role stringclasses 1
value | content stringlengths 80 4.77k | ground_truth stringlengths 0 1.45k |
|---|---|---|
user | What cellular organelles would you expect to be absent from fungi? Please reason step by step, and put your final answer within \boxed{}. | Chloroplast |
user | I need to generate random numbers in $[0,1]$ which are more dense at the end points. Is there a better way than using numbers from $N(0,1)$ and $N(1,1)$? Any command in SAGE will be most helpful! Please reason step by step, and put your final answer within \boxed{}. | Generate random variables \(U_n\) uniformly distributed on (0,1), then use the transformation
\[X_n = \frac{1}{2}(1 + \mathrm{sgn}(2U_n-1) \cdot |2U_n-1|^{\alpha})\]
where \(\alpha < 1\) controls the concentration at the endpoints. If \(\alpha \to 0\), this converges to the uniform Bernoulli distribution on \(\{0, 1... |
user | What is the mass in grams of .000221 mol of carbon? Please reason step by step, and put your final answer within \boxed{}. | 2.652e-3g |
user | Consider an electron near the Earth's equator where the Earth's magnetic field is horizontal and pointing north. In which direction does it (electron) tend to deflect if its velocity is directed downward? Please reason step by step, and put your final answer within \boxed{}. | west |
user | A student is shaking a flexible string attached to a wooden board in a rhythmic manner. Which of the following choices will decrease the wavelength within the rope?
I. The student could shake her hand back and forth with greater frequency.
II. The student could shake her hand back and forth with a greater amplitude.... | b |
user | Suppose a battery output a voltage of 9 volt. Calculate how many joules of energy are imparted to every individual electron moving through this battery? Please reason step by step, and put your final answer within \boxed{}. | 1.44e-18 J |
user | As the number of estimates that you have for p increase, what happens to the distribution of all \hat{p}?
It becomes more Normal.
A. Its center more closely approximates the true population proportion p.
B. Its standard deviation is approximately equal to {eq}\sqrt{\frac{p(1-p)}{n}}
{/eq}
C. All of the above. Plea... | C |
user | Why is the atomic mass of chlorine quoted on the Periodic Table NON-INTEGRAL? Please reason step by step, and put your final answer within \boxed{}. | 35.45 amu |
user | The mean cost of a five pound bag of shrimp is 40 dollars with a standard deviation of 7.
If a sample of 51 bags of shrimp is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 0.6 dollars? Please reason step by step, and put your final answer within \boxed{}. | 0.4595 |
user | A Tevatron can accelerate particles to energies in the TeV range (1.00 terra-eV = {eq}1.00 \times 10^{12}
{/eq} eV). Its circumference is 6.40 km, and in a certain medical experiment, protons will be accelerated to energies of 1.25 MeV and aimed at a tumor to destroy its cells. How fast are these protons moving when t... | 1.54e7 m/s |
user | What is an atheroma made of? Please reason step by step, and put your final answer within \boxed{}. | Cholesterol esters |
user | Calculate the p-value for {eq}\displaystyle H_0: \mu = 20,\ H_a: \mu < 20;\ \bar x = 16.5,\ \sigma = 9.7,\ n = 35 {/eq}. Please reason step by step, and put your final answer within \boxed{}. | 0.0166 |
user | The triangular region with vertices $(0,−1)$, $(1,0)$ and $(0,1)$ is rotated about the line $x=2$. Find the volume of the region so generated. Please reason step by step, and put your final answer within \boxed{}. | 4π∫_1^2 t(t-1)dt |
user | Find the general solution to the differential equation: sin(x)sec(y)dx = dy. Please reason step by step, and put your final answer within \boxed{}. | sin(x) + sin(y) = C |
user | Calcuate the pH of a 0.20 M solution of HCN, Ka = 4.9x10-9. Please reason step by step, and put your final answer within \boxed{}. | 4.50 |
user | What is the probability that, when randomly selecting 4 words from a set of 1000 unique words every day for a period of 7 days, one of the selected words will be repeated more than once? Assume that on a given day, when choosing the 4 four words, there is no replacement on that given day, but the set resets its length ... | $1-\prod_{d=1}^7\prod_{n=1}^4\frac{1000-(n-1)-4(d-1)}{1000-(n-1)}$ |
user | Find the limit: {eq}\lim_{x\to 0} \frac{x^3+x-e^x+1}{\ln(2x+1)} Please reason step by step, and put your final answer within \boxed{}. | 0 |
user | Show complete solutions with its corresponding results.
