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  • ...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
  • ;Is this correct? <math>(\sqrt{x} = 5)</math> = <math>(x=25)</math> = <math>(\sqrt{625} = x)
    206 bytes (28 words) - 21:15, 29 April 2012
  • ...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 (191 words) - 06:08, 6 April 2024
  • ...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
  • ...wrong link sometime in the past <math>5</math> seconds... Please promptly correct your mistake.
    175 bytes (28 words) - 16:52, 19 May 2012
  • 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
  • The currently uploaded solution is correct until the part where it says <math> x=\sqrt{3}\/b/2 </math>.
    973 bytes (163 words) - 01:34, 26 February 2013
  • ...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 (193 words) - 22:05, 20 April 2024
  • 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
  • ...much more chocolates and junk foods within the stores and they're not take correct brushing it prospects to tooth problem. The dentist las Vegas give permanen
    3 KB (537 words) - 01:55, 17 October 2013
  • 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
  • ...is is certainly one of the mental illnesses so it should be stopped in the correct time. If you reside with this psychological depression, read this post to o
    3 KB (435 words) - 03:04, 30 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
  • <math>\textbf{(E)}\ \text{none of these is correct} </math>
    1 KB (256 words) - 22:39, 10 April 2023
  • ..., with <math>a ! a = a</math>. Which of the following three rules is (are) correct? The first rule must be correct as both sides of the equation pick the larger out of a and b.
    1 KB (258 words) - 22:25, 17 April 2023
  • ...math>2</math>, leaving us with <math>\boxed{\textbf{(C)}\ 3}</math> as the correct answer.
    2 KB (261 words) - 18:19, 25 March 2021
  • Testing the answer choices, we see that <math>\boxed{B}</math> is the correct answer.
    2 KB (294 words) - 17:01, 28 June 2023
  • \textbf{(E)}\ \text{none of these is correct} </math> Which of the following three rules is (are) correct?
    17 KB (2,459 words) - 22:40, 10 April 2023
  • Which of the following methods of proving a geometric figure a locus is not correct?
    1 KB (188 words) - 15:21, 19 April 2014
  • ...er hour on Wednesday and at 4 miles per hour on Friday. If Grandfather had always walked at 4 miles per hour, he would have spent less time on the treadmill. .... By which of the following might her incorrect sum have differed from the correct one?
    15 KB (2,162 words) - 20:05, 8 May 2023
  • .... By which of the following might her incorrect sum have differed from the correct one? The correct score was <math>10a+b</math>. Clara misinterpreted it as <math>10b+a</math>
    1 KB (203 words) - 21:40, 3 January 2024
  • ...th>14</math>. After these mistakes, the result was <math>16</math>. If the correct operations had been used, the value produced would have been
    14 KB (2,124 words) - 13:39, 19 February 2020
  • <math> f(1)=\frac{3}{0} </math>, which is undefined. Hence, the (in)correct answer is <math> \boxed{\textbf{(C)}\ f(1)=0} </math>.
    870 bytes (142 words) - 20:45, 2 January 2014
  • ...questions in both tests, with 2 1/2 hours given to complete the problems. Correct answers are worth 4 points, incorrect answers worth -1, and unanswered ques
    554 bytes (87 words) - 12:01, 15 February 2014
  • <math>\textbf{(A)}\ \text{always an even integer}\qquad \textbf{(C)}\ \text{always an odd integer}\qquad
    3 KB (437 words) - 01:40, 16 August 2023
  • ...<math>6</math> instead of being multiplied by <math>6.</math> Based on the correct answer, the error thus committed, to the nearest percent, is : ...OG</math> increases toward the value <math>a</math>, while <math>JH</math> always equals <math>HG</math>, the ratio <math>K:R</math> becomes arbitrarily clos
    16 KB (2,571 words) - 14:13, 20 February 2020
  • ...th>14</math>. After these mistakes, the result was <math>16</math>. If the correct operations had been used, the value produced would have been We reverse the operations that he did and then use the correct operations. His end result is <math>16</math>. Before that, he subtracted <
    1 KB (179 words) - 17:26, 9 January 2021
  • ...there. I undid his edits because they seemed like plagiarism, but please correct me if this was wrong.
    286 bytes (42 words) - 17:41, 2 July 2014
  • ...and Terry are each told to calculate <math>8-(2+5)</math>. Harry gets the correct answer. Terry ignores the parentheses and calculates <math>8-2+5</math>. If
    800 bytes (123 words) - 11:18, 2 July 2023
  • We will estimate the answer using a wrong method then guess the correct answer choice. ...ead ''about'' 4. We can asume that the closest other answer choice to 4 is correct: <cmath>\boxed{\textbf{(D) }2+\sqrt3}</cmath>
    7 KB (1,191 words) - 23:37, 23 June 2022
  • Scored +4 points correct, 0 for blank, -1 for incorrect '''PLUS''' 3 tie breaker completion question Scored 5 points for correct in first interval, 2 points for correct in second interval<br>
    885 bytes (129 words) - 19:56, 13 February 2014
  • ...traint that the answer is an integer, we can be certain that our answer is correct.)
    10 KB (1,653 words) - 00:30, 27 January 2024
  • ...<math>6</math> instead of being multiplied by <math>6.</math> Based on the correct answer, the error thus committed, to the nearest percent, is :
    472 bytes (66 words) - 01:52, 16 August 2023
  • So the correct answer is <math>201</math>, which is <math>\fbox{E}</math>
    1 KB (189 words) - 20:13, 23 January 2017
  • ...f <math>S</math> which is divisible by 11. Thus, <math>\fbox{B}</math> is correct.
