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 |
|---|---|---|---|---|---|
1650071 | Regard {eq}\displaystyle y {/eq} as the independent variable and {eq}\displaystyle x {/eq} as the dependent variable and use implicit differentiation to find {eq}\displaystyle \frac{dx}{dy}. {/eq} {eq}\displaystyle x^4y^2 - x^3y + 2xy^3 = 0 {/eq} | \frac{dx}{dy} = \frac{x^3 - 2x^4y - 6xy^2}{4x^3y^2 - 3x^2y + 2y^3} | Expression | Mathematics | University |
757821 | What are Germany's main imports? | Germany's main imports are petroleum products, raw metal, industrial machinery, automobiles, and food. | List | Economics | Junior High School |
887560 | Which blood group is best termed as a universal donor? | O- | String | Biology | Senior High School |
1213564 | Overhead applied to jobs during the period was $270,000. Actual overhead costs incurred were$268,000. Budgeted overhead used to calculate the predetermined overhead rate was $275,000. Which of the following is the correct entry to close the Manufacturing Overhead account?
a. Debit - Cost of Goods Sold: 2,000; Credit -... | b | Multiple Choice | Business | University |
27992 | Use the procedures developed in this chapter to find the general solution of the differential equation.
{eq}x^{2}{y}''-6x{y}'+10y=-2x^{4}+3x^{2}
{/eq} | y = c_1x^2 + c_2 x^5 + x^4 - x^2ln(x) | Expression | Mathematics | University |
373713 | In peas, axial (A) flower position is dominant to terminal (a), and tall (L) is dominant to short (l). If a plant that is heterozygous for both traits is allowed to self-fertilize, how many of the offspring would also be heterozygous for both traits? | 1/4 | Fraction | Biology | Senior High School |
343992 | Find the solution to the homogeneous equation (yh) of the differential equation \frac {d^2y}{dx^2} + 4y = 4 \sec 2x \tan 2x subject to the initial conditions y(0) = 3 and y'(0) = -4. | yh(x) = 3cos(2x) - 2sin(2x) | Expression | Mathematics | University |
1787300 | Storr disease isinherited as an autosomal recessive in hobbits. In a certain hobbit population, the frequency of Storr disease is 1%. If the population is assumed to be in Hardy-Weinberg equilibrium with respect to Storr disease, what would be the frequency of the heterozygotes? | 0.18 | Float | Biology | Senior High School |
930873 | Evaluate the following integral: {eq}\int \tan^7 x \sec^3 x dx{/eq} | \frac{\sec^9 (x)}{9} - \frac{3\sec^5(x)}{5} + \sec^4(x)- \frac{\sec^3(x)}{3} +C | Expression | Mathematics | University |
1777993 | This question already has answers here: Natural deduction, Proof $\vdash$ $P\Rightarrow(Q\Rightarrow P)$ (2 answers) Closed 6 years ago. One of the problems in my latest logic homework asks us to prove ⊢B→(A→B) using any of the many rules of natural deduction. I've been at it for several minutes yet can't seem to find ... | B→(A→B) | String | Mathematics | University |
822965 | Evaluate the surface integral {eq}\int \int_C F \cdot dS{/eq} to determine the flux across the surface S given that {eq}F(x,y,z) = xze^y i - xze^y j +zk{/eq} and S is the part of the plane x + y + z = 1 in the first octant and has downward orientation. | 1/6 | Fraction | Mathematics | University |
1867723 | Consider $$h(z)=\sum_{n=1}^{\infty}\frac{(z-2)^n}{n}.$$ Find an expression for $h$ as an elementary function. | Log(3-z) | Expression | Mathematics | University |
2081850 | Why delta(S2O8^-2) = 1/2 initial (S2O3^-2) when the dark color appears? | rate = -delta[S2O8^-2]/delta_t = 1/2 delta[S2O3^-2]/delta_t | Expression | Chemistry | Senior High School |
