unique_id stringlengths 2 7 | problem stringlengths 9 11.6k | answer stringlengths 0 2.49k | answer_type stringclasses 11
values | category stringclasses 16
values | difficulty stringclasses 5
values |
|---|---|---|---|---|---|
452801 | Let $M$ be a relatively compact differentiable manifold equipped with a Riemannian metric and the Levi-Civita connection $\nabla$. Assume that every couple of points in $M$ are linked by one geodesic of minimal length. Let $x, x', y$ be three points of $M$. If $\overrightarrow{xy}$ denotes the initial velocity vector o... | $E \le C(n)(1 + \max(d, d')\max(|H_K(d)|, |H_K(d')|))d(x, x')$, where $d = d(x, y), d' = d(x', y)$, and $H_K(r)$ is the mean curvature of the sphere of radius $r$ in the space of constant curvature $K$. | Expression | Mathematics | PhD |
1052779 | True or false? The marginal product of labor (MPL) is at its maximum when APL = MPL. | False | Boolean | Economics | University |
371909 | What energy is used in cellular respiration? | ATP | String | Biology | Senior High School |
1039113 | What mistakes have I made in calculating the gradient of the function $\psi(t) = \frac{1}{2} \ln det\left(-\frac{\Omega(t)^{-1}}{2}\right)$ where $\Omega(t)$ is a symmetric matrix semi-definite positive of size $k$, and what is the correct solution (specifically case (1))? | -\frac{1}{2} \Omega(t)^{-1} | Expression | Mathematics | University |
767538 | The wavelength of a nonrelativistic electron is 3.970e-6 m. How fast is it moving? Express your answer as a fraction of the speed of light. | 6.11e-7 c | Float | Physics | University |
2007361 | A long solenoid of {eq}\displaystyle \rm n
{/eq} turns per unit length carries a current {eq}\displaystyle \rm I
{/eq}, and a long straight wire lying along the axis of this solenoid carries a current {eq}\displaystyle \rm I
{/eq}. Find the net magnetic field within the solenoid, at a distance {eq}\displaystyle \rm ... | μ_0nI | Expression | Physics | University |
1299836 | A mass of 2.3 kg of air at 160 kPa and 12{eq}^o{/eq}C is contained in a gas-tight, frictionless piston-cylinder device. The air is now compressed to a final pressure of 635 kPa. During the process, heat is transferred from the air such that the temperature inside the cylinder remains constant.
Calculate the workinput ... | 259.32 kJ | Float | Physics | University |
1051307 | Investment is equal to all purchases of newly produced capital goods
a. minus changes in business inventories.
b. plus fixed investment minus inventory investment.
c. plus changes in business inventories.
d. plus changes in business inventories plus purchases of new residential housing | d | Multiple Choice | Economics | University |
1877621 | Everything else held constant, if the expected return on RST stock declines from 12 to 9 percent and the expected return on XYZ stock declines from 8 to 7 percent, then the expected return of holding RST stock __________ relative to XYZ stock and demand for XYZ stock __________.
A) rises; rises
B) rises; falls
C) f... | C | Multiple Choice | Finance | University |
712128 | Ni{eq}^{2+}
{/eq} can be analyzed by back titration using standard Zn{eq}^{2+}
{/eq} at pH 5.5 with xylenol orange indicator. A solution containing 25.00 mL of Ni{eq}^{2+}
{/eq} in dilute HCl is treated with 25.00 mL of 0.05283 M Na{eq}_2
{/eq}EDTA. The solution is neutralized with NaOH, and the pH is adjusted to 5... | 0.03664 M | Float | Chemistry | University |
759830 | What is the net reaction for the nuclear decay chain of #"U"-234#? | "_92^234U → _82^206Pb + 7_2^4He + 4_-1^0e" | Expression | Chemistry | Senior High School |
487227 | Ballina Beaches Pty Ltd. has two products, Shelly Beach Fantasy and Lighthouse Joy. Present revenue, cost and sales data on the two products are:
Shelly Beach Fantasy
Lighthouse Joy
Selling price per unit
$10
$50
Variable cots per unit
8
20
Numb... | Contribution margin income statement
| Particulars | Shelly Beach Fantasy | Proportionate % | Lighthouse Joy | Proportionate % | Total | Total % |
|---|---|---|---|---|---|---|
| Sales revenue | $150,000.00 | 37.50% | $250,000.00 | 62.50% | $400,000.00 | 100.00% |
| Less: Variable costs | $120,000.00 | 54.55% | $100,0... | Matrix | Business | University |
2104082 | A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15{eq}^o
{/eq}, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end.
