Difference between revisions of "User:Bissue"

Revision as of 15:34, 25 December 2020

i suppose i have a user page now

P7: When expressed as a decimal rounded to the nearest ten-thousandth, what is the value of $\dfrac{125+3}{125 \times 3}$ ?

$\textbf{(A)} ~ 0.3412 \qquad \textbf{(B)} ~ 0.3413 \qquad \textbf{(C)} ~ 0.3414 \qquad \textbf{(D)} ~ 0.3415 \qquad \textbf{(E)} ~ 0.3416$

P9: Kayla writes down the first $N$ positive integers. What is the sum of all possible values of $N$ if Kayla writes five multiples of $13$ and six multiples of $12$ ?

$\textbf{(A)} ~ 447 \qquad \textbf{(B)} ~ 453 \qquad \textbf{(C)} ~ 518 \qquad \textbf{(D)} ~ 525 \qquad \textbf{(E)} ~ 548$

P17: Kurtis' school schedule is made up of four classes, followed by lunch, followed by three more classes. In how many ways can Kurtis arrange his schedule if two of his classes (Reading and Writing) must occur one immediately after the other?

$\textbf{(A)} ~ 600 \qquad \textbf{(B)} ~ 840 \qquad \textbf{(C)} ~ 1200 \qquad \textbf{(D)} ~ 1440 \qquad \textbf{(E)} ~ 1680$

P18: When the number $25$ is added to a list of numbers with total sum $S$ , the average of all the numbers increases by one. What is the sum of the digits of the greatest possible value of $S$ ?

$\textbf{(A)} ~ 6 \qquad \textbf{(B)} ~ 7 \qquad \textbf{(C)} ~ 8 \qquad \textbf{(D)} ~ 9 \qquad \textbf{(E)} ~ 12$

P19: A magician randomly picks a three digit positive integer to put into her hat and pulls out the same number with its digits in reverse order. (For example $496$ would become $694$ and $720$ would become $27$ .) What is the probability the magician pulls out a multiple of $22$ ?

$\textbf{(A)} ~ \dfrac{1}{15} \qquad \textbf{(B)} ~ \dfrac{1}{18} \qquad \textbf{(C)} ~ \dfrac{1}{20} \qquad \textbf{(D)} ~ \dfrac{1}{25} \qquad \textbf{(E)} ~ \dfrac{1}{30}$

P23: In rectangle $ABCD$ , the perpendicular from $B$ to diagonal $AC$ bisects segment $CD$ . Which of the following is closest to $\frac{AB}{BC}$ ?

$\textbf{(A)} ~ \dfrac{5}{4} \qquad \textbf{(B)} ~ \dfrac{4}{3} \qquad \textbf{(C)} ~ \dfrac{7}{5} \qquad \textbf{(D)} ~ \dfrac{3}{2} \qquad \textbf{(E)} ~ \dfrac{8}{5}$

P24: How many ordered triples of positive integers $(a, b, c)$ satisfy $\text{gcd}(a, b, c)=20$ and $\text{lcm}(a, b, c)=240$ ?

$\textbf{(A)} ~ 18 \qquad \textbf{(B)} ~ 24 \qquad \textbf{(C)} ~ 36 \qquad \textbf{(D)} ~ 54 \qquad \textbf{(E)} ~ 72$

P25: Cheyanne rolls two standard six sided dice, then repeatedly rerolls all dice which show an odd number and stops as soon as all dice show an even number. What is the probability Cheyanne stops after exactly four rounds of rerolling?

