inclusionAI/Ring-lite-rl-data huggingface dataset:
Given the vector space $P_3$ consisting of polynomials with a degree of 3 or less, and a basis $\{1, (1-x), (1-x)^2, (1-x)^3\}$. Consider the linear functional (evaluation function) $ev_3: P_3 \rightarrow \mathbb{R}$ that evaluates a polynomial at $x=3$. If $\{f_1, f_2, f_3, f_4\}$ is the dual basis of $P_3$, compute $f_3(p)$ for the polynomial $p = x^3 + 5x^2 + 3x + 4$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
Given that \( n \) is a natural number and \( b = n^{3} - 4an^{2} - 12n + 144 \) is a prime number, find the value of \( b \).
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Answer: \boxed{11}
3 cloves of garlic have a 100% repulsion rate for vampires and wights but a 75% effectiveness rate for vampire bats, 60% for werewolves, and 50% for ghosts. How many cloves of garlic are needed to repel 30 vampires, 12 wights, 40 vampire bats, 20 werewolves, and 15 ghosts, considering their varying garlic compatibility percentages?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{476}
Let  $\mathcal S$  be a set of  $16$  points in the plane, no three collinear. Let  $\chi(S)$  denote the number of ways to draw  $8$  lines with endpoints in  $\mathcal S$ , such that no two drawn segments intersect, even at endpoints. Find the smallest possible value of  $\chi(\mathcal S)$  across all such  $\mathcal S$ . 

*Ankan Bhattacharya*
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1430}
Determine the number of distinct ways to color a cube using four different colors, with each color appearing on at least one face of the cube. Consider two colorings to be the same if one can be obtained from the other by rotating the cube.
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Answer: \boxed{68}
Find the derivative of the quadratic form $z^TX^TXz$ with respect to the vector $z$.
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Answer: \boxed{2 X^T X z}
Find the number of positive integers less than or equal to $2019$ that are no more than $10$ away from a perfect square.
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Answer: \boxed{829}
A 6-liter solution is 30% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2.4}
The midpoints of the sides of a rectangle with a perimeter of 32 are connected by segments. Then, the same operation is performed on the resulting quadrilateral: the midpoints of its sides are connected by segments. How many times must this operation be repeated until the perimeter of the resulting quadrilateral is less than 1 for the first time?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
Find the sum of the values of $x$ such that $\cos^{3}3x+\cos^{3}5x= 8\cos^{3}4x\cos^{3}x$, where $x$ is measured in degrees and $100 ^\circ < x < 200^\circ$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{906}
The number of intersection points between the graphs of the functions \( y = \sin x \) and \( y = \log_{2021} |x| \) is:
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1286}
3. Given in the tetrahedron $D-ABC$, $\angle ACB=\angle ABD=90^{\circ}$, $CA=CB$, $\angle BAD=30^{\circ}$. If the projection of point $C$ on the plane $ABD$ is exactly on $AD$, then the sine value of the dihedral angle $C-AB-D$ is $\qquad$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\sqrt{6}}{3}}
Given an odd function \( f(x) \) with a domain of \([-2,2]\), which is decreasing on the interval \([-2,0]\), and satisfies \( f(1-m)+f\left(1-m^{2}\right)<0 \), determine the range of values for the real number \( m \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1 \leq m < 1}
Evaluate the limit \( \lim_{n \to \infty} \int_0^1 \left( \frac{n}{1+n^2x^2} - \frac{ne^x\cos x}{1 + n^2x^2} \right) \, dx \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
one bacterium splits into 8 bacteria of the next generation . but due to environment , only 50 % of one generation can produced the next generation . if the seventh generation number is 4096 million , what is the number in first generation ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Calculate the limit: $$\lim_{h\rightarrow0}\sup_{n\in\mathbb{N}}\left\|\sqrt{n}\,\mathbb{1}_{(0,\frac{1}{n})}(x+h)-\sqrt{n}\,\mathbb{1}_{(0,\frac{1}{n})}(x)\right\|_{L^2(\mathbb{R})}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{2}}
Given that the angle between vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ is $\frac {π}{3}$, and the magnitudes of $\overrightarrow {a}$ and $\overrightarrow {b}$ are 2 and 1 respectively, find the dot product of $\overset{ -}{a}$ and ($ \overrightarrow {a}$$+2 \overrightarrow {b}$).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Find the value of sum $\sum\limits_{n=1}^\infty A_n$, where 
$$
A_n=\sum\limits_{k_1=1}^\infty\cdots\sum\limits_{k_n=1}^\infty \frac{1}{k_1^2}\frac{1}{k_1^2+k_2^2}\cdots\frac{1}{k_1^2+\cdots+k_n^2}
$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{
The answer is \( e^{\frac{\pi^2}{6}} - 1 \).