What is the linear speed of the sphere when it reaches the bottom of the ramp? (Take g = 9.8 {eq}m/s^2
{/eq}) | 4.1 m/s | Float | Physics | Senior High School |
1989653 | Block A and block B are forced together, compressing a spring with spring constant k = 2500 N/m between them 3.00 cm from its equilibrium length. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded.
a. What are the speeds of block A and block B at this ... | v_a = -7.5 m/s, v_b = 2.5 m/s | List | Physics | Senior High School |
170512 | When I graph the marginal cost function (line) does it always have to start in the y-axis? | no | Boolean | Economics | University |
972952 | Does Kepler's law depend on the mass of an orbiting body? | No | Boolean | Physics | Senior High School |
1520443 | Let $(H, \langle \cdot,\cdot \rangle)$ be a Hilbert space with the induced norm defined by $v \mapsto \|v \| := \big( \langle v, v \rangle \big)^{1/2}$. How can we show that $\| \cdot \|^2$ is strictly convex? | $||\alpha v + (1-\alpha)w||^2 < \alpha ||v||^2 + (1 - \alpha) ||w||^2$ | Expression | Mathematics | University |
658703 | Suppose the following items are taken from the 2017 balance sheet of Windsor, Inc.
Goodwill $4,060
Common stock 6,060
Equipment 1,560
Accounts payable 150
Patents 210
Stock investments (long-term) 3,230
Accounts receivable 1,200
Prepaid rent 230
Debt investments (short-term) 1,300
Retained earnings 6,580
Cash 2,330
N... | Classified Balance Sheet
As of December 31, 2017
Assets
Current Assets
Cash $2,330
Short-term Investments $1,300
Accounts Receivable $1,200
Prepaid Rent $230
Total Current Assets $5,060
Long-term Investments
Stock investments (long-term) $3,230
Property, Plant, & Equipment
Equipment $1,560
Accumulated depreciation-equi... | List | Business | University |
1225713 | The money supply consists of:
(a) Mutual funds plus credit cards
(b) M2 only
(c) M1 and M2
(d) M1 only | c | Multiple Choice | Economics | University |
342826 | Evaluate the integral: {eq}\displaystyle \int_{0}^{2} \sin (x^2) \ dx{/eq}. | {eq}\sqrt{\frac{\pi}{2}}S\left ( \sqrt{\frac{2}{\pi}}2 \right )-\sqrt{\frac{\pi}{2}}S(0){/eq} | Expression | Mathematics | University |
775701 | Research on media violence concludes that
A. there is a circular connection between media violence and aggressive behavior.
B. there is a causal relationship between media violence and aggressive behavior.
C. media violence causes aggression.
D. there is no connection between media violence and aggression. | A | Multiple Choice | Psychology | Senior High School |
719437 | I want to find the eigenvectors of: $$A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{bmatrix}$$ I am interested in where I went wrong in my calculation of the eigenvector associated with eigenvalue 6, and particularly what theoretical hole in my understanding lead me to this wrong answer. | The eigenvectors are e1 = (1, 0, 0), (2/3, 1, 0) and (8/5, 5/2, 1) | List | Mathematics | University |
1430467 | Three particles P, Q and R of masses $0.1$ , $0.2$ and $0.5$ respectively lie on a smooth horizontal table , P is projected towards Q with speed $5$ ,after the collision P rebounds with speed $1$ , then Q collides with R , after the collision R moves with speed $v$ . Given that there is no subsequent collision between ... | 1.6 | Float | Physics | Senior High School |
1239840 | Here are comparative statement data for Duke Company and Lord Company, two competitors. All balance sheet data are as of December 31, 2020, and December 31, 2019.
