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  • 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 (775 words) - 23:53, 13 April 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>.
    6 KB (926 words) - 23:38, 8 April 2024
  • ...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) - 09:58, 5 May 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
  • [Errors to correct below: We don't totally discard 0 (mod 5), since we can still have one of t
    3 KB (519 words) - 19:01, 30 March 2024
  • ...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 (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

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