kreasof-ai/SPL-100K-finemath · Datasets at Hugging Face

text stringlengths 420 3.71k	corrupted_text stringlengths 420 3.71k	input_ids sequencelengths 2.05k 2.05k	attention_mask sequencelengths 2.05k 2.05k	labels sequencelengths 2.05k 2.05k
[CLS]# Five numbers have an average of 90. Four of the numbers are 87, 93, 89, and 85. What is the remaining number? Jan 19, 2017 Remaining number is $96$ #### Explanation: Average of given set of numbers is their sum divided by their count. Here we have five numbers and as their average is $90$, their sum must be $5 \times 90 = 450$ Bur four of them add up to $87 + 93 + 89 + 85 = 354$ Hence, remaining number is $450 - 354 = 96$[SEP]	[CLS]# favor numbers have an average found 90. Four of the numbers are 87, 93, 96, and 85... What is the remaining number? – 19, 2017 Circle Remaining number is $75$ #### existsplanation: pattern of given set of numbers is whether sum divided by their countby Here we have five numbers and as their average > $90$, their sum must be }$5 \times 90 = 450 25 Bur four of them � struggle Te $71 (- 93 *. 89 + 85 = 354$ ocHence, remaining number is >450 - min = 96$[SEP]	[ 50281, 4, 3718, 3904, 452, 271, 3388, 1119, 5091, 15, 7874, 273, 253, 3904, 403, 11422, 13, 11456, 13, 9161, 13, 285, 9330, 1051, 1737, 310, 253, 5780, 1180, 32, 187, 187, 1108, 655, 13, 4240, 29572, 187, 8494, 1776, 1180, 310, 370, 1976, 5, 187, 187, 1835, 4961, 45525, 27, 187, 187, 3102, 273, 1677, 873, 273, 3904, 310, 1880, 2020, 4272, 407, 616, 1385, 1615, 187, 187, 4943, 359, 452, 2620, 3904, 285, 347, 616, 3388, 2239, 370, 2270, 1366, 187, 187, 14094, 2020, 1364, 320, 27324, 22, 393, 3181, 5091, 426, 20156, 2030, 187, 187, 21784, 1740, 273, 731, 3384, 11182, 2745, 370, 3677, 3383, 11456, 33481, 11289, 559, 9330, 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[CLS]Question 10 # A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted? Solution Total number of cubes will be = $$\frac{12 \times 12 \times 12}{3 \times 3 \times 3}$$ = 64 Cubes with 3 sides painted = cubes at corner sides = 8 Cubes with 2 sides painted = cubes on lines = 24 Cubes with 1 sides painted = cubes on middle of surface = 24 So cubes with no side painted = 64 - (8+24+24) = 8[SEP]	[CLS]Question 10 # A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted? Solution Total number of cubes will be = $$\frac{12 \times 12 \times 12}{3 \times 3 \times 3}$$ = 64 Cubes with 3 sides painted = cubes at corner sides = 8 Cubes with 2 sides painted = cubes on lines = 24 Cubes with 1 sides painted = cubes on middle of surface = 24 So cubes with no side painted = 64 - (8+24+24) = 8[SEP]	[ 50281, 23433, 884, 187, 187, 4, 329, 23636, 273, 1930, 1249, 7892, 310, 16264, 2502, 327, 512, 253, 9365, 285, 840, 2624, 715, 4577, 37072, 13, 1016, 273, 1930, 495, 7892, 15, 1737, 310, 253, 2264, 1180, 273, 4577, 37072, 1907, 5293, 273, 616, 9365, 16264, 32, 187, 187, 37533, 187, 187, 12481, 1180, 273, 37072, 588, 320, 426, 1764, 1124, 92, 805, 393, 3181, 1249, 393, 3181, 1249, 1217, 20, 393, 3181, 495, 393, 3181, 495, 2138, 426, 6705, 187, 36, 31571, 342, 495, 7123, 16264, 426, 37072, 387, 7145, 7123, 426, 854, 187, 36, 31571, 342, 374, 7123, 16264, 426, 37072, 327, 3104, 426, 2164, 187, 36, 31571, 342, 337, 7123, 16264, 426, 37072, 327, 