    2 KB (297 words) - 20:09, 6 January 2018
  • ..., the LHS is always equal to the RHS, so <math>\fbox{D}</math> is the only correct statement.
    2 KB (287 words) - 21:34, 13 July 2019
  • ...math>, which directly contradicts <math>A</math>. Thus, <math>A</math> is always false. ...s do not follow from the premises, leading to <math>\fbox{E}</math> as the correct answer.
    2 KB (282 words) - 02:37, 17 December 2021
  • ...cents of first-class postage on a letter weighing <math>W</math> ounces is always .../math> cents, while option <math>E</math> gives <math>12</math> cents, the correct answer. Thus, the answer is <math>\fbox{E}</math>.
    1 KB (244 words) - 06:54, 15 July 2019
  • We can force this triangle to be equilateral because the ratios are always <math>3:3:1</math> no matter which rotation, and with the symmetry of the e ...o this, the coordinate bash with all these calculations should get you the correct answer. Also, there is an even bashier way using all the points and shoelac
    7 KB (1,136 words) - 10:01, 23 December 2023
  • That is, whatever <math>C</math> is, the announced value must be the correct result when <math>C</math> is rounded to that number of digits.
    17 KB (2,535 words) - 13:45, 19 February 2020
  • ...new scoring system that year, one received <math>5</math> points for each correct answer, ...started with <math>30</math> points, received <math>4</math> more for each correct answer,
    17 KB (2,512 words) - 18:30, 12 October 2023
  • ...ath> dollars and <math> x</math> cents, the incorrect amount exceeding the correct amount by <math> &#036;17.82</math>. Then: \textbf{(D)}\ \text{the incorrect amount can equal twice the correct amount}\qquad \\
    795 bytes (124 words) - 06:29, 3 October 2014
  • ...^3</math>, and <math>a-b = x</math>, which of the following conclusions is correct? ...th>CD</math> intersects side <math>AC</math> at <math>N</math>. Then it is always true that
    16 KB (2,512 words) - 04:48, 27 November 2021
  • If <math>(1.0025)^{10}</math> is evaluated correct to <math>5</math> decimal places, then the digit in the fifth decimal place
    18 KB (2,703 words) - 20:50, 11 September 2023
  • ...<math>\frac {1}{1 + y}, |y| < 1</math>, the ratio of the error made to the correct value is: ...atter how <math>a, b, c, d</math>, and <math>e</math> are chosen, we shall always have:
    19 KB (2,873 words) - 18:57, 16 August 2023
  • If a certain operation on one or more members of the set always yields a member of the set, \textbf{(E)}\ \text{None of these are correct}</math>
    18 KB (2,905 words) - 18:33, 5 April 2023
  • ...7 points. Partial credit will be awarded for significant progress toward a correct solution.
    1 KB (215 words) - 18:48, 5 July 2021
  • The guests know that the March Hare always does this, but they has more correct guesses than all the others, that guest wins. When
    7 KB (1,209 words) - 18:07, 19 October 2014
  • The guests know that the March Hare always does this, but they has more correct guesses than all the others, that guest wins. When
    2 KB (297 words) - 03:33, 13 January 2019
  • The guests know that the March Hare always does this, but they has more correct guesses than all the others, that guest wins. When
    7 KB (1,228 words) - 15:10, 20 August 2020
  • = Part A: Each correct answer is worth 5 points = = Part B: Each correct answer is worth 6 points =
    6 KB (770 words) - 00:51, 26 October 2014
  • That is, whatever <math>C</math> is, the announced value must be the correct result when <math>C</math> is rounded to that number of digits.
    1 KB (148 words) - 18:11, 26 February 2018
  • ...the height of the plant on May 8th is <math>2 + 7.35 = 9.35 m</math>. The correct answer is <math>E</math>.
    776 bytes (126 words) - 02:06, 23 October 2014
  • ...1}{2}bh = \frac{1}{2}(9)(4) = \frac{1}{2}(36) = 18</math>. Therefore, the correct answer is <math>D</math>
    1,020 bytes (149 words) - 02:14, 23 October 2014
  • ...of the numbers on the six unseen faces is <math>42 - 21 = 21</math>. The correct answer is <math>C</math>.
    2 KB (320 words) - 02:23, 23 October 2014
  • ...d the area of triangle <math>PVT</math>, or <math>12 + 6 = 18</math>. The correct answer is <math>A</math>.
    2 KB (349 words) - 02:41, 23 October 2014
  • ...new scoring system that year, one receives <math>5</math> points for each correct answer, ...started with <math>30</math> points, received <math>4</math> more for each correct answer, lost <math>1</math> point for each wrong answer, and neither gained
    1 KB (208 words) - 18:32, 1 April 2018
  • <math>\textbf{(A)}\ \text{correct}\quad \textbf{(B)}\ \text{always less than A}\quad
    1 KB (185 words) - 18:43, 1 April 2018
  • = Part A: Each correct answer is worth 5 points = = Part B: Each correct answer is worth 6 points =
    10 KB (1,590 words) - 16:43, 29 January 2021
  • = Part A: Each correct answer is worth 5 points = = Part B: Each correct answer is worth 6 points =
    5 KB (621 words) - 00:50, 26 October 2014
  • ...and Terry are each told to calculate <math>8-(2+5)</math>. Harry gets the correct answer. Terry ignores the parentheses and calculates <math>8-2+5</math>. If ...ntify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random wil
    13 KB (1,957 words) - 12:08, 13 January 2024
  • ...math>10-6=4</math> paths possible. <math>\boxed{(\text{A})4}</math> is the correct answer.
