inclusionAI/Ring-lite-rl-data huggingface dataset:
The country Omega grows and consumes only vegetables and fruits. It is known that in 2014, 1200 tons of vegetables and 750 tons of fruits were grown in Omega. In 2015, 900 tons of vegetables and 900 tons of fruits were grown. During the year, the price of one ton of vegetables increased from 90,000 to 100,000 rubles, and the price of one ton of fruits decreased from 75,000 to 70,000 rubles. By what percentage (%) did the real GDP of this country change in 2015, if the base year in Omega is 2014? Round your answer to two decimal places. If the real GDP of the country decreased, put a minus sign in the answer, and if it increased, put a plus sign.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-9.59\%}
Given that $(1-2x)^{9}=a_{9}x^{9}+a_{8}x^{8}+...+a_{2}x^{2}+a_{1}x+a_{0}$, find the value of $a_{1}+a_{2}+...+a_{8}+a_{9}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2}
6. 135 Let $N$ be the set of all positive integers, and $f$ a function from $N$ to $N$ itself, such that for any $s$ and $t$ in $N$, the following holds:
$$f\left(t^{2} f(s)\right)=s(f(t))^{2}$$

Determine the smallest possible value of $f(1998)$ among all such functions $f$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{120}
A box contains red, green, blue, and white balls, totaling 111 balls. If you take out 100 balls without looking, there will always be 4 balls of different colors among them. What is the smallest number of balls you must take out without looking to ensure that among them there will always be balls of at least 3 different colors?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{88}
In triangle $ABC$, the median $AM$ is perpendicular to the angle bisector $BD$. Find the perimeter of the triangle given that $AB = 1$ and the lengths of all sides are integers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Given the function $f(x)=2\sin (2x+ \frac {\pi}{4})$, let $f_1(x)$ denote the function after translating and transforming $f(x)$ to the right by $φ$ units and compressing every point's abscissa to half its original length, then determine the minimum value of $φ$ for which $f_1(x)$ is symmetric about the line $x= \frac {\pi}{4}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{3\pi}{8}}
If vector $\overrightarrow{a}=(1,-x)$ and vector $\overrightarrow{b}=(x,-6)$ are in opposite directions, then $x=$ ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\sqrt{6}}
Four two-inch squares are placed with their bases on a line. The second square from the left is lifted out, rotated 45 degrees, then centered and lowered back until it touches its adjacent squares on both sides. Determine the distance, in inches, of point P, the top vertex of the rotated square, from the line on which the bases of the original squares were placed.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1 + \sqrt{2}}
数列$\left\{ {{a}_{n}} \right\}$满足${{an+1}}={{a}_{n}}\cdot \cos (n\pi )+2n-1,n\in {{N}^{*}}$，若${{a6}}+{{a}_{20}}=2m$，则实数$m=$___.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
The numbers 2, 3, 4, 5, 6, 7, 8 are to be placed, one per square, in a 2x2 grid such that the four numbers in the horizontal row add up to 21 and the four numbers in the vertical column add up to 21. Calculate the value of x that satisfies these conditions. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
9. Let set $A$ consist entirely of positive integers, and for any $x, y \in A (x \neq y)$, we have $|x-y| \geqslant \frac{1}{25} x y$. How many numbers can $A$ contain at most?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
If the equation $(x-2)(x^2-4x+m)=0$ has three roots, and these three roots can exactly serve as the lengths of the sides of a triangle, then the range of $m$ is.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3<m\leq4}
The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, $30 = 6\times5$. What is the missing number in the top row?

[asy] unitsize(0.8cm); draw((-1,0)--(1,0)--(1,-2)--(-1,-2)--cycle); draw((-2,0)--(0,0)--(0,2)--(-2,2)--cycle); draw((0,0)--(2,0)--(2,2)--(0,2)--cycle); draw((-3,2)--(-1,2)--(-1,4)--(-3,4)--cycle); draw((-1,2)--(1,2)--(1,4)--(-1,4)--cycle); draw((1,2)--(1,4)--(3,4)--(3,2)--cycle); label("600",(0,-1)); label("30",(-1,1)); label("6",(-2,3)); label("5",(0,3)); [/asy]

Find the missing number in the top row.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
On a cubic planet, cubic mice live only on the faces of the cube and not on the edges or vertices. The number of mice on different faces is different and on any two neighboring faces, this number differs by at least 2. What is the minimum number of cubic mice that can live on this planet if there is at least one mouse on each face?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{27}
Three pipes, a, b, & c are attached to a tank. Pipe a can fill it in 20 minutes, b can fill it in 30 minutes, and c can empty it in some time. If a, b & c are kept open successively for 4 minute each, the tank will be filled in 12 minutes. How soon can pipe c empty the tank?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
What is the value of $o-w$, if $gun^2 = wowgun$ where $g,n,o,u,w \in \{0,1,2,\dots, 9\}$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
A dot is marked at each vertex of a triangle $A B C$. Then, 2,3 , and 7 more dots are marked on the sides $A B, B C$, and $C A$, respectively. How many triangles have their vertices at these dots?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{357}
Find the third even number in a sequence of 6 consecutive even numbers with a sum of 180.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
There are three piles with 40 stones each. Petya and Vasya take turns, starting with Petya. Each turn, a player must combine two piles, then divide the combined stones into four piles. The player who cannot make a move loses. Which player (Petya or Vasya) can guarantee a win, regardless of the opponent's moves?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Vasya}
In three-dimensional space, find the number of lattice points that have a distance of 5 from the origin.