Duke Company
Lord Company
2020 ($)
2019 ($)
2020 ($)
2019 ($)
Net sales
1,812,000
... | Duke:
Net Sales: 100%
Cost of Goods Sold: 56.30%
Gross Margin: 43.70%
Operating Expenses: 14.90%
Operating Income: 28.80%
Interest Expense: 0.50%
Income Before Taxes: 28.30%
Income Tax Expense: 3%
Net Income: 25.30%
Lord:
Net Sales: 100%
Cost of Goods Sold: 53.20%
Gross Margin: 46.80%
Operating Expenses: 14.10%
Operat... | Percentage | Finance | Senior High School |
1402122 | ________ management is based on the belief that productivity is maximized when organizations are rationalized with precise sets of instructions based on time-and-motion studies. | Scientific Management | String | Business | University |
1414226 | Is an analytic solution possible for the given reaction-diffusion equation in radial coordinates with the specified boundary conditions:
\begin{align} \frac{\partial C(r,t)}{\partial t}&=D\left(\frac{\partial^2 C(r,t)}{\partial r^2}+\frac{1}{r}\frac{\partial C(r,t)}{\partial r}\right)-R C(r,t)\,,\\ \frac{\partial C(r=0... | c(r,t)=\mathcal{L}^{-1}\left\{\frac{I_0(r\sqrt{n^2+s})}{s I_0(\sqrt{n^2+s})} \right\} | Expression | Mathematics | PhD |
1426580 | One ship is sailing South at the rate of 5 knots, and another is sailing East at a rate of 10 knots. At 2 p.m the second ship was at the place occupied by the first ship one hour before. At what time was the distance between the ships not changing? | 1:48 PM | Other | Physics | Senior High School |
667790 | How do you differentiate #y=2^(arcsin(sqrtt))#? | dy/dt=(2^arcsinsqrttln2)/(2sqrt(t-t^2)) | Expression | Mathematics | University |
1138905 | If you are suffering from bilateral periorbital hematoma, what condition do you have? | BLACK EYE or SHINER | String | Health | Junior High School |
964020 | The resistance of the primary coil of a well-designed, 1:10 step-down transformer is 1 Ohm. With the secondary circuit open, the primary is connected to a 12 V ac generator.
The primary current is:
A. essentially zero
B. about 12 A
C. about 120 A
D. depends on the actual number of turns in the primary coil | A | Multiple Choice | Physics | Senior High School |
1636365 | Find the approximate solubility (g/100 g water) of sugar at {eq}60^{\circ}C
{/eq}. | 288.8 g/100 g | Float | Chemistry | Senior High School |
375090 | As idle time gaming, inc.s business and product lines continue to grow, it wants to limit the need to build additional space to house programmers and other personnel who work on new products. the company has strategically decided to adopt ________ so skilled employees can work from remote locations. | telecommuting | String | Business | Senior High School |
279580 | Evaluate the Riemann sum for {eq}f(x) = 1 - \frac{1}{3}x; \quad 2 \leq x \leq 14{/eq}, with six sub intervals, taking the sample points to be left endpoints. | -16 | Integer | Mathematics | University |
1741799 | A toy cannon uses a spring to project a 5.36 g soft rubber ball. The spring is originally compressed by 4.90 cm and has a force constant of 7.95 N/m. When the cannon is fired, the ball moves 15.8 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.0324 N on the ball. Wit... | 1.25 m/s | Float | Physics | Senior High School |
714050 | Calculate a closed interval of $\mathbb{R}$ that contains the roots of $$ x^5 + x^4 + x^3 + x^2 + 1 $$ | [-2, 2] | List | Mathematics | University |
1587193 | Use the Chain Rule to find {eq}\frac{\mathrm{d} z}{\mathrm{d} t} where {eq}z = \cos(x + 8y), \; x = 4t^5, \; y = \frac{9}{t}
{/eq}. | {eq}\frac{\mathrm{d} z}{\mathrm{d} t} = \sin(4t^5 + 72/t)\left( \frac{72}{t^2} - 20t^4 \right){/eq} | Expression | Mathematics | University |
1363240 | What is $\pi_1(\mathbb{R}^3 \setminus (S^1 \vee S^1))$? I would say that the space deformation retracts to a sphere $S^2$ surrounding the missing eight with two sticks stuck in the two loops of the eight. Those sticks can each be closed to form a loop, so that the space would be homotopy equivalent to $S^1 \vee S^2 \ve... | \mathbb{Z} * \mathbb{Z} | String | Mathematics | University |
45652 | ABC Corporation has 40,286 shares outstanding at a market price per share of $31.05. The company has decided to repurchase $106,011 worth of shares.
