conversations listlengths 3 3 |
|---|
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$A$ and $B$ play a game where $A$ chooses a positive integer $n$ from the set $S = \\{1, 2, \\dots, 1001\\}$. $B$ must guess the value of $n$ by selecting subsets of $S$ an... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$ABCD$ is a quadrilateral with right angles at $A$ and $C$. Points $E$ and $F$ are on $AC$, and $DE$ and $BF$ are perpendicular to $AC$. If $AE=3$, $DE=5$, and $CE=7$, then... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$ABCD$ is a regular tetrahedron (right triangular pyramid). If $M$ is the midpoint of $\\overline{CD}$, then what is $\\cos \\angle AMB$?"
},
{
"from": "gpt",
... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$ABCD$ is a square such that $AB$ lies on the line $y=x+4$ and points $C$ and $D$ lie on the graph of the parabola $y^2 = x$. Compute the sum of all possible areas of $ABCD... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$ABCDEF$ is an equiangular hexagon with side lengths $AB=2015$, $BC=2016$, $CD=2017$, and $DE=2018$. Find the perimeter of $ABCDEF$."
},
{
"from": "gpt",
"value... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$E$ is a point on side $AD$ of rectangle $ABCD$, so that $DE = 12$, while $DA = 16$, and $DC = 12$. If $CE$ extended meets the circumcircle of the rectangle at $F$, find th... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$M, A, T, H$, and $L$ are all not necessarily distinct digits, with $M \\ne 0$ and $L \\ne 0$. Given that the sum $MATH + LMT$, where each letter represents a digit, equals... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$N$ visitors of the LycoReco cafe each give an integer rating from 1 to 10 on Takina Inoue's chocolate parfait. Given that the sum of all ratings given is 83 and the mean o... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$\\triangle ABC$ has all of its vertices on the parabola $y=x^{2}$. The slopes of $AB$ and $BC$ are $10$ and $-9$, respectively. If the $x$-coordinate of the triangle's cen... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$\\triangle ABC$ has all of its vertices on the parabola $y=x^{2}$. The slopes of $AB$ and $BC$ are $10$ and $-9$, respectively. If the x-coordinate of the triangle's centr... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$\\triangle ABC$ is an equilateral triangle with side length $3$. Point $D$ lies on the segment $BC$ such that $BD = 1$ and $E$ lies on $AC$ such that $AE = AD$. Compute th... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$a, b, c, d$ are positive numbers with product 1. What is the minimum of $a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd$?"
},
{
"from": "gpt",
"value": "<think>\n<think>\nO... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$x = {1+\\frac{\\sqrt{2}}{1+\\frac{\\sqrt{2}}{1+...}}}$. Find $\\frac{1}{(x+1)(x-2)}$. When your answer is in the form $\\frac{A+\\sqrt{B}}{C}$, where $A$, $B$, and $C$ are... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "$x$ and $y$ are complex numbers such that $x^3 + y^3 = -16$ and $(x + y)^2 = xy$. What is the value of $|x + y|$?"
},
{
"from": "gpt",
"value": "<think>\n<think... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "(A) If \\(\\theta\\) is any quadrant 2 angle, what quadrant(s) could \\(2\\theta\\) lie in?\n(B) Given \\(\\sin \\theta = \\frac{8}{17}\\) where \\(\\frac{\\pi}{2} < \\thet... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "(b) Compute the remainder of $100!$ when divided by $101$."
},
{
"from": "gpt",
"value": "<think>\n<think>\nOkay, so I need to find the remainder when 100! is d... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "(ii) Given a set $A = \\{a_1, a_2, a_3, \\ldots, a_n\\}$, find the total number of binary operations on $A$ such that $a_i * a_j \\neq a_i * a_k$ if $j \\neq k$."
},
{
... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "2 diagonals of a regular heptagon (a 7-sided polygon) are chosen. What is the probability that they intersect inside the heptagon?"
},
{
"from": "gpt",
"value"... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "2 distinct vertices of an octagon are chosen at random. What is the probability that they are adjacent?"
},
{
"from": "gpt",
"value": "<think>\n<think>\nOkay, ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "23 people attend a party. Each person shakes hands with at least two other people. What is the minimum possible number of handshakes?"