Note: A point is a lattice point if all its coordinates are integers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Randomly and without replacement, select three numbers \(a_1, a_2, a_3\) from the set \(\{1, 2, \cdots, 2014\}\). Then, from the remaining 2011 numbers, again randomly and without replacement, select three numbers \(b_1, b_2, b_3\). What is the probability that a brick with dimensions \(a_1 \times a_2 \times a_3\) can fit inside a box with dimensions \(b_1 \times b_2 \times b_3\)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/4}
John saves 10% of his monthly salary and invests an additional 5% into a retirement fund. At the end of each month, he is able to save $400 in a general savings account, after accounting for his expenses and a fluctuating increase of 5-7% in expenses due to dearness of things. Furthermore, his retirement fund has a cap of $1500 per month. During some months, John receives an extra allowance with a conversion rate of Rs. 70 per dollar. He pays income tax at a rate of 20% on his base salary and 10% on his extra allowance. The increase in expenses depends on specific monthly conditions related to his consumption patterns. What is John's monthly base salary in dollars, accounting for the various savings, expenses, and additional parameters?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$4000}
Determine the number of zeros of the function $f(z)=z^4+2z^3+3z^2+z+2$ in the annulus $1<|z|<2$ using Rouche's theorem.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Nora's mother tells her to go and pick oranges from their farm. She picks 80 oranges from the first tree, 60 from the second tree, 120 from the third tree, 45 from the fourth tree, 25 from the fifth tree, and 97 from the sixth tree. After picking oranges, she gives half of the oranges from the second and fourth trees to her neighbor. Additionally, she finds out that 20% of the oranges from the third and fifth trees are not ripe and decides not to take these unripe oranges. What's the total number of oranges she picked after considering all the changes?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{345}
Given a tetrahedron \( A B C D \) with side lengths \( A B = 41 \), \( A C = 7 \), \( A D = 18 \), \( B C = 36 \), \( B D = 27 \), and \( C D = 13 \), let \( d \) be the distance between the midpoints of edges \( A B \) and \( C D \). Find the value of \( d^{2} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{137}
Draw 63 south lines on the coordinate plane: $y=b, y=\sqrt{3} x+2 b, y=-\sqrt{3} x+2 b$, where $b=-10$, $-9,-8, \cdots, 8,9,10$. These lines divide the plane into several equilateral triangles. The number of equilateral triangles with side length $\frac{2}{\sqrt{3}}$ is $\qquad$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{660}
Last year, Manfred received 26 paychecks. Each of his first 6 paychecks was $750, and each of his remaining paychecks was $20 more than each of his first 6 paychecks. Additionally, Manfred had a bonus of $250 added to his 10th paycheck and a medical deductible of $120 taken from his 20th paycheck. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year, taking into account his bonus and the medical deductible?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$770}
Richard starts with the string HHMMMMTT. A move consists of replacing an instance of HM with MH , replacing an instance of MT with TM, or replacing an instance of TH with HT. Compute the number of possible strings he can end up with after performing zero or more moves.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{70}
Problem 9.6. A white checkered $8 \times 8$ table is given. In it, 20 cells are painted black. What is the minimum number of pairs of adjacent white cells that could remain?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{34}
Black and white balls are arranged in a circle, with black balls being twice as many as white balls. It is known that among the pairs of neighboring balls, there are three times as many pairs of the same color as there are pairs of different colors. What is the minimum number of balls that could have been arranged?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
Find the value of $\cot{t}$ if $$\sum_{i=1}^{\infty} \cot^{-1}\biggl(\frac{1}{2i^{2}}\biggr)= t.$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
At a chamber music festival, six musicians have gathered. At each concert, some of the musicians perform while the others listen from the audience. What is the minimum number of concerts needed for each of the six musicians to listen (from the audience) to all the others?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Find the angle of the minor arc corresponding to the chord intercepted by the line $6x+8y-10=0$ on the circle $x^{2}+y^{2}=4$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2\pi}{3}}
Three concentric circles form two rings. The inner and middle circumference of the first ring are 352 / 7 m and 528 / 7 m, respectively. The outer circumference of the second ring is 704 / 7 m. Find the combined width of the two rings.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
In the $xy$-coordinate plane, the $x$-axis and the line $y=x$ are mirrors. If you shoot a laser beam from the point $(126, 21)$ toward a point on the positive $x$-axis, there are $3$ places you can aim at where the beam will bounce off the mirrors and eventually return to $(126, 21)$. They are $(126, 0)$, $(105, 0)$, and a third point $(d, 0)$. What is $d$? 

