HanxuHU/raw_15k_reason · Datasets at Hugging Face

id stringlengths 2 7	question stringlengths 15 4.06k	answer stringlengths 0 2.22k	answer_type stringclasses 11 values	category stringclasses 16 values	difficulty stringclasses 5 values
1147723	If I have $y_i=$ $ \begin{cases} 1& w/probability \ p_i \\ 0& w/probability \ 1-p_i \end{cases}$ and $p_i=1-e^{-\alpha x_i}$, i=1,2,... $\alpha>=0$ and $x_i>=0$, and a sample of a single observation $(y_1,x_1)=(0,20)$, what is the maximum likelihood of this sample?	0	Integer	Mathematics	University
1766596	What are the end products of the HYDROLYSIS of a polysaccharide?	glucose molecules	String	Chemistry	Senior High School
1474920	Preston Inc.'s stock has a 25% chance of producing a 30% return, a 50% chance of producing a 12% return, and a 25% chance of producing a -18% return. What is the firm's expected rate of return? a. 7.72% b. 8.12% c. 8.55% d. 9.00%	d. 9.00%	Percentage	Finance	Senior High School
628994	Compute the (pseudo)inverse of $\left( \begin{array}{cc} \frac{19}{7} & -\frac{2}{7} \\ \frac{25}{7} & -\frac{30}{7} \\ \end{array} \right)$.	\frac{7}{520}\left( \begin{array}{cc} 30 & -2 \\ 25 & -19 \\ \end{array} \right)	Matrix	Mathematics	University
972234	True or false. If false, why? Each spermatogonium produces 4 genetically unique gametes (spermatozoa).	false	Boolean	Biology	Senior High School
121423	Which are true about the differential equation dy/dx = (x)/(x-4)? I. will have a slope field with negative slopes in quadrant I. II. will have a slope field with positive slopes in all quadrants. III. will produce a slope field with columns of parallel tangents.	III	Multiple Choice	Mathematics	University
986875	If electricity costs 7.06 cents/kWh, how much would it cost you to run a 120-W stereo system 4.0 hours per day for 4.0 weeks?	95 cents	Float	Physics	Junior High School
1048260	If a student had used an RNA virus (genome composed of RNA) instead of a DNA virus in his experiment, would radioactivity still have been found in the pellet? A) No, because the RNA genome would not enter the bacteria upon infection. B) No, because while DNA and RNA nucleotides are similar, they are not identical. C) Yes, because DNA and RNA nucleotides are similar. D) Yes, because genome in any form (DNA, RNA, protein) would be labeled similarly.	C	Multiple Choice	Biology	Senior High School
1322451	How many light years is Mars away from the sun?	0.000024105 light years	Float	Physics	Primary School
1243190	A person holding a lunch bag is moving upward in a hot air balloon at a constant speed of 6.1 m/s. When the balloon is 28 m above the ground, she accidentally releases the bag. What is the speed of the bag just before it reaches the ground?	24.2 m/s	Float	Physics	Senior High School
40158	Which trisomy is associated with molar pregnancy?	Triploidy	String	Biology	University
1028381	An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 2420 kg. When that occupant drops a coin, its acceleration relative to the cab is 8.20 m/s2 downward. What is the tension in the cable?	3896.20 N	Float	Physics	Senior High School
1992363	Can low hemoglobin cause memory loss?	Yes	Boolean	Biology	Junior High School
512719	James, Inc. incurred the following infrequent losses during 2012: I. $140000 write-down of equipment leased to others. II. $80000 adjustment of accruals on long-term contracts. III. $120000 write-off of obsolete inventory. In its 2012 income statement, what amount should James report as total infrequent losses that are not considered extraordinary? a. $220,000. b. $260,000. c. $340,000. d. $200,000.	c	Multiple Choice	Business	University
1092484	How does Grendel's characterization in Beowulf differ from his characterization in Grendel? (A.) In Beowulf, he is a round character, but in Grendel, he is a flat character. (B.) In Beowulf, he is a story character, but in Grendel, he is the story's narrator. (C.) In Beowulf, his family is part of the story, but in Grendel, he is a solitary monster with no family. (D.) In Beowulf, he is a static character, but in Grendel, he is a dynamic character.	D	Multiple Choice	Other	Senior High School
55055	Only a ............. shift of the ................ curve can reduce unemployment and inflation at the same time.	right-ward, aggregate supply	String	Economics	University
