Search results

  • ...use it is both the median and the mode of the set. Thus <math>90</math> is correct.
    2 KB (268 words) - 18:19, 27 September 2023
  • ...idate. Multiplying <math>63\cdot64</math> confirms that our assumption is correct.
    2 KB (315 words) - 15:34, 18 June 2022
  • ...l area gives us <math>40-33\frac{1}{2}=\boxed{6\frac{1}{2}}</math>, so the correct answer is <math>\boxed{\textbf{(D)}}</math>.
    8 KB (1,016 words) - 00:17, 31 December 2023
  • ...ath>1</math> and <math>2016</math>, inclusive. Which of the following is a correct statement about the probability <math>p</math> that the product of the thre
    2 KB (297 words) - 14:54, 25 June 2023
  • ...ectly answer the question receives one point. The person who gets the most correct out of three questions (not necessarily two out of three) is the winner. ...ritten competitors. Starting then, the first person to get three questions correct wins (as opposed to the best-out-of-three rule).
    10 KB (1,497 words) - 11:42, 10 March 2024
  • ...econd minute 4 points, or third minute 3 points. The first team to get the correct answer receives a bonus of 2 points. ...rs are worth 2 points each. Bonus points are given if all four answers are correct and the answer sheet is submitted at the 3 minute mark (First Command – 5
    8 KB (1,178 words) - 22:48, 17 October 2015
  • ...ation competition, a mental math competition (where only exact answers are correct), and a physical estimation competition. Grades 4-9 compete in this format.
    2 KB (216 words) - 16:59, 17 December 2016
  • A correct solution would be to move everything to the left side of the inequality, an
    12 KB (1,798 words) - 16:20, 14 March 2023
  • ...blems are graded on a scale from 0 to 5. The full 5 points are awarded for correct, concise solutions, and points are taken off from there for mistakes or oth
    4 KB (613 words) - 13:08, 18 July 2023
  • The AMC 10 is scored in a way that penalizes guesses. Correct answers are worth 6 points, incorrect questions are worth 0 points, and una
    4 KB (574 words) - 15:28, 22 February 2024
  • The AMC 12 is scored in a way that penalizes guessing. Correct answers are worth 6 points, incorrect answers are worth 0 points, and unans
    4 KB (520 words) - 12:11, 13 March 2024
  • ...ve, making guessing almost futile. Wrong answers receive no credit, while correct answers receive one point of credit, making the maximum score 15. Problems ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
    8 KB (1,057 words) - 12:02, 25 February 2024
  • *4 points for each correct question *5 points for each correct question
    4 KB (632 words) - 17:09, 11 October 2020
  • The test is scored as 5 points for every correct response, 1 point for a blank response, and 0 points for an incorrect respo
    972 bytes (141 words) - 11:12, 30 September 2018
  • ...pping the problem can help you check and solve other problems, and you can always return to the problem that you skipped. This concept helps double where yo ...good guess, saving you time and giving you a chance of getting the answer correct. This tactic helps the most in competitions with multiple choice answers. I
    3 KB (538 words) - 13:13, 16 January 2021
  • ...e triangle. It is easy to verify that this placement of the orthocenter is correct and that the orthic triangle will remain the same as before the swapping, a
    8 KB (1,408 words) - 11:54, 8 December 2021
  • ...rcount several numbers, such as 12, which is divisible by both 2 and 3. To correct for this overcounting, we must subtract out the numbers that are divisible Another basic example is combinations. In these, we correct for overcounting with division, by dividing out what we overcount (as oppos
    4 KB (635 words) - 12:19, 2 January 2022
  • * 4 points for each correct answer ...consists of 5 short-answer questions. Your score is 5 times the number of correct answers, for a maximum score of 25.
    4 KB (644 words) - 12:56, 29 March 2017
  • Each correct answer will earn 5 points, a question left blank will earn 1 point, and an
    2 KB (366 words) - 22:59, 17 November 2007
  • ...> [[factor]]s, two of them are small. If we want to make sure that this is correct, we could test with a smaller number, like <math>30</math>. It becomes much
    2 KB (276 words) - 05:25, 9 December 2023
  • ...le (inclusive and integers only). Full credit is only given for complete, correct solutions. Each solution is intended to be in the form of a [[proof writin
    3 KB (490 words) - 03:32, 23 July 2023
  • For every correct answer: 5 points
    3 KB (388 words) - 23:07, 5 February 2024
  • ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
    3 KB (391 words) - 16:00, 21 February 2024
  • On the AMC 12, each correct answer is worth <math>6</math> points, each incorrect answer is worth <math
    13 KB (1,953 words) - 00:31, 26 January 2023
  • ...ssumes he is the first to arrive. If each takes what he believes to be the correct share of candy, what fraction of the candy goes unclaimed?
    13 KB (1,955 words) - 21:06, 19 August 2023
  • ..., and <math>R</math> the area of the red square. Which of the following is correct?
    12 KB (1,792 words) - 13:06, 19 February 2020
  • Cassandra sets her watch to the correct time at noon. At the actual time of 1:00 PM, she notices that her watch rea
    13 KB (1,987 words) - 18:53, 10 December 2022
  • Inductive Step: Suppose the formula is correct for <math>z_k</math>, then ...z|</math>. Therefore, the magnitude of <math>\frac{iz_n}{|z_n|}</math> is always <math>1</math>, meaning that all of the numbers in the sequence <math>z_k</
    4 KB (660 words) - 17:40, 24 January 2021
  • ...4}</math> But, this over-counts since it counts numbers like 0213. We can correct for this over-counting. Lock the first digit as 0 and permute 3 other chose
    3 KB (562 words) - 18:12, 4 March 2022
  • ...clear from the problem setup that <math>0<\theta<\frac\pi2</math>, so the correct value is <math>\tan(\theta)=\frac53</math>. Next, extend rays <math>\overri
    9 KB (1,501 words) - 05:34, 30 October 2023
  • ...the formula <math>s=30+4c-w</math>, where <math>c</math> is the number of correct answers and <math>w</math> is the number of wrong answers. Students are not
    6 KB (933 words) - 01:15, 19 June 2022
  • ...ailable ten-button lock may be opened by depressing -- in any order -- the correct five buttons. The sample shown below has <math>\{1, 2, 3, 6, 9\}</math> as
    6 KB (902 words) - 08:57, 19 June 2021
  • ...bsent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive
    7 KB (1,177 words) - 15:42, 11 August 2023
  • ...the formula <math>s=30+4c-w</math>, where <math>c</math> is the number of correct answers and <math>w</math> is the number of wrong answers. (Students are no Let Mary's score, number correct, and number wrong be <math>s,c,w</math> respectively. Then
    7 KB (1,163 words) - 23:53, 28 March 2022
  • Since this is an AIME problem, there is exactly one correct answer, and thus, exactly one possible value of <math>f(14,52)</math>.
