False Example: Is 778 a factor of 1149884? Solution: True Example: Is 43852 a multiple of 88? Solution: False Example: Is 10617603 a multiple of 1119? Solution: False Example: Does 8 divide 1295? Solution: False Example: Is 24 a multiple of 8? Solution: True Example: Is 51 a factor of 51? Solution: True Example: Does 7 divide 2850? Solution: False Example: Does 179 divide 46440118? Solution: True Example: Is 3156075 a multiple of 83? Solution: True Example: Is 576768 a multiple of 32? Solution: True Example: Is 9 a factor of 1146? Solution: False Example: Does 69 divide 260021670? Solution: True Example: Is 1713 a factor of 856129733? Solution: False Example: Is 179 a factor of 24836187? Solution: False Example: Is 275 a factor of 2330900? Solution: True Example: Is 455 a multiple of 2? Solution: False Example: Does 1915 divide 45280175? Solution: True Example: Is 1314227698 a multiple of 57? Solution: False Example: Does 10 divide 574479465? Solution: False Example: Does 17 divide 2431? Solution: True Example: Is 4625 a multiple of 37? Solution: True Example: Is 11 a factor of 1453
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numbers: is factor ------------------ Example: Does 15 divide 2166063645? Calculation: True Example: Does 110 divide 183120? Calculation: False Example: Does 81 divide 136566? Calculation: True Example: Is 9297437 a multiple of 103? Calculation: False Example: Does 2 divide 5268? Calculation: True Example: Does 8 divide 808? Calculation: True Example: Does 202 divide 1811334? Calculation: True Example: Is 909 a factor of 8721855? Calculation: True Example: Is 127 a factor of 43741848? Calculation: True Example: Is 162335 a multiple of 468? Calculation: False Example: Is 36 a factor of 864? Calculation: True Example: Does 14 divide 16587? Calculation: False Example: Does 13 divide 2389328? Calculation: False Example: Is 6521869 a multiple of 945? Calculation: False Example: Is 1476076 a multiple of 14? Calculation: True Example: Is 1157 a multiple of 22? Calculation: False Example: Does 7 divide 18228? Calculation: True Example: Is 17233 a multiple of 71? Calculation: False Example: Is 70 a factor of 19477668? Calculation: False Example: Does 10 divide 18930? Calculation: True Example: Does 2835 divide 628088111? Calculation: False Example: Is 20 a factor of 9741? Calculation: False Example: Is 122272 a multiple of 8? Calculation: True Example: Is 17 a factor of 544082467? Calculation: True Example: Is 94 a factor of 43167427? Calculation: False Example: Does 176 divide 110429616? Calculation: True Example: Is 1394 a multiple of 2? Calculation: True Example: Is 88 a factor of 39165? Calculation: False Example: Is 8 a factor of 5148748? Calculation: False Example: Does 439 divide 863023515? Calculation: True Example: Does 49 divide 794562097? Calculation: True Example: Is 832 a multiple of 26? Calculation: True Example: Does 35 divide 821? Calculation: False Example: Does 26 divide 272? Calculation: False Example: Is 3038 a multiple of 49? Calculation: True Example: Is 156135 a multiple of 35? Calculation: True Example: Does 4269 divide 51237069? Calculation: False Ex
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probability: swr p sequence --------------------------- Q: Calculate prob of sequence rrs when three letters picked without replacement from {r: 4, s: 2}. Reply: 1/5 Q: What is prob of sequence id when two letters picked without replacement from sisisiddsi? Reply: 4/45 Q: Calculate prob of sequence tntt when four letters picked without replacement from {n: 1, t: 7}. Reply: 1/8 Q: Three letters picked without replacement from iiiiiiiieiiiiiiiii. What is prob of sequence iee? Reply: 0 Q: What is prob of sequence chcc when four letters picked without replacement from {a: 1, d: 5, c: 3, h: 1}? Reply: 1/840 Q: Three letters picked without replacement from qqsq. Give prob of sequence sqs. Reply: 0 Q: Three letters picked without replacement from {b: 4}. Give prob of sequence bbb. Reply: 1 Q: Four letters picked without replacement from {p: 1, w: 3, z: 1}. Give prob of sequence pwww. Reply: 1/20 Q: Two letters picked without replacement from {k: 17, n: 2}. What is prob of sequence nn? Reply: 1/171 Q: What is prob of sequence rrqr when four letters picked without replacement from {g: 1, d: 3, o: 10, r: 5, q: 1}? Reply: 1/1938 Q: What is prob of sequence zz when two letters picked without replacement from zzzzeeeeezeezzzzeze? Reply: 5/19 Q: Three letters picked without replacement from dxkddddxdxkxxdod. What is prob of sequence oxd? Reply: 1/84 Q: Two letters picked without replacement from aaaaabaa. What is prob of sequence ab? Reply: 1/8 Q: Three letters picked without replacement from {x: 5, n: 1, t: 4}. Give prob of sequence ttt. Reply: 1/30 Q: Three letters picked without replacement from {i: 5, m: 2, k: 3, c: 3}. Give prob of sequence kkk. Reply: 1/286 Q: What is prob of sequence vhhh when four letters picked without replacement from {v: 2, o: 1, h: 4}? Reply: 2/35 Q: Two letters picked without replacement from {i: 5, q: 3}. Give prob of sequence qi. Reply: 15/56 Q: Three letters picked without replacement from {h: 1, u: 6, e: 2, x: 5, p: 2, t: 1}. Give prob of sequenc
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numbers: gcd ------------ Query: Calculate the highest common factor of 7140 and 5040. Thus: 420 Query: What is the greatest common divisor of 184 and 6532? Thus: 92 Query: What is the highest common divisor of 32 and 224? Thus: 32 Query: Calculate the greatest common factor of 14745728 and 64. Thus: 64 Query: Calculate the greatest common factor of 735 and 75. Thus: 15 Query: What is the highest common divisor of 2275558 and 5024? Thus: 314 Query: Calculate the highest common factor of 35 and 1169. Thus: 7 Query: What is the highest common divisor of 5072 and 32? Thus: 16 Query: What is the greatest common divisor of 427476 and 588? Thus: 588 Query: What is the highest common factor of 640 and 120? Thus: 40 Query: Calculate the greatest common factor of 120 and 3996. Thus: 12 Query: What is the highest common divisor of 80212 and 1045? Thus: 11 Query: Calculate the highest common divisor of 413 and 56. Thus: 7 Query: What is the highest common divisor of 119 and 199937? Thus: 17 Query: What is the greatest common divisor of 770 and 165? Thus: 55 Query: Calculate the highest common divisor of 34071 and 287. Thus: 41 Query: What is the highest common divisor of 168 and 8736996? Thus: 12 Query: Calculate the greatest common divisor of 908 and 5675. Thus: 227 Query: What is the greatest common divisor of 448429 and 4072? Thus: 509 Query: What is the highest common factor of 19 and 6517? Thus: 19 Query: Calculate the highest common factor of 760 and 80. Thus: 40 Query: What is the greatest common factor of 1061570 and 9130? Thus: 830 Query: Calculate the highest common factor of 300 and 99613650. Thus: 150 Query: Calculate the greatest common factor of 14743418 and 5238. Thus: 194 Query: Calculate the greatest common factor of 10368 and 14418. Thus: 162 Query: What is the greatest common divisor of 120 and 567540? Thus: 60 Query: What is the highest common divisor of 868 and 127232? Thus: 28 Query: What is the highest common factor of 515 and 19343915? Thus: 515 Query:
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measurement: conversion ----------------------- Exercise: How many nanograms are there in fifty-four fifths of a microgram? Soln: 10800 Exercise: Convert 5856.33 kilograms to milligrams. Soln: 5856330000 Exercise: How many seconds are there in 9/25 of a day? Soln: 31104 Exercise: How many millilitres are there in 12/25 of a litre? Soln: 480 Exercise: Convert 33.35215 years to months. Soln: 400.2258 Exercise: How many months are there in 5/6 of a year? Soln: 10 Exercise: What is 2/27 of a day in seconds? Soln: 6400 Exercise: Convert 287.3233 days to nanoseconds. Soln: 24824733120000000 Exercise: What is 7/2 of a meter in millimeters? Soln: 3500 Exercise: How many seconds are there in three fifths of a hour? Soln: 2160 Exercise: What is 7/4 of a millennium in decades? Soln: 175 Exercise: What is one quarter of a litre in millilitres? Soln: 250 Exercise: What is thirty-two fifths of a tonne in kilograms? Soln: 6400 Exercise: What is 2083852.2 months in centuries? Soln: 1736.5435 Exercise: How many months are there in five sixths of a year? Soln: 10 Exercise: Convert 0.042063 centimeters to micrometers. Soln: 420.63 Exercise: What is 63.5064g in tonnes? Soln: 0.0000635064 Exercise: How many millilitres are there in 12/25 of a litre? Soln: 480 Exercise: What is three fifths of a microgram in nanograms? Soln: 600 Exercise: What is 18.33952t in nanograms? Soln: 18339520000000000 Exercise: What is thirty-one sixths of a week in hours? Soln: 868 Exercise: How many years are there in 5/4 of a century? Soln: 125 Exercise: Convert 843788.3m to micrometers. Soln: 843788300000 Exercise: Convert 3138.644 micrometers to meters. Soln: 0.003138644 Exercise: What is 1/4 of a century in years? Soln: 25 Exercise: What is fifty-one halves of a hour in minutes? Soln: 1530 Exercise: Convert 887.3577ug to nanograms. Soln: 887357.7 Exercise: What is 0.6439441 millimeters in micrometers? Soln: 643.9441 Exercise: What is seventy-seven halves of a meter in millimeters? Soln: 38500 Exercise: How
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probability: swr p sequence --------------------------- Task: Two letters picked without replacement from hrroaohrharoaa. What is prob of sequence or? Hence: 6/91 Task: What is prob of sequence kdw when three letters picked without replacement from iwmdxki? Hence: 1/210 Task: What is prob of sequence lvtt when four letters picked without replacement from {l: 1, v: 1, s: 1, t: 2}? Hence: 1/60 Task: Three letters picked without replacement from {s: 5, c: 3}. Give prob of sequence csc. Hence: 5/56 Task: Two letters picked without replacement from {x: 1, v: 3, a: 3, q: 2, b: 1, e: 5}. Give prob of sequence xv. Hence: 1/70 Task: What is prob of sequence rp when two letters picked without replacement from {p: 1, j: 2, r: 2}? Hence: 1/10 Task: Calculate prob of sequence prr when three letters picked without replacement from {p: 2, y: 3, x: 1, s: 3, a: 2, r: 3}. Hence: 1/182 Task: Two letters picked without replacement from rrrrryryrrryry. Give prob of sequence ry. Hence: 20/91 Task: What is prob of sequence ebew when four letters picked without replacement from {a: 2, w: 1, e: 5, l: 1, b: 1}? Hence: 1/252 Task: Two letters picked without replacement from xenn. What is prob of sequence ex? Hence: 1/12 Task: Two letters picked without replacement from {z: 8, w: 2}. Give prob of sequence wz. Hence: 8/45 Task: What is prob of sequence uuu when three letters picked without replacement from {g: 3, u: 6, q: 7, h: 3}? Hence: 20/969 Task: Three letters picked without replacement from mxkkemys. What is prob of sequence sex? Hence: 1/336 Task: What is prob of sequence lxlx when four letters picked without replacement from {y: 2, x: 11, l: 7}? Hence: 77/1938 Task: What is prob of sequence xxx when three letters picked without replacement from uuuxuuuuuuxuxxuuuu? Hence: 1/204 Task: What is prob of sequence vp when two letters picked without replacement from lvvmvlvvfflmfmmlpllw? Hence: 1/76 Task: Calculate prob of sequence ua when two letters picked without replacement from dudadaudi.
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numbers: place value -------------------- Exercise: What is the tens digit of 3235362? Explanation: 6 Exercise: What is the units digit of 529806451? Explanation: 1 Exercise: What is the tens digit of 8391865? Explanation: 6 Exercise: What is the thousands digit of 39646? Explanation: 9 Exercise: What is the ten millions digit of 15953652? Explanation: 1 Exercise: What is the units digit of 28844637? Explanation: 7 Exercise: What is the thousands digit of 693684? Explanation: 3 Exercise: What is the tens digit of 243? Explanation: 4 Exercise: What is the tens digit of 93? Explanation: 9 Exercise: What is the tens digit of 6689? Explanation: 8 Exercise: What is the ten thousands digit of 74083? Explanation: 7 Exercise: What is the tens digit of 521132? Explanation: 3 Exercise: What is the thousands digit of 2565024? Explanation: 5 Exercise: What is the ten thousands digit of 66890? Explanation: 6 Exercise: What is the units digit of 116910004? Explanation: 4 Exercise: What is the tens digit of 3232? Explanation: 3 Exercise: What is the ten thousands digit of 32672648? Explanation: 7 Exercise: What is the ten thousands digit of 205133? Explanation: 0 Exercise: What is the units digit of 511? Explanation: 1 Exercise: What is the thousands digit of 10589? Explanation: 0 Exercise: What is the hundred thousands digit of 12744587? Explanation: 7 Exercise: What is the units digit of 2427? Explanation: 7 Exercise: What is the ten thousands digit of 137901? Explanation: 3 Exercise: What is the hundred millions digit of 476244862? Explanation: 4 Exercise: What is the hundred thousands digit of 264790? Explanation: 2 Exercise: What is the tens digit of 61014607? Explanation: 0 Exercise: What is the ten thousands digit of 57802? Explanation: 5 Exercise: What is the thousands digit of 93583? Explanation: 3 Exercise: What is the hundreds digit of 46461? Explanation: 4 Exercise: What is the thousands digit of 1432? Explanation: 1 Exercise: What is the tens digit of 1611? Explanatio
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numbers: place value -------------------- Given: What is the units digit of 13621666? Final Answer: 6 Given: What is the units digit of 1532162168? Final Answer: 8 Given: What is the millions digit of 1123537? Final Answer: 1 Given: What is the ten thousands digit of 33674? Final Answer: 3 Given: What is the tens digit of 468? Final Answer: 6 Given: What is the hundred millions digit of 8404391244? Final Answer: 4 Given: What is the tens digit of 9242? Final Answer: 4 Given: What is the hundreds digit of 890905950? Final Answer: 9 Given: What is the units digit of 200067774? Final Answer: 4 Given: What is the ten thousands digit of 2803715? Final Answer: 0 Given: What is the tens digit of 254136? Final Answer: 3 Given: What is the ten millions digit of 1343164191? Final Answer: 4 Given: What is the units digit of 13896523? Final Answer: 3 Given: What is the hundreds digit of 82479457? Final Answer: 4 Given: What is the hundreds digit of 4237? Final Answer: 2 Given: What is the hundreds digit of 1729459? Final Answer: 4 Given: What is the ten thousands digit of 154117276? Final Answer: 1 Given: What is the units digit of 679619? Final Answer: 9 Given: What is the tens digit of 84215411? Final Answer: 1 Given: What is the tens digit of 9514? Final Answer: 1 Given: What is the tens digit of 141? Final Answer: 4 Given: What is the units digit of 389185? Final Answer: 5 Given: What is the hundred thousands digit of 1206395100? Final Answer: 3 Given: What is the hundred thousands digit of 105180? Final Answer: 1 Given: What is the millions digit of 2320115622? Final Answer: 0 Given: What is the thousands digit of 2121? Final Answer: 2 Given: What is the ten thousands digit of 1145557687? Final Answer: 5 Given: What is the ten thousands digit of 34111? Final Answer: 3 Given: What is the units digit of 20786777? Final Answer: 7 Given: What is the ten thousands digit of 1906302? Final Answer: 0 Given: What is the hundreds digit of 150? Final Answer: 1 Given: What is the tens
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numbers: place value -------------------- Q/A: What is the tens digit of 4271? Math A: 7 Q/A: What is the thousands digit of 25964? Math A: 5 Q/A: What is the hundreds digit of 3677? Math A: 6 Q/A: What is the tens digit of 157138? Math A: 3 Q/A: What is the tens digit of 1520? Math A: 2 Q/A: What is the hundreds digit of 3425666? Math A: 6 Q/A: What is the units digit of 1203253? Math A: 3 Q/A: What is the millions digit of 54865221? Math A: 4 Q/A: What is the hundred thousands digit of 11541966? Math A: 5 Q/A: What is the millions digit of 2145274003? Math A: 5 Q/A: What is the millions digit of 26161812? Math A: 6 Q/A: What is the thousands digit of 37460? Math A: 7 Q/A: What is the tens digit of 156844529? Math A: 2 Q/A: What is the ten thousands digit of 15775? Math A: 1 Q/A: What is the ten thousands digit of 14539? Math A: 1 Q/A: What is the ten millions digit of 562271414? Math A: 6 Q/A: What is the ten millions digit of 6334779951? Math A: 3 Q/A: What is the tens digit of 333009? Math A: 0 Q/A: What is the units digit of 63? Math A: 3 Q/A: What is the hundreds digit of 11906? Math A: 9 Q/A: What is the hundred thousands digit of 2259843? Math A: 2 Q/A: What is the ten thousands digit of 85273269? Math A: 7 Q/A: What is the tens digit of 2627011? Math A: 1 Q/A: What is the hundreds digit of 12339? Math A: 3 Q/A: What is the hundred thousands digit of 23991871? Math A: 9 Q/A: What is the ten thousands digit of 3829036161? Math A: 3 Q/A: What is the tens digit of 5000699? Math A: 9 Q/A: What is the hundreds digit of 4194472? Math A: 4 Q/A: What is the hundreds digit of 73087912? Math A: 9 Q/A: What is the ten millions digit of 2163610490? Math A: 6 Q/A: What is the thousands digit of 3544702? Math A: 4 Q/A: What is the hundreds digit of 968578? Math A: 5 Q/A: What is the tens digit of 209685? Math A: 8 Q/A: What is the thousands digit of 70366? Math A: 0 Q/A: What is the tens digit of 88177? Math A: 7 Q/A: What is the ten thousands digit of 65123? Math A: 6 Q/
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measurement: conversion ----------------------- Prompt: What is 7/8 of a millimeter in micrometers? Soln: 875 Prompt: What is 11.66962ml in litres? Soln: 0.01166962 Prompt: How many millilitres are there in three eighths of a litre? Soln: 375 Prompt: How many decades are there in 3/10 of a century? Soln: 3 Prompt: What is 1/4 of a litre in millilitres? Soln: 250 Prompt: How many litres are there in 95.09157ml? Soln: 0.09509157 Prompt: Convert 25250.142 microseconds to minutes. Soln: 0.0004208357 Prompt: Convert 27.408495 months to centuries. Soln: 0.0228404125 Prompt: How many decades are there in 21/2 of a millennium? Soln: 1050 Prompt: Convert 19544.238 months to millennia. Soln: 1.6286865 Prompt: Convert 71.99604mg to tonnes. Soln: 0.00000007199604 Prompt: How many millimeters are there in 0.0129818 meters? Soln: 12.9818 Prompt: How many decades are there in 30.0894 years? Soln: 3.00894 Prompt: What is 21/8 of a microgram in nanograms? Soln: 2625 Prompt: What is three eighths of a week in hours? Soln: 63 Prompt: Convert 690.629 milligrams to micrograms. Soln: 690629 Prompt: What is 1/5 of a century in decades? Soln: 2 Prompt: What is 1/16 of a gram in micrograms? Soln: 62500 Prompt: How many millilitres are there in 19/10 of a litre? Soln: 1900 Prompt: What is three tenths of a centimeter in millimeters? Soln: 3 Prompt: How many micrometers are there in 94624.8nm? Soln: 94.6248 Prompt: What is one fifth of a centimeter in millimeters? Soln: 2 Prompt: How many micrometers are there in three tenths of a millimeter? Soln: 300 Prompt: What is 30.89255 days in seconds? Soln: 2669116.32 Prompt: Convert 5.095955l to millilitres. Soln: 5095.955 Prompt: Convert 0.5830531mg to grams. Soln: 0.0005830531 Prompt: What is 2.370885 decades in millennia? Soln: 0.02370885 Prompt: How many decades are there in 19/10 of a century? Soln: 19 Prompt: How many months are there in 1/20 of a decade? Soln: 6 Prompt: Convert 233.255 nanograms to milligrams. Soln: 0.000233255 Prompt: What i