A 1,200-kg automobile moving at 25 m/s has the brakes applied with a deceleration of 8.0 m/s{eq}^{2}
{/eq}. How far does the car travel before it stops? Please reason step by step, and put your final answer within \boxed{}. | 39 m |
user | Find the work in this Vector field
{eq}F(x, y, z) = (y - x^2) i + (z - y^2) j + (x - z^2) k
{/eq} a particle moving on the curve: {eq}r(t) = i + t^2 j + t^3k, 0 \leq t \leq 1
{/eq}. Please reason step by step, and put your final answer within \boxed{}. | W = (y - x^2) + (z - y^2)\frac{1}{3} + (x - z^2)\frac{1}{4} |
user | Where is most of the energy produced in cellular respiration? Please reason step by step, and put your final answer within \boxed{}. | Electron transport chain |
user | Calculate the mass carbon monoxide, CO, that was needed to produce 78 g of methanol, {eq}CH_3OH,
{/eq} by the following reaction: {eq}2H_2 + CO \to CH_3OH.
{/eq} Please reason step by step, and put your final answer within \boxed{}. | 68 g CO |
user | It takes {eq}\displaystyle \rm 11.2 \ kJ
{/eq} of energy to raise the temperature of {eq}\displaystyle \rm 145 \ g
{/eq} of benzene from {eq}\displaystyle \rm 25 ^{\circ} C
{/eq} to {eq}\displaystyle \rm 70 ^{\circ} C
{/eq}. What is the specific heat of benzene? Please reason step by step, and put your final answe... | 1.72 J/g-°C |
user | Find the derivative of {eq}\displaystyle m(x) = \left(x^{5} - 5x^{3} + 7x - 4\right)^{10} \left(4x^{9} + 19\right)^{23} {/eq} Please reason step by step, and put your final answer within \boxed{}. | \(m'(x)=2 \left(x^5-5x^3+7x-4\right)^9\left(4x^9+19\right)^{22} \left(514x^{13}-2370x^{11}+3038x^9-1656x^8 +475x^4-1425x^2+665\right)\) |
user | How do you show that the kinetic energy is equal to the atoms rest energy when its velocity equals 0.886 times the speed of light? Please reason step by step, and put your final answer within \boxed{}. | 0.866c |
user | What is the mass number of an ion with 107 electrons, 159 neutrons, and a +1 charge? Please reason step by step, and put your final answer within \boxed{}. | 266 |
user | What is the primary evolutionary difference between Anthophyta and Coniferophyta? Please reason step by step, and put your final answer within \boxed{}. | Flowers |
user | I would like to understand how this generic type of BBP formula relates to the famous BBP formula: $$\pi=\sum_{k=0}^\infty \frac1{16^k}\left[\frac4{8k+1}-\frac2{8k+4}-\frac1{8k+5}-\frac1{8k+6}\right]$$ I only understand that $b$ is base $= 16$. The variables I'm not sure about are $n = 8$ and $s = 1$. $P(s,b,n,A) = P(1... | P(1, 16, 8, (4, 0, 0, -2, -1, -1, 0, 0)) |
user | Find the first three non-zero terms of each linearly independent power series solution around {eq}x_0 = 0{/eq} for y{eq}^{n}{/eq}-x{eq}^{-n}{/eq}y=0 Please reason step by step, and put your final answer within \boxed{}. | 0 |
user | Given the Ellipsoid $x^2+4y^2+4z^2\le 4$, how can I calculate its volume using the volume of revolution around the $x$ axis? Please reason step by step, and put your final answer within \boxed{}. | \pi \int_{-2}^2 (4- x^2)dx |
user | A multiple regression model has the form: {eq}\hat y = 8 + 3 x_1 + 5 x_2 - 4 x_3
{/eq}. As {eq}x_3
{/eq} increases by one unit, with {eq}x_1
{/eq} and {eq}x_2
{/eq} held constant, the y on average is expected to
a. Increase by 1 unit.