What will be the new total market value of equity? | $1,144,869.30 | Float | Business | Senior High School |
981403 | How do you integrate ∫e^(5x)cos3x? | 5/34 e^(5x)cos 3x+3/34 e^(5x)sin 3x+C | Expression | Mathematics | University |
1921844 | In solving the initial value problem: dx/dt + x = f(t), x(0) = 5 where f(t) = (0, 0 ≤ t < π, 3cost, t ≥ π), find the Laplace transform Xˆ(s) and hence x(t) | Xˆ(s) = (-3e^{-πs}s+5(s^2+1))/((s+1)(s^2+1)) | Expression | Mathematics | University |
703450 | Evaluate the integral {eq}\int x^2(1-x^2)^{1/2} \,dx | \displaystyle \frac{1}{8} arcsin\left(x\right)-\frac{ \sin(4 \ arcsin\left(x\right))}{32} + C | Expression | Mathematics | University |
227840 | Let the vectors be $(1, 1, 1), (1, x, 2)$ and $(1, 2, x)$. Solve for $x$ such that the vectors form a basis for $\mathbb{R}^3$. The determinant of the matrix formed by these vectors is $x^2 - 2x = 0$, which gives $x = 2$. Is it correct to say that the vectors form a basis when $x \neq 2$? | x ≠ 0 and x ≠ 2 | Expression | Mathematics | University |
122386 | One year ago, the Jenkins Family Fun Center deposited $5,300 in an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $7,100 to this account. They plan on making a final deposit of $9,300 to the account next year. How much will be available when they are rea... | B | Multiple Choice | Finance | University |
618313 | How do you compute ending inventory if given is beginning inventory, purchases, and expenses? | Beginning Inventory + Net Purchases - Cost of Goods Sold (COGS) = Ending Inventory | Expression | Business | Senior High School |
1871761 | the penalties for ignoring the requirements for protecting classified information when using social networking services are _______ when using other media and methods of dissemination? | the same as | String | Computer Science | Senior High School |
209908 | Let $f_i,g_i: [0,1] \rightarrow [0,1]$, where $i=1, \ldots, N$, be continuous functions. Does there exist $y \in [0,1]$ such that $$\sum_{i=1}^N f_i(y) \int_0^1 g_i(x) dx= \sum_{i=1}^N \int_0^1 f_i(x) g_i(x) dx?$$ If the answer is no can you find a counterexample? | No | Boolean | Mathematics | University |
966492 | Which Italian Renaissance painter and inventor lived from 1452-1519? | Leonardo da Vinci | String | History | Junior High School |
1636256 | Aspirin (acetylsalicylic acid, {eq}C_9H_8O_4
{/eq}) may be formed from salicylic acid ({eq}C_7H_6O_3
{/eq}) and acetic acid ({eq}CH_3COOH
{/eq}) as follows:
{eq}C_7H_6O_3(aq)+CH_3COOH(aq) \rightarrow C_9H_8O_4(s) +H_2O(l)
{/eq}.
How many grams of acetic acid are required to react completely with {eq}9.37 \times 1... | 5.63*10^4 g | Float | Chemistry | Senior High School |
1666568 | The comparative balance sheet of Flack Inc. for December 31, 2014, and 2013, is as follows:
Dec. 31, 2014 Dec. 31, 2013
Assets
Cash $ 203,160 $ 192,610
Accounts receivable (net) 74,86068,680
Inventories211,000202,880
Investments078,940
Land108,1500
Equipment230,580181,560
Accumulated depreciation-equipment(54,800)... | Cash Flows From Operating Activities
Cash received from customers: $1,276,600
Cash payments for merchandise: $790,370
Cash payments for operating expenses: $421,700
Cash payments for income tax: $33,190
Net cash flow from operating activities: $31,340
Cash Flows From Investing Activities
Cash received from sale of inv... | List | Business | University |
1572295 | Find a unit vector that is orthogonal to both
{eq}\displaystyle{
\begin{alignat}{3}
\vec u &=&& \; \hat i + 2 \hat k, \\
\vec v &=&& \; \hat i - 2 \hat j + 3 \hat k.