    2 KB (352 words) - 21:47, 6 January 2024
  • ...ntify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random wil There is a <math>\frac{1}{3}</math> chance that the reader will choose the correct baby picture for the first person. Next, the second person gives a <math>\f
    2 KB (310 words) - 11:12, 2 July 2023
  • ...ratio of 1/3, so the angle it carves is 120 degrees, which leads us to the correct answer of 4 o' clock. <math>\boxed{\textbf{(C) }4 \ \text{o' clock}}</math
    9 KB (1,380 words) - 09:00, 1 December 2023
  • Let --- denote any of the 6 racers not named. Then the correct order looks like this:
    1 KB (224 words) - 14:57, 23 November 2023
  • ...we can conclude that for a grid that is <math>n \times n</math>, there are always <math>4</math> corners squares, <math>4(n-2)</math> edge squares, and <math ...plication and simplification finds us with <math>\boxed{090}</math> as the correct answer.
    4 KB (653 words) - 17:40, 1 July 2023
  • ...ing both sides of the inequality by 2b - 3, but otherwise this solution is correct)
    5 KB (856 words) - 22:39, 14 February 2024
  • ...[[algorithm|algorithms]] are formed by adjusting the greedy process to be correct, often through the use of clever [[sorting]]. ...rally very interesting unless they're <i>correct</i>; in other words, they always produce the maximal overall benefit. In order to prove the correctness of a
    9 KB (1,535 words) - 17:44, 24 November 2016
  • The times between <math>7</math> and <math>8</math> o'clock, correct to the nearest minute, when the hands of a clock will form an angle of <mat ...for the two hands to make <math>84^{\circ}</math> angles. Thus the times, correct to the nearest minute, at which the hands of the clock will form an <math>8
    2 KB (361 words) - 11:59, 21 January 2021
  • ...result of 77 but 2 gives a problematically close 78. And the trend is not always decreasing: ...ime in 2001=7*11*13 will give an incorrect answer of <math>177</math>. The correct answer will be <math>164</math>.
    1 KB (175 words) - 11:54, 29 August 2021
  • (c) Give an explanation that shows that the formula you give is correct.
    6 KB (1,055 words) - 12:37, 30 July 2021
  • (c) Give an explanation that shows that the formula you give is correct.
    1 KB (176 words) - 21:02, 28 October 2023
  • ...tion <math>\frac{P(x+1)}{P(x)}=\frac{x+2}{x-1}</math> but will give us the correct values of <math>P(2)</math> and <math>P(3)</math>. Thus <math>P(x)=a(x-1)x(
    8 KB (1,415 words) - 14:00, 22 December 2021
  • ...th>, so <math>b=9, 7, 5, 3</math>. Testing out <math>b=9</math> yields the correct answer of <math>\boxed{262}</math>. Note that even if this answer were asso
    6 KB (983 words) - 01:18, 2 February 2023
  • ...<math>12</math> of these <math>20</math> multiple choice questions correct, given that you don't know how to work any of them and are for ...robability that exactly <math>6</math> of the books were returned to their correct (original) position can be expressed as <math>\frac{m}{n}</math>, where <ma
    31 KB (4,811 words) - 00:02, 4 November 2023
  • \textbf{(E)}\ \text{none of these is correct} </math>
    3 KB (560 words) - 10:11, 3 May 2020
  • ...^3</math>, and <math>a-b = x</math>, which of the following conclusions is correct?
    850 bytes (151 words) - 17:09, 19 January 2021
  • correct to four decimal places.
    4 KB (553 words) - 08:32, 18 May 2018
  • ...l after they have sat down, and it turns out that no one is sitting in the correct seat. Prove that the table can be rotated so that at least two of the guest
    3 KB (499 words) - 12:17, 11 August 2016
  • ...l after they have sat down, and it turns out that no one is sitting in the correct seat. Prove that the table can be rotated so that at least two of the guest
    717 bytes (123 words) - 16:45, 4 August 2016
  • be placed in the envelopes so that no letter is in a correct envelope?
    14 KB (2,904 words) - 18:24, 16 May 2017
  • Note: we can easily verify that this is the correct answer; for example, <math>\left(\frac{1}{2}, \frac{1}{2}\right)</math> wor
    2 KB (272 words) - 11:17, 4 September 2022
  • ...has been negated as well as reversed.) We know that the contrapositive is always true if the given statement is true. Note: An A is usually 90%-100% of the questions correct.
    3 KB (485 words) - 16:50, 5 August 2022
  • <math>\fbox{C}</math> is the correct answer.
    4 KB (533 words) - 19:01, 15 March 2024
  • ...account for the negative 2016th-root of 2017, because that will still have correct, desired solutions for (a, b). Based on that, the answer would be E - 597.
    241 bytes (42 words) - 16:22, 8 February 2017
  • ...uantities is no greater than the common value. Which of the following is a correct description of <math>S</math>?