4766, 273, 2553, 426, 2164, 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[CLS]# How do you solve 8-2x is greater than or equal to -4? ## When are you supposed to flip the greater than or equal to sign? ##### 1 Answer Mar 31, 2018 $x \le 6$ #### Explanation: $8 - 2 x \ge - 4$ is our equation To solve for the inequality you do it normally like you would for an equation, although if you multiply or divide by a negative number you flip the inequality $- 2 x \ge - 12$ Now we have to divide both sides by $- 2$ so we will flip the inequality $x \le 6$[SEP]	[CLS]# How do you solve 8Are2x -- grap thanro equal to -4? CC## John are you showed toips the greater than throughout equal to sort? ##### 1 Answer Mar 31, 2018 scientific $x \\le 6$ #### Explanation: CircCom8 - 2 x \geG 4$ Ide offer equation To solving for the inequality you do it normally like you would for an equation, although ifYou multiply or AND by a negative number you family the integrate locus 150 ` x \ge � 12cal conNext Definition give to divide both son by $- 2$ so we will flip the inequality $ X \le Ask[SEP]	[ 50281, 4, 1359, 513, 368, 8415, 854, 6723, 19, 89, 1969, 17309, 685, 287, 4503, 281, 428, 21, 32, 187, 2648, 817, 2516, 403, 368, 2692, 281, 2824, 253, 3687, 685, 4768, 4503, 281, 3686, 32, 187, 187, 22002, 337, 37741, 187, 9709, 4562, 13, 4765, 8249, 187, 5, 89, 3202, 282, 721, 5, 187, 187, 1835, 1889, 45525, 27, 187, 5819, 2115, 25, 428, 374, 1269, 393, 463, 40, 577, 5, 17315, 3959, 5150, 187, 187, 1992, 16161, 323, 253, 11370, 368, 513, 352, 9403, 751, 368, 651, 323, 271, 5150, 13, 3738, 604, 1394, 30247, 390, 4889, 407, 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[CLS]# Beth has $900 in the bank. Every time she rides the bus she spends$2. How do you write an inequality that Beth can use to see how many times she can ride the bus and still have more than $500 in the bank? ##### 1 Answer This is the answer for (b) bus rides she takes. $500 < 900 - 2 b$#### Explanation: $500 < 900 - 2 b$$500 - 900 < - 2 b$$- 400 < - 2 b$$\frac{- 400}{- 2} > b$We reverse the signs above because we are dividing by a negative number. $200 > b\$ She can take less than 200(a lot of) bus rides.[SEP]	[CLS]# Beth has $900 in the bank. Every time she rides the bus step spends$-. How do you write apart Inter that Beth can use to see how many technology she bracket ride the bus and still have more than $150 in t bank? ##### 1 Answer taught identities the An for GoBC) bus rides such takes. $500 < 900 - 2 b$#### Explanation: -500 < 9 - 2 b$$500 - 900 < - 2 bapprox- 400 < - 2 b$$\frac{- 400}{- 2} > b$We represent the signs above because we are dividing by a negative number. $200 > b $$ She can taken less than 200(a lot of) bus rides.[SEP]	[ 50281, 4, 22169, 556, 370, 18104, 275, 253, 4310, 15, 6000, 673, 703, 28742, 253, 1685, 3213, 30885, 5, 14, 15, 1359, 513, 368, 3630, 7419, 5383, 326, 22169, 476, 897, 281, 923, 849, 1142, 4302, 703, 24312, 9549, 253, 1685, 285, 1335, 452, 625, 685, 370, 8970, 275, 246, 4310, 32, 209, 22002, 337, 37741, 10256, 22925, 253, 743, 323, 3617, 3979, 10, 1685, 28742, 824, 3936, 15, 370, 5388, 654, 22908, 428, 374, 270, 5, 1835, 1889, 45525, 27, 428, 5388, 654, 898, 428, 374, 270, 1890, 5388, 428, 22908, 654, 428, 374, 270, 9887, 14, 