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numbers: gcd ------------ Case: Calculate the greatest common factor of 13124 and 8. Soln: 4 Case: What is the greatest common factor of 368 and 5224? Soln: 8 Case: Calculate the greatest common divisor of 330 and 1265. Soln: 55 Case: Calculate the highest common factor of 575 and 4485. Soln: 115 Case: Calculate the greatest common divisor of 32 and 36. Soln: 4 Case: Calculate the highest common factor of 91 and 689. Soln: 13 Case: What is the highest common divisor of 12 and 6804? Soln: 12 Case: What is the highest common divisor of 740 and 4889180? Soln: 740 Case: Calculate the greatest common divisor of 1812 and 804. Soln: 12 Case: Calculate the greatest common divisor of 117 and 65013. Soln: 39 Case: Calculate the greatest common factor of 774468 and 13632. Soln: 852 Case: Calculate the highest common divisor of 88 and 22. Soln: 22 Case: What is the greatest common divisor of 75 and 33819? Soln: 3 Case: Calculate the highest common divisor of 43912112 and 7456. Soln: 3728 Case: Calculate the highest common factor of 10 and 4430. Soln: 10 Case: What is the greatest common divisor of 34 and 1225547? Soln: 17 Case: Calculate the greatest common divisor of 20 and 380. Soln: 20 Case: What is the highest common divisor of 15 and 2397360? Soln: 15 Case: What is the highest common factor of 80 and 2183248? Soln: 16 Case: Calculate the highest common factor of 871299 and 9009. Soln: 1287 Case: What is the highest common factor of 2349 and 435? Soln: 87 Case: Calculate the greatest common factor of 24587518 and 3561. Soln: 1187 Case: What is the highest common factor of 7173 and 3618? Soln: 9 Case: Calculate the greatest common divisor of 4312 and 98. Soln: 98 Case: What is the greatest common factor of 8804 and 1420? Soln: 284 Case: What is the greatest common divisor of 1017 and 14266137? Soln: 339 Case: What is the highest common divisor of 522 and 494286788? Soln: 58 Case: What is the highest common divisor of 198 and 66078? Soln: 18 Case: Calculate the greatest commo
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numbers: place value -------------------- Q: What is the millions digit of 1323708? Fix: 1 Q: What is the hundred thousands digit of 307036374? Fix: 0 Q: What is the hundreds digit of 490? Fix: 4 Q: What is the hundreds digit of 645982? Fix: 9 Q: What is the thousands digit of 52578263? Fix: 8 Q: What is the units digit of 62874? Fix: 4 Q: What is the hundreds digit of 3992? Fix: 9 Q: What is the hundred thousands digit of 1155878? Fix: 1 Q: What is the tens digit of 1004? Fix: 0 Q: What is the hundreds digit of 4382? Fix: 3 Q: What is the hundred thousands digit of 78145183? Fix: 1 Q: What is the tens digit of 8272269? Fix: 6 Q: What is the thousands digit of 6920377? Fix: 0 Q: What is the hundred thousands digit of 819171? Fix: 8 Q: What is the thousands digit of 247124? Fix: 7 Q: What is the tens digit of 108? Fix: 0 Q: What is the hundred millions digit of 2365586056? Fix: 3 Q: What is the tens digit of 946? Fix: 4 Q: What is the thousands digit of 33787541? Fix: 7 Q: What is the units digit of 171720516? Fix: 6 Q: What is the thousands digit of 71074794? Fix: 4 Q: What is the hundred millions digit of 3921225296? Fix: 9 Q: What is the units digit of 11312? Fix: 2 Q: What is the hundreds digit of 29008942? Fix: 9 Q: What is the thousands digit of 340108517? Fix: 8 Q: What is the tens digit of 2748? Fix: 4 Q: What is the hundreds digit of 3104? Fix: 1 Q: What is the hundreds digit of 2481918? Fix: 9 Q: What is the hundreds digit of 995? Fix: 9 Q: What is the hundreds digit of 755817? Fix: 8 Q: What is the hundreds digit of 1098? Fix: 0 Q: What is the hundreds digit of 742? Fix: 7 Q: What is the tens digit of 3196? Fix: 9 Q: What is the units digit of 5736? Fix: 6 Q: What is the tens digit of 55250? Fix: 5 Q: What is the ten thousands digit of 94649298? Fix: 4 Q: What is the units digit of 12948? Fix: 8 Q: What is the tens digit of 881884723? Fix: 2 Q: What is the tens digit of 65081? Fix: 8 Q: What is the tens digit of 5538582? Fix: 8 Q: What is the hundreds digi
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numbers: place value -------------------- Challenge: What is the ten thousands digit of 5456962? Final Answer: 5 Challenge: What is the hundreds digit of 1313? Final Answer: 3 Challenge: What is the units digit of 22033? Final Answer: 3 Challenge: What is the tens digit of 949737390? Final Answer: 9 Challenge: What is the hundred millions digit of 368717526? Final Answer: 3 Challenge: What is the hundreds digit of 162428120? Final Answer: 1 Challenge: What is the units digit of 78093? Final Answer: 3 Challenge: What is the hundreds digit of 13371? Final Answer: 3 Challenge: What is the tens digit of 1671956? Final Answer: 5 Challenge: What is the ten thousands digit of 137077? Final Answer: 3 Challenge: What is the units digit of 29205? Final Answer: 5 Challenge: What is the ten thousands digit of 287574? Final Answer: 8 Challenge: What is the units digit of 29837? Final Answer: 7 Challenge: What is the hundreds digit of 134312? Final Answer: 3 Challenge: What is the tens digit of 324254822? Final Answer: 2 Challenge: What is the hundreds digit of 894185? Final Answer: 1 Challenge: What is the thousands digit of 3891? Final Answer: 3 Challenge: What is the ten thousands digit of 5492620? Final Answer: 9 Challenge: What is the hundred thousands digit of 157880? Final Answer: 1 Challenge: What is the thousands digit of 45740968? Final Answer: 0 Challenge: What is the units digit of 928? Final Answer: 8 Challenge: What is the units digit of 79? Final Answer: 9 Challenge: What is the thousands digit of 30585? Final Answer: 0 Challenge: What is the millions digit of 9595406? Final Answer: 9 Challenge: What is the units digit of 19809? Final Answer: 9 Challenge: What is the hundred thousands digit of 46407507? Final Answer: 4 Challenge: What is the ten thousands digit of 1135868543? Final Answer: 6 Challenge: What is the ten millions digit of 203750765? Final Answer: 0 Challenge: What is the hundred thousands digit of 190933706? Final Answer: 9 Challenge: What is the hund
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numbers: div remainder ---------------------- Qn: What is the remainder when 38789231 is divided by 119? Reply: 110 Qn: What is the remainder when 959 is divided by 192? Reply: 191 Qn: Calculate the remainder when 64392 is divided by 21394. Reply: 210 Qn: What is the remainder when 324630 is divided by 5687? Reply: 471 Qn: What is the remainder when 645 is divided by 13? Reply: 8 Qn: Calculate the remainder when 2659962 is divided by 409. Reply: 235 Qn: What is the remainder when 16728440 is divided by 712? Reply: 0 Qn: What is the remainder when 89157 is divided by 249? Reply: 15 Qn: Calculate the remainder when 350370 is divided by 70072. Reply: 10 Qn: What is the remainder when 470 is divided by 19? Reply: 14 Qn: What is the remainder when 368833 is divided by 92204? Reply: 17 Qn: What is the remainder when 99 is divided by 71? Reply: 28 Qn: What is the remainder when 10631 is divided by 294? Reply: 47 Qn: What is the remainder when 651310 is divided by 343? Reply: 296 Qn: Calculate the remainder when 11238317 is divided by 176. Reply: 13 Qn: What is the remainder when 32413 is divided by 145? Reply: 78 Qn: Calculate the remainder when 1280604 is divided by 1042. Reply: 1028 Qn: Calculate the remainder when 577 is divided by 295. Reply: 282 Qn: Calculate the remainder when 457 is divided by 136. Reply: 49 Qn: Calculate the remainder when 188764 is divided by 97. Reply: 2 Qn: Calculate the remainder when 174928956 is divided by 547. Reply: 544 Qn: What is the remainder when 4959 is divided by 423? Reply: 306 Qn: What is the remainder when 797038 is divided by 6871? Reply: 2 Qn: Calculate the remainder when 17373 is divided by 4340. Reply: 13 Qn: Calculate the remainder when 3517 is divided by 543. Reply: 259 Qn: Calculate the remainder when 398 is divided by 9. Reply: 2 Qn: Calculate the remainder when 10003 is divided by 9062. Reply: 941 Qn: Calculate the remainder when 7689431 is divided by 768936. Reply: 71 Qn: What is the remainder when 1087 is divided by 10?
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probability: swr p level set ---------------------------- Item: What is prob of picking 1 q, 1 p, 1 t, and 1 s when four letters picked without replacement from hhqphqqtshsqhshqthqs? Outcome: 16/1615 Item: Four letters picked without replacement from {y: 6}. Give prob of picking 4 y. Outcome: 1 Item: Three letters picked without replacement from apapxpllpprp. Give prob of picking 2 p and 1 l. Outcome: 3/22 Item: What is prob of picking 1 x and 1 y when two letters picked without replacement from iipcpxiipipyiippypi? Outcome: 2/171 Item: Calculate prob of picking 2 j and 1 n when three letters picked without replacement from {e: 1, l: 4, j: 3, n: 12}. Outcome: 3/95 Item: What is prob of picking 1 y and 1 q when two letters picked without replacement from {y: 5, q: 8}? Outcome: 20/39 Item: Calculate prob of picking 2 t and 1 x when three letters picked without replacement from ttoyooovvvtxotvo. Outcome: 3/280 Item: What is prob of picking 2 c when two letters picked without replacement from {t: 4, c: 3}? Outcome: 1/7 Item: What is prob of picking 2 p when two letters picked without replacement from {p: 2, i: 1, j: 1}? Outcome: 1/6 Item: Four letters picked without replacement from {f: 4, w: 2, p: 4, a: 3, h: 1}. What is prob of picking 2 w and 2 f? Outcome: 6/1001 Item: What is prob of picking 1 g and 3 k when four letters picked without replacement from hhfkhgkhkf? Outcome: 1/210 Item: What is prob of picking 2 o and 1 p when three letters picked without replacement from {i: 3, p: 4, o: 2}? Outcome: 1/21 Item: Calculate prob of picking 1 r, 1 i, and 1 x when three letters picked without replacement from {i: 1, r: 4, g: 4, n: 3, x: 1}. Outcome: 2/143 Item: Calculate prob of picking 3 e when three letters picked without replacement from {e: 5}. Outcome: 1 Item: Calculate prob of picking 1 r and 1 j when two letters picked without replacement from rurjjrjjwjouruojow. Outcome: 8/51 Item: Calculate prob of picking 2 p and 2 l when four letters picked without replacement f
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numbers: is factor ------------------ Conundrum: Is 12 a factor of 809292? Derivation: True Conundrum: Is 5 a factor of 4342097? Derivation: False Conundrum: Is 14086260 a multiple of 36? Derivation: True Conundrum: Does 2194 divide 853373429? Derivation: False Conundrum: Is 30 a factor of 110? Derivation: False Conundrum: Is 1006 a factor of 73760759? Derivation: False Conundrum: Is 734977 a multiple of 101? Derivation: True Conundrum: Is 36535460 a multiple of 95? Derivation: False Conundrum: Is 274564200 a multiple of 450? Derivation: False Conundrum: Is 18032 a multiple of 161? Derivation: True Conundrum: Does 109 divide 10900? Derivation: True Conundrum: Does 137 divide 4493? Derivation: False Conundrum: Is 5663 a multiple of 6? Derivation: False Conundrum: Is 210 a multiple of 21? Derivation: True Conundrum: Is 2 a factor of 2001528? Derivation: True Conundrum: Is 8305 a multiple of 55? Derivation: True Conundrum: Is 13620 a multiple of 30? Derivation: True Conundrum: Does 95 divide 232063815? Derivation: True Conundrum: Is 256 a multiple of 4? Derivation: True Conundrum: Does 86 divide 87301071? Derivation: False Conundrum: Does 67 divide 2578509? Derivation: False Conundrum: Is 1247 a factor of 931507753? Derivation: True Conundrum: Does 12 divide 241743? Derivation: False Conundrum: Is 24912 a multiple of 35? Derivation: False Conundrum: Does 63 divide 229257? Derivation: True Conundrum: Is 14237 a multiple of 23? Derivation: True Conundrum: Is 2884 a multiple of 3? Derivation: False Conundrum: Is 548390 a multiple of 145? Derivation: True Conundrum: Is 256 a factor of 2462572? Derivation: False Conundrum: Is 32 a factor of 1509379? Derivation: False Conundrum: Is 25 a factor of 496? Derivation: False Conundrum: Is 274 a factor of 2289959110? Derivation: True Conundrum: Does 4 divide 5266637? Derivation: False Conundrum: Is 581904907 a multiple of 1107? Derivation: False Conundrum: Is 138197094 a multiple of 14? Derivation: True Conundrum: Is 7368196 a mult
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probability: swr p level set ---------------------------- Given: Calculate prob of picking 3 x when three letters picked without replacement from {a: 5, x: 14}. A.: 364/969 Given: What is prob of picking 2 k and 1 y when three letters picked without replacement from mmykmyyky? A.: 1/21 Given: Calculate prob of picking 2 c and 2 z when four letters picked without replacement from cddzczddzdazczc. A.: 4/91 Given: Two letters picked without replacement from pppppppnppppppp. Give prob of picking 2 p. A.: 13/15 Given: Two letters picked without replacement from {q: 2, a: 1, b: 1, m: 1, j: 2, f: 1}. What is prob of picking 1 b and 1 f? A.: 1/28 Given: Calculate prob of picking 2 h when two letters picked without replacement from {v: 2, h: 2}. A.: 1/6 Given: Three letters picked without replacement from {z: 4, d: 7, a: 2, w: 2, b: 1, e: 4}. What is prob of picking 1 b and 2 z? A.: 1/190 Given: Calculate prob of picking 1 p and 3 d when four letters picked without replacement from dddppdpddd. A.: 1/2 Given: Calculate prob of picking 3 d when three letters picked without replacement from {d: 6, h: 4}. A.: 1/6 Given: What is prob of picking 1 r and 1 v when two letters picked without replacement from {z: 2, v: 3, r: 12}? A.: 9/34 Given: Calculate prob of picking 2 t when two letters picked without replacement from ththttt. A.: 10/21 Given: Four letters picked without replacement from {w: 3, c: 5}. Give prob of picking 2 c and 2 w. A.: 3/7 Given: Three letters picked without replacement from {l: 2, e: 5}. What is prob of picking 2 e and 1 l? A.: 4/7 Given: Three letters picked without replacement from oooq. Give prob of picking 2 o and 1 q. A.: 3/4 Given: Calculate prob of picking 1 l and 2 v when three letters picked without replacement from xvlv. A.: 1/4 Given: Three letters picked without replacement from zzxzozzzxoeox. What is prob of picking 1 e, 1 z, and 1 o? A.: 9/143 Given: Three letters picked without replacement from {f: 1, x: 5, s: 4, e: 1}. What is prob of picking
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numbers: is prime ----------------- Situation: Is 14632134587 prime? Key: False Situation: Is 305703527 prime? Key: True Situation: Is 3049 a prime number? Key: True Situation: Is 53276291 a composite number? Key: True Situation: Is 80337935 prime? Key: False Situation: Is 9403 composite? Key: False Situation: Is 823713811 a composite number? Key: False Situation: Is 5068776641 composite? Key: True Situation: Is 29222197 a prime number? Key: False Situation: Is 260320553 a composite number? Key: False Situation: Is 71694517 a prime number? Key: True Situation: Is 2417893831 a composite number? Key: True Situation: Is 70713056983 a prime number? Key: True Situation: Is 376667309 prime? Key: True Situation: Is 5693859299 composite? Key: False Situation: Is 80813 a prime number? Key: False Situation: Is 46969296247 composite? Key: False Situation: Is 797972183 a composite number? Key: False Situation: Is 326652709 a prime number? Key: True Situation: Is 22318057 a prime number? Key: False Situation: Is 1963521101 a prime number? Key: False Situation: Is 12658019 a composite number? Key: True Situation: Is 7144793 a prime number? Key: True Situation: Is 418800209 composite? Key: True Situation: Is 10428174013 a prime number? Key: True Situation: Is 1057047 a composite number? Key: True Situation: Is 39279 composite? Key: True Situation: Is 12536621189 prime? Key: True Situation: Is 433835881 composite? Key: True Situation: Is 37397 a prime number? Key: True Situation: Is 579067 a composite number? Key: True Situation: Is 739033 a composite number? Key: True Situation: Is 4523977 a composite number? Key: True Situation: Is 76888884179 composite? Key: True Situation: Is 474854993 a composite number? Key: True Situation: Is 87881 prime? Key: True Situation: Is 60101 composite? Key: False Situation: Is 380704739 a composite number? Key: False Situation: Is 23512919 composite? Key: False Situation: Is 4493 prime? Key: True Situation: Is 807251339 a prime number? Key: False S
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numbers: is prime ----------------- Given: Is 59577275299 composite? Calculation: False Given: Is 1496179 composite? Calculation: True Given: Is 10611899 a composite number? Calculation: True Given: Is 132541 a prime number? Calculation: True Given: Is 2595286307 composite? Calculation: True Given: Is 97406549 a prime number? Calculation: False Given: Is 521554759 composite? Calculation: True Given: Is 59159579 composite? Calculation: True Given: Is 21911 a composite number? Calculation: False Given: Is 29789 a prime number? Calculation: True Given: Is 58593217 a prime number? Calculation: True Given: Is 218678303 prime? Calculation: True Given: Is 27474943037 prime? Calculation: True Given: Is 18187 a composite number? Calculation: True Given: Is 2307533881 composite? Calculation: True Given: Is 2394880139 a composite number? Calculation: True Given: Is 231161509 prime? Calculation: True Given: Is 331 prime? Calculation: True Given: Is 196611 prime? Calculation: False Given: Is 10433629 prime? Calculation: False Given: Is 2406983 a composite number? Calculation: False Given: Is 36059 composite? Calculation: True Given: Is 404941 a composite number? Calculation: False Given: Is 11147443 prime? Calculation: False Given: Is 25045233559 a composite number? Calculation: True Given: Is 171465607 prime? Calculation: True Given: Is 730972421 a composite number? Calculation: True Given: Is 11435447497 composite? Calculation: False Given: Is 66133796591 a prime number? Calculation: False Given: Is 6076857547 composite? Calculation: True Given: Is 9302682839 a composite number? Calculation: False Given: Is 10311673283 prime? Calculation: False Given: Is 813584378 a prime number? Calculation: False Given: Is 15591131401 a composite number? Calculation: False Given: Is 28248253 a composite number? Calculation: True Given: Is 1307209 a composite number? Calculation: False Given: Is 3839 a prime number? Calculation: False Given: Is 1639 prime? Calculation: False Given: Is 3570643
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numbers: place value -------------------- Let: What is the units digit of 126241? Yields: 1 Let: What is the ten thousands digit of 699938693? Yields: 3 Let: What is the millions digit of 2007725? Yields: 2 Let: What is the hundreds digit of 498139885? Yields: 8 Let: What is the thousands digit of 3225007? Yields: 5 Let: What is the thousands digit of 1162? Yields: 1 Let: What is the hundred millions digit of 6825445809? Yields: 8 Let: What is the hundreds digit of 36828? Yields: 8 Let: What is the ten thousands digit of 103217949? Yields: 1 Let: What is the millions digit of 618787625? Yields: 8 Let: What is the units digit of 918? Yields: 8 Let: What is the units digit of 983? Yields: 3 Let: What is the units digit of 102527? Yields: 7 Let: What is the ten thousands digit of 126855004? Yields: 5 Let: What is the hundreds digit of 85368? Yields: 3 Let: What is the ten thousands digit of 78679? Yields: 7 Let: What is the hundred millions digit of 236222557? Yields: 2 Let: What is the units digit of 305843? Yields: 3 Let: What is the tens digit of 5739? Yields: 3 Let: What is the tens digit of 1967? Yields: 6 Let: What is the ten millions digit of 1257637709? Yields: 5 Let: What is the thousands digit of 5276? Yields: 5 Let: What is the thousands digit of 591439562? Yields: 9 Let: What is the ten millions digit of 1083900591? Yields: 8 Let: What is the millions digit of 1173322? Yields: 1 Let: What is the tens digit of 2371593? Yields: 9 Let: What is the tens digit of 1397631377? Yields: 7 Let: What is the thousands digit of 2072174? Yields: 2 Let: What is the units digit of 1234? Yields: 4 Let: What is the millions digit of 921041156? Yields: 1 Let: What is the units digit of 6708263? Yields: 3 Let: What is the hundred thousands digit of 16806932? Yields: 8 Let: What is the thousands digit of 71609450? Yields: 9 Let: What is the hundreds digit of 330? Yields: 3 Let: What is the ten millions digit of 26693316? Yields: 2 Let: What is the units digit of 33787? Yields:
