inclusionAI/Ring-lite-rl-data huggingface dataset:
A dragon has 40 piles of gold coins, with the number of coins in any two piles differing. After the dragon plundered a neighboring city and brought back more gold, the number of coins in each pile increased by either 2, 3, or 4 times. What is the minimum number of different piles of coins that could result?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14}
How many roots of the equation $f(z)=z^4+8z^3+3z^2+8z+3=0$ lie in the right half plane?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Determine the limit of the function $\frac{(\lg n)!}{(\lg(2/5))^{\lg n}(2/5)^n}$ as $n$ approaches infinity.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Find the limit of \( \frac{(x+3)^x}{\sum_{n=3}^{x+2}n^x} \) as \( x \) approaches infinity.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{e - 1}
Determine a lower bound for the cardinality of the set \( A \), where \( A = \{ R \subset \mathbb{N} \times \mathbb{N} : R \text{ is transitive} \} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{\aleph_0}}
Given the homomorphism \(\varphi: \mathbb{Z}^2 \to S_{15}\) defined by:
\[\varphi(1,0)=(2,7,3)(3,11,5)(12,13)\]
\[\varphi(0,1)=(14,15)(1,4,6,8,9,10)\]
Calculate the number of elements in the group \(\mathbb{Z}^2/\!\ker\varphi\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60}
Alex, a film critique with a passion for old Christmas movies, is planning a holiday movie marathon. He has a collection of 12 classic Christmas films, each with a soundtrack composed by different artists. However, 5 of these soundtracks were composed by his favorite composer, Harry Gregson-Williams.

Alex decides to watch 3 movies per day leading up to Christmas. On the first day, he randomly selects and watches 2 movies with soundtracks not composed by Harry Gregson-Williams and 1 movie with a soundtrack by him.

If Alex continues to watch the same pattern of movies (2 non-Gregson-Williams and 1 Gregson-Williams) each day, how many days will it take him to watch all 12 movies from his collection?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Let $Y = \operatorname{Pois}(n)$. Using the Normal approximation, also known as the Central Limit Theorem (CLT), estimate the probability \( p\Big[|Y-n| \geq 2\sqrt{n}\Big] \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.0456}
Bill is stocking the kitchenware section of the Walmart. He needs to stack 60 pots, but they come in different shapes and sizes. On each shelf, he can stack the following combinations of pots:

- 3 large pots vertically and two sets of vertically stacked large pots side-by-side
- 5 medium pots vertically and three sets of vertically stacked medium pots side-by-side
- 7 small pots vertically and four sets of vertically stacked small pots side-by-side