    4 KB (538 words) - 13:24, 12 October 2021
  • ...available ten-button lock may be opened by pressing -- in any order -- the correct five buttons. The sample shown below has <math>\{1,2,3,6,9\}</math> as its
    1 KB (181 words) - 18:23, 26 August 2019
  • ...As no other option choice fits, <math>\boxed{\textbf{(A)}-x}</math> is the correct solution.
    1 KB (179 words) - 10:33, 19 August 2022
  • THIS SOLUTION IS INCORRECT, PLEASE CORRECT IT IF YOU HAVE TIME!
    3 KB (447 words) - 17:02, 24 November 2023
  • ...r of <math>11</math> is <math>(5,11)</math>, and checking shows that it is correct.
    4 KB (628 words) - 22:05, 7 June 2021
  • ...way to do the problem is by the process of elimination. The only possible correct choices are the highest powers of each prime, <math>2^3=8</math>, <math>3^2
    5 KB (878 words) - 14:39, 3 December 2023
  • ...th> to <math>96</math> alternate in fake-real-fake-real, where we have the correct order of cards once the first <math>96</math> have moved and we can start p ...the spacing of the cards moved, <math>a</math> is an integer such that the correct first card is moved, and <math>k</math> is an integer greater than or equal
    15 KB (2,673 words) - 19:16, 6 January 2024
  • ...ing <math>2</math> and <math>7</math> for <math>w_1</math> does not give a correct product. Thus, <math>\frac{27}{50}</math> must be a reduced form of the ac
    7 KB (1,011 words) - 20:09, 4 January 2024
  • ...ination counts only one of the permutations; we can say that it counts the correct (ascending order) permutation. ...sformations of the problem, a recursion formula can be a robust way to the correct answer.
    11 KB (1,729 words) - 20:50, 28 November 2023
  • ...th> and <math>C</math>. Oh wait they are symmetric. So then if this is the correct answer, why am I wrong, or what happened to that factor of <math>3</math>?"
    15 KB (2,406 words) - 23:56, 23 November 2023
  • ...bsent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive
    2 KB (336 words) - 19:30, 24 June 2020
  • ...math>11</math> while <math>(a-b)</math> is a factor of nine (1 or 9). The correct guesses are <math>a = 6, b = 5</math> causing <math>x = 65, y = 56,</math>
    5 KB (845 words) - 19:23, 17 September 2023
  • ...h>, we see <math>6\cdot8=30+18</math>. Therefore, we can see our answer is correct.
    1 KB (155 words) - 17:30, 16 December 2021
  • Thus, the correct answer is <math>\boxed{\textbf{(C) }3}.</math> Note to readers: make sure to always read the problem VERY carefully before attempting; it could mean the differ
    3 KB (450 words) - 02:00, 13 January 2024
  • ...= 72</math>. 28 is not divisible by 3, so we know that this number is not correct. Moving on to 7, <math>13 \cdot 7 = 91</math>. We know that 9 is a multiple
    3 KB (429 words) - 18:14, 26 September 2020
  • The test is scored as 1 point for each correct answer, 0 points for blank answers, and -.25 for incorrect answers except f
    2 KB (365 words) - 21:21, 18 March 2017
  • ...lifying of the brackets. Open the brackets and you should notice why it is correct. If you are also wondering whether or not if we got all the sets in the abo
    2 KB (263 words) - 18:13, 19 October 2021
  • ...rn techniques. However, a flaw was discovered soon after. Wiles managed to correct the proof by October 1994, thus solving the last of Fermat's problems. It i
    5 KB (860 words) - 17:10, 21 March 2023
  • The [[Clay Mathematics Institute]] has offered a USD \$1,000,000 prize for a correct solution, as it has listed it as one of its [[Millennium Problems]].
    6 KB (1,104 words) - 15:11, 25 October 2017
  • ...given side of <math>A'</math> on the straight line <math>a'</math>, we can always find one and only one point <math>B'</math> so that the segment <math>AB</m Every segment is congruent to itself; that is, we always have
    10 KB (1,655 words) - 21:43, 24 March 2022
  • So our correct answer choice is <math>\boxed{\textbf{(B) }\frac{2}{5}x^2}</math>
    2 KB (265 words) - 19:07, 25 December 2022
  • ...c{1}{1} + \frac{1}{2} - \frac{1}{6}\right) = 2</math>, which we know to be correct.
    3 KB (473 words) - 12:57, 20 February 2024
  • ...ive minute, twenty-five question multiple-choice test worth six points per correct response, and ten ciphering questions. Each ciphering question is worth te
    2 KB (307 words) - 20:25, 12 March 2012
  • ...s. Every test case has equal weight within the problem. For each test case correct, you receive the points for the test case. Programs get 4 seconds per test Each test case will give feedback on how well your program did. Correct test cases show how much time and memory used. Incorrect test cases are dif
    2 KB (297 words) - 01:41, 21 January 2023
  • ...ts must answer 30 multiple choice mathematics problems in 60 minutes. Each correct answer gives 4 points, each wrong answer subtracts 1 point and no answer gi
    2 KB (366 words) - 14:26, 4 September 2017
  • Altogether, Tori answered <math>7 + 12 + 21 = 40</math> questions correct. ...e needed to answer <math>45 - 40 = 5</math> more questions to pass, so the correct answer is <math>\boxed{(B) 5}</math>
    1 KB (167 words) - 20:30, 11 January 2024
  • ...ciple of Relativity says it is impossible to ascertain that one of them is correct while the other is wrong.
