inclusionAI/Ring-lite-rl-data huggingface dataset:
A scuba diver descends at a rate of 80 feet per minute under normal conditions. However, during this dive, the diver encounters two different currents and must make stops for decompression. From the surface to 1500 feet, the diver faces a downward current, which increases the descending speed by 30 feet per minute. Between 1500 and 3000 feet, there is an upward current slowing the diver's descent by 20 feet per minute. Below 3000 feet, the diver resumes the normal descending speed.

Additionally, the diver must make two decompression stops, one at 1800 feet for 5 minutes and another at 3600 feet for 8 minutes. The lost ship is located at a depth of 4000 feet below sea level.

Considering these factors, how long will it take the diver to reach the lost ship?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{64.14}
Jane started babysitting when she was 20 years old. Whenever she babysat for a child, that child was no more than half her age at the time. Jane stopped babysitting 10 years ago when she was 22 years old. She babysat for kids with age gaps between them not more than 1 year. If Jane is currently 32 years old, what is the current age of the oldest person for whom Jane could have babysat, given that this person's age is a prime number?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
Given the line $L: x+y-9=0$ and the circle $M: 2x^2+2y^2-8x-8y-1=0$, point $A$ is on line $L$, and points $B$ and $C$ are on circle $M$. In $\triangle ABC$, $\angle BAC=45^\circ$, and $AB$ passes through the center $M$ of the circle. The range of the $x$-coordinate of point $A$ is \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[3, 6]}
Find the number which when multiplied by 15 is increased by 196. What is the result?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{210}
A sample of 5 individuals has values a, 0, 1, 2, 3. Given that the average value of the sample is 1, calculate the variance of the sample using the formula for variance. Express your answer as a single numerical value.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Consider nine points in space, no four of which lie in a plane. We connect each pair of points with an edge (i.e., a straight line segment), and color each such edge red, blue, or leave it uncolored. Determine the smallest value of $n$ such that whenever the number of colored edges is exactly $n$, the set of colored edges necessarily contains a triangle whose edges are all the same color.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{33}
Find the domain of the function $f(x)= \frac{ \sqrt{x}}{\ln (2-x)}$. Express your answer as an interval or union of intervals.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[0,1)\cup(1,2)}
Split a face of a regular tetrahedron into four congruent equilateral triangles. How many different ways can the seven triangles of the tetrahedron be colored using only the colors orange and black? (Two tetrahedra are considered to be colored the same way if you can rotate one so it looks like the other.)

Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{48}
Split a face of a regular tetrahedron into four congruent equilateral triangles. How many different ways can the seven triangles of the tetrahedron be colored using only the colors orange and black? (Two tetrahedra are considered to be colored the same way if you can rotate one so it looks like the other.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{48}
Evaluate the contour integral $$\oint\limits_{|z-3|=4}^{}\frac{z}{\cos z-1}dz$$ using the residue theorem.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-8\pi i}
Let $O$ be the set of odd numbers between 0 and 100. Let $T$ be the set of subsets of $O$ of size 25. For any finite subset of integers $S$, let $P(S)$ be the product of the elements of $S$. Define $n = \sum_{S \in T} P(S)$. If you divide $n$ by 17, what is the remainder?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
A positive integer is called oddly even if the sum of its digits is even. Find the sum of the first 2013 oddly even numbers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4055187}
Evaluate the following integral:
$$I=\int_0^1 \frac{\log^3(1-x)}{x}dx$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\frac{\pi^4}{15}}
A robot walks 1m in a certain direction, then turns left 45°, walks another 1m, then turns left 45° again, and repeats the instruction "walk 1m, then turn left 45°". When the robot returns to the starting point for the first time, it has walked     m.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
The decimal representation of 
$$\dfrac{1}{20^{20}}$$ 
consists of a string of zeros after the decimal point, followed by a $9$ and then several more digits. How many zeros are in that initial string of zeros after the decimal point?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{26}
Sebastian plays drums for percussion in an orchestra seated in various sections. In the percussion section, there are three more players besides Sebastian: one playing the timpani, another playing the marimba, and a third who switches between the xylophone and the triangle. 