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numbers: is prime ----------------- Question: Is 223631699 prime? Calculation: False Question: Is 1271483 prime? Calculation: True Question: Is 30669953 prime? Calculation: True Question: Is 36845 prime? Calculation: False Question: Is 27767996057 a composite number? Calculation: False Question: Is 23708665993 prime? Calculation: True Question: Is 25001 a prime number? Calculation: False Question: Is 8053 composite? Calculation: False Question: Is 15739878767 a prime number? Calculation: False Question: Is 110725591 composite? Calculation: False Question: Is 21115947317 a composite number? Calculation: False Question: Is 109271 composite? Calculation: True Question: Is 139505 prime? Calculation: False Question: Is 138092331301 prime? Calculation: False Question: Is 59991 a composite number? Calculation: True Question: Is 8707 composite? Calculation: False Question: Is 1692040085 a composite number? Calculation: True Question: Is 790957018 prime? Calculation: False Question: Is 32608448381 a composite number? Calculation: False Question: Is 2767 composite? Calculation: False Question: Is 20737 a prime number? Calculation: False Question: Is 499823 composite? Calculation: True Question: Is 5029160893 a prime number? Calculation: False Question: Is 87654109 a composite number? Calculation: False Question: Is 16516551463 composite? Calculation: False Question: Is 3935 composite? Calculation: True Question: Is 570733 a prime number? Calculation: True Question: Is 3427 prime? Calculation: False Question: Is 28666247 a prime number? Calculation: True Question: Is 168040163 a composite number? Calculation: False Question: Is 3150242593 composite? Calculation: False Question: Is 865899259 a prime number? Calculation: False Question: Is 439102915 composite? Calculation: True Question: Is 1997326687 prime? Calculation: True Question: Is 1066577 composite? Calculation: False Question: Is 1094458291 a composite number? Calculation: False Question: Is 419555 a composite number? C
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numbers: is factor ------------------ Let: Does 681 divide 39423680? Resolution: False Let: Is 63 a multiple of 5? Resolution: False Let: Does 153 divide 38986593? Resolution: False Let: Is 1152877 a multiple of 19? Resolution: False Let: Is 73 a factor of 1314? Resolution: True Let: Is 192 a factor of 7557312? Resolution: True Let: Is 2035 a factor of 1209900508? Resolution: False Let: Does 34 divide 1836? Resolution: True Let: Is 7 a factor of 466457? Resolution: False Let: Is 11920 a multiple of 16? Resolution: True Let: Is 51 a factor of 18905598? Resolution: True Let: Is 1017772 a multiple of 223? Resolution: True Let: Is 333 a factor of 762483420? Resolution: True Let: Does 19 divide 608? Resolution: True Let: Is 7666 a factor of 2904129793? Resolution: False Let: Is 51 a factor of 3618047188? Resolution: False Let: Is 17 a factor of 446607? Resolution: True Let: Is 1676 a factor of 293196088? Resolution: True Let: Is 105 a factor of 6507313? Resolution: False Let: Is 13173440 a multiple of 167? Resolution: False Let: Is 2359 a factor of 2359000? Resolution: True Let: Is 40431 a multiple of 5? Resolution: False Let: Does 1248 divide 6405401? Resolution: False Let: Is 473315 a multiple of 162? Resolution: False Let: Is 23 a factor of 315698943? Resolution: True Let: Does 12 divide 8712? Resolution: True Let: Is 22 a factor of 12742148? Resolution: False Let: Does 96 divide 136894? Resolution: False Let: Does 29 divide 5452? Resolution: True Let: Is 11 a factor of 304? Resolution: False Let: Does 37 divide 4668? Resolution: False Let: Is 1942 a multiple of 3? Resolution: False Let: Is 10 a factor of 329? Resolution: False Let: Is 17 a factor of 18186109? Resolution: False Let: Does 311 divide 123579? Resolution: False Let: Does 37 divide 372095755? Resolution: False Let: Is 9 a factor of 45747? Resolution: True Let: Is 286888836 a multiple of 996? Resolution: True Let: Does 248 divide 9678? Resolution: False Let: Does 1581 divide 1904600661? Resolution: True Let
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probability: swr p sequence --------------------------- Case: Four letters picked without replacement from {t: 15, o: 5}. Give prob of sequence otot. Fix: 35/969 Case: Two letters picked without replacement from {a: 5, x: 3, i: 9, s: 2}. What is prob of sequence xs? Fix: 1/57 Case: Four letters picked without replacement from mmmzmmzz. Give prob of sequence zzmz. Fix: 1/56 Case: Three letters picked without replacement from {q: 1, j: 11, y: 5, w: 3}. Give prob of sequence wjy. Fix: 11/456 Case: Calculate prob of sequence tvpp when four letters picked without replacement from {v: 2, t: 1, p: 2}. Fix: 1/30 Case: What is prob of sequence ee when two letters picked without replacement from {e: 2, m: 17}? Fix: 1/171 Case: What is prob of sequence cc when two letters picked without replacement from cccrrrrcccccccrccccc? Fix: 21/38 Case: Three letters picked without replacement from fnfnnnnnff. What is prob of sequence fnn? Fix: 1/6 Case: Calculate prob of sequence ine when three letters picked without replacement from {e: 6, o: 1, i: 3, b: 5, n: 2, m: 2}. Fix: 2/323 Case: Calculate prob of sequence kbk when three letters picked without replacement from {a: 2, b: 8, k: 4}. Fix: 4/91 Case: Two letters picked without replacement from kgbk. Give prob of sequence kg. Fix: 1/6 Case: Four letters picked without replacement from {l: 2, e: 4, h: 4, s: 2, u: 5}. What is prob of sequence eeuh? Fix: 1/238 Case: What is prob of sequence xxv when three letters picked without replacement from xxxxxvxxxxxxx? Fix: 1/13 Case: What is prob of sequence op when two letters picked without replacement from {p: 1, o: 2, t: 1}? Fix: 1/6 Case: Two letters picked without replacement from {k: 3}. What is prob of sequence kk? Fix: 1 Case: Four letters picked without replacement from eeeeeeeeee. Give prob of sequence eeee. Fix: 1 Case: Two letters picked without replacement from {u: 1, v: 1, f: 1, z: 4, x: 1}. What is prob of sequence xz? Fix: 1/14 Case: Calculate prob of sequence xe when two letters
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numbers: place value -------------------- Inquiry: What is the ten thousands digit of 12766710? Response: 6 Inquiry: What is the tens digit of 3230? Response: 3 Inquiry: What is the units digit of 1103371593? Response: 3 Inquiry: What is the hundreds digit of 1511? Response: 5 Inquiry: What is the hundreds digit of 6043? Response: 0 Inquiry: What is the hundred thousands digit of 173072? Response: 1 Inquiry: What is the hundreds digit of 2555? Response: 5 Inquiry: What is the ten thousands digit of 26117? Response: 2 Inquiry: What is the tens digit of 70310256? Response: 5 Inquiry: What is the thousands digit of 236461? Response: 6 Inquiry: What is the millions digit of 900619017? Response: 0 Inquiry: What is the hundred thousands digit of 2801991? Response: 8 Inquiry: What is the millions digit of 26364712? Response: 6 Inquiry: What is the hundreds digit of 7462476? Response: 4 Inquiry: What is the units digit of 1139501? Response: 1 Inquiry: What is the ten thousands digit of 438676? Response: 3 Inquiry: What is the thousands digit of 64943? Response: 4 Inquiry: What is the hundred millions digit of 124163101? Response: 1 Inquiry: What is the hundreds digit of 39044? Response: 0 Inquiry: What is the billions digit of 2928824982? Response: 2 Inquiry: What is the tens digit of 541919782? Response: 8 Inquiry: What is the hundreds digit of 1961? Response: 9 Inquiry: What is the ten thousands digit of 2333526? Response: 3 Inquiry: What is the tens digit of 21040834? Response: 3 Inquiry: What is the thousands digit of 14533? Response: 4 Inquiry: What is the hundred thousands digit of 168949? Response: 1 Inquiry: What is the tens digit of 1100? Response: 0 Inquiry: What is the units digit of 2182121? Response: 1 Inquiry: What is the hundreds digit of 1230? Response: 2 Inquiry: What is the hundreds digit of 154828? Response: 8 Inquiry: What is the tens digit of 63791? Response: 9 Inquiry: What is the ten millions digit of 734439375? Response: 3 Inquiry: What is the hundre
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probability: swr p sequence --------------------------- Exercise: Three letters picked without replacement from pupprrrrurrrrpp. What is prob of sequence uup? Solution: 1/273 Exercise: Calculate prob of sequence ooow when four letters picked without replacement from {w: 2, o: 7}. Solution: 5/36 Exercise: Calculate prob of sequence kwj when three letters picked without replacement from ufwwjjjkwjujuffjjff. Solution: 7/1938 Exercise: Four letters picked without replacement from welunnllelwete. What is prob of sequence ewut? Solution: 1/3003 Exercise: Calculate prob of sequence tvm when three letters picked without replacement from rrrarcmraratavrtv. Solution: 1/1020 Exercise: Two letters picked without replacement from wppppwppwppbpwpwprp. Give prob of sequence pb. Solution: 2/57 Exercise: Four letters picked without replacement from {v: 7}. What is prob of sequence vvvv? Solution: 1 Exercise: Four letters picked without replacement from tthx. Give prob of sequence htxh. Solution: 0 Exercise: Calculate prob of sequence ww when two letters picked without replacement from {d: 3, c: 1, k: 6, r: 2, w: 5}. Solution: 5/68 Exercise: Three letters picked without replacement from {a: 4, b: 1, k: 1, f: 2, n: 3}. Give prob of sequence aka. Solution: 2/165 Exercise: Calculate prob of sequence bn when two letters picked without replacement from {a: 4, n: 3, b: 2, f: 1}. Solution: 1/15 Exercise: Calculate prob of sequence jjq when three letters picked without replacement from qjeejjejjeejfjejeq. Solution: 7/306 Exercise: Calculate prob of sequence pddd when four letters picked without replacement from {p: 1, d: 7}. Solution: 1/8 Exercise: What is prob of sequence uu when two letters picked without replacement from {u: 7, s: 3}? Solution: 7/15 Exercise: Three letters picked without replacement from hhohhhthohohthoo. What is prob of sequence hto? Solution: 3/112 Exercise: Calculate prob of sequence lz when two letters picked without replacement from zkkl. Solution: 1/12 Exercise: Two
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numbers: gcd ------------ Issue: Calculate the greatest common factor of 54 and 7803. Gives: 27 Issue: What is the greatest common divisor of 21079811 and 3131? Gives: 101 Issue: Calculate the highest common divisor of 201561443 and 2185. Gives: 437 Issue: What is the highest common divisor of 64665 and 23625? Gives: 135 Issue: Calculate the greatest common divisor of 30 and 195. Gives: 15 Issue: What is the greatest common divisor of 1432 and 992? Gives: 8 Issue: What is the greatest common factor of 44 and 93456? Gives: 44 Issue: Calculate the highest common factor of 6035 and 95285. Gives: 85 Issue: What is the highest common factor of 53652 and 306? Gives: 102 Issue: What is the highest common factor of 406 and 6293? Gives: 203 Issue: Calculate the greatest common factor of 3282 and 78. Gives: 6 Issue: What is the highest common divisor of 28795 and 6669365? Gives: 2215 Issue: What is the highest common divisor of 57720 and 10140? Gives: 780 Issue: Calculate the highest common divisor of 68 and 35411. Gives: 17 Issue: Calculate the highest common factor of 195 and 1040. Gives: 65 Issue: What is the greatest common factor of 183826 and 31886? Gives: 214 Issue: What is the highest common factor of 88 and 187? Gives: 11 Issue: What is the greatest common divisor of 476 and 595? Gives: 119 Issue: Calculate the highest common divisor of 1350 and 356044950. Gives: 1350 Issue: What is the greatest common factor of 704 and 484? Gives: 44 Issue: What is the greatest common divisor of 22743 and 9? Gives: 9 Issue: What is the greatest common factor of 68258970 and 10530? Gives: 3510 Issue: What is the greatest common factor of 2472 and 24? Gives: 24 Issue: Calculate the greatest common divisor of 80 and 19676. Gives: 4 Issue: Calculate the highest common factor of 10 and 74360. Gives: 10 Issue: Calculate the highest common factor of 332 and 3154. Gives: 166 Issue: What is the highest common factor of 612 and 68? Gives: 68 Issue: What is the highest common factor of 18792 a
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numbers: is prime ----------------- Issue: Is 1531295 prime? Eval: False Issue: Is 39281 composite? Eval: True Issue: Is 21548783 a composite number? Eval: True Issue: Is 15959 a prime number? Eval: True Issue: Is 265 a composite number? Eval: True Issue: Is 1586867869 a composite number? Eval: False Issue: Is 90072607 composite? Eval: True Issue: Is 7913 prime? Eval: False Issue: Is 10162357 prime? Eval: False Issue: Is 24814367 prime? Eval: True Issue: Is 11921473 a composite number? Eval: False Issue: Is 4861 a composite number? Eval: False Issue: Is 79644334877 a prime number? Eval: True Issue: Is 408380023 a prime number? Eval: True Issue: Is 80137 a prime number? Eval: False Issue: Is 54082829 a composite number? Eval: True Issue: Is 2977578599 composite? Eval: True Issue: Is 32117 composite? Eval: False Issue: Is 80188601 a prime number? Eval: False Issue: Is 9411 a composite number? Eval: True Issue: Is 35723213 a prime number? Eval: True Issue: Is 7187743 prime? Eval: True Issue: Is 153107 a prime number? Eval: True Issue: Is 3238 composite? Eval: True Issue: Is 300047 composite? Eval: True Issue: Is 16680173 prime? Eval: False Issue: Is 3013 prime? Eval: False Issue: Is 4547 a composite number? Eval: False Issue: Is 560389 a prime number? Eval: False Issue: Is 4444397 a composite number? Eval: False Issue: Is 117080083 prime? Eval: True Issue: Is 253934353 a prime number? Eval: False Issue: Is 350699 a composite number? Eval: False Issue: Is 21373231001 composite? Eval: True Issue: Is 50284727 composite? Eval: False Issue: Is 15817 prime? Eval: True Issue: Is 1123777 a prime number? Eval: True Issue: Is 1830298069 prime? Eval: True Issue: Is 30584210819 composite? Eval: True Issue: Is 385876547 prime? Eval: False Issue: Is 1066595 prime? Eval: False Issue: Is 82797509 composite? Eval: True Issue: Is 307026323 a prime number? Eval: True Issue: Is 37960649 a composite number? Eval: True Issue: Is 316993 composite? Eval: True Issue: Is 8183550563 composite? E
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measurement: time ----------------- Conundrum: What is 293 minutes after 6:51 AM? Output: 11:44 AM Conundrum: How many minutes are there between 9:15 AM and 3:09 PM? Output: 354 Conundrum: What is 467 minutes before 7:27 AM? Output: 11:40 PM Conundrum: What is 20 minutes after 10:59 AM? Output: 11:19 AM Conundrum: How many minutes are there between 1:41 AM and 9:46 AM? Output: 485 Conundrum: What is 394 minutes after 4:54 AM? Output: 11:28 AM Conundrum: What is 223 minutes before 9:01 AM? Output: 5:18 AM Conundrum: How many minutes are there between 5:29 AM and 7:57 AM? Output: 148 Conundrum: How many minutes are there between 10:49 AM and 7:52 PM? Output: 543 Conundrum: What is 92 minutes before 8:12 PM? Output: 6:40 PM Conundrum: How many minutes are there between 12:28 PM and 11:04 PM? Output: 636 Conundrum: What is 572 minutes before 9:33 PM? Output: 12:01 PM Conundrum: How many minutes are there between 12:33 PM and 1:35 PM? Output: 62 Conundrum: How many minutes are there between 3:00 AM and 12:59 PM? Output: 599 Conundrum: How many minutes are there between 5:43 PM and 8:04 PM? Output: 141 Conundrum: How many minutes are there between 2:03 AM and 4:35 AM? Output: 152 Conundrum: How many minutes are there between 5:32 AM and 8:54 AM? Output: 202 Conundrum: What is 470 minutes before 6:23 PM? Output: 10:33 AM Conundrum: What is 172 minutes before 10:00 PM? Output: 7:08 PM Conundrum: What is 679 minutes before 5:28 PM? Output: 6:09 AM Conundrum: What is 605 minutes after 3:41 AM? Output: 1:46 PM Conundrum: What is 592 minutes after 9:16 PM? Output: 7:08 AM Conundrum: How many minutes are there between 10:25 PM and 3:04 AM? Output: 279 Conundrum: How many minutes are there between 11:11 PM and 4:31 AM? Output: 320 Conundrum: What is 194 minutes before 1:58 AM? Output: 10:44 PM Conundrum: What is 322 minutes after 12:11 PM? Output: 5:33 PM Conundrum: What is 300 minutes after 10:30 AM? Output: 3:30 PM Conundrum: How many minutes are there between 1:20 AM and 12:53
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measurement: conversion ----------------------- Statement: How many meters are there in 15/4 of a kilometer? Steps: 3750 Statement: How many millilitres are there in 738.0962 litres? Steps: 738096.2 Statement: How many kilometers are there in 0.6475354 nanometers? Steps: 0.0000000000006475354 Statement: Convert 72.05234 nanoseconds to microseconds. Steps: 0.07205234 Statement: What is 320737.7 years in decades? Steps: 32073.77 Statement: What is 33/5 of a century in years? Steps: 660 Statement: Convert 56421.81 grams to milligrams. Steps: 56421810 Statement: Convert 0.9965679t to kilograms. Steps: 996.5679 Statement: What is 51792.35 hours in milliseconds? Steps: 186452460000 Statement: What is 21/4 of a kilometer in meters? Steps: 5250 Statement: What is 33/5 of a litre in millilitres? Steps: 6600 Statement: How many nanograms are there in twenty-five halves of a microgram? Steps: 12500 Statement: What is 544.7318 meters in micrometers? Steps: 544731800 Statement: Convert 0.2591984 years to decades. Steps: 0.02591984 Statement: Convert 634573.1km to centimeters. Steps: 63457310000 Statement: How many millilitres are there in 6252.575 litres? Steps: 6252575 Statement: How many hours are there in 13/4 of a week? Steps: 546 Statement: What is 0.2703871 days in minutes? Steps: 389.357424 Statement: What is 0.7817875 milliseconds in nanoseconds? Steps: 781787.5 Statement: Convert 3.060487 weeks to nanoseconds. Steps: 1850982537600000 Statement: Convert 134.0893 weeks to microseconds. Steps: 81097208640000 Statement: Convert 0.8589311 centuries to millennia. Steps: 0.08589311 Statement: What is 18.63069 litres in millilitres? Steps: 18630.69 Statement: How many months are there in 29/3 of a year? Steps: 116 Statement: How many minutes are there in 1/6 of a day? Steps: 240 Statement: How many millilitres are there in 3/25 of a litre? Steps: 120 Statement: How many milligrams are there in 13.47409 nanograms? Steps: 0.00001347409 Statement: What is 3/5 of a litre in millili
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arithmetic: nearest integer root -------------------------------- Let us solve: What is 54774 to the power of 1/5, to the nearest integer? Output: 9 Let us solve: What is 2406 to the power of 1/4, to the nearest integer? Output: 7 Let us solve: What is the sixth root of 35844 to the nearest integer? Output: 6 Let us solve: What is 4397705812 to the power of 1/7, to the nearest integer? Output: 24 Let us solve: What is the third root of 10907 to the nearest integer? Output: 22 Let us solve: What is 30271974 to the power of 1/7, to the nearest integer? Output: 12 Let us solve: What is 418 to the power of 1/5, to the nearest integer? Output: 3 Let us solve: What is 1151 to the power of 1/2, to the nearest integer? Output: 34 Let us solve: What is 1480431 to the power of 1/6, to the nearest integer? Output: 11 Let us solve: What is the third root of 35576621 to the nearest integer? Output: 329 Let us solve: What is the tenth root of 17287 to the nearest integer? Output: 3 Let us solve: What is 204289 to the power of 1/10, to the nearest integer? Output: 3 Let us solve: What is the fourth root of 110813 to the nearest integer? Output: 18 Let us solve: What is the fourth root of 5776 to the nearest integer? Output: 9 Let us solve: What is the square root of 21235 to the nearest integer? Output: 146 Let us solve: What is the fifth root of 341349 to the nearest integer? Output: 13 Let us solve: What is 821 to the power of 1/2, to the nearest integer? Output: 29 Let us solve: What is the sixth root of 8758 to the nearest integer? Output: 5 Let us solve: What is 2827 to the power of 1/9, to the nearest integer? Output: 2 Let us solve: What is the square root of 1001226173 to the nearest integer? Output: 31642 Let us solve: What is 1879640480 to the power of 1/9, to the nearest integer? Output: 11 Let us solve: What is 3145823 to the power of 1/2, to the nearest integer? Output: 1774 Let us solve: What is the fourth root of 93276 to the nearest integer? Output: 17 Let us solve
