problem stringlengths 10 3.15k | answer stringlengths 1 1.22k | source stringclasses 11
values | domain listlengths 1 4 | llama8b_solve_rate float64 0 1 ⌀ |
|---|---|---|---|---|
A gigantic box contains 50 large boxes, each large box contains 25 medium boxes, each medium box contains 10 small boxes, and each small box contains 45 chocolate bars. How many chocolate bars are in the gigantic box? | 562,500 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.890625 |
Some camels cost as much as 24 horses, 16 horses cost as much as 4 oxen, and 6 oxen cost as much as 4 elephants. The cost of 10 elephants is Rs. 110000. If the cost of a camel is Rs. 4400, how many camels are we talking about? | 10 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.125 |
Point $P(-1,3)$ lies on the graph of the inverse proportion function $y=\frac{k}{x}$. Find the value of $k$. | -3 | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 1 |
Find two numbers whose sum is 44, where the smaller number is negative. The percentage relationship of the difference between the larger and smaller numbers to the smaller number matches the smaller number. | -220 \text{ and } 264 | olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.46875 |
Calculate
Given $2x+y=6$, find the value of $\left[(x-y)^{2}-(x+y)^{2}+y(2x-y)\right]÷(-2y)$. | 3 | cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.171875 |
Given the function $f(x) = \sqrt{2}\sin(x + \frac{π}{4})$, where $x \in [0,π]$, determine the interval on which the function $f(x)$ is monotonically increasing. | [0, \frac{\pi}{4}] | cn_k12 | [
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.421875 |
What compound weighs 612 grams when you have 6 moles of it? | 102 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.703125 |
In an election between two candidates, the first candidate got 80% of the votes and the second candidate got some votes. The total number of votes was 2400. How many votes did the second candidate get? | 480 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.9375 |
The sum of 100 numbers is 1990. If we subtract 1 from the first number, add 2 to the second number, subtract 3 from the third number, ..., and add 100 to the 100th number, then the sum of the new numbers is . | 2040 | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0 |
In a poverty alleviation and disability assistance activity, a total of 3,185,800 yuan was donated. Express 3,185,800 yuan in scientific notation, accurate to the hundred thousand place. | 3.2 \times 10^6 | cn_k12 | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.78125 |
Let $z$ be a non-real complex number with $z^{23}=1$. Compute $$ \sum_{k=0}^{22} \frac{1}{1+z^{k}+z^{2 k}} $$ | 46 / 3 | omnimath | [
"Mathematics -> Algebra -> Other"
] | 0 |
What is $\frac{-5}{9}\cdot \frac{8}{17}$? | -\frac{40}{153} | math | [
"Mathematics -> Algebra -> Prealgebra -> Fractions"
] | 1 |
The lateral surface of a cylinder is a square with a side length of $2 \sqrt[3]{\pi}$. Find the volume of the cylinder. | 2 | olympiads | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.046875 |
In the Cartesian coordinate plane, if the three lines $2x+y-5=0$, $x-y-1=0$ and $ax+y-3=0$ intersect at a single point, then the value of the real number $a$ is __________. | 1 | cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.59375 |
Find the value of the algebraic expression $(a-\sqrt{2})(a+\sqrt{2})-a(a-3)$, where $a=\sqrt{3}+2$. | 3\sqrt{3} + 4 | cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.390625 |
Find the exact number of real roots of the equation sin(x) = lg(x). Express your answer as a whole number. | 3 | big_math | [
"Mathematics -> Calculus -> Other"
] | 0.109375 |
Determine \( p \) and \( q \) such that the function \( x^{2} + p x + q \) reaches its minimum value when \( x = q \) and that this minimum value is \( (p+q)^{2} \). | (p, q) = (0, 0) \quad \text{or} \quad (-1, \frac{1}{2}) | olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.46875 |
Given the complex number ${{z}_{1}}=i{{(1-i)}^{3}}$, if the complex number $z$ satisfies $| z |=1$, then the maximum value of $| z-{{z}_{1}} |$ is ______. | 2\sqrt{2}+1 | cn_k12 | [
"Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers"
] | 0.078125 |
For which natural numbers $n$ is the expression $n^{2} - 4n + 11$ a square of a natural number? | n = 5 | olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.203125 |