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[CLS]# How do you find the GCF of 24 and 42? Jan 9, 2017 $6$ #### Explanation: The Greatest Common Factor is the highest number that can be used to divide the two given numbers. It is easily found by writing down the factors of the two numbers and selecting the common one(s) which are the highest. In the given examples, the factors of the two numbers are as follows: $24 : 2 , 2 , 2 , 3$ $42 : 2 , 3 , 7$ Since there are two numbers common between the two sets of factors, the GCF is: $2 \times 3 = 6$[SEP]	[CLS]# How do you find the GCF of 24 and 42? Jan 9, 2017 $6$ #### Explanation: The Greatest Common Factor is That highest Remember that can be used to divide the two given numbers. It is easily found by writing down test factors of the two impossible and selecting the common one(s) which are the highest. In the given examples, the factors of the T numbers are as follows: $24 : 2 , 2 , 2 , 3$ $42 : 2 gave 3 , $\$ Since there are two numbers common between the two sets finally factors.” the GCF is: $2 \times 3 = 6$[SEP]	[ 50281, 4, 1359, 513, 368, 1089, 253, 443, 7386, 273, 2164, 285, 5976, 32, 187, 187, 14060, 898, 13, 4240, 187, 187, 5, 23, 5, 187, 187, 1835, 1889, 45525, 27, 187, 187, 510, 6495, 383, 10200, 16090, 310, 2064, 4585, 18741, 326, 476, 320, 908, 281, 10957, 253, 767, 1677, 3904, 15, 733, 310, 4354, 1119, 407, 4028, 1066, 1071, 2616, 273, 253, 767, 7479, 285, 17221, 253, 1846, 581, 9, 84, 10, 534, 403, 253, 4585, 15, 187, 187, 688, 253, 1677, 6667, 13, 253, 2616, 273, 253, 308, 3904, 403, 347, 3637, 27, 187, 187, 5, 1348, 1163, 374, 1157, 374, 1157, 374, 1157, 495, 5, 187, 187, 5, 2945, 1163, 374, 3534, 495, 1157, 669, 5, 187, 187, 7542, 627, 403, 767, 3904, 1846, 875, 253, 767, 5239, 4720, 2616, 1425, 253, 443, 7386, 310, 27, 187, 187, 5, 19, 393, 3181, 495, 426, 721, 5, 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[CLS]# How do you solve 7x = 2x + 15? Jun 2, 2017 $x = 3$ #### Explanation: $7 x = 2 x + 15$ We can move $2 x$ to the other side, changing it from positive to negative. $7 x - 2 x = 15$ $5 x = 15$ Now we can work backwards. The last thing that happened to $x$ is that it was multiplied by $5$ to get to $15$, so in working backwards, we will do the opposite to $15$ to get $x$. x= 15 ÷ 5 color(blue)(x = 3[SEP]	[CLS]# How do you solve 7x = 2x + 15? Jun 2, 2017 $x = 3$ #### Explanation: $7 x = 2 x + 15$ We can move $2 x$ to the other side, changing it from positive to negative. $7 x - 2 x = 15$ $5 x = 15$ Now we can work backwards. The last thing that happened to $x$ is that it was multiplied by $5$ to get to $15$, so in working backwards, we will do the opposite to $15$ to get $x$. x= 15 ÷ 5 color(blue)(x = 3[SEP]	[ 50281, 4, 1359, 513, 368, 8415, 818, 89, 426, 374, 89, 559, 1458, 32, 187, 187, 29627, 374, 13, 4240, 187, 187, 5, 89, 426, 495, 5, 187, 187, 1835, 1889, 45525, 27, 187, 187, 5, 24, 1269, 426, 374, 1269, 559, 1458, 5, 187, 187, 1231, 476, 2118, 370, 19, 1269, 5, 281, 253, 643, 1930, 13, 6890, 352, 432, 2762, 281, 4016, 15, 187, 187, 5, 24, 1269, 428, 374, 1269, 426, 1458, 5, 187, 187, 5, 22, 1269, 426, 1458, 5, 187, 187, 4125, 359, 476, 789, 24291, 15, 380, 1390, 2181, 326, 4592, 281, 370, 89, 5, 310, 326, 352, 369, 31458, 407, 370, 22, 5, 281, 755, 281, 370, 1010, 1366, 594, 275, 2444, 24291, 13, 359, 588, 513, 253, 7285, 281, 370, 1010, 5, 281, 755, 370, 89, 1352, 187, 187, 89, 30, 1458, 1325, 117, 608, 187, 187, 4897, 9, 11863, 2769, 89, 426, 495, 50282, 50283, 50283, 50283, 50283, 50283, 50283, 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[CLS]Stella makes 2% royalties on a book she wrote. How much money did her book earn in sales last year if she made $53,000 in royalties? 