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probability: swr p sequence --------------------------- Task: Three letters picked without replacement from zhllzhalhlzllz. What is prob of sequence llz? Hence: 5/91 Task: Three letters picked without replacement from fpjlpzpjfp. What is prob of sequence jjz? Hence: 1/360 Task: Three letters picked without replacement from {h: 2, u: 3, v: 1, o: 1, a: 4}. What is prob of sequence vuo? Hence: 1/330 Task: Two letters picked without replacement from fffff. What is prob of sequence ff? Hence: 1 Task: Two letters picked without replacement from pssppspp. Give prob of sequence pp. Hence: 5/14 Task: Three letters picked without replacement from zebbbjbjbbbbbbbbb. Give prob of sequence jzj. Hence: 1/2040 Task: Calculate prob of sequence gg when two letters picked without replacement from {m: 2, g: 4}. Hence: 2/5 Task: What is prob of sequence yyi when three letters picked without replacement from {y: 3, i: 8}? Hence: 8/165 Task: Four letters picked without replacement from {y: 5, a: 15}. What is prob of sequence yaya? Hence: 35/969 Task: What is prob of sequence rre when three letters picked without replacement from {e: 5, r: 13}? Hence: 65/408 Task: Calculate prob of sequence yad when three letters picked without replacement from aidym. Hence: 1/60 Task: What is prob of sequence hq when two letters picked without replacement from lgyqqygqyykhqggqql? Hence: 1/51 Task: Four letters picked without replacement from dxxmdxxxddcxc. What is prob of sequence xxdc? Hence: 2/143 Task: Calculate prob of sequence nenn when four letters picked without replacement from eeeneenneee. Hence: 1/165 Task: Calculate prob of sequence vq when two letters picked without replacement from {q: 10, v: 2}. Hence: 5/33 Task: Three letters picked without replacement from {n: 7, p: 7}. Give prob of sequence pnn. Hence: 7/52 Task: Calculate prob of sequence kgbf when four letters picked without replacement from {b: 1, f: 1, k: 2, g: 2, x: 2}. Hence: 1/420 Task: What is prob of sequence pm when two letters
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numbers: gcd ------------ Prompt: Calculate the greatest common factor of 28 and 2034767. Therefore: 7 Prompt: What is the highest common factor of 15 and 48? Therefore: 3 Prompt: What is the greatest common divisor of 459 and 26707? Therefore: 17 Prompt: Calculate the highest common factor of 28728 and 151007976. Therefore: 1512 Prompt: What is the greatest common divisor of 24 and 20305256? Therefore: 8 Prompt: What is the greatest common factor of 4 and 2945086? Therefore: 2 Prompt: Calculate the greatest common divisor of 146152153 and 56. Therefore: 7 Prompt: Calculate the highest common factor of 165 and 1245. Therefore: 15 Prompt: Calculate the greatest common factor of 2390 and 200. Therefore: 10 Prompt: Calculate the greatest common factor of 1969744 and 86. Therefore: 86 Prompt: Calculate the greatest common factor of 27356 and 56. Therefore: 28 Prompt: Calculate the greatest common factor of 35549480 and 160. Therefore: 40 Prompt: What is the greatest common divisor of 5202 and 288? Therefore: 18 Prompt: What is the highest common divisor of 108 and 175999104? Therefore: 36 Prompt: What is the highest common divisor of 10060 and 2423454? Therefore: 1006 Prompt: Calculate the highest common factor of 7051 and 1243. Therefore: 11 Prompt: Calculate the highest common divisor of 90 and 10770. Therefore: 30 Prompt: What is the greatest common factor of 765 and 43210? Therefore: 5 Prompt: What is the greatest common divisor of 218 and 16023? Therefore: 109 Prompt: Calculate the highest common divisor of 50785 and 1505. Therefore: 35 Prompt: Calculate the highest common factor of 99954 and 81486. Therefore: 162 Prompt: What is the highest common factor of 8112 and 5304? Therefore: 312 Prompt: What is the highest common divisor of 477 and 695943? Therefore: 477 Prompt: Calculate the greatest common divisor of 352 and 189552. Therefore: 176 Prompt: Calculate the greatest common divisor of 31246 and 612. Therefore: 34 Prompt: Calculate the highest common divisor of
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arithmetic: nearest integer root -------------------------------- Q=: What is the third root of 5882695 to the nearest integer? Compute: 181 Q=: What is 1029819 to the power of 1/8, to the nearest integer? Compute: 6 Q=: What is the cube root of 775734319 to the nearest integer? Compute: 919 Q=: What is the cube root of 4156 to the nearest integer? Compute: 16 Q=: What is the eighth root of 4139569 to the nearest integer? Compute: 7 Q=: What is the eighth root of 120398 to the nearest integer? Compute: 4 Q=: What is 143810830 to the power of 1/4, to the nearest integer? Compute: 110 Q=: What is 105222336 to the power of 1/3, to the nearest integer? Compute: 472 Q=: What is the sixth root of 8389 to the nearest integer? Compute: 5 Q=: What is 2917752 to the power of 1/2, to the nearest integer? Compute: 1708 Q=: What is the cube root of 16227 to the nearest integer? Compute: 25 Q=: What is 1532700968 to the power of 1/8, to the nearest integer? Compute: 14 Q=: What is 3001205091 to the power of 1/7, to the nearest integer? Compute: 23 Q=: What is the fourth root of 1144709035 to the nearest integer? Compute: 184 Q=: What is 321921 to the power of 1/9, to the nearest integer? Compute: 4 Q=: What is the cube root of 37082264 to the nearest integer? Compute: 333 Q=: What is 329916755 to the power of 1/2, to the nearest integer? Compute: 18164 Q=: What is 22730667 to the power of 1/3, to the nearest integer? Compute: 283 Q=: What is the square root of 485621743 to the nearest integer? Compute: 22037 Q=: What is 8100678 to the power of 1/3, to the nearest integer? Compute: 201 Q=: What is 302577834 to the power of 1/2, to the nearest integer? Compute: 17395 Q=: What is 1124076028 to the power of 1/3, to the nearest integer? Compute: 1040 Q=: What is the sixth root of 1786732206 to the nearest integer? Compute: 35 Q=: What is the seventh root of 1580 to the nearest integer? Compute: 3 Q=: What is the fifth root of 408035 to the nearest integer? Compute: 13 Q=: What is the
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measurement: time ----------------- Query: What is 292 minutes after 9:02 PM? Solution: 1:54 AM Query: What is 400 minutes after 1:40 PM? Solution: 8:20 PM Query: How many minutes are there between 7:52 AM and 1:33 PM? Solution: 341 Query: What is 154 minutes before 5:49 PM? Solution: 3:15 PM Query: What is 154 minutes after 7:29 PM? Solution: 10:03 PM Query: How many minutes are there between 5:34 PM and 9:59 PM? Solution: 265 Query: What is 52 minutes after 5:39 PM? Solution: 6:31 PM Query: How many minutes are there between 8:30 AM and 5:47 PM? Solution: 557 Query: What is 246 minutes after 2:02 PM? Solution: 6:08 PM Query: What is 367 minutes after 4:33 PM? Solution: 10:40 PM Query: What is 132 minutes before 1:16 PM? Solution: 11:04 AM Query: What is 501 minutes before 12:58 AM? Solution: 4:37 PM Query: How many minutes are there between 7:28 AM and 5:40 PM? Solution: 612 Query: How many minutes are there between 5:56 AM and 3:16 PM? Solution: 560 Query: What is 517 minutes before 7:00 PM? Solution: 10:23 AM Query: What is 636 minutes after 7:45 AM? Solution: 6:21 PM Query: What is 617 minutes before 2:07 AM? Solution: 3:50 PM Query: What is 641 minutes before 7:22 AM? Solution: 8:41 PM Query: How many minutes are there between 11:17 PM and 8:47 AM? Solution: 570 Query: What is 538 minutes before 7:07 PM? Solution: 10:09 AM Query: What is 699 minutes before 9:40 PM? Solution: 10:01 AM Query: What is 323 minutes after 11:44 AM? Solution: 5:07 PM Query: What is 127 minutes before 10:38 PM? Solution: 8:31 PM Query: What is 53 minutes after 7:07 PM? Solution: 8:00 PM Query: What is 266 minutes before 1:35 AM? Solution: 9:09 PM Query: How many minutes are there between 9:56 PM and 7:38 AM? Solution: 582 Query: How many minutes are there between 9:32 AM and 12:49 PM? Solution: 197 Query: How many minutes are there between 10:15 AM and 1:38 PM? Solution: 203 Query: What is 27 minutes before 1:37 PM? Solution: 1:10 PM Query: What is 76 minutes after 1:12 PM? Solution:
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numbers: is factor ------------------ Exercise: Is 1565 a factor of 575264775? Answer: False Exercise: Is 56 a factor of 889? Answer: False Exercise: Is 37872 a multiple of 24? Answer: True Exercise: Is 39 a factor of 7413354? Answer: True Exercise: Does 13 divide 1186861? Answer: True Exercise: Is 1607 a factor of 3220964843? Answer: False Exercise: Does 4 divide 88? Answer: True Exercise: Is 3 a factor of 12301? Answer: False Exercise: Is 127 a factor of 2521204? Answer: True Exercise: Is 6822 a multiple of 9? Answer: True Exercise: Is 15 a factor of 82134375? Answer: True Exercise: Does 12 divide 414? Answer: False Exercise: Is 5418512 a multiple of 65? Answer: False Exercise: Does 79 divide 5609? Answer: True Exercise: Is 32 a factor of 7276? Answer: False Exercise: Is 8565 a multiple of 33? Answer: False Exercise: Does 7 divide 6654557? Answer: True Exercise: Is 2954 a multiple of 24? Answer: False Exercise: Is 2884303262 a multiple of 3386? Answer: False Exercise: Does 13 divide 6612391? Answer: False Exercise: Is 558844 a multiple of 44? Answer: True Exercise: Does 36 divide 38830320? Answer: True Exercise: Does 54 divide 283824? Answer: True Exercise: Is 14 a factor of 195202537? Answer: False Exercise: Is 16 a factor of 189904? Answer: True Exercise: Is 69 a factor of 2553? Answer: True Exercise: Is 494543 a multiple of 7? Answer: True Exercise: Is 15 a factor of 245? Answer: False Exercise: Is 45 a factor of 68625? Answer: True Exercise: Is 6 a factor of 240834? Answer: True Exercise: Is 19 a factor of 59106023? Answer: False Exercise: Is 1984 a factor of 1611343296? Answer: True Exercise: Is 102 a factor of 2958? Answer: True Exercise: Is 5 a factor of 83188060? Answer: True Exercise: Is 408 a multiple of 8? Answer: True Exercise: Does 353 divide 876659486? Answer: False Exercise: Is 1495 a factor of 546370968? Answer: False Exercise: Is 188960936 a multiple of 98? Answer: False Exercise: Is 9 a factor of 24906? Answer: False Exercise: Does 19 divide 9725
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probability: swr p sequence --------------------------- Puzzle: Three letters picked without replacement from cscsskcikiikckic. Give prob of sequence kcs. Answer: 1/56 Puzzle: Two letters picked without replacement from {h: 5}. Give prob of sequence hh. Answer: 1 Puzzle: Calculate prob of sequence ieie when four letters picked without replacement from eqqceieeiq. Answer: 1/210 Puzzle: What is prob of sequence uh when two letters picked without replacement from {u: 5, q: 2, h: 3}? Answer: 1/6 Puzzle: Calculate prob of sequence ng when two letters picked without replacement from {g: 6, n: 2, y: 10}. Answer: 2/51 Puzzle: Two letters picked without replacement from aeeeeaeeeee. What is prob of sequence aa? Answer: 1/55 Puzzle: What is prob of sequence epq when three letters picked without replacement from xqeqxmmp? Answer: 1/168 Puzzle: Four letters picked without replacement from {n: 9, h: 3}. What is prob of sequence nnnn? Answer: 14/55 Puzzle: What is prob of sequence wsf when three letters picked without replacement from sbswfb? Answer: 1/60 Puzzle: Three letters picked without replacement from oomufmffmo. Give prob of sequence oom. Answer: 1/40 Puzzle: What is prob of sequence lgmy when four letters picked without replacement from glygkeml? Answer: 1/420 Puzzle: Calculate prob of sequence lwu when three letters picked without replacement from wlwwlwulllwlllwwwuuu. Answer: 32/855 Puzzle: Four letters picked without replacement from xxxxxxyyxyxxxx. Give prob of sequence xyyx. Answer: 5/182 Puzzle: Two letters picked without replacement from {j: 1, f: 1, h: 2, g: 2, p: 14}. What is prob of sequence jh? Answer: 1/190 Puzzle: Three letters picked without replacement from fjjjjjjf. What is prob of sequence fjf? Answer: 1/28 Puzzle: Calculate prob of sequence oo when two letters picked without replacement from {o: 12, t: 4, w: 4}. Answer: 33/95 Puzzle: Three letters picked without replacement from {w: 2, l: 2, n: 2, a: 7, o: 5}. Give prob of sequence onw. Answer: 5/1224 P
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arithmetic: nearest integer root -------------------------------- Task: What is the cube root of 1651398 to the nearest integer? Explanation: 118 Task: What is the third root of 2594 to the nearest integer? Explanation: 14 Task: What is the seventh root of 16937 to the nearest integer? Explanation: 4 Task: What is the square root of 46573483 to the nearest integer? Explanation: 6824 Task: What is the cube root of 1872262 to the nearest integer? Explanation: 123 Task: What is the cube root of 99853 to the nearest integer? Explanation: 46 Task: What is 51685058 to the power of 1/3, to the nearest integer? Explanation: 372 Task: What is the seventh root of 228 to the nearest integer? Explanation: 2 Task: What is 138426 to the power of 1/3, to the nearest integer? Explanation: 52 Task: What is 3396829848 to the power of 1/3, to the nearest integer? Explanation: 1503 Task: What is 7341349 to the power of 1/3, to the nearest integer? Explanation: 194 Task: What is 14879 to the power of 1/6, to the nearest integer? Explanation: 5 Task: What is the fourth root of 2669732 to the nearest integer? Explanation: 40 Task: What is 105353603 to the power of 1/2, to the nearest integer? Explanation: 10264 Task: What is the eighth root of 368361854 to the nearest integer? Explanation: 12 Task: What is 36357590 to the power of 1/6, to the nearest integer? Explanation: 18 Task: What is the ninth root of 9900298 to the nearest integer? Explanation: 6 Task: What is the third root of 9071 to the nearest integer? Explanation: 21 Task: What is 24606400 to the power of 1/3, to the nearest integer? Explanation: 291 Task: What is 131421322 to the power of 1/3, to the nearest integer? Explanation: 508 Task: What is 14569 to the power of 1/5, to the nearest integer? Explanation: 7 Task: What is 14783589 to the power of 1/10, to the nearest integer? Explanation: 5 Task: What is the sixth root of 4066 to the nearest integer? Explanation: 4 Task: What is 3768328975 to the power of 1/3, to the neare
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numbers: is factor ------------------ Prompt: Is 148514 a multiple of 118? Compute: False Prompt: Does 79 divide 28845033? Compute: True Prompt: Does 146 divide 327642688? Compute: True Prompt: Does 42 divide 798? Compute: True Prompt: Is 6005 a factor of 1243451415? Compute: False Prompt: Is 27387 a multiple of 71? Compute: False Prompt: Is 4408973695 a multiple of 49? Compute: True Prompt: Is 10 a factor of 9690640? Compute: True Prompt: Is 241245 a multiple of 16? Compute: False Prompt: Is 44820903 a multiple of 117? Compute: False Prompt: Does 5 divide 74090? Compute: True Prompt: Is 4446 a multiple of 3? Compute: True Prompt: Is 39 a multiple of 9? Compute: False Prompt: Is 1905893885 a multiple of 9265? Compute: True Prompt: Does 84 divide 2436? Compute: True Prompt: Is 90028719 a multiple of 363? Compute: True Prompt: Is 375291 a multiple of 49? Compute: True Prompt: Is 15 a factor of 601193? Compute: False Prompt: Is 206406 a multiple of 12? Compute: False Prompt: Is 139743 a multiple of 22? Compute: False Prompt: Is 289344489 a multiple of 98? Compute: False Prompt: Does 56 divide 2576? Compute: True Prompt: Is 13 a factor of 40560832? Compute: True Prompt: Does 42 divide 536015340? Compute: True Prompt: Is 57 a factor of 1067212455? Compute: False Prompt: Does 62 divide 981668? Compute: False Prompt: Is 29 a factor of 75060149? Compute: True Prompt: Does 63 divide 83726433? Compute: True Prompt: Is 2811710 a multiple of 12? Compute: False Prompt: Is 18665265 a multiple of 46? Compute: False Prompt: Does 1214 divide 630391352? Compute: True Prompt: Does 85 divide 150875? Compute: True Prompt: Is 30104567 even? Compute: False Prompt: Is 579670 a multiple of 70? Compute: True Prompt: Is 785133 a multiple of 538? Compute: False Prompt: Is 50 a factor of 2878027? Compute: False Prompt: Does 13 divide 1264120? Compute: True Prompt: Is 25 a factor of 5375? Compute: True Prompt: Is 1395 a factor of 733455366? Compute: False Prompt: Is 461689 a multiple of 6? Compu
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numbers: gcd ------------ Request: What is the greatest common divisor of 40495 and 43680? Steps: 455 Request: What is the greatest common factor of 26434902 and 975? Steps: 39 Request: Calculate the greatest common factor of 520700947 and 3914. Steps: 1957 Request: What is the greatest common factor of 73673223 and 17901? Steps: 663 Request: What is the highest common factor of 602 and 28? Steps: 14 Request: What is the highest common factor of 148627991 and 34? Steps: 17 Request: What is the highest common factor of 171 and 36? Steps: 9 Request: What is the greatest common divisor of 316 and 191812? Steps: 316 Request: What is the highest common factor of 8 and 57176? Steps: 8 Request: Calculate the greatest common factor of 74 and 74. Steps: 74 Request: Calculate the greatest common factor of 144143 and 947563. Steps: 2363 Request: Calculate the greatest common divisor of 96 and 244672. Steps: 32 Request: Calculate the highest common factor of 1484115 and 21. Steps: 3 Request: Calculate the highest common factor of 693 and 63. Steps: 63 Request: What is the highest common factor of 4845 and 30? Steps: 15 Request: Calculate the highest common factor of 14 and 55297466. Steps: 14 Request: What is the highest common divisor of 104 and 661752? Steps: 104 Request: What is the highest common divisor of 64 and 2? Steps: 2 Request: Calculate the highest common factor of 78 and 9009. Steps: 39 Request: Calculate the greatest common divisor of 8143720 and 200. Steps: 40 Request: Calculate the greatest common divisor of 30 and 490. Steps: 10 Request: Calculate the highest common factor of 5080 and 371364510. Steps: 1270 Request: What is the greatest common factor of 91 and 465829? Steps: 91 Request: What is the greatest common factor of 34599 and 114? Steps: 57 Request: Calculate the greatest common factor of 196159 and 11. Steps: 1 Request: What is the greatest common factor of 1 and 457? Steps: 1 Request: What is the greatest common divisor of 918 and 14397453? Steps: 459
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probability: swr p sequence --------------------------- Math Problem: Two letters picked without replacement from {w: 2, g: 2}. What is prob of sequence gw? Interpretation: 1/3 Math Problem: What is prob of sequence zzzv when four letters picked without replacement from {z: 7, v: 7}? Interpretation: 35/572 Math Problem: Calculate prob of sequence df when two letters picked without replacement from {s: 2, f: 6, t: 10, d: 2}. Interpretation: 3/95 Math Problem: Calculate prob of sequence qht when three letters picked without replacement from {j: 3, t: 9, q: 1, o: 2, h: 3}. Interpretation: 3/544 Math Problem: Two letters picked without replacement from {r: 1, v: 2, z: 4, k: 3, l: 2}. What is prob of sequence ll? Interpretation: 1/66 Math Problem: Two letters picked without replacement from uqc. What is prob of sequence cu? Interpretation: 1/6 Math Problem: Three letters picked without replacement from {i: 3, o: 1, t: 4, n: 1, r: 1, b: 4}. What is prob of sequence nbt? Interpretation: 2/273 Math Problem: Calculate prob of sequence nt when two letters picked without replacement from ndndnnndnnnddtnnddn. Interpretation: 11/342 Math Problem: Calculate prob of sequence uut when three letters picked without replacement from vuvvuttvt. Interpretation: 1/84 Math Problem: Calculate prob of sequence nfa when three letters picked without replacement from aanffffnnffannff. Interpretation: 1/28 Math Problem: Four letters picked without replacement from nsssssssnsnnn. What is prob of sequence nsss? Interpretation: 14/143 Math Problem: Calculate prob of sequence oix when three letters picked without replacement from {i: 5, x: 3, o: 1}. Interpretation: 5/168 Math Problem: Calculate prob of sequence xsz when three letters picked without replacement from xocxszzzoooczozoc. Interpretation: 1/408 Math Problem: Calculate prob of sequence voj when three letters picked without replacement from {e: 4, j: 3, h: 3, s: 4, o: 5, v: 1}. Interpretation: 1/456 Math Problem: What is prob of sequence f
