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### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The states $|1\rangle,|2\rangle$, and $|3\rangle$ are orthonorma...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Simplify $\frac{\left(\left(\frac{21}{2}+8\right)^2-2\right)-18}...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the eigenvectors of the following matrix (round your answer...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Normalize the following vector $d$: $$ \left( \begin{array}{c} ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the chiral anomaly for a massless Weyl fermion in 2+1 ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Solve for $x$. $\frac {x}{9}+\frac{2}{3}=\frac{7}{3} $" ### Inf...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Some questions on regression and the `lm()` function... Assume ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the expected amplitude $[v]$ and frequency $[v1]$ of gra...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the critical current density of a Josephson junction $[v...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the optimal laser frequency for exciting a Rydberg atom ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A small circular wire loop of radius $a$ is located at the cente...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A quantum communication system using qubits is prone to errors d...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the missing value. $56={?}\times7$ $?=$" ### Information: ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The energy required to remove both electrons from the helium ato...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the standard free energy change of the reaction ATP + ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\begin{aligned} &F(x)=|4x-20| \\\\ &f(x)=F'(x) \end{aligned}$ $...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the minimum amount of enriched uranium-235 required for ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A gas at temperature $T$ is composed of molecules of mass $m$. W...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$ { \left[\begin{array}{r}{4} \\ {-2} \\ {-2}\end{array}\right]-...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the expected rate of dark matter particle detection in a...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A sample of Uranium-238 has an initial activity of 300 $[u]$. If...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\int \sin^3(x)\cos(x)\,= $ $+~C$" ### Information: The convent...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Simplify the following expression and state the condition under ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The circuit shown in the figure above consists of eight resistor...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the energy loss per unit path length of a $5 M[u]$ alpha...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "An incompressible fluid of density $\phi$ flows through a horizo...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The distribution of relative intensity $I$ of blackbody radiatio...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Captain Gabriela has a ship, the H.M.S. Khan. The ship is two fu...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A particle of mass $m$ is confined to an infinitely deep square-...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the greatest common divisor of $\{659,838\}$." ### Informa...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the Hubble parameter for a universe with a scale facto...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Region $R$ is enclosed by the curves $y=x^2$ and $y=4x-x^2$. Wha...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "According to the inflationary universe model, the universe exper...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A physics student is asked to calculate the activity coefficient...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "${18}/{2} = {?}$" ### Information: There are no units and notat...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Which of the following equations is a consequence of the equatio...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\overline{AC}$ is $7$ kg long ${BC}$ is $4$ km long $\overline{...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Express $4.67$ as a mixed number." ### Information: There are n...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Jessica's Furniture Store buys a couch at a wholesale price of $...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\dfrac{d}{dx}\left(\sqrt{x^5}\right)=$" ### Information: The c...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A nuclear fusion reactor safety assessment study has identified ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is $\frac{F(R)}{F(2 R)}$ ?" ### Information: The conventio...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A tank contains $10 [u]$ of nitrogen gas and $6 [u]$ of oxygen g...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find $\frac{x}{y}$ where $x=(3-6i) \log (2)$ and $y=(8-4i) \log ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Two trusses are shown below: | | ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the refractive index of a material if its reflectivity a...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A hovercraft takes off from a platform. Its height (in meters), ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Return up to the first 10 primitive roots of $20369$." ### Info...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Eigenfunctions for a rigid dumbbell rotating about its center ha...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A heat engine operates between a hot temperature source of $400 ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Complete the square to rewrite this expression in the form $(x +...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Ming had $59$ birthday cupcakes. He gave $30$ cupcakes to his cl...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The code chunks below create vectors, and then index them. Below...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the maximum Reynolds number for water flowing through a ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\sum\limits_{k=0}^{{19}}{{{6(1.5)^{k}}}} \approx $" ### Inform...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A tropical punch recipe calls for $300 \text{m}$ of sugar for ev...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Let $f(x, y, z) = z - 3x^2 + 2y^2$ and $g(t) = (2t, \sqrt{2t}, t...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$f(x, y) = (x\sin(y), y^2 e^y)$ $\text{curl}(f) = $" ### Inform...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the curvature of spacetime around a massive spherical ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Write the following system of equations as an augmented matrix. ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The ground-state binding energy of hydrogen is 13.6 electron vol...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Let $y=\log_4(x^3-7x+5)$. Find $\dfrac{dy}{dx}$" ### Informatio...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the output, $y$, when the input, $x$, is $3$. $y = -5x+13$ ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the $\ell_\infty$ norm of the following vector $y$: $$ \lef...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the projection of the first vector $a$ onto the second $b$:...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the energy of a cosmic ray particle that travels through...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the maximum weight that can be lifted by a superconducto...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the dot product of the following two vectors m and n: $\lef...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find $\lim_{x\to\infty}\dfrac{\sin(x)}{2x-3}$. Choose 1 answe...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the dot product of the following two vectors $g$ and $f$: $...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A supersonic aircraft is flying at Mach $2.5$ at an altitude of ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the least squares vector given the matrix $\left( \begin{ar...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Let f be a function defined for all real numbers except for $0$....
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the maximum magnetic field sensitivity of a superconduct...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "In an inertial reference frame $S$, two events occur on the $x$-...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the phonon dispersion relation for a 2D hexagonal lattic...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Which of the following expressions is proportional to the total ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is $\lvert -4.9 \rvert$ ?" ### Information: There are no u...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Which of these numbers is prime? {25, 27, 42, 53, 65}" ### Info...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Determine the mass of a W boson that has a velocity of $0.8c$ an...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$g(x)=\dfrac{8x-1}{x+4}$. $f(x)=3x+10$ Write $(g \cdot f)(x)$ as...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The $5$ points plotted below are on the graph of y=log_b(x). Bas...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Consider a system of $N$ noninteracting particles confined in a ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Without using a calculator, convert the decimal to a simplified ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A rectangular wire loop of length $10 c[u]$ and width $5 c[u]$ i...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the efficiency of a nuclear power plant that produces ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A rectangular block of wood, $6 c[u]$ long, $4 c[u]$ wide and $2...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Three wire loops and an observer are positioned as shown in the ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A gas with an initial pressure $[v]$ of 500 kPa and a temperatur...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the minimum power $[v]$ required for a plasma-based co...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A car of rest length 5w passes through a garage of rest length 4...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "### Sure! How about this question: *** Consider a system with t...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "One of Maxwell's equations is $\nabla \cdot \mathbf{B}=0$." ###...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the minimum uncertainty in the velocity of a tennis ball...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Determine the $n=8$ $40$-gonal number." ### Information: There ...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Expand $\dfrac{-2x-5}{x^2+9x+20}$ using partial fractions." ###...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$g(x)=(3x^5)(6x^4+x)^4$ Find $g'(x)$." ### Information: The con...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Is the following number prime? 35383" ### Information: There ar...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the greatest common divisor of complex numbers {711-878j,32...
### Instruction: Using your knowledge and information from "Information", propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Apply the distributive property to create an equivalent expressi...