    3 KB (446 words) - 14:58, 10 June 2023
  • ...antities is no greater than this common value. Which of the following is a correct description for <math>S?</math>
    2 KB (421 words) - 00:34, 1 August 2021
  • ...antities is no greater than this common value. Which of the following is a correct description for <math>S?</math>
    15 KB (2,285 words) - 18:02, 28 October 2023
  • ...h>\textbf{(E)}</math> tried? This is because the problem can only have one correct answer, so if we have an option that already works, we can conclude that no
    5 KB (864 words) - 01:42, 17 August 2023
  • ...that we can use for this problem is that a multiple of <math>9</math> will always have its digits sum to a multiple of <math>9</math>. We can find out that t ...sible by <math>9</math>). But since it does not, <math>1</math> is not the correct answer.
    5 KB (798 words) - 14:35, 14 October 2022
  • ...uantities is no greater than the common value. Which of the following is a correct description of <math>S</math>?
    15 KB (2,418 words) - 16:58, 7 November 2022
  • doesn't correct use grammar
    487 bytes (68 words) - 14:53, 4 December 2017
  • ...e 3 ways has a probability associated with it, so probability of getting 1 correct is <math>3 * \frac{4}{27} = \frac{4}{9} </math>
    3 KB (452 words) - 08:16, 4 November 2021
  • .../math> is divided by the positive integer <math>n</math>, the remainder is always the positive integer <math>s \neq r</math>. Find <math>m+n+r+s</math>. ...so yields remainders of <math>5</math>, which means our work up to here is correct.
    4 KB (580 words) - 03:08, 5 January 2024
  • First, note that the first two digits will always be a positive number. We will start with base twelve because of its repetit ...h> and <math>64.30_8</math>. Since <math>d\neq0</math>, the first value is correct. Compiling the necessary digits leaves us a final answer of <math>\boxed{32
    6 KB (961 words) - 22:03, 18 January 2024
  • ...math>n=2\sqrt{3}</math>. When we plug in these two values, we recover the correct answer of <math>\frac{75\sqrt3}{67}</math>.
    22 KB (3,622 words) - 17:11, 6 January 2024
  • Since <math>21</math> is a factor of <math>63</math>, this solutions is correct. ...e <math>112</math> is a factor of <math>224</math>, this solutions is also correct.
    3 KB (503 words) - 00:40, 17 November 2023
  • ...h> of the problems she solved alone. What was Zoe's overall percentage of correct answers? ...= \frac{93}{100} = \boxed{\textbf{(C) } 93}</math> percent of the problems correct.
    4 KB (649 words) - 13:49, 14 January 2024
  • *Feel free to edit answer if this is not correct, but do not edit the process.
    1,002 bytes (137 words) - 13:25, 22 June 2018
  • Choose the correct answer. ...epetition, such that the sum of the numbers of three adjacent triangles is always a multiple of 3? Solutions obtained by rotation or reflection are different
    8 KB (1,278 words) - 09:46, 11 January 2018
  • Choose the correct answer.
    502 bytes (63 words) - 20:57, 7 January 2018
  • ...math>x^2, a^2,</math> and <math>ax</math> are all positive. Hence the only correct answer is <math>\fbox{B}</math>.
    603 bytes (103 words) - 22:17, 7 July 2018
  • ...145}{147}</math>, so <math>\boxed{\textbf{(D) } \frac{145}{147}}</math> is correct.
    16 KB (2,454 words) - 13:30, 23 September 2023
  • ...4</math> total roots (counting multiplicity). We see that <math>x=0</math> always has at least one intersection at <math>(0,-a)</math> (and is in fact a doub ...from the vertex. Therefore, <math>\boxed{\textbf{(E) }a>\frac12}</math> is correct.
    9 KB (1,502 words) - 23:31, 19 August 2023
  • ...a non-multiple of 3 is always <math>1 \pmod{3}</math>, the only expression always a multiple of <math>3</math> is <math>\boxed{\textbf{(C) } p^2+26} </math>. Therefore, <math>\framebox{C}</math> is the correct answer.
    2 KB (279 words) - 14:35, 5 November 2023
  • ...sum with equal probability as <math>10</math> is <math>39</math>. So, the correct answer is <math>\boxed{\textbf{(D)} \text{39}}</math>, and we are done. ...d on and on and on. This means that <math>P(10)=P(39)</math>, and thus the correct answer is <math>\boxed{\textbf{(D)} \text{ 39}}</math>.
    5 KB (835 words) - 13:48, 16 February 2024
  • ...<math>3</math> to get our answer of <math>32 \cdot 3 = 96</math>. So, the correct answer is <math>\boxed{\textbf{(D)} \text{ 96}}</math>. ..., <math>B</math>, and <math>C</math>. Now, notice that you can only form a correct grouping either like this:
    7 KB (1,281 words) - 17:24, 8 January 2024
  • ...of the figure we are trying to find is <math>2</math>. This means that the correct answer choice is <math>\boxed{E}</math>.
    8 KB (1,286 words) - 13:29, 21 April 2024
  • Substitute values for each answer choice to determine which one is correct for all <math>r</math>.
    3 KB (508 words) - 20:33, 17 August 2022
  • \textbf{(E)}\ \text{None of these are correct}</math>
    1 KB (193 words) - 18:10, 19 May 2018
  • \textbf{(E)}\ \text{None of these is correct } </math>
    2 KB (258 words) - 20:50, 22 May 2018
  • ...ath>. Square both sides, we find that <math>\boxed{\textbf{(A)}}</math> is correct. ...he absolute maximum, we can find that <math>\boxed{\textbf{(A)}}</math> is correct.
    3 KB (545 words) - 04:29, 17 October 2022
  • ...equation results in <math>\sin(30^{\circ}) = \frac{1}{2}</math>, which is correct. Thus, the answer is <math>\boxed{\textbf{(C)}}</math>.