\end{alignat}
}
{/eq} | < -4/sqrt(21), 1/sqrt(21), 2/sqrt(21) > | List | Mathematics | University |
97706 | List the following structures in order from smallest to largest:
a. Protein.
b. Bacterial cell.
c. Atom.
d. Human muscle cell.
e. Ribosome.
f. Nucleus.
g. Human epithelial cell. | c. Atom, a. Protein, e. Ribosome, f. Nucleus, b. Bacterial cell, g. Human epithelial cell, d. Human muscle cell | List | Biology | Senior High School |
475677 | When stock is exchanged for noncash assets,
A. debit the asset for prior book value and credit Common Stock for cash received.
B. debit assets for market value and credit Common Stock for par value; if needed, credit Paid-In Capital in Excess of Par.
C. debit assets for market value and credit Common Stock for market v... | B | Multiple Choice | Business | University |
982614 | Let {eq}f(x) = \left\{\begin{matrix}
\sin x & x \lt 0\\
1 - \cos x & 0 \leq x \leq \pi \\
\cos x & x \gt \pi
\end{matrix}\right.
{/eq}
Identify values for {eq}c
{/eq} for which {eq}\lim_{x \rightarrow c} f(x)
{/eq} is not continuous. | x=pi | Expression | Mathematics | University |
1702798 | A buffer solution is composed of 1.360 g of KH{eq}_2
{/eq}PO{eq}_4
{/eq} and 5.677 g of Na{eq}_2
{/eq}HPO{eq}_4
{/eq}. What is the pH of the buffer solution? | 7.8015 | Float | Chemistry | University |
301084 | Which of the following is not a characteristic of data that can strongly affect cluster analysis?
a. Size
b. Spareseness
c. Skewness
d. Scale | c | Multiple Choice | Computer Science | University |
201973 | How much invested now at 9% would be sufficient to provide three payments, with the first payment in the amount of $29,000 occurring two years, then $36,000 five years, and finally $43,000 seven years? | $71,328.49 | Float | Finance | University |
1245239 | I am trying to non-dimensionalise the following equations:
\begin{align} \frac{dx}{dt} &= k_1A-k_2Bx+k_3x^2y-k_4x \tag{1} \\ \frac{dy}{dt} &= k_2Bx-k_3x^2y \tag{2} \end{align} to get this result \begin{align} \frac{du}{dT} &= 1-(b+1)u+au^2v \tag{3} \\ \frac{dv}{dT} &= bu-au^2v \tag{4} \end{align} where $x$ and $y$ corr... | a = (k_1^2 * k_3 * A^2) / k_4^3 and b = (k_2 * B) / k_4 | Expression | Mathematics | University |
1500080 | What came before medieval art? | Classical art | String | History | Junior High School |
815834 | Given {eq}w = xe^{y/z}, x = t^9, y = 4 - t, z = 3 + 6t{/eq}, use the Chain Rule to find {eq}\frac{\mathrm{d} w}{\mathrm{d} t}{/eq} | {eq}\frac{\mathrm{d} w}{\mathrm{d} t}=9t^8e^{y/z}-\frac{xe^{y/z}}{z}-\frac{6xe^{y/z}}{z^2}{/eq} | Expression | Mathematics | University |
1594563 | Determining the present value of bonds payable and journalizing using the effective-interest amortization method:
Spa, Inc. is authorized to issue 11%, 10-year bonds payable. On January 1, 2016, when the market interest rate is 12%, the company issues $600,000 of the bonds. The bonds pay interest semiannually.