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numbers: gcd ------------ Q: Calculate the greatest common factor of 126 and 1062. Derivation: 18 Q: What is the highest common factor of 87 and 233160? Derivation: 87 Q: What is the highest common divisor of 1320 and 96? Derivation: 24 Q: Calculate the highest common divisor of 6390269 and 14191. Derivation: 617 Q: Calculate the highest common divisor of 340 and 23477. Derivation: 17 Q: Calculate the highest common factor of 80 and 140. Derivation: 20 Q: Calculate the highest common divisor of 15 and 11934591. Derivation: 3 Q: What is the greatest common divisor of 156 and 390? Derivation: 78 Q: Calculate the highest common factor of 2796 and 23875524. Derivation: 12 Q: Calculate the highest common factor of 2162 and 1426. Derivation: 46 Q: Calculate the highest common divisor of 90856 and 164. Derivation: 164 Q: What is the greatest common factor of 2430816 and 72? Derivation: 24 Q: What is the highest common factor of 800 and 2075? Derivation: 25 Q: Calculate the highest common factor of 12 and 1713690. Derivation: 6 Q: What is the greatest common divisor of 126 and 2591722? Derivation: 14 Q: What is the highest common factor of 4 and 82? Derivation: 2 Q: Calculate the greatest common divisor of 93687 and 389028. Derivation: 51 Q: Calculate the highest common factor of 24 and 1412. Derivation: 4 Q: Calculate the greatest common factor of 119 and 56. Derivation: 7 Q: Calculate the highest common divisor of 448738 and 178. Derivation: 178 Q: What is the greatest common divisor of 51276 and 1212? Derivation: 12 Q: What is the highest common factor of 1180014 and 357? Derivation: 3 Q: Calculate the greatest common factor of 8 and 769516320. Derivation: 8 Q: What is the greatest common divisor of 44234056 and 13896? Derivation: 1544 Q: What is the highest common factor of 1 and 1369? Derivation: 1 Q: Calculate the greatest common factor of 920581 and 2955. Derivation: 197 Q: What is the highest common divisor of 193060 and 29652? Derivation: 28 Q: Calculate the highes
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numbers: is factor ------------------ Example: Does 305 divide 611852? Interpretation: False Example: Is 801 a factor of 774075186? Interpretation: True Example: Does 36 divide 36? Interpretation: True Example: Is 653 a multiple of 3? Interpretation: False Example: Is 69 a factor of 2101993989? Interpretation: True Example: Is 2400 a multiple of 30? Interpretation: True Example: Is 238622 a multiple of 4? Interpretation: False Example: Does 3017 divide 635838784? Interpretation: True Example: Is 1502420 a multiple of 103? Interpretation: False Example: Is 46 a factor of 2951? Interpretation: False Example: Does 16 divide 2384? Interpretation: True Example: Is 28 a factor of 140? Interpretation: True Example: Is 586574892 a multiple of 13? Interpretation: False Example: Does 79 divide 3268230? Interpretation: True Example: Is 240 a factor of 614195054? Interpretation: False Example: Is 1501 a multiple of 2? Interpretation: False Example: Is 68641 a multiple of 115? Interpretation: False Example: Is 47 a factor of 502471125? Interpretation: True Example: Is 931560 a multiple of 21? Interpretation: True Example: Is 71 a factor of 85453? Interpretation: False Example: Is 4830720 a multiple of 51? Interpretation: True Example: Does 616 divide 3537072? Interpretation: True Example: Does 70 divide 338388712? Interpretation: False Example: Does 8 divide 2057957906? Interpretation: False Example: Is 822511800 a multiple of 2497? Interpretation: True Example: Does 21 divide 30228? Interpretation: False Example: Is 8 a factor of 37368? Interpretation: True Example: Does 6 divide 493758269? Interpretation: False Example: Is 18 a factor of 40806? Interpretation: True Example: Is 32 a factor of 3168? Interpretation: True Example: Is 140 a factor of 2100? Interpretation: True Example: Is 12979200 a multiple of 64? Interpretation: True Example: Is 387 a factor of 531870353? Interpretation: False Example: Is 654576 a multiple of 52? Interpretation: True Example: Is 24 a factor of 31
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measurement: time ----------------- Test item: How many minutes are there between 1:39 PM and 3:45 PM? Hence: 126 Test item: How many minutes are there between 12:23 PM and 4:48 PM? Hence: 265 Test item: What is 82 minutes after 11:53 AM? Hence: 1:15 PM Test item: How many minutes are there between 4:42 PM and 2:01 AM? Hence: 559 Test item: What is 128 minutes after 6:20 PM? Hence: 8:28 PM Test item: How many minutes are there between 11:36 AM and 7:46 PM? Hence: 490 Test item: What is 194 minutes after 11:45 AM? Hence: 2:59 PM Test item: How many minutes are there between 8:43 PM and 6:21 AM? Hence: 578 Test item: How many minutes are there between 11:29 AM and 6:17 PM? Hence: 408 Test item: How many minutes are there between 9:39 PM and 1:34 AM? Hence: 235 Test item: How many minutes are there between 6:23 AM and 4:34 PM? Hence: 611 Test item: How many minutes are there between 4:50 PM and 3:53 AM? Hence: 663 Test item: How many minutes are there between 5:28 AM and 1:55 PM? Hence: 507 Test item: How many minutes are there between 1:10 AM and 3:43 AM? Hence: 153 Test item: What is 508 minutes before 1:17 PM? Hence: 4:49 AM Test item: How many minutes are there between 2:20 PM and 7:15 PM? Hence: 295 Test item: How many minutes are there between 10:44 AM and 9:02 PM? Hence: 618 Test item: How many minutes are there between 8:39 AM and 5:29 PM? Hence: 530 Test item: How many minutes are there between 4:27 AM and 9:01 AM? Hence: 274 Test item: What is 374 minutes after 11:33 AM? Hence: 5:47 PM Test item: What is 251 minutes before 5:41 AM? Hence: 1:30 AM Test item: How many minutes are there between 9:27 PM and 6:26 AM? Hence: 539 Test item: What is 675 minutes after 8:40 AM? Hence: 7:55 PM Test item: What is 373 minutes before 12:06 PM? Hence: 5:53 AM Test item: How many minutes are there between 4:11 AM and 7:22 AM? Hence: 191 Test item: How many minutes are there between 6:57 AM and 5:15 PM? Hence: 618 Test item: What is 607 minutes after 3:09 PM? Hence: 1:16 AM T
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probability: swr p level set ---------------------------- Query: Four letters picked without replacement from ufffffuf. What is prob of picking 2 f and 2 u? Solution: 3/14 Query: Three letters picked without replacement from {p: 2, r: 4, g: 4, f: 1}. What is prob of picking 2 p and 1 f? Solution: 1/165 Query: What is prob of picking 2 o when two letters picked without replacement from {d: 1, j: 1, o: 2, w: 1, g: 1, n: 1}? Solution: 1/21 Query: Two letters picked without replacement from {z: 5, x: 7, q: 1, f: 3}. What is prob of picking 2 x? Solution: 7/40 Query: Two letters picked without replacement from {k: 1, m: 5, y: 3, n: 1}. What is prob of picking 1 y and 1 k? Solution: 1/15 Query: Calculate prob of picking 2 u when two letters picked without replacement from {j: 2, u: 8}. Solution: 28/45 Query: Calculate prob of picking 3 f when three letters picked without replacement from sofffoffsoso. Solution: 1/22 Query: Three letters picked without replacement from {e: 5, s: 1, t: 7, k: 1}. Give prob of picking 1 e, 1 s, and 1 k. Solution: 5/364 Query: Calculate prob of picking 3 w and 1 e when four letters picked without replacement from wwwewwwewwewewwwwww. Solution: 455/969 Query: Two letters picked without replacement from {x: 2, r: 1, t: 1, d: 1, y: 2, s: 1}. What is prob of picking 1 y and 1 t? Solution: 1/14 Query: Three letters picked without replacement from vvmzdvzbdd. What is prob of picking 1 d, 1 v, and 1 b? Solution: 3/40 Query: Four letters picked without replacement from {t: 3, l: 9}. Give prob of picking 1 l and 3 t. Solution: 1/55 Query: Two letters picked without replacement from {g: 1, h: 1, l: 1, z: 2, q: 1, t: 1}. Give prob of picking 1 h and 1 q. Solution: 1/21 Query: Three letters picked without replacement from {r: 3, o: 12}. Give prob of picking 1 o and 2 r. Solution: 36/455 Query: Four letters picked without replacement from sesssgssssisssslgi. What is prob of picking 1 s, 1 i, 1 l, and 1 g? Solution: 4/255 Query: Calculate prob of picking 2
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measurement: conversion ----------------------- Problem: What is fifty-five quarters of a litre in millilitres? Finding: 13750 Problem: What is nine tenths of a micrometer in nanometers? Finding: 900 Problem: How many millilitres are there in 339.8019l? Finding: 339801.9 Problem: How many millilitres are there in five eighths of a litre? Finding: 625 Problem: What is 11/10 of a minute in milliseconds? Finding: 66000 Problem: What is ten sevenths of a week in hours? Finding: 240 Problem: What is three fifths of a microgram in nanograms? Finding: 600 Problem: How many centuries are there in 44/5 of a millennium? Finding: 88 Problem: What is 3/5 of a litre in millilitres? Finding: 600 Problem: How many months are there in 46/5 of a decade? Finding: 1104 Problem: What is 5.690103 nanograms in grams? Finding: 0.000000005690103 Problem: What is 7386.333 millilitres in litres? Finding: 7.386333 Problem: What is 249830.1 seconds in minutes? Finding: 4163.835 Problem: How many milliseconds are there in 3/128 of a hour? Finding: 84375 Problem: What is four fifteenths of a hour in seconds? Finding: 960 Problem: How many nanometers are there in 21/4 of a micrometer? Finding: 5250 Problem: How many millilitres are there in 6719.743l? Finding: 6719743 Problem: Convert 972555.5t to micrograms. Finding: 972555500000000000 Problem: Convert 877858.3ml to litres. Finding: 877.8583 Problem: What is seven quarters of a century in years? Finding: 175 Problem: Convert 964.524 weeks to days. Finding: 6751.668 Problem: How many milligrams are there in 1/4 of a gram? Finding: 250 Problem: How many centuries are there in 21/5 of a millennium? Finding: 42 Problem: Convert 762.127 centuries to years. Finding: 76212.7 Problem: How many millilitres are there in thirteen eighths of a litre? Finding: 1625 Problem: How many microseconds are there in 3/40 of a second? Finding: 75000 Problem: What is 94.35562 hours in minutes? Finding: 5661.3372 Problem: What is 5/6 of a hour in minutes? Finding: 50 P
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probability: swr p level set ---------------------------- Task: Three letters picked without replacement from {b: 3, w: 11}. What is prob of picking 3 w? Calculation: 165/364 Task: Two letters picked without replacement from {l: 15, y: 5}. What is prob of picking 2 y? Calculation: 1/19 Task: What is prob of picking 1 e and 1 t when two letters picked without replacement from yyeeyytytyyyyyyytyyy? Calculation: 3/95 Task: What is prob of picking 1 g and 1 i when two letters picked without replacement from uuuuiguiuuiuuggig? Calculation: 2/17 Task: Four letters picked without replacement from aaataaaaataata. Give prob of picking 1 t and 3 a. Calculation: 45/91 Task: Three letters picked without replacement from nngcnnngdddnndcccnd. Give prob of picking 1 d and 2 g. Calculation: 5/969 Task: Two letters picked without replacement from kjnzzja. Give prob of picking 1 n and 1 a. Calculation: 1/21 Task: What is prob of picking 1 c, 2 j, and 1 k when four letters picked without replacement from {c: 1, j: 7, k: 6}? Calculation: 18/143 Task: Two letters picked without replacement from {g: 4, m: 3, l: 2}. Give prob of picking 1 m and 1 l. Calculation: 1/6 Task: What is prob of picking 1 o and 1 u when two letters picked without replacement from {u: 6, y: 2, o: 5}? Calculation: 5/13 Task: What is prob of picking 1 q and 1 i when two letters picked without replacement from diiqm? Calculation: 1/5 Task: Four letters picked without replacement from {h: 1, z: 1, k: 4, s: 5}. What is prob of picking 1 z, 1 h, and 2 s? Calculation: 1/33 Task: Two letters picked without replacement from {s: 4, m: 1, v: 3}. Give prob of picking 2 s. Calculation: 3/14 Task: What is prob of picking 1 o and 1 n when two letters picked without replacement from {o: 3, p: 2, n: 6, z: 2, y: 1}? Calculation: 18/91 Task: Two letters picked without replacement from {o: 3, t: 6, a: 3, h: 3, c: 2}. What is prob of picking 2 a? Calculation: 3/136 Task: What is prob of picking 3 j when three letters picked without re
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measurement: time ----------------- Example: What is 439 minutes before 1:40 PM? Calculation: 6:21 AM Example: How many minutes are there between 7:18 PM and 10:19 PM? Calculation: 181 Example: What is 366 minutes before 11:08 PM? Calculation: 5:02 PM Example: How many minutes are there between 1:10 AM and 7:21 AM? Calculation: 371 Example: How many minutes are there between 1:31 AM and 9:09 AM? Calculation: 458 Example: How many minutes are there between 11:16 PM and 10:35 AM? Calculation: 679 Example: What is 399 minutes before 9:37 AM? Calculation: 2:58 AM Example: What is 416 minutes after 9:22 AM? Calculation: 4:18 PM Example: What is 166 minutes before 4:41 AM? Calculation: 1:55 AM Example: What is 266 minutes after 1:47 PM? Calculation: 6:13 PM Example: How many minutes are there between 1:54 PM and 12:25 AM? Calculation: 631 Example: What is 583 minutes after 9:05 AM? Calculation: 6:48 PM Example: How many minutes are there between 6:41 AM and 4:25 PM? Calculation: 584 Example: What is 559 minutes after 9:55 PM? Calculation: 7:14 AM Example: What is 715 minutes before 7:18 AM? Calculation: 7:23 PM Example: How many minutes are there between 10:40 PM and 12:43 AM? Calculation: 123 Example: How many minutes are there between 9:56 AM and 5:58 PM? Calculation: 482 Example: What is 185 minutes after 10:18 AM? Calculation: 1:23 PM Example: What is 682 minutes before 8:50 PM? Calculation: 9:28 AM Example: How many minutes are there between 10:00 PM and 5:25 AM? Calculation: 445 Example: How many minutes are there between 3:05 AM and 2:37 PM? Calculation: 692 Example: How many minutes are there between 11:50 PM and 7:16 AM? Calculation: 446 Example: What is 578 minutes before 10:25 PM? Calculation: 12:47 PM Example: What is 582 minutes after 4:11 PM? Calculation: 1:53 AM Example: What is 520 minutes after 3:56 AM? Calculation: 12:36 PM Example: What is 270 minutes after 10:05 AM? Calculation: 2:35 PM Example: What is 10 minutes before 6:10 AM? Calculation: 6:00 AM E
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numbers: div remainder ---------------------- Item: Calculate the remainder when 211 is divided by 13. Solution: 3 Item: What is the remainder when 443 is divided by 30? Solution: 23 Item: Calculate the remainder when 746 is divided by 153. Solution: 134 Item: What is the remainder when 598974 is divided by 199651? Solution: 21 Item: Calculate the remainder when 504 is divided by 196. Solution: 112 Item: Calculate the remainder when 17448 is divided by 2466. Solution: 186 Item: What is the remainder when 308039 is divided by 630? Solution: 599 Item: Calculate the remainder when 437417 is divided by 109223. Solution: 525 Item: What is the remainder when 6369 is divided by 74? Solution: 5 Item: What is the remainder when 33 is divided by 3? Solution: 0 Item: What is the remainder when 2148 is divided by 83? Solution: 73 Item: What is the remainder when 62698 is divided by 2030? Solution: 1798 Item: Calculate the remainder when 477263 is divided by 27. Solution: 11 Item: What is the remainder when 9430 is divided by 3136? Solution: 22 Item: What is the remainder when 277 is divided by 63? Solution: 25 Item: Calculate the remainder when 96 is divided by 80. Solution: 16 Item: Calculate the remainder when 75510 is divided by 2787. Solution: 261 Item: Calculate the remainder when 726041 is divided by 377. Solution: 316 Item: What is the remainder when 38319 is divided by 2297? Solution: 1567 Item: Calculate the remainder when 35 is divided by 33. Solution: 2 Item: What is the remainder when 730907 is divided by 5111? Solution: 34 Item: Calculate the remainder when 235869 is divided by 206. Solution: 205 Item: What is the remainder when 9740 is divided by 52? Solution: 16 Item: Calculate the remainder when 1730683 is divided by 935. Solution: 933 Item: Calculate the remainder when 698570 is divided by 14. Solution: 12 Item: Calculate the remainder when 393 is divided by 344. Solution: 49 Item: What is the remainder when 114171 is divided by 112? Solution: 43 Item: What is
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numbers: is factor ------------------ Let us solve: Is 594 a factor of 318384? Key: True Let us solve: Is 219 a factor of 4225167? Key: True Let us solve: Is 17 a factor of 568? Key: False Let us solve: Is 1853 a factor of 30561529? Key: True Let us solve: Is 637 a factor of 1049906431? Key: False Let us solve: Is 6 a factor of 1476888604? Key: False Let us solve: Does 22 divide 4267350? Key: False Let us solve: Does 23 divide 716657? Key: True Let us solve: Is 598 a factor of 143419536? Key: True Let us solve: Is 140 a multiple of 5? Key: True Let us solve: Is 3 a factor of 756564? Key: True Let us solve: Is 998793 a multiple of 5? Key: False Let us solve: Is 9960 a multiple of 83? Key: True Let us solve: Is 59 a factor of 22062818? Key: False Let us solve: Is 58 a factor of 7656? Key: True Let us solve: Is 1779866332 a multiple of 390? Key: False Let us solve: Is 305826381 a multiple of 366? Key: False Let us solve: Is 51 a factor of 3469938? Key: True Let us solve: Does 8 divide 110829? Key: False Let us solve: Does 10 divide 1364? Key: False Let us solve: Does 120 divide 31388040? Key: True Let us solve: Does 41 divide 2911? Key: True Let us solve: Is 5874234492 a multiple of 12? Key: True Let us solve: Is 118 a factor of 439910243? Key: False Let us solve: Is 99 a factor of 5880? Key: False Let us solve: Is 22002328 a multiple of 9256? Key: False Let us solve: Is 37 a factor of 1517? Key: True Let us solve: Is 1210837 a multiple of 971? Key: True Let us solve: Is 58 a factor of 263? Key: False Let us solve: Is 6 a factor of 943? Key: False Let us solve: Does 8 divide 524? Key: False Let us solve: Is 32412 a multiple of 6? Key: True Let us solve: Is 151 a factor of 6946? Key: True Let us solve: Is 249977699 a multiple of 361? Key: True Let us solve: Does 20 divide 14441? Key: False Let us solve: Does 61 divide 747617? Key: False Let us solve: Is 2983 a multiple of 31? Key: False Let us solve: Is 10085470 a multiple of 1526? Key: False Let us solve: Does 348 divi
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numbers: is factor ------------------ Qn: Is 44 a factor of 287320? Resolution: True Qn: Does 56 divide 7269002? Resolution: False Qn: Is 866945456 a multiple of 2021? Resolution: False Qn: Does 4 divide 414? Resolution: False Qn: Does 126 divide 17473? Resolution: False Qn: Is 7 a factor of 6475? Resolution: True Qn: Is 19800 a multiple of 185? Resolution: False Qn: Is 57 a factor of 71719? Resolution: False Qn: Is 15672 a multiple of 24? Resolution: True Qn: Is 23281 a multiple of 7? Resolution: False Qn: Does 4 divide 191890? Resolution: False Qn: Is 962750 a multiple of 14? Resolution: False Qn: Is 12 a factor of 948? Resolution: True Qn: Is 2303 a multiple of 13? Resolution: False Qn: Is 13 a factor of 70838? Resolution: False Qn: Is 2547 a multiple of 52? Resolution: False Qn: Does 48 divide 1200? Resolution: True Qn: Does 43 divide 16813? Resolution: True Qn: Does 112 divide 841304? Resolution: False Qn: Does 132 divide 323101284? Resolution: True Qn: Is 27 a factor of 153? Resolution: False Qn: Is 37 a factor of 22866? Resolution: True Qn: Does 7 divide 27377? Resolution: True Qn: Does 12 divide 423828? Resolution: True Qn: Is 1819162 a multiple of 3? Resolution: False Qn: Is 2321 a factor of 2177528476? Resolution: False Qn: Does 6 divide 176751972? Resolution: True Qn: Is 498 a factor of 51535530? Resolution: True Qn: Is 108 a multiple of 3? Resolution: True Qn: Does 898 divide 3186231? Resolution: False Qn: Is 3487015 a multiple of 335? Resolution: True Qn: Is 121 a factor of 7744? Resolution: True Qn: Does 42 divide 1260? Resolution: True Qn: Is 209526 a multiple of 141? Resolution: True Qn: Is 47673014 a multiple of 28? Resolution: False Qn: Does 17 divide 29648? Resolution: True Qn: Does 352 divide 184305? Resolution: False Qn: Is 415043 a multiple of 41? Resolution: True Qn: Is 29 a factor of 24099? Resolution: True Qn: Is 9448569 a multiple of 81? Resolution: True Qn: Is 2154250 a multiple of 25? Resolution: True Qn: Is 498 a multiple of 6? Resolutio