He sits next to the brass section where five people play trombone, four play trumpet, two play the tuba, two play a French horn and one person alternates between the French horn and trumpet. In front of them are the strings section with seven violinists, five violists, four cellists, and two contrabassists. Among the violinists, one also plays the viola, and a cellist sometimes switches to double bass. 

Adjacent to the strings are the woodwinds section with three clarinet players, a quartet of flute players, two bassoonists, and an oboist. One of the clarinet players also doubles as a bass clarinet player. A pianist, a harpist, and a musician who plays both the celesta and the organ join the orchestra as well in the keyboards and harp section. 

The maestro conducts them all. How many people are in the orchestra considering the musicians who play multiple instruments?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{49}
If the largest angle in a triangle is twice the size of the smallest angle, and the lengths of its sides are three consecutive natural numbers, find the side lengths of the triangle. Express your answer as three consecutive natural numbers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4, 5, 6}
What is the maximum number of \(4 \times 1\) rectangles that can be placed in a \(6 \times 6\) square (without crossing the cell boundaries)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
A ball of radius R and mass m is magically put inside a thin shell of the same mass and radius 2R. The system is at rest on a horizontal frictionless surface initially. When the ball is, again magically, released inside the shell, it sloshes around in the shell and eventually stops at the bottom of the shell. Calculate the distance the shell moves from its initial contact point with the surface. Express your answer in terms of R.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{R}{2}}
How many natural numbers \(n\) are there such that

\[ 100 < \sqrt{n} < 101 ? \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{200}
3. (1990 Vietnam Olympiad) Let $a, b, c \in \mathbf{R}^{+}$, and $a b c + a + c = b$, try to determine the maximum value of $p = \frac{2}{a^{2}+1} - \frac{2}{b^{2}+1} + \frac{3}{c^{2}+1}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{10}{3}}
Tuition at the music school is $45 per person for regular enrollments. There is a $15 discount for early bird enrollments, a $15 discount for the first sibling, and a $10 discount for each additional sibling. Additionally, there is a $20 extra cost per person for weekend classes and a $10 discount per person if enrolled in more than one musical instrument.

Ali, an early bird registrant, and her brother, Matt, signed up for weekday classes for one instrument each. Their two sisters, Jane and Sarah, enlisted for weekend classes to learn two instruments each. How much will it cost for all four children?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$150}
5. [5 points] On a plane with a given rectangular Cartesian coordinate system, a square is drawn with vertices at points $(0 ; 0),(0 ; 59),(59 ; 59)$, and $(59 ; 0)$. Find the number of ways to choose two grid nodes inside this square (not including its boundary) such that at least one of these nodes lies on one of the lines $y=x$ or $y=59-x$, but neither of the chosen nodes lies on any line parallel to any of the coordinate axes.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{370330}
Let $A=\{x\in \mathbb{N} | -2 \leq x \leq 2\}$ and $B=\{2,4\}$. Find the union of sets A and B, denoted as A∪B. Express your answer as a set of numbers, including all unique elements from both sets.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\{0, 1, 2, 4\}}
In the polar coordinate system, the curve $\rho=4\sin \left( \theta- \frac{\pi}{3} \right)$ is symmetric about what axis?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{5\pi}{6}}
An arrangement is defined as any way to seat $n$ couples at a round table with $2n$ places. A couple is said to be together if the two members are seated next to each other. What is the average number of couples that are together per arrangement?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2n}{2n-1}}
Each segment with endpoints at the vertices of a regular 100-gon is colored red if there is an even number of vertices between its endpoints, and blue otherwise (in particular, all sides of the 100-gon are red). Numbers were placed at the vertices such that the sum of their squares equals 1, and at the segments, the products of the numbers at the endpoints were placed. Then, the sum of the numbers on the red segments was subtracted by the sum of the numbers on the blue segments. What is the largest possible value that could be obtained?