1897428	Who wants a branisttttt!!!!! if so answer this question n less than 6 min lets goooo smarties Which of the following items demonstrate poor choices made by private property owners? Select all that apply. A privately-owned chicken farm deposits the majority of chicken poop into the river that flows through the property. A wind farm is installed on the property of a factory warehouse to provide for cheap and efficient electricity for the workers. A family piles its garbage bags in the adjacent empty lot to clear their yard of any debris. Solar panels are installed in the parking lot of a private school to shade cars from harsh weather while providing electricity to the school. A family that owns a small yard raises chickens to help keep the scorpion population down, then sells the eggs at a local market.	A, C	Multiple Choice	Economics	Senior High School
1863737	A system does 100 J of work on the surroundings by absorbing 150 J of heat. Calculate the change in internal energy.	50 J	Integer	Physics	Senior High School
578302	What is the derivative of this function #y=sin^-1(e^x)#?	# \y' =(e^x)/sqrt(1 - e^(2x))#	Expression	Mathematics	University
1779630	If {eq}3x^2 - y^2 = 7{/eq}, then evaluate {eq}\dfrac{d^2y}{dx^2}{/eq} when {eq}x = 1{/eq} and {eq}y = 2{/eq}.	0.38	Float	Mathematics	University
1780792	35.0 mL of 0.255 M nitric acid is added to 45.0 mL of 0.328 M Mg(NO3)2. What is the concentration of nitrate ion in the final solution?	0.418 M	Float	Chemistry	Senior High School
581303	How can I rewrite $\int\frac{1}{(2x^2+x+1)}dx$ into something like $\int\frac{1}{(u^2+1)}dx$? Also, how is $2t^2+t+1$ rewritten as $\frac{7}{8}\left( \left( \frac{4t+1}{\sqrt{7}} \right)^2 +1 \right)$?	$\frac{2}{\sqrt{7}}\arctan\left(\frac{4x+1}{\sqrt{7}}\right)+c$	Expression	Mathematics	University
103897	If you bought a $5,000 face value CD that matured in nine months, and which was advertised as paying 9% annual interest, compounded monthly, how much would you receive when you cashed in your CD at maturity?	$5,347.80	Float	Finance	Senior High School
1192886	Let $\mathbb A$ be a set of infinitely differentiable functions $f:(-1,1)\to \mathbb{R}$, such that for every $n \in \mathbb{N}$ the relation $f(\frac 1n)=\frac{3n^2}{(5n+1)^2}$ holds. Find the minimum value of $\frac{f^{1000}(0)}{f^{999}(0)}$ on $\mathbb A$.	$\frac{g^{1000}(0)}{g^{999}(0)}$	Expression	Mathematics	University
656315	a speaker fixed to a moving platform moves toward a wall emitting a steady sound with a frequency of {eq}220\ Hz {/eq}. A person on the platform right next to the speaker detects the sound waves reflected off the wall and those emitted by the speaker. How fast should the platform move, {eq}v_p {/eq}, for the person to detect a beat frequency of {eq}6.00\ Hz {/eq}? Take the speed of sound to be {eq}344\ \dfrac ms {/eq}. Express your answer numerically in meters per second using three significant figures.	4.62 m/s	Float	Physics	Senior High School
1906972	If a soap bubble is 96.7 nm thick, what colour will appear at the centre when illuminated normally by white light? Take n = 1.34 for soap and make use of the table of colour ranges below. colour = __________ {eq}\quad \begin{array}{\|c\|c\|} \hline \rm Colour & \rm Range \\ \hline \rm violet & 400 - 446\ \rm nm \\ \hline \rm blue & 446 - 500\ \rm nm \\ \hline \rm green & 500 - 578\ \rm nm \\ \hline \rm yellow & 578 - 592\ \ \rm nm \\ \hline \rm orange & 592 - 620\ \rm nm \\ \hline \rm red & 620 - 700\ \rm nm \\ \hline \end{array} \, {/eq}	green	String	Physics	Senior High School
1070807	A parallel-plate capacitor of capacitance {eq}\displaystyle \rm C {/eq} is cha a battery whose potential difference is {eq}\displaystyle \rm V {/eq}. The battery is disconnected and a dielectric with constant {eq}\displaystyle \rm k \lambda {/eq} is inserted and completely fills the space between the plates. Find the energy stored in the capacitor.	U'= \frac{1}{k\lambda}\left(\frac{1}{2}CV^2\right)	Expression	Physics	University
1724773	A solution is made containing 22.8 g of magnesium nitrate per 325 g of water, what is the weight or percent by mass of the solute?	6.55%	Percentage	Chemistry	Senior High School
903179	Compute $e^\left( \begin{array}{cccc} -1 & -1 & 0 & 1 \\ 0 & -2 & 0 & 2 \\ 3 & -7 & 2 & 9 \\ 0 & 0 & 0 & 0 \\ \end{array} \right)$.	\left( \begin{array}{cccc} \frac{1}{e} & \frac{1}{e^2}-\frac{1}{e} & 0 & \frac{1}{e}-\frac{1}{e^2} \\ 0 & \frac{1}{e^2} & 0 & 1-\frac{1}{e^2} \\ e^2-\frac{1}{e} & \frac{1}{e^2}+\frac{1}{e}-2 e^2 & e^2 & -1-\frac{1}{e^2}-\frac{1}{e}+3 e^2 \\ 0 & 0 & 0 & 1 \\ \end{array} \right)	Matrix	Mathematics	University
1815101	How much work would it take to push a # 9 kg # weight up a # 1 m # plane that is at an incline of # pi / 4 #?	62.37J	Float	Physics	Senior High School
1457482	Hydrochloric acid reacts faster with powdered zinc than with an equal mass of zinc strips because the greater the surface area of the powdered zinc decreases the frequency of particle collisions	False	Boolean	Chemistry	Junior High School