1271773 | Exercise 5. Consider the path $$f(t) = (\cos 2\pi t, \sin 2\pi t) \times (\cos 4\pi t, \sin 4\pi t)$$ in $S^1\times S^1$. Sketch what $f$ looks like when $S^1\times S^1$ is identified with the doughnut surface $D$. Here, doughnut-shaped surface $D$ in $\Bbb{R}^3$ is obtained by rotating the circle $C_1$ in the $xz$-pla... | h((x,y),(u,v)) = (x(1+u/3),y(1+u/3),v/3) | Expression | Mathematics | University |
172391 | How do you use the limit definition to find the derivative of #f(x)=(x+1)/(x-1)#? | -2/(x-1)^2 | Expression | Mathematics | University |
373435 | Find the eigenvalues of the following matrix:
$\left(
\begin{array}{cc}
0 & 1 \\
-3 & -2 \\
\end{array}
\right)$. | $\lambda = i\sqrt{2}-1$ or $\lambda = -i\sqrt{2}-1$ | List | Mathematics | University |
1090097 | How do you calculate the diameter of the sun with the following information? | 1.394e+9m | String | Physics | Primary School |
293247 | HOW to solve the integral $$\iiint_K \frac{4z}{(1+\frac{(x^2+y^2)}{(x^2+y^2+z^2}} dxdydz$$ with $$r \in [1,2]$$ $$\theta \in [\frac{3 \pi}{4},\frac{7 \pi}{4}]$$ $$\phi \in [0, \frac{\pi}{2}]$$ $$|J| = r^2 \sin \phi$$? | \frac{15 \pi \ln{2}}{2} | Expression | Mathematics | University |
2046973 | Find the Fourier transform of $$\frac{\sin(ax)}{x}$$ for $a >0$. Evaluate $$\int_{-\infty}^{\infty} \cos(kx) \sin(ax) \frac{dx}{x}. $$ | \pi(H(\omega+a)-H(\omega-a)) | Expression | Mathematics | University |
1426911 | How do you integrate ∫ln(sint)cost dt by integration by parts method? | #intln(sint)costdt=sint(ln(sint)-1)+C# | Expression | Mathematics | University |
747870 | Given $Arg(z)=\theta$ if and only if $z=re^{i\theta}$ and $\theta\in(-\pi,\pi]$, $r>0$. For $0<x<1$ and a positive integer $m$, determine $$ Arg\big[\sin((m+1)x\pi) e^{-mx\pi i}\big]$$ given that if $\frac{2k}{m+1}<x<\frac{2k+1}{m+1}$, then $\sin((m+1)x\pi)>0$, so $(\ast)=Arg\big[e^{-mx\pi i}\big]$, and if $\frac{2k+1}... | If $\frac{2k}{m+1} < x < \frac{2k+1}{m+1}$, then $Arg[\sin((m+1)x\pi)e^{-mx\pi i}] = r$ if $r \in [0,\pi)$, and $\pi-r$ if $r \in (\pi,2\pi)$, where $-mx\pi = 2\pi n + r$. If $\frac{2k+1}{m+1} < x < \frac{2k+2}{m+1}$, then $|Arg(z)| + |Arg(-z)| = \pi$. | Expression | Mathematics | University |
964300 | The key to any successful product promotion is selecting the right promotional mix. True False | True | Boolean | Business | Junior High School |
1034921 | When does Johnny Tremain take place? | Summer of 1773 to April 1775 | Other | History | Junior High School |
2022221 | The soot produced by a garbage incinerator spreads out in a circular pattern. The depth {eq}H(r) {/eq}, in millimeters, of the soot deposited each month at a distance of {eq}r {/eq} kilometers from the incinerator, is given by {eq}H(r) = 0.4e^{3r} {/eq}. Write a Riemann sum which approximates the total volume of soot d... | 0.0181 km^3 | Float | Mathematics | University |
417114 | What should the compact & rigorous form of proof or solution look like for a functional equation problem where substituting x=0, y=0 yields f(x)=f(y) and f(x)=g(0), and substituting x=1 & y=1 gives g(x)=f(1+x), and so on, because I found myself stuck between results and not comprehending results very well? | f = g = c, where c is a constant | Expression | Mathematics | University |
895654 | At the beginning of April, Brooke Gable launched a custom computer solutions company called Softways. The company had the following transactions during April.