$\textbf{(A)} ~ \dfrac{61}{1024} \qquad \textbf{(B)} ~ \dfrac{1}{16} \qquad \textbf{(C)} ~ \dfrac{67}{1024} \qquad \textbf{(D)} ~ \dfrac{9}{128} \qquad \textbf{(E)} ~ \dfrac{29}{256}$

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 i suppose i have a user page now
+P7: When expressed as a decimal rounded to the nearest ten-thousandth, what is the value of <math>\dfrac{125+3}{125 \times 3}</math>?
+<math>\textbf{(A)} ~ 0.3412 \qquad \textbf{(B)} ~ 0.3413 \qquad \textbf{(C)} ~ 0.3414 \qquad \textbf{(D)} ~ 0.3415 \qquad \textbf{(E)} ~ 0.3416</math>
+P9: Kayla writes down the first <math>N</math> positive integers.  What is the sum of all possible values of <math>N</math> if Kayla writes five multiples of <math>13</math> and six multiples of <math>12</math>?
+<math>\textbf{(A)} ~ 447 \qquad \textbf{(B)} ~ 453 \qquad \textbf{(C)} ~ 518 \qquad \textbf{(D)} ~ 525 \qquad \textbf{(E)} ~ 548</math>
+P17: Kurtis' school schedule is made up of four classes, followed by lunch, followed by three more classes. In how many ways can Kurtis arrange his schedule if two of his classes (Reading and Writing) must occur one immediately after the other?
+<math>\textbf{(A)} ~ 600 \qquad \textbf{(B)} ~ 840 \qquad \textbf{(C)} ~ 1200 \qquad \textbf{(D)} ~ 1440 \qquad \textbf{(E)} ~ 1680</math>
+P18: When the number <math>25</math> is added to a list of numbers with total sum <math>S</math>, the average of all the numbers increases by one.  What is the sum of the digits of the greatest possible value of <math>S</math>?
+<math>\textbf{(A)} ~ 6 \qquad \textbf{(B)} ~ 7 \qquad \textbf{(C)} ~ 8 \qquad \textbf{(D)} ~ 9 \qquad \textbf{(E)} ~ 12</math>
+P19: A magician randomly picks a three digit positive integer to put into her hat and pulls out the same number with its digits in reverse order. (For example <math>496</math> would become <math>694</math> and <math>720</math> would become <math>27</math>.) What is the probability the magician pulls out a multiple of <math>22</math>?
+<math>\textbf{(A)} ~ \dfrac{1}{15} \qquad \textbf{(B)} ~ \dfrac{1}{18} \qquad \textbf{(C)} ~ \dfrac{1}{20} \qquad \textbf{(D)} ~ \dfrac{1}{25} \qquad \textbf{(E)} ~ \dfrac{1}{30}</math>
+P23: In rectangle <math>ABCD</math>, the perpendicular from <math>B</math> to diagonal <math>AC</math> bisects segment <math>CD</math>.  Which of the following is closest to <math>\frac{AB}{BC}</math>?
+<math>\textbf{(A)} ~ \dfrac{5}{4} \qquad \textbf{(B)} ~ \dfrac{4}{3} \qquad \textbf{(C)} ~ \dfrac{7}{5} \qquad \textbf{(D)} ~ \dfrac{3}{2} \qquad \textbf{(E)} ~ \dfrac{8}{5}</math>
+P24: How many ordered triples of positive integers <math>(a, b, c)</math> satisfy <math>\text{gcd}(a, b, c)=20</math> and <math>\text{lcm}(a, b, c)=240</math>?
+<math>\textbf{(A)} ~ 18 \qquad \textbf{(B)} ~ 24 \qquad \textbf{(C)} ~ 36 \qquad \textbf{(D)} ~ 54 \qquad \textbf{(E)} ~ 72 </math>
+P25: Cheyanne rolls two standard six sided dice, then repeatedly rerolls all dice which show an odd number and stops as soon as all dice show an even number.  What is the probability Cheyanne stops after exactly four rounds of rerolling?
+<math>\textbf{(A)} ~ \dfrac{61}{1024} \qquad \textbf{(B)} ~ \dfrac{1}{16} \qquad \textbf{(C)} ~ \dfrac{67}{1024} \qquad \textbf{(D)} ~ \dfrac{9}{128} \qquad \textbf{(E)} ~ \dfrac{29}{256}</math>

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Difference between revisions of "User:Bissue"

Revision as of 15:34, 25 December 2020