87206	An unknown liquid fills a square container of sides 10 m. What is the density of a material if the pressure 5 m below the surface is 1.6 atm? Assume g=10 m/s{eq}^2 {/eq} and the pressure at the surface of the liquid is 1 atm. Also assume that 1 atm = {eq}10^5 {/eq} Pa. (Hint: make sure to use the reference surface pressure in solving the problem).	1223.24159 kg/m^3	Float	Physics	Senior High School
1780653	A girl of height 120 cm is walking towards a light on the ground at a speed of 0.6 m/s. Her shadow is being cast on a wall behind her that is 5 m from the light. How is the size of her shadow changing when she is 1.5 m from the light?	160 cm/sec	Float	Physics	Senior High School
1687159	Find {eq}\int_C \overrightarrow f · d \overrightarrow r{/eq} where C is a circle of radius 1 in the plane x + y + 2 = 7, centered at (4, 3, 0) and oriented clockwise when viewed from the origin, if {eq}\overrightarrow F= y\overrightarrow i - 2 x\overrightarrow j+ 3 (y - x)\overrightarrow k \int_C \overrightarrow F · d \overrightarrow r = {/eq}	3\pi	Expression	Mathematics	University
984997	A box of mass 7 kg is pulled up a frictionless 30 degree incline by a force of 381 N which acts parallel to the incline surface. The box has an initial speed of 5 m per s and is pulled 9 m. What is the speed of the box at the end of the 9 m?	31.7 m/s	Float	Physics	Senior High School
1182112	How can I show that $$ P(\{\omega:t\to B_t(\omega) \uparrow \})<1$$ given that the proof is just one line and each independent increment must be increasing and therefore each $B_t − B_{t+1}$ > 0, which has probability $lim_{t \to \infty} \frac{1}{2^t} = 0$?	0	Integer	Mathematics	University
1935088	What groups are organized to back a particular candidate in an election?	Political parties	List	Other	Junior High School
1131812	Depreciation provides a sort of shield against taxes. If there were no taxes, there would be no depreciation tax shields. Does this mean that a project's net present value would be less if there were no taxes?	No, the net present value would be greater without taxes.	Boolean	Business	University
662415	Laura joined a multinational corporation. She expects to get her first salary of {eq}\$100,000 {/eq} one year from today. Also, her salary will grow by {eq}4 {/eq} percent each year, starting next year. Laura is {eq}50 {/eq} years old and plans to work {eq}20 {/eq} years, drawing only twenty salaries. What is the present value of Laura's salary if the discount rate is {eq}8 {/eq} percent?	$1,324,746.24	Float	Finance	University
207143	Assume that today is December 31, 2016, and that the following information applies to Artic Supply: 1. After-tax operating income [EBIT(1 - T)] for 2017 is expected to be $450 million. 2. The depreciation expense for 2017 is expected to be $180 million. 3. The capital expenditures for 2017 are expected to be $400 million. 4. No change is expected in net operating working capital. 5. The free cash flow is expected to grow at a constant rate of 4% per year. 6. The required return on equity is 14%. 7. The WACC is 11%. 8. The market value of the company's debt is $3 billion. 9. 250 million shares of stock are outstanding. Using the corporate valuation model approach, what should be the company's stock price today?	$1.14	Float	Finance	University
1666080	Use the characteristic polynomial to solve the differential equation: 14y"-15iy'-4y = 0.	y = c_1e^(4/7 x) + c_2e^(1/2 x)	Expression	Mathematics	University
2105294	An object's two dimensional velocity is given by #v(t) = (3t-sqrtt , 2t-4 )#. What is the object's rate and direction of acceleration at #t=3 #?	The rate of acceleration is 3.14 and the direction is 39.6 degrees	Float	Physics	Senior High School
2042490	In terms of debits and credit, which account below will have the same normal balance? a) assets b) common stock c) revenue	None	Multiple Choice	Business	Senior High School
1924497	Net income for a period appears in all but which one of the following? a. Income Statement debit column of the worksheet. b. Statement of Retained Earnings credit column of the worksheet. c. Statement of retained earnings. d. Balance sheet.	D	Multiple Choice	Business	University
1379578	Which type of loan requires that you pay the interest accumulated during college?	Unsubsidized loan	String	Economics	Senior High School
144787	William Tell shoots an apple from his son's head. The speed of the 142-g arrow just before it strikes the apple is 23.9 {eq}\frac{m}{s}{/eq}, and at the time of impact it is traveling horizontally. If the arrow sticks in the apple and the arrow-apple combination strikes the ground 8.00 m behind the son's feet, how massive was the apple? Assume the son is 1.85 m tall.	119 g	Integer	Physics	Senior High School