Kelly gives away 250 nintendo games. How many did she have initially if she still has 300 games left? | 550 | orca_math | [
"Mathematics -> Algebra -> Prealgebra -> Simple Equations"
] | 1 |
Steve decides to read a new book. He reads a certain number of pages Monday, Wed, and Friday. The book is 2100 pages long, and it takes him 7 weeks to read them all. How many pages does he read on each of those days? | 100 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.4375 |
The integers $ 1,2,...,n$ are placed in order so that each value is either strictly bigger than all the preceding values or is strictly smaller than all preceding values. In how many ways can this be done? | 2^{n-1} | aops_forum | [
"Mathematics -> Discrete Mathematics -> Combinatorics -> Other"
] | 0.140625 |
Given points O(0,0) and A(1,1), and point P is on the right branch of the hyperbola $x^2 - y^2 = 1$, determine the range of values for $\overrightarrow{OA} \cdot \overrightarrow{OP}$. | (0, +\infty) | cn_k12 | [
"Mathematics -> Geometry -> Other"
] | 0.046875 |
Given that $α$, $β$, and $γ$ are distinct planes, and $m$ and $n$ are distinct lines, the following four propositions are provided:
$①$ If $α ⟂ γ$ and $β ⟂ γ$, then $α // β$;
$②$ If $α ⟂ β$ and $β ⟂ γ$, then $α ⟂ γ$;
$③$ If $m ⟂ α$ and $α ⟂ β$, then $m // β$;
$④$ If $m ⟂ α$ and $n ⟂ α$, then $m // n$.
Determine the n... | 1 | cn_k12 | [
"Mathematics -> Geometry -> Other"
] | 0.375 |
Consider a circle with a radius of 5 cm. If we draw a rectangle of maximum size inside the circle and a parallelogram of maximum size tangent to the circle from outside such that the longer sides of the parallelogram are tangent to the circle and the vertices of the rectangles are touching the shorter sides of the para... | 100 | orca_math | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.171875 |
Find all natural numbers \( n \) for which prime numbers \( p \) and \( q \) exist such that
\[ p(p+1) + q(q+1) = n(n+1) \] | n=3 \text{ or } n=6 | olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0.0625 |
A trader sells 66 meters of cloth at the profit of Rs. 5 per meter of cloth. The cost price of one meter of cloth is Rs. 5. What is the total selling price of the cloth? | 660 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.984375 |
The equation \( x^{2}+2x=i \) has two complex solutions. Determine the product of their real parts. | \frac{1 - \sqrt{2}}{2} | olympiads | [
"Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers"
] | 0.15625 |
Given vectors $\overrightarrow{a}=(x-1,2)$ and $\overrightarrow{b}=(4,y)$, if $\overrightarrow{a} \perp \overrightarrow{b}$, find the minimum distance from point $P(x,y)$ to the origin. | \frac{2\sqrt{5}}{5} | cn_k12 | [
"Mathematics -> Geometry -> Other",
"Mathematics -> Algebra -> Other"
] | 0.625 |
Given that the minimum value of the function $f(x) = \cos 2x - 2a(1 + \cos x)$ is $-\frac{1}{2}$, find the value of $a$. | -2 + \sqrt{3} | cn_k12 | [
"Mathematics -> Calculus -> Other"
] | 0.015625 |
For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production raises the average to 54 units per day, and the value of n is 9, how many units were produced today? | 90 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.921875 |
Find the equation of the tangent line to the curve y = x^3 - 3x^2 + 1 at the point (1, -1). Express your answer in the form y = mx + b, where m is the slope and b is the y-intercept. | y = -3x + 2 | big_math | [
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.796875 |
Given the circle \(x^{2} + y^{2} = 9\) with chord \(AB\) having its midpoint at \((1,1)\), and the line \(AB\) intersects the x-axis at point \(P\), find the value of \(|PA| \cdot |PB|\). | 7 | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.015625 |
A hyperbola passes through the point (m, n) where m > n > 0, and its asymptote equations are y = ±x. Determine the axis on which the foci of the hyperbola are located. | The foci of the hyperbola are located on the x-axis. | big_math | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.046875 |
There was a solution in a glass, consisting of 99% water. The glass with the solution was weighed and found to weigh 500 grams. After some water evaporated, the water content became 98%. How much will the glass with the resulting solution weigh if the empty glass weighs 300 grams? | 400 \, \text{grams} | olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 |