}
Let  $F$  be the focus of parabola  $y^2=2px(p>0)$ , with directrix  $l$  and two points  $A,B$  on it. Knowing that  $\angle AFB=\frac{\pi}{3}$ , find the maximal value of  $\frac{|MN|}{|AB|}$ , where  $M$  is the midpoint of  $AB$  and  $N$  is the projection of  $M$  to  $l$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
A woman has $\$1.58$ in pennies, nickels, dimes, quarters, half-dollars and silver dollars. If she has a different number of coins of each denomination, how many coins does she have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
Suppose in a right triangle $PQR$, $\cos Q = 0.5$. Point $Q$ is at the origin, and $PQ = 15$ units along the positive x-axis. What is the length of $QR$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Determine the number of involutory $3 \times 3$ matrices over the field $\mathbb{Z}_{13}$. An involutory matrix is one that is its own inverse.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{61856}
In a race, all runners must start at point $A$, touch any part of a 1500-meter wall, and then stop at point $B$. Given that the distance from $A$ directly to the wall is 400 meters and from the wall directly to $B$ is 600 meters, calculate the minimum distance a participant must run to complete this. Express your answer to the nearest meter.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1803}
8. $[7]$ Two circles with radius one are drawn in the coordinate plane, one with center $(0,1)$ and the other with center $(2, y)$, for some real number $y$ between 0 and 1 . A third circle is drawn so as to be tangent to both of the other two circles as well as the $x$ axis. What is the smallest possible radius for this third circle?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3-2\sqrt{2}}
There are 5 green candies, 3 blue candies, and 4 red candies in a bag. If Violet randomly picks a candy from the bag, how likely is it that it's blue?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25\%}
Students Alekseev, Vasiliev, Sergeev, and Dmitriev were cleaning the classrooms of the 7th, 8th, 9th, and 10th grades. During an inspection, it was found that the 10th grade was cleaned poorly. They started to find out who cleaned this classroom. Alekseev said, "I cleaned 7th grade, and Dmitriev cleaned 8th grade." Vasiliev: "I cleaned 9th grade, and Alekseev cleaned 8th grade." Sergeev: "I cleaned 8th grade, and Vasiliev cleaned 10th grade." Dmitriev left for home before the inspection. Who cleaned the 10th grade if exactly one part of each of these statements is true?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Dmitriev}
Determine the winding number of the curve \( \alpha(t) = ((2 \cos t - 1) \cos t, (2 \cos t - 1) \sin t) \) with respect to the point \( p = (1/2, 0) \) using complex analysis.
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Answer: \boxed{2}
A water tank has the shape of the bottom half of a sphere with radius $r=1$ meter. If the tank is full, how much work is required to pump all the water out the top of the tank?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$2450 \pi \mathrm{N}-\mathrm{m}$}
Given that \( f(0) = 0 \), \( f(1) = 2 \), and \( \int_0^1 f(x) \, dx = 3 \), find the value of \( \int_0^1 x f(x) \, dx \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{5}{3}}
Given \( f(x) \) is an odd function defined on \( \mathbf{R} \), \( f(1) = 1 \), and for any \( x < 0 \), it holds that
\[ 
f\left(\frac{1}{x}\right) = x f\left(\frac{1}{1-x}\right) . 
\]
Then find the value of the sum
\[ 
\sum_{k=1}^{1009} f\left(\frac{1}{k}\right) f\left(\frac{1}{2019-k}\right).