    1 KB (242 words) - 17:13, 18 April 2019
  • ...s <math>t</math> ranges from <math>0</math> to <math>127</math>. Hence,the correct answer is <math>127</math>, <math>\boxed{\textbf{(D)}}</math>.
    2 KB (342 words) - 14:07, 14 January 2024
  • ...y of surface area to product ratio. The pub speed was decided to input the correct amount of"energy" to reach the task at hand. Time has a significant part in
    6 KB (1,092 words) - 02:17, 18 July 2018
  • ...ath>2</math> and the height is <math>2</math>, so <math>XBE</math> is also correct! Those are the only three cases, so there are <math>12*3=36</math> cases fo
    6 KB (1,023 words) - 10:38, 21 November 2023
  • Always remember; the simpler your code is the better it will preform! ...ist of integers from 1 to 51, but excludes 51. This is because python will always think of the last number as a barrier and the number before as the stopping
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  • There's an error in the solution. It's correct to say that the answer is C, but that's because z (not, as stated, x) must
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  • I believe the correct answer is 267. There is a relatively simple dynamic programming solution fo
    632 bytes (102 words) - 21:03, 15 April 2018
  • ...which any Christian likes about individuals varieties of sites. As may be correct with equivalent web dating net sites that these Religious internet websites
    4 KB (574 words) - 08:17, 29 June 2018
  • ...ceremony you happen to be more than prone for, and hence that we within an correct and long-lasting London Escort enterprise normally motivate our consumers t
    3 KB (566 words) - 00:34, 1 July 2018
  • But Alexis scribbles some work on her napkin and declares the correct answer. What answer did Alexis find?
    2 KB (421 words) - 20:19, 6 August 2023
  • Assuming Michael is correct, compute <math>m+n</math>. In this problem, assume that gas mileage is cons
    2 KB (287 words) - 18:54, 12 July 2018
  • ...f circles intersects in two points. After careful doodling, Tony finds the correct answer, and is proud that he can solve a problem from late on an AMC 10 exa
    2 KB (319 words) - 19:50, 12 July 2018
  • .... Each question has answer choices A through E. 4 points are awarded for a correct answer, 0 for an incorrect answer, and 1 for a question left blank. The top
    1 KB (211 words) - 18:22, 13 May 2024
  • Then if <math>x = \overline{CD}</math> and <math>y = \overline{BD}</math> the correct proportion is:
    1 KB (267 words) - 17:00, 20 July 2018
  • "That's correct," confirms Joshua's mother. "Also, the base <math>10</math> logarithm of <m Assuming Hannah's prediction of volume reduction is correct and effects are compounded continuously, compute the first year that the nu
    4 KB (595 words) - 20:32, 4 August 2018
  • ...point. He smiles for a moment, then keeps jogging. If Michael’s work is correct, what distance did he compute as the shortest possible distance one of the
    3 KB (550 words) - 17:03, 7 August 2018
  • Josh recognizes that the cubes of the sums are always larger than the sum of cubes of positive integers. For instance, What is the correct value of <math>n</math> that Joshua found?
    3 KB (436 words) - 17:57, 5 November 2018
  • ...robability that exactly <math>6</math> of the books were returned to their correct (original) position can be expressed as <math>\frac{m}{n}</math>, where <ma
    2 KB (335 words) - 00:02, 4 November 2023
  • Which of the following is the correct order of the fractions <math>\frac{15}{11},\frac{19}{15},</math> and <math>
    5 KB (664 words) - 11:28, 23 January 2024
  • ...The claim that <math>f(i)</math> has to be <math>0</math> at some point is correct, but only because of discrete continuity. Would someone confirm this? I don
    416 bytes (77 words) - 04:18, 25 March 2019
  • Not sure what you mean, but the solution seems correct. You might be confusing the length of the strip (and the side length of the
    358 bytes (63 words) - 20:05, 7 April 2019
  • If <math>x>0</math>, then the correct relationship is:
    467 bytes (74 words) - 18:51, 22 April 2020
  • ...ath>9</math>, which means it's a composite number and not prime. Thus, the correct answer must be <math>\boxed{\textbf{(B) } 996}</math>.
    3 KB (561 words) - 16:31, 5 February 2024
  • ...er, <math>\text{gcd}(16, 8) = 8</math>. Here <math>a+b-\gcd(a,b)</math> is correct when a = 17 and b = 10.
    3 KB (529 words) - 02:24, 8 September 2023
  • ..._4{x} + 3 > \log_2{x}.</cmath> The second inequality is redundant, as it's always less restrictive than the last inequality. ...quality <math>3+\log_4{x} > \log_2{x}</math> we see <math>64</math> is the correct number. Now we have <math>64 > x > 4</math> and the number of integers in b
    2 KB (345 words) - 12:25, 18 September 2021
  • ...Luckily, <math>4</math> is the largest answer choice so we know it must be correct.