a. Brooke Gable invested $45,000 cash, office equipment with a value of $4,500, and $28,000 of computer equipment in the company in exchange for common stock.
... | a. Cash 45,000
Office equipment 4,500
Computer equipment 28,000
Common stock 77,500
b. Land 24,000
Cash 4,800
Notes payable 19,200
c. Building 21,000
Cash 21,000
d. Prepaid insurance 6,600
Cash 6,600
e. Cash 3,200
Fees earned 3,200
f. Computer equipment 3,500
Cash 700
Notes payable 2,800
g. Accounts receivable ... | List | Business | University |
1024518 | Springfield Energy Inc bonds are currently trading at $640.45. The bonds have a face value of $1000, a coupon rate of 6% with coupons paid annually, and they mature in 15 years. What is the yield to maturity of the bonds? (Percentage) | 10.24% | Percentage | Finance | University |
1180404 | Main Street Restaurant incurred salaries expense of {eq}\$60,000
{/eq} for 2016. The payroll expense includes employer FICA tax, in addition to state unemployment tax and federal unemployment tax. Of the total salaries, {eq}\$17,000
{/eq} is subject to unemployment tax. The percentages for the taxes are as follows: O... | Date General Journal Debit Credit
2016 FICA Tax Expense 4,590
State Unemployment Tax Expense 952
Federal Unemployment Tax Expense 102
FICA Taxes Payable 4,590
State Unemployment Taxes Payable 952
Federal Unemployment Taxes Payable 102 | List | Business | University |
1811312 | Solve the initial-value problem: √(x² − 49) * dy/dx = 1, x > 7, y(14) = ln(2 + 7√3) | y(x) = ln(x + sqrt(x^2 - 7^2)) + ln((2+7sqrt(3))/(14+7sqrt(3))) | Expression | Mathematics | University |
1022605 | Solve the differential equation: y'' - 4y = e^{-2x} | $y = C_1e^{2x} + C_2 e^{-2x} - \dfrac {x e^{-2x} }{4}$ | Expression | Mathematics | University |
1395070 | How do I solve the differential equation $y''+x^2y=0$ to obtain a solution of the form $\sqrt x\left(AJ_\frac{1}{4}+BJ_{-\frac{1}{4}}\right)$? I am getting an equation $t^2\frac{du}{dt}+t\frac{du}{dt}+(t^2+\frac{5}{64})u$ which does not yield the desired solution. | $ y(x) = \sqrt{x}(AJ_{\frac{1}{4}}(t) + BJ_{-\frac{1}{4}}(t)) $ where $t=\frac{x^2}{2}$ | Expression | Mathematics | University |
392083 | Calcium metal (Ca) can be produced by passing an electric current through molten calcium chloride (#CaCl_2#). Chlorine gas (#Cl_2#) is also formed. What is the balanced equation for this reaction? | CaCl_2(l) +Deltararr Ca(l) + Cl_2(g) | Expression | Chemistry | Senior High School |
783843 | Find an equation of the tangent plane to the parametrized surface at the point corresponding to {eq}u = 2 {/eq} and {eq}v = -2 {/eq}.
Given that {eq}x = 2u^2 {/eq}, {eq}y = -3v^2 {/eq}, and {eq}z = 2u^2 - 3v^2 {/eq}. (Give the answer in the variables {eq}x {/eq}, {eq}y {/eq}, {eq}z {/eq}.)