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2^{2016}}{2017!}}
The base of the pyramid \(TABC\) is a triangle \(ABC\), all sides of which are equal to 3, and the height of the pyramid, equal to \(\sqrt{3}\), coincides with the lateral edge \(TA\). Find the area of the cross-section of the pyramid by a plane that passes through the center of the circumscribed sphere of the pyramid, is parallel to the median \(AD\) of the base, and forms an angle of \(60^{\circ}\) with the base plane.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{11 \sqrt{3}}{10}}
Triangle $ABC$ has side lengths $AB=7, BC=8, CA=9.$ Let $E$ be the foot from $B$ to $AC$ and $F$ be the foot from $C$ to $AB.$ Denote $M$ the midpoint of $BC.$ The circumcircles of $\triangle BMF$ and $\triangle CME$ meet at another point $G.$ Compute the length of $GC.$
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Answer: \boxed{
$\frac{36}{7}$}
Points $R$, $S$ and $T$ are vertices of an equilateral triangle, and points $X$, $Y$ and $Z$ are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices?
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Answer: \boxed{4}
Calculate the difference $A - B$, where $A$ is the number of 6-digit tickets (from 000000 to 999999) that are considered lucky, and $B$ is the number of tickets that are considered medium. A ticket is lucky if the sum of its first three digits equals the sum of its last three digits. A ticket is medium if the sum of all its digits equals 27.
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Answer: \boxed{0}
In a plane, given a point Q and n distinct points P1, P2, ..., Pn. For each 1 ≤ k ≤ n, |QPk| is different. Furthermore, for each 1 ≤ k ≤ n, consider the circle with center Pk and radius PkQ. Suppose that none of the circles contain more than two points (these two points are Q and Pk), i.e., there is no other point inside or on the circle. Find the maximum value of n.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Determine the cardinality of the set \( B \), where \( B \) is defined as: \[ B = \{g \in \Bbb N \to \Bbb N \mid \exists T\subseteq \Bbb N, \left.g\right|_T = \operatorname{Id}_T \land g(\Bbb N \setminus T)\subseteq \Bbb N \setminus T\} \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{\aleph_0}}
Convex quadrilateral \(EFGH\) has its vertices \(E\), \(F\), \(G\), and \(H\) situated on the sides \(AB\), \(BC\), \(CD\), and \(DA\) of convex quadrilateral \(ABCD\) respectively, and they satisfy the condition \(\frac{AE}{EB} \cdot \frac{BF}{FC} \cdot \frac{CG}{GD} \cdot \frac{DH}{HA}=1\). Points \(A\), \(B\), \(C\), and \(D\) are located on the sides \(H_1E_1\), \(E_1F_1\), \(F_1G_1\), and \(G_1H_1\) of convex quadrilateral \(E_1F_1G_1H_1\) respectively, and they satisfy the conditions \(E_1F_1 \parallel EF\), \(F_1G_1 \parallel FG\), \(G_1H_1 \parallel GH\), and \(H_1E_1 \parallel HE\). Given that \(\frac{E_1A}{AH_1}=\lambda\), find the value of \(\frac{F_1C}{CG_1}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\lambda}
14. How many polynomials $P$ with integer coefficients and degree at most 5 satisfy $0 \leq P(x)<120$ for all $x \in\{0,1,2,3,4,5\} ?$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{86400000}
For which real numbers \(a\) does the series \( \sum_{n=0}^\infty \frac{1}{u_n} \) converge, where the sequence \( \{u_n\} \) is defined recursively by \( u_0 = 2 \) and \( \int_{u_n}^{u_{n+1}} (\ln u)^a \, du = 1 \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{a < -1}
Evaluate the double integral \( \iint \frac{(x^2+y^2)^2}{x^2y^2} \, dx \, dy \) over the region common to the circles \( x^2+y^2=7x \) and \( x^2+y^2=11y \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{77}
Let $k=\int_{0}^{\pi }{(\sin x-\cos x)}dx$. If ${{(1-kx)}^{8}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+\cdots +{{a}_{8}}{{x}^{8}}$, find the sum of coefficients $a_1 + a_2 + \cdots + a_8$. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
For any positive integer $n$, define 
\[ E(n) = n(n+1)(2n+1)(3n+1)\cdots (10n+1). \]
Find the greatest common divisor of $E(1), E(2), E(3), \dots, E(2009)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2310}
The sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ is $S_n$. If $S_7 > S_8 > S_6$, then the positive integer $n$ that satisfies $S_n \cdot S_{n+1} < 0$ is $\underline{\hspace{1cm}}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14}
It takes 10 minutes to wash a car, 15 minutes to change oil, 30 minutes to change a set of tires, 45 minutes to paint a car, and 60 minutes to service an engine. Mike works on sedans and SUVs. For sedans, he washes 9 cars, changes the oil on 6 cars, changes two sets of tires, paints 4 cars, and services 2 engines. For SUVs, he washes 7 cars, changes the oil on 4 cars, changes 3 sets of tires, paints 3 cars, and services 1 engine. However, since SUVs are larger, it takes 1.5 times longer to wash and paint them than it does for sedans. How many hours did Mike work?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{17.625}
Determine the cardinality of all triangular subsets of the Sierpinski triangle.