    3 KB (538 words) - 23:39, 2 March 2008
  • On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and eac
    13 KB (1,994 words) - 13:04, 18 February 2024
  • ...ng questions, each of which contestants have three minutes to answer. Each correct answer is worth five points. Each team's score is determined by the top fou
    3 KB (475 words) - 21:51, 31 December 2013
  • ...twenty-five question multiple-choice test. Four points are given for each correct answer, and 1.1 points are given for each blank answer. On this round a [[
    2 KB (324 words) - 10:23, 24 April 2007
  • ...ears. The tests consist of 25 questions which are worth 4 point each for a correct answer, minus 1 point for an incorrect answer. Ciphering rounds- 4 of them,
    1 KB (160 words) - 12:31, 27 December 2006
  • ...ons and five free-response questions; a student's score is five points per correct questions, plus one point per answer left blank; there is no penalty for in
    2 KB (353 words) - 17:02, 7 June 2009
  • ...nior high division; a student's score is forty points plus four points per correct question minus one point per incorrect question. No calculators are permit
    1 KB (154 words) - 09:45, 21 March 2010
  • ...o we divide the whole sum by 3 and we add or subtract <math>q(n)</math> to correct for the integer based on the modularity of the sum with 3
    4 KB (595 words) - 12:14, 25 November 2023
  • The answer is clearly correct, but the proof has a gap, i.e. there is no reason that <math>f(-2)\neq1</ma
    7 KB (1,335 words) - 17:44, 25 January 2022
  • All possibilities yield a contradiction, so our assumption can not be correct.
    3 KB (438 words) - 01:19, 27 December 2023
  • ...ac{1}{\sqrt{2006}}-\frac{1}{\sqrt{2007}}</math>, which of the following is correct?
    13 KB (1,990 words) - 08:29, 19 December 2009
  • ...ac{1}{\sqrt{2006}}-\frac{1}{\sqrt{2007}}</math>, which of the following is correct?
    808 bytes (139 words) - 16:56, 6 May 2007
  • Which of the following is correct, about the graph of <math>f</math>? ...and <math>y=\sqrt[3]{6}-\sqrt[3]{3}</math>, then which of the following is correct?
    11 KB (1,672 words) - 10:56, 27 April 2008
  • ...s have three problems to solve in five hours. Students with three to four correct problems are usually invited to the final round, which has the same format
    1 KB (223 words) - 22:34, 2 January 2008
  • The 2007 AMC 12 contests will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and 1.5 points for each pro
    864 bytes (121 words) - 10:50, 4 July 2013
  • Which of the following is correct, about the graph of <math>f</math>? From above, <math>\mathrm{(A)}</math> is not correct because the graph does not intersect the x-axis (it is tangent to it).
    1 KB (216 words) - 10:46, 27 April 2008
  • ...and <math>y=\sqrt[3]{6}-\sqrt[3]{3}</math>, then which of the following is correct?
    1 KB (182 words) - 10:40, 27 April 2008
  • ...ind out that out of the 9 cases, in 4 the value <math>n_{?}</math> has the correct sum of digits. <br/> ...s of whether the sum carries or not, the modulo 9 of the sum of the digits always increases by <math>1</math>.
    15 KB (2,558 words) - 19:33, 4 February 2024
  • ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
    924 bytes (121 words) - 00:41, 12 October 2013
  • The 2007 AMC 12 contests will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and 1.5 points for each pro
    12 KB (1,814 words) - 12:58, 19 February 2020
  • ...; the number that Cindy started with is <math>3(43)+9=138</math>. Now, the correct result is <math>\frac{138-3}{9}=\frac{135}{9}=15</math>. Our answer is <mat ...ath>. Solve for <math>x</math> gives us <math>x=138</math>. Therefore, the correct result is <math>\frac{138-3}{9}=\frac{135}{9}=\boxed{\textbf{(A) }15}</math
    1 KB (163 words) - 12:46, 8 November 2021
  • Which one of the following must necessarily be correct?
    13 KB (1,945 words) - 18:28, 19 June 2023
  • On the AMC 12, each correct answer is worth <math>6</math> points, each incorrect answer is worth <math
    837 bytes (122 words) - 20:14, 3 July 2013
  • ...-[[density]], low-pressure gases. For higher densities, it is necessary to correct this equation. For greater precision, the [[van der Waals equation]] is ano
    1 KB (225 words) - 08:59, 11 March 2008
  • ...whence we immediately obtain <math>\framebox[1.2\width]{(A)}</math> as the correct answer.
    5 KB (814 words) - 18:02, 17 January 2023
  • Therefore the correct answer is <math>\mathrm{(E)}</math>
    2 KB (268 words) - 12:40, 3 June 2021
  • The addition below is incorrect. The display can be made correct by changing one digit <math>d</math>, wherever it occurs, to another digit
    17 KB (2,387 words) - 22:44, 26 May 2021
  • <math> \textbf{(B)}\ \text{In some cases there is more than one correct order in proving certain propositions.} </math> <math> \textbf{(D)}\ \text{It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposi
    23 KB (3,641 words) - 22:23, 3 November 2023
  • For all integers x, <math>x^2</math> is always a positive integer. So solve for <math>\frac{n}{20-n} = 0</math>, getting < ...hat also yield an integer n value, meaning that there are 4 values, so the correct answer is <math>\boxed{(D)}</math>
    4 KB (579 words) - 05:54, 17 October 2023
  • ...e of <math>2004</math>, so there is a very high probability that it is the correct answer.
    3 KB (533 words) - 14:52, 29 October 2023
  • Subtracting that from 1 to get the probability she can park, the correct answer is <math>\boxed{E}</math>.
    4 KB (653 words) - 11:06, 15 October 2022
  • ...Indeed, note that <math>a(1,k) = 2^{1-1}(1+2k-2)=2k-1</math>, which is the correct formula for the first row. We claim the result by [[induction]] on <math>n<
    3 KB (509 words) - 17:21, 22 March 2018
  • ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
    1 KB (115 words) - 13:51, 1 May 2008
  • |4 points per correct answer, 0 points per blank answer, -1 points per incorrect answer |1 point per correct answer, 0 points otherwise
    5 KB (801 words) - 12:47, 23 September 2023
  • ...<math>a+b+c+d=7+5+11+8=31</math>. <math>\boxed{\textbf{(B)}\ 31}</math> is correct.
    6 KB (914 words) - 11:07, 7 September 2023
  • The addition below is incorrect. The display can be made correct by changing one digit <math>d</math>, wherever it occurs, to another digit ...either a <math>5</math> (no carry) or a <math>6</math> (carry) to create a correct statement.