Bill has 25 large pots, 20 medium pots, and 15 small pots to stack. How many shelves does he need to stock all the pots?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
Consider a sequence of figures starting with an equilateral triangle $ABC$ with side length 1. The leading edge of the triangle, going clockwise around $A$, is labeled $\overline{AB}$ and is darkened. The second figure in the sequence is formed by attaching a square with side length 1 to the leading clockwise edge of the triangle. The third figure is formed by attaching a regular pentagon with side length 1 to the leading clockwise edge of the square. This process continues, with each subsequent figure formed by attaching a regular polygon with an increasing number of sides (hexagon, heptagon, etc.) to the leading clockwise edge of the previous polygon. By the eighth figure, a regular decagon is attached. After attaching the decagon, its leading clockwise edge forms an angle of less than $180^\circ$ with the side $\overline{AC}$ of the equilateral triangle. Express this angle in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, and find $m + n$. \( \text{[asy diagram omitted]} \)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{668}
Determine the number of distinct $3 \times 3$ matrices with entries in \(\{0,1\}\) such that each row is non-zero, distinct, and the matrix has a real rank of 2 or 3, excluding matrices that are permutations of each other.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{35}
Let \( S = \{1, 2, 3, 4\} \); a sequence \( a_{1}, a_{2}, \ldots, a_{n} \) of \( n \) terms has the following property: for any non-empty subset \( B \) of \( S \) (denoted by \( |B| \) as the number of elements in set \( B \)), there exists a sequence of \( |B| \) consecutive terms in the sequence that exactly forms the set \( B \). Find the minimum value of \( n \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
Evaluate the surface integral \( \iint_S z \, dx \, dy \) over the complete surface \( S \) of a circular cylinder with radius \( a \) and axis along the \( OZ \) direction, where the ends of the cylinder are located at \( z = 0 \) and \( z = 2a \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\pi a^3}
设$a$为整数，若对任意的$x\in (0,+\infty )$，不等式$\frac{{{e}^{x}}+3}{x}\ge {{ea}}$恒成立，则$a$的最大值是__________．
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Find a quadratic polynomial that is orthogonal to both \( p(x) = 1 \) and \( q(x) = x \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3x^2 - 1}
Given a geometric sequence $\{a_n\}$ with a common ratio $q$, and the product of its first $n$ terms is $T_n$, where the first term $a_1 > 1$, and $a_{2014}a_{2015} - 1 > 0$, $\frac{a_{2014} - 1}{a_{2015} - 1} < 0$, find the largest natural number $n$ such that $T_n > 1$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4028}
Evaluate the limit: \[ \lim_{x \to 0} \left( 1 + \sin \left( \frac{3}{x} \right) \right)^x \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
A rectangle has dimensions 12 by 15, and a circle centered at one of its vertices has a radius of 15. What is the area of the union of the regions enclosed by the rectangle and the circle? Express your answer in terms of \( \pi \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{180 + 168.75\pi}
Given the vector field $\mathbf{F}: \mathbb{R}^2 \setminus\{(0,0)\} \to \mathbb{R}^2$ defined by $\mathbf{F}(x,y) = \frac{y}{x^2+y^2}\mathbf{i} - \frac{x}{x^2+y^2}\mathbf{j}$, consider the curves $\gamma, \alpha : [0,1] \to \mathbb{R}^2$ defined by $\gamma(t) = (8\cos(2\pi t), 17\sin(2\pi t))$ and $\alpha(t) = (26\cos(2\pi t), -10\sin(2\pi t))$. If $3\int_{\alpha} \mathbf{F \cdot dr} - 4\int_{\gamma} \mathbf{F \cdot dr} = 2m\pi$, find the value of $m$. \[ \text{(Hint: Consider the properties of the vector field and the curves.)} \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Patty ordered a pizza to be delivered. The bill was $\$$12.00. Patty pays $\$$15 and tells the delivery person to keep the change as a tip. What percent tip did she give?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
Find another value of $x$ that satisfies both equations $a=x^{x^{x^{.^{.^{.}}}}}$ and $x=a^{1/a}$, besides $x=3$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{2}}
Given the parabola $y=x^{2}+2x-3$ intersects the line $l_{1}$: $y=-x+m$ at points $A$ and $C$, and the line $l_{2}$ is symmetric with respect to the axis of symmetry of the parabola. Line $l_{2}$ intersects the parabola at points $B$ and $D$, where points $A$ and $D$ are above the $x$-axis, and points $B$ and $C$ are below the $x$-axis. If $AC \cdot BD = 26$, then the value of $m$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2}
On side $AC$ of triangle $ABC$, points $M$ and $N$ are marked such that $M$ lies on segment $AN$. It is known that $AB = AN$ and $BC = MC$. The circumcircles of triangles $ABM$ and $CBN$ intersect at points $B$ and $K$. What is the angle $\angle AKC$ if $\angle ABC = 68^\circ$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{124^{\circ}}
Given the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ $(a > b > 0)$, the symmetric point $Q$ of the right focus $F(c, 0)$ with respect to the line $y = \dfrac{b}{c}x$ is on the ellipse. Find the eccentricity of the ellipse.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{["\\dfrac{\\sqrt{2}}{2}"]}
The least number which, when increased by 7, is divisible by some numbers including 24, 36, and 54 is 857. What is the other number that the least number should be divisible by when increased by 7?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{32}
The time on a cell phone is 3:52. Calculate the number of minutes that will pass before the phone next shows a time using each of the digits 2, 3, and 5 exactly once. Express your answer in minutes.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{91}
Petra had natural numbers from 1 to 9 written down. She added two of these numbers, erased them, and wrote the resulting sum in place of the erased addends. She then had eight numbers left, which she was able to divide into two groups with the same product.