1586423	Assume that the power radiated by the television transmitter uniformly fills the upper hemisphere. A UHF television with a single turn circular loop antenna of radius 9 cm requires a maximum induced voltage above 18 mV for operation. The speed of light is {eq}2.99792 \times 10^8 {/eq} m/s. Find the distance d at which reception is lost from a 630 kW transmitter operating at 0.16 GHz. Answer in units of km.	7.4 km	Float	Physics	University
486897	An object is thrown upwards and after 2 seconds is 78 m above where it was initially thrown. Assume no air resistance, and determine the initial speed the object was thrown at.	48.8 m/s	Float	Physics	Senior High School
702977	Nitrogen trifluoride decomposes to form nitrogen and fluorine gases according to the following equation: {eq}\rm \displaystyle 2NF_3 \rightleftharpoons N_2 (g) + 3 F_2 (g) {/eq} When {eq}\rm 2.2400000000000002\ mol {/eq} of {eq}\rm NF_3 {/eq} is placed in a {eq}\rm 4.5-L {/eq} container and allowed to come to equilibrium at {eq}\rm 800\ K {/eq}, the mixture is found to contain {eq}\rm 0.0354\ mol {/eq} of {eq}\rm N_2 {/eq}. What is the value of {eq}\rm K_p {/eq} at this temperature? {eq}\rm \displaystyle (R = 0.082057\ L \cdot atm/mol \cdot K) {/eq}	1.92e-3	Float	Chemistry	Senior High School
1778977	A container in the shape of an inverted pyramid with a square base of 2 m by 2 m and a height of 5 m is filled to a depth of 4 m with corn slurry. How much work is required to pump all the slurry over the top of the container? (The density of corn slurry is {eq}\rho = 17.9 kg/m^3 {/eq}) Round the answer to two decimal places. Assume {eq}g = 9.8 m/s^2. {/eq}	1197.53 J	Float	Physics	University
737223	Integrate: {eq}\int \frac{x-4}{x^2+2x+5}dx	\frac{1}{2}\arctan \left(\frac{1}{2}\left(x+1\right)\right)\left(x-4\right) - \frac{1}{2}\left(x\arctan \left(\frac{1}{2}\left(x+1\right)\right)-\ln \left\|x^2+2x+5\right\|+\arctan \left(\frac{1}{2}\left(x+1\right)\right)\right)+c	Expression	Mathematics	University
1997668	Let $A:H\rightarrow H$ be a densely defined operator in the set of smooth functions of compact support. Assume $\|\|v\|\|_{H}\le(\|\|v\|\|_{\infty}+1)\|\|Av\|\|_{H}$ for all $v\in C_{o}^{\infty}$, where $\|\|v\|\|_{\infty}$ is the sup norm of $v$. Define $K:A(C_{o}^{\infty})\rightarrow \mathbb{R}$ by $K(Av)=(f,v)_{H}$ where $f\in H$. Can $K$ be extended to $H$ by applying Hahn-Banach? More generally, if the estimate is of the form $\|\|v\|\|_{H}\le (g(v)+C)\|\|Av\|\|_{H}$ where $g(v)$ is a positive function and $C$ a positive constant, can we conclude that we can apply Hahn-Banach to extend $K$ to the whole $H$?	Yes	Boolean	Mathematics	University
1154552	What is the IUPAC name for {eq}(CH_3)_2CHF {/eq}?	2-fluoropropane	String	Chemistry	Senior High School
1166673	Estimate the magnitude of the error involved in using the sum to approximate the sum of the entire series. {eq}\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1} (0.7)^n}{n}	A	Multiple Choice	Mathematics	University
1706478	Let $$x = [1/n, 1/n,\dots, 1/n]$$ and $$y = [y_1, \dots, y_n]$$ be probability vectors on $n$ elements (i.e., $\sum x_i = \sum y_i = 1$ and $x_i,y_i\geq 0$). Is it true that $x$ is always majorized by $y$?	Yes	Boolean	Mathematics	University
70886	The driver of a car, traveling at a constant 25 m/s, sees a child suddenly run into the road. It takes the driver 0.45 s to hit the brakes. As it slows, the car has a steady acceleration of 8.5 m/s{eq}^2 {/eq}. What's the total distance the car moves before it stops?	48 m	Integer	Physics	Senior High School
2030739	Consider a random projection of a deterministic positive $m\times m$ Hermitian matrix $A$, defined as $B:=PUAU^\dagger P$, where $U$ is an $m\times m$ Haar random unitary matrix and $P$ is a fixed $m\times m$ projector with rank $n<m$. Does the spectrum of $B$ typically match approximately (up to normalisation) with the spectrum of $A$ ordered in decreasing order at the first $n$ eigenvalues, as $n,m$ become large enough?	no	Boolean	Mathematics	PhD
1228768	Find the area of the surface obtained by rotating the curve x = 4e^{2y} from y = 0 to y = 2 about the y-axis.	149792.17	Float	Mathematics	University
89705	Two point charges are on the y-axis. 4.5 {eq}\mu {/eq}C is at y = 1.25 cm and -2.24 {eq}\mu {/eq}C at y = -1.80 cm. Find V at the origin.	2.12e6 V	Float	Physics	University