Note: When light bounces off a mirror, the angle of incidence has the same measure as the angle of reflection.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{111}
Nick has a $3 \times 3$ grid and wants to color each square in the grid one of three colors such that no two squares that are adjacent horizontally or vertically are the same color. Compute the number of distinct grids that Nick can create.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{246}
Find the smallest positive integer \( n \) such that a cube with side length \( n \) can be divided into 1996 smaller cubes, each with side length a positive integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
Arrange the numbers 1 to 9 in a row from left to right such that every three consecutive numbers form a three-digit number that is a multiple of 3. How many arrangements are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1296}
For the power function $f(x) = (m^2 - m - 1)x^{m^2 + m - 3}$ to be a decreasing function on the interval $(0, +\infty)$, then $m = \boxed{\text{answer}}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1}
$ABCDE$ is a regular pentagon inscribed in a circle of radius 1. What is the area of the set of points inside the circle that are farther from $A$ than they are from any other vertex?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\pi}{5}}
Find the number of solutions in positive integers \(\left(k; a_{1}, a_{2}, \ldots, a_{k}; b_{1}, b_{2}, \ldots, b_{k}\right)\) to the equation
\[ 
a_{1}\left(b_{1}\right) + a_{2}\left(b_{1}+b_{2}\right) + \cdots + a_{k}\left(b_{1}+b_{2}+\cdots+b_{k}\right)= 7.
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
Find the surface area of the part of the paraboloid \( z = x^2 - y^2 \) that is enclosed between the paraboloids \( z = 3x^2 + y^2 - 2 \) and \( z = 3x^2 + y^2 - 4 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\pi}{6} (27 - 5\sqrt{5})}
On the banks of an island, which has the shape of a circle (viewed from above), there are the cities $A, B, C,$ and $D$. A straight asphalt road $AC$ divides the island into two equal halves. A straight asphalt road $BD$ is shorter than road $AC$ and intersects it. The speed of a cyclist on any asphalt road is 15 km/h. The island also has straight dirt roads $AB, BC, CD,$ and $AD$, on which the cyclist's speed is the same. The cyclist travels from point $B$ to each of points $A, C,$ and $D$ along a straight road in 2 hours. Find the area enclosed by the quadrilateral $ABCD$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{450}
Evaluate the expression:
\[4(1+4(1+4(1+4(1+4(1+4(1+4(1+4(1))))))))\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{87380}
Segments \(AA', BB'\), and \(CC'\), each of length 2, all intersect at a point \(O\). If \(\angle AOC'=\angle BOA'=\angle COB'=60^{\circ}\), find the maximum possible value of the sum of the areas of triangles \(AOC', BOA'\), and \(COB'\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{3}}
There is a set of points M on a plane and seven different circles C1, C2,..., C7. Circle C7 passes through exactly 7 points in M, circle C6 passes through exactly 6 points in M, and so on, with circle C1 passing through exactly 1 point in M. Find the minimum number of points in M. Express your answer as a whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
How many ways can you color the squares of a $2 \times 2008$ grid in 3 colors such that no two squares of the same color share an edge?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 \cdot 3^{2008}}
Heinz produces a mixed vegetable puree by combining and boiling tomato juice, carrot juice, and spinach juice. The final mixed vegetable puree has 25% water content. The tomato juice has 90% water content, the carrot juice has 88% water content, and the spinach juice has 91% water content. They use 20 liters of tomato juice, 12 liters of carrot juice, and 8 liters of spinach juice. How many liters of mixed vegetable puree will be obtained from this combination of vegetable juices?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5.55}
In how many ways can two disjoint subsets be selected from a set with $n$ elements?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3^n}
Let $ABCD$ be a rhombus with $\angle ADC = 46^\circ$. Let $E$ be the midpoint of $\overline{CD}$, and let $F$ be the point on $\overline{BE}$ such that $\overline{AF}$ is perpendicular to $\overline{BE}$. What is the degree measure of $\angle BFC$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$113$}
For any positive integer \( n \), let \( f(n) \) denote the number of 1's in the base-2 representation of \( n \). For how many values of \( n \) with \( 1 \leq n \leq 2002 \) do we have \( f(n) = f(n+1) \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{501}
If n divided by a certain number has a remainder of 2, and the remainder when 2 times n is divided by the same number is 4, what is that number?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Calculate the limit: 