Determine the largest possible product of these groups.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{504}
A ray passes through points $P(-3,1)$ and $Q(a,0)$ and reflects off the $x$-axis, then it is tangent to the circle $x^{2}+y^{2}=1$. Find the value of $a$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\dfrac{5}{3}}
Does the equation

$$
x^{2}+y^{2}+z^{2}=2 x y z
$$

have a solution in non-negative integers?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(0, 0, 0)}
There are 2000 nodes, and every pair of nodes is connected by a wire. Varia and Petya take turns cutting these wires, with Varia starting first. Varia can only cut one wire at a time, while Petya can cut 2 or 3 wires at a time. The rule is that the player who cuts the last wire loses. Who will be the winner?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Petya}
设函数$f\left( x \right)=\frac{3}{2}{{x}^{2}}-2ax(a>0)$与$g\left( x \right)={{a2}}\ln x+b$有公共点，且在公共点处的切线方程相同，则实数$b$的最大值为__________．
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\frac{1}{2{{e}^{2}}}$.}
In the plane, there are $10$ lines in general position, meaning that no two are parallel and no three are concurrent. At each intersection of two lines, we measure the smaller of the two angles formed between them. What is the maximum value of the sum of the measures of these $45$ angles?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4050}
A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have lengths $13, 19, 20, 25$ and $31$, although this is not necessarily their order around the pentagon. The area of the pentagon is
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$745$}
Calculate the expectation of the product of the minimum values of two independent uniform random variables from the distribution $\mathrm{Unif}(0, 1)$. Specifically, find $E[\min\{U_{1}, U_{2}\}\times \min\{U_{1}, U_{3}\}]$ where $U_{1}, U_{2}, U_{3}$ are independent and identically distributed.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{2}{15}}
Determine the number of lattice points \((v, w, x, y, z)\) that lie on or inside a 5-sphere centered at the origin with radius 3.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1343}
Let $S$ be the set of points on the rays forming the sides of a $120^{\circ}$ angle, and let $P$ be a fixed point inside the angle on the angle bisector. Consider all distinct equilateral triangles $PQR$ with $Q$ and $R$ in $S$. Count the number of distinct equilateral triangles that can be formed. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
If the equation $1-k(x-2e)\cdot\ln x=0$ has two different solutions on $(1,+\infty)$, where $e$ is the base of the natural logarithm, then the range of the real number $k$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-\infty,- \dfrac {1}{e})}
Determine the value of \(x\) for which the matrices \(A = \begin{pmatrix} 3&0&-1 \\ -2&1&1 \\ 2&0&0 \end{pmatrix}\) and \(B = \begin{pmatrix} 1&x&0 \\ 0&1&0 \\ -1&x&2 \end{pmatrix}\) are similar.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
There are $15$ (not necessarily distinct) integers chosen uniformly at random from the range from $0$ to $999$, inclusive. Yang then computes the sum of their units digits, while Michael computes the last three digits of their sum. The probability of them getting the same result is $\frac{m}{n}$ for relatively prime positive integers $m, n$. Find $100m + n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{200}
已知椭圆 $\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$ 的左右焦点分别为 $F_{1}$ 与 $F_{2}$, 点 $P$ 在直线 $l: x-\sqrt{3} y+8+2 \sqrt{3}=0$ 上. 当 $\angle F_{1} P F_{2}$ 取最大值时, 比 $\frac{\left|P F_{1}\right|}{\left|P F_{2}\right|}$ 的值为\sqrt{m}-n的形式, 请给出m - n的值.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
For positive integers \( n \), let \( L(n) \) be the largest factor of \( n \) other than \( n \) itself. Determine the number of ordered pairs of composite positive integers \( (m, n) \) for which \( L(m) L(n) = 80 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
Katie writes a different positive integer on the top face of each of the fourteen cubes in the pyramid shown. The sum of the nine integers written on the cubes in the bottom layer is 50. The integer written on each of the cubes in the middle and top layers of the pyramid is equal to the sum of the integers on the four cubes underneath it. What is the greatest possible integer that she can write on the top cube?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{118}
## Task B-1.6.

