inclusionAI/Ring-lite-rl-data huggingface dataset:
Find the value of the limit:

$$\lim_{x\to0}\frac{\log_{\sin^2x}\cos x}{\log_{\sin^2(x/2)}\cos(x/2)}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Nylah has her living room lights on a timer. Each evening, the timer switches the lights on at exactly 7:00 p.m., 7:30 p.m., 8:00 p.m., 8:30 p.m., or 9:00 p.m. Later in the evening, the timer switches the lights off at any random time between 11 p.m. and 1 a.m. What is the probability that the lights are on for 4 < t < 5 hours? Express your answer as a fraction.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{7}{20}}
A convex 2011-gon is drawn on the board. Peter keeps drawing its diagonals in such a way that each newly drawn diagonal intersects no more than one of the already drawn diagonals. What is the greatest number of diagonals that Peter can draw?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4016}
已知a、b、c、d取某些实数值时，方程$x ^ { 4 } + a x ^ { 3 } + b x ^ { 2 } + c x + d = 0$有4个非实数根，其中2个根的积为13+i,，另2个根的和为3+4i，这里i为虚数单位，求b.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{51}
There is a strip with a length of 100, and each cell of the strip contains a chip. You can swap any two adjacent chips for 1 ruble, or you can swap any two chips that have exactly three chips between them for free. What is the minimum number of rubles needed to rearrange the chips in reverse order?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{50}
An event has some adults and 20 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. The greatest number of tables the planner can set up is 4. How many adults are at the event?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
For which values of \( p \) does the triangle inequality \( ||x + y||_p \leq ||x||_p + ||y||_p \) hold true for the \( \ell^p \) norm in \( \mathbb{R}^n \)? Here, \( ||x||_p = \left( \sum_{k=1}^n |x_k|^p \right)^{1/p} \) for \( p \in (0, \infty) \) and \( ||x||_\infty = \sup |x_k| \) for \( 1 \leq k \leq n \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[1, \infty]}
In the final of the giraffe beauty contest, two giraffes, Tall and Spotted, reached the finals. There are 135 voters divided into 5 districts, with each district divided into 9 precincts, and each precinct having 3 voters. The voters in each precinct choose the winner by majority vote; in a district, the giraffe that wins in the majority of precincts wins the district; finally, the giraffe that wins in the majority of the districts is declared the winner of the final. The giraffe Tall won. What is the minimum number of voters who could have voted for Tall?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Evaluate the integral \( \int_0^{\frac{\pi}{4}} Re^{-R^2 \sin x} \, dx \) as \( R \to \infty \) using a suitable substitution.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Define the sequence $a_1, a_2, a_3, \cdots$ by $a_n = \sum\limits_{k=1}^n \sin{k}$, where $k$ represents radian measure. Find the index of the $100$th term for which $a_n < 0$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{628}
In a rectangle \(ABCD\) with an area of 1 (including the boundary), there are 5 points, none of which are collinear. Find the minimum number of triangles, formed by these 5 points as vertices, that have an area not exceeding \(\frac{1}{4}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
When \( 2x^3 - 5x^2 - 12x + 7 \) is divided by \( 2x + 3 \), the quotient is \( x^2 - 4x + 2 \). What is the remainder?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-4x + 1}
John climbs up some flights of stairs. Each flight is 10 feet. He then climbs a rope that is half that height. Finally, he climbs a ladder that is 10 feet longer than the rope. He went up 70 feet high. How many flights of stairs did he climb?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Suppose we have an infinite number of counters (numbered $0,1,2,\dots$) which fire (i.e. increment by $1$) independently according to a Poisson process of rate $1$. All counters are initially switched off. At time $0$ we turn on counter $0$. Each time counter $0$ fires, the next counter which is still off turns on (e.g. the first time counter $0$ fires, counter $1$ turns on, the second time counter $0$ fires, counter $2$ turns on, etc.). What is the expected number of fires over all counters in the interval $[1,2]$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5/2}
$\begin{aligned} & \mathrm{Let~}ABCDE\text{ be a convex pentagon such that }AB=AE=CD=1,\angle ABC=\angle DEA=90^{\circ}\mathrm{~and~}BC+DE=1 \\ & \text{Compute the area of the pentagon.} \end{aligned}$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1

}
Determine all real values of \( \alpha \) for which the improper integral \( \int_{0}^{\infty} x(x^2/2 + 1)^{\alpha} \, dx \) converges.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-\infty, -1)}
