inclusionAI/Ring-lite-rl-data huggingface dataset:
Determine the number of minimal elements in the ordered set \((A\times A, \preceq)\), where \(A=\{n\in\mathbb{N} \mid n\geq 2\}\) and \((a,b)\preceq (c,d)\) if and only if \(a\mid c\) and \(b\leq d\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\infty}
A circle with radius $R$ is tangent to a line $l$ at point $A$. $AB$ is a diameter of this circle, and $BC$ is an arbitrary chord. Let $D$ be the foot of the perpendicular dropped from $C$ to $AB$. Point $E$ lies on the extension of $CD$ beyond point $D$, such that $|ED| = |BC|$. Tangents to the circle passing through $E$ intersect the line $l$ at points $K$ and $N$. Find the length of the segment $|KN|$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2R}
Determine the limit of the following expression as $n$ approaches infinity: $$\lim_{n\to +\infty}\left(\frac{1}{n^3}\sum_{k=1}^n\left(3k^2-2k\right) \cos\left(\frac{k}{n}\right)\right)$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
What is the remainder when $34!$ is divided by $71$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{69}
Suppose  $w,x,y,z$  satisfy \begin{align*}w+x+y+z&=25,wx+wy+wz+xy+xz+yz&=2y+2z+193\end{align*} The largest possible value of  $w$  can be expressed in lowest terms as  $w_1/w_2$  for some integers  $w_1,w_2>0$ .  Find  $w_1+w_2$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{27}
If the consecutive integers from $50$ to $1$ were written as $$5049484746...,$$ what would be the $67^{\text{th}}$ digit to be written?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
If $f(x)=3x+2$ for all real $x$, then the statement:
"$|f(x)+4|<a$ whenever $|x+2|<b$ and $a>0$ and $b>0$"
is true when
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$b \le a/3$}
What is the minimum number of times you need to roll a six-sided die so that the probability of rolling each number at least once is greater than 0.5?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
The electronic clock on the International Space Station displayed time in the format HH:MM. Due to an electromagnetic storm, the device malfunctioned, and each digit on the display either increased by 1 or decreased by 1. What was the actual time of the storm if the clock displayed 20:09 immediately after it?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11:18}
In the given circle, the diameter $\overline{EB}$ is parallel to $\overline{DC}$, and $\overline{AB}$ is parallel to $\overline{ED}$. The angles $AEB$ and $ABE$ are in the ratio $4 : 5$. What is the degree measure of angle $BCD$? If the answer is $x^\circ$, what is the value of $x$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{130}
Find the number of ideals in the ring $R[X]/(X^3)$, where $R$ is a field.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
A time is chosen randomly and uniformly in a 24-hour day. The probability that at that time, the non-reflex angle between the hour hand and minute hand on a clock is less than $\frac{360}{11}$ degrees is $\frac{m}{n}$ for coprime positive integers $m$ and $n$. Find $100m + n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{211}
Determine the Galois group of the polynomial $x^4 - 5x^2 + 6$ over the field of rational numbers $\mathbb{Q}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{V_4}
A permutation $(a_1, a_2, a_3, \dots, a_{2012})$ of $(1, 2, 3, \dots, 2012)$ is selected at random. If $S$ is the expected value of
\( \mathop{\sum }\limits_{{i = 1}}^{{2012}}\left| {{a}_{i} - i}\right| \)
 then compute the sum of the prime factors of \( S \) .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{
2083
}
An acute-angled isosceles triangle and a trapezoid are inscribed in a circle. One base of the trapezoid is the diameter of the circle, and the lateral sides of the trapezoid are parallel to the lateral sides of the triangle. Find the ratio of the areas of the trapezoid and the triangle.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Max likes to collect model trains.  He asks for one for every birthday of his, and asks for two each Christmas.  Max always gets the gifts he asks for, and asks for these same gifts every year for 5 years.  At the end of the 5 years, his parents give him double the number of trains he already has.  How many trains does Max have now?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{45}