    8 KB (1,306 words) - 22:18, 1 February 2020
  • Note : If our answer is correct, then <math>QX=\frac{11}{2}</math>, which made <math>Q</math> the midpoint
    13 KB (2,252 words) - 11:32, 1 February 2024
  • ...and we can turn any point (such as 3 + 4i) into reix form (by finding the correct value of x and r)
    3 KB (543 words) - 15:24, 13 June 2019
  • In section A, 2 points are given for a correct answer, 0 points are given for an unanswered question and 1 point is deduct
    2 KB (262 words) - 04:09, 18 July 2020
  • ...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
    514 bytes (84 words) - 18:34, 14 January 2020
  • ...selected and the women who were not selected, the committee would have the correct number of men and women. Conversely, for every committee that could be form
    7 KB (1,023 words) - 23:56, 13 February 2023
  • ...to <math>x = 28 \cdot \frac{5}{4}</math>, or <math>35</math> dollars. The correct answer is <math>\boxed{\textbf{(E)}}</math>
    1 KB (195 words) - 12:19, 23 July 2019
  • ...at most three contestants have the same number of new friends, so Amin is correct. ...d and hence constructing such a graph is not possible meaning that Amin is correct.
    3 KB (508 words) - 19:58, 3 February 2024
  • ...the third statement ("On this card exactly three statements are false") is correct. ...false, that would mean that only <math>1</math> statement is true. This is correct since if only <math>1</math> statement is true, the card that is true is th
    2 KB (302 words) - 18:17, 6 November 2021
  • ...ble on the AoPS wiki. Please do take your time to get spelling and grammar correct. Please make sure your contribution sounds informational.
    518 bytes (87 words) - 14:20, 19 September 2020
  • Which of the following is the correct order of the fractions <math>\frac{15}{11},\frac{19}{15},</math> and <math>
    17 KB (2,585 words) - 15:27, 4 May 2024
  • ...nday occured; thus, <math>\boxed{\textbf{(C)}\ \text{Wednesday}}</math> is correct. ...0</math>, then if you minus 3 from the first number of this cycle, it will always be <math>0</math>. So, the answer is <math>\boxed{\textbf{(C) Wednesday}}</
    6 KB (903 words) - 16:23, 30 December 2023
  • .../math>, leaving <math>\boxed{\textbf{(C)}\ 96}</math> as the only possible correct answer.
    11 KB (1,770 words) - 08:56, 17 May 2024
  • .../math> must be <math>7</math>, since the unit digit of <math>60y</math> is always <math>0</math> and the unit digit of <math>57</math> is <math>7</math>. The ...on, <math>\gcd(63, n + 120) = 21</math>, we know that if <math>n</math> is correct, after we add <math>120</math> to it, it should be divisible by <math>21</m
    17 KB (2,544 words) - 12:09, 1 September 2023
  • find <math>-9</math> and <math>-1</math> for the roots. The correct equation was: Let <math>x^2+bx+c=0</math> represent the correct equation. Since the coefficient of the <math>x^2</math> term is <math>1</ma
    1 KB (220 words) - 22:56, 14 February 2020
  • ...being correct, this solution does not work. (Arcticturn or anybody, please correct me if I am wrong. I only THINK this solution is invalid and have provided m
    4 KB (693 words) - 17:49, 12 November 2023
  • ...t{2}-1 \pm \sqrt{8-4\sqrt{2}}</math> (technically the smaller value is the correct one but it doesn’t matter for our purposes). We can then calculate <math>
    11 KB (1,850 words) - 23:33, 27 March 2024
  • ...}.</math> Later he found that his answer is <math>0.5</math> less than the correct answer. What is the <math>2</math>-digit number <math>\underline{a} \ \unde
    15 KB (2,302 words) - 23:41, 14 April 2024
  • ...stion is followed by answers marked A, B, C, D and E. Only one of these is correct. # You will receive 5 points for each correct answer, 2 points for each problem left unanswered, and 0 points for each in
    3 KB (364 words) - 19:28, 22 December 2021
  • ...stion is followed by answers marked A, B, C, D and E. Only one of these is correct. # You will receive ? points for each correct answer, ? points for each problem left unanswered, and ? points for each in
    3 KB (332 words) - 19:54, 22 December 2021
  • ...stion is followed by answers marked A, B, C, D and E. Only one of these is correct. # You will receive ? points for each correct answer, ? points for each problem left unanswered, and ? points for each in
    3 KB (396 words) - 19:36, 22 December 2021
  • For every correct answer: ? points
    3 KB (389 words) - 14:50, 19 February 2020
  • ...stion is followed by answers marked A, B, C, D and E. Only one of these is correct. # You will receive ? points for each correct answer, ? points for each problem left unanswered, and ? points for each in
    3 KB (396 words) - 20:21, 22 December 2021
  • ...stion is followed by answers marked A, B, C, D and E. Only one of these is correct. # You will receive ? points for each correct answer, ? points for each problem left unanswered, and ? points for each in
    3 KB (426 words) - 20:18, 22 December 2021
  • ...stion is followed by answers marked A, B, C, D and E. Only one of these is correct. # You will receive ? points for each correct answer, ? points for each problem left unanswered, and ? points for each in
    4 KB (491 words) - 14:38, 19 February 2020
  • ...rns to <math>(\frac{x+y}{2}+1)\geq \sqrt{2}\sqrt{x+y}</math>. It is always correct according to <math>AM-GM</math> inequality, it happens when <math>x=y=1</ma
    3 KB (473 words) - 00:09, 4 December 2021
  • #You will receive 4 points for each correct answer, and 0 points for each problem left unanswered or incorrect.
    5 KB (729 words) - 18:41, 11 July 2021
  • ...portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, for an
    4 KB (581 words) - 19:20, 26 May 2020
  • ...90 minutes long, but part I consists of 25 multiple choice questions. Each correct answer is worth 4 points, incorrect answer is -1 points, and 0 points for l
    1 KB (229 words) - 00:04, 29 May 2020
  • ...ed. The intersections of the pairs of trisectors adjacent to the same side always form: ...our points form a parallelogram with no special properties. Therefore, the correct answer is <math>\boxed{\text{C}}</math>, and we are done.