    1 KB (223 words) - 13:59, 5 July 2013
  • ...of them as soon as the mathematical community had pronounced his solution correct. All but one of these problems had been solved by the meeting in 2000, and
    13 KB (1,969 words) - 17:57, 22 February 2024
  • Michael plays catcher for his school's baseball team. He has always been a great player behind the plate, but this year as a junior, Michael's Joshua finds an answer which Michael confirms is correct. What is Joshua's correct answer (the units digit of <math>2008^{2008}</math>)?
    71 KB (11,749 words) - 01:31, 2 November 2023
  • ...e are what you really need to compile it - the first 2 are to get into the correct folder), in the terminal, run:
    5 KB (732 words) - 00:47, 13 December 2023
  • have divided the number by 2 to get the correct answer. What is the correct
    13 KB (1,821 words) - 22:18, 5 December 2023
  • ...ssumes he is the first to arrive. If each takes what he believes to be the correct share of candy, what fraction of the candy goes unclaimed?
    1 KB (213 words) - 10:16, 4 July 2013
  • ...have given up, they turn them in for 4 more. A scoreboard reports how many correct answers various teams have. There are a total of 36 problems, to be complet
    1 KB (243 words) - 17:53, 1 November 2014
  • ...9, but instead, Cindy subtracted 9, then divided by 3, getting 43. If the correct instructions were followed, what would the result be? ..., and <math>R</math> the area of the red square. Which of the following is correct?
    11 KB (1,733 words) - 11:04, 12 October 2021
  • ...}5.5) + (\text{a little})</math>, and as all the options are integers, the correct one is <math>\boxed{\textbf{(C) }6}</math>.
    1,017 bytes (138 words) - 12:26, 8 November 2021
  • ..., and <math>P</math> the area of the red square. Which of the following is correct?
    2 KB (345 words) - 12:50, 8 November 2021
  • ...if he clearly understands what he is doing- just a little mistake) Here is correct soluton:
    3 KB (581 words) - 02:00, 6 May 2023
  • Can someone change this answer so it's correct?
    3 KB (415 words) - 00:51, 15 September 2023
  • Clearly, <math>M = A+C \Longrightarrow</math> the correct answer is <math>\mathrm{(A)}</math>. ...math> which is negative. Thus <math>\mathrm{(A)}</math> is indeed the only correct answer.
    1 KB (187 words) - 14:29, 5 July 2013
  • Only <math>1</math> quantity changes, so the correct answer is <math>\boxed{\text{B}}</math>.
    1 KB (242 words) - 01:24, 27 July 2023
  • ...if one of these is correct, then the other option in its pair must also be correct. There can't be 2 answers. So, the only remaining answer choice is <math>\b
    2 KB (300 words) - 09:07, 22 January 2023
  • This is equal to the area of a small circle, hence the correct answer is <math>\boxed{\text{(B)}\ 1}</math>.
    2 KB (277 words) - 21:32, 3 July 2013
  • ...sts of <math>20</math> questions. The scoring is <math>+5</math> for each correct answer, <math>-2</math> for each incorrect answer, and <math>0</math> for e
    12 KB (1,568 words) - 09:35, 31 October 2021
  • &= 1800 & \text{ Thus \boxed{\text{E}} is the correct answer}
    1 KB (138 words) - 01:03, 22 January 2020
  • The entire situation is in the picture below. The correct answer is <math>\boxed{\mathrm{(E)}\ (3,2)}</math>.
    955 bytes (149 words) - 19:56, 3 July 2013
  • ...th>. So we place bets on <math>\boxed{\mathbf{(D)}240/13} </math> which is correct!
    7 KB (1,083 words) - 22:41, 23 November 2020
  • ...w verify which of <math>n=96</math> and <math>n=97</math> will give us the correct imaginary part.
    4 KB (634 words) - 16:34, 3 December 2020
  • Therefore the correct answer is <math>\boxed{\textbf{(C)} \text{ A cone with slant height of } 10
    2 KB (279 words) - 00:32, 30 December 2023
  • Note: I think this solution is not correct. the products of the roots are integers do not mean the product of the two Note: I believe this solution is correct. We know that the two real solutions are integers and that the final produc
    6 KB (1,035 words) - 09:18, 3 September 2023
  • ...hings on all legs is <math>\frac{1}{2^{8}}</math>. Therefore the number of correct permutations must be <math>\boxed{\frac {16!}{2^8}}</math>.
    3 KB (418 words) - 23:48, 3 July 2022
  • This is correct.
    7 KB (1,110 words) - 15:20, 30 May 2022
  • ...ch puts the center on the wrong side of <math>A</math>, so this is not the correct case.
    5 KB (822 words) - 01:35, 7 February 2024
  • ...us <math>D</math> outside the first quadrant, hence the first case is the correct one. As <math>(6,3)</math> is the midpoint of <math>CD</math>, we can compu
    2 KB (238 words) - 11:21, 7 April 2022
  • ...or <math>3.00</math> dollars. So, <math>\boxed{\textbf{(B) } 2}</math> is correct.
    4 KB (585 words) - 22:41, 14 September 2021
  • ...ncorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?
    13 KB (2,030 words) - 03:04, 5 September 2021
  • ...general content of this solution, that would be great. If the notation is correct, then just delete this footnote)
    6 KB (1,071 words) - 22:25, 9 October 2021
  • ...ncorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time? ...or any given hour. Hence the fraction of the day that the clock shows the correct time is <math>\frac 23 \cdot \left(1 - \frac {15}{60}\right) = \frac 23 \cd
    2 KB (372 words) - 17:36, 28 June 2021
  • ...ncorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?