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Answer: \boxed{\aleph_0}
How many different positive three-digit integers can be formed using only the digits in the set $\{2, 3, 5, 5, 7, 7, 7\}$ if no digit may be used more times than it appears in the given set of available digits?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{43}
In a complete graph $G$ with 25 vertices, each edge is colored either red or blue. Given that there are no red triangles in $G$, determine the largest integer $m$ such that a blue complete subgraph $K_m$ is guaranteed to exist. Use Ramsey theory to find your answer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
The coordinates of the point $A(-4,3)$ with respect to the $x$-axis are ____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-4,-3)}
In $\triangle Q R S$, point $T$ is on $Q S$ with $\angle Q R T=\angle S R T$. Suppose that $Q T=m$ and $T S=n$ for some integers $m$ and $n$ with $n>m$ and for which $n+m$ is a multiple of $n-m$. Suppose also that the perimeter of $\triangle Q R S$ is $p$ and that the number of possible integer values for $p$ is $m^{2}+2 m-1$. What is the value of $n-m$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
What is the cardinality of the set of hyperreal numbers?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{\aleph_0}}
Given two distinct lines OA and OB, take any point on OA and draw a perpendicular to OB. Then, from the foot of this perpendicular, draw another perpendicular to OA, and from the second foot, draw a perpendicular to OB, and so on, indefinitely. If the lengths of the initial two perpendicular segments are a and b (a!= b), what is the sum of these perpendicular segments as the process continues indefinitely? Express your answer in terms of a and b.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{a^2}{a - b}}
A bicycle wheel has a certain diameter. It makes 522.0841599665866 complete revolutions in 1 km. What is the diameter of the wheel?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.6096}
Find the number of subgroups of the group $\mathbb{Z}_3 \times \mathbb{Z}_3 \times \mathbb{Z}_9$ that are isomorphic to $\mathbb{Z}_3 \times \mathbb{Z}_3$. Provide your answer as a single integer.