To normalize the answer, ma... | x + y - z = -24 | Expression | Mathematics | University |
800229 | Use Inverse Form of First Translation Theorem to find {eq}L^{-1}\left\{\frac{5s}{(s-2)^{2}}\right\} {/eq} | 5e^{2t}(1+2t) | Expression | Mathematics | University |
320913 | What is the equivalent pressure of 0.432 atm in units of mm Hg? | 328 mm Hg | Integer | Chemistry | Senior High School |
1288645 | Suppose a company produces two products A and B which have demand functions \begin{gather*} D_{A}=30-P_{A} \\ D_{B}=25-P_{B} \end{gather*} With $P_{A}$ and $P_{B}$ being their prices. If the combined cost function is \begin{gather*} C=x^{2}+2xy+y^{2}+10 \end{gather*} where $x$ denotes number of units of product A and $... | x=5 and y=5 | List | Mathematics | University |
678623 | Can someone explain the formula (for sufficiently nice $f$), $$df^{-1} = df\circ f^{-1}$$ | $d(f^{-1})_{f(p)} = (df_p)^{-1}$ | Expression | Mathematics | University |
678023 | True or false? A brand-name product is more narrowly defined than a product in general and thus has more elastic demand. | True | Boolean | Economics | Senior High School |
34503 | A hiker inspects a tree frog sitting on a small stick in his hand. Suddenly startled, the hiker drops the stick from rest at a height of 1.85 m above the ground and, at the same instant, the frog leaps vertically upward, pushing the stick down so that it hits the ground 0.450 s later.
Find the height of the frog at th... | 1.39 m | Float | Physics | Senior High School |
636901 | Use a 95% confidence interval to investigate whether the filling process is working properly given a sample of 24 bags with an average net weight of 289.7 grams and a sample standard deviation of 5.6 grams, where the bags are labeled with a net weight of 288.5 grams. | (287.3337, 292.066) | List | Mathematics | University |
1950268 | "industry incumbents discourage customers to move to new entrants by __________. " | raising the shifting costs | String | Economics | Senior High School |
602960 | A pulse of electromagnetic radiation is propagating in the +y direction. You have two devices that can detect electric and magnetic fields. You place detector 1 at location (0, -3, 0) m and detector 2 at location (0, 3, 0) m. At time t = 0, detector 1 detects an electric field in the -x direction. At that instant, what... | +z | String | Physics | University |
1724816 | What contains sensory & motor nerves in the brain/body? | peripheral nervous system | String | Biology | Junior High School |
739217 | When was the first shower invented? | 1767 | Integer | History | Junior High School |
1096217 | A piece of metal is composed of atoms. Each atom in the metal contains 29 protons. How is the metal classified? | transition metal | String | Chemistry | Junior High School |
759077 | What are the oxidation numbers in the compound H2O2? | The oxidation number of H is +1. The oxidation number of O is -1. | List | Chemistry | Senior High School |
987122 | When deciding how much of their income to save for retirement, should workers consider the real or the nominal interest rate that their savings will earn? | real interest rate | String | Economics | Senior High School |
1152808 | Given $G(x)=_2F_1(a,b,c;-|x|^2)$ where $x\in \mathbb{R}^n$ and $_2F_1$ is analytic everywhere except at $0, 1, \infty$, does this imply that $G$ is continuous everywhere except when $x=0$ or $|x|^2=1$? | Yes | Boolean | Mathematics | University |
1680682 | Evaluate the integral {eq}\int p^3 \ln p \, \mathrm{d}p {/eq}. | \frac{1}{4} p^3 \ln p - \frac{1}{12} p^3 + C | Expression | Mathematics | University |
1043530 | which type of account typically has a very high liquidity,low or no interest,and low minimum balance? | basic savings account | String | Finance | Junior High School |
1433539 | A local pizzeria raised its price from $9 to $11 for each pizza, and the sales of its pizzas decreased from 150 to 100 per day. What is the price elasticity of demand? | 1.5 | Float | Economics | Senior High School |
1891624 | How many moles are in 24.0 grams of iron? | 0.45 mol | Float | Chemistry | Senior High School |
1735682 | Given $f(x) = \frac{1}{x^2 + a}, a>0$, $g(x) > 0, \forall x \in \mathbb R$, and $g(x)$ is a polynomial of degree $n$, and $h(x)=f(x)g(x)$, what assumptions are needed on the smoothness of $g(x)$ for $h(x)$ to maintain a local maximum/minimum at $x = 0$ even as a local "bump" in the product? | $g'(0) = 0$ | Expression | Mathematics | University |
452352 | Let $f(x)$ be a monotonically decreasing positive function with $y$-intercept $1.$ Which of the following guarantees the volume of the region bounded by rotating $f(x)$ about the $x$-axis is finite?
