problem stringlengths 10 3.15k | answer stringlengths 1 1.22k | source stringclasses 11
values | domain listlengths 1 4 | llama8b_solve_rate float64 0 1 ⌀ |
|---|---|---|---|---|
January 1, 2015 was a Thursday. Based on this information, determine the day of the week on which February 1, 2015 falls. | Sunday | olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.28125 |
Tommy's mother lets him ride his bike 2 blocks north of his block, 3 blocks east, 2 blocks west, and 2 blocks south. Each block is rectangular in shape, with a length of 200 meters and a width of 150 meters. Due to a special rule enforced for Tommy, he needs to alternate between going north and east or west for every b... | 14.4 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 |
Given vectors \\(a+b=(m,2)\\) and \\(b=(0,1)\\), if the angle between vector \\(a\\) and \\(b\\) is \\(\dfrac{\pi}{3}\\), then the value of the real number \\(m\\) is \_\_\_\_\_\_\_\_. | ± \sqrt{3} | cn_k12 | [
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 0.125 |
Find the domain of the function $y=\frac{{2x}}{{\sqrt{3-x}}}+\sqrt{x-2}$. | \left[2,3\right) | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.765625 |
The number of short students in a class is 2/5 of the total number of students. There are some tall students, and the class has 400 students. There are 150 students with average height. How many tall students are there in the class? | 90 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.953125 |
Let $\alpha > 0$ be a real number. Compute the limit of the sequence $\{x_n\}_{n\geq 1}$ defined by $$ x_n=\begin{cases} \sum \limits_{k=1}^n \sinh \left(\frac{k}{n^2}\right),& \text{when}\ n>\frac{1}{\alpha} 0,& \text{when}\ n\leq \frac{1}{\alpha}\end{cases} $$ | \frac{1}{2} | aops_forum | [
"Mathematics -> Calculus -> Other"
] | 0.15625 |
Given that the lateral surface of a cone, when unfolded, is a semicircle with an area of $2\pi$, find the area of the base of the cone. Express your answer in terms of $\pi$. | \pi | big_math | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.171875 |
If 20% of (x - y) = 15% of (x + y) and 30% of (x - z) = 25% of (x + z), then what percent of x is y when z is 10% of y? | 10\% | orca_math | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 |
Given the sets $A={x|-1\leq x<3}$ and $B={x|2<x\leq 5}$, find the union of sets A and B. Express your answer as an interval, using square brackets or parentheses to denote inclusion or exclusion of endpoints. | [-1,5] | big_math | [
"Mathematics -> Algebra -> Other"
] | 0.234375 |
Six pepperoni circles will exactly fit across the diameter of a $12$-inch pizza when placed. If a total of $24$ circles of pepperoni are placed on this pizza without overlap, what fraction of the pizza is covered by pepperoni? | $\frac 23$ | harp | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0 |
Pete has a bag with 10 marbles. 40% are blue and the rest are red. His friend will trade him some number of blue marbles for every red one. If Pete keeps 1 red marble and ends up with 15 total marbles after trading with his friend, how many blue marbles does his friend trade for each red marble? | 2 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.34375 |
A rectangular solid has dimensions of $3$, $2$, and $1$. All the vertices of the solid lie on the surface of a sphere. Find the surface area of the sphere. | 14\pi | cn_k12 | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.46875 |
Over the course of a week, a restaurant served 3 types of cakes: chocolate, vanilla, and strawberry. The restaurant served chocolate cakes twice as often as vanilla cakes, and strawberry cakes half as often as chocolate cakes. If the restaurant served 12 vanilla cakes during lunch and 18 during dinner over the entire w... | 30 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.15625 |
From the set $\{1, 2, 3, \ldots, 20\}$, choose $k$ distinct numbers to form a set $M$, such that there are always 4 distinct numbers $a, b, c, d$ in $M$ which satisfy $a - b + c - d$ being divisible by 20. Find the smallest value of $k$. | 7 | olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Other"
] | 0.046875 |
Four students from a class are assigned to serve in three different pavilions, A, B, and C, with at least one person assigned to each pavilion. If student A requests not to be assigned to Pavilion A, find the number of different assignment plans. Express your answer as a whole number. | 24 | big_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.03125 |
Simplify $\sqrt{\frac{1}{3}}$ to ______. | \frac{\sqrt{3}}{3} | cn_k12 | [
"Mathematics -> Algebra -> Prealgebra -> Other"
] | 0.984375 |
If p, q, and r are distinct positive digits and the product of the two-digit integers pq and pr is 221, what is the sum of the digits p, q, and r? | 11 | orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.515625 |
The equation of a circle is given as $x^2+y^2-2y=0$. Find the radius of the circle. Express your answer as a numerical value. | 1 | big_math | [
"Mathematics -> Algebra -> Intermediate Algebra -> Other"
] | 0.921875 |
If a particle $M$ moves according to the law $s=3t^{2}$, what is its instantaneous velocity at $t=3$? | 18 | cn_k12 | [
"Mathematics -> Calculus -> Differential Calculus -> Derivatives"
] | 1 |
Ravi purchased a refrigerator for Rs. 15000 and a mobile phone for some amount. He sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent. Overall, he made a profit of Rs. 500. What was the cost of the mobile phone? | 8000 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.46875 |
Kyle initially bought 4 glass bottles that can hold 25 origami stars each. Later, he purchased another 5 identical glass bottles. How many stars must Kyle make to fill all the glass bottles he bought? | 225 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.984375 |
Solve the system of equations:
\[
\left\{\begin{array}{l}
a + b + c = 0 \\
a^{2} + b^{2} + c^{2} = 1 \\
a^{3} + b^{3} + c^{3} = 4abc
\end{array}\right.
\] | \left( \pm \frac{\sqrt{2}}{2}, \mp \frac{\sqrt{2}}{2}, 0 \right), \left( \pm \frac{\sqrt{2}}{2}, 0, \mp \frac{\sqrt{2}}{2} \right), \left( 0, \pm \frac{\sqrt{2}}{2}, \mp \frac{\sqrt{2}}{2} \right). | olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.078125 |
When the number of sides of a polygon increases by 1, what is the change in the sum of its interior angles? Express your answer in degrees as a whole number. | 180 | big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.8125 |
Compute the definite integral: $\int_{-1}^{1}(2 \sqrt{1-{x}^{2}}-\sin x)dx = \boxed{\_\_\_\_}$. | \pi + 2\cos(1) | cn_k12 | [
"Mathematics -> Calculus -> Integral Calculus -> Applications of Integrals"
] | 0.03125 |
What is the angle of inclination of the line $2x+y-1=0$? (Express in terms of inverse trigonometric function) | \pi - \arctan 2 | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.953125 |
Given $f(x) = x + x^3$ ($x \in \mathbb{R}$), find the solution set of the inequality $f(\log_2{x}) > f(0)$. | (1, \infty) | cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.515625 |
Read the following material and solve the problem:<br/>Solve the equation $x^{4}-5x^{2}+4=0$. This is a fourth-degree equation. Based on the characteristics of this equation, the solution method is usually as follows:<br/>Let $x^{2}=y$, then $x^{4}=y^{2}$, so the original equation can be transformed into $y^{2}-5y+4=0$... | x_{1}=-3, x_{2}=2 | cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Polynomial Operations"
] | 0.375 |
What can be the product of several distinct prime numbers if it is divisible by each of them minus 1? Find all possible values of this product. | 6, 42, 1806 | olympiads | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 0.0625 |
16 balls are numbered 1 to 16 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ? | 7/30 | orca_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combinations"
] | 0.984375 |
Determine the mass percentage of N in Ammonium iodide (NH4I) after it reacts with Sodium phosphate (Na3PO4) to form Ammonium phosphate ((NH4)3PO4) and Sodium iodide (NaI). | 28.19\% | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 |
Given the equation $z(1+i) = i - 2$, calculate the conjugate of $z$, denoted as $\overline{z}$. Express your answer as a complex number in the form $a+bi$. | -\frac{1}{2} - \frac{3}{2}i | big_math | [
"Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers"
] | 0.046875 |
Given the hyperbola equation $x^{2}-2y^{2}=1$, find the coordinates of its right focus. Express your answer as a coordinate pair (x, y) using boxed notation. | \left(\frac{\sqrt{6}}{2}, 0\right) | big_math | [
"Mathematics -> Geometry -> Other"
] | 0.203125 |
The eccentricity of the ellipse $\frac{x^2}{9} + \frac{y^2}{5} = 1$ is __________. | \frac{2}{3} | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 1 |
The average age of the 40 members of a computer science camp is 17 years. There are 20 girls, 15 boys, and 5 adults. If the average age of the girls is 15 and the average age of the boys is 16, what is the average age of the adults? | 28 | math | [
"Mathematics -> Applied Mathematics -> Statistics -> Mathematical Statistics"
] | 0.984375 |
Given the floor values of x, y, and z as 5, -3, and -1 respectively, calculate the number of possible integer values that the floor of x - y - z can take. Express your answer as a single integer. | 3 | big_math | [
"Mathematics -> Algebra -> Other"
] | 0.15625 |
A baseball league has 6 teams. To decide the schedule for the league, for each pair of teams, a coin is flipped. If it lands heads, they will play a game this season, in which one team wins and one team loses. If it lands tails, they don't play a game this season. Define the imbalance of this schedule to be the minimum... | \frac{5055}{2^{15}} | olympiads | [
"Mathematics -> Applied Mathematics -> Probability -> Other"
] | 0.34375 |
Three equally spaced parallel lines intersect with a circle, resulting in three chords of lengths 38, 38, 34 units. Calculate the distance between two adjacent parallel chords. Express your answer in units. | 6 | big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 |
On dividing 14698 by 164.98876404494382, we get a certain quotient and 14 as remainder. What is the quotient? | 88 | orca_math | [
"Mathematics -> Algebra -> Other"
] | 0.078125 |
60% of a certain number is greater than 4/5 of 25 by 4. What is that number? | 40 | orca_math | [
"Mathematics -> Algebra -> Simple Equations"
] | 0.875 |
Given $n$ lines ($n\geq 3$) in a plane, where exactly two lines are parallel to each other and no three lines intersect at the same point. Let $f(n)$ represent the number of intersection points of these $n$ lines. When $n>4$, express $f(n)$ as a formula. | f(n)=\frac {1}{2}(n+1)(n-2) | cn_k12 | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.21875 |
Given the function $f(x)=\sin \left( \frac{5}{4}\pi - x \right)-\cos \left( \frac{\pi}{4}+x \right)$ and $\cos (\alpha-\beta)=\frac{3}{5}$, $\cos (\alpha+\beta)=-\frac{3}{5}$, where $0 < \alpha < \beta\leqslant \frac{\pi}{2}$, find $f(\beta)$. | 2\sin \frac{\pi}{4}=\sqrt{2} | cn_k12 | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.15625 |
Given the sequence $\{a_n\}$ with the general term formula $a_n= \frac{4}{11-2n}$ ($n\in\mathbb{N}^*$), find the value of $n$ that satisfies the condition $a_{n+1} < a_n$. Express your answer as a single integer. | 5 | big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.171875 |
Given that the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{π}{3}$, and $\overrightarrow{a}⋅\overrightarrow{b}=3$, vector $\overrightarrow{c}$ satisfies $\overrightarrow{c}=λ\overrightarrow{a}+({1-λ})\overrightarrow{b}$ ($0＜λ＜1$), and $\overrightarrow{a}⋅\overrightarrow{c}=\overrightarr... | \frac{27}{8} | cn_k12 | [
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 0.03125 |
Pete must finish paying off the last $90 he owes on a bike. He goes through his wallet and finds two $20 bills. Checking his pockets, he finds some $10 bills. Unhappy that he doesn't have the entire amount, he suddenly remembers that he has plastic bottles that can be returned to his local store for cash. If the store ... | 4 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.796875 |
In a kingdom, there are counts, dukes, and marquises. One day, each count dueled with three dukes and several marquises. Each duke dueled with two counts and six marquises. Each marquis dueled with three dukes and two counts. It is known that all counts dueled with an equal number of marquises. With how many marquises ... | 6 marquises | olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 |
The area of a square is equal to some times the area of a rectangle of dimensions 32 cm * 10 cm. The perimeter of the square is 160 cm. What is the ratio of the area of the square to the area of the rectangle? | 5:1 | orca_math | [
"Mathematics -> Geometry -> Plane Geometry -> Area"
] | 0.484375 |
A pet store had 13 siamese cats and some house cats. During a sale they sold 10 cats. They have 8 cats left. How many house cats did the pet store have initially? | 5 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.96875 |
A candidate got 25% of the votes polled and he lost to his rival by a certain number of votes. There were 8000 votes cast. By how many votes did the candidate lose to his rival? | 4000 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.921875 |
If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. Let f(n) be another function that raises p(n) to the power of its smallest prime factor. Find the fifth smallest prime factor of f(20) + 101. | 11 | orca_math | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 0.296875 |
Find the sum of real roots of the equation $x^4-7x^3+14x^2-14x+4=0$. Express your answer as a single number. | 5 | big_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.3125 |
Rachel has 3 apple trees. She picked a certain number of apples from each of her trees. Now the trees have a total of 9 apples still on them. There were initially 33 apples on all trees. How many apples did Rachel pick from each tree? | 8 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.84375 |
A non-constant function $f(x)$ defined on $R$ satisfies: $f(-x) = f(x)$ and $f(2-x) + f(x) = 0$. Please write down an analytical expression for the function that satisfies the conditions: $f(x) =$ ____. | f(x) = \cos\left(\frac{\pi}{2}x\right) | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.078125 |
Graph the set of points on the coordinate plane whose coordinates satisfy the equation: \( x^{2}(y + y^{2}) = y^{3} + x^{4} \). | y = x, y = -x, y = x^{2} | olympiads | [
"Mathematics -> Algebra -> Other"
] | 0.015625 |
The Rotary Club is holding its annual fundraising Omelet Breakfast, with tickets sold in advance. They sold 53 small children tickets, 35 older children tickets, 75 adult tickets, and 37 senior tickets. They estimate that small children can eat a half omelet, older children can eat a whole omelet, adults will eat two o... | 2 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.796875 |
Given that the lines \( 2x + y - 2 = 0 \) and \( x + my - 1 = 0 \) are perpendicular to each other, find the distance from the point \( P(m, m) \) to the line \( x + y + 3 = 0 \). | \frac{\sqrt{2}}{2} | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.203125 |
Two cars start simultaneously from locations A and B, respectively, heading towards each other. Car A travels at a speed of 80 kilometers per hour, and Car B travels at a speed of 100 kilometers per hour. After 2 hours, the two cars have covered 60% of the total distance between A and B. What is the distance between A ... | 600 | cn_k12 | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.953125 |
Of the 35 students in Taehyung's class, 3 of them scored 93, 83, and 87 points on the Korean language test, respectively. If the average Korean language score of the rest of the students is 76, what is the average Korean language score of the whole class? | 77 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.65625 |
Tim is a frequent traveler who sleeps according to the following schedule:
- 6 hours per day for 5 days a week while in his home country.
- 10 hours a day for the other 2 days during his weekend trips.
However, due to his travels, he sometimes experiences time zone changes and daylight saving adjustments. In a parti... | 48 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.109375 |
The polar coordinate equation for the rectangular coordinate equation $y^{2}=12x$ is $\_\_\_\_\_\_\_.$ | ρ\sin ^{2}θ=12\cos θ | cn_k12 | [
"Mathematics -> Geometry -> Other"
] | 0.0625 |
Given an ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) where \(a > b > 0\), and its foci \(F_{1}\) and \(F_{2}\) lie on the left and right, respectively. A line passing through the right focus \(F_{2}\) intersects the ellipse at points \(A\) and \(B\). If \(\left|F_{1} B\right|=\frac{2}{3}\left|F_{1} A\right|\)... | \frac{11 - \sqrt{41}}{10} | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 |
Bryan has always been fond of studying rocks and minerals. He has a room full of books about and samples of the different types of rocks. One particular day, he went in the room to take a look at his mineral samples. He has a certain number of samples of minerals per shelf, and he has a total of 7 shelves. He has 455 m... | 65 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.984375 |
Calculate: $-\sqrt{9}-4\times(-2)+2\cos60°$. | 6 | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.5625 |
Let $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ be unit vectors forming an angle of $\frac{2\pi}{3}$ with each other, and let $\overrightarrow{a}=2\overrightarrow{e_{1}}+3\overrightarrow{e_{2}}$, $\overrightarrow{b}=k\overrightarrow{e_{1}}-4\overrightarrow{e_{2}}$. If $\overrightarrow{a}$ is perpendicular to ... | \frac{32}{7} | big_math | [
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 0.03125 |
Sally had 39 baseball cards , and 9 were torn . Sara bought 24 of Sally 's baseball cards. Now , Sally has _____ baseball cards . | 15 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 |
Let f(x) and g(x) be odd and even functions defined on ℝ, respectively. If f'(x)g(x) + f(x)g'(x) > 0 for x < 0, and g(-3) = 0, find the solution set for the inequality f(x)g(x) < 0. Express your answer as an interval or a union of intervals. | (-∞, -3) ∪ (0, 3) | big_math | [
"Mathematics -> Algebra -> Other"
] | 0 |
Given that $x, y \in (0, +\infty)$ and they satisfy $\frac{1}{x} + \frac{1}{2y} = 1$, find the minimum value of $x + 4y$. Express your answer as a single mathematical expression. | 3 + 2\sqrt{2} | big_math | [
"Mathematics -> Calculus -> Other"
] | 0.03125 |
A grocer has a sale of Rs. 2500, Rs. 6500, Rs. 9855, Rs. 7230, and Rs. 7000 for 5 consecutive months. In the sixth month, he must have a sale of Rs. 11915. What is the average sale he wants to achieve for the six months? | 7500 | orca_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Other"
] | 0.140625 |
A fence that is 2022 meters long forms a triangle, and the lengths of all three sides are integers in meters. Two of the sides differ in length by 1 meter, and two of the sides differ in length by 2 meters. What is the length, in meters, of the middle side when the three sides are ordered by size? | 674 | olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.484375 |
Given the function $f(x)= \begin{cases} 2^{x-1},x < 4 \\ 2x+3,x\geqslant 4 \end{cases}$, find $f[f(3)]=$ _____ . | 11 | cn_k12 | [
"Mathematics -> Algebra -> Functions"
] | 1 |
The parabolas with equations \( y = x^2 - 2x - 3 \) and \( y = -x^2 + 4x + c \) intersect at points \( A \) and \( B \). Determine the value of \( c \) so that the sum of the \( x \)-coordinate and \( y \)-coordinate of the midpoint of \( AB \) is 2017. | 4031 | olympiads | [
"Mathematics -> Algebra -> Quadratic Functions"
] | 0 |
Given that $x, y \in \mathbb{R}^+$ and $\frac{1}{x} + \frac{4}{y} = 2$, find the minimum value of $x + y$. | \frac{9}{2} | cn_k12 | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.109375 |
Given that $\alpha$ is an acute angle, if $1+\frac{{\sqrt{3}}}{{\tan80°}}=\frac{1}{{\sin\alpha}}$, then $\alpha =$____. | 50° | cn_k12 | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.046875 |
Given that $α$ is an angle in the third quadrant, and $\tan (α+ \frac {π}{4})=-2$, then $\sin (α- \frac {π}{4})=$ ______. | -\frac{\sqrt{5}}{5} | cn_k12 | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.234375 |
Given that \( p, q, n \in \mathbf{N}^{+} \), find the sum: \(\sum_{k=0}^{\infty} C_{p+k}^{p} \cdot C_{q+n-k}^{q} \). | C_{p+q+n+1}^{p+q+1} | olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Other"
] | 0.03125 |
Given the sets $P=\{0, m\}$ and $Q=\{x|2x^2-5x<0, x\in \mathbb{Z}\}$, if $P\cap Q \neq \emptyset$, then find all possible values of $m$. Express your answer as a list of integers. | 1, 2 | big_math | [
"Mathematics -> Algebra -> Other"
] | 0.15625 |
The average of some numbers is 4 more than the average of 10, 70, and 28. If the other two numbers are 20 and 60, what is the second number? | 60, | orca_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Other"
] | 0.28125 |
In a video game, each enemy defeated gives you 8 points. If a level has a certain number of enemies total and you destroy all but 2 of them, you would earn 40 points. How many enemies are there in total on the level? | 7 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.96875 |
Simplify and then evaluate the expression: $\left(2a^{2}-b\right)-\left(a^{2}-4b\right)-\left(b+c\right)$, where $a=\dfrac{1}{3}$, $b=\dfrac{1}{2}$, $c=1$. | \dfrac{1}{9} | cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.515625 |
A mailman has to give 32 pieces of junk mail to each of the 55 blocks. If he gives some mails to each house in a block and there are 4 houses in a block, how many mails does he give to each house? | 8 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.75 |
The complex number $z$ satisfies $|z-i|=1$ (where $i$ is the imaginary unit), then the maximum value of $|z+2+i|$ is ______. | 2\sqrt{2}+1 | cn_k12 | [
"Mathematics -> Geometry -> Other"
] | 0.046875 |
Given a unit right prism \( ABCD-A_1B_1C_1D_1 \), there are two moving points \( E \) and \( F \) on the edges \( BB_1 \) and \( DD_1 \) respectively, such that \( BE = D_1F \). Let the angle between line segment \( EF \) and plane \( AB \) be \(\alpha\), and the angle between line segment \( EF \) and plane \( BC_1 \)... | 90^\circ | big_math | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.28125 |
If $f(x) = -\dfrac{1}{x},$ what is $f(f(f(f(f(6)))))$? | -\dfrac{1}{6} | math | [
"Mathematics -> Algebra -> Other"
] | 0.65625 |
In triangle DEF, angle DEF is equal to \(60^{\circ}\). Find the area of triangle DEF, given that \(DF = 3\) and \(EF = \frac{6}{\sqrt{3}}\). | \frac{3\sqrt{3}}{2} | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 |
What is the value of the following expression: $1 - 3 + 5 - 7 + 9 - \cdots - 43 + 45 - 47 + 49$ ? | 25 | math | [
"Mathematics -> Algebra -> Other"
] | 0.171875 |
$(3a+b)(a-b)$ | 3a^2 - 2ab - b^2 | cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.96875 |
Given the sequence $S_n = \sin \frac{π}{7} + \sin \frac{2π}{7} +... + \sin \frac{nπ}{7} \quad (n \in \mathbb{N}^+)$, find the number of zero values among $S_1$, $S_2$,..., $S_{2017}$. Express your answer as a single integer. | 288 | big_math | [
"Mathematics -> Calculus -> Other"
] | 0.203125 |
Given $\frac{a}{b}=\frac{c}{d}=\frac{3}{2}$, $(b+d\neq 0)$, then $\frac{{a+c}}{{b+d}}=$____. | \frac{3}{2} | cn_k12 | [
"Mathematics -> Algebra -> Rational Expressions"
] | 0.890625 |
In triangle \(ABC\), two identical rectangles \(PQRS\) and \(P_1Q_1R_1S_1\) are inscribed (with points \(P\) and \(P_1\) lying on side \(AB\), points \(Q\) and \(Q_1\) lying on side \(BC\), and points \(R, S, R_1,\) and \(S_1\) lying on side \(AC\)). It is known that \(PS = 3\) and \(P_1S_1 = 9\). Find the area of tri... | 72 | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 |
41 campers went rowing and 4 campers went hiking in the morning. Some campers went rowing in the afternoon. In all, 71 campers went rowing and hiking. How many campers went rowing in the afternoon? | 26 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.546875 |
If the distance between a point $M$ on the parabola $y^{2}=3x$ and the origin is $2$, then the distance between point $M$ and the focus of the parabola is \_\_\_\_\_\_. | \frac{7}{4} | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.640625 |
If there is one larger cube with a certain surface area and a number of smaller cubes with surface area 24, 125 small cubes are required to make a larger cube. What is the surface area of the larger cube? | 600 | orca_math | [
"Mathematics -> Geometry -> Solid Geometry -> Surface Area"
] | 0.8125 |
Express the repeating decimal 2.5252525... as a fraction in lowest terms and calculate the sum of the numerator and denominator. | 349 | big_math | [
"Mathematics -> Algebra -> Other"
] | 0.8125 |
Two variables \( x \) and \( y \) are inversely proportional; what can be said about their reciprocals? | \frac{1}{x} \text{ is inversely proportional to } \frac{1}{y}. | olympiads | [
"Mathematics -> Algebra -> Other"
] | 0.421875 |
The graph of the function $y=a^x+1$ (where $a>0$ and $a \neq 1$) must pass through which point? (Fill in the coordinates of the point) | (0, 2) | cn_k12 | [
"Mathematics -> Algebra -> Functions"
] | 0.921875 |
Given a point P on the parabola $y^2 = 4x$, the distance from P to the line $x = -3$ is 5. Find the distance from point P to the focus of the parabola. | 3 | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.5 |
In △ABC, if AC⊥BC, AC=b, BC=a, then the radius of the circumcircle of △ABC is $$r= \frac { \sqrt {a^{2}+b^{2}}}{2}$$. Extend this conclusion to space, the correct conclusion is: In the tetrahedron S-ABC, if SA, SB, SC are pairwise perpendicular, SA=a, SB=b, SC=c, then the radius R of the circumscribed sphere of the tet... | R = \frac { \sqrt {a^{2}+b^{2}+c^{2}}}{2} | cn_k12 | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.078125 |
If the odd function $f(x) = x\cos(x) + c$ has a domain of $[a, b]$, then $a + b + c = \_\_\_\_\_\_$. | 0 | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.71875 |
Philatelist Andrey decided to distribute all his stamps equally into 3 envelopes, but there was one extra stamp left. When he distributed them equally into 5 envelopes, there were 3 stamps left; finally, when he distributed them equally into 7 envelopes, 5 stamps were left over. How many stamps does Andrey have in tota... | 208 | olympiads | [
"Mathematics -> Number Theory -> Congruences"
] | 0 |
Find the value of $\tan 690^{\circ}$. Express your answer as a simplified fraction or decimal, including any necessary radicals. | -\frac{\sqrt{3}}{3} | big_math | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.40625 |
The function defined by
\[f(x) = \left\{
\begin{array}{cl}
x + k & \text{if $x < 4$}, \\
2x - 3 & \text{if $x \ge 4$}
\end{array}
\right.\]has an inverse, and the inverse is defined for all real numbers. Enter all possible values of $k,$ separated by commas. | 1 | math | [
"Mathematics -> Algebra -> Functions"
] | 0.296875 |
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