There are some baskets of peaches. Each basket has 4 red peaches and a certain number of green peaches. There are a total of 7 peaches in all baskets, and there is 1 basket of peaches. How many green peaches are in each basket? | 3 | orca_math | [
"Mathematics -> Algebra -> Prealgebra -> Simple Equations"
] | 0.984375 |
There are 1,895 trees in the park, 63.5% of which are pine trees. How many are not pine trees? | 692 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.328125 |
Gloria has a certain number of dimes and quarters in her graduation money. She decides to put 2/5 of the quarters aside for future use. She has 350 dimes. After putting aside 2/5 of the quarters, she has a combined number of 392 quarters and dimes. What is the ratio of the number of dimes to the number of quarters she ... | 25:3 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.5625 |
Janet has 1/3 of a bottle of rose shampoo and 1/4 of a bottle of jasmine shampoo. If she uses 1/12 of a bottle of shampoo per day, how many days will her shampoo last? | 7 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.96875 |
Calculate $(-3)^n + 2(-3)^{n-1}$ | -(-3)^{n-1} | cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.90625 |
The sum of the coefficients in the expansion of the binomial $$(3x - \frac{1}{2 \cdot 3x})^n$$ is $\frac{1}{64}$. Find the constant term in the expansion. | -\frac{5}{2} | cn_k12 | [
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.03125 |
Billy had some Lemon Heads. He gave equal numbers of Lemon Heads to his 6 friends, and each person ate 12 Lemon Heads. How many Lemon Heads did Billy have initially? | 72 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.484375 |
How many solutions does the equation sin(2θ) - cos(2θ) = √6/2 have in the interval (-π/2, π/2)? Express your answer as a whole number. | 4 | big_math | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.09375 |
Given that the first three terms of the arithmetic sequence $\\{a_{n}\\}$ are $a-1$, $2a+1$, and $a+4$, find the value of $a$. | \frac{1}{2} | cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.65625 |
Given a geometric sequence \(\left\{a_{n}\right\}\) where all terms are positive, \(a_{1}=2\) and \(a_{8}+a_{10}=16\left(a_{4}+a_{6}\right)\). Another sequence \(\left\{b_{n}\right\}\) satisfies the relation \(a_{1} b_{1}+a_{2} b_{2}+\cdots+a_{n} b_{n}=(n-1) \cdot 2^{n+1}+2\) for any positive integer \(n\). Find the va... | 2 - \frac{n+2}{2^n} | olympiads | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Sequences and Series -> Other"
] | 0.0625 |
The distance from point $P$ in the fourth quadrant to the $x$-axis is $5$, and to the $y$-axis is $3$. The coordinates of point $P$ are ______. | \left(3,-5\right) | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.515625 |
What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{1050}$ is defined? | 11 | math | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 0.90625 |
Jack, who weighs a certain amount, wants to play on the see-saw with his cousin Anna, who weighs 40 pounds. To make their weights equal, Jack needs to hold 5 4-pound rocks. How much does Jack weigh? | 20 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.421875 |
A cubic function $f(x)$ has a local maximum value of 4 when $x=1$ and a local minimum value of 0 when $x=3$. Additionally, the graph of the function passes through the origin. Find $f(x)$. | x^3 - 6x^2 + 9x | cn_k12 | [
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.234375 |
Given that the area of a sector is 2 cm² and the central angle of the sector in radians is 4, find the perimeter of the sector. | 6 cm | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.84375 |
The domain of the function $f \left(x\right)=\frac{1}{x+1}+\ln x$ is ____. | \{x | x > 0\} | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.15625 |
Given that the infection rate of the novel coronavirus in a certain foreign country is $0.5\%$, and the probability that a citizen is infected with the novel coronavirus and the specimen tests positive is $99\%$. If all citizens in that area participate in nucleic acid testing, then the probability that a citizen in th... | 0.495\% | cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0.53125 |