},
{
"from": "gpt",
"valu... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "23 people attend a party. Each person shakes hands with at most 22 other people. What is the maximum possible number of handshakes, assuming that any two people can shake h... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "5 cows eat 2 acres of grass in 10 days. 7 cows eat 3 acres of grass in 30 days. The grass grows at a constant rate and each cow eats at a constant rate. How many days will ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "6 men and 8 boys can complete a piece of work in 10 days. 26 men and 48 boys can complete the same piece of work in 2 days. Find the time taken by 15 men and 21 boys to com... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A $100$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $100$ vertices equals 2009. The midpoints of the sides of $P_1$ form a second $10... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A $\\textit{palindrome}$ is a number which reads the same forward as backward, for example 313 or 1001. Ignoring the colon, how many different palindromes are possible on a... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A 10*10*10 cube is formed of small unit cubes. A grasshopper sits in the center of one of the corner cubes. At any given moment, it can jump to the center of any adjacent c... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A 12 cm long wire is bent to form a triangle with one angle of $60^\\circ$. Find the sides of the triangle if its area is maximized."
},
{
"from": "gpt",
"value... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A 17 ft ladder is leaning against a wall. If the bottom of the ladder is pulled away from the wall at a constant rate of 5 ft/sec, how fast will the top of the ladder be mo... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A 20-foot ladder rests vertically against a wall. A bug starts at the bottom of the ladder and climbs up at a rate of 1 foot per minute. At the same time, the foot of the l... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A 236 mile trip is made by boat and by train. The boat averages 32 mph and the train averages 52 mph. If the total trip took 5.5 hours, how many miles was the train trip?"
... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A 6-foot man standing in front of a 15-foot lamppost has a shadow of 8 feet. If he steps another 3 feet away from the lamppost, how much will his shadow lengthen?"
},
{... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A 7-card hand is dealt from a standard deck of 52 cards. What is the probability that the hand will contain 3 clubs and 4 red cards?"
},
{
"from": "gpt",
"value... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A French Club collected the same amount from each student going on a trip to Le Cercle Moliere in Winnipeg. When six students could not go, each of the remaining students w... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A Hotel corridor has 10 rooms on each side. A math olympiad team leader wants to reserve 7 rooms such that, on each side of the corridor, no two rooms are adjacent. In how ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bag contains $a$ blue balls, $b$ red balls, and $c$ white balls. You will take out a ball at random, note its color, and replace it into the bag. This operation is repeat... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bag contains 10 black and 16 white balls. Twenty-two balls are drawn one by one until 4 white balls remain in the bag. What is the probability that the 22nd ball drawn is... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bag contains 3 red marbles and 2 black marbles. Two persons, A and B, take turns drawing a marble from the bag without replacement. The first person to draw a black marbl... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bag contains 5 white balls. In each trial, a ball is drawn uniformly at random. If the ball is white, it is colored black and returned to the bag. If the ball is black, i... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bag contains 8 pennies and 1 quarter. Four coins are picked at random from the bag and placed into an urn that already contains 12 pennies. Then, three coins are picked f... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bag contains 8 red and 6 green balls. Three balls are drawn one after another without replacement. Find the probability that at least 2 of the balls drawn are green."
}... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bag contains 99 black beans and 1 white bean. Beans are drawn one at a time from the bag until the white bean is drawn. Find the expected number of black beans drawn befo... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bag has 4 red marbles, 5 white marbles, and 6 blue marbles. Three marbles are drawn from the bag (without replacement). What is the probability that they are all the sa... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bakery sells three kinds of rolls. How many different combinations of rolls could Jack purchase if he buys a total of six rolls and includes at least one of each kind?"
... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A ball is dropped from a height of 20 feet onto a perfect flat surface. Each time the ball hits the surface after falling \\(h\\) feet it bounces a distance of \\(\\frac{2}... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A ball of radius 1 is placed in the corner of a room, tangent to the floor and walls. A sequence of additional balls is placed such that each ball is tangent to the walls, ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A ball starts at a height of 124 meters and bounces such that each bounce reaches half the height of the previous bounce. What total distance will the ball cover before it ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A ball travels on a parabolic path in which the height (in feet) is given by the expression $-16t^2+64t+31$, where $t$ is the time after launch. What is the maximum height ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A ball travels on a parabolic path in which the height (in feet) is given by the expression $-16t^2+80t+21$, where $t$ is the time after launch. What is the maximum height ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bank discounted a 3-month, \\$2,200, noninterest-bearing note for Jenny Woods. The discount rate was 15.5%, and Jenny received \\$2,114.75 as proceeds. What true rate of ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bank plans to offer a savings account at 4.8% simple annual interest. If the bank compounds monthly, what is the annual yield for this savings account? (The annual yield ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A baseball league consists of two four-team divisions. Each team plays every other team in its division $N$ games and every team in the other division $M$ games, with $N > ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A baseball league has nine teams. During the season, each of the nine teams plays exactly three games with each of the other teams. What is the total number of games played... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A basement has a 24-foot by 32-foot rectangular floor. The basement is flooded with water to a depth of 18 inches. Three pumps are used to pump the water out of the basemen... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A basketball player has a constant probability of $.4$ of making any given shot, independent of previous shots. Let $a_n$ be the ratio of shots made to shots attempted afte... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A basketball player shoots $100$ times. The first shot is a success, and the second is a miss. For each subsequent shot, the probability of scoring is the number of points ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bicycle tire has a 30-inch diameter. If the tire spins at a rate of 80 revolutions per minute, what distance is traveled in one minute?"
},
{
"from": "gpt",
"... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A binary operation $\\diamondsuit$ has the properties that $a\\,\\diamondsuit\\, (b\\,\\diamondsuit \\,c) = (a\\,\\diamondsuit \\,b)\\cdot c$ and that $a\\,\\diamondsuit \\... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A biologist catches a random sample of 60 fish from a lake, tags them, and releases them. Six months later, she catches a random sample of 70 fish and finds that 3 are tagg... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A biologist catches and tags 60 fish in a lake on May 1 and releases them. On September 1, she catches a random sample of 70 fish and finds that 3 of them are tagged. Assum... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A board game spinner is divided into three parts labeled $A$, $B$ and $C$. The probability of the spinner landing on $A$ is $\\frac{1}{3}$ and the probability of the spinn... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A board has 4 rows and 4 columns. A piece starts at the bottom left square $(1, 1)$ and must move to the upper right square $(4, 4)$. The piece can only move to the square ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A boat follows the curve given by \\( x = -2 + 3h \\) and \\( y = 9 - 4h \\). Lengths are in meters and time in seconds.\nA) Draw the curve for \\( h \\) between 0 and 3.\n... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A boat is manned by 8 men, where 2 can only row on the bow side and 3 can only row on the stroke side. How many ways can the crew be arranged?"
},
{
"from": "gpt",
... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A boat made of wood 1.5 times heavier than water has an internal volume 2/3 of its external volume. When filled with oil to the brim, it barely floats in water. Find the de... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A book with 53 pages numbered 1 to 53 has its pages renumbered in reverse, from 53 to 1. For how many pages do the new page number and old page number share the same units ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bored mathematician notices that the increase of water droplets in his shower every minute can be expressed as $WI = \\frac{3 WO}{5} \\cdot \\frac{3T}{4}$, where $WI$ is ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bowling ball is a solid ball with a spherical surface and diameter 30 cm. To custom fit a bowling ball for each bowler, three holes are drilled in the ball. Bowler Kris h... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains 10 dice, 5 of which are crooked and produce a '6' with probability 0.4, while the other 5 are fair. A die is selected at random from the box and thrown twice... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains 2 coins with heads on both sides, 1 standard coin, and 1 coin with tails on both sides. If one coin is picked from the box and flipped twice, what is the pro... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains 3 black balls, 4 red balls, and 7 green balls. Two balls are drawn at random. What is the probability of drawing at least one red ball?"
},
{
"from":... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains 4032 answer scripts, exactly half of which have an odd number of marks. We randomly choose 2 scripts and follow these rules:\n- If both scripts have odd scor... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains 5 fair coins and 5 biased coins, where each biased coin has a probability of heads of $\\frac{4}{5}$. A coin is drawn at random from the box and tossed. Then... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains 5 white balls and 6 black balls. Five balls are drawn out of the box at random. What is the probability that they all are white?"