    15 KB (2,262 words) - 00:53, 18 June 2021
  • ...sts of <math>20</math> questions. The scoring is <math>+5</math> for each correct answer, <math>-2</math> for each incorrect answer, and <math>0</math> for e Let <math>c</math> be the number of questions correct, <math>w</math> be the number of questions wrong, and <math>b</math> be the
    2 KB (325 words) - 12:17, 28 July 2020
  • echo "I should never be seen since the API sends in correct parameters.<br>\n";
    2 KB (210 words) - 08:37, 17 November 2022
  • ...2\times 2</math> cube is included in each of these three cuts. To get the correct result, we can take the sum of the volumes of the three cuts, and subtract
    2 KB (383 words) - 17:42, 28 June 2021
  • Thus we conclude that 4 is the correct choice or <math>\boxed{\textbf{(A)}}</math> We can check that this is the correct answer by having <math>4, 9, 6,</math> and <math>1</math> as our numbers. T
    4 KB (679 words) - 19:11, 17 September 2023
  • ...gnored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for <math>a</math>, <m ...multiple choice math contest, students receive <math>4</math> points for a correct answer, <math>0</math> points for an answer left blank, and <math>-1</math>
    12 KB (1,817 words) - 22:44, 22 December 2020
  • ...gnored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for <math>a</math>, <m
    12 KB (1,845 words) - 13:00, 19 February 2020
  • ...ou can imagine that any balls in the "repeat" urns are moved on top of the correct balls in the first <math>n</math> urns, moving from left to right. There is
    5 KB (768 words) - 03:59, 30 January 2024
  • ...b</math>, adding a positive number (<math>a</math>) to <math>c</math> will always make it greater than <math>b</math>. ...see that <math>3+1>2</math>, so <math>\boxed{\textbf{(A) }a+c<b}</math> is correct.
    1 KB (187 words) - 17:18, 3 November 2023
  • ...ignored the parenthese but added and subtracted correctly and obtained the correct result by coincidence. The number Larry substituted for <math>a</math>, <ma
    1 KB (183 words) - 17:02, 1 August 2022
  • ...cial kind of function called a constructor. The name of the constructor is always the name of the corresponding class. t.right(90) # point in the correct direction
    28 KB (4,762 words) - 21:20, 12 June 2023
  • We can check each answer choice from left to right to see which one is correct. Suppose the Unicorns played <math>48</math> games in total. Then, after di
    6 KB (958 words) - 18:32, 20 January 2024
  • ...answer is <math>5 \cdot 5 \cdot 4 - 5 \cdot 3 \cdot 4 = 40</math>, and the correct choice is <math>\boxed{D}</math> ...s. So, <math>100-60=\boxed{40}</math> ADDITIONAL plates can be made.So the correct choice is <math>\boxed{D}</math>
    3 KB (516 words) - 14:50, 21 December 2022
  • Calculating, <math>0.8 - 0.07 = 0.80 - 0.07 = 0.73</math> The correct answer is <math>\boxed E</math>.
    347 bytes (43 words) - 23:04, 1 January 2020
  • ...multiple choice math contest, students receive <math>4</math> points for a correct answer, <math>0</math> points for an answer left blank, and <math>-1</math>
    1 KB (210 words) - 02:44, 26 September 2020
  • ...ath> dollars and <math> x</math> cents, the incorrect amount exceeding the correct amount by <math> \$17.82</math>. Then: \textbf{(D)}\ \text{the incorrect amount can equal twice the correct amount}\qquad \\
    25 KB (3,872 words) - 14:21, 20 February 2020
  • ...=25</math>. This time, <math>p^2+300=22^2+300=784=28^2</math>. This is the correct pair. Now, we find the percent increase from <math>22^2=484</math> to <math ...iffer by <math>300</math>, and we can confirm that <math>484</math> is the correct starting number by noting that <math>484+150=634=25^2+9</math>. Thus, the a
    3 KB (545 words) - 20:54, 21 August 2023
  • ...mod {729}</math> and less than <math>1,000</math> is <math>365</math>, the correct answer is <math> \boxed{365\ \mathbf{(C)}} </math>.
    5 KB (816 words) - 18:26, 10 August 2023
  • ...previous tens digit plus the ones digit (or one) and the hundreds digit is always the previous hundreds digit plus the previous tens digit. Knowing this, we ...previous tens digit plus the ones digit (or one) and the hundreds digit is always the previous hundreds digit plus the previous tens digit. Knowing this, we
    9 KB (1,287 words) - 20:37, 20 August 2023
  • ...-digit number <math>a</math>. His erroneous product was 161. What is the correct value of the product of <math>a</math> and <math>b</math>? ...ath>y</math> integers, makes successive jumps of length <math>5</math> and always lands on points with integer coordinates. Suppose that the frog starts at <
    13 KB (1,978 words) - 16:28, 12 July 2020
  • ...er <math>a</math>. His erroneous product was <math>161.</math> What is the correct value of the product of <math>a</math> and <math>b</math>? ...Therefore, <math>a = 32</math> and <math>b = 7.</math> Multiplying our two correct values of <math>a</math> and <math>b</math> yields
    1 KB (187 words) - 14:13, 19 January 2021
  • After testing, we find that <math>\boxed{\textbf{(C)}\ 0.02}</math> is the correct answer.
    940 bytes (141 words) - 14:25, 28 July 2022
  • ...ct answer. If Olivia answered every problem and her score was 29, how many correct answers did she have?
    15 KB (2,102 words) - 11:35, 19 February 2024
  • ...answers (which contradict the problem statement), but the final answer is correct.
    3 KB (466 words) - 15:06, 16 January 2023
  • ...h>, we can see from the arrangement provided above that that cannot be the correct answer.
    2 KB (328 words) - 15:48, 7 January 2020
  • We can look at the graphs and note that the only one that has all the correct points is <math>\boxed{E}</math>
    3 KB (406 words) - 17:29, 22 October 2020
  • ...er <math>a</math>. His erroneous product was <math>161</math>. What is the correct value of the product of <math>a</math> and <math>b</math>? ...>n</math> people in this room have birthdays falling in the same month" is always true?
    13 KB (2,090 words) - 18:05, 7 January 2021
  • ...er <math>a</math>. His erroneous product was <math>161</math>. What is the correct value of the product of <math>a</math> and <math>b</math>?
    817 bytes (121 words) - 13:07, 24 January 2024
  • On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and eac
    1 KB (177 words) - 03:14, 12 March 2024
  • ...<math>10</math> will be scored by awarding <math>6</math> points for each correct response, <math>0</math> points for each incorrect response, and <math>1.5<
    15 KB (2,297 words) - 12:57, 19 February 2020
  • ...{ AMC }10</math> will be scored by awarding <math>6</math> points for each correct response, <math>0</math> points for each incorrect response, and <math>1.5<
    1 KB (184 words) - 21:15, 25 July 2018
  • ...is either cool or cloudy, which means <math>\boxed{\textbf{(B)}}</math> is correct.
