inclusionAI/Ring-lite-rl-data huggingface dataset:
Xiaoming's father departs from home to go shopping at the supermarket. If he first rides a bicycle for 12 minutes and then walks for 20 minutes, he can reach the supermarket; if he first rides a bicycle for 8 minutes and then walks for 36 minutes, he can also reach the supermarket. How many minutes will it take to reach the supermarket if he first rides a bicycle for 2 minutes and then walks?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60}
求所有可用十进制表示$\overline {13xy45z}$，且能被792整除的正整数，其中，$x,y,z$为未知数.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1380456}
Given the integers $1, 2, \ldots, n$ ($n \geq 2, n \in \mathbb{N^*}$), there are $n!$ different permutations $a_1, a_2, \ldots, a_n$. How many distinct permutations satisfy the condition that for all $k = 1, 2, \ldots, n$, $a_k \geq k-2$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 \times 3^{n-2}}
Figure \(ABCD\) is a trapezoid with \(AB \parallel DC\), \(AB = 5\), \(BC = 3 \sqrt{2}\), \(\angle BCD = 45^\circ\), and \(\angle CDA = 60^\circ\). Find the length of \(DC\). The original answer is in the form \(m + \sqrt{n}\). Please give the value of \(m + n\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
How many of the first 1000 positive integers can be expressed in the form $\lfloor 2x \rfloor + \lfloor 4x \rfloor + \lfloor 6x \rfloor + \lfloor 8x \rfloor$, where $x$ is a real number, and $\lfloor z \rfloor$ denotes the greatest integer less than or equal to $z$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$600$}
Joe is right at the middle of a train tunnel and he realizes that a train is coming. The train travels at a speed of $50$ miles per hour, and Joe can run at a speed of $10$ miles per hour. Joe hears the train whistle when the train is a half mile from the point where it will enter the tunnel. At that point in time, Joe can run toward the train and just exit the tunnel as the train meets him. Instead, Joe runs away from the train when he hears the whistle. If the number of seconds he has to spare when he gets to the tunnel entrance is $x$, find the value of $10x$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{144}
A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. C then sells the bicycle to D at a profit of P%, where P% is an unknown profit percentage. If the final selling price of the bicycle after the transaction between C and D was Rs. 225, find out the cost price of the bicycle for A.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{150}
Car A and Car B start from points A and B, respectively, at the same time (Car A starts from point A), and travel towards each other. The speeds of Car A and Car B are 40 km/h and 50 km/h, respectively. The distance between points A and B is 900 km. When Car A reaches point B, it immediately turns around and heads back to point A at a speed of 50 km/h. When Car B reaches point A, it immediately turns around and heads back to point B at a speed of 40 km/h. When Car A reaches point A, it immediately turns around and heads back to point B, resuming a speed of 40 km/h. When Car B reaches point B, it immediately turns around and heads back to point A, resuming a speed of 50 km/h. This pattern continues, with both cars traveling back and forth between points A and B, and their speeds alternating between 40 km/h and 50 km/h.