},
{
"from": "gpt... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You p... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains tickets serially numbered from 1 to \\( N \\). Two tickets are drawn using simple random sampling without replacement (SRSWOR). If \\( X \\) and \\( Y \\) ar... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box contains tiles, numbered 1, 2, 3,..., 49, 50. Only tiles which are marked with a number congruent to $2 \\pmod{5}$ are blue. One tile is chosen randomly from the box.... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box with edge lengths $l, m, n \\in \\mathbb{N}$ is divided into $lmn$ unit cubes. Determine how many of these unit cubes a main diagonal of the box intersects."
},
{... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A box with height \\((x+5)\\) cm has a square base with side \\(x\\) cm. A second box with height \\((x+2)\\) cm has a square base with side \\((x+1)\\) cm. If the two boxe... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A boy has a box of cookies which he doesn't know the number of. He decides that, in order to find out how many cookies are in the box, he will empty the box and arrange the... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A boy has a certain number of sweets. If he eats 16 sweets a day, they will last him 2 days longer than if he eats 18 sweets a day. How many sweets does he have?"
},
{
... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A boy is traveling with a speed $s = 17\\cos^2(t) + e^{17t}$, where $t$ is the time in seconds. How many units is the boy’s displacement in the first 10 seconds?"
},
{
... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bridge is to be built in the shape of a parabolic arch with a span of 100 feet. The height of the arch, a distance of 40 feet from the center, is 10 feet. Find the height... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A bus left point X for point Y. Two hours later, a car left point X for Y and arrived at Y at the same time as the bus. If the car and the bus left simultaneously from oppo... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A businessman has some money in his pocket. For the first two days, he spends \\(\\frac{1}{3}\\) of his money plus 100 YTL. For the last two days, he spends \\(\\frac{1}{5}... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A camera tripod has three equally spaced legs, each of length 1.75m, around a circle of radius 52cm on horizontal ground. Find the angle that the legs make with the horizon... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A campus only gives out parking permits to people greater than 1 mile away from the campus. Oak Lane starts 2 miles west and 1 mile north of the campus, and ends 5 miles ea... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A canoeist paddled upstream for 2 hours, then downstream for 3 hours. The rate of the current was 2 mph. When she stopped, she was 20 miles downstream from her starting poi... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A canoeist passes a log floating in the river's current two miles upstream from his starting point. After paddling upstream for one more hour, he turns back and reaches his... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A car traveled 75% of the way from town A to town B at an average speed of 50 mph. The car travels at an average speed of \\( S \\) mph for the remaining part of the trip. ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A car travels downhill at 72 mph, on the level at 63 mph, and uphill at 56 mph. The car takes 4 hours to travel from town A to town B and 4 hours 40 minutes to return. Find... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A car travels due east at $\\frac{2}{3}$ mile per minute on a long, straight road. At the same time, a circular storm with a radius of 51 miles moves southeast at $\\frac{1... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A card is drawn at random from a standard deck of 52 cards. What is the probability that it is used in the game of Schafkopf?"
},
{
"from": "gpt",
"value": "<th... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A certain ellipse is tangent to both the $x$-axis and the $y$-axis, and its foci are at $(2, -3 + \\sqrt{5})$ and $(2, -3 - \\sqrt{5}).$ Find the length of the major axis.... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A certain function \\( f \\) has the properties that \\( f(3x) = 3f(x) \\) for all positive real values of \\( x \\), and that \\( f(x) = 1 - |x - 2| \\) for \\( 1 \\le x \... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A certain integer has $4$ digits when written in base $8$. The same integer has $d$ digits when written in base $2$. What is the sum of all possible values of $d$?"
},
... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs each consisting of 1 junior and 1 sen... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A certain regular tetrahedron has three of its vertices at the points $(0,1,2),$ $(4,2,1),$ and $(3,1,5).$ Find the coordinates of the fourth vertex, given that they are a... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A charity sells 140 benefit tickets for a total of $2001. Some tickets sell for full price (a whole dollar amount), and the rest sell for half price. How much money is rais... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A charity sells 140 benefit tickets for a total of 2001 dollars. Some tickets sell for full price (a whole dollar amount), and the rest sell for half price. How much money ... |
[
{
"from": "system",
"value": "You are a mathematical reasoning expert. Solve step-by-step."
},
{
"from": "human",
"value": "A child is standing 10 ft away from a statue mounted on a pedestal. The angle of elevation to the head of the statue is 60 degrees, and to the foot of the statue is 30 degr... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.