q_nl stringclasses 8
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values | q_fl stringclasses 8
values | header stringclasses 1
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|---|---|---|---|
What is the value of $(26^2 - 24^2 - 10)^2 - 10^2$? | 8000 | theorem math500_arithmetic_987654 : (26^2 - 24^2 - 10)^2 - 10^2 = 8000 := by
sorry | import Mathlib
import Aesop
open BigOperators Real Nat Topology Rat Complex EuclideanGeometry SimpleGraph.Walk Metric Finset Matrix Function ENNReal symmDiff ProbabilityTheory MvPolynomial Multiset intervalIntegral RingHom InnerProductSpace Bornology Classical Equiv Interval Polynomial MeasureTheory List Set Filter
set... |
How many $y$-intercepts does the graph of the parabola $x = y^2 - 4y - 1$ have? | 2 | theorem math500_what_is_asked : 2 = 2.
:= by sorry | import Mathlib
import Aesop
open BigOperators Real Nat Topology Rat Complex EuclideanGeometry SimpleGraph.Walk Metric Finset Matrix Function ENNReal symmDiff ProbabilityTheory MvPolynomial Multiset intervalIntegral RingHom InnerProductSpace Bornology Classical Equiv Interval Polynomial MeasureTheory List Set Filter
set... |
$441+2(21)(19)+361=x$. Solve for $x$. | 1600 | theorem math500_arithmetic_883 :
441 + 2 * 21 * 19 + 361 = 16000 := by
sorry | import Mathlib
import Aesop
open BigOperators Real Nat Topology Rat Complex EuclideanGeometry SimpleGraph.Walk Metric Finset Matrix Function ENNReal symmDiff ProbabilityTheory MvPolynomial Multiset intervalIntegral RingHom InnerProductSpace Bornology Classical Equiv Interval Polynomial MeasureTheory List Set Filter
set... |
The arithmetic mean of 7, 2, $x$ and 10 is 9. What is the value of $x$? | 17 | theorem math500_X : x = 17 :=
by
sorry | import Mathlib
import Aesop
open BigOperators Real Nat Topology Rat Complex EuclideanGeometry SimpleGraph.Walk Metric Finset Matrix Function ENNReal symmDiff ProbabilityTheory MvPolynomial Multiset intervalIntegral RingHom InnerProductSpace Bornology Classical Equiv Interval Polynomial MeasureTheory List Set Filter
set... |
A line is parameterized by
\[\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 8 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \end{pmatrix}.\]The equation of the line can be expressed in the form $y = mx + b.$ Enter the ordered pair $(m,b).$ | \left( \frac{3}{2}, -13 \right) | theorem math500_analyses_63 :
(m, b) = (3/2, -13) := by
sorry | import Mathlib
import Aesop
open BigOperators Real Nat Topology Rat Complex EuclideanGeometry SimpleGraph.Walk Metric Finset Matrix Function ENNReal symmDiff ProbabilityTheory MvPolynomial Multiset intervalIntegral RingHom InnerProductSpace Bornology Classical Equiv Interval Polynomial MeasureTheory List Set Filter
set... |
The smallest distance between the origin and a point on the graph of $y=\frac{1}{2}x^2-9$ can be expressed as $a$. Find $a^2$. | 17 | theorem math500_671 : 17 = 17 := by
sorry | import Mathlib
import Aesop
open BigOperators Real Nat Topology Rat Complex EuclideanGeometry SimpleGraph.Walk Metric Finset Matrix Function ENNReal symmDiff ProbabilityTheory MvPolynomial Multiset intervalIntegral RingHom InnerProductSpace Bornology Classical Equiv Interval Polynomial MeasureTheory List Set Filter
set... |
In the diagram, the three concentric circles have radii of $4,$ $6,$ and $7.$ Three regions are labeled $X,$ $Y,$ or $Z$ below. Of these three regions, what is the difference between the area of the region with the greatest area and the area of the region with the smallest area? Express your answer in exact form.
[asy... | 7\pi | theorem math500_geometry_ConcentricCircles : 7 * 蟺 = 7 * 蟺 := by
sorry | import Mathlib
import Aesop
open BigOperators Real Nat Topology Rat Complex EuclideanGeometry SimpleGraph.Walk Metric Finset Matrix Function ENNReal symmDiff ProbabilityTheory MvPolynomial Multiset intervalIntegral RingHom InnerProductSpace Bornology Classical Equiv Interval Polynomial MeasureTheory List Set Filter
set... |
In the diagram, what is the area of the shaded triangle? [asy]
fill((0,0)--(2,3)--(10,0)--cycle,gray);
draw((0,0)--(10,0)--(10,3)--(0,3)--cycle,linewidth(1));
draw((0,0)--(2,3)--(10,0),linewidth(1));
label("10 cm",(5,3),N);
label("10 cm",(5,0),S);
label("3 cm",(0,1.5),W);
label("3 cm",(10,1.5),E);
draw((0,2.5)--(.5,2.5... | 15\mbox{ cm}^2 | theorem math500_figure_774 : 15 = 15 := by sorry | import Mathlib
import Aesop
open BigOperators Real Nat Topology Rat Complex EuclideanGeometry SimpleGraph.Walk Metric Finset Matrix Function ENNReal symmDiff ProbabilityTheory MvPolynomial Multiset intervalIntegral RingHom InnerProductSpace Bornology Classical Equiv Interval Polynomial MeasureTheory List Set Filter
set... |
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