How many kilometers has Car A traveled in total by the time the 2016th meeting occurs?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1813900 \text{ km}}
5. Given the number $5300 \ldots 0035$ (100 zeros). It is required to replace some two zeros with non-zero digits so that after the replacement, the resulting number is divisible by 495. In how many ways can this be done?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{22100}
What is the largest real number $\theta$ less than $\pi$ (i.e. $\theta<\pi$ ) such that $\prod_{k=0}^{10} \cos \left(2^{k} \theta\right) \neq 0$ and $\prod_{k=0}^{10}\left(1+\frac{1}{\cos \left(2^{k} \theta\right)}\right)=1 ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2046 \pi}{2047}}
Solve the equation \(2 x^{3} + 24 x = 3 - 12 x^{2}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt[3]{\frac{19}{2}} - 2}
Given the function $f(x) = x^2e^x + \ln t - a$, if for any $t \in [1,e]$, $f(x)$ always has a unique zero in the interval $[-1,1]$, then the range of the real number $a$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(1+ \frac{1}{e},e]}
Let \( S = \{1, 2, \ldots, 2005\} \). If any set of \( n \) pairwise co-prime numbers in \( S \) always contains at least one prime number, what is the minimum value of \( n \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{16}
Sasha wrote down numbers from one to one hundred, and Misha erased some of them. Among the remaining numbers, 20 contain the digit one, 19 contain the digit two, and 30 contain neither one nor two. How many numbers did Misha erase?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{33}
It will cost $60 to rent a sailboat and $80 per hour to rent a ski boat. Ken rented a sailboat while Aldrich rented a ski boat. Additionally, there are fuel costs of $10 per hour for Ken's sailboat rental and $20 per hour for Aldrich's ski boat rental. The company is offering a discount of 10% on the second day of rental. How much more did it cost Aldrich to rent the ski boat than Ken to rent a sailboat for three hours a day in two days?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$402}
Determine the transfer function of a system that produces a sinusoidal output with a frequency of 5 Hz and an amplitude proportional to the input when a step input is applied.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$$\frac{10 \pi s}{s^2 + (10 \pi)^2}$$}
满足正整数 $y \leqslant 2022$ 且 $100 \mid 2^{y}+y$ 的 $y$ 的个数是多少？
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
A rectangular floor that is $12$ feet wide and $19$ feet long is tiled with rectangular tiles that are $1$ foot by $2$ feet. Find the number of tiles a bug visits when walking from one corner to the diagonal opposite corner.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Let $A_{10}$ denote the answer to problem $10$. Two circles lie in the plane; denote the lengths of the internal and external tangents between these two circles by $x$ and $y$, respectively. Given that the product of the radii of these two circles is $15/2$, and that the distance between their centers is $A_{10}$, determine $y^2-x^2$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
A workshop produces products of types $A$ and $B$. Producing one unit of product $A$ requires 10 kg of steel and 23 kg of non-ferrous metals, while producing one unit of product $B$ requires 70 kg of steel and 40 kg of non-ferrous metals. The profit from selling one unit of product $A$ is 80 thousand rubles, and for product $B$, it's 100 thousand rubles. The daily steel reserve is 700 kg, and the reserve of non-ferrous metals is 642 kg. How many units of products $A$ and $B$ should be produced per shift to maximize profit without exceeding the available resources? Record the maximum profit (in thousands of rubles) that can be obtained under these conditions as an integer without indicating the unit.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2180}
Let $L_n$ be the least common multiple of the integers $1, 2, \dots, n$. For example, $L_{10} = 2,520$ and $L_{30} = 2,329,089,562,800$. Find the remainder when $L_{31}$ is divided by $100,000$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{46800}
Given the hyperbola \({{x}^{2}}-\dfrac{{{y}^{2}}}{{{b}^{2}}}=1\) has an eccentricity of \(\dfrac{\sqrt{5}}{2}\), with the left focus being \({{F}_{1}}\). When point \(P\) moves on the right branch of the hyperbola and point \(Q\) moves on the circle \({{x}^{2}}+{{\left( y-1 \right)}^{2}}=1\), the minimum value of \(\left| PQ \right|+\left| PF_{1} \right|\) is \_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{5}{2}}
It takes Avery 3 hours to build a brick wall, while Tom can do it in 2 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20 minutes}
Find the mass of the body enclosed by the cylindrical surface $x^{2}=2 y$ and the planes $y+z=1$ and $2y+z=2$, given that at each point its volume density is numerically equal to the ordinate of that point.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{8 \sqrt{2}}{35}}
37. Tetrahedron. There are 6 rods of different lengths, and it is known that in any order, a tetrahedron (triangular pyramid) can be formed from them. How many different tetrahedrons can result from this?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Given a function $f(x)$ whose domain is $D$, if for any $x_1, x_2 \in D$, it holds that $f(x_1) \leq f(x_2)$ whenever $x_1 < x_2$, then the function $f(x)$ is called a non-decreasing function on $D$. Suppose $f(x)$ is a non-decreasing function on the interval $[0,1]$ and satisfies the following three conditions:
1. $f(0) = 0$;
2. $f\left(\frac{x}{3}\right) = \frac{1}{2}f(x)$;
3. $f(1-x) = 1-f(x)$.

Find the value of $f(1) + f\left(\frac{1}{2}\right) + f\left(\frac{1}{3}\right) + f\left(\frac{1}{6}\right) + f\left(\frac{1}{7}\right) + f\left(\frac{1}{8}\right)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{11}{4}}
Store A purchased several units of a certain model of mobile phone and set a selling price. Later, Store B purchased the same model at the same selling price but at a 10% lower purchase price, resulting in a 12 percentage point increase in profit margin compared to Store A. Calculate the profit margin of Store A for selling this type of mobile phone. Express your answer as a percentage.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8\%}
Find the range of the function \( f(x)=\frac{\sin x-1}{\sqrt{3-2 \cos x-2 \sin x}} \) for \( 0 \leq x \leq 2\pi \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[-1, 0]}
How many distinct four-tuples $(a, b, c, d)$ of rational numbers are there such that:

$$a \log_{10} 2 + b \log_{10} 3 + c \log_{10} 5 + d \log_{10} 7 = 2005$$

Find the number of such distinct four-tuples.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
The scores (in points) of the 15 participants in the final round of a math competition are as follows: $56$, $70$, $91$, $98$, $79$, $80$, $81$, $83$, $84$, $86$, $88$, $90$, $72$, $94$, $78$. What is the $80$th percentile of these 15 scores?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{90.5}
Maxim will go to first grade on September 1, 2014, at the age of 6, and this day will not be his birthday. What is the probability that he was born in 2008?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{244}{365}}
A set of data is arranged in ascending order as follows: $9$, $10$, $12$, $15$, $x$, $17$, $y$, $22$, $26$. The median of this data set is $16$, and the $75\%$ percentile is $20$. Find the value of $x + y$. Express your answer as a single numerical value.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{36}
Suppose that $P(x, y, z)$ is a homogeneous degree 4 polynomial in three variables such that $P(a, b, c)=P(b, c, a)$ and $P(a, a, b)=0$ for all real $a, b$, and $c$. If $P(1,2,3)=1$, compute $P(2,4,8)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{56}
Rohit walked some distance towards south. Then he turned to his left and walked 20 m. He then turned to his left and walked the same distance as he initially walked towards south. He again turned to his right and walked 15 m. Rohit is at a distance of 35 m from the starting point in a certain direction. How far did Rohit walk towards south initially?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
Given \( z \in \mathbb{C} \), if the equation in terms of \( x \): \( x^2 - 2zx + \frac{3}{4} + \text{i} = 0 \) (where \( i \) is the imaginary unit) has real roots, find the minimum value of the modulus \( |z| \) of the complex number \( z \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Calculate the sum: $$ \sum_{i = 0}^{n}(-1)^i \binom{n}{i} \binom{n}{n-i}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-1)^{n/2} \binom{n}{n/2}}
Let $\{a_n\}_{n \geq 1}$ be an increasing and bounded sequence. Calculate the limit:

$$\lim_{{n \to \infty}} \left( 2a_n - a_1 - a_2 \right) \left( 2a_n - a_2 - a_3 \right) \cdots \left( 2a_n - a_{n-2} - a_{n-1} \right) \left( 2a_n - a_{n-1} - a_1 \right).$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
A T-tetromino is formed by adjoining three unit squares to form a $1 \times 3$ rectangle, and adjoining on top of the middle square a fourth unit square. Determine the least number of unit squares that must be removed from a $202 \times 202$ grid so that it can be tiled using T-tetrominoes.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Let $U$ be a square with side length 1. Two points are randomly chosen on the sides of $U$. The probability that the distance between these two points is at least $\frac{1}{2}$ is $\frac{a - b \pi}{c}\left(a, b, c \in \mathbf{Z}_{+}, (a, b, c)=1\right)$. Find the value of $a + b + c$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{59}
The cash realized on selling a 14% stock is a certain amount, with the brokerage being 1/4%. The total amount including brokerage is Rs. 108. What is the cash realized on selling the stock without considering the brokerage?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{107.73}
In regular hexagon \(ABCDEF\), points \(W\), \(X\), \(Y\), and \(Z\) are chosen on sides \(\overline{BC}\), \(\overline{CD}\), \(\overline{EF}\), and \(\overline{FA}\) respectively, so lines \(AB\), \(ZW\), \(YX\), and \(ED\) are parallel and equally spaced. The original answer for the ratio of the area of hexagon \(WCXYFZ\) to the area of hexagon \(ABCDEF\) is in the form \(\frac{k}{m}\). Please find the value of \(k + m\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{38}
How many nonempty subsets of \( \{1, 2, \dots, 15\} \) are there such that the sum of the squares of each subset is a multiple of \( 5 \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7583}
If there exist \( n \) integers \( a_1, a_2, \cdots, a_n \) satisfying the following equations
$$
a_1 + a_2 + \cdots + a_n = a_1 a_2 \cdots a_n = 1990,
$$
find the smallest natural number \( n \) (where \( n \geqslant 2 \)).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
An article is sold for Rs. 350, and 4% more is gained than by selling it for a certain lower price. The cost of the article is Rs. 250. What is the lower selling price of the article?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{340}
In how many ways can the numbers $1, 2, \ldots, n$ be arranged in such a way that, except for the number in the first position, each number is preceded by at least one of its (originally ordered) neighbors?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{n-1}}
Find the volume of a parallelepiped where two faces are rhombuses with side length 1 and an acute angle of $60^{\circ}$, and the other faces are squares.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\sqrt{3}}{2}}
Some people of a village in Sri Lanka died by bombardment, 20 % of the remainder left the village on account of fear. Now the population is reduced to 4500. The population was 6249 in the beginning. What percentage of people died by bombardment?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9.99\%}
Circles $C_1$ and $C_2$ intersect at points $X$ and $Y$. Point $A$ is a point on $C_1$ such that the tangent line with respect to $C_1$ passing through $A$ intersects $C_2$ at $B$ and $C$, with $A$ closer to $B$ than $C$, such that $2016 \cdot AB = BC$. Line $XY$ intersects line $AC$ at $D$. If circles $C_1$ and $C_2$ have radii of $20$ and $16$, respectively, find $\sqrt{1+\frac{BC}{BD}}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2017}
Determine the maximum possible Jaccard Similarity of bags when the size of the intersection is twice the size of the smaller bag.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Start by writing the integers $1, 2, 4, 6$ on the blackboard. At each step, write the smallest positive integer $n$ that satisfies both of the following properties on the board:
1. $n$ is larger than any integer currently on the board.
2. $n$ cannot be written as the sum of two distinct integers already on the board.