1 Answer S=($53000)/.02=$2,650,000 Explanation: We can take the book sales ($S$), multiply it by the royalty percentage (%), and see how much she makes in royalties ($R$): S xx % = R Now let's substitute in what we know: S xx 2% =$53,000 To find $S$ (book sales) we now divide both sides by 2% (which is the same as 0.02): S=($53000)/.02=$2,650,000[SEP]	[CLS] Scienceella makes 2% royFind on a BY she wrote. How much Me divides her book earn in sales last ban if she mar $ 42,000 in royalties-( Be annual S=($53000)/,-02=$2.,650Of)} Explanation: We can take THE book sales ($S$), biggest it by the royalty percentage (%), and see how man she makes infinitely royalties ($R $): Same xx %=- R Now let's signs in what we know* S xx 2 Greek =)$14,000 To find $S95 (book sales) we now dividend both sides buy ($ variance (which is the Side as 150or02): ____=($53000)/.02=$2,650OR000[SEP]	[ 50281, 6875, 5021, 2789, 374, 6, 12869, 9867, 327, 247, 9149, 703, 4159, 15, 1359, 1199, 3189, 37141, 617, 1984, 6233, 275, 6224, 1390, 8913, 604, 703, 2304, 370, 5976, 13, 933, 275, 12869, 17511, 8422, 2325, 7970, 322, 30, 3914, 3357, 933, 1933, 6567, 2640, 18340, 19, 904, 31036, 4527, 3117, 1889, 45525, 27, 844, 476, 1379, 3003, 1984, 6224, 4816, 52, 17673, 5962, 352, 407, 253, 37283, 7155, 313, 9498, 285, 923, 849, 637, 703, 2789, 29556, 12869, 17511, 4816, 51, 370, 2262, 26197, 35564, 2462, 11468, 416, 3954, 1339, 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[CLS]# Mary sold half of her comic books and then bought 8 more. she now has 18. how many did she begin with? May 24, 2018 #### Explanation: If she bought 8 more and in total she have 18 before she buy those 8 books she had 10 so $10 \cdot 2 = 20$ because she sold half of her books that means she had double the amount of 10. May 24, 2018 20 #### Explanation: Work backwards from the final count. Final count $\to 18$ This was after adding eight more $18 - 8 = 10$ This was after selling half the original amount original amount $\to 2 \times 10 = 20$[SEP]	[CLS]# Mary sold half of her comic books and then bought 8 more.... s now has 18 once how mar did she begin with? May 110, 2018 IC#### Equplanation: specificIf she bought 8 more and in total she have 18 before st buy those 8 B she had 0 so _ 101 \cdot 2 = 20$ because she sur half of her books that means sum had double the amount of 10. May 24, 2018 circle 2017GC Cl#### Explement: Work backwards from the followed count. Final purchase $\to 18 97 This was after adding eight more $18 - 8 = 10$ This was after selling half the original amount om amount $\to 2 \times 10 = 20$[SEP]	[ 50281, 4, 6393, 4211, 2716, 273, 617, 17478, 5098, 285, 840, 8686, 854, 625, 2391, 256, 1024, 556, 1283, 2378, 849, 2304, 858, 703, 3135, 342, 32, 187, 187, 6791, 9199, 13, 4765, 187, 1864, 1835, 8721, 