Evaluate the line integral \( \oint_C x\,dx \) where the curve \( C \) is composed of the segments \( x=0 \), \( y=0 \), and \( y=-x+1 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Evaluate the improper integral $$ I=\int_{-\infty}^{\infty} \frac{x^2 e^x}{(e^x+1)^2} dx $$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$$ \frac{\pi^2}{3} $$}
Compute the first Chern class \( c_1(L_D) \) of the line bundle \( L_D \) associated with the effective divisor \( D = [F] \) on \( \mathbb{C}\mathbb{P}^3 \), where \( F = z_0z_1^2 + z_2z_3(z_2 - z_3) \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3H}
Determine the modulo classes for which the product of two twin primes plus 2 is always congruent to 1.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Find the local or global extrema of the function \( f(x_1, \ldots, x_n) = (1+x_1)\cdots(1+x_n) \) using the method of Lagrange multipliers, given the constraint \( x_1\cdots x_n = a^n \), where \( a > 0 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(1 + a)^n}
Calculate the flux of the vector field \( \mathbb{v} = (x^2-2xz, -2xy, z^2-x) \) downwards through the paraboloid \( z = 1 - x^2 - y^2 \) for \( x \geq 0 \) and \( z \geq 0 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{2}{3}}
Given that in triangle $ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, the radius of the circumcircle is $1$, and it satisfies $\frac{\tan A}{\tan B} = \frac{2c - b}{b}$, then the maximum area of $\triangle ABC$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{3\sqrt{3}}{4}}
One material particle entered the opening of a pipe, and after 6.8 minutes, a second particle entered the same opening. Upon entering the pipe, each particle immediately began linear motion along the pipe: the first particle moved uniformly at a speed of 5 meters per minute, while the second particle covered 3 meters in the first minute and in each subsequent minute covered 0.5 meters more than in the previous minute. How many minutes will it take for the second particle to catch up with the first?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{17}
Calculate the fundamental group \( \pi_1 \) of the space \( S^2 - \{N, S\} \), where \( N \) and \( S \) are the north and south poles of the 2-sphere \( S^2 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\mathbb{Z}}
Evaluate the contour integral \( \oint_{|z|=2} \frac{\sum_{k=0}^\infty (k^2/2^k)z^k}{z^3} \, dz \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\pi i}
How many diagonals in a regular 32-gon are not parallel to any of its sides?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{240}
Weng earns $12 an hour for babysitting. Yesterday, she just did some babysitting and earned $10. How much time did she spend on babysitting?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{50}
Evaluate the Legendre symbol \( \left( \frac{2017}{5003} \right) \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
What is the value of 
$$\log_3 7 \cdot \log_5 9 \cdot \log_7 11 \cdot \log_9 13 \cdots \log_{21} 25 \cdot \log_{23} 27?$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
棱长为 $\sqrt{2}$ 的正四面体 $A B C D$ 中, 已知 $\overrightarrow{A P}=\frac{1}{2} \overrightarrow{A B}, \overrightarrow{A Q}=\frac{1}{3} \overrightarrow{A C}, \overrightarrow{A R}=\frac{1}{4} \overrightarrow{A D}$, 若点 K 为 $\triangle B C D$ 的重心, 则四面体 $K P Q R$ 的体积为  ?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{37}
In the arithmetic sequence $\{a_n\}$, $a_1 > 0$, and $S_n$ is the sum of the first $n$ terms, and $S_9=S_{18}$, find the value of $n$ at which $S_n$ is maximized.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
Determine the number of non-constant polynomial factors with leading coefficient 1, where the other coefficients may be complex, for the polynomial \(x^{2015} + 18\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{2015} - 1}
Suppose there exists a convex $n$-gon such that each of its angle measures, in degrees, is an odd prime number. Compute the difference between the largest and smallest possible values of $n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{356}