b. Increase by 12 units.
c. Decrease by 4 units.
d. Decrease by 16 units. Ple... | c |
user | The curve {eq}y = \sqrt[3]{x}{/eq}, {eq}4 \leq y \leq 5{/eq} is rotated about the {eq}y{/eq}-axis. Compute the area of the resulting surface. Please reason step by step, and put your final answer within \boxed{}. | 36,224.13 |
user | Two cars are driving down a straight country road when the driver of the first car (traveling at a speed of 18 m/s) sees a deer crossing the road in front of her. She quickly applies the brake, causing her car to slow down with a (negative) acceleration of 6 m/s{eq}^{2}
{/eq}. The second car is a distance D behind her... | 143.67 m |
user | Compute the nullity of
$\left(
\begin{array}{ccc}
-2 & -5 & 2 \\
-8 & 1 & 6 \\
\end{array}
\right)$. Please reason step by step, and put your final answer within \boxed{}. | 1 |
user | Interpret the magnitude of the gradient vector at a point.
Choose the correct answer below.
A. The direction of steepest ascent at the point.
B. The rate of increase of the function in the direction of steepest ascent at the point.
C. The rate of increase of the function along the level curve at the point.
D. The ... | B |
user | Find the absolute maximum and minimum values of {eq}f(x, y) = x^4 + y^4 - 4xy + 4{/eq} on the set {eq}D = \left \{ (x, y) \mid \; 0 \leq x \leq 3, \; 0 \leq y \leq 2 \right \}{/eq}. Please reason step by step, and put your final answer within \boxed{}. | The absolute maximum of the function is 85 at (3,0) and absolute minimum value is 2 at (1,1). |
user | $$(z+1)^3 = 36(z^*+1)$$ Solve the equation where z is a complex number and z* is the conjugate of z. Please reason step by step, and put your final answer within \boxed{}. | z=-1 or z=2 |
user | A sample of 300.0 g of drinking water is found to contain 38 mg Pb. What this concentration in parts per million? Please reason step by step, and put your final answer within \boxed{}. | 130 ppm Pb |
user | A man pushes a lawn mower on a level lawn with a force of 203 N. If 26% of this force is directed downward, how much work is done by the man in pushing the mower 7.0 m? Please reason step by step, and put your final answer within \boxed{}. | 1372.7 J |
user | Use the squeeze theorem to determine whether the sequence
{eq}\left \{ (-1)^k\dfrac{\cos k}{k^2}\right \}_{k=1}^{\infty}
{/eq} converges or diverges. Please reason step by step, and put your final answer within \boxed{}. | 0 |
user | Determine the capacitance for a cylindrical shell of inner radius r, thickness d, and length L. ({eq}d \ll r
{/eq})
Hint: you can unfold the cylindrical shell and model it as a plane. Please reason step by step, and put your final answer within \boxed{}. | {\frac{2\pi \epsilon_0L}{\ln\left(\frac{r+d}{r}\right)}} |
user | A 1:2:1 phenotypic ratio in the F2 generation of a monohybrid cross is a sign of: Please reason step by step, and put your final answer within \boxed{}. | A |
user | What is the total force on the bottom of a swimming pool 18.0 m by 5.0 m whose uniform depth is 2.2 m? Please reason step by step, and put your final answer within \boxed{}. | 1.94 MN |
user | Let $X$ be a uniform random variable on $(-1 , 1)$ and $Y = \frac{1}{X}$. Find the pdf of the random variable $Y$. Please reason step by step, and put your final answer within \boxed{}. | 1/y^2 |
user | A helium-filled weather balloon has a volume of 683 L at 17.9 {eq}^o
{/eq}C and 754 mmHg. It is released and rises to an altitude of 6.60 km, where the pressure is 395 mmHg and the temperature is -22.1 {eq}^o
{/eq}C. The volume of the balloon at this altitude is _____ L. Please reason step by step, and put your final... | 1120 L |
user | What are the functions of the promoter sequence and the terminator sequence in DNA?