45525, 27, 187, 2173, 2042, 703, 8686, 854, 625, 285, 275, 2264, 703, 452, 1283, 1078, 331, 4489, 1110, 854, 378, 703, 574, 470, 594, 795, 8437, 393, 3830, 374, 426, 1384, 5, 984, 703, 919, 2716, 273, 617, 5098, 326, 2097, 2020, 574, 4021, 253, 2408, 273, 884, 15, 187, 187, 6791, 2164, 13, 4765, 9096, 187, 4240, 7258, 1639, 1835, 1889, 3018, 27, 187, 187, 10282, 24291, 432, 253, 3560, 1385, 15, 187, 187, 21747, 7471, 669, 936, 1283, 10694, 187, 187, 1552, 369, 846, 6240, 4314, 625, 370, 1093, 428, 854, 426, 884, 5, 187, 187, 1552, 369, 846, 10156, 2716, 253, 3236, 2408, 187, 187, 297, 2408, 669, 936, 374, 393, 3181, 884, 426, 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[CLS]# How do you simplify 65 + -5? Jan 30, 2016 $65 - 5 = 60$ #### Explanation: re white as $\left(65\right) + \left(- 5\right)$ The plus sign can be considers as the action 'Put with then count' from where you are on the number line towards the right. (+ve direction). The minus sign can be considered as 'change direction of count' So the + is first telling you to count to the right on the number line. The we have the minus which is saying "now change the direction of count on the number line. Put all this together and you end up with: $65 - 5 = 60$[SEP]	[CLS]# How do you simplify 65 + -5? Jan 30, 2016 $65 - 5 = 60$ #### Explanation: re white as $\left(65\right) + \left(- 5\right)$ The plus sign can be considers as the action 'Put with then count' from where you are on the number line towards the right. (+ve direction). The minus sign can be considered as 'change direction of count' So the + is first telling you to count to the right on the number line. The we have the minus which is saying "now change the direction of count on the number line. Put all this together and you end up with: $65 - 5 = 60$[SEP]	[ 50281, 4, 1359, 513, 368, 25636, 7251, 559, 428, 22, 32, 187, 187, 14060, 1884, 13, 4022, 187, 187, 5, 2082, 428, 608, 426, 3925, 5, 187, 187, 1835, 1889, 45525, 27, 187, 187, 250, 3168, 347, 669, 1274, 9, 2082, 61, 918, 10, 559, 393, 1274, 1490, 608, 61, 918, 1009, 187, 187, 510, 5043, 861, 476, 320, 19401, 347, 253, 2250, 686, 12501, 342, 840, 1385, 8, 432, 835, 368, 403, 327, 253, 1180, 1386, 4404, 253, 987, 15, 21757, 306, 3884, 481, 187, 187, 510, 19734, 861, 476, 320, 2783, 347, 686, 4168, 3884, 273, 1385, 8, 187, 187, 2598, 253, 559, 310, 806, 7746, 368, 281, 1385, 281, 253, 987, 327, 253, 1180, 1386, 15, 187, 510, 359, 452, 253, 19734, 534, 310, 3981, 346, 2666, 1818, 253, 3884, 273, 1385, 327, 253, 1180, 1386, 15, 187, 187, 12501, 512, 436, 2366, 285, 368, 990, 598, 342, 27, 187, 187, 5, 2082, 428, 608, 426, 3925, 5, 50282, 50283, 50283, 50283, 50283, 50283, 50283, 50283, 50283, 50283, 50283, 50283, 50283, 50283, 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"[CLS]# The sum of two times a number and 5 is 45 what is the number?\n\nNov 21, 2016\n\n20\n\n#### (...TRUNCATED)	"[CLS]# The sum of two times a number and 5 � 45 what is the number?\n\nNov 21, 2016 reciproc\n20\(...TRUNCATED)	[50281,4,380,2020,273,767,2069,247,1180,285,608,1454,5329,752,310,253,1180,32,187,187,27303,3127,13,(...TRUNCATED)	[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED)	[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0(...TRUNCATED)