I. Bogdanov
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{2}}
Find the minimum value of $k$ such that the inequality $$\sin{a}\leq\frac{a}{\sqrt{1+\frac{a^2}{k}}}$$ holds for all $a>0$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
There are 3 garages at Liam's house. In the first garage, there are 5 bicycles, 6 tricycles, 9 unicycles, and 3 quadracycles, but 2 of the bicycles are missing a wheel. Each bicycle typically has 2 wheels, each tricycle has 3 wheels, each unicycle has 1 wheel, and each quadracycle has 4 wheels. In the second garage, there are 2 bicycles, 1 tricycle, 3 unicycles, 4 quadracycles, and 2 pentacycles, with 1 of the pentacycles missing 2 wheels. Each pentacycle typically has 5 wheels. In the third garage, there are 3 bicycles, 4 tricycles, 2 unicycles, 2 quadracycles, 1 pentacycle, and a hexacycle with a sidecar, but 1 of the unicycles is missing a wheel, and the hexacycle with a sidecar is missing 1 wheel. Each hexacycle typically has 6 wheels, and a sidecar adds 1 extra wheel. How many wheels are there in total across all three garages?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{119}
A 470 m long train is running at a speed of 55 km/hr. It crossed a platform of a certain length in 64.79481641468682 seconds. What is the length of the platform?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{520}
Ian started saving a certain amount of money every day. After 40 days, he would have saved 4 dimes in total. How much money does Ian save each day?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Five points lie on a straight line. Alex finds the distances between every pair of points. He obtains, in increasing order, 2, 5, 6, 8, 9, \( k \), 15, 17, 20, and 22. What is the value of \( k \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14}
Let $G = (V,E)$ be a connected graph and $\alpha \in \mathbb{R}$. A graph $H =(V_H, E_H)$ is called an $\alpha$-Spanning Tree of $G$ if $V_H = V$, $E_H\subseteq E$, and for every pair of vertices $u,v$, the inequality $d_H(u,v) \leq \alpha \cdot d_G(u,v)$ applies. What is the smallest possible value of $\alpha$ such that a grid graph $M_{n,n}$ has an $\alpha$-spanning tree?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Let $f(x)$ be an odd function with a period of 3 defined over $\mathbb{R}$. Given that $f(2) = 0$, the number of solutions to the equation $f(x) = 0$ in the interval $[0, 6]$ is \_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
已知 \(z, w \in \mathbf{C},|z+w|=1,\left|z^{2}+w^{2}\right|=4\)，求 \(|z w|\) 的最大值。原始答案的形式为 \(\frac{k}{m}\)，请给出\(k+m\)的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Four points are marked on a straight line and one point is marked outside the line. There are six triangles that can be formed with vertices at these points.

What is the maximum number of these triangles that can be isosceles?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
In a convex 13-gon, all the diagonals are drawn. They divide it into polygons. Consider a polygon among them with the largest number of sides. What is the maximum number of sides it can have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
Esmeralda writes $2n$ real numbers $x_1, x_2, \dots , x_{2n}$, all belonging to the interval $[0, 1]$, around a circle and multiplies all the pairs of numbers neighboring to each other, obtaining, in the counterclockwise direction, the products $p_1 = x_1x_2$, $p_2 = x_2x_3$, $\dots$ , $p_{2n} = x_{2n}x_1$. She adds the products with even indices and subtracts the products with odd indices. What is the maximum possible number Esmeralda can get?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{ \left\lfloor \frac{n}{2} \right\rfloor }
While there do not exist pairwise distinct real numbers  $a,b,c$  satisfying  $a^2+b^2+c^2 = ab+bc+ca$ , there do exist complex numbers with that property. Let  $a,b,c$  be complex numbers such that  $a^2+b^2+c^2 = ab+bc+ca$  and  $|a+b+c| = 21$ . Given that  $|a-b| = 2\sqrt{3}$ ,  $|a| = 3\sqrt{3}$ , compute  $|b|^2+|c|^2$ .
<details><summary>Clarifications</summary>