    1 KB (162 words) - 14:17, 24 April 2020
  • ...se requirements. Checking the answer choices, <math>\fbox{A}</math> is the correct solution.
    1 KB (240 words) - 18:31, 2 May 2022
  • ...the form of <math>(x - a)(x - b) = 0</math>, where a and b are roots, the correct quadratic, once factored, would look like <math>(x - 7)(x + 1) = 0</math>
    1 KB (207 words) - 11:11, 12 July 2021
  • ...h>\textbf{(C)}</math> is the only answer choice left and there must be one correct answer, the answer must be <math>\boxed{\textbf{(C)}}</math>.
    2 KB (263 words) - 11:33, 12 August 2020
  • ...s a fabulous hashing technique upon computer help equipment to receive the correct hash signifying a ventures relating to bitcoin and when you get this operat
    3 KB (530 words) - 12:26, 3 June 2020
  • The correct character for a red queen is "@" and the correct character for a blue queen is "&".
    2 KB (267 words) - 17:25, 9 July 2020
  • We first draw a diagram with the correct Cartesian coordinates and a center of rotation <math>P</math>. Note that <m
    10 KB (1,542 words) - 13:29, 19 January 2024
  • (Edit: While the guess would be technically correct, the assumption that the radius would have to be a whole number for the ans
    13 KB (2,197 words) - 23:00, 8 January 2024
  • .... The AIME is a 15-question examination giving <math>10</math> points each correct answer and <math>0</math> points for each wrong or blank answer. An USAMO i
    14 KB (2,267 words) - 12:49, 9 June 2020
  • Isn't it correct that you only have one move? We are waiting for you. I'm sorry if I sounded
    16 KB (2,169 words) - 22:46, 21 August 2020
  • ...>\sqrt{4 \cdot 6 + 5 \cdot 7} = \sqrt{59}.</math> [I don't believe this is correct... are the two diagonals of <math>ABCD</math> necessarily congruent? -peace
    16 KB (2,635 words) - 19:56, 24 December 2023
  • ...{(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} <math>\textbf{(A)}\ \text{always increases as } x\text{ increases}</math> is wrong due to the quadratic natu
    1 KB (216 words) - 17:25, 1 August 2020
  • Therefore, the correct answer is <math>\textbf{(A)}</math>
    873 bytes (137 words) - 12:38, 3 August 2020
  • <math>\textbf{(E) }</math> It is always true. ...}.</math> Later he found that his answer is <math>0.5</math> less than the correct answer. What is the <math>2</math>-digit number <math>\underline{a} \ \unde
    15 KB (2,383 words) - 09:49, 25 June 2023
  • It is not fully correct, and I am fixing its bugs. [https://artofproblemsolving.com/wiki/index.php/
    822 bytes (120 words) - 15:59, 8 August 2020
  • <div style="display:var(--answerab-{{{2|none}}}, none);">Correct!</div> <div style="display:var(--answerba-{{{2|none}}}, none);">Correct!</div>
    1 KB (154 words) - 22:40, 8 August 2020
  • Obviously, to find the correct answer, we need to get the largest denominator with the smallest numerator.
    4 KB (684 words) - 12:04, 16 January 2023
  • ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
    812 bytes (128 words) - 18:54, 2 January 2021
  • ...00</math> to <math>999</math>, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answ
    2 KB (242 words) - 17:29, 30 August 2020
  • ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
    3 KB (416 words) - 18:13, 31 August 2020
  • ...you go with <math>\boxed{\textbf{(D) }576}</math>, and this is indeed the correct answer!
    7 KB (1,071 words) - 00:19, 10 July 2023
  • So the correct option is either <math>\textbf{(B)}</math> or <math>\textbf{(E)}</math>. Le ...math>20210A</math> divisible by <math>11</math>. Thus, by elimination, the correct choice must be option <math>\boxed{\textbf{(E)}\ 9}</math>.
    3 KB (491 words) - 21:13, 12 July 2023
  • ...stion is followed by answers marked A, B, C, D and E. Only one of these is correct. # You will receive 6 points for each correct answer, 2.5 points for each problem left unanswered if the year is before 2
    3 KB (364 words) - 19:48, 27 December 2021
  • ...numbers must correspond to the color in the center square, so Leo's sum is always <math>1+3+5+\cdots+25=169</math> ...number of correct <math>x_{i}</math>, since the probability of rolling the correct number on a given roll is higher by a factor of <math>2 .</math>
    20 KB (3,568 words) - 23:42, 4 January 2022
  • <math>\textbf{(E) }</math> It is always true. ...ues only holds true for nonnegative values of <math>a+b</math>, making the correct answer <math>\boxed{\textbf{(D)}}.</math>
    3 KB (472 words) - 00:02, 30 August 2023
  • ...stion is followed by answers marked A, B, C, D and E. Only one of these is correct. # You will receive 1 point for each correct answer. There is no penalty for wrong answers.
    3 KB (321 words) - 23:10, 19 January 2023
  • ...very conditional statement <math>\boldsymbol{p\Longrightarrow q}</math> is always logically equivalent to its contrapositive <math>\boldsymbol{\lnot q\Longri ...le. That leaves statement D. <math>\boxed{\textbf{(D)}}</math> is the only correct statement.