If a die is rolled 500 times, what is the most probable number of times that the face showing 1 dot will appear? | 83 | olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Other"
] | 0.703125 |
Given segments \( a \) and \( b \) (\( a > b \)). Construct a segment of length \( \frac{a^2 + b^2}{a - b} \) using a compass and straightedge. | AG = \frac{a^2 + b^2}{a - b} | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.484375 |
The simple interest on a certain sum of money for 2 years at 4% per annum is half the compound interest on a certain amount for 2 years at 10% per annum. The sum placed on simple interest is Rs. 5250. What is the amount placed on compound interest? | 2000 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 |
Solve the inequality group: $-9 \lt 2x-1\leqslant 6$. | -4 \lt x \leqslant 3.5 | cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.203125 |
Statement: The negation of "There exists an $x_0 \in \mathbb{R}$ such that $x_0^2 - x_0 + \frac{1}{4} \leq 0$" is _______ . | \forall x \in \mathbb{R}, x^2 - x + \frac{1}{4} > 0 | cn_k12 | [
"Mathematics -> Discrete Mathematics -> Logic -> Other"
] | 0.703125 |
If the inequality \(\frac{y}{4} - \cos^2 x \geq a \sin x - \frac{9}{y}\) holds for all positive real numbers \(x\) and \(y\), then what is the range of the real number \(a\)? | [-3, 3] | olympiads | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125 |
A polygon with $n$ ($n \geq 4$) sides has all its exterior angles equal and the degree of each angle is an odd number. How many such polygons are there? | 5 | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 0.140625 |
If the ratio of the corresponding heights of two similar triangles is 2:3, and the sum of their perimeters is 50cm, then the perimeters of these two similar triangles are \_\_\_\_\_\_. | \text{20cm, 30cm} | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Similarity"
] | 0.75 |
Juan rolls a fair regular octahedral die marked with the numbers 1 through 8. Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3? | \frac{1}{2} | math | [
"Mathematics -> Applied Mathematics -> Probability -> Other"
] | 0.375 |
400 adults and 200 children go to a Broadway show. The price of an adult ticket is twice that of a child's ticket. What is the price of an adult ticket if the total amount collected is $16,000? | \$32 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.90625 |
Carrie is wrapping three birthday presents. One present needs 2 square feet of wrapping paper to cover. The second present needs a certain fraction of that amount. The third present needs the same amount as both other presents put together. Carrie needs 7 square feet of wrapping paper for all three presents. What is th... | 1 : (4/3) | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 |
Kaleb had sixty-seven cherries. After eating some, he had a certain number of cherries left. Kaleb ate 25 cherries. How many cherries did Kaleb have left? | 42 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
The sum of 49 natural numbers \(a_{1}, a_{2}, \cdots, a_{49}\) is 999. Let \(d\) be the greatest common divisor (GCD) of \(a_{1}, a_{2}, \cdots, a_{49}\). What is the maximum value of \(d\)? | 9 | olympiads | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 0 |
A square piece of paper is folded in half vertically. The folded paper is then cut in half along the dashed line. Three rectangles are formed - a large one and two small ones. Calculate the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle. Express your answer as a simplified... | \frac{3}{4} | big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.078125 |
Frieda the frog begins a sequence of hops on a $3 \times 3$ grid of squares, moving one square on each hop and choosing at random the direction of each hop-up, down, left, or right. She does not hop diagonally. When the direction of a hop would take Frieda off the grid, she "wraps around" and jumps to the opposite edge... | $\frac{25}{32}$ | harp | [
"Mathematics -> Applied Mathematics -> Probability -> Other"
] | 0 |
A wheel rotates a certain number of times every minute and moves 20 cm during each rotation. The wheel moves 120000 cm in 1 hour. How many times does the wheel rotate every minute? | 100 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.96875 |