Prepar... | Date Interest Payment Interest Expense Discount Amortization Carrying Value
Jan 1, 2016 565,590
Jun 30, 2016 33,000 33,935 935 566,526
Dec 31, 2016 33,000 33,992 992 567,517 | List | Business | University |
962136 | What is the expected number of samples that do not appear in a bootstrap sample of size B drawn with replacement from a dataset of n samples? | (n-1)^B / n^(B-1) | Expression | Mathematics | University |
459679 | A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 6.04 m per s. The car is a distance {eq}d
{/eq} away. The bear is 28.8 m behind the tourist and running at 7.26 m per s. The tourist reaches the car safely. What is the maximum possible value for {eq}d
{/eq}? | 142.584 m | Float | Physics | Senior High School |
2010871 | Evaluate the integral by converting to polar coordinates: {eq}\displaystyle \int_0^2 \int_0^{\sqrt {4 - x^2}} \sin {\sqrt {x^2 + y^2}} dy dx{/eq} | 0.87\pi | Expression | Mathematics | University |
1214855 | Balance the following redox in acidic media
{eq}\displaystyle
{\text{C}_2\text{O}_4}^{2-}\text{(aq)}\quad +\quad {\text{MnO}_4}^-\text{(aq)} \quad\to\quad \text{CO}_2\text{(aq)} \quad+\quad \text{Mn}^{2+}\text{(aq)}
{/eq} | 2MnO_4^-(aq) + 16H^+(aq) + 5C_2O_4^{2-}(aq) → 2Mn^{2+}(aq) + 8H_2O(l) + 10CO_2(aq) | Expression | Chemistry | Senior High School |
1045193 | Sodium-24 is used to treat leukemia and has a half-life of 15 hours. A patient was injected with a salt solution containing sodium-24. What percentage of the 24Na remained after 48 hours? | 10.88% | Percentage | Chemistry | Senior High School |
1823837 | A psychologist would like to determine whether there is a relation between depression and aging. It is known that the general population averages {eq}\mu = 40
{/eq} on a standard depression test. The psychologist obtains a sample of {eq}N = 36
{/eq} individuals who are all over the age of {eq}70
{/eq}. The average d... | 2.25 | Float | Psychology | University |
984046 | A hollow aluminum shaft having an inner diameter d of 25 mm, calculate the outer diameter D of the shaft. Take applied torque T = 25 kN.m, angle of twist {eq}\phi=5rad {/eq}, modulus of rigidity {eq}G= 29 GPa {/eq}, length {eq}L = 500 mm {/eq}.
Select one:
a. 30.94 mm
b. 33.56 mm
c. 31.92 mm
d. 32.48 mm | b | Multiple Choice | Physics | University |
76943 | Fred Corp. is considering a project that has the following cash flow data. What is the project's IRR?
Year 0 1 2 3
Cash flows-$1000 $425 $425 $425 | 13.206% | Percentage | Business | University |
796232 | Danielle owns a vacation cottage. During the current year, she rented it for $1,500 for 2 weeks, lived in it for 2 months, and left it vacant the remainder of the year. The year's expenses were $6,000 mortgage interest expense, $500 property taxes, $1,500 in utilities, and $2,400 depreciation. As a consequence of the a... | b | Multiple Choice | Economics | Senior High School |
1714607 | An investment promises a return of $8,000 per year at the end of each of the next six years. How much will you be willing to invest today to receive the $8,000 payments and earn a return of 7%? | $38,136 | Float | Finance | University |
849615 | Write the balanced equation for the reaction that occurs when potassium bisulfite solution is reacted with nitric acid. | KHSO3(aq) + HNO3(aq) → KNO3(aq) + SO2(g) + H2O(l) | Expression | Chemistry | Senior High School |
1784118 | Uber Inc purchased a car for $43,100. The car has a salvage value of $2,800 and is estimated to be in use for 150,000 miles. What is the accumulated depreciation at the end of Year 2 assuming mileage used in year 1 was 13,310, year 2 was 16,670, and year 3 was 18,040? | $8,094.60 | Float | Business | Senior High School |
730928 | Recall that {eq}\cosh x = \frac{e^x + e^{-x}}{2}{/eq}. Suppose {eq}\sum_{n=0}^{\infty} a_n x^n{/eq} is the Maclaurin series for {eq}\cosh x{/eq} What is the formula for {eq}a_n{/eq} | $a_n=\frac{1}{(2n)!}$ if $n$ is even, $a_n=0$ if $n$ is odd | Expression | Mathematics | University |
31713 | The aiap is a stand-alone program.
a. true
b. false | a | Multiple Choice | Computer Science | Senior High School |
1538355 | What is the name given to the process of maintaining internal conditions? | Homeostasis | String | Biology | Junior High School |
791100 | For a t-distribution with 1,000 degrees of freedom, 99% of the distribution is within how many standard deviations of the mean? | 2.581 | Float | Mathematics | University |
574716 | Use Hess's Law and the following information to calculate the change in enthalpy for the reaction 2C + H2 -> C2H2? | 227 kJ/mol | Integer | Chemistry | Senior High School |
1486660 | Derive an expression for the vertical position of a projectile in terms of its horizontal position.