952184	What are the PCR steps after DNA has been cut?	1. Denaturation: The double helix is unwound by separating the two DNA strands. This is done by increasing the temperature to 95 degrees Celsius, which breaks the hydrogen bonds between the nucleotides holding the two strands together. 2. Annealing: The temperature is lowered so that two forms of primers can be attached to the now separated strands. The forward primer attaches to the template DNA at the start codon and the reverse primer attaches the complementary strand at the stop codon. 3. Extension: The primers synthesize new strands of DNA from the original template strands. The Taq polymerase enzyme then allows the union of free DNA nucleotides, whose sequence depends on the sequence in the template DNA strand.	List	Biology	Senior High School
1300806	A 0.1428 g sample of carbonate rock was pulverized and heated in a closed system causing the evolution of {eq}CO_2 {/eq}. {eq}MgCO_3 \rightarrow MgO+CO_2(g) {/eq} A stream of nitrogen was used to sweep the {eq}CO_2 {/eq} into 100.0 mL of 0.05172 M {eq}NaOH {/eq} solution. {eq}CO_2(g)+2NaOH \rightarrow Na_2CO_3+H_2O {/eq} The excess {eq}NaOH {/eq} required 28.14 mL of 0.1788 M {eq}HCl {/eq} for titration. Calculate the amount of carbonate in the sample as % {eq}CaCO_3 {/eq}.	4.94%	Percentage	Chemistry	University
1009046	How do you find the integral of #int (sin(pix))^2*(cos(pix))^5 dx#?	1/pi int (u^2-2u^4+u^6)du	Expression	Mathematics	University
1586340	How do you say 'cleaning' in Spanish?	limpieza (noun), limpiando (verb)	List	Other	Primary School
1360908	The ________ was a german school of art and design that operated in the early twentieth century. the students at the school were immersed in the idea that form follows function.	Bauhaus	String	Other	Senior High School
1036704	How do you convert COGS under LIFO to COGS under FIFO? a. Add the change in the LIFO reserve to COGS under LIFO to yield COGS under FIFO. b. Deduct the change in the LIFO reserve from COGS under LIFO to yield COGS under FIFO. c. Neither of the above.	b	Multiple Choice	Business	University
1908968	A sample of gas is held in a 4506-mL vial at 4.9 atm and 28.6 degrees Celsius. How many moles of gas are there in the vial? Answer in scientific notation using 3 significant figures.	8.92e-1 mol	Float	Chemistry	Senior High School
39367	Evaluate: {eq}\int (x+1)^2(1-x)^5 dx	\frac{2(1-x)^6}{6}- \frac{4(1-x)^7}{7}+ \frac{(1-x)^8}{8}+C	Expression	Mathematics	University
425065	How does one obtain the above bound for the product $\|x-x_{0}\|\|x+x_{0}\|$, if $x$ and $x_{0}$ are assumed to be points in the closed interval $[a,b]$?	$\|x\| \le \|a\|+\|b\|$	Expression	Mathematics	University
241482	An application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared deviations between the _____.	c	Multiple Choice	Mathematics	University
1608030	How do you take the derivative of the Lagrangian functional $L = \int_0^1 f(x)^{1 - \frac{1}{\alpha}}dx - \lambda\int_0^1 g(x) f(x) dx$ with respect to the function $f(x)$, and what are the first-order conditions?	$$ f(x) = \left( \frac{\lambda \alpha}{\alpha-1} g(x)\right)^{-\alpha} $$	Expression	Mathematics	University
204356	Books Brothers' stock was priced at $15 per share two years ago. The stock sold for $15 last year and now, it sells for $20. A $2 dividend was also paid over the last year. What was the total return for owning Books Brothers' stock during the most recent year?	46.67%	Percentage	Finance	Senior High School
1874036	You are deciding whether to purchase some shares of a corporation. You expect that the corporation will not pay any dividends in the first three years. The estimated dividends for years four and five are as follows: End of year four: $1.00 per share End of year five: $1.20 per share The dividends are expected to grow at 5% per year thereafter, in perpetuity. Assuming a required return of 12% per year, calculate the current value of one share of the corporation.	11.53	Float	Business	University
1407787	An inverted conical water tank with a height of 8 feet and radius 4 feet is drained through a hole in the vertex at a rate of 5 cubic feet per second. What is the rate of change of water depth when the water is 2 feet?	1.59 ft/s	Float	Mathematics	University
1561190	Is the equation $ 2 b \cos(t+2r) \sin(a t) - 2 \sin(t) \cos(a t + 2 b (\pi - r - t)) + 2 \sin(t) \cos(a t) - 2 b \cos(t) \sin(a t)$ equivalent to $ \sin(b(\pi-r-t)) \sin(t) \sin(b(\pi - r - t) + a t) - b \sin(r) \sin(a t) \sin(r+t)$ and if so, how was the simplification performed?	-4[bsin(r)sin(r+t)sin(at)+sin(b(π-r-t))sin(at+b(π-r-t))*sin(t)]	Expression	Mathematics	University
566089	Find the area of the surface given parametrically by the equation {eq}R(u,v)=uvi+2(u-v)j+2(u+v)k \ \ for \ \ u^2+v^2 <= 1{/eq}.	25.9025	Float	Mathematics	University