    1 KB (214 words) - 21:04, 5 February 2018
  • Which one of the following must necessarily be correct? Three of the statements are correct, and only one digit is on the card. Thus, one of I and III are false. There
    788 bytes (137 words) - 14:34, 5 July 2013
  • ...}</math>, <math>\text{(B)}</math>, or <math>\text{(C)}</math> could be the correct answer. Clearly, there are more than <math>125</math> ways, thus yielding <
    3 KB (397 words) - 02:40, 16 January 2023
  • ...r, <math>\frac{A+B}{C+D} = \frac{17}{1} = 17</math>, and so the values are correct, and <math>A+B = 17</math>, giving the answer <math>\boxed{E}</math>.
    1,008 bytes (167 words) - 14:28, 5 July 2013
  • ...s a 5th root of unity as a root. We will show that we were \textit{almost} correct in our initial assumption; that is that <math>z_0</math> is at most a 5th r
    11 KB (1,979 words) - 17:25, 6 September 2021
  • .... Altogether, the three had <math>144 + 108 = 252</math> dollars, and the correct answer is <math>\boxed{D}</math>
    1 KB (216 words) - 13:56, 18 August 2019
  • ...t. Thus, the answer is <math>\frac{28}{64} = \frac{7}{16}</math>, and the correct choice is <math>\boxed{C}</math>
    2 KB (279 words) - 15:23, 29 May 2021
  • ...th> has the largest thousandths digit of the remaining answers, and is the correct answer. <math>A</math> has an "invisible" thousandths digit of <math>0</ma
    1 KB (154 words) - 00:26, 5 July 2013
  • If you find a mistake, feel free to correct it or inform RTG by [http://www.artofproblemsolving.com/Forum/ucp.php?i=pm&
    4 KB (616 words) - 14:42, 28 March 2021
  • = Part A: Each correct answer is worth 5 points = = Part B: Each correct answer is worth 6 points =
    16 KB (2,317 words) - 03:54, 24 October 2014
  • <math>\frac{3\times{4}}{6}=\frac{12}{6}=2</math> The correct answer is <math>B</math>.
    372 bytes (50 words) - 01:36, 23 October 2014
  • (Note: The above solution looks generally correct, but the actual answer should be <math>\{11a, a, 5a, 7a\}</math>,<math>\{a,
    9 KB (1,718 words) - 23:08, 26 June 2014
  • ...ct answer. If Olivia answered every problem and her score was 29, how many correct answers did she have? ...he got <math>10 - x</math> questions wrong. Since she gains 5 points for a correct answer and loses 2 for an incorrect one, we can solve <math>5x - 2(10 - x)
    2 KB (288 words) - 18:31, 20 January 2024
  • ...=Z</math>, which is one of the answer choices. Since there can only be one correct answer, and there is already one, we see that the answer must be <math>\box
    2 KB (336 words) - 20:00, 15 April 2023
  • Thus, the correct answer is <math>\boxed{E}</math>.
    3 KB (516 words) - 20:05, 15 April 2023
  • ...ivided the number by <math>2</math> to get the correct answer. What is the correct answer?
    832 bytes (128 words) - 09:10, 8 January 2024
  • Joshua finds an answer which Michael confirms is correct. What is Joshua's correct answer (the units digit of <math>2008^{2008}</math>)?
    2 KB (245 words) - 19:23, 4 August 2018
  • ...<math>\left\lceil \frac{162}{15} \right\rceil = 11</math> batches, and the correct answer is <math>\boxed{E}</math>. ...raph above to find that there needs to be <math>11</math> batches, and the correct answer is <math>\boxed{E}</math>.
    2 KB (296 words) - 02:00, 28 February 2022
  • ...{ 42} \cdot 100\% = 30.9\%</math> of all jellybeans are yellow. Thus, the correct answer is <math>\boxed{A}</math>
    2 KB (226 words) - 00:26, 5 July 2013
  • ...th> is thus indeed a negative number. So option <math>\boxed{A}</math> is correct. Option <math>B</math> is the product of two negatives, which is always positive.
    3 KB (506 words) - 00:24, 5 July 2013
  • ...e is <math>6\cdot \frac{1}{2}\cdot\frac{16}{3}\cdot 4 = 64</math>, and the correct answer is <math>\boxed{D}</math>.
    2 KB (406 words) - 20:44, 15 February 2024
  • Ryan got <math>80\%</math> of the problems correct on a <math>25</math>-problem test, <math>90\%</math> on a <math>40</math>-p ...on the third. This amounts to a total of <math>20+36+7=63</math> problems correct. The total number of problems is <math>25+40+10=75.</math> Therefore, the p
    946 bytes (131 words) - 23:30, 6 January 2024
  • What is the correct ordering of the three numbers, <math>10^8</math>, <math>5^{12}</math>, and ...follows that <math>\boxed{\textbf{(A)}\ 2^{24}<10^8<5^{12}}</math> is the correct answer.
    2 KB (324 words) - 16:08, 31 December 2023
  • ...orrect. What is the largest digit that can be changed to make the addition correct?
    15 KB (2,343 words) - 13:39, 19 February 2020
  • ...orrect. What is the largest digit that can be changed to make the addition correct?
    1,005 bytes (141 words) - 16:06, 14 July 2021
  • ...6\cdot 20 + 8\cdot 20 = (0 + 2 + 4 + 6 + 8)\cdot 20 = 400</math>, and the correct answer is <math>\boxed{C}</math>.
    1 KB (166 words) - 14:07, 5 July 2013
  • ...6</math>, this number should be just a little over <math>2</math>, and the correct answer is <math>\boxed{\text{(C)}}</math>.
    3 KB (545 words) - 10:21, 16 September 2022
  • ...count the factors of <math>2n</math>, to see which prime factorization is correct and has <math>28</math> factors.
    5 KB (828 words) - 05:52, 26 October 2023
  • // NOTE: I've tampered with the angles to make the diagram not-to-scale. The correct numbers should be 72 instead of 76, and 45 instead of 55.
    22 KB (3,694 words) - 23:58, 3 June 2022
  • ...s that <math>N</math> is around these numbers. This suspicion proves to be correct, as we see that <math>\binom{14}{4} = 1001</math>, giving us our answer of
    4 KB (630 words) - 15:13, 8 October 2023
  • ...so <math>[BED]=12</math>, which makes <math>\boxed{\textbf{B}}</math> the correct answer.
    2 KB (303 words) - 20:28, 2 October 2023
  • Therefore the correct answer is <math>\boxed{\textbf{(B)}}</math>.