Let $D$ be the foot of the internal angle bisector of the angle $A$ of a triangle $ABC$. Let $E$ be a point on side $[AC]$ such that $|CE|= |CD|$ and $|AE|=6\sqrt{5}$; let $F$ be a point on the ray $[AB$ such that $|DB|=|BF|$ and $|AB|<|AF| = 8\sqrt{5}$. The original answer for the length of $|AD|$ is in the form $k\sqrt{m}$. Please find the value of k + m.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
11. In the Cartesian coordinate system $x O y$, let $A B$ be a chord of the parabola $y^{2}=4 x$ passing through the point $F(1,0)$, and the circumcircle of $\triangle A O B$ intersects the parabola at point $P$ (different from points $O, A, B$). If $P F$ bisects $\angle A P B$, find all possible values of $|P F|$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{["\\sqrt{13}-1"]}
In triangle $ABC, AB=32, AC=35$, and $BC=x$. What is the smallest positive integer $x$ such that $1+\cos^{2}A, \cos^{2}B$, and $\cos^{2}C$ form the sides of a non-degenerate triangle?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{48}
Determine the number of tournaments with five vertices that have at least one vertex with an in-degree of zero, up to isomorphism.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
The entries of a $7 \times 5$ table are filled with numbers such that in each $2 \times 3$ rectangle (either vertical or horizontal), the sum of the numbers is $0$. For $100$ dollars, Peter may choose any single entry and learn the number in it. What is the least amount of dollars he should spend to determine the total sum of numbers in the table for sure?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
In a right triangle, medians are drawn from point $A$ to segment $\overline{BC}$, which is the hypotenuse, and from point $B$ to segment $\overline{AC}$. The lengths of these medians are 5 and $3\sqrt{5}$ units, respectively. Calculate the length of segment $\overline{AB}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\sqrt{14}}
Determine the values of \( \kappa \) for which the integral \( \int_{0}^{+\infty} z^{\kappa-1} \sin(z) \, dz \) converges, given that \( z > 0 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-1, 1)}
Given the hyperbola equation x^2/a^2 - y^2/b^2 = 1 (a > 0, b > 0), let the right focus be F, and the left and right vertices be A1 and A2, respectively. A perpendicular line to A1A2 passing through F intersects the hyperbola at points B and C. If A1B is perpendicular to A2C, calculate the slope of the asymptotes of the hyperbola. Express your answer as a slope (±value).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{±1}
What is the maximum area of the orthogonal projection of a rectangular prism with dimensions $3 \times 4 \times 12$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12\sqrt{26}}
In trapezoid $ABCD$, $AD // BC$ and $\angle B=40^{\circ}$, $\angle C=50^{\circ}$. Points $E, M, F, N$ are the midpoints of $AB$, $BC$, $CD$, and $DA$ respectively. If $EF = a$ and $MN = b$, then express $BC$ in terms of $a$ and $b$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{a+b}
In a finite sequence of real numbers, the sum of any three consecutive terms is negative, and the sum of any four consecutive terms is positive. Find the maximum number of terms \( r \) in this sequence.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
In the acute-angled triangle $ABC$, the altitudes $AL$ and $CN$ are drawn. Find the radius of the circle passing through the points $B, L,$ and $N$, given that $AC = a$ and $\angle ABC = \alpha$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{a}{2} \cdot \cot \alpha}
on a certain island , 5 % of the 10000 inhabitants are one - legged and half of the others go barefooted . what is the least number of shoes needed in the island ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10,000}
Pipe A can fill a tank in 12 minutes and Pipe B can empty it in some minutes. If both the pipes are opened together, Pipe B should be closed after 36 minutes so that the tank is filled in 30 minutes. How many minutes does it take for Pipe B to empty the tank?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
Determine the number of subgroups of index \( p \), where \( p \) is a prime, in the additive group \( \mathbb{Z}^2 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{p + 1}