a, b, c, or d? Please reason step by step, and put your final answer within \boxed{}. | a |
user | A tank in the shape of an inverted right circular cone has height 12 meters and radius 16 meters. It is filled with 10 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: The density of hot chocolate is {eq}\rho = 1470~kg/m^3
{/eq}. Please reas... | 120*10^6 J |
user | A heavier person will have a lower blood level due to a greater amount of ___ in their Please reason step by step, and put your final answer within \boxed{}. | water |
user | Compute the rank of
$\left(
\begin{array}{c}
-\frac{19}{6} \\
\frac{16}{3} \\
\frac{3}{2} \\
\end{array}
\right)$. Please reason step by step, and put your final answer within \boxed{}. | 1 |
user | A proton has an initial speed of 4.0 x 10{eq}^{5}
{/eq} m/s.
What potential difference is required to reduce the initial kinetic energy of the proton by a factor of 2? Please reason step by step, and put your final answer within \boxed{}. | 4.2e2 V |
user | How do I show that the fractional part of $n!e$ will stop around 0 or 0.5 when calculating $\lim \sin(2\pi n!e)$? Please reason step by step, and put your final answer within \boxed{}. | 0 |
user | Write the chemical equation for:
{eq}\displaystyle \rm Barium \ chloride + Sulfate \ ions (aq)
{/eq} Please reason step by step, and put your final answer within \boxed{}. | BaCl_2(aq) + SO_4^{2-}(aq) → BaSO_4(s) + 2Cl^-(aq) |
user | How do I find the $\int \dfrac{1}{\sin^6(x)}dx$? What will be the degree of the resultant polynomial and will it be in cotx or tanx? Please reason step by step, and put your final answer within \boxed{}. | $-\frac{\cos(x)\csc^5(x)}{5}+\frac{4}{5}\int\csc^{4}(x)\space\text{d}x$ |
user | Chromium metal crystallizes as body-centered lattice. If the atomic radius of Cr is 1.25 angstroms, what is the density of Cr metal in {eq}g/cm^3?
{/eq} Please reason step by step, and put your final answer within \boxed{}. | 7.30 g/cm^3 |
user | Find the solution of y'' - 4y' + 4y = 648 e^{7t} with y(0) = 5 and y'(0) = 9. Please reason step by step, and put your final answer within \boxed{}. | y= \frac{648}{49}e^{7t} + -83.57x + -8.22 |
user | A particle undergoes uniform circular motion of radius {eq}\rm 15.4 \ \mu m
{/eq} in a uniform magnetic field. The magnetic force on the particle has a magnitude of {eq}\rm 2.25 \times 10^{-17} \ N
{/eq}. What is the kinetic energy of the particle? Please reason step by step, and put your final answer within \boxed{}... | 1.73e-22 J |
user | A bag has 3 coins a, b and c with probability of heads 0.9, 0.6 and 0.5. I flip a randomly drawn coin and get heads. What is the probability that it will come up heads again once re-flipped ? Please reason step by step, and put your final answer within \boxed{}. | (1/3)*0.9 + (1/3)*0.6 + (1/3)*0.5 |
user | Determine if the pair of vectors {eq}\displaystyle
v_1 = \begin{bmatrix} 12 \\3 \\-5 \end{bmatrix}, v_2 = \begin{bmatrix} 2\\ -3\\ 3 \end{bmatrix}
{/eq} are orthogonal. Please reason step by step, and put your final answer within \boxed{}. | 0 |
user | A 79.1 {eq}\mu
{/eq}F capacitor is initially uncharged. After you expend 263 J of energy to charge it up, how much charge does it hold on each plate? Please reason step by step, and put your final answer within \boxed{}. | 0.205 C |
user | Regulatory proteins
A) are influenced by small molecules.
B) bind to specific DNA sites.
C) regulate transcription.