All letters in the equality $(a+b)(c+d)(e+f)(g+h)=5005$ should be replaced with different numbers from 1 to 8 so that the equality is correct. In how many ways can this be done?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{768}
Define a polynomial $f_{n}(x)$, where $n \geqslant 0$ is $f_{0}(x)=1$, $n \geqslant 1$ is $f_{n}(0)=0$, and $n \geqslant 0$ is
$$
\frac{d}{d x}\left(f_{n+1}(x)\right)=(n+1) f_{n}(x+1)
$$
. Clearly decompose $f_{100}(1)$ into powers of different prime numbers, $a^{b}$, and find the value of $a+b$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{200}
Each Kinder Surprise contains exactly 3 different Smurfs, and there are a total of 11 types of Smurfs. The box contains a sufficient number of Kinder Surprises, where no two of them have identical sets of three Smurfs. What is the minimum number of Kinder Surprises that need to be purchased so that after opening them, there is at least one of each of the 11 types of Smurfs?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{121}
Consider a "Modulo $m$ graph paper," with $m = 17$, forming a grid of $17^2$ points. Each point $(x, y)$ represents integer pairs where $0 \leq x, y < 17$. We graph the congruence $$5x \equiv 3y + 2 \pmod{17}.$$ The graph has single $x$-intercept $(x_0, 0)$ and single $y$-intercept $(0, y_0)$, where $0 \leq x_0, y_0 < 17$. Determine $x_0 + y_0$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
The function \( f(x) \) satisfies the equation \( f(x+y) = f(x \cdot y) \) for any real numbers \( x \) and \( y \), and given \( f\left(-\frac{1}{2}\right) = -\frac{1}{2} \), find \( f(2000) \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\frac{1}{2}}
If \(60^a=360^b=5\), then what is the value of \(12^{\frac{1-a-b}{2(1-b)}}\)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
In the first week, New York recorded 5,000 new coronavirus cases. In the second week, there was a 30% increase in new cases compared to the first week. In the third week, there was a 20% decrease in new cases compared to the second week. In the fourth week, the daily number of vaccinations increased by 10% compared to the third week, which resulted in a 25% decrease in new cases. During this time, the population of New York grew by 0.5%. Taking into account the population growth, what is the total number of recorded new coronavirus cases in the state after the four weeks?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20,600}
A swing is initially stationary with its footboard one foot off the ground. When pushed forward by 10 feet (two steps of 5 feet each), the footboard becomes level with a person who is 5 feet tall. If the rope of the swing is pulled very straight at this point, what is the length of the rope? Express your answer in feet, rounded to one decimal place.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14.5}
In a \(7 \times 7\) table, some cells are black while the remaining ones are white. In each white cell, the total number of black cells located with it in the same row or column is written; nothing is written in the black cells. What is the maximum possible sum of the numbers in the entire table?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{168}
For real  $\theta_i$ ,  $i = 1, 2, \dots, 2011$ , where  $\theta_1 = \theta_{2012}$ , find the maximum value of the expression