Alice and Bob are on a 1 km long closed and dark train. They start at random positions and can only see their own and each other's information on their iPhone 133, which includes their facing direction, total walking distance, and whether they are at the front or end of the train. They can discuss their strategy before the game starts. Determine the minimum total walking distance, \( x \), that guarantees they will meet, with \( x \leq 1 \) km.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Determine the highest dimension for which the classification of nilpotent Lie algebras is currently unknown.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
The distance between Luga and Volkhov is 194 km, between Volkhov and Lodeynoe Pole is 116 km, between Lodeynoe Pole and Pskov is 451 km, and between Pskov and Luga is 141 km. What is the distance between Pskov and Volkhov?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{335 \text{ km}}
A plane parallel to the base of a cone divides the height of the cone into two equal segments. What is the ratio of the lateral surface areas of the two parts of the cone?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{3}}
Calculate: $$\int_{0}^{2\pi}e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
A bag contains eight yellow marbles, seven red marbles, and five black marbles. Without looking in the bag, Igor removes N marbles all at once. If he is to be sure that, no matter which choice of N marbles he removes, there are at least four marbles of one color and at least three marbles of another color left in the bag, what is the maximum possible value of N? Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
John has 20% more boxes than Jules. Jules has 5 boxes more than Joseph. Joseph has 80% fewer boxes than Stan. Stan has twice as many boxes as Lily. Martin has 150% of the boxes Jules has. Alice has 3 boxes less than half the boxes Martin has. Gabriel has the average number of boxes between Martin and Alice. Emma has the median number of boxes among John, Jules, Joseph, Stan, Lily, Martin, Alice and Gabriel. If Stan has 150 boxes, how many boxes does Emma have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{40}
Evaluate the double integral \( \int_{-5}^5 \int_{-5}^5 -\frac{3}{2}|x+y| - \frac{3}{2}|x-y| + 15 \,\mathrm{d}x\,\mathrm{d}y \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{500}
Given the line $y=kx$ is tangent to the circle $C$: $(x-4)^{2}+y^{2}=r^{2}$, and the surface area of the geometric solid obtained by rotating circle $C$ around the $x$-axis for one week is $S=16π$, the value of $k$ is $\_\_\_\_\_\_$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\pm \frac{\sqrt{3}}{3}}
定义 $x * y=\frac{x+y}{1+x y}$, 则 $(\cdots((2 * 3) * 4) \cdots) * 21=$ $\qquad$.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{231}
A product of five primes is of the form $A B C, A B C$, where $A, B$, and $C$ represent digits. If one of the primes is 491, find the product $A B C, A B C$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{982,982}
Each segment with endpoints at the vertices of a regular 100-gon is painted 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 are placed at the vertices such that the sum of their squares equals 1, and the products of the numbers at the endpoints are placed on the segments. Then the sum of the numbers on the red segments is subtracted from the sum of the numbers on the blue segments. What is the largest possible result?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/2}
Let $ABC$ be an acute triangle with incenter $I$ and circumcenter $O$. Assume that $\angle OIA=90^{\circ}$. Given that $AI=97$ and $BC=144$, compute the area of $\triangle ABC$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14040}
Consider a symmetric random walk on a graph constructed from two cycles, $C_{m}$ and $C_{n}$, which share exactly two consecutive common vertices. Let $S$ and $S'$ be the common vertices, $A$ be a vertex of $C_{m}$ not in $C_{n}$, and $B$ be a vertex of $C_{n}$ not in $C_{m}$. Given $m = 2 \times 10^{6} + 1$ with the $SS'A$-arc being a path of $10^{6} + 1$ edges and the other $SA$-arc being a path of $10^{6}$ edges, and $n = 4 \times 10^{6} + 1$ with the $SS'B$-arc being a path of $2 \times 10^{6} + 1$ edges and the other $SB$-arc being a path of $2 \times 10^{6}$ edges, calculate the probability that a symmetric random walk starting from $S$ ends at vertex $A$. Assume the walk ends immediately upon reaching $A$. What is this probability?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{2}{3}}
Compute the Gini index for the probability density function \( f(x) \) defined as \( f(x) = 1 \) for \( 0 \leq x \leq 1 \) and \( f(x) = 0 \) elsewhere.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{1}{3}}
For every positive integeer  $n>1$ , let  $k(n)$  the largest positive integer  $k$  such that there exists a positive integer  $m$  such that  $n = m^k$ .