I. $\sum_{n=0}^{\infty} f(n)< \infty$
II. $\sum_{n=0}^{\infty} (f(n))^2< \infty$
III. $\sum_{n=0}^{\infty} (f(n))^3< \inf... | A | Multiple Choice | Mathematics | University |
2101723 | In Florida, when would you be required to have bodily injury liability insurance?
A) A crash where you collide light post
B) A crash where you collide with a wild animal
C) A crash where your vehicle has caused damage to the property of others
D) A crash where your vehicle receives more than $200 in damages | C | Multiple Choice | Finance | Senior High School |
1854058 | Evaluate the iterated integral: {eq}\int_{0}^{9} \int_{1}^{9} \sqrt{x+4y} \ dx\ dy{/eq} | \frac{1}{15}\left[ 45^{\frac{5}{2}} - 37^{\frac{5}{2}} - 242 \right] | Expression | Mathematics | University |
2070210 | Native and English colonial groups traded many goods and ideas. Identify the goods and ideas Indians shared with the colonists | Furs and animal skins, Native farming techniques, and free and uncultivated land. | List | History | Junior High School |
825828 | Find: {eq}\mathcal{L}(2 - 4t^4 + \cos 3t) | \dfrac{2}{s}-\left (\dfrac{96}{s^{5}} \right )+\dfrac{s}{s^{2}+9} | Expression | Mathematics | University |
750858 | Is the following statement correct? A quintic polynomial in the form:
$$x^5+B x^4+C x^3+D x^2+E x+F,~~~~~B,C,D,E,F \in \mathbb{Q}$$
can be factored into $(x^2+a x+b)(x^3+p x+q)$ over $\mathbb{Q}$ iff:
$$E=BD+\frac{1}{4}(B^2-C)^2-n^2,~~~~~n \in \mathbb{Q}$$
$$F=\frac{1}{2} \left(B^5-B^3C+3B^2D-2BE+CD \color{blue}{\pm} 2... | True | Boolean | Mathematics | University |
1152449 | When a business adopts a strategy of reducing and/or discontinuing production in response to a sustained patter of loses, it is
a) considering opportunity costs
b) considering capital investments
c) preparing to reach its shutdown point
d) preparing to exit operations | c | Multiple Choice | Economics | University |
1833571 | Two years ago, Darlene Darby opened a delivery service. Darlene reports the following accounts on her income statement:
Sales: $69,000
Advertising Expense: $3,500
Salaries Expense: $39,000
Rent Expense: $10,000
These amounts represent two years of revenue and expenses. Darlene asks you how she can tell how much of... | Year 1:
Sales Revenue: $23,000
Advertising Expense: $2,000
Salaries Expense: $15,000
Rent Expense: $5,000
Total Expenses: $22,000
Net Income: $1,000
Year 2:
Sales Revenue: $46,000
Advertising Expense: $1,500
Salaries Expense: $24,000
Rent Expense: $5,000
Total Expenses: $30,500
Net Income: $15,500 | Other | Business | Senior High School |
2080051 | A vertical right-circular cylindrical tank measures 30 ft high and 20 ft in diameter. It is full of kerosene weighing 51.2 lb/ft{eq}^3
{/eq}. How much work does it take to pump the kerosene to the level of the top of the tank? | 7238229 ft⋅lbs | Integer | Physics | University |
1265751 | A metal ring, of Radius R, has a total charge Q distributed uniformly on it. {eq}\left( \sigma =Q/A \right)
{/eq}. We found that the electric field, {eq}E\left( x \right)
{/eq}, at a distance x on the line from the ring center is
{eq}E\left( x \right)=\frac{1Qx}{4\pi {{\varepsilon }_{0}}{{\left( {{x}^{2}}+{{R}^{2}} ... | {eq}{{x}_{m}} = \frac{R}{\sqrt 2 }{/eq} | Expression | Physics | University |
1982100 | Integral of (6x-1)dx/sqrt(x^2+3x+8) | 6sqrt(x^2+3x+8)-(10sqrt23)/23ln(sqrt(4x^2+12x+32)+2x+3)+C | Expression | Mathematics | University |