\[
\sum_{i=1}^{2011} \sin^{2012} \theta_i \cos^{2012} \theta_{i+1}.
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1005}
Given the sequence $\{a_n\}$ where $a_n = (\sqrt{2}+1)^n - (\sqrt{2}-1)^n \quad (n \in \mathbf{N})$, and let $[x]$ denote the greatest integer not exceeding the real number $x$, what is the units digit of $\left[ a_{2017} \right]$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Given points E and D are on sides AB and BC of triangle ABC, where AE:EB=1:3 and CD:DB=1:2, find the value of EF/FC + AF/FD.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3}{2}}
Given a subgroup \( H \) of \( \mathbb{Z}^2 \) generated by the vectors \((1, 6), (3, 5), (7, 11)\), how many distinct cosets are there in the quotient group \( \mathbb{Z}^2/H \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Inside a cylinder with a base radius of 6, there are two spheres each with a radius of 6 and with their centers 13 units apart. If a plane \(\alpha\) is tangent to both spheres and intersects the cylindrical surface forming an ellipse, what is the length of the major axis of this ellipse?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
求所有的正整数 n，使得存在正整数 a,b，满足 a^2+b+3 不能被任何质数的立方整除，且n=\df{ab+3b+8}{a^2+b+3}.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
If you draw a card with a value of five or less from a standard deck of cards, I will pay you \$49. If not, you pay me \$25. (Aces are considered the highest card in the deck.)

Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2.23}
Mary is baking a cake. The recipe calls for 5 cups of flour and a certain amount of sugar. She already put in 10 cups of flour and 2 cups of sugar. She needs to add 12 more cups of sugar. How many cups of sugar does the recipe call for?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Call a positive integer 'mild' if its base-3 representation never contains the digit 2. How many values of $n(1 \leq n \leq 1000)$ have the property that $n$ and $n^{2}$ are both mild?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
The coefficients of the fifth and sixth terms in the binomial expansion of $(x- \dfrac {2}{ \sqrt {x}})^{n}$ are the largest. Find the sum of the coefficients of all the terms.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1}
The base side length of the regular triangular prism \( ABC-A_1B_1C_1 \) is \( a \), and the side edge length is \( \sqrt{2}a \). Find the angle between \( AC_1 \) and the lateral face \( ABB_1A_1 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30^\circ}
Find the formula for the summation \( S = \sum_{i=1}^{n} \frac{n}{i} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{n H_n}
The base of a quadrilateral pyramid is a square, and all the lateral faces are right triangles with the vertices of the right angles lying on the base of the pyramid. Find the volume of the pyramid if its height is 1 and one of the dihedral angles at the apex is $120^{\circ}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{3}}
Given the functions $f(x)=x+ \frac {4}{x}$ and $g(x)=2^{x}+a$, if there exists $x_{1} \in \left[ \frac {1}{2},3\right]$ and for all $x_{2} \in \left[2,3\right]$, such that $f(x_{1}) \geqslant g(x_{2})$, then the range of the real number $a$ is \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{a \leqslant \frac {1}{2}}
Heath spent his weekend helping at his uncle's farm planting carrots and potatoes. He planted 400 rows in total; 250 rows were carrots and 150 rows were potatoes. The number of plants in each row and the time taken to plant them varied. 

For the carrot rows, the first 100 rows had 275 plants each and took Heath 10 hours to plant, while the remaining 150 rows had 325 plants each and took 20 hours to complete. Meanwhile, Heath's cousin, Jake, planted the 150 rows of potatoes. In the first 50 rows, Jake planted 300 plants per row, taking 12 hours to complete. The remaining 100 rows had 400 plants per row and took 18 hours to finish.

Calculate the weighted average of the number of carrot and potato plants planted per hour by both Heath and Jake during the entire weekend.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2,187.5}
Given an ordered triplet \((x, y, z)\) of real numbers satisfying \(x < 1\), \(y < 2\), \(z < 3\), and \(x + \frac{y}{2} + \frac{z}{3} > 0\), determine the values of \(a\), \(b\), and \(c\) that maximize the expression \((1 - x)(2 - y)(3 - z)(x + \frac{y}{2} + \frac{z}{3})\). Find the sum \(a + b + c\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{3}{2}}