Find   $$ lim_{n \rightarrow \infty} \frac{\sum_{j=2}^{j=n+1}{k(j)}}{n} $$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Find the period of the function: $$f(x) = \left\lfloor x + 2 \right\rfloor - 
         \left\lfloor x - 1 \right\rfloor - 
        3\left\lfloor -x \right\rfloor$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Use the Horner's Rule to calculate the value of the polynomial: $f(x) = 1 + x + 2x^2 + 3x^3 + 4x^4 + 5x^5 + 7x^7$ at $x = 2$, the value of $v_3$ is \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{70}
Define a positive integer \( n \) as a "factorial tail" if there exists a positive integer \( m \) such that the decimal representation of \( m! \) ends in exactly \( n \) zeros. How many positive integers less than 1992 are not "factorial tails"?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{396}
How many values of $\theta$ in the interval $0 < \theta \le 2\pi$ satisfy $1 - 3\sin\theta + 5\cos3\theta = 0$? Provide your answer as an integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
For any real number x, find the range of values for the real number k such that the inequality |x+2|+|x+1|>k is always true. Express your answer as an inequality using standard notation (e.g., <, >, ≤, ≥).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{k<1}
The radius of a circle is increased by some percentage. Its area increases by 2.01%. By what percentage was the radius increased?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1.00\%}
David and Evan each repeatedly flip a fair coin. David will stop when he flips a tail, and Evan will stop once he flips 2 consecutive tails. Find the probability that David flips more total heads than Evan.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{5}}
Calculate the integral $$\int_{C}{xy^{2}dy-yx^{2}dx}$$ where C is the circle $x^{2}+(y-1)^{2}=1$ using polar coordinates and Green's theorem.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3\pi}{2}}
The vertices of a regular nonagon are colored such that:
1. Adjacent vertices are different colors.
2. If three vertices form an equilateral triangle, they are all different colors.

Let $m$ be the minimum number of colors needed for a valid coloring, and $n$ be the total number of colorings using $m$ colors. Determine $mn$. (Assume each vertex is distinguishable.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{54}
In rectangle PQRS, the ratio of ∠PSQ to ∠PQS is 1:5. Find the size of ∠QSR. Express your answer in degrees as a whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{75^\circ}
Let $s(n)$ denote the sum of the digits (in base ten) of a positive integer $n$. Compute the number of positive integers $n$ at most $10^{4}$ that satisfy $$s(11 n)=2 s(n)$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2530}
Given a function \( f: \mathbf{R} \rightarrow \mathbf{R} \) such that for any real numbers \( x \) and \( y \), \( f(2x) + f(2y) = f(x+y) f(x-y) \). Additionally, \( f(\pi) = 0 \) and \( f(x) \) is not identically zero. What is the period of \( f(x) \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4\pi}
23. Using the digits $1,2,3,4$ (digits can be repeated), how many $n(n \geqslant 2)$-digit numbers can be formed that contain an odd number of 1s, an even number of 2s, and at least one 3?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{4^{n}-3^{n}+(-1)^{n}}{4}}
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{\ln(n+1)^{n+1}}{\ln n^n} \right)^n. \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{e}
Mark and William are playing a game with a stored value. On his turn, a player may either multiply the stored value by 2 and add 1 or he may multiply the stored value by 4 and add 3. The first player to make the stored value exceed $2^{100}$ wins. The stored value starts at 1 and Mark goes first. Assuming both players play optimally, what is the maximum number of times that William can make a move?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{33}
设 m 是正整数，n=2^m-1，P_n=\{1,2,\cdots,n\} 是数轴上 n 个点构成的集合. 一只蚱蜢在这些点上跳跃，每步从一个点跳到与之相邻的点. 求 m 的最大值，使得对任意 x,y\in P_n，从点 x 跳 2012 步到点 y 的跳法种数为偶数（允许中途经过点 x,y）.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
An ice ballerina rotates at a constant angular velocity at one particular point. That is, she does not translationally move. Her arms are fully extended as she rotates. Her moment of inertia is $I$. Now, she pulls her arms in and her moment of inertia is now $\frac{7}{10}I$. Calculate the ratio of the new kinetic energy (arms in) to the initial kinetic energy (arms out). Express your answer as a simplified ratio.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{10}{7}}
In a party with \( n + 1 \) couples, where handshakes between spouses are forbidden, a total of \( 2n + 1 \) guests (excluding the host and hostess) report \( 2n + 1 \) unique numbers of handshakes. Determine the number of handshakes the host made.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{n}
A company sells a brand of cars in locations A and B, with profits (in units of ten thousand yuan) given by $L_1 = 5.06x - 0.15x^2$ and $L_2 = 2x$ respectively, where $x$ is the sales volume (in units of vehicles). If the company sells a total of 15 cars in both locations, calculate the maximum profit attainable. Express your answer as a single number in units of ten thousand yuan.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{45.6}
Consider the Hilbert space \(\mathcal H=L^2(\mathbb R_{+})\) and the operator \(Af(x)=-f''(x)\) with domain \(D(A)=\{f\in H_2(\mathbb R_{+})\;\;| \;\;f'(0)+\beta f(0)=0\}\) for some \(\beta \in \mathbb R\). Determine the conditions on \(\beta\) for which the operator \(A\) has a point spectrum.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\beta > 0}
Inside a cylinder with a base radius of 6, there are two spheres each with a radius of 6, and the distance between their centers is 13. A plane is tangent to these two spheres and intersects the cylinder to form an ellipse. Find the sum of the lengths of the major and minor axes of this ellipse.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
An up-right path from lattice points $P$ and $Q$ on the $xy$-plane is a path in which every move is either one unit right or one unit up. The probability that a randomly chosen up-right path from $(0,0)$ to $(10,3)$ does not intersect the graph of $y=x^2+0.5$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{248}
Among the four numbers $-\frac{1}{2}$, $-\frac{2}{3}$, $4$, $-5$, find the number with the smallest absolute value. Express your answer as a single number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$-\frac{1}{2}$}
Given three numbers \(x, y=x^{x}, \quad z=x^{x^{x}}\), where \(0.9<x<1.0\), determine the order of them in increasing sequence.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{x < z < y}
Side \(AB\) of triangle \(ABC\) has length \(8\) inches. Line \(DEF\) is drawn parallel to \(AB\) so that \(D\) is on segment \(AC\), and \(E\) is on segment \(BC\). Line \(AE\) extended bisects angle \(FEC\). If \(DE\) has length \(5\) inches, then find the length of \(CE\) in inches. The original answer is in \(\frac{k}{m}\) format, please give the value of \(k + m\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{43}
If it is assumed that 60 percent of those who receive a questionnaire by mail will respond initially, and the response rate declines exponentially by 20% for each of the 2 follow-up attempts. If 750 responses are needed, and there is a deadline of 30 days to receive all responses, what is the minimum number of questionnaires that should be mailed initially to achieve the desired number of responses?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{513}
A train with varying speeds crosses three poles in the following way:
- At the first pole, the train is moving at a speed of 50 km/h and takes 18 seconds to cross it.