This expression is called parametric equation or path equation for the projectile. | y = y_0 + \frac{v_{y,0}}{v_{x,0}} (x - x_0) - \frac{g}{2v_{x,0}^2} (x - x_0)^2 | Expression | Physics | Senior High School |
2068458 | The compound dimethylamine, {eq}\rm (CH_3)_2N
{/eq}, is a weak base when dissolved in water. Write the {eq}\rm K_b
{/eq} expression for the weak base equilibrium that occurs in an aqueous solution of dimethylamine. | Kb = [OH-][(CH3)2NH2+]/[(CH3)2NH] | Expression | Chemistry | Senior High School |
1744297 | Let a function $ f $ be continuous and differentiable for all $ x $, such that it satisfies $$ f ( x + y ) f( x - y ) = f ^ 2 ( x ) \text . $$ Given that $ f ( 0 ) $ is nonzero and $ f ( 1 ) $ is $ 1 $, find $ f $. | $f(x)=f_0^{1-x}$ | Expression | Mathematics | University |
60733 | I have $l$ pairs $(x,y)$ with $x,y \in \{ 1,2,...,n \}$. How many different elements (in $ \{ 1,...n\}$) do we at least see among these pairs (depending on $l$)? | \lceil\sqrt{l}\rceil | Integer | Mathematics | University |
1012697 | A beaker with 170 mL of an acetic acid buffer with a pH of 5.00 is sitting on a benchtop. The total molarity of acid and conjugate base in this buffer is 0.100 M. A student adds 7.70 mL of a 0.470 M HCl solution to the beaker. How much will the pH change? The {eq}pK_a
{/eq} of acetic acid is 4.760. | 0.38 | Float | Chemistry | University |
2090608 | Let $f(x,y)$ be continuous on $Q=\{(x,y)\mid x>0,y>0\}$ and $\iint_Q |f(x,y)|$ converge. $$\int_{0}^{\infty}\int_{0}^{\infty}f(x,y)\, \mathrm{d}x\, \mathrm{d}y \stackrel{?}{=}\int_{0}^{\infty}\int_{0}^{\infty}f(x,y)\, \mathrm{d}y\, \mathrm{d}x$$ Is there any example to show that the equality is wrong? | No | Boolean | Mathematics | University |
827439 | GS Cookie Co. forecast cash receipts for January and February of $9,000 and $10,000, respectively. Cash payments of $4,000 and $55,000 are expected in these two months. GS cookie's Cash balance at the beginning of January was $5,000 a level that it attempts to maintain. At the beginning of the year. GS Cookie has a $13... | d | Multiple Choice | Business | University |
1126225 | You are conducting an experiment inside a train car that may move horizontally along rail tracks. A load is hung from the ceiling on a string. The load is not swinging, and the string is observed to make a constant angle of {eq}45 ^o
{/eq} with the horizontal. No other forces are acting on the load. Which of the follo... | b, h | Multiple Choice | Physics | Senior High School |
522270 | A charge {eq}q_1 = -7\mu C
{/eq} is located at the origin, a second charge {eq}q_2 = 3\mu C
{/eq} at {eq}x_2 = lm
{/eq} and a third charge {eq}q_3 = -3\mu C
{/eq} at the point {eq}x_3 = 2m
{/eq}. Find the potential at {eq}x = 6m
{/eq}. | -11.85*10^3 V | Float | Physics | Senior High School |
196586 | How do you say been in Spanish? | estado | String | Other | Junior High School |
1656825 | A 0.150 T magnetic field B crosses the xy-plane perpendicular to the x-axis and at an angle of 65.0{eq}^\circ {/eq} to the y-axis. A square surface with sides of length 7.00 m lies mainly in the xy-plane, but a 1.50 m section of it at one end is bent 90{eq}^\circ {/eq} in the negative z-direction. What is the total mag... | 5.895 T-m^2 | Float | Physics | University |