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Answer: \boxed{13}
Let $a$ and $b$ be positive real numbers such that $\log_{43}{a} = \log_{47} (3a + 4b) = \log_{2021}b^2$. Then, the value of $\frac{b^2}{a^2}$ can be written as $m + \sqrt{n}$, where $m$ and $n$ are integers. Find $m + n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{123}
Evaluate the integral \( \int (10x^2 + 3y^3 - 4z^2 + 8) \delta(2\vec{r}) \, d^3\vec{r} \), where \( \delta(2\vec{r}) \) is a three-dimensional delta function.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
The angle bisector of angle \( A \) of triangle \( ABC \) intersects side \( BC \) at point \( D \). A circle with radius 35, whose center lies on the line \( BC \), passes through points \( A \) and \( D \). It is known that \( AB^2 - AC^2 = 216 \), and the area of triangle \( ABC \) is \( 90 \sqrt{3} \). Find the radius of the circumcircle of triangle \( ABC \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7 \sqrt{3}}
Determine the Galois group of the splitting field of the polynomial $x^4 - 2x^2 - 2$ over the finite field $F_7$, where $F_7$ is the field with 7 elements.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\mathbb{Z}/4\mathbb{Z}}
Cagney can frost a cupcake every 15 seconds and Lacey can frost a cupcake every 45 seconds. Working together, calculate the number of cupcakes they can frost in 10 minutes.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{53}
For the integer numbers $i,j,k$ satisfying the condition $i^2+j^2+k^2=2011$, what is the largest possible value of $i+j+k$? Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{77}
In the tetrahedron $ABCD$, it is given that $AB=BD=CD=3$, $AD=BC=4$, and $AC=5$. Determine the size of the dihedral angle $A-BD-C$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\\pi - \\arccos \left( \frac{1}{10} \right)}
How many 10-digit numbers with distinct digits are divisible by 98765?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Given a regular tetrahedron with edge length $a$, find the radius of a sphere centered at the center of the tetrahedron such that the total volume of the part of the tetrahedron outside the sphere and the part of the sphere outside the tetrahedron is minimized.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{a \frac{1}{3} \sqrt{\frac{2}{3}}}
B2. In a top hat, there are a hundred tickets numbered from 1 to 100. You want to have three tickets with the property that each of the three numbers is smaller than the sum of the other two numbers. For example, the three tickets with numbers 10, 15, and 20 would be suitable (since $10<15+20, 15<10+20$, and $20<10+15$), but the tickets with numbers 3, 4, and 7 would not (since 7 is not less than $3+4$). You may (without looking at the numbers) take a number of tickets from the hat.

How many tickets must you take at a minimum to be sure that there are three tickets among them that meet your requirement?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
Find the expected value of \( N = \min\{n: U_1 + U_2 + \cdots + U_n > 1\} \), where \( U_1, U_2, \ldots \) are independent uniform (0,1) random variables.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{e}
Consider a continuous distribution on \((0,1)\) with probability distribution function \(f\) and cumulative distribution function \(F\). Define the function
\[ g(r) = \frac{\int_r^1 x f(x) \, dx}{2 - F(r)} \]
where \(r \in (0,1)\). Let \(r_M\) be the value of \(r\) that maximizes \(g(r)\). Determine if there exists a positive constant \(c\), independent of the distribution, such that
\[ \int_{r_M}^1 x f(x) \, dx \geq c \int_0^1 x f(x) \, dx. \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{1}{2}}
Alice and Bob take turns removing balls from a bag containing 10 black balls and 10 white balls, with Alice going first. Alice always removes a black ball if there is one, while Bob removes one of the remaining balls uniformly at random. Once all balls have been removed, the expected number of black balls which Bob has can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are relatively prime positive integers. Compute \(100a + b\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4519}
A TV station is scheduled to broadcast two series for a company. Series A has a runtime of 80 minutes per episode, including 1 minute of commercials, attracting 600,000 viewers; Series B has a runtime of 40 minutes per episode, including 1 minute of commercials, attracting 200,000 viewers. If the company and the TV station agree that the station must broadcast at least 6 minutes of commercials per week and the station can only provide up to 320 minutes of program time for the company each week, what is the maximum number of viewers the TV station can attract per week by scheduling these two series accordingly? Express your answer in millions of viewers, rounded to the nearest tenth if necessary.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 \text{ million}}
7. (10 points) There is a sufficiently deep water tank with a rectangular base that is 16 cm long and 12 cm wide. Originally, the tank contains 6 cm of water and 6 cm of oil (the oil is above the water). If a block of iron with dimensions 8 cm in length, 8 cm in width, and 12 cm in height is placed in the tank, the height of the oil layer will be $\qquad$ cm.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
At the end of the month, a certain ocean desalination plant’s reservoir, which is irregularly shaped, contained 14 million gallons of water. This amount is twice the normal level due to an unusually high yield this month. It's known that this amount represents 70% of the reservoir’s total capacity, but it also should take into account a monthly 10% water loss due to evaporation. How many million gallons short of total capacity is the normal level, after factoring in the monthly evaporation loss?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13.7}