D) regulate transcription, bind specific DNA sites, and can be influenced by small molecules. Please reason step by step, and put your final answer within \boxed{}. | D |
user | How do I solve the stochastic differential equation $dr(t)=a(b-r(t))dt+c dW(t)$ to find $r(t)$, and then evaluate the integral $\int^T_0r(t)dt$, given a starting value $V_0$ and a period of time from $0$ to $T$, so that I can model the final value as $V_T=V_0e^{\int^T_0r(t)dt}$? Please reason step by step, and put your... | r(T)= e^{-aT}r_0+ ab\int_0^T e^{-a(T-t)}dt +c \int_0^T e^{-a(T-t)} dW_t |
user | Find the first four non-zero terms of the Taylor series about 0 for the function {eq}f(x) = \sqrt{1+x} \cos (2x)
{/eq}. Please reason step by step, and put your final answer within \boxed{}. | 1 + x/2 - (17/8)x^2 - (15/16)x^3 |
user | Eric Cartman has stolen a '72 pinto and is cruising down the Colorado parkway at 20 mph. He sees Kenny in the street and slams on the breaks. The tires are worn on Eric's pinto so the car only manages a kinetic friction between the tires and the road of 0.15. How far will it take the car to stop? Please reason step by ... | 26 m |
user | Find the Maclaurin series for {eq}f(x) = 9(1-x)^{-2} {/eq} Please reason step by step, and put your final answer within \boxed{}. | 9(1+2x+3x^2+4x^3+...+(n+1)x^n+...) |
user | A system comprising one mole of an ideal gas at {eq}\displaystyle \rm p1=10 \ bar
{/eq} and volume {eq}\displaystyle \rm 2 \ liters
{/eq} expands isothermally and irreversibly to a final pressure ({eq}\displaystyle \rm p2
{/eq}) of {eq}\displaystyle \rm 5 \ bar
{/eq}. The temperature is {eq}\displaystyle \rm 300 \ ... | 5.762 J/K |
user | An object with a mass of # 8 kg# is traveling in a circular path of a radius of #12 m#. If the object's angular velocity changes from # 15 Hz# to # 6 Hz# in # 5 s#, what torque was applied to the object? Please reason step by step, and put your final answer within \boxed{}. | 13028.8Nm |
user | Consider the titration of 40.0 mL of 0.120 M benzoic acid with 0.120 M NaOH. What is the pH after the addition of 5.0 mL of NaOH? The {eq}K_a
{/eq} of benzoic acid is {eq}6.3 \times 10^{-5}
{/eq}. Please reason step by step, and put your final answer within \boxed{}. | 3.35 |
user | Find the volume of the solid which is above the cone {eq}z = \sqrt{x^2 + y^2} {/eq} and inside the sphere given by {eq}x^2 + y^2 + z^2 = 18 {/eq}. Please reason step by step, and put your final answer within \boxed{}. | 36\pi (\sqrt{2} - 1) |
user | The R groups of amino acids located on the surface of protein molecules in the interior of biological membranes are ...? Please reason step by step, and put your final answer within \boxed{}. | hydrophobic |
user | Which of the following statements regarding the clotting cascade is correct?
A) The intrinsic pathway uses tissue factor to activate prothrombin
B) Both the intrinsic and extrinsic pathways unite to activate prothrombin
C) The intrinsic pathways start when collagen is exposed
D) A and B
E) B and C Please reason st... | E |
user | A man has a mass of 70 kg on the Earth's surface. How far above the surface of the Earth would he have to go to "lose" 13% of his body weight? Please reason step by step, and put your final answer within \boxed{}. | 463038 meters |
user | Use the series for {eq}f(x) = \arctan(x){/eq} to approximate the value of {eq}\arctan\left(\frac{1}{3}\right){/eq}, using {eq}R_N = 0.001{/eq}. (Round your answer to three decimal place.) Please reason step by step, and put your final answer within \boxed{}. | 0.32175 |
user | The position vector of a particle is {eq}\displaystyle r (t) = \langle t^2,\ 5 t,\ t^2 - 16 \rangle
{/eq}. When is the speed minimum? Please reason step by step, and put your final answer within \boxed{}. | t=0 |
user | A 60kg person rides in an elevator to go down to the first floor. As the elevator approaches the first floor, it slows down at rate of 1.2m/s2. Determine the apparent weight experienced by the person while the elevator was slowing down. Please reason step by step, and put your final answer within \boxed{}. | 660 N |
user | Express $\int \sin(x^2)dx$ as a series, given $\sin x = \Sigma_{n = 0}^\infty (-1)^n \frac{x^{2n +1}}{(2n + 1)!}$. Please reason step by step, and put your final answer within \boxed{}. | f(x)=\sum_{n = 0}^\infty (-1)^n \frac{x^{4n +2}}{(2n + 1)!} |
user | Evaluate the integral using U substitution: {eq}\displaystyle \int (\cos^2(x) \sin^2(x))dx. {/eq} Please reason step by step, and put your final answer within \boxed{}. | \frac{x}{8} - \frac{\cos 4x}{32} + c |
user | 1. Which of the following statements are TRUE? Select all that are true.