[CLS]# Five numbers have an average of 90. Four of the numbers are 87, 93, 89, and 85. What is the remaining number? Jan 19, 2017 Remaining number is $96$ #### Explanation: Average of given set of numbers is their sum divided by their count. Here we have five numbers and as their average is $90$, their sum must be $5 \times 90 = 450$ Bur four of them add up to $87 + 93 + 89 + 85 = 354$ Hence, remaining number is $450 - 354 = 96$[SEP]

[CLS]# favor numbers have an average found 90. Four of the numbers are 87, 93, 96, and 85... What is the remaining number? – 19, 2017 Circle Remaining number is $75$ #### existsplanation: pattern of given set of numbers is whether sum divided by their countby Here we have five numbers and as their average > $90$, their sum must be }$5 \times 90 = 450 25 Bur four of them � struggle Te $71 (- 93 *. 89 + 85 = 354$ ocHence, remaining number is >450 - min = 96$[SEP]

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[CLS]Question 10 # A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted? Solution Total number of cubes will be = $$\frac{12 \times 12 \times 12}{3 \times 3 \times 3}$$ = 64 Cubes with 3 sides painted = cubes at corner sides = 8 Cubes with 2 sides painted = cubes on lines = 24 Cubes with 1 sides painted = cubes on middle of surface = 24 So cubes with no side painted = 64 - (8+24+24) = 8[SEP]

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[CLS]# How do you solve 8-2x is greater than or equal to -4? ## When are you supposed to flip the greater than or equal to sign? ##### 1 Answer Mar 31, 2018 $x \le 6$ #### Explanation: $8 - 2 x \ge - 4$ is our equation To solve for the inequality you do it normally like you would for an equation, although if you multiply or divide by a negative number you flip the inequality $- 2 x \ge - 12$ Now we have to divide both sides by $- 2$ so we will flip the inequality $x \le 6$[SEP]

[CLS]# How do you solve 8Are2x -- grap thanro equal to -4? CC## John are you showed toips the greater than throughout equal to sort? ##### 1 Answer Mar 31, 2018 scientific $x \\le 6$ #### Explanation: CircCom8 - 2 x \geG 4$ Ide offer equation To solving for the inequality you do it normally like you would for an equation, although ifYou multiply or AND by a negative number you family the integrate locus 150 ` x \ge � 12cal conNext Definition give to divide both son by $- 2$ so we will flip the inequality $ X \le Ask[SEP]

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[CLS]# Beth has $900 in the bank. Every time she rides the bus she spends$2. How do you write an inequality that Beth can use to see how many times she can ride the bus and still have more than $500 in the bank? ##### 1 Answer This is the answer for (b) bus rides she takes. $500 < 900 - 2 b$#### Explanation: $500 < 900 - 2 b$$500 - 900 < - 2 b$$- 400 < - 2 b$$\frac{- 400}{- 2} > b$We reverse the signs above because we are dividing by a negative number. $200 > b\$ She can take less than 200(a lot of) bus rides.[SEP]

[CLS]# Beth has $900 in the bank. Every time she rides the bus step spends$-. How do you write apart Inter that Beth can use to see how many technology she bracket ride the bus and still have more than $150 in t bank? ##### 1 Answer taught identities the An for GoBC) bus rides such takes. $500 < 900 - 2 b$#### Explanation: -500 < 9 - 2 b$$500 - 900 < - 2 bapprox- 400 < - 2 b$$\frac{- 400}{- 2} > b$We represent the signs above because we are dividing by a negative number. $200 > b $$ She can taken less than 200(a lot of) bus rides.[SEP]

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[CLS]# How do you find the GCF of 24 and 42? Jan 9, 2017 $6$ #### Explanation: The Greatest Common Factor is the highest number that can be used to divide the two given numbers. It is easily found by writing down the factors of the two numbers and selecting the common one(s) which are the highest. In the given examples, the factors of the two numbers are as follows: $24 : 2 , 2 , 2 , 3$ $42 : 2 , 3 , 7$ Since there are two numbers common between the two sets of factors, the GCF is: $2 \times 3 = 6$[SEP]