Find all triples of complex numbers $(x, y, z)$ for which $$ (x + y)^3 + (y + z)^3 + (z + x)^3 - 3(x + y)(y + z)(z + x) = x^2(y + z) + y^2(z + x ) + z^2(x + y) = 0 $$ | (x, y, z) such that x + y + z = 0 and xyz = 0 | aops_forum | [
"Mathematics -> Algebra -> Other"
] | 0.1875 |
Albert has 35 oranges stored in boxes. If there are 7 boxes, how many oranges must go in each box? | 5 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
Given a sequence \(\{a_n\}\) which satisfies \(a_n = a_{n-1} - a_{n-2}\) for \(n \geqslant 3\), if the sum of its first 1492 terms is 1985 and the sum of its first 1985 terms is 1492, find the sum of its first 2001 terms. | 986 | olympiads | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0 |
A salesman's commission is 5% on all sales up to Rs. 10,000 and 4% on all sales exceeding this. He remits a certain amount to his parent company after deducing his commission. The total sales were Rs. 32,500. How much did he remit to his parent company? | 31,100 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.96875 |
A company that sells keychains has to pay $\mathdollar500$ in maintenance fees each day and then it pays each work $\mathdollar15$ an hour. Each worker makes $5$ keychains per hour, which are sold at $\mathdollar3.10$ each. What is the least number of workers the company has to hire in order to make a profit in... | 126 | aops_forum | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.90625 |
Given $0 < \alpha < \frac{\pi}{2}$, $-\frac{\pi}{2} < \beta < 0$, $\cos(\alpha - \beta) = -\frac{5}{13}$, and $\sin\alpha = \frac{4}{5}$, calculate $\sin\beta$. Express your answer as a fraction. | -\frac{56}{65} | big_math | [
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0 |
Nancy takes 3 antacids per day when she eats Indian food, 2 antacids per day when she eats Mexican food, and 1 antacid per day otherwise. If Nancy eats Indian three times a week and Mexican twice a week, how many antacids does she take per month? | 60 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.671875 |
Two runners are competing in a 10-mile race. The first runs at an average pace of 8 minutes per mile, while the second runs at an average pace of 7 minutes per mile. At some point, the second runner stops for a drink of water. The second runner could remain stopped for 8 minutes before the first runner catches up with ... | 56 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375 |
Write the canonical equations of the line.
\(6x - 7y - z - 2 = 0\)
\(x + 7y - 4z - 5 = 0\) | \frac{x - 1}{35} = \frac{y - \frac{4}{7}}{23} = \frac{z}{49} | olympiads | [
"Mathematics -> Geometry -> Other"
] | 0.0625 |
Eugene, Brianna, and Katie are going on a run. Eugene runs at a rate of 4 miles per hour. If Brianna runs $\frac{2}{3}$ as fast as Eugene, and Katie runs $\frac{7}{5}$ as fast as Brianna, how fast does Katie run? | \frac{56}{15} | math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
The acute angle \( A \) of rhombus \( A B C D \) is \( 45^{\circ} \), and the projection of side \( A B \) onto side \( A D \) is 12. Find the distance from the center of the rhombus to side \( C D \). | 6 | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.09375 |
Calculate the value of the integral $$\int_{0}^{1} \sqrt{1-x^2}\,dx + \int_{1}^{2} \frac{1}{x}\,dx.$$ | \frac{\pi}{4} + \ln{2} | cn_k12 | [
"Mathematics -> Calculus -> Integral Calculus -> Applications of Integrals"
] | 0.9375 |
Let $\overline{z}$ be the conjugate of the complex number $z$. Given that $z + \overline{z} = 3$ and $(z - \overline{z}) = 3i$ (where $i$ is the imaginary unit), find the sum of the real part and imaginary part of $z$. Express your answer as a single number. | 3 | big_math | [
"Mathematics -> Algebra -> Complex Numbers"
] | 0.859375 |
The point $P=(1,2,3)$ is reflected in the $xy$-plane, then its image $Q$ is rotated by $180^\circ$ about the $x$-axis to produce $R$, and finally, $R$ is translated by 5 units in the positive-$y$ direction to produce $S$. What are the coordinates of $S$? | (1,3,3) | math | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 0.296875 |
In the arithmetic sequence $\{a_n\}$, if $a_3 + a_9 + a_{27} = 12$, then find $a_{13}$. | 4 | cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.828125 |