$$\lim_{{x \to 0}} \frac{\cos(\sin x) - \cos x}{x^4}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/6}
Given the floor function \( \left\lfloor x \right\rfloor \) represents the largest integer not greater than \( x \), find all positive integer values of \( n \) that satisfy the equation:
\[
\left\lfloor \frac{\left\lfloor \frac{91}{n} \right\rfloor}{n} \right\rfloor = 1
\]
Express your answer as a list of integers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7, 8, 9}
Circles $\omega$ and $\gamma$, both centered at $O$, have radii $20$ and $17$, respectively. Equilateral triangle $ABC$, whose interior lies in the interior of $\omega$ but in the exterior of $\gamma$, has vertex $A$ on $\omega$, and the line containing side $\overline{BC}$ is tangent to $\gamma$. Segments $\overline{AO}$ and $\overline{BC}$ intersect at $P$, and $\dfrac{BP}{CP} = 3$. Then $AB$ can be written in the form $\dfrac{m}{\sqrt{n}} - \dfrac{p}{\sqrt{q}}$ for positive integers $m$, $n$, $p$, $q$ with ${gcd}(m,n) = {gcd}(p,q) = 1$. What is the value of $m+n+p+q$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{130}
7. [6] Let $a_{1}, a_{2}$, and $a_{3}$ be nonzero complex numbers with non-negative real and imaginary parts. Find the minimum possible value of
$$
\frac{\left|a_{1}+a_{2}+a_{3}\right|}{\sqrt[3]{\left|a_{1} a_{2} a_{3}\right|}} .
$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{3}\sqrt[3]{2}}
Given the function $y=\cos \left(x+ \frac {\pi}{3}\right)$, derive the horizontal shift of the graph of the function $y=\sin x$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{5\pi}{6}}
Jackson begins at $1$ on the number line. At each step, he remains in place with a probability of $85\%$ and increases his position on the number line by $1$ with a probability of $15\%$. Let $d_n$ be his position on the number line after $n$ steps, and let $E_n$ be the expected value of $\frac{1}{d_n}$. Find the least $n$ such that $\frac{1}{E_n} > 2017$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13446}
Points \(A\) and \(C\) lie on a circle centered at \(O\), each of \(\overline{BA}\) and \(\overline{BC}\) are tangent to the circle, and \(\triangle ABC\) is equilateral. The circle intersects \(\overline{BO}\) at \(D\). The original answer 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{3}
How many solutions does the equation $\tan x = \tan (\tan x)$ have in the interval $0 \le x \le \tan^{-1} 1000$? Assume $\tan \theta > \theta$ for $0 < \theta < \frac{\pi}{2}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{318}
Let the function $f(x)$ have a derivative $f'(x)$ for all $x \in \mathbb{R}$, and for all $x \in \mathbb{R}$, it holds that $f(-x) + f(x) = x^2$. If $f'(x) < x$ for $x \in (0, +\infty)$ and $f(2-m) - f(m) > 2 - 2m$, then the range of values for the real number $m$ is \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(1, +\infty)}
What is the minimum number of bits required to represent the numbers 25, 18.5, and 9.25 precisely, using a system similar to the IEEE floating point standard?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
In the diagram, \( S \) lies on \( R T \), \( \angle Q T S = 40^{\circ} \), \( Q S = Q T \), and \( \triangle P R S \) is equilateral. Find the value of \( x \) in degrees.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{80}
Nikita schematically drew the graph of the quadratic polynomial \( y = ax^{2} + bx + c \). It turned out that \( AB = CD = 1 \). Consider the four numbers \(-a, b, c\), and the discriminant of the polynomial. It is known that three of these numbers are equal to \( \frac{1}{4}, -1, -\frac{3}{2} \) in some order. Find the value of the fourth number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1/2}
Meredith drives in a series of directions:

1. 5 miles to the northeast.
2. 15 miles to the southeast.
3. 25 miles to the southwest.
4. 35 miles to the northwest.
5. 20 miles to the northeast.

Calculate how many miles Meredith is from her starting point after completing her journey.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
A circle can be inscribed in and circumscribed around quadrilateral \(ABCD\). The diagonals of this quadrilateral are mutually perpendicular. Find its area if the radius of the circumscribed circle is \(R\) and \(AB = 2BC\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{8R^2}{5}}
# Task 14. (1 point)

Calculate the amount of personal income tax (NDFL) paid by Sergey for the past year, if he is a Russian resident and during this period had a stable income of 30000 rub./month and a one-time vacation bonus of 20000 rub. In the past year, Sergey sold a car he inherited two years ago for 250000 rub. and bought a land plot for building a residential house for 300000 rub. Sergey claimed all the tax deductions he was entitled to. (Provide the answer without spaces and units of measurement.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10400}
For the function $y=\left(m-2\right)x^{|m|}-4$ with respect to $x$, $m=$____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2}