A. The t distribution gets closer to the standard normal distribution as the degrees of freedom increase.
B. We use the t distribution in confidence intervals for the population mean when the population variance is known.
C. The standard normal... | A, C, F |
user | A seesaw consists of a plank/rod of mass m and length 2x allowed to pivot freely about its center. A small sphere of mass m1 is attached to the left end of the rod and a larger sphere of mass m2 is attached to the right end. The spheres can be considered as point particles. The gravitational force acts downwards. The m... | I = (m/3 + m1 + m2) * x^2 |
user | Phosgene, {eq}\displaystyle
COCl_2
{/eq}, used in the manufacture of polyurethane plastics, is prepared from CO and {eq}\displaystyle
Cl_2
{/eq}. An equilibrium mixture at {eq}\displaystyle
395^\circ C
{/eq} contains 0.012 mol CO and 0.025 mol {eq}\displaystyle
Cl_2
{/eq} per liter, as well as {eq}\displaystyle... | 0.369 M |
user | Find the Taylor polynomial of degree 4 for the function f(x) = x^4 about x=1. Please reason step by step, and put your final answer within \boxed{}. | 1+4(x-1)+6(x-1)^2+4(x-1)^3+ (x-1)^4 |
user | Starting at {eq}t =0
{/eq}, an object at rest is subjected to a force {eq}f(t) = at^3 +bt^2 + et + d{/eq} where {eq}a = 1\tfrac{N}{s^3}, b = 3\tfrac{N}{s^2}, c = 7\tfrac{N}{s}{/eq} , and {eq}d = 13N{/eq}. Find the displacement of the object from its starting location at time {eq}t = 4s
{/eq}. Please reason step by st... | 294 m |
user | What are the three events during sexual reproduction that prevent identical children? Please reason step by step, and put your final answer within \boxed{}. | Independent assortment, crossing over, and random segregation |
user | One coin in a collection of 17 is rigged to have a probability of showing heads equal to 0.8. The rest are fair (probability 0.5). A coin is chosen at random from the lot and tossed 4 times. It turns up heads 4 times in a row. What is the probability that it is the rigged coin given that it showed heads in 4 out of 4 t... | 0.29058 |
user | A particle of mass M = 1.35 kg is subject to force F = 0.850 x, where x is the displacement of the particle from equilibrium. The unit for force F is Newtons, and the units of x are in meters. What is the period T of its motion? Please reason step by step, and put your final answer within \boxed{}. | 7.92 s |
user | How do you express the chemical equation for the ionization of benzoic acid? Please reason step by step, and put your final answer within \boxed{}. | C6H5COOH → C6H5COO- + H+ |
user | Fill in the blank.
The thoracic duct and the right lymphatic duct empty lymph into _____ vessel. Please reason step by step, and put your final answer within \boxed{}. | subclavian blood |
user | A cup with refractive index {eq}n_2
{/eq} = 1.8 has outer radius b = 6.0 cm and inner radius a = 4.0 cm. It is filled with a liquid with refractive index {eq}n_3
{/eq} = 1.3. In the surrounding medium with {eq}n_1
{/eq} = 1.0, a ray of light travels along a trajectory that is at a perpendicular distance y from the c... | 5.2 cm |
user | Four identical charged particles (q = 10.4 C) are located on the corners of a rectangle. The dimensions of the rectangle are: large, L = 59.4 cm and width, W = 16.2 cm.
(a) Calculate the magnitude of the total electric force exerted on one charge located at the lower left corner by the other three charges. Please reas... | 3.81e13 N |
user | Name the phenol with two chlorines, one at the third and one at the fourth positions.