932485	Consider a project to supply 106 million postage stamps per year to the U.S. Postal Service for the next five years. You have an idle parcel of land available that cost $1,960,000 five years ago; if the land were sold today, it would net you $2,160,000 aftertax. The land can be sold for $2,360,000 after taxes in five years. You will need to install $5.46 million in new manufacturing plant and equipment to actually produce the stamps; this plant and equipment will be depreciated straight-line to zero over the project?s five-year life. The equipment can be sold for $560,000 at the end of the project. You will also need $660,000 in initial net working capital for the project, and an additional investment of $56,000 in every year thereafter. Your production costs are .56 cents per stamp, and you have fixed costs of $1,080,000 per year. If your tax rate is 34 percent and your required return on this project is 12 percent, what bid price should you submit on the contract?	0.59	Float	Finance	University
459162	A company can manufacture a product with off-the-shelf hand tools. Fixed costs will be $1,500 for tools and $1.50 manufacturing cost per unit. As an alternative, an automated system will cost $15,000 with a $0.50 manufacturing cost per unit. With an annual anticipated volume of 5,000 units, the break-even point in years is?	3 years	Integer	Business	Senior High School
144001	A 60.0 kg crate starts from rest on an incline of {eq}28.0 ^\circ {/eq} that is 85.0 meters long. The coefficient of friction is 0.0900 along the incline. If the ground is level at the base of the incline and has the same coefficient of friction, how far will the crate slide horizontally?	368 m	Integer	Physics	Senior High School
1985437	An operator is required to apply 66 ft-lbs of torque to a bolt. The operator can apply a maximum of 37 pounds of force to the end of the wrench. What is the minimum length of torque wrench required, in inches?	21.40 inches	Float	Physics	Junior High School
120534	A particular solution of the differential equation y'' - 2y' + y = sin x is ____.	1/2cosx	Expression	Mathematics	University
1554596	How many partitions of $[n]$ into sequences exist?	The number of partitions of $[n]$ into sequences is given by the $n$th ordered Bell number, which can be calculated as the sum $a_n = \sum_{k=0}^n k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling numbers of the second kind, given by $S(n, k) = \frac{1}{k!} \sum_{j=0}^k (-1)^{k-j} \binom{k}{j} j^n$.	Expression	Mathematics	University
37156	How many Australian soldiers died in the Battle of Fromelles?	2000	Integer	History	Junior High School
415756	The value of equity in a firm is an increasing function of the duration of the debt in the firm (i.e., equity will be more valuable in a firm with longer-term debt than an otherwise similar firm with short-term debt). a. True b. False	b	Boolean	Business	University
239529	A solenoid that is {eq}\displaystyle \rm 54 \ cm {/eq} long has a cross-sectional area of {eq}\displaystyle \rm 17 \ cm^2 {/eq}. The magnetic field inside the solenoid has a magnitude of {eq}\displaystyle \rm 130 \ mT {/eq}. What is the total energy stored by the magnetic field inside the solenoid?	6.2 J	Float	Physics	University
938756	A ball is thrown straight upwards at a speed of 32.3 m/s and from a height of 1.5 m above the ground. How fast is it traveling when it hits the ground? (m/s)	32.752 m/sec	Float	Physics	Senior High School
874676	Convert the following matrix to reduced row echelon form: $\left( \begin{array}{ccccccc} -7 & -6 & -9 & -5 & -8 & -10 & -4 \\ 6 & 8 & 6 & -5 & 7 & 5 & 2 \\ 5 & 4 & -6 & 3 & 1 & -1 & -8 \\ \end{array} \right)$.	\\$ \left( \begin{array}{ccccccc} 1 & 0 & 0 & \frac{23}{7} & \frac{3}{7} & \frac{9}{7} & -\frac{4}{7} \\ 0 & 1 & 0 & -\frac{89}{28} & \frac{23}{84} & -\frac{71}{84} & \frac{1}{42} \\ 0 & 0 & 1 & \frac{5}{42} & \frac{47}{126} & \frac{85}{126} & \frac{55}{63} \\ \end{array} \right) $	Matrix	Mathematics	University
742708	What is the IUPAC name for CH3CH(CH3)CH2CH2-O-CH3	1-methoxy-3-methyl butane	String	Chemistry	Senior High School
859981	The Photo Film Company's bonds have 4 years remaining to maturity. Interest is paid semi annually. The bonds have a $1,000 par value and the coupon interest rate is 8.75%. Would you pay $935 for one of these bonds if you thought that the market rate of interest was 9.5%?	$975.52	Float	Finance	University
868068	{eq}8.7\times10^{24} \space H_2 {/eq} molecules are produced by the reaction of zinc and 30% W/W {eq}H_2SO_4 {/eq} solution of density {eq}1.25\space g/cm^3 {/eq}. For the reaction {eq}Zn(s) +H_2SO_4(aq) \rightarrow H_2(g) + ZnSO_4(s) {/eq} Calculate the volume of sulphuric acid solution used. (Zn = 65, O = 16, S = 32, H = 1 g/mol)	3774.96 cm^3	Float	Chemistry	Senior High School