1961040 | What is the estimate of earnings for a small company with $54 million in sales, given the provided data on sales and earnings for a sample of 12 companies, where sales is the independent variable and earnings is the dependent variable? | 6.40 | Float | Mathematics | University |
948642 | You have just taken out a $20,000 car loan with a 6% APR, compounded monthly. The loan is for five years. When you make your first payment in one month, how much of the payment will go toward the principal of the loan, and how much will go toward interest? | The interest amount paid as a part of the first monthly payment is $100 while the monthly payment amount is $386.66 | Float | Finance | Senior High School |
354324 | Evaluate the following integrals. Simplify as much as possible.
{eq}\int \tan^3 (x) \sec^4 (x) dx | \frac{\sec^6(x)}{6} - \frac{\sec^4(x)}{4} + C | Expression | Mathematics | University |
1258965 | Construct and interpret a 90% confidence interval for the population mean of all tree ring dates from this archeological site given the following years A.D.: 1189 1271 1267 1272 1268 1316 1275 1317 1275. Assume it is known that the population of tree ring dates is normally distributed. | 1249.21 < μ < 1295.23 | Expression | Mathematics | University |
1489281 | Convert 614 cal to J. Only include the numerical value in your answer. | 2568.976 | Float | Physics | Junior High School |
439701 | Use Stokes' Theorem to evaluate {eq}\int_C \mathbf F \cdot \mathbf r{/eq} where {eq}\mathbf F = \langle -y,x,z \rangle{/eq} and {eq}C{/eq} is the curve of intersection of the cylinder {eq}x^2 +y^2 = 1{/eq} and the plane {eq}z = 1{/eq} oriented clockwise when viewed from above. | 2π | Integer | Mathematics | University |
152267 | Calculate the percent yield of aspirin if 4.52 grams of aspirin is produced when 4.95 grams of salicylic acid is reacted with excess acetic anhydride. | 70.1% | Percentage | Chemistry | Senior High School |
533548 | The reason there is danger in exposure to high energy radiation is that the radiation can rupture chemical bonds. In some cases cancer can be caused by it. A C-C single bond has a bond energy of approximately 348 kJ/mol. What wavelength ( in nm) of light is required to provide sufficient energy to break the C-C bond? | 343 nm | Integer | Chemistry | Senior High School |
1014440 | What substance is acting as the Brønsted-Lowry base in the forward reaction below? H2O + HCl yields H3O+ + Cl- | H2O | String | Chemistry | Senior High School |
1847367 | How fast must a meter stick be moving if its length is observed to shrink to 0.55 m? Units are s, m, m/s, degrees, {eq}\text{kg}\text{.m/s} {/eq}, J, and kg show work. | 2.5e8 m/s | Float | Physics | University |
863055 | let $h\colon \mathbb{R} \to [0,\alpha]$ be a nonnegative bounded function. Show that for $0\leq a<\alpha$ that the following holds: \begin{equation} Pr(h(X)\leq a) \geq \frac{E[h(X)]-a}{\alpha-a} \end{equation} | $P[Y\geqslant a]\geqslant\frac{E[Y]-a}{\alpha-a}$ | Expression | Mathematics | University |
581250 | How to calculate the allocation of utilities to the cost of goods sold? | Over(Under) Applied = Applied - Actual costs, where Applied = Predetermined overhead rate * Actual activity level, and Predetermined overhead rate = (Total estimated utility costs)/(Total estimated activity level) | Expression | Business | University |