Find the $100$-th integer that you write on the board. Recall that at the beginning, there are already $4$ integers on the board.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{388}
What number is formed from five consecutive digits (not necessarily in order) such that the number formed by the first two digits, when multiplied by the middle digit, gives the number formed by the last two digits? (For example, if we take the number 12896, 12 multiplied by 8 gives 96. However, since 1, 2, 6, 8, 9 are not consecutive digits, this example is not suitable as a solution.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13452}
Given a parallelepiped \( A B C D A_{1} B_{1} C_{1} D_{1} \). On edge \( A_{1} D_{1} \), point \( X \) is selected, and on edge \( B C \), point \( Y \) is selected. It is known that \( A_{1} X = 5 \), \( B Y = 3 \), and \( B_{1} C_{1} = 14 \). The plane \( C_{1} X Y \) intersects the ray \( D A \) at point \( Z \). Find \( D Z \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
In a certain country, there are exactly 2019 cities and between any two of them, there is exactly one direct flight operated by an airline company, that is, given cities $A$ and $B$, there is either a flight from $A$ to $B$ or a flight from $B$ to $A$. Find the minimum number of airline companies operating in the country, knowing that direct flights between any three distinct cities are operated by different companies.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2019}
A trapezoid has side lengths $10, 10, 10$, and $22$. Each side of the trapezoid is the diameter of a semicircle. The two semicircles on the parallel sides of the trapezoid face outside the trapezoid, while the other two semicircles face inside, as shown in the figure.

The region bounded by these four semicircles has an area expressed as $m + n\pi$, where $m$ and $n$ are positive integers. Find $m + n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{176}
Evaluate the triple integral
$$ \int^2_{-2} \int_0^{\sqrt{4-x^2}} \int_0^{\sqrt{4-x^2-y^2}} (x^2+y^2+z^2) \, dz \, dy \, dx $$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\(\frac{32\pi}{5}\)}
Given that point $P(m,4)$ lies on the ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$, and $F\_{1}$, $F\_{2}$ are the two foci of the ellipse. If the inscribed circle of $\triangle PF\_{1}F\_{2}$ has a radius of $\frac{3}{2}$, find the eccentricity of this ellipse.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3}{5}}
A quadrilateral \(ABCD\) is inscribed in a circle, with \(BC = CD\), \(AC = c\), and \(\angle BAD = 2\alpha\). Find the area of this quadrilateral.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{c^2 \sin(\alpha) \cos(\alpha)}
On the radius \( AO \) of a circle with center \( O \), a point \( M \) is chosen. On the same side of \( AO \) on the circle, points \( B \) and \( C \) are chosen so that \( \angle AMB = \angle OMC = \alpha \). Find the length of \( BC \), given that the radius of the circle is 12 and \( \sin \alpha = \frac{\sqrt{11}}{6} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
The coefficient of $x^2$ in the expansion of $(x^2+x+1)(1-x)^4$ is.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Determine the total number of pairs of integers \(x\) and \(y\) that satisfy the equation
\[ \frac{1}{y} - \frac{1}{y+2} = \frac{1}{3 \cdot 2^{x}} \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
During the softball season, Judy had $35$ hits.  Among her hits were $1$ home run, $1$ triple and $5$ doubles.  The rest of her hits were single.  What percent of her hits were single?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{80\%}
Given points \( A(4,0) \) and \( B(2,2) \) are inside the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 \), and \( M \) is a point on the ellipse, find the maximum value of \( |MA| + |MB| \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10 + 2 \sqrt{10}}
A cube with a side length of \( n \) ( \( n \geq 3 \) ) is divided into unit cubes by partitions. What is the minimum number of partitions between unit cubes that need to be removed so that each unit cube can be reached from the boundary of the larger cube?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(n-2)^3}
In a certain solution, the ratio, by volume, of bleach to detergent to water is 2 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution contains 60 liters of detergent, how many liters of water does it contain?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{150}
Two congruent parallelograms have equal sides parallel to each other. In both parallelograms, we mark the vertices, the midpoints of the sides, and the intersection point of the diagonals. We choose one point from the marked points of the first parallelogram and another point from the marked points of the second parallelogram in every possible way, and construct the midpoint of the segment connecting the two chosen points.

How many different midpoints do we get in this way?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
How many even divisors does $9!$ have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{140}