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numbers: is prime ----------------- Subject: Is 167074 a prime number? Response: False Subject: Is 39360272447 prime? Response: True Subject: Is 17657 composite? Response: False Subject: Is 2334678223 composite? Response: False Subject: Is 21816155489 composite? Response: False Subject: Is 66446 composite? Response: True Subject: Is 2001268623 a prime number? Response: False Subject: Is 199114579 a composite number? Response: False Subject: Is 4672928861 a composite number? Response: True Subject: Is 613068185 prime? Response: False Subject: Is 206939245391 composite? Response: True Subject: Is 132944033 a prime number? Response: False Subject: Is 2603197 composite? Response: True Subject: Is 30151921 prime? Response: True Subject: Is 135887 a composite number? Response: False Subject: Is 1364821057 composite? Response: False Subject: Is 4328428061 a prime number? Response: False Subject: Is 16072108257 prime? Response: False Subject: Is 19553 a composite number? Response: False Subject: Is 598421 composite? Response: False Subject: Is 157488767 composite? Response: True Subject: Is 75441 prime? Response: False Subject: Is 25409 prime? Response: True Subject: Is 45763139 a composite number? Response: False Subject: Is 2339759039 a composite number? Response: True Subject: Is 13777 a prime number? Response: False Subject: Is 6099123 a composite number? Response: True Subject: Is 12616271 a composite number? Response: False Subject: Is 12842049797 a prime number? Response: False Subject: Is 45352217 a prime number? Response: False Subject: Is 133292936159 a composite number? Response: False Subject: Is 2381737 prime? Response: True Subject: Is 8779 composite? Response: False Subject: Is 1340540219 a composite number? Response: True Subject: Is 12812227997 a prime number? Response: True Subject: Is 30307 composite? Response: False Subject: Is 28607465155 prime? Response: False Subject: Is 85001 composite? Response: True Subject: Is 1067823929 prime? Response: False Sub
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numbers: gcd ------------ What if: What is the highest common factor of 1383 and 12538278? Response: 1383 What if: Calculate the greatest common factor of 90 and 110. Response: 10 What if: Calculate the highest common divisor of 245 and 2009. Response: 49 What if: Calculate the highest common factor of 20585 and 3401. Response: 179 What if: Calculate the highest common divisor of 304735 and 140420. Response: 295 What if: Calculate the greatest common factor of 425 and 10. Response: 5 What if: Calculate the greatest common divisor of 9 and 34669620. Response: 9 What if: What is the greatest common factor of 27 and 30? Response: 3 What if: Calculate the highest common divisor of 37516 and 35256. Response: 452 What if: Calculate the highest common divisor of 100 and 1525. Response: 25 What if: What is the highest common factor of 19 and 96064? Response: 19 What if: What is the highest common divisor of 808 and 1144? Response: 8 What if: Calculate the highest common divisor of 810755297 and 439. Response: 439 What if: Calculate the greatest common divisor of 37334 and 50. Response: 2 What if: Calculate the greatest common factor of 26 and 61906. Response: 26 What if: Calculate the greatest common factor of 2241 and 216. Response: 27 What if: Calculate the greatest common divisor of 7229343 and 693. Response: 33 What if: Calculate the greatest common divisor of 215 and 19049. Response: 43 What if: Calculate the highest common factor of 192100 and 97950. Response: 50 What if: What is the greatest common factor of 1392441 and 9? Response: 3 What if: What is the highest common divisor of 2434071 and 1539? Response: 57 What if: Calculate the greatest common factor of 880 and 517. Response: 11 What if: Calculate the greatest common divisor of 4424 and 4648. Response: 56 What if: Calculate the greatest common factor of 114585 and 165. Response: 15 What if: What is the highest common factor of 156 and 18? Response: 6 What if: What is the greatest common divisor of 4 and 652? Re
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numbers: is prime ----------------- Qn: Is 217851877 prime? Therefore: True Qn: Is 32576419 prime? Therefore: False Qn: Is 123815 a prime number? Therefore: False Qn: Is 141084967 a composite number? Therefore: True Qn: Is 8545967 a prime number? Therefore: True Qn: Is 7632842509 a composite number? Therefore: True Qn: Is 39139 a prime number? Therefore: True Qn: Is 99071 a prime number? Therefore: False Qn: Is 2121343 a prime number? Therefore: False Qn: Is 693992911 a composite number? Therefore: False Qn: Is 4900877 composite? Therefore: False Qn: Is 5810863 a composite number? Therefore: False Qn: Is 107609 prime? Therefore: True Qn: Is 59190767 composite? Therefore: False Qn: Is 4952239 a prime number? Therefore: True Qn: Is 58515222071 a prime number? Therefore: False Qn: Is 2159 prime? Therefore: False Qn: Is 228910663 a composite number? Therefore: True Qn: Is 212258 prime? Therefore: False Qn: Is 15086998 prime? Therefore: False Qn: Is 34115 prime? Therefore: False Qn: Is 1619 composite? Therefore: False Qn: Is 19449991 prime? Therefore: False Qn: Is 13108807 prime? Therefore: False Qn: Is 1724299 prime? Therefore: True Qn: Is 504019 a composite number? Therefore: True Qn: Is 34088146247 prime? Therefore: False Qn: Is 94282385 a composite number? Therefore: True Qn: Is 66326243 composite? Therefore: False Qn: Is 4610997929 prime? Therefore: True Qn: Is 22913 composite? Therefore: True Qn: Is 3060179 composite? Therefore: False Qn: Is 2837473 prime? Therefore: True Qn: Is 4191801 prime? Therefore: False Qn: Is 393818255 a composite number? Therefore: True Qn: Is 657272557 a composite number? Therefore: True Qn: Is 13985087 a prime number? Therefore: True Qn: Is 1831103 a prime number? Therefore: True Qn: Is 1620107 a composite number? Therefore: False Qn: Is 30933803 prime? Therefore: False Qn: Is 13595 prime? Therefore: False Qn: Is 12052939 a prime number? Therefore: False Qn: Is 134623 a prime number? Therefore: False Qn: Is 161429 prime? Therefore: False
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probability: swr p sequence --------------------------- Math Q: Calculate prob of sequence ounn when four letters picked without replacement from oxunoxxnxxoxtouuxxn. A: 1/1292 Math Q: Three letters picked without replacement from {i: 1, r: 1, y: 1, z: 1, f: 1}. Give prob of sequence fiy. A: 1/60 Math Q: What is prob of sequence esh when three letters picked without replacement from {e: 7, s: 1, p: 1, r: 4, z: 4, h: 1}? A: 7/4896 Math Q: Three letters picked without replacement from {j: 4, k: 1, z: 2, n: 2}. What is prob of sequence zjj? A: 1/21 Math Q: Calculate prob of sequence ka when two letters picked without replacement from {a: 2, t: 1, i: 1, f: 1, k: 4}. A: 1/9 Math Q: Two letters picked without replacement from {g: 1, a: 5, y: 6, m: 7}. Give prob of sequence ya. A: 5/57 Math Q: Three letters picked without replacement from occccocffccc. What is prob of sequence ofc? A: 4/165 Math Q: What is prob of sequence lll when three letters picked without replacement from {a: 4, l: 7}? A: 7/33 Math Q: Three letters picked without replacement from xxxxfpfxxbpxfxpfpfxp. What is prob of sequence bpx? A: 1/152 Math Q: Two letters picked without replacement from {f: 5, r: 3}. What is prob of sequence rr? A: 3/28 Math Q: Calculate prob of sequence vq when two letters picked without replacement from vkqqq. A: 3/20 Math Q: Calculate prob of sequence gee when three letters picked without replacement from etdiddeegi. A: 1/120 Math Q: Three letters picked without replacement from bbbiibb. Give prob of sequence bii. A: 1/21 Math Q: What is prob of sequence wooy when four letters picked without replacement from oowwwywlooo? A: 1/99 Math Q: What is prob of sequence dn when two letters picked without replacement from {d: 1, k: 1, e: 2, n: 1}? A: 1/20 Math Q: What is prob of sequence kptt when four letters picked without replacement from ppkptkpppkptk? A: 7/2145 Math Q: Two letters picked without replacement from {v: 2, l: 1, f: 1, h: 1, o: 1, c: 2}. What is prob of sequence co? A: 1
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probability: swr p sequence --------------------------- What if: Two letters picked without replacement from {l: 5, q: 4, c: 1, a: 4, k: 1}. Give prob of sequence lk. Calculation: 1/42 What if: Three letters picked without replacement from {a: 4, f: 1, g: 1, o: 7, b: 2}. Give prob of sequence gba. Calculation: 4/1365 What if: Calculate prob of sequence ep when two letters picked without replacement from {x: 2, y: 2, c: 1, p: 1, e: 1}. Calculation: 1/42 What if: Calculate prob of sequence cx when two letters picked without replacement from {x: 2, i: 1, e: 3, o: 5, c: 1}. Calculation: 1/66 What if: What is prob of sequence pppp when four letters picked without replacement from gpppgppp? Calculation: 3/14 What if: Calculate prob of sequence zz when two letters picked without replacement from {i: 7, z: 7}. Calculation: 3/13 What if: Three letters picked without replacement from ojsoooooroooj. Give prob of sequence soo. Calculation: 6/143 What if: Two letters picked without replacement from {z: 1, i: 2, r: 6, s: 3, f: 2, y: 1}. Give prob of sequence rr. Calculation: 1/7 What if: Calculate prob of sequence dvvz when four letters picked without replacement from {j: 3, c: 2, v: 4, t: 1, z: 1, d: 1}. Calculation: 1/990 What if: Calculate prob of sequence rv when two letters picked without replacement from ovcrvoyrrr. Calculation: 4/45 What if: Calculate prob of sequence cc when two letters picked without replacement from {v: 2, f: 1, a: 1, y: 1, c: 4}. Calculation: 1/6 What if: Four letters picked without replacement from qvvvsqsqcqiviqtsscqi. What is prob of sequence sqtc? Calculation: 2/4845 What if: Two letters picked without replacement from ccjwtcocciccctw. Give prob of sequence ji. Calculation: 1/210 What if: Two letters picked without replacement from {z: 12, h: 1}. What is prob of sequence hz? Calculation: 1/13 What if: Four letters picked without replacement from qjqiuzqcquciii. Give prob of sequence cucj. Calculation: 1/6006 What if: Four letters picked without rep
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probability: swr p sequence --------------------------- What if: What is prob of sequence sv when two letters picked without replacement from sasrrvvshhrt? Calculation: 1/22 What if: Calculate prob of sequence grp when three letters picked without replacement from {g: 2, p: 1, w: 9, k: 1, r: 3, a: 3}. Calculation: 1/969 What if: Calculate prob of sequence dvd when three letters picked without replacement from dddldleedeedvldevl. Calculation: 7/408 What if: Calculate prob of sequence ete when three letters picked without replacement from {t: 3, e: 7}. Calculation: 7/40 What if: Calculate prob of sequence tf when two letters picked without replacement from {t: 14, f: 1, u: 1}. Calculation: 7/120 What if: Four letters picked without replacement from cqceccfbcceqbbnbbfe. Give prob of sequence nbeq. Calculation: 5/15504 What if: Calculate prob of sequence ko when two letters picked without replacement from kookok. Calculation: 3/10 What if: What is prob of sequence ww when two letters picked without replacement from wwwww? Calculation: 1 What if: Three letters picked without replacement from sqtsdqsls. Give prob of sequence qqd. Calculation: 1/252 What if: Calculate prob of sequence khe when three letters picked without replacement from {e: 6, o: 1, h: 1, k: 1}. Calculation: 1/84 What if: What is prob of sequence zwqy when four letters picked without replacement from {l: 1, q: 1, z: 2, w: 1, k: 1, y: 1}? Calculation: 1/420 What if: What is prob of sequence ss when two letters picked without replacement from uuuuesuuuseuu? Calculation: 1/78 What if: Two letters picked without replacement from {r: 10, g: 7, b: 1}. What is prob of sequence rr? Calculation: 5/17 What if: Calculate prob of sequence kj when two letters picked without replacement from kyjyvkvyyyykjvjvyyj. Calculation: 2/57 What if: Two letters picked without replacement from {d: 4, m: 1, c: 3}. Give prob of sequence cd. Calculation: 3/14 What if: Two letters picked without replacement from {h: 1, e: 1, w: 1}. W
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numbers: is factor ------------------ Math Q: Is 1000149696 a multiple of 5? Derivation: False Math Q: Is 220 a multiple of 22? Derivation: True Math Q: Is 2001617 a multiple of 28? Derivation: False Math Q: Is 9 a factor of 20907? Derivation: True Math Q: Does 39 divide 64248? Derivation: False Math Q: Is 5 a factor of 5547735? Derivation: True Math Q: Is 335 a factor of 6073758? Derivation: False Math Q: Is 2240573014 a multiple of 113? Derivation: False Math Q: Is 23 a factor of 455331? Derivation: True Math Q: Is 35 a factor of 48124265? Derivation: True Math Q: Does 166 divide 141437? Derivation: False Math Q: Is 640 a multiple of 4? Derivation: True Math Q: Does 622 divide 34474972? Derivation: True Math Q: Does 1432 divide 29172390? Derivation: False Math Q: Does 61 divide 4826385? Derivation: False Math Q: Is 15 a factor of 1545? Derivation: True Math Q: Does 3 divide 158618? Derivation: False Math Q: Is 52 a factor of 3665? Derivation: False Math Q: Is 15 a factor of 1288554480? Derivation: True Math Q: Does 144 divide 190572? Derivation: False Math Q: Does 1411 divide 16751392? Derivation: True Math Q: Does 16 divide 18640? Derivation: True Math Q: Is 678060 a multiple of 9? Derivation: True Math Q: Is 13752 a multiple of 36? Derivation: True Math Q: Is 2898220 a multiple of 142? Derivation: True Math Q: Does 17 divide 1734? Derivation: True Math Q: Is 81503 a multiple of 54? Derivation: False Math Q: Does 84 divide 3425? Derivation: False Math Q: Is 1171940 a multiple of 133? Derivation: False Math Q: Is 81 a factor of 3568253? Derivation: False Math Q: Is 155931 a multiple of 314? Derivation: False Math Q: Is 12 a factor of 94394978? Derivation: False Math Q: Is 312673476 a multiple of 802? Derivation: False Math Q: Is 9 a factor of 10386? Derivation: True Math Q: Is 2082704 a multiple of 884? Derivation: True Math Q: Does 23 divide 19161026? Derivation: False Math Q: Is 20901 a multiple of 3? Derivation: True Math Q: Is 7434 a multiple of 9? Derivation:
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numbers: is prime ----------------- Problem #: Is 4663 a composite number? Calculation: False Problem #: Is 3668801 a composite number? Calculation: False Problem #: Is 1829 prime? Calculation: False Problem #: Is 1597 prime? Calculation: True Problem #: Is 6329 prime? Calculation: True Problem #: Is 6128531 prime? Calculation: True Problem #: Is 308777 a prime number? Calculation: False Problem #: Is 3989 composite? Calculation: False Problem #: Is 3278947 composite? Calculation: True Problem #: Is 24829270157 prime? Calculation: True Problem #: Is 4282043 a composite number? Calculation: True Problem #: Is 20719943 composite? Calculation: True Problem #: Is 1481489843 a composite number? Calculation: True Problem #: Is 301759 composite? Calculation: False Problem #: Is 358673 prime? Calculation: False Problem #: Is 32705507 composite? Calculation: False Problem #: Is 4717 a composite number? Calculation: True Problem #: Is 2617909 a composite number? Calculation: True Problem #: Is 56843 a prime number? Calculation: True Problem #: Is 7832302007 a prime number? Calculation: True Problem #: Is 1650983 prime? Calculation: True Problem #: Is 4956697 a prime number? Calculation: False Problem #: Is 15465389 composite? Calculation: True Problem #: Is 48943 a composite number? Calculation: True Problem #: Is 31502065319 composite? Calculation: False Problem #: Is 95742763 prime? Calculation: True Problem #: Is 324305063 composite? Calculation: True Problem #: Is 55643 a composite number? Calculation: True Problem #: Is 6543663173 prime? Calculation: False Problem #: Is 149263 prime? Calculation: False Problem #: Is 18166387069 a prime number? Calculation: True Problem #: Is 1113401 a composite number? Calculation: False Problem #: Is 11542931 a prime number? Calculation: True Problem #: Is 53129 a prime number? Calculation: True Problem #: Is 3954101 prime? Calculation: True Problem #: Is 1107998233 a prime number? Calculation: True Problem #: Is 672634381 a prime numbe
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measurement: time ----------------- Step: How many minutes are there between 11:35 PM and 7:18 AM? Explanation: 463 Step: What is 481 minutes before 1:07 PM? Explanation: 5:06 AM Step: What is 630 minutes before 1:01 PM? Explanation: 2:31 AM Step: What is 700 minutes after 5:18 PM? Explanation: 4:58 AM Step: How many minutes are there between 8:11 AM and 3:10 PM? Explanation: 419 Step: What is 394 minutes after 11:14 AM? Explanation: 5:48 PM Step: How many minutes are there between 3:18 PM and 6:04 PM? Explanation: 166 Step: How many minutes are there between 11:29 PM and 1:13 AM? Explanation: 104 Step: What is 623 minutes before 7:26 AM? Explanation: 9:03 PM Step: What is 703 minutes before 5:50 AM? Explanation: 6:07 PM Step: How many minutes are there between 11:11 AM and 4:21 PM? Explanation: 310 Step: What is 52 minutes before 6:39 AM? Explanation: 5:47 AM Step: What is 90 minutes before 4:11 AM? Explanation: 2:41 AM Step: What is 605 minutes before 2:43 PM? Explanation: 4:38 AM Step: How many minutes are there between 6:34 AM and 9:38 AM? Explanation: 184 Step: How many minutes are there between 7:46 AM and 6:14 PM? Explanation: 628 Step: How many minutes are there between 4:45 PM and 8:28 PM? Explanation: 223 Step: How many minutes are there between 11:13 AM and 3:16 PM? Explanation: 243 Step: What is 194 minutes after 4:40 AM? Explanation: 7:54 AM Step: What is 655 minutes after 8:24 PM? Explanation: 7:19 AM Step: What is 171 minutes after 5:59 PM? Explanation: 8:50 PM Step: How many minutes are there between 4:59 PM and 11:49 PM? Explanation: 410 Step: How many minutes are there between 4:09 AM and 8:33 AM? Explanation: 264 Step: How many minutes are there between 4:03 AM and 11:53 AM? Explanation: 470 Step: What is 117 minutes after 5:56 AM? Explanation: 7:53 AM Step: What is 707 minutes before 12:25 AM? Explanation: 12:38 PM Step: How many minutes are there between 9:14 PM and 2:45 AM? Explanation: 331 Step: What is 50 minutes before 2:24 AM? Explanation:
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probability: swr p level set ---------------------------- Prompt: Calculate prob of picking 2 x when two letters picked without replacement from xmxhrxxh. Reply: 3/14 Prompt: Two letters picked without replacement from {s: 3, e: 4}. What is prob of picking 2 e? Reply: 2/7 Prompt: What is prob of picking 2 y when two letters picked without replacement from yyyyyyy? Reply: 1 Prompt: What is prob of picking 1 m, 1 b, and 1 u when three letters picked without replacement from nmbzmbbbbununn? Reply: 5/91 Prompt: Two letters picked without replacement from {o: 5}. Give prob of picking 2 o. Reply: 1 Prompt: Calculate prob of picking 1 a and 2 e when three letters picked without replacement from asxtxefexfsf. Reply: 1/220 Prompt: Calculate prob of picking 2 e and 1 z when three letters picked without replacement from {e: 6, z: 4}. Reply: 1/2 Prompt: What is prob of picking 1 z and 1 p when two letters picked without replacement from pyzzzzzzzzz? Reply: 9/55 Prompt: Calculate prob of picking 1 c and 1 f when two letters picked without replacement from {f: 4, a: 1, h: 6, b: 5, c: 4}. Reply: 8/95 Prompt: Four letters picked without replacement from xssskqoksssoss. What is prob of picking 1 q, 1 o, 1 x, and 1 k? Reply: 4/1001 Prompt: Two letters picked without replacement from {n: 1, f: 1, j: 2, g: 2, c: 1, b: 1}. Give prob of picking 2 g. Reply: 1/28 Prompt: Two letters picked without replacement from {t: 9, a: 7, z: 3}. What is prob of picking 1 a and 1 z? Reply: 7/57 Prompt: Two letters picked without replacement from caccclaalallccccaac. Give prob of picking 1 a and 1 c. Reply: 6/19 Prompt: Calculate prob of picking 1 z and 1 t when two letters picked without replacement from {x: 1, t: 4, u: 3, z: 1, g: 7}. Reply: 1/30 Prompt: Calculate prob of picking 2 r and 1 w when three letters picked without replacement from {r: 3, w: 1}. Reply: 3/4 Prompt: Two letters picked without replacement from aqaaaaqqaq. What is prob of picking 2 q? Reply: 2/15 Prompt: Three letters picked wit