133428 | How do you express #(x^4+1)/(x^5+6 x^3)# in partial fractions? | #(x^4+1)/(x^5+6x^3) = -1/(36x)+1/(6x^3)+(37x)/(36(x^2+6))# | Expression | Mathematics | University |
1243833 | Solve the following differential equation: $ty' + 2y = \sin(t)$ | y = \frac{C}{t^2} - \frac{\cos t}{t} | Expression | Mathematics | University |
1992916 | Everest inc. is presently enjoying relatively high growth because of a surge in the demand for its new product. Management expects earnings and dividends to grow at a rate of 28% for the next 2 years, 21.90% in years 3 and 4, and after which competition will probably reduce the growth rate in earnings and dividends to ... | $16.29 | Float | Finance | University |
582449 | Robin Corporation, a calendar year taxpayer, has a deficit in current E&P of $200,000 and a $580,000 positive balance in accumulated E&P. If Robin determines that a $700,00 distribution to its shareholders is appropriate at some point during the year, what is the maximum of the distribution that could potentially be tr... | b | Multiple Choice | Business | University |
751708 | The price of burgers increases by {eq}22\%
{/eq} and the quantity of burgers demanded falls by {eq}25\%
{/eq}. This indicates that the demand for burgers is _____. | -1.136 | Float | Economics | Senior High School |
1994707 | Two runners run in a straight line and their positions are given by functions {eq}g(t){/eq} and {eq}h(t){/eq}, where {eq}t{/eq} is the time in seconds, and {eq}g(t){/eq} is the number of meters from the starting point for the first runner and {eq}h(t){/eq} is the number of meters from the starting point for the second ... | g'(t_0) = h'(t_0) | Expression | Mathematics | University |
789023 | Explain the cause-and-effect relationship among the plot events that result in Antigone’s punishment. | Polyneices rebels against Thebes and is killed in battle -> Creon decrees that Polyneices cannot be buried -> Antigone buries Polyneices -> Antigone is arrested and sentenced to death | String | Other | Senior High School |
2102085 | Which acid would be best to use when preparing a buffer with a pH of 4.70?
a. formic acid
b. chloroacetic acid
c. hypobromous acid
d. propanoic acid | d | Multiple Choice | Chemistry | Senior High School |
551210 | How do you say rest in French? | se reposer | String | Other | Primary School |
915139 | Given $c^d \mod n = m$, and values for $d$, $n$, and $m$, how would one solve for $c$? Specifically, $d = 65537$, $n = 152415787532388368909312594615759791673$, and $m = 488569901884183584797299$. | $c = 91214686076077110636849974356599684137$ | Integer | Mathematics | University |
918697 | Which of the following issues relate most to foreign policy | trade, diplomacy, sanctions, military/defense, intelligence, foreign aid, and global environmental policy | List | Other | Senior High School |
1170792 | A train accelerates at 1.28 m/s{eq}^2
{/eq} from rest to a steady speed in 58.43 seconds. It maintains that speed for 25.24 miles and then starts slowing down at 1.58 m/s{eq}^2
{/eq} until coming to a stop at its destination. What is the total distance traveled in meters? | 44575 m | Integer | Physics | Senior High School |
260428 | Tano issues bonds with a par value of $99,000 on January 1, 2015. The bonds' annual contract rate is 6%, and interest is paid semiannually on June 30 and December 31. The bonds mature in three years. The annual market rate at the date of issuance is 8%, and the bonds are sold for $93,809.