1706691 | A student bought $1000 worth of furniture. What is the equivalent annual cost if it is expected to last 10 years and can be sold for $200? Choose all the correct answers
a- (1000-200)(A/F,i,10)+1000i
b- 1000(A/F,i,10)+1000i+200(A/F,i,10)
c- 1000(A/P,i,10)+200(A/F,i,10)
d- 800(A/P,i,10)+200i
e- 1000(A/P,i,10)-200(A... | e | Multiple Choice | Mathematics | University |
715256 | Champion Baker uses specialized oven to bake its bread. One oven costs {eq}\$689,000
{/eq} and lasts about {eq}4
{/eq} years before it needs to be replaced. The annual operating cost per oven is {eq}\$41,000
{/eq}. What is the equivalent annual cost of an oven if the required rate of return is {eq}13 \%
{/eq}? | $272,637.80 | Float | Finance | University |
1324918 | Sketch the level curve of the function {eq}\displaystyle f(x,y) = \frac{x^2}{4}-\frac{y^2}{4} {/eq} for {eq}\displaystyle c=-4,-1,0,1,4 {/eq}. | The level curves are a family of hyperbolas described by the equation {eq}x^2 - y^2 = 4c{/eq}, except the degenerate case where {eq}c = 0{/eq}, which gives a pair of crossed lines described by {eq}y = \pm x{/eq}. | Expression | Mathematics | University |
650250 | $$\lim_{n\to\infty} \sum_{i=0}^n \frac{1}{i+n} $$ | log 2 | Expression | Mathematics | University |
1274481 | Is there an easy and general way to get an analytical solution for the autocorrelation of a signal that is a sum of sinusoids, e.g. $x(t)=Asin(at)+Bcos(bt)$? If we have a larger sum of sinusoids like $x(t)=Asin(at)+Bcos(bt)+Csin(ct)+Dcos(dt)+...$, do I just have to bite the bullet and do the all the algebra, or is ther... | $R_{xx}(\tau)=\frac{1}{2}\sum_{ij}C_iC_jr_{ij}(\tau)$, where
$r_{ij}(\tau) = \begin{cases} cos(a_i\tau) & \text{if $f_i(a_it)=sin(a_it)$ and $f_j(a_jt)=sin(a_jt)$ }\\ cos(a_i\tau) & \text{if $f_i(a_it)=cos(a_it)$ and $f_j(a_jt)=cos(a_jt)$ }\\ sin(a_i\tau) & \text{if $f_i(a_it)=sin(a_it)$ and $f_j(a_jt)=cos(a_jt)$ }\\ -... | Expression | Mathematics | University |
717349 | What are the subatomic particles? | electrons, protons, and neutrons | List | Chemistry | Junior High School |
526014 | How can partial pressure change? | By changing the volume of the container, by changing the molar quantity of the gas in question, or by increasing the temperature | List | Chemistry | Senior High School |
1163790 | What major types of items are reported in the retained earnings statement? | 1. Beginning balance
2. Adjustments
3. Dividends
4. Ending balance | List | Business | University |
59145 | The electric potential outside a living cell is higher than the inside by 0.097 V. How much work is done by the electric force when a sodium ion (charge=+e) moves from the outside to the inside? | 1.55e-20 J | Float | Physics | Senior High School |
1434227 | My best guess is that somehow $$xz + x'y = zy$$ I know that $$A + A'B = A + B$$ but can that be applied here since there is an extra variable? Is there a relevant rule I'm missing? | xz + x'y = xz + x'y + zy | Expression | Mathematics | University |
1816356 | If you're standing on the ground 15 m directly below the center of a spherical water tank containing {eq}\rm 4.0 \times 10^6 \ kg
{/eq} of water, by what fraction is your weight reduced due to the water's gravitational attraction? | 1.1e-7 | Float | Physics | University |
468483 | What agency developed forensic facial reconstruction? | The FBI | String | History | Senior High School |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.