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probability: swr p level set ---------------------------- Q-: Two letters picked without replacement from {i: 3, r: 1, w: 1}. Give prob of picking 1 i and 1 r. Gives: 3/10 Q-: Calculate prob of picking 1 f and 1 m when two letters picked without replacement from fmmfmf. Gives: 3/5 Q-: Two letters picked without replacement from {c: 1, e: 3, y: 2, t: 7, h: 1}. What is prob of picking 1 c and 1 h? Gives: 1/91 Q-: What is prob of picking 2 d when two letters picked without replacement from {n: 7, d: 12}? Gives: 22/57 Q-: Calculate prob of picking 1 s, 1 g, and 1 p when three letters picked without replacement from {m: 6, g: 1, v: 1, c: 1, s: 4, p: 2}. Gives: 8/455 Q-: Two letters picked without replacement from {o: 2, e: 1, u: 1, v: 2, x: 1, g: 1}. Give prob of picking 1 e and 1 u. Gives: 1/28 Q-: Calculate prob of picking 1 b, 2 r, and 1 d when four letters picked without replacement from dtttrrtbtrtrt. Gives: 6/715 Q-: Calculate prob of picking 3 e when three letters picked without replacement from dojeqve. Gives: 0 Q-: Calculate prob of picking 1 z and 2 o when three letters picked without replacement from {z: 1, o: 3}. Gives: 3/4 Q-: Three letters picked without replacement from {o: 2, d: 1, y: 6, f: 1, b: 7}. What is prob of picking 1 y and 2 b? Gives: 63/340 Q-: Calculate prob of picking 2 z when two letters picked without replacement from {z: 15, p: 5}. Gives: 21/38 Q-: Three letters picked without replacement from {j: 2, g: 2, c: 4}. What is prob of picking 1 c and 2 g? Gives: 1/14 Q-: Three letters picked without replacement from poffdqd. Give prob of picking 1 d, 1 q, and 1 p. Gives: 2/35 Q-: Three letters picked without replacement from {z: 2, g: 1, c: 1, w: 1}. Give prob of picking 1 w, 1 z, and 1 c. Gives: 1/5 Q-: What is prob of picking 1 n and 1 j when two letters picked without replacement from jjnjjnjjnnnjjjnjjjj? Gives: 26/57 Q-: Two letters picked without replacement from kkd. Give prob of picking 2 k. Gives: 1/3 Q-: What is prob of picking 2 w when
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numbers: div remainder ---------------------- Example: What is the remainder when 6179 is divided by 1257? A: 1151 Example: What is the remainder when 284 is divided by 41? A: 38 Example: Calculate the remainder when 90 is divided by 13. A: 12 Example: What is the remainder when 12635 is divided by 33? A: 29 Example: Calculate the remainder when 2361 is divided by 1156. A: 49 Example: Calculate the remainder when 213774255 is divided by 23. A: 19 Example: What is the remainder when 113 is divided by 71? A: 42 Example: What is the remainder when 897 is divided by 10? A: 7 Example: What is the remainder when 15728637 is divided by 963? A: 921 Example: Calculate the remainder when 337397143 is divided by 17. A: 13 Example: Calculate the remainder when 92256 is divided by 30683. A: 207 Example: Calculate the remainder when 10394 is divided by 29. A: 12 Example: What is the remainder when 18079 is divided by 855? A: 124 Example: What is the remainder when 4642 is divided by 521? A: 474 Example: Calculate the remainder when 2487 is divided by 489. A: 42 Example: Calculate the remainder when 9069072 is divided by 24915. A: 12 Example: Calculate the remainder when 1743052 is divided by 424. A: 412 Example: What is the remainder when 3030 is divided by 190? A: 180 Example: Calculate the remainder when 5791 is divided by 1153. A: 26 Example: What is the remainder when 311 is divided by 66? A: 47 Example: Calculate the remainder when 589 is divided by 87. A: 67 Example: What is the remainder when 70468557 is divided by 58? A: 7 Example: What is the remainder when 440 is divided by 13? A: 11 Example: What is the remainder when 1793 is divided by 22? A: 11 Example: Calculate the remainder when 56 is divided by 3. A: 2 Example: Calculate the remainder when 424 is divided by 416. A: 8 Example: Calculate the remainder when 24513 is divided by 1168. A: 1153 Example: What is the remainder when 14769 is divided by 53? A: 35 Example: Calculate the remainder when 18 is divided by 13. A:
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numbers: place value -------------------- Puzzle: What is the tens digit of 61207? Calculation: 0 Puzzle: What is the units digit of 38036? Calculation: 6 Puzzle: What is the hundred millions digit of 106080707? Calculation: 1 Puzzle: What is the tens digit of 223680? Calculation: 8 Puzzle: What is the ten millions digit of 173061085? Calculation: 7 Puzzle: What is the hundreds digit of 107898? Calculation: 8 Puzzle: What is the hundred thousands digit of 100335384? Calculation: 3 Puzzle: What is the hundred thousands digit of 38280155? Calculation: 2 Puzzle: What is the hundreds digit of 11887? Calculation: 8 Puzzle: What is the ten thousands digit of 10091366? Calculation: 9 Puzzle: What is the ten thousands digit of 56444? Calculation: 5 Puzzle: What is the units digit of 29? Calculation: 9 Puzzle: What is the thousands digit of 541876310? Calculation: 6 Puzzle: What is the thousands digit of 7958? Calculation: 7 Puzzle: What is the hundred thousands digit of 2589804573? Calculation: 8 Puzzle: What is the hundreds digit of 2464? Calculation: 4 Puzzle: What is the hundreds digit of 869? Calculation: 8 Puzzle: What is the hundreds digit of 345? Calculation: 3 Puzzle: What is the thousands digit of 55248? Calculation: 5 Puzzle: What is the units digit of 419? Calculation: 9 Puzzle: What is the tens digit of 368356608? Calculation: 0 Puzzle: What is the units digit of 3077? Calculation: 7 Puzzle: What is the thousands digit of 4674? Calculation: 4 Puzzle: What is the units digit of 48387880? Calculation: 0 Puzzle: What is the millions digit of 1781653? Calculation: 1 Puzzle: What is the hundreds digit of 1809? Calculation: 8 Puzzle: What is the tens digit of 88835? Calculation: 3 Puzzle: What is the hundred thousands digit of 15375157? Calculation: 3 Puzzle: What is the tens digit of 48? Calculation: 4 Puzzle: What is the tens digit of 243? Calculation: 4 Puzzle: What is the ten thousands digit of 95714? Calculation: 9 Puzzle: What is the units digit of 417324255? Ca
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numbers: is prime ----------------- Example: Is 2020171 a prime number? Steps: True Example: Is 6995 composite? Steps: True Example: Is 168466819 composite? Steps: True Example: Is 145403209 prime? Steps: False Example: Is 74566981101 prime? Steps: False Example: Is 1835666611 composite? Steps: True Example: Is 1250649061 composite? Steps: False Example: Is 3679500047 prime? Steps: False Example: Is 548996243 prime? Steps: True Example: Is 8902637 composite? Steps: False Example: Is 176068883399 a prime number? Steps: True Example: Is 11723807 a composite number? Steps: True Example: Is 282221 a prime number? Steps: True Example: Is 650911 a prime number? Steps: True Example: Is 38794367 a prime number? Steps: True Example: Is 61431 composite? Steps: True Example: Is 4031 a prime number? Steps: False Example: Is 6023897 a composite number? Steps: True Example: Is 4049 a prime number? Steps: True Example: Is 6013377833 a prime number? Steps: True Example: Is 136848967 prime? Steps: False Example: Is 36677 prime? Steps: True Example: Is 234917 prime? Steps: True Example: Is 17513 a prime number? Steps: False Example: Is 25111117 prime? Steps: False Example: Is 3115276453 prime? Steps: False Example: Is 284112047 a composite number? Steps: False Example: Is 22757 a prime number? Steps: False Example: Is 128746 a composite number? Steps: True Example: Is 1467597707 composite? Steps: True Example: Is 2797783 prime? Steps: True Example: Is 54956527 prime? Steps: False Example: Is 5220749 a composite number? Steps: False Example: Is 51327709571 a composite number? Steps: False Example: Is 838262764939 a composite number? Steps: False Example: Is 36226783 composite? Steps: True Example: Is 5042 composite? Steps: True Example: Is 5696849 prime? Steps: True Example: Is 279153247 a composite number? Steps: True Example: Is 3495672241 a composite number? Steps: True Example: Is 448127677 prime? Steps: True Example: Is 22789 a prime number? Steps: False Example: Is 14570172893 p
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probability: swr p level set ---------------------------- Q): Two letters picked without replacement from {j: 1, t: 11}. Give prob of picking 1 j and 1 t. Gives: 1/6 Q): Two letters picked without replacement from {u: 5}. What is prob of picking 2 u? Gives: 1 Q): What is prob of picking 2 a when two letters picked without replacement from aaaaaaaaaa? Gives: 1 Q): Three letters picked without replacement from tttteeette. What is prob of picking 2 e and 1 t? Gives: 3/10 Q): Calculate prob of picking 1 o, 2 s, and 1 g when four letters picked without replacement from sffssggsjosjsg. Gives: 45/1001 Q): What is prob of picking 1 q and 1 u when two letters picked without replacement from {t: 1, q: 1, u: 1, f: 3, e: 1}? Gives: 1/21 Q): Two letters picked without replacement from {v: 2, w: 1, e: 2}. What is prob of picking 1 v and 1 w? Gives: 1/5 Q): Three letters picked without replacement from {v: 2, p: 2, t: 6, e: 6, b: 1}. What is prob of picking 1 v and 2 e? Gives: 3/68 Q): Two letters picked without replacement from kvkvvkkk. Give prob of picking 2 k. Gives: 5/14 Q): Two letters picked without replacement from hhhhhhhmmhhhh. Give prob of picking 2 m. Gives: 1/78 Q): Four letters picked without replacement from {x: 6, s: 5, i: 4}. What is prob of picking 4 i? Gives: 1/1365 Q): Three letters picked without replacement from {u: 2, p: 5}. What is prob of picking 1 u and 2 p? Gives: 4/7 Q): Two letters picked without replacement from wdwdeewwidccceec. What is prob of picking 1 e and 1 c? Gives: 2/15 Q): Four letters picked without replacement from iiqqmiipxqmqilp. What is prob of picking 1 q, 2 m, and 1 p? Gives: 8/1365 Q): What is prob of picking 2 k and 2 b when four letters picked without replacement from {m: 1, k: 1, b: 2, y: 4}? Gives: 0 Q): Two letters picked without replacement from uuuupuuupu. What is prob of picking 2 p? Gives: 1/45 Q): Calculate prob of picking 1 e and 1 z when two letters picked without replacement from {z: 10, e: 10}. Gives: 10/19 Q): What is p
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numbers: is prime ----------------- Subquestion: Is 17276917247 prime? Compute: False Subquestion: Is 4471 a composite number? Compute: True Subquestion: Is 183851671 a composite number? Compute: True Subquestion: Is 14479884589 prime? Compute: False Subquestion: Is 7283 prime? Compute: True Subquestion: Is 78377 prime? Compute: False Subquestion: Is 249005161 a composite number? Compute: False Subquestion: Is 860837 a prime number? Compute: False Subquestion: Is 28829 prime? Compute: False Subquestion: Is 1034461 prime? Compute: True Subquestion: Is 59665 a prime number? Compute: False Subquestion: Is 5027082161 a composite number? Compute: True Subquestion: Is 74699817 composite? Compute: True Subquestion: Is 16695335 prime? Compute: False Subquestion: Is 2770367 a composite number? Compute: False Subquestion: Is 535063 prime? Compute: False Subquestion: Is 1277 prime? Compute: True Subquestion: Is 46373269 a prime number? Compute: True Subquestion: Is 62173 a composite number? Compute: True Subquestion: Is 171573847 composite? Compute: True Subquestion: Is 26158950143 composite? Compute: False Subquestion: Is 284719 composite? Compute: True Subquestion: Is 128926960247 a composite number? Compute: False Subquestion: Is 70934533 composite? Compute: False Subquestion: Is 397949 prime? Compute: False Subquestion: Is 6482654873 prime? Compute: True Subquestion: Is 36407699 composite? Compute: False Subquestion: Is 32445013 prime? Compute: False Subquestion: Is 135073539283 composite? Compute: False Subquestion: Is 17461 a prime number? Compute: False Subquestion: Is 31908133 composite? Compute: True Subquestion: Is 68701665073 composite? Compute: True Subquestion: Is 38178744031 a composite number? Compute: True Subquestion: Is 161608463 a prime number? Compute: True Subquestion: Is 7129345007 a composite number? Compute: True Subquestion: Is 483416471 prime? Compute: False Subquestion: Is 1071388001 a prime number? Compute: False Subquestion: Is 1694321 a prime numb
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probability: swr p sequence --------------------------- Exercise: Four letters picked without replacement from rvrvssssvssrsz. Give prob of sequence ssrv. Response: 9/572 Exercise: Four letters picked without replacement from {h: 2, v: 7, z: 1}. What is prob of sequence hhvv? Response: 1/60 Exercise: Three letters picked without replacement from iiigigiioggggi. Give prob of sequence igo. Response: 1/52 Exercise: Three letters picked without replacement from ctzzcztcjictczioztjt. Give prob of sequence ioz. Response: 1/684 Exercise: Calculate prob of sequence ij when two letters picked without replacement from jiijrrrj. Response: 3/28 Exercise: Three letters picked without replacement from {s: 5, t: 5}. Give prob of sequence ttt. Response: 1/12 Exercise: Four letters picked without replacement from {w: 5}. Give prob of sequence wwww. Response: 1 Exercise: Calculate prob of sequence evv when three letters picked without replacement from {e: 3, v: 3}. Response: 3/20 Exercise: Calculate prob of sequence vp when two letters picked without replacement from vvpvvvvv. Response: 1/8 Exercise: Calculate prob of sequence iczz when four letters picked without replacement from {k: 2, z: 4, i: 1, c: 2, b: 4, o: 2}. Response: 1/1365 Exercise: Three letters picked without replacement from tdtttddttd. What is prob of sequence ttd? Response: 1/6 Exercise: Calculate prob of sequence am when two letters picked without replacement from {x: 1, l: 2, a: 1, r: 1, y: 1, m: 2}. Response: 1/28 Exercise: Four letters picked without replacement from {w: 4, z: 6, a: 4, o: 3}. What is prob of sequence aoww? Response: 3/1190 Exercise: Calculate prob of sequence jz when two letters picked without replacement from {u: 7, r: 4, z: 4, i: 1, j: 3, d: 1}. Response: 3/95 Exercise: Three letters picked without replacement from {n: 2, g: 10}. Give prob of sequence ngg. Response: 3/22 Exercise: What is prob of sequence bbb when three letters picked without replacement from vbvvvvvvvbvvvvvvbvvv? Response: 1/1
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numbers: is prime ----------------- Question: Is 87753 composite? Calculation: True Question: Is 3893215 a prime number? Calculation: False Question: Is 201210441 composite? Calculation: True Question: Is 250460761 a prime number? Calculation: False Question: Is 73134431 a prime number? Calculation: True Question: Is 20419 a composite number? Calculation: True Question: Is 53161861 a composite number? Calculation: True Question: Is 10299911 prime? Calculation: False Question: Is 3982302943 composite? Calculation: True Question: Is 41545984583 a prime number? Calculation: False Question: Is 3639439 composite? Calculation: True Question: Is 2906401 a prime number? Calculation: True Question: Is 14235973 prime? Calculation: False Question: Is 55948002767 composite? Calculation: True Question: Is 29789209 a prime number? Calculation: False Question: Is 909235091 a composite number? Calculation: True Question: Is 51022493569 composite? Calculation: True Question: Is 4618347 composite? Calculation: True Question: Is 13567 prime? Calculation: True Question: Is 2106091 a composite number? Calculation: True Question: Is 5779 a composite number? Calculation: False Question: Is 36965 a prime number? Calculation: False Question: Is 325027 composite? Calculation: False Question: Is 522371 prime? Calculation: True Question: Is 4631149 prime? Calculation: False Question: Is 295167727 composite? Calculation: True Question: Is 114391 a composite number? Calculation: True Question: Is 3230445139 a prime number? Calculation: False Question: Is 10794683533 a prime number? Calculation: True Question: Is 16338163 a composite number? Calculation: False Question: Is 1109 composite? Calculation: False Question: Is 462991 prime? Calculation: False Question: Is 28415 a composite number? Calculation: True Question: Is 72023 a prime number? Calculation: False Question: Is 507233 prime? Calculation: False Question: Is 998 a prime number? Calculation: False Question: Is 924877577 a composite numb
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probability: swr p level set ---------------------------- Problem: Three letters picked without replacement from {n: 2, s: 5, j: 9}. Give prob of picking 2 n and 1 s. Steps: 1/112 Problem: Calculate prob of picking 1 d and 3 i when four letters picked without replacement from diddidddid. Steps: 1/30 Problem: Calculate prob of picking 1 r, 1 y, and 1 z when three letters picked without replacement from clrzzyrc. Steps: 1/14 Problem: Two letters picked without replacement from {h: 3, s: 17}. Give prob of picking 2 h. Steps: 3/190 Problem: Two letters picked without replacement from pppppppppjppp. Give prob of picking 2 p. Steps: 11/13 Problem: Calculate prob of picking 1 n and 1 z when two letters picked without replacement from ncqzzzznnnnczdzzznz. Steps: 6/19 Problem: Four letters picked without replacement from ghxxhxghhggg. What is prob of picking 4 h? Steps: 1/495 Problem: Four letters picked without replacement from {i: 2, d: 4, j: 5, n: 2}. What is prob of picking 1 d, 2 i, and 1 n? Steps: 8/715 Problem: What is prob of picking 1 b and 1 n when two letters picked without replacement from nobbnmmomvoo? Steps: 2/33 Problem: Three letters picked without replacement from {o: 8, w: 2}. Give prob of picking 2 o and 1 w. Steps: 7/15 Problem: What is prob of picking 4 n when four letters picked without replacement from nnnnnnnnnlnnn? Steps: 9/13 Problem: Calculate prob of picking 1 j and 2 r when three letters picked without replacement from {j: 3, v: 2, r: 10}. Steps: 27/91 Problem: What is prob of picking 1 d, 1 v, and 1 z when three letters picked without replacement from {n: 1, d: 1, z: 2, v: 1}? Steps: 1/5 Problem: Two letters picked without replacement from {w: 7, f: 6}. Give prob of picking 2 w. Steps: 7/26 Problem: What is prob of picking 4 j when four letters picked without replacement from njnjnnnjnjnnnn? Steps: 1/1001 Problem: Four letters picked without replacement from nnnlb. What is prob of picking 4 l? Steps: 0 Problem: Calculate prob of picking 1 z and
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numbers: is prime ----------------- Question: Is 1029103 composite? Result: False Question: Is 320035249 prime? Result: True Question: Is 3784775227 a composite number? Result: False Question: Is 1575259 composite? Result: True Question: Is 150711427 composite? Result: False Question: Is 7455179 prime? Result: True Question: Is 90833659 composite? Result: True Question: Is 2782441 a composite number? Result: True Question: Is 628249 composite? Result: True Question: Is 257138903 a composite number? Result: True Question: Is 460040701 prime? Result: False Question: Is 12209964617 composite? Result: True Question: Is 68089247 a prime number? Result: False Question: Is 2330605 a composite number? Result: True Question: Is 78539 prime? Result: True Question: Is 8140279 prime? Result: False Question: Is 7164083549 prime? Result: False Question: Is 970418629 a composite number? Result: True Question: Is 55532074979 prime? Result: False Question: Is 21138633001 composite? Result: True Question: Is 74199 composite? Result: True Question: Is 6458867 a composite number? Result: True Question: Is 28799 a prime number? Result: False Question: Is 12098837659 a prime number? Result: True Question: Is 15518250221 prime? Result: False Question: Is 1234099 prime? Result: True Question: Is 44041 prime? Result: True Question: Is 1692879131 a prime number? Result: True Question: Is 53055343207 a composite number? Result: False Question: Is 276844496039 a composite number? Result: True Question: Is 104281 a composite number? Result: False Question: Is 10689905 a prime number? Result: False Question: Is 16363253 prime? Result: True Question: Is 120467 prime? Result: False Question: Is 3497 prime? Result: False Question: Is 193582751 a composite number? Result: True Question: Is 3702421 a composite number? Result: True Question: Is 25093 composite? Result: True Question: Is 6157079 composite? Result: False Question: Is 3029603 composite? Result: False Question: Is 9551741 composite? Resul