Prepare an amortization table... | PeriodInterest Expense (a) b + cInterest Payable (b) (99,000 X 3%)Discount Amortization (c)Carrying Value 93,809.00Period 13,835.172,970865.1794,674.17Period 23,835.172,970865.1795,539.33Period 33,835.172,970865.1796,404.50Period 43,835.172,970865.17 97,269.67Period 53,835.172,970865.17 98,134.83Period 63,835.172,9... | List | Business | University |
1192620 | What is more important in determining the amount of damage an object sustains in a collision? 1. the total momentum change per unit time 2. the total momentum change 3. Both 1 and 2 4. None of these | 1 | Multiple Choice | Physics | Senior High School |
1792699 | Why is there a discrepancy between the two expressions for $c_n$ in the Faà di Bruno formula calculation, specifically between $c_n = \sum_{k=1}^n\sum_{\pi=\left\{B_1,\ldots,B_k\right\}} a_{\left|B_1\right|}\cdots a_{\left|B_k\right|} b_k= \sum_{k=1}^n b_k\, B_{n,k}(a_1,\ldots,a_{n-k+1})$ and $c_n = \sum_{k=1}^{n}\frac... | $c_n = \sum_{k=1}^{n} b_k\, B_{n,k} \big(a_{1}\,a_{2},\,\cdots \, , a_{n-k+1} \big)$ | Expression | Mathematics | PhD |
26028 | What country sent the Zimmermann Telegram note? | The German Empire | String | History | Senior High School |
2029732 | The place where tectonic plates meet is called what? | boundary | String | Other STEM | Junior High School |
506015 | What is the practice of colluding with other firms to control prices known as? | Cartel | String | Economics | Senior High School |
1812098 | Michael is a business tycoon residing in the United States. Over the last five years, he has been funding other countries to manufacture weapons that they would later use to declare a war against the United States. Which crime is Michael committing in the given scenario? | Treason | String | Law | Senior High School |
1230096 | Find the first four non-zero terms of a Taylor series solution, centered at {eq}\displaystyle 0 {/eq}, of the initial value problem {eq}\displaystyle y'= xy + 2y^2, \quad y(0) = 3. {/eq} | y = 3 + 18x + (219/2)x^2 + 660x^3 | Expression | Mathematics | University |
1286316 | Is it possible to improve the upper bound $e^{-\pi y/4}$ for the integral $I(y)=\int_0^\infty x \Gamma(1/2+i (y+x)/2) \Gamma(1/2+i(y-x)/2) dx$, $y>0$, to $e^{-\pi y/2}$? | (π*y^2+4y+8/π)*exp(-πy/2) | Expression | Mathematics | PhD |
231367 | A spelunker is surveying a cave. She follows a passage 170 m straight west, then 230 m in a direction 45 degrees east of south, and then 280 m at 30 degrees east of north. After a fourth unmeasured displacement, she finds herself back where she started. What was the fourth displacement? | 154.8 m, 31.1 degrees south of west | Other | Physics | Senior High School |
3074 | Find the $\ell_2$ norm of the following vector:
$\left(
\begin{array}{c}
\frac{196}{25} \\
-\frac{127}{50} \\
-\frac{471}{50} \\
\frac{8}{5} \\
\frac{421}{100} \\
-\frac{293}{100} \\
-\frac{167}{50} \\
\end{array}
\right)$. | \frac{\sqrt{\frac{983391}{2}}}{50} | Expression | Mathematics | University |
1674613 | If X is a Poisson distribution with parameter (u) and Y|X is a binomial distribution with parameters (n,p), then how do I prove that Y is a Poisson distribution with parameter (pu), using something like the convolution formula? | \frac{e^{-up}(pu)^y}{y!} | Expression | Mathematics | University |
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