    7 KB (1,027 words) - 22:45, 28 October 2022
  • ...}.</math> Later he found that his answer is <math>0.5</math> less than the correct answer. What is the <math>2</math>-digit number <math>\underline{a} \ \unde
    4 KB (569 words) - 22:46, 28 October 2022
  • ...</math> the ray entering <math>P</math> and the ray leaving <math>P</math> always have negative slopes. In this problem, <math>\overline{AB}</math> and <math .../math> all involve <math>\sqrt2,</math> we suspect that one of them is the correct answer. We take a guess in faith that <math>\overline{AB},\overline{BC},</m
    10 KB (1,514 words) - 01:28, 1 November 2023
  • So, <math>AD=2\sqrt{760}=4\sqrt{190}</math>. The correct answer is <math>\boxed{\textbf{(D) }194}</math>
    10 KB (1,548 words) - 00:08, 12 February 2024
  • ...ir solution writing skills, since grading is not just based on getting the correct answer.
    308 bytes (48 words) - 04:08, 5 October 2020
  • ...nted as quarters and <math>x</math> of the dimes were counted as cents. To correct the total obtained the clerk must: ...hen every mistake inflates the total by <math>20</math> cents. In order to correct this, we have to subtract <math>20</math> cents <math>x</math> times, for a
    1 KB (211 words) - 12:57, 18 November 2020
  • ...B loses } \textdollar{ 100}\qquad\textbf{(E)}\ \text{none of the above is correct}</math> ...nse, but none of the options says this. We can therefore conclude that the correct answer is <math>\boxed{\textbf{(C)}}</math>.
    1 KB (227 words) - 13:01, 18 November 2020
  • ...</math> are either both correct or both incorrect. Since there is only one correct answer, <math>\textbf{(A)}</math> and <math>\textbf{(C)}</math> are both in
    3 KB (527 words) - 11:05, 16 June 2023
  • ...receive <math>d=\frac{3}{2},d=-5</math>. So, we have to test which one is correct. We repeat a similar process as we did above for equations 1 and 2. We fact ...ac{10}{3}</math> or <math>c=-2</math>. So, we must AGAIN test which one is correct.
    10 KB (1,680 words) - 00:20, 28 April 2024
  • ...results. The producers of the aforementioned labels apply all things in a correct variety though crafting CBD oil as a primary aim should be to provide bette
    3 KB (552 words) - 00:35, 13 August 2021
  • If there are any mistakes, feel free to edit so that it is correct.
    1 KB (168 words) - 11:52, 27 April 2024
  • ...80+70+60+90+80 are added together the total is 380 ÷ 5 = 76 so (B) 76 is correct answer.
    743 bytes (90 words) - 18:28, 12 May 2024
  • Therefore when 1, 9, 1, 2 are added together the total is 13, so (A) 13 is correct answer.
    1 KB (138 words) - 17:30, 12 May 2024
  • ...ave to show a card with a vowel. However, this is not possible. If Jane is correct, then the contrapositive ("If an odd number is on one side of the card, the
    1 KB (217 words) - 23:18, 17 May 2024
  • ...tes to solve 40 multiple choice problems. Four points are awarded for each correct answer, one point is deducted for each wrong answer, and zero points are aw
    709 bytes (96 words) - 00:46, 16 March 2021
  • Each correct answer bags 5 points, while <i>either an incorrect answer or a skipped prob
    972 bytes (156 words) - 16:41, 2 April 2024
  • ...get <math>x=\frac{ab}{\sqrt{a^2+b^2}}</math>, and we can observe that the correct answer is <math>\boxed{\textbf{(D) \ }}</math>.
    1 KB (176 words) - 23:35, 2 January 2024
  • ...^2-n+f((k+1)^2)=k^2+3k+2-n</math>. Note that this formula also returns the correct value when <math>n=(k+1)^2</math>, but not when <math>n=k^2</math>. Thus <m ...than <math>k^2</math>, so <math>k-10>0, k>10</math>. The LHS expression is always even (since <math>3k^2+k-10</math> factors to <math>k(3k+1)-10</math>, and
    14 KB (2,569 words) - 09:28, 28 March 2024
  • ...een reproduced here. It was published in <math>1321</math>, if the date is correct. We apologize for any errors in transcript. What follows is the manuscript,
    744 bytes (119 words) - 13:08, 19 April 2023
  • ...of the Indian-Mathematical-Scientist '''[[Jyotiraditya Jadhav]]''' has got correct solution set for the process with a proof.
    3 KB (466 words) - 20:07, 4 February 2023
  • Overview : I got problems 1-20 correct on my first try. Although I got the last 5 wrong, i have since then improve
    2 KB (271 words) - 14:12, 31 May 2021
  • ...estment and several other fields, but not all websites on the web give the correct information. Folks should think about a number of things ahead of selecting
    8 KB (1,279 words) - 09:32, 25 June 2021
  • Although the answer is correct, solution 2 below is a more accurate way to approach this problem. I agree,
    3 KB (481 words) - 11:08, 28 January 2024
  • ...gging this back into the original problem shows that this answer is indeed correct. Therefore, <math>\underline{a}\,\underline{b}\,\underline{c}=\boxed{227}.<
    5 KB (755 words) - 16:05, 2 February 2024
  • #You will receive 3 points for each correct answer, and 0 points for each problem left unanswered or incorrect.
    7 KB (1,100 words) - 18:40, 11 July 2021
  • #You will receive 15 points for each correct answer, and 0 points for each problem left unanswered or incorrect.
    6 KB (985 words) - 18:39, 11 July 2021

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