- At the second pole, the speed increases to 60 km/h, and it takes 20 seconds to cross it.
- At the third pole, the speed further increases to 70 km/h, and it takes 22 seconds to cross it.

The distances between the poles are 500 meters from the first to the second, and 800 meters from the second to the third. Find the total length of the train.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{250}
There are 100 silver coins, ordered by weight, and 101 gold coins, also ordered by weight. It is known that all coins have different weights. We have a two-pan balance scale that allows us to determine which of any two coins is heavier. How can we find the coin that ranks 101st in weight among all the coins with the minimum number of weighings?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8 \text{ weighings}}
In a test, the teacher gave five problems and awarded a grade equal to the number of problems solved. All students, except Peter, solved the same number of problems, and Peter solved one more problem. Nine students solved the first problem, seven solved the second, five solved the third, three solved the fourth, and one solved the fifth.

How many grades of four and five were given on the test?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Sets \(A, B\), and \(C\) satisfy \(|A| = 92\), \(|B| = 35\), \(|C| = 63\), \(|A \cap B| = 16\), \(|A \cap C| = 51\), and \(|B \cap C| = 19\). Compute the number of possible values of \(|A \cap B \cap C|\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
Evaluate the volume of solid $T$ defined by the inequalities $|x| + |y| \leq 2$, $|x| + |z| \leq 2$, and $|y| + |z| \leq 2$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{32}{3}}
Given $\sin\left(\frac{\pi}{3}+\frac{\alpha}{6}\right)=-\frac{3}{5}$, $\cos\left(\frac{\pi}{12}-\frac{\beta}{2}\right)=-\frac{12}{13}$, $-5\pi < \alpha < -2\pi$, $-\frac{11\pi}{6} < \beta < \frac{\pi}{6}$,

Find the value of $\sin \left(\frac{\alpha }{6}+\frac{\beta }{2}+\frac{\pi }{4}\right)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{16}{65}}
Compute the following expression: $$(-(-2)+(1+\pi)^{0}-|1- \sqrt {2}|+ \sqrt {8}-\cos 45^{\circ})$$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 + \frac{5}{\sqrt{2}}}
John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $57,000 and Ingrid makes $72,000, what is their combined tax rate?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{35.58\%}
Let $n$ be a positive integer. Let $B_{n}$ be the set of all binary strings of length $n$. For a binary string $s_{1} s_{2} \ldots s_{n}$, we define its twist in the following way. First, we count how many blocks of consecutive digits it has. Denote this number by $b$. Then, we replace $s_{b}$ with $1-s_{b}$. A string $a$ is said to be a descendant of $b$ if $a$ can be obtained from $b$ through a finite number of twists. A subset of $B_{n}$ is called divided if no two of its members have a common descendant. Find the largest possible cardinality of a divided subset of $B_{n}$. Please provide the value when $n = 4$. The answer should be an integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Let \[P(x) = (3x^4 - 39x^3 + ax^2 + bx + c)(4x^4 - 96x^3 + dx^2 + ex + f),\] where $a, b, c, d, e, f$ are real numbers. Suppose that the set of all complex roots of $P(x)$ is $\{1, 2, 2, 3, 3, 4, 6\}.$ Find $P(7).$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{86400}
John makes $30 a week from his job. After six months, he earns a raise and begins to make $40 a week. Four months later, he earns another raise and starts making $50 a week. What is the total percentage increase in John's weekly earnings after ten months?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{66.67\%}