A) 4-pentano
B) pentanol
C) 2-pentanol
D) 2-heptanol Please reason step by step, and put your final answer within \boxed{}. | 3,4-Dichloro phenol |
user | Four balls are suspended by cords. The longer, top cord loops over a frictionless pulley and pulls with a force of magnitude 95 N on the wall to which it is attached. The tensions in the shorter cords are T1 = 56.0 N (between ball A & B), T2 = 46.7 N (between ball B & C), and T3 = 9.3 N (between ball C & D).
a. What a... | m_D = 0.95 kg, m_C = 3.82 kg, m_B = 0.95 kg, m_A = 3.98 kg |
user | At 7.0°C, the volume of a gas is 49 mL. At the same pressure, its volume is 74 mL at what temperature? Please reason step by step, and put your final answer within \boxed{}. | 423K |
user | Find an equation of the tangent plane to G(u,w) = \sin(uw) at the point (\frac \pi 6, 1). Please reason step by step, and put your final answer within \boxed{}. | 1/2 + sqrt(3)/2(u-pi/6) + (pi*sqrt(3))/12(w-1) |
user | What is the net yield of ATP when each of the following substrates is completely oxidized to CO2 via glycolysis, the citric acid cycle electron transport, and oxidative phosphorylation using the glycerol 3-phosphate shuttle?
(a) pyruvate Please reason step by step, and put your final answer within \boxed{}. | 12.5 |
user | The solubility of CO2 in water at 0 C and 1 atm is 0.335 g/100 g of H2O. At 20 C and 1 atm, the solubility of CO2 in water is 0.169 g/100 g of H2O.What volume of CO2 would be released by warming 750 g of water saturated with CO2 from 0 C to 20 C? Please reason step by step, and put your final answer within \boxed{}. | 0.681 L |
user | How do we represent the ionization of lithium? Please reason step by step, and put your final answer within \boxed{}. | Li(g) rarr Li(g)^+ + e^- |
user | Use POM for windows' least squares-linear regression module to develop a relationship to forecast the yearly maintenance cost based on the age of a tractor, given the following data:
Age (year) Yearly Maintenance Cost($) Age (years) Yearly Maintenance Cost ($)
6.5 819 8.0 1,394
5.5 1,249 2.5 363
6.5 1,233 2.5 382
7.0 ... | ŷ = 423.49+103.88(x) |
user | Find the area of the surface generated when the curve {eq}y = \displaystyle \frac{1}{18} \left ( e^{9x} + e^{-9x} \right ){/eq} on {eq}[-4,4]{/eq} is revolved around the x-axis. Please reason step by step, and put your final answer within \boxed{}. | \frac{e^{-72}(e^{144}+144e^{72}-1)\pi}{162} |
user | Which type of randomness can be fully described by a probability distribution?
a) Risk
b) Uncertainty
c) Both of the above
d) None of the above Please reason step by step, and put your final answer within \boxed{}. | a |
user | If {eq}\displaystyle \rm 1.10 \ moles \ of \ P_4O_{10}
{/eq} were used in the equation
{eq}\displaystyle \rm P_{4}O_{10} + H_2O \to H_2PO_4
{/eq}
How many grams of {eq}\displaystyle \rm H_2PO_4
{/eq} would be produced?
Explain? Please reason step by step, and put your final answer within \boxed{}. | 431 g H3PO4 |
user | A bullet of mass 6 g is fired into the bob of a ballistic pendulum of mass 2.25 kg. When the bob is at its maximum height, the strings make an angle of 45{eq}^{\circ}
{/eq} with the vertical. The length of the pendulum is 1.9 m.
Find the speed of the bullet. The acceleration due to gravity is 9.81 m/s{eq}^{2}
{/eq}.... | 63.95 m/s |
user | Imagine $X$ and $Y$ are the times at which two components in a system fail. There's some probability $p$ that they fail at the same time and $1-p$ that they fail at different times. If they fail simultaneously with pdf $f(x)$ and fail at different times with pdf $g(x,y)$, then from what I understand, the joint distribu... | $F(x,y) = p F_1(min(x,y)) + (1-p) G(x,y)$ |
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