    3 KB (447 words) - 21:21, 17 July 2020
  • ...es zero}\qquad\\ \textbf{(E)}\ \text{Only some of the above statements are correct} </math> Of these statements, the correct ones are:
    22 KB (3,306 words) - 19:50, 3 May 2023
  • The journey took 8 hours, so the correct answer is <math>\boxed{\textbf{(D)}}</math>.
    2 KB (327 words) - 15:55, 6 April 2020
  • As the AMC 8 only rewards 1 point for each correct answer, everything is irrelevant except the number Billy answered correctly
    526 bytes (71 words) - 01:13, 5 July 2013
  • Adding them up gets <math> 7+16+27=50 </math>. The overall percentage correct would be <math> \frac{50}{60}=\frac{5}{6}=5 \cdot 16.\overline{6}=83.\overl
    778 bytes (98 words) - 01:13, 5 July 2013
  • ...},</cmath> where <math>i^2 = -1</math>, then which of the following is not correct?
    17 KB (2,488 words) - 03:26, 20 March 2024
  • ...},</cmath> where <math>i^2 = -1</math>, then which of the following is not correct?
    3 KB (578 words) - 00:47, 20 March 2024
  • Ryan got <math>80\%</math> of the problems correct on a <math>25</math>-problem test, <math>90\%</math> on a <math>40</math>-p What is the correct ordering of the three numbers, <math>10^8</math>, <math>5^{12}</math>, and
    18 KB (2,768 words) - 21:05, 9 January 2024
  • Occasionally you will encounter multiple choice problems. Simply enter the correct letter for these problems. Probabilities, decimal values, and ratios should always be expressed as simplified common fractions unless otherwise specified.
    3 KB (533 words) - 10:55, 7 February 2023
  • Of these statments, the correct ones are: ...we can choose some term that is less than any given positive quantity. The correct answer is therefore <math>\boxed{\textbf{(E)}\ \text{Only }4\text{ and }5}<
    1 KB (217 words) - 16:13, 9 May 2015
  • \textbf{(D)}\ \text{If }0<x<1,y\text{ is always less than 0 and decreases without limit as }x\text{ approaches zero} \qquad \textbf{(E)}\ \text{Only some of the above statements are correct}</math>
    2 KB (313 words) - 17:09, 15 March 2017
  • ...the total amount of combinations is <math>6!=720</math>. However, we must correct for our overcounting because of rotation and reflection. We have that ther
    5 KB (815 words) - 17:53, 12 October 2023
  • ...acted her rounded values. Which of the following statements is necessarily correct? ...or screening for this disease. For a person who has this disease, the test always turns out positive. For a person who does not have the disease, however, th
    18 KB (2,350 words) - 18:48, 9 July 2023
  • ...acted her rounded values. Which of the following statements is necessarily correct?
    1 KB (246 words) - 07:32, 29 June 2023
  • ...acted her rounded values. Which of the following statements is necessarily correct?
    1 KB (187 words) - 16:07, 18 January 2020
  • ...acted her rounded values. Which of the following statements is necessarily correct?
    20 KB (2,681 words) - 09:47, 29 June 2023
  • ....4 = 32/5</math>. Thus, answer choice <math>\boxed{\textbf{(C)}}</math> is correct.
    12 KB (2,183 words) - 21:05, 23 December 2023
  • ...\sqrt{2}}{4}</math>. Thus, Answer choice <math>\boxed{\text{A}}</math> is correct.
    5 KB (815 words) - 21:59, 19 September 2023
  • ...dfrac{3c}{2}} = 40</math> seconds. Answer choice <math>\boxed{B}</math> is correct.
    2 KB (351 words) - 21:42, 21 August 2023
  • ...s that <math>x=3</math>. Thus, <math>\boxed{\textbf{(A)}\ 3}</math> is the correct answer.
    2 KB (297 words) - 09:05, 10 March 2023
  • Thus, answer choice <math>\boxed{\textbf{(D)}\ \frac{10}{3}}</math> is correct.
    669 bytes (94 words) - 19:59, 5 February 2023
  • ...= 11</math>. Thus, answer choice <math>\boxed{\textbf{(E)}\ 11}</math> is correct. ...+9=30</math>. Thus, answer choice <math>\boxed{\textbf{(E)}\ 11}</math> is correct.
    1 KB (212 words) - 20:54, 22 January 2023
  • ...p up when you run the program. Once you are confident that your program is correct, you can double-click on the Python file directly to run it.
    2 KB (373 words) - 21:44, 15 March 2012
  • ...t for the <math>9</math> different ways in which the person to receive the correct meal could be picked. Note, this implies that the dishes are indistinguisha Note: This solution gets the correct answer through coincidence and should not be used.
    3 KB (572 words) - 18:56, 13 June 2023
  • ...h> of the problems she solved alone. What was Zoe's overall percentage of correct answers?
    12 KB (1,771 words) - 21:13, 20 January 2024
  • This construction is correct because, for any <math>k> 1</math>,
    4 KB (790 words) - 06:38, 27 October 2022
  • ...ement <math>\boxed{\textbf{(C)}}</math> is therefore incorrect, and is the correct answer choice. ...th>A = \frac{1}{2} bh</math>). Statement <math>\textbf{(D)}</math> is also correct: let <math>q = \frac{a}{b}</math>. Then <math>q' = \frac{a \div 2}{2b} = \f
    2 KB (255 words) - 12:20, 5 July 2013
  • <math> \textbf{(B)}\ \text{In some instances there is more than one correct order in proving certain propositions.}</math> <math> \textbf{(D)}\ \text{It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposi
    1,021 bytes (157 words) - 12:20, 5 July 2013
  • ...^3</math> - <math>n</math> always for any integer <math>n</math>.Hence,the correct answer is <math>6</math>.
    1 KB (190 words) - 07:39, 31 December 2023
  • ...x > y</math> and <math> z\ne 0</math>. The inequality which is not always correct is:
    1 KB (189 words) - 02:34, 28 June 2017
  • Which statement is correct?
    15 KB (2,151 words) - 14:04, 19 February 2020
  • Which statement is correct?