1459511	Forces with a magnitude of 125 newtons and 300 newtons act on an object. The angle between the two forces is 45 degrees. Find the direction and magnitude of the resultant forces.	398.32 N with a direction of 32.17 ° below the positive x axis (SE direction)	Float	Physics	Senior High School
1676621	Let f(x)=x^3tan^{-1}(2x). Find f'(x)	2x^3/(4x^2+1)+3x^2arctan(2x)	Expression	Mathematics	University
533351	Terry Monson starts a merchandising business on December 1 and enters into the following three inventory purchases. Also, on December 15, Monson sells 15 units for $20 each. Purchases on December 7 10 units @ $6.00 cost Purchases on December 14 20 units @ $12.00 cost Purchases on December 21 10 units @ $14.00 cost Required: Monson uses a perpetual inventory system. Determine the costs assigned to the December 31 ending inventory based on the FIFO method. Perpetual FIFO: Goods Purchased Cost of Goods Sold Inventory Balance Date # of Units Cost Per Unit Goods Purchased # of Units Sold Cost Per Unit Cost of Goods Sold # of Units Cost Per Unit Inventory Balance December 7 ____________________________________________________________________________________________________________________________________________________________________ December 14 ____________________________________________________________________________________________________________________________________________________________________ December 15 ____________________________________________________________________________________________________________________________________________________________________ December 21 Totals ____________________________________________________________________________________________________________________________________________________________________	200	Integer	Business	Senior High School
154837	Determine the upper-tail critical value when 1 - {eq}\alpha{/eq} = 0.95 and n = 16.	1.75	Float	Mathematics	University
384913	Write the net ionic equation for the following reaction. {eq}Hg_2Cl_2(s) + 2NH_3(aq) \to Hg(s) + HgNH_2Cl(s) + NH_4Cl(aq) {/eq}	Hg_2Cl_2(s) + 2NH_3(aq) o Hg(s) + HgNH_2Cl(s) + NH_4^+(aq)+Cl^-(aq)	Expression	Chemistry	Senior High School
1954303	The journal entry to record the issuance of a stock dividend is to: a) debit Common Stock Dividend Distributable (number of shares × par value common stock); credit Common Stock (same). b) debit Common Stock Dividends Distributable (number of shares × market value common stock); credit Common Stock (same). c) debit Retained Earnings (market value × number of shares); credit Common Stock Dividends Distributable (number of shares × par value); credit Paid-in Capital in Excess of Par-Stock Dividend d) debit Common Stock Dividend Distributable (number of shares × par value); credit Cash.	c	Multiple Choice	Business	University
610537	Which of the words printed in italics in the following sentences is most likely to convey a denotative meaning? A. What time did he call? B. Deliver the goods soon, or else. C. The recipe calls for one pint of cream. D. Do you know what the owl signifies?	C	Multiple Choice	Other	Senior High School
730851	Light from a helium-neon laser {eq}(\lambda = 633 \ n m) {/eq} is used to illuminate two narrow slits. The interference pattern is observed on a screen {eq}3.1 \ m {/eq} behind the slits. Eleven bright fringes are seen, spanning a distance of {eq}54 \ mm {/eq}. What is the spacing (in mm) between the slits?	0.36 mm	Float	Physics	Senior High School
1726393	Find the exponential generating function for the number of ways to distribute $r$ distinct objects into five different boxes when $b_1<b_2\le 4$, where $b_1,b_2$ are the numbers of objects in boxes $1$ and $2$, respectively.	$e^{3x}\left(\frac{x}{1!}+\frac{x^2}{2!}+\frac{4x^3}{3!}+\frac{5x^4}{4!}+ \frac{15x^5}{5!}+\frac{15x^6}{6!}+\frac{35x^7}{7!}\right)$	Expression	Mathematics	University
1201004	How do you evaluate the integral #int 1/(xsqrt(2+x^2))#?	#1/sqrt2lnabs(x/(sqrt(x^2+2)+sqrt2))+C#	Expression	Mathematics	University
1191477	Find $\int _0^{\frac{\pi }{6}}\:\sqrt{1+\sin^2\left(x\right)}dx$ to within an accuracy of at least $1/10$. The provided approach involves approximating $\sin x$ using a Taylor series with one term and an error term, analyzing the error, and then calculating $\int _0^{\frac{\pi }{6}}\:\sqrt{1+x^2}dx$. Why is this approach possibly wrong, and what is the correct method to solve this problem?	0.55	Float	Mathematics	University