Multiples of 4 are written sequentially. Those multiples are greater than 0 and less than 100. How many numbers are there between the 5th from the left and the 8th from the right?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11\)}
Consider a  $2 \times n$  grid where each cell is either black or white, which we attempt to tile with  $2 \times 1$  black or white tiles such that tiles have to match the colors of the cells they cover. We first randomly select a random positive integer  $N$  where  $N$  takes the value  $n$  with probability  $\frac{1}{2^n}$ . We then take a  $2 \times N$  grid and randomly color each cell black or white independently with equal probability. Compute the probability the resulting grid has a valid tiling.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{9}{23}}
Determine the convergence and value, if any, of the integral $$\int_{0}^{+\infty }\frac{x \log(x)}{(x^{2}+1)^{2}}dx.$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Let \( n \) be any positive integer. Consider a sequence containing only the letters \( \mathrm{A} \) and \( \mathrm{B} \), where at most three consecutive \( \mathrm{A} \)s and at most three consecutive \( \mathrm{B} \)s are allowed. Let \( S(n) \) represent the number of such sequences of length \( n \). Find the remainder of \( S(2015) \) when divided by 12. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
Find the smallest real number \(\lambda\) such that there exists a sequence \(\{a_n\}\) with all terms greater than 1, and for any positive integer \(n\), the following inequality is satisfied:
\[
\prod_{i=1}^{n+1} a_i < a_n^\lambda.
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Given that $f(x)$ is an even function defined on $\mathbb{R}$ and satisfies $f(x+2)=f(x)$ for any $x\in[0,+\infty)$. If $f(x)=|x^{2}-x-1|$ when $x\in[0,2)$, find the number of zeros of the function $y=f(x)-1$ on $[-2,4]$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Let $T$ be the smallest positive real number such that the tangent to the helix \( \cos t \mathbf{i} + \sin t \mathbf{j} + \frac{t}{\sqrt{2}} \mathbf{k} \) at \( t = T \) is orthogonal to the tangent at \( t = 0 \). Find the line integral of the vector field \( \mathbf{F} = x \mathbf{j} - y \mathbf{i} \) along the section of the helix from \( t = 0 \) to \( t = T \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{2\pi}{3}}
In triangle $\triangle ABC$ with $|BC| > |BA|$, $D$ is a point inside the triangle such that $\angle ABD = \angle DBC$, $\angle BDC = 150^\circ$, and $\angle DAC = 60^\circ$. If the measure of $\angle BAD$ is $x^\circ$, what is the value of $x$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60}
[ Properties and characteristics of a parallelogram ] [ Isosceles, inscribed, and circumscribed trapezoids ]

A circle passing through the vertices $A, B$, and $C$ of parallelogram $A B C D$ intersects the lines $A D$ and $C D$ at points $M$ and $N$ respectively. Point $M$ is at distances 4, 3, and 2 from vertices $B, C$, and $D$ respectively. Find $M N$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{8}{3}}
Find the smallest positive value of \( a \) such that \( \left(1+\frac{1}{x}\right)^{x+a} > e \) for all \( x \geq 1 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{1}{2}}
Determine the smallest dimension a non-commutative C*-algebra can have.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
An ant starts at the point $(0,0)$ in the coordinate plane. It can make moves from lattice point $(x_1,y_1)$ to lattice point $(x_2,y_2)$ whenever $x_2\geq x_1$, $y_2\geq y_1$, and $(x_1,y_1)\neq(x_2,y_2)$. For all nonnegative integers $m,n$, define $a_{m,n}$ to be the number of possible sequences of moves from $(0,0)$ to $(m,n)$ (e.g. $a_{0,0}=1$ and $a_{1,1}=3$). Compute
\[\sum_{m=0}^{\infty}\sum_{n=0}^{\infty} \frac{a_{m,n}}{10^{m+n}}.\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{81}{62}}
If  $x_1=5, x_2=401$ , and 
\[
    x_n=x_{n-2}-\frac 1{x_{n-1}}
\]
for every  $3\leq n \leq m$ , what is the largest value of  $m$ ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2007}
Fresh grapes contain a certain percentage of water by weight, while dried grapes contain 20% water by weight. The weight of dry grapes available from 40 kg of fresh grapes is 5 kg. What is the percentage of water in fresh grapes by weight?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{90\%}