    866 bytes (136 words) - 12:43, 5 July 2013
  • ...th> (0.6, 0.4) </math>. Assuming for the moment that this approximation is correct (it is, to better than <math> 1\% </math>) and so the point lies on Alan's
    3 KB (525 words) - 13:59, 27 May 2012
  • ...et right <math> 3\frac{1}{2} </math> hours ago. Now another clock which is correct shows noon. In how many minutes, to the nearest minute, will the alarm cloc ...nd/or minus signs between the digits on the left side to make the equation correct: <math> 1+2+3-4+5+6+78+9=100 </math>. Do this with only three plus or minus
    10 KB (1,477 words) - 16:02, 27 May 2012
  • 37: <math>\textbf{(E)}\ \text{Only some of the above statements are correct}</math>
    3 KB (443 words) - 06:25, 20 January 2023
  • Then if <math>x = \overline{CD}</math> and <math>y = \overline{BD}</math> the correct proportion is: ...ed. The intersections of the pairs of trisectors adjacent to the same side always form:
    21 KB (3,123 words) - 14:24, 20 February 2020
  • ...s are <math>a</math> units and <math>b</math> units respectively. Then the correct relation between them is: Since both lengths are positive, the [[AM-GM Inequality]] is satisfied. The correct relationship between <math>a</math> and <math>b</math> is <math>\boxed{\tex
    689 bytes (111 words) - 23:02, 14 February 2020
  • ...}\\ \textbf{(D)}\ \text{are always acute angles}\\ \textbf{(E)}\ \text{are always unequal to each other} </math> ...The expression has only the value 1.}\\ \textbf{(D)}\ \text{The expression always has a value between }-1\text{ and }+2.\\ \textbf{(E)}\ \text{The expression
    23 KB (3,535 words) - 16:29, 24 April 2020
  • To correct the total obtained the clerk must: ...{(A)}\ \text{always increases as }x\text{ increases}\\ \textbf{(B)}\ \text{always decreases as }x\text{ decreases to 1}\\ \textbf{(C)}\ \text{cannot equal 0}
    22 KB (3,509 words) - 21:29, 31 December 2023
  • correct to four decimal places.
    2 KB (284 words) - 14:44, 18 July 2016
  • ...other mathlete's problem, so it's critical that Role 1 gets his/her answer correct.
    931 bytes (153 words) - 17:05, 4 October 2012
  • .../math> nickel, <math>2</math> dimes, and <math>4</math> pennies. Thus, the correct answer is <math>3+2+1+4=\boxed{\textbf{(B)}\ 10}</math>.
    1 KB (183 words) - 14:33, 28 December 2023
  • ...as <math> 8:15\textsc{pm} </math>. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set? What is the correct ordering of the three numbers <math> \frac{5}{19} </math>, <math> \frac{7}{
    13 KB (1,835 words) - 08:51, 8 March 2024
  • ...as <math> 8:15\textsc{pm} </math>. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
    1 KB (234 words) - 21:18, 28 June 2022
  • ...h>, looking into the answers, <math>2</math> or <math>4</math> is possibly correct. It gives us the price of each pencil should be <math> 0.44/2=0.22 </math>
    2 KB (309 words) - 15:36, 28 December 2023
  • What is the correct ordering of the three numbers <math> \frac{5}{19} </math>, <math> \frac{7}{ ...\frac{14}{(x+14)^2}</math> and this is positive. Because the derivative is always positive and the values of <math>x</math> given by this question <math>(5,
    4 KB (513 words) - 18:34, 20 January 2024
  • ...{4}</math> cup of sugar. How many times must she fill that cup to get the correct amount of sugar?
    978 bytes (150 words) - 13:10, 1 July 2023
  • ...{4}</math> cup of sugar. How many times must she fill that cup to get the correct amount of sugar?
    12 KB (1,894 words) - 15:59, 3 January 2024
  • ...is lower than 240. Therefore, <math>\boxed{\textbf{(D) }240}</math> is the correct answer.
    3 KB (443 words) - 12:32, 8 January 2021
  • ...ithout the use of a table (note: in 1951, calculators were very rare). The correct answer is therefore <math>\boxed{\textbf{(A)}\ \log 17}</math>.
    1 KB (194 words) - 12:27, 5 July 2013
  • ...frac{(21)(49)}{400}</cmath> so <cmath>PQ=\frac{7}{20}\sqrt{21}</cmath> The correct answer is <math>\fbox{(B)}</math>.
    1 KB (194 words) - 13:50, 11 November 2023
  • Cassandra sets her watch to the correct time at noon. At the actual time of 1:00 PM, she notices that her watch rea
    1 KB (168 words) - 00:54, 5 January 2014
  • ...th>3 \cdot 5 = 15</math>, so <math>{\boxed{\textbf{(D)15}}}</math> is the correct answer.
    2 KB (357 words) - 16:43, 29 June 2021
  • ...e first curly bracket, always starts with a colon ( : ), and this colon is always immediately followed by the name of the pseudo-class. is not correct; you cannot nest a :not() pseudo-class inside a :not() pseudo-class. <!-- S
    15 KB (2,197 words) - 22:49, 24 July 2023
  • Calculating, <math>0.8 - 0.07 = 0.80 - 0.07 = 0.73</math> The correct answer is <math>E</math>.
    377 bytes (47 words) - 01:43, 23 October 2014
  • Whatever AoPS says is correct, and AoPS says that Mr. Sato is amazing. Thus, Mr. Sato is amazing. (Proved
    605 bytes (95 words) - 16:50, 28 January 2024
  • Note: It is correct, original one was the first one posted but was incorrect.
    1 KB (243 words) - 03:24, 9 January 2017
  • -edited by srisainandan6 to clarify and correct a small mistake
    11 KB (1,442 words) - 19:28, 21 October 2023
  • ...t{y - 1} + \sqrt{z - 1}</math> for x = y = z. We suspect if the inequality always holds. We are almost done, but we need to find the correct argument. (How frustrating!)
    3 KB (517 words) - 20:02, 30 April 2014
  • ...ath>1</math> and <math>2016</math>, inclusive. Which of the following is a correct statement about the probability <math>p</math> that the product of the thre
    14 KB (2,104 words) - 22:26, 16 September 2022
  • ...of its correct envelope, so it is not possible to have exactly nine in the correct envelopes. Therefore, the answer is <math>\boxed{0}</math>.
    607 bytes (93 words) - 21:45, 15 October 2013
  • Since we cannot simplify further, the correct answer is <math>\boxed{\textbf{(A)}\ \frac{\sqrt{3}}{6}}</math>
    847 bytes (107 words) - 22:45, 26 December 2015

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