1147723

If I have $y_i=$ $ \begin{cases} 1& w/probability \ p_i \\ 0& w/probability \ 1-p_i \end{cases}$ and $p_i=1-e^{-\alpha x_i}$, i=1,2,... $\alpha>=0$ and $x_i>=0$, and a sample of a single observation $(y_1,x_1)=(0,20)$, what is the maximum likelihood of this sample?

0

Integer

Mathematics

University

1766596

What are the end products of the HYDROLYSIS of a polysaccharide?

glucose molecules

String

Chemistry

Senior High School

1474920

Preston Inc.'s stock has a 25% chance of producing a 30% return, a 50% chance of producing a 12% return, and a 25% chance of producing a -18% return. What is the firm's expected rate of return? a. 7.72% b. 8.12% c. 8.55% d. 9.00%

d. 9.00%

Percentage

Finance

Senior High School

628994

Compute the (pseudo)inverse of $\left( \begin{array}{cc} \frac{19}{7} & -\frac{2}{7} \\ \frac{25}{7} & -\frac{30}{7} \\ \end{array} \right)$.

\frac{7}{520}\left( \begin{array}{cc} 30 & -2 \\ 25 & -19 \\ \end{array} \right)

Matrix

Mathematics

University

972234

True or false. If false, why? Each spermatogonium produces 4 genetically unique gametes (spermatozoa).

false

Boolean

Biology

Senior High School

121423

Which are true about the differential equation dy/dx = (x)/(x-4)? I. will have a slope field with negative slopes in quadrant I. II. will have a slope field with positive slopes in all quadrants. III. will produce a slope field with columns of parallel tangents.

III

Multiple Choice

Mathematics

University

986875

If electricity costs 7.06 cents/kWh, how much would it cost you to run a 120-W stereo system 4.0 hours per day for 4.0 weeks?

95 cents

Float

Physics

Junior High School

1048260

If a student had used an RNA virus (genome composed of RNA) instead of a DNA virus in his experiment, would radioactivity still have been found in the pellet? A) No, because the RNA genome would not enter the bacteria upon infection. B) No, because while DNA and RNA nucleotides are similar, they are not identical. C) Yes, because DNA and RNA nucleotides are similar. D) Yes, because genome in any form (DNA, RNA, protein) would be labeled similarly.

C

Multiple Choice

Biology

Senior High School

1322451

How many light years is Mars away from the sun?

0.000024105 light years

Float

Physics

Primary School

1243190

A person holding a lunch bag is moving upward in a hot air balloon at a constant speed of 6.1 m/s. When the balloon is 28 m above the ground, she accidentally releases the bag. What is the speed of the bag just before it reaches the ground?

24.2 m/s

Float

Physics

Senior High School

40158

Which trisomy is associated with molar pregnancy?

Triploidy

String

Biology

University

1028381

An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 2420 kg. When that occupant drops a coin, its acceleration relative to the cab is 8.20 m/s2 downward. What is the tension in the cable?

3896.20 N

Float

Physics

Senior High School

1992363

Can low hemoglobin cause memory loss?

Yes

Boolean

Biology

Junior High School

512719

James, Inc. incurred the following infrequent losses during 2012: I. $140000 write-down of equipment leased to others. II. $80000 adjustment of accruals on long-term contracts. III. $120000 write-off of obsolete inventory. In its 2012 income statement, what amount should James report as total infrequent losses that are not considered extraordinary? a. $220,000. b. $260,000. c. $340,000. d. $200,000.

c

Multiple Choice

Business

University

1092484

How does Grendel's characterization in Beowulf differ from his characterization in Grendel? (A.) In Beowulf, he is a round character, but in Grendel, he is a flat character. (B.) In Beowulf, he is a story character, but in Grendel, he is the story's narrator. (C.) In Beowulf, his family is part of the story, but in Grendel, he is a solitary monster with no family. (D.) In Beowulf, he is a static character, but in Grendel, he is a dynamic character.

D

Multiple Choice

Other

Senior High School

55055

Only a ............. shift of the ................ curve can reduce unemployment and inflation at the same time.

right-ward, aggregate supply

String

Economics

University

1897428

Who wants a branisttttt!!!!! if so answer this question n less than 6 min lets goooo smarties Which of the following items demonstrate poor choices made by private property owners? Select all that apply. A privately-owned chicken farm deposits the majority of chicken poop into the river that flows through the property. A wind farm is installed on the property of a factory warehouse to provide for cheap and efficient electricity for the workers. A family piles its garbage bags in the adjacent empty lot to clear their yard of any debris. Solar panels are installed in the parking lot of a private school to shade cars from harsh weather while providing electricity to the school. A family that owns a small yard raises chickens to help keep the scorpion population down, then sells the eggs at a local market.

A, C

Multiple Choice

Economics

Senior High School

1863737

A system does 100 J of work on the surroundings by absorbing 150 J of heat. Calculate the change in internal energy.

50 J

Integer

Physics

Senior High School

578302

What is the derivative of this function #y=sin^-1(e^x)#?

# \y' =(e^x)/sqrt(1 - e^(2x))#

Expression

Mathematics

University

1779630

If {eq}3x^2 - y^2 = 7{/eq}, then evaluate {eq}\dfrac{d^2y}{dx^2}{/eq} when {eq}x = 1{/eq} and {eq}y = 2{/eq}.

0.38

Float

Mathematics

University

1780792

35.0 mL of 0.255 M nitric acid is added to 45.0 mL of 0.328 M Mg(NO3)2. What is the concentration of nitrate ion in the final solution?

0.418 M

Float

Chemistry

Senior High School

581303

How can I rewrite $\int\frac{1}{(2x^2+x+1)}dx$ into something like $\int\frac{1}{(u^2+1)}dx$? Also, how is $2t^2+t+1$ rewritten as $\frac{7}{8}\left( \left( \frac{4t+1}{\sqrt{7}} \right)^2 +1 \right)$?

$\frac{2}{\sqrt{7}}\arctan\left(\frac{4x+1}{\sqrt{7}}\right)+c$

Expression

Mathematics

University

103897

If you bought a $5,000 face value CD that matured in nine months, and which was advertised as paying 9% annual interest, compounded monthly, how much would you receive when you cashed in your CD at maturity?

$5,347.80

Float

Finance

Senior High School

1192886

Let $\mathbb A$ be a set of