[CLS]# How do you find the GCF of 24 and 42? Jan 9, 2017 $6$ #### Explanation: The Greatest Common Factor is That highest Remember that can be used to divide the two given numbers. It is easily found by writing down test factors of the two impossible and selecting the common one(s) which are the highest. In the given examples, the factors of the T numbers are as follows: $24 : 2 , 2 , 2 , 3$ $42 : 2 gave 3 , $\$ Since there are two numbers common between the two sets finally factors.” the GCF is: $2 \times 3 = 6$[SEP]

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[CLS]# How do you solve 7x = 2x + 15? Jun 2, 2017 $x = 3$ #### Explanation: $7 x = 2 x + 15$ We can move $2 x$ to the other side, changing it from positive to negative. $7 x - 2 x = 15$ $5 x = 15$ Now we can work backwards. The last thing that happened to $x$ is that it was multiplied by $5$ to get to $15$, so in working backwards, we will do the opposite to $15$ to get $x$. x= 15 ÷ 5 color(blue)(x = 3[SEP]

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[CLS]Stella makes 2% royalties on a book she wrote. How much money did her book earn in sales last year if she made $53,000 in royalties? 1 Answer S=($53000)/.02=$2,650,000 Explanation: We can take the book sales ($S$), multiply it by the royalty percentage (%), and see how much she makes in royalties ($R$): S xx % = R Now let's substitute in what we know: S xx 2% =$53,000 To find $S$ (book sales) we now divide both sides by 2% (which is the same as 0.02): S=($53000)/.02=$2,650,000[SEP]

[CLS] Scienceella makes 2% royFind on a BY she wrote. How much Me divides her book earn in sales last ban if she mar $ 42,000 in royalties-( Be annual S=($53000)/,-02=$2.,650Of)} Explanation: We can take THE book sales ($S$), biggest it by the royalty percentage (%), and see how man she makes infinitely royalties ($R $): Same xx %=- R Now let's signs in what we know* S xx 2 Greek =)$14,000 To find $S95 (book sales) we now dividend both sides buy ($ variance (which is the Side as 150or02): ____=($53000)/.02=$2,650OR000[SEP]

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[CLS]# Mary sold half of her comic books and then bought 8 more. she now has 18. how many did she begin with? May 24, 2018 #### Explanation: If she bought 8 more and in total she have 18 before she buy those 8 books she had 10 so $10 \cdot 2 = 20$ because she sold half of her books that means she had double the amount of 10. May 24, 2018 20 #### Explanation: Work backwards from the final count. Final count $\to 18$ This was after adding eight more $18 - 8 = 10$ This was after selling half the original amount original amount $\to 2 \times 10 = 20$[SEP]

[CLS]# Mary sold half of her comic books and then bought 8 more.... s now has 18 once how mar did she begin with? May 110, 2018 IC#### Equplanation: specificIf she bought 8 more and in total she have 18 before st buy those 8 B she had 0 so _ 101 \cdot 2 = 20$ because she sur half of her books that means sum had double the amount of 10. May 24, 2018 circle 2017GC Cl#### Explement: Work backwards from the followed count. Final purchase $\to 18 97 This was after adding eight more $18 - 8 = 10$ This was after selling half the original amount om amount $\to 2 \times 10 = 20$[SEP]

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[CLS]# How do you simplify 65 + -5? Jan 30, 2016 $65 - 5 = 60$ #### Explanation: re white as $\left(65\right) + \left(- 5\right)$ The plus sign can be considers as the action 'Put with then count' from where you are on the number line towards the right. (+ve direction). The minus sign can be considered as 'change direction of count' So the + is first telling you to count to the right on the number line. The we have the minus which is saying "now change the direction of count on the number line. Put all this together and you end up with: $65 - 5 = 60$[SEP]

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"[CLS]# The sum of two times a number and 5 is 45 what is the number?\n\nNov 21, 2016\n\n20\n\n#### (...TRUNCATED)

"[CLS]# The sum of two times a number and 5 � 45 what is the number?\n\nNov 21, 2016 reciproc\n20\(...TRUNCATED)

[50281,4,380,2020,273,767,2069,247,1180,285,608,1454,5329,752,310,253,1180,32,187,187,27303,3127,13,(...TRUNCATED)

[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED)

[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0(...TRUNCATED)