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arithmetic: nearest integer root -------------------------------- Scenario: What is 94054 to the power of 1/7, to the nearest integer? Finding: 5 Scenario: What is 1011706954 to the power of 1/2, to the nearest integer? Finding: 31807 Scenario: What is the third root of 1602481 to the nearest integer? Finding: 117 Scenario: What is 1729900 to the power of 1/2, to the nearest integer? Finding: 1315 Scenario: What is the square root of 40079 to the nearest integer? Finding: 200 Scenario: What is 932171 to the power of 1/2, to the nearest integer? Finding: 965 Scenario: What is 1355 to the power of 1/5, to the nearest integer? Finding: 4 Scenario: What is 195059628 to the power of 1/2, to the nearest integer? Finding: 13966 Scenario: What is 2838294232 to the power of 1/4, to the nearest integer? Finding: 231 Scenario: What is 120210 to the power of 1/3, to the nearest integer? Finding: 49 Scenario: What is the third root of 1582387770 to the nearest integer? Finding: 1165 Scenario: What is 4151 to the power of 1/4, to the nearest integer? Finding: 8 Scenario: What is the third root of 2527 to the nearest integer? Finding: 14 Scenario: What is the fourth root of 1100484 to the nearest integer? Finding: 32 Scenario: What is the square root of 2337 to the nearest integer? Finding: 48 Scenario: What is the square root of 1083 to the nearest integer? Finding: 33 Scenario: What is the fourth root of 94435823 to the nearest integer? Finding: 99 Scenario: What is 418 to the power of 1/9, to the nearest integer? Finding: 2 Scenario: What is the square root of 797 to the nearest integer? Finding: 28 Scenario: What is the square root of 340 to the nearest integer? Finding: 18 Scenario: What is the square root of 11247194 to the nearest integer? Finding: 3354 Scenario: What is the square root of 1346590 to the nearest integer? Finding: 1160 Scenario: What is 824 to the power of 1/2, to the nearest integer? Finding: 29 Scenario: What is 6290433 to the power of 1/2, to the nearest
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numbers: place value -------------------- Task: What is the tens digit of 92319829? Calculation: 2 Task: What is the hundreds digit of 14137761? Calculation: 7 Task: What is the ten thousands digit of 2202551281? Calculation: 5 Task: What is the hundreds digit of 155196? Calculation: 1 Task: What is the hundreds digit of 29286? Calculation: 2 Task: What is the ten thousands digit of 71227120? Calculation: 2 Task: What is the thousands digit of 290393? Calculation: 0 Task: What is the thousands digit of 4373338265? Calculation: 8 Task: What is the tens digit of 259? Calculation: 5 Task: What is the thousands digit of 57184? Calculation: 7 Task: What is the tens digit of 49341? Calculation: 4 Task: What is the millions digit of 28753386? Calculation: 8 Task: What is the ten millions digit of 11442544? Calculation: 1 Task: What is the units digit of 2442530? Calculation: 0 Task: What is the thousands digit of 11264? Calculation: 1 Task: What is the hundreds digit of 429107? Calculation: 1 Task: What is the units digit of 3537538843? Calculation: 3 Task: What is the millions digit of 222240766? Calculation: 2 Task: What is the ten thousands digit of 496180? Calculation: 9 Task: What is the ten millions digit of 12550956? Calculation: 1 Task: What is the ten thousands digit of 58606? Calculation: 5 Task: What is the hundreds digit of 70464? Calculation: 4 Task: What is the tens digit of 4534333? Calculation: 3 Task: What is the hundred thousands digit of 311387652? Calculation: 3 Task: What is the ten thousands digit of 276632373? Calculation: 3 Task: What is the hundreds digit of 16594? Calculation: 5 Task: What is the hundred thousands digit of 35456700? Calculation: 4 Task: What is the thousands digit of 30992269? Calculation: 2 Task: What is the hundred thousands digit of 23515003? Calculation: 5 Task: What is the thousands digit of 11946? Calculation: 1 Task: What is the thousands digit of 1797444? Calculation: 7 Task: What is the ten thousands digit of 92633? Calcu
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arithmetic: nearest integer root -------------------------------- Request: What is 3235929 to the power of 1/9, to the nearest integer? Conclusion: 5 Request: What is 549466 to the power of 1/2, to the nearest integer? Conclusion: 741 Request: What is the fifth root of 296019433 to the nearest integer? Conclusion: 49 Request: What is 11437 to the power of 1/2, to the nearest integer? Conclusion: 107 Request: What is the square root of 855092 to the nearest integer? Conclusion: 925 Request: What is 42217634 to the power of 1/5, to the nearest integer? Conclusion: 34 Request: What is 224764 to the power of 1/5, to the nearest integer? Conclusion: 12 Request: What is the ninth root of 152239814 to the nearest integer? Conclusion: 8 Request: What is 2776 to the power of 1/10, to the nearest integer? Conclusion: 2 Request: What is 538735145 to the power of 1/10, to the nearest integer? Conclusion: 7 Request: What is the tenth root of 1598612714 to the nearest integer? Conclusion: 8 Request: What is 5465 to the power of 1/4, to the nearest integer? Conclusion: 9 Request: What is the square root of 839742 to the nearest integer? Conclusion: 916 Request: What is 616 to the power of 1/6, to the nearest integer? Conclusion: 3 Request: What is the eighth root of 1180 to the nearest integer? Conclusion: 2 Request: What is the square root of 1271011468 to the nearest integer? Conclusion: 35651 Request: What is the fifth root of 26874475 to the nearest integer? Conclusion: 31 Request: What is 3826792807 to the power of 1/3, to the nearest integer? Conclusion: 1564 Request: What is the ninth root of 11517 to the nearest integer? Conclusion: 3 Request: What is the square root of 31213 to the nearest integer? Conclusion: 177 Request: What is 5650 to the power of 1/8, to the nearest integer? Conclusion: 3 Request: What is 1165 to the power of 1/7, to the nearest integer? Conclusion: 3 Request: What is the square root of 3159241736 to the nearest integer? Conclusion: 56207 Request: Wh
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probability: swr p level set ---------------------------- Part A: Calculate prob of picking 2 d and 2 l when four letters picked without replacement from {x: 1, l: 4, d: 5, q: 1}. Response: 2/11 Part A: Calculate prob of picking 4 w when four letters picked without replacement from {w: 11, s: 1}. Response: 2/3 Part A: Three letters picked without replacement from cctzwqw. Give prob of picking 1 c, 1 w, and 1 q. Response: 4/35 Part A: Calculate prob of picking 1 w, 2 j, and 1 m when four letters picked without replacement from jcwjjcjjmajmjj. Response: 8/143 Part A: Four letters picked without replacement from ruurxuuuxuuxxuuu. What is prob of picking 1 x, 2 u, and 1 r? Response: 18/91 Part A: Two letters picked without replacement from {j: 2, z: 4, i: 2}. What is prob of picking 1 j and 1 z? Response: 2/7 Part A: Calculate prob of picking 1 p and 2 c when three letters picked without replacement from ucpcwwupwwcc. Response: 3/55 Part A: What is prob of picking 2 u when two letters picked without replacement from {c: 4, u: 5, j: 1}? Response: 2/9 Part A: Two letters picked without replacement from yykkykk. What is prob of picking 1 k and 1 y? Response: 4/7 Part A: Calculate prob of picking 2 s when two letters picked without replacement from {z: 1, m: 2, s: 3, c: 6, b: 4, v: 2}. Response: 1/51 Part A: What is prob of picking 2 g when two letters picked without replacement from cgggcgc? Response: 2/7 Part A: Three letters picked without replacement from mnnmmn. Give prob of picking 2 m and 1 n. Response: 9/20 Part A: Three letters picked without replacement from wwwuwwwwwewwwwww. Give prob of picking 2 w and 1 e. Response: 13/80 Part A: Three letters picked without replacement from mrwicwmrnimmm. What is prob of picking 1 r, 1 n, and 1 w? Response: 2/143 Part A: What is prob of picking 2 h when two letters picked without replacement from {h: 7, y: 1}? Response: 3/4 Part A: Calculate prob of picking 1 h and 1 r when two letters picked without replacement from {d: 1, r:
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probability: swr p sequence --------------------------- What if: What is prob of sequence unnz when four letters picked without replacement from unnuuuz? A: 1/105 What if: Four letters picked without replacement from fhmppdphfffhhppppd. What is prob of sequence mpdf? A: 7/9180 What if: Three letters picked without replacement from {i: 7, u: 5, e: 7}. What is prob of sequence iee? A: 49/969 What if: What is prob of sequence nyt when three letters picked without replacement from {n: 1, y: 1, t: 2}? A: 1/12 What if: Two letters picked without replacement from {u: 1, v: 2, l: 5, s: 1, d: 2, q: 4}. What is prob of sequence vd? A: 2/105 What if: Two letters picked without replacement from ogttogtggggrgttoto. Give prob of sequence ro. A: 2/153 What if: Calculate prob of sequence vl when two letters picked without replacement from {i: 8, v: 2, l: 2, u: 4}. A: 1/60 What if: What is prob of sequence ni when two letters picked without replacement from nziiinziiziin? A: 7/52 What if: Four letters picked without replacement from yyyyyiiyyyyiyyyy. What is prob of sequence iyiy? A: 3/140 What if: Four letters picked without replacement from {g: 4, a: 8, v: 5}. What is prob of sequence gagv? A: 1/119 What if: Three letters picked without replacement from {o: 1, h: 1, p: 1}. What is prob of sequence ohh? A: 0 What if: Three letters picked without replacement from {e: 1, y: 3, w: 2, g: 4, c: 2}. Give prob of sequence eec. A: 0 What if: Two letters picked without replacement from {t: 4, m: 1, l: 1, p: 4, y: 5}. What is prob of sequence py? A: 2/21 What if: Calculate prob of sequence oo when two letters picked without replacement from otoooootto. A: 7/15 What if: Calculate prob of sequence df when two letters picked without replacement from fyywdeywyywfwwwfywy. A: 1/114 What if: Two letters picked without replacement from ckicscyscssicfcciyci. What is prob of sequence yf? A: 1/190 What if: Calculate prob of sequence aj when two letters picked without replacement from cccjccawacfcclal.
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numbers: is prime ----------------- What if: Is 21677 composite? Result: True What if: Is 336481 a prime number? Result: False What if: Is 53137273 prime? Result: False What if: Is 10055 a composite number? Result: True What if: Is 212285 composite? Result: True What if: Is 993 composite? Result: True What if: Is 3895091653 a composite number? Result: True What if: Is 1787921 composite? Result: True What if: Is 1852879 composite? Result: True What if: Is 3557 a prime number? Result: True What if: Is 678367 prime? Result: True What if: Is 21727451 composite? Result: False What if: Is 62141570063 a composite number? Result: False What if: Is 92269 prime? Result: True What if: Is 236393 prime? Result: False What if: Is 10994612753 a prime number? Result: True What if: Is 12005677 prime? Result: False What if: Is 15823 prime? Result: True What if: Is 8955881497 composite? Result: False What if: Is 2419661261 prime? Result: False What if: Is 27871783189 a composite number? Result: False What if: Is 479 composite? Result: False What if: Is 46343441 prime? Result: True What if: Is 148302058 composite? Result: True What if: Is 931161289 composite? Result: False What if: Is 8538407603 prime? Result: False What if: Is 470021 composite? Result: False What if: Is 7863143 a composite number? Result: False What if: Is 47191 composite? Result: True What if: Is 165441 a prime number? Result: False What if: Is 32710523491 a composite number? Result: True What if: Is 9382 a prime number? Result: False What if: Is 15124939 prime? Result: True What if: Is 11162445691 a composite number? Result: False What if: Is 120019 a prime number? Result: False What if: Is 811099 a composite number? Result: False What if: Is 4874629547 prime? Result: True What if: Is 32740361 composite? Result: False What if: Is 248315 a prime number? Result: False What if: Is 1170194651 composite? Result: False What if: Is 54493013 a prime number? Result: False What if: Is 2584902891 a prime number? Result: False
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numbers: place value -------------------- Request: What is the hundred thousands digit of 110421? Workthrough: 1 Request: What is the hundred thousands digit of 869030? Workthrough: 8 Request: What is the millions digit of 5401603263? Workthrough: 1 Request: What is the hundred thousands digit of 9497306? Workthrough: 4 Request: What is the hundred thousands digit of 659396648? Workthrough: 3 Request: What is the thousands digit of 677871? Workthrough: 7 Request: What is the hundred thousands digit of 21217908? Workthrough: 2 Request: What is the thousands digit of 2702? Workthrough: 2 Request: What is the units digit of 18110? Workthrough: 0 Request: What is the units digit of 1703362? Workthrough: 2 Request: What is the units digit of 51967? Workthrough: 7 Request: What is the hundreds digit of 203719? Workthrough: 7 Request: What is the units digit of 865665786? Workthrough: 6 Request: What is the tens digit of 2381? Workthrough: 8 Request: What is the millions digit of 1922922? Workthrough: 1 Request: What is the hundreds digit of 3866250702? Workthrough: 7 Request: What is the units digit of 23804313? Workthrough: 3 Request: What is the units digit of 896724273? Workthrough: 3 Request: What is the tens digit of 198? Workthrough: 9 Request: What is the ten millions digit of 1911506474? Workthrough: 1 Request: What is the hundreds digit of 16255? Workthrough: 2 Request: What is the ten millions digit of 13641440? Workthrough: 1 Request: What is the ten thousands digit of 156203039? Workthrough: 0 Request: What is the thousands digit of 296187? Workthrough: 6 Request: What is the units digit of 5979? Workthrough: 9 Request: What is the ten thousands digit of 105183387? Workthrough: 8 Request: What is the thousands digit of 120832? Workthrough: 0 Request: What is the ten thousands digit of 684594? Workthrough: 8 Request: What is the tens digit of 2482? Workthrough: 8 Request: What is the tens digit of 15758? Workthrough: 5 Request: What is the hundred millions digi
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measurement: conversion ----------------------- Situation: What is 601878.5cm in millimeters? A: 6018785 Situation: What is 7/4 of a kilometer in meters? A: 1750 Situation: What is 3/8 of a litre in millilitres? A: 375 Situation: What is 1.55208 kilograms in grams? A: 1552.08 Situation: What is seven halves of a micrometer in nanometers? A: 3500 Situation: How many micrograms are there in seven eighths of a milligram? A: 875 Situation: How many millilitres are there in thirteen quarters of a litre? A: 3250 Situation: What is 553.908 milligrams in kilograms? A: 0.000553908 Situation: What is 19/4 of a litre in millilitres? A: 4750 Situation: How many grams are there in twenty-one fifths of a kilogram? A: 4200 Situation: What is 4/15 of a decade in months? A: 32 Situation: What is seventeen quarters of a meter in millimeters? A: 4250 Situation: What is 21/8 of a litre in millilitres? A: 2625 Situation: What is 5739.428l in millilitres? A: 5739428 Situation: Convert 2.383078us to seconds. A: 0.000002383078 Situation: How many millilitres are there in 64/5 of a litre? A: 12800 Situation: What is 79265.52 micrometers in centimeters? A: 7.926552 Situation: Convert 1392905.7s to hours. A: 386.91825 Situation: What is 0.7238455 litres in millilitres? A: 723.8455 Situation: Convert 69.8957 weeks to nanoseconds. A: 42272919360000000 Situation: Convert 80518.49um to millimeters. A: 80.51849 Situation: Convert 27.9977 litres to millilitres. A: 27997.7 Situation: Convert 74.75556 millimeters to meters. A: 0.07475556 Situation: Convert 0.3647554m to kilometers. A: 0.0003647554 Situation: How many nanometers are there in 3488.9m? A: 3488900000000 Situation: Convert 3.344858s to microseconds. A: 3344858 Situation: What is fifty-one fifths of a litre in millilitres? A: 10200 Situation: How many weeks are there in 159453422.1 seconds? A: 263.64653125 Situation: How many millilitres are there in 25/4 of a litre? A: 6250 Situation: How many weeks are there in 1812.287736 seconds? A: 0.
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probability: swr p level set ---------------------------- Q-: Four letters picked without replacement from {h: 4, s: 1, u: 2, b: 1}. Give prob of picking 1 h, 1 s, and 2 u. Solution: 2/35 Q-: Two letters picked without replacement from {f: 2, b: 11}. Give prob of picking 2 b. Solution: 55/78 Q-: Three letters picked without replacement from {u: 2, r: 1, p: 1, n: 1, z: 1, g: 1}. What is prob of picking 2 u and 1 n? Solution: 1/35 Q-: Three letters picked without replacement from vaavemaaa. What is prob of picking 2 v and 1 e? Solution: 1/84 Q-: Calculate prob of picking 1 a and 1 u when two letters picked without replacement from {y: 3, g: 3, q: 1, a: 1, b: 5, u: 6}. Solution: 2/57 Q-: What is prob of picking 1 v and 2 q when three letters picked without replacement from qjvqjqvjjqqq? Solution: 3/22 Q-: Calculate prob of picking 2 i when two letters picked without replacement from iqqiqi. Solution: 1/5 Q-: Two letters picked without replacement from {u: 2, y: 1, b: 1, p: 2, w: 1}. What is prob of picking 1 y and 1 p? Solution: 2/21 Q-: Calculate prob of picking 1 n and 1 d when two letters picked without replacement from {n: 7, d: 3}. Solution: 7/15 Q-: Three letters picked without replacement from vzvzzlzlszzzszvzszv. Give prob of picking 2 l and 1 z. Solution: 10/969 Q-: Calculate prob of picking 3 u and 1 x when four letters picked without replacement from {u: 6, x: 6}. Solution: 8/33 Q-: Two letters picked without replacement from {l: 2, q: 2, a: 2, w: 2, k: 1, i: 3}. Give prob of picking 1 l and 1 a. Solution: 2/33 Q-: What is prob of picking 3 k and 1 e when four letters picked without replacement from {e: 14, k: 4}? Solution: 14/765 Q-: Four letters picked without replacement from {s: 1, z: 3, u: 1, p: 5, o: 1, b: 1}. Give prob of picking 1 u, 1 p, and 2 z. Solution: 1/33 Q-: Calculate prob of picking 2 m when two letters picked without replacement from mmmmmbbmbihhyiymmyy. Solution: 28/171 Q-: Two letters picked without replacement from ruuruuuuuuruuuruuuu. G
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measurement: time ----------------- Case: How many minutes are there between 12:56 PM and 12:24 AM? A: 688 Case: What is 605 minutes before 2:11 PM? A: 4:06 AM Case: How many minutes are there between 12:53 AM and 2:48 AM? A: 115 Case: How many minutes are there between 4:26 PM and 5:25 PM? A: 59 Case: How many minutes are there between 8:09 AM and 3:37 PM? A: 448 Case: How many minutes are there between 12:36 PM and 10:43 PM? A: 607 Case: What is 462 minutes after 10:49 PM? A: 6:31 AM Case: How many minutes are there between 5:32 PM and 9:47 PM? A: 255 Case: What is 573 minutes before 5:22 PM? A: 7:49 AM Case: What is 240 minutes after 8:26 PM? A: 12:26 AM Case: What is 524 minutes before 6:40 PM? A: 9:56 AM Case: How many minutes are there between 9:42 PM and 9:52 PM? A: 10 Case: How many minutes are there between 8:55 PM and 7:59 AM? A: 664 Case: How many minutes are there between 4:45 AM and 6:42 AM? A: 117 Case: What is 324 minutes before 4:42 PM? A: 11:18 AM Case: What is 44 minutes before 5:23 PM? A: 4:39 PM Case: How many minutes are there between 12:57 AM and 6:06 AM? A: 309 Case: How many minutes are there between 9:26 AM and 10:14 AM? A: 48 Case: How many minutes are there between 8:22 PM and 4:23 AM? A: 481 Case: How many minutes are there between 7:14 AM and 6:57 PM? A: 703 Case: What is 405 minutes after 5:06 AM? A: 11:51 AM Case: How many minutes are there between 8:29 PM and 11:24 PM? A: 175 Case: What is 90 minutes before 9:23 PM? A: 7:53 PM Case: What is 98 minutes after 1:40 PM? A: 3:18 PM Case: What is 296 minutes after 7:39 PM? A: 12:35 AM Case: What is 708 minutes before 8:28 PM? A: 8:40 AM Case: How many minutes are there between 7:12 AM and 6:17 PM? A: 665 Case: How many minutes are there between 1:37 AM and 7:00 AM? A: 323 Case: How many minutes are there between 11:58 AM and 10:26 PM? A: 628 Case: How many minutes are there between 10:03 PM and 5:49 AM? A: 466 Case: What is 573 minutes after 6:47 AM? A: 4:20 PM Case: How many minutes are th
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