Let $ABCDEF$ be a regular hexagon with side length 10 inscribed in a circle $\omega$. $X$, $Y$, and $Z$ are points on $\omega$ such that $X$ is on minor arc $AB$, $Y$ is on minor arc $CD$, and $Z$ is on minor arc $EF$, where $X$ may coincide with $A$ or $B$ (and similarly for $Y$ and $Z$). Compute the square of the smallest possible area of $\triangle XYZ$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7500}
Given that \(A^2=\begin{bmatrix} -2 & 2 & -4 \\ 2 & 1 & -2 \\ 4 & -6 & 6 \end{bmatrix}\) and the trace of matrix \(A\) is \(-1\), find the determinant of matrix \(A\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-6}
Determine the smallest natural number $n$ such that $n^n$ is not a divisor of the product $1 \cdot 2 \cdot 3 \cdot \ldots \cdot 2015 \cdot 2016$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{47}
One hundred musicians are planning to organize a festival with several concerts. In each concert, while some of the one hundred musicians play on stage, the others remain in the audience assisting to the players. What is the least number of concerts so that each of the musicians has the chance to listen to each and every one of the other musicians on stage?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
Evaluate \( \lim_{x \to \infty} \frac{\gamma(x+1, x)}{\Gamma(x+1)} \), where \( \gamma(x+1, x) \) is the lower incomplete gamma function and \( \Gamma(x+1) \) is the complete gamma function.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{1}{2}}
In the 2016 art exam of a certain high school, there were 6 contestants, including 3 females and 3 males. Now, these six contestants are to perform their talents in sequence. If any two of the three males cannot perform consecutively, and the female contestant A cannot be the first to perform, then calculate the number of possible sequences for the contestants to perform.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{132}
Let's call a number "remarkable" if it has exactly 4 different natural divisors, among which there are two such that neither is a multiple of the other. How many "remarkable" two-digit numbers exist?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Three cones with vertex \(A\) touch each other externally, with the first two having an apex angle of \(\frac{\pi}{6}\). Each of the cones touches internally a fourth cone with a vertex at point \(A\) and an apex angle of \(\frac{\pi}{3}\). Determine the apex angle of the third cone.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{\pi}{9}}
Find the large number from the problem below: The difference between two numbers is 20775. On dividing the larger number by the smaller, we get 23 as quotient and 143 as remainder.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{21713}
Determine the largest possible value of $k \in \mathbb{N}$ such that there exists an integer $n$ for which the digit sum of $k$ consecutive perfect squares, starting from $(n+1)^2$ to $(n+k)^2$, is a perfect square for each square in the sequence. Note that $k \geq 7$, and an example of $k=8$ has been found: $S(46045846^2) = 8^2, S(46045847^2) = 7^2, \ldots, S(46045853^2) = 8^2$. What is this largest $k$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
Suppose we flip 100 fair coins. If there are more heads than tails, what is the expected number of heads? Use the central limit theorem and the empirical rule to approximate this value.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{54}
James goes to a pet store to adopt a puppy and a kitten. The adoption fee for the puppy is $200 and the adoption fee for the kitten is $150. The store offers a 10% discount on the total adoption fees for adopting multiple pets. Additionally, his friend agrees to cover 25% of the puppy's adoption fee and another friend contributes 15% towards the kitten's adoption fee. There is also a 7% sales tax applied to the total adoption fees after discounts. James is required to purchase pet supplies worth $95 alongside the adoptions. How much does James have to pay in total, including the sales tax and pet supplies?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$354.48,}