- The problem should read  $|a+b+c| = 21$ .  An earlier version of the test read  $|a+b+c| = 7$ ; that value is incorrect.
- $|b|^2+|c|^2$  should be a positive integer, not a fraction; an earlier version of the test read ``... for relatively prime positive integers  $m$  and  $n$ .  Find  $m+n$ .''
</details>

*Ray Li*
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{132}
Let $ABCD$ be a square with vertices $A=(0,0)$ and $B=(1,1)$. A point $P\left(\frac{2}{7},\frac{1}{4}\right)$ is located inside the square. An ant begins its journey from point $P$, touches three sides of the square, and returns to point $P$. The shortest possible distance the ant can travel is expressed as $\frac{\sqrt{a}}{b}$, where $a$ and $b$ are integers, and $a$ is not divisible by any square number other than $1$. Determine the value of $(a+b)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
Find the sum of the two smallest odd primes  $p$  such that for some integers  $a$  and  $b$ ,  $p$  does not divide  $b$ ,  $b$  is even, and  $p^2=a^3+b^2$ .


*2021 CCA Math Bonanza Individual Round #13*
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{122}
A fair six-sided die has faces numbered 1, 2, 3, 4, 5, 6. The die is rolled four times, resulting in numbers a, b, c, d. Calculate the probability that one of the numbers in the set {a, a+b, a+b+c, a+b+c+d} equals 4. Express your answer as a simplified fraction.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{343}{1296}}
The new individual income tax law has been implemented since January 1, 2019. According to the "Individual Income Tax Law of the People's Republic of China," it is known that the part of the actual wages and salaries (after deducting special, additional special, and other legally determined items) obtained by taxpayers does not exceed $5000$ yuan (commonly known as the "threshold") is not taxable, and the part exceeding $5000$ yuan is the taxable income for the whole month. The new tax rate table is as follows:

2019年1月1日后个人所得税税率表

| 全月应纳税所得额 | 税率$(\%)$ |
|------------------|------------|
| 不超过$3000$元的部分 | $3$ |
| 超过$3000$元至$12000$元的部分 | $10$ |
| 超过$12000$元至$25000$元的部分 | $20$ |
| 超过$25000$元至$35000$元的部分 | $25$ |

Individual income tax special additional deductions refer to the six special additional deductions specified in the individual income tax law, including child education, continuing education, serious illness medical treatment, housing loan interest, housing rent, and supporting the elderly. Among them, supporting the elderly refers to the support expenses for parents and other legally supported persons aged $60$ and above paid by taxpayers. It can be deducted at the following standards: for taxpayers who are only children, a standard deduction of $2000$ yuan per month is allowed; for taxpayers with siblings, the deduction amount of $2000$ yuan per month is shared among them, and the amount shared by each person cannot exceed $1000$ yuan per month.

A taxpayer has only one older sister, and both of them meet the conditions for supporting the elderly as specified. If the taxpayer's personal income tax payable in May 2020 is $180$ yuan, then the taxpayer's monthly salary after tax in that month is ____ yuan.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9720}
Points $F$, $G$, $H$, $I$, and $J$ are positioned in 3-dimensional space with $FG = GH = HI = IJ = JF = 3$ and $\angle FGH = \angle HIJ = \angle JIF = 90^\circ$. The plane of triangle $FGH$ is parallel to $\overline{IJ}$. Determine the area of triangle $GIJ$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4.5}
Find the maximum value of the following expression:
$$
|\cdots|\left|x_{1}-x_{2}\right|-x_{3}\left|-\cdots-x_{1990}\right|,
$$
where \( x_{1}, x_{2}, \cdots, x_{1990} \) are distinct natural numbers from 1 to 1990.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1989}
In trapezoid \(ABCD\), \(AB\) is parallel to \(DC\) and \(\angle DAF = 90^\circ\). Point \(E\) is on \(DC\) such that \(EB = BC = CE\). Point \(F\) is on \(AB\) such that \(DF\) is parallel to \(EB\). In degrees, what is the measure of \(\angle FDA\)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30^\circ}
如图， $A B$ 是单位圆的直径，在 $A B$ 上任取一点 $D$ ，作 $D C \perp A B$, 交圆周于 $C$ 。若点 $D$ 的坐标为 $(x, 0)$,则当 $x \in$ $(a, b)$时，线段 $A D 、 B D 、 C D$ 可以构成锐角三角形。请给出a + b的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
The parabola $P$ has its focus at $(0,0)$ and passes through the points $(4,3)$ and $(-4,-3)$. Determine the number of points $(x,y) \in P$ with integer coefficients such that $|4x + 3y| \leq 1000$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{40}
某班有 47 个学生，所用教室有 6 排，每排有 8个座位，用 $(i, j)$ 表示位于第 $i$ 排第 $j$ 列的座位。新学期准备调整座位，设某学生原来的座位为 $(i, j)$ ，如果调整后的座位为 $(m, n)$ ，则称该生作了移动 $[a$, $b]=[i-m, j-n]$ ，并称 $a+b$ 为该生的位置数。所有学生的位置数之和记为 $S$ 。求 $S$ 的最大可能值与最小可能值之差。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
Teams A, B, and C are to complete two projects, Project A and Project B. The workload of Project B is 25% more than that of Project A. The time it takes for teams A, B, and C to individually complete Project A are 20 days, 24 days, and 30 days, respectively. To complete these two projects together, team A was first assigned to Project A, while teams B and C worked on Project B. After a few days, team C was reassigned to work with team A to finish Project A. How many days did teams B and C work together?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
Let \( n \in \mathbf{Z}_{+} \). A volleyball team has \( n \) male players and \( n \) female players. Initially, each player is assigned to one of the positions numbered \( 1, 2, \cdots, 2n \), with only positions 1 and \( n+1 \) being outside the field. During the game, position swaps occur, with each player at position \( i \) (for \( i = 1, 2, \cdots, 2n \)) moving to \( i+1 \). Position \( 2n+1 \) is considered position 1. How many different initial arrangements of the players ensure that no matter how many swaps are made, at least \( n-1 \) female players are always on the field?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^n (n!)^2}
Hugo can fold a small box in 3 seconds and a medium one in twice that time. Tom can fold both the small and medium boxes in 4 seconds. If Hugo and Tom want to leave as early as possible, how long (in seconds) will it take them to fold 2400 small boxes and 1800 medium boxes?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7200}
Given point $P(-1,1)$, let $C$ be the family of circles described by the equation $(x-t)^{2}+(y-t)^{2}=1$, where $t \in R$. Let $A$ and $B$ be the points of tangency of the tangent lines to circle $C$ that pass through point $P$. Find the minimum value of $\overrightarrow{PA} \cdot \overrightarrow{PB}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Alice and Bob are playing a game where Alice declares, "My number is 36." Bob has to choose a number such that all the prime factors of Alice's number are also prime factors of his, but with the condition that the exponent of at least one prime factor in Bob's number is strictly greater than in Alice's. What is the smallest possible number Bob can choose?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{72}
Find the smallest value x such that, given any point inside an equilateral triangle of side 1, we can always choose two points on the sides of the triangle, collinear with the given point and a distance x apart.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2}{3}}
In the diagram shown, \( M \) is the midpoint of \( PQ \). The line \( PS \) bisects \( \angle RPQ \) and intersects \( RQ \) at \( S \). The line \( ST \) is parallel to \( PR \) and intersects \( PQ \) at \( T \). The length of \( PQ \) is 12 and the length of \( MT \) is 1. The angle \( SQT \) is \( 120^{\circ} \). Calculate the length of \( SQ \). Express your answer as a single number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Two trains of length 90 m and 100 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 71 kmph and 89 kmph. After how much time will the trains meet?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4.5}