Some chess players take part in a tournament. Every player plays twice with each of his opponents. There are 380 games to be played. How many players are participating in the tournament? | 19 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 |
The ratio of pens to pencils is 5 to 6. There are 7 more pencils than pens. How many pencils are there? | 42 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
Find the maximum value of the function $f(x) = x(4 - x)$, where $x \in (0, 4)$. | 4 | cn_k12 | [
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.953125 |
Given two lines $l_1: x + y + 1 = 0$ and $l_2: x + y - 1 = 0$, find the distance between $l_1$ and $l_2$. | \sqrt{2} | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.890625 |
Leila spent $40 which is 1/4 of her money on a sweater. She was then left with some money after spending the rest of her money on buying pieces of jewelry. Leila spent $60 more on jewelry than on the sweater. How much money was Leila left with after buying the jewelry? | \$20 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.828125 |
A chocolate cake needs 3 eggs per cake. Cheesecake requires a certain number of eggs for each cheesecake. 57 more eggs are needed for 9 cheesecakes than are needed for 5 chocolate cakes. How many eggs are needed for each cheesecake? | 8 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
The function $f(x)=\sin^4x-\cos^4x$, if the inequality $1+\frac{2}{3}f(x)-mf\left(\frac{x}{2}\right)\geqslant 0$ holds for any $x\in \mathbb{R}$, then the range of the real number $m$ is \_\_\_\_\_\_\_\_\_. | \left[-\frac{1}{3}, \frac{1}{3}\right] | cn_k12 | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.03125 |
In the expansion of $\left(3-x\right)^{7}$, the coefficient of $x^{5}$ is ____ (provide your answer as a number). | -189 | cn_k12 | [
"Mathematics -> Algebra -> Intermediate Algebra -> Polynomial Operations"
] | 0.71875 |
Let us call the staircase of height \( n \) a figure consisting of all the cells of an \( n \times n \) square that lie above the diagonal (an example of a staircase of height 4 is shown in the image). How many different ways can the staircase of height \( n \) be divided into several rectangles, the sides of which lie... | 2^{n-1} | olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 |
When toys are grouped into 12 and 18, always 3 toys remain ungrouped. What is the minimum number of toys to be added so that when they are grouped into 7, no toys will remain ungrouped? | 4 | orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.125 |
The units digit of $2^{2012}$ is $\qquad$ . (Where $2^n$ represents $n$ twos multiplied together) | 6 | olympiads | [
"Mathematics -> Number Theory -> Other"
] | 1 |
Given a quadratic function $y=f(x)$ whose graph passes through the origin, and $1 \leqslant f(-1) \leqslant 2$, $2 \leqslant f(1) \leqslant 4$, find the range of $f(-2)$. | [5,10] | cn_k12 | [
"Mathematics -> Algebra -> Algebra -> Quadratic Functions"
] | 0.015625 |
Kelly has 106 Nintendo games. She gives away some games and has 42 games left. How many games did Kelly give away? | 64 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
Given the function $f(x)=\sin \omega x+\cos \omega x (\omega > 0), x\in \mathbb{R}$, if the function $f(x)$ is monotonically increasing in the interval $(-\omega,\omega)$, and the graph of $f(x)$ is symmetric about the line $x=\omega$, then the value of $\omega$ is \_\_\_\_\_\_\_\_. | \frac{\sqrt{\pi}}{2} | cn_k12 | [
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.0625 |
Given a triangular prism \( P-ABC \) where the three face angles at the top vertex are all \( 60^\circ \), i.e., \( \angle APB = \angle BPC = \angle CPA = 60^\circ \), and the areas of the three lateral faces are \( \frac{\sqrt{3}}{2}, 2, \text{and}\, 1 \), find the volume of the triangular prism. | \frac{2 \sqrt{2}}{3 \sqrt{3}} | olympiads | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 0.0625 |
When you divide a certain number by 10, the result is 6. What is the value of the certain number minus 15? | 45 | orca_math | [
"Mathematics -> Algebra -> Prealgebra -> Simple Equations"
] | 1 |
a person is traveling at 25 km / hr and reached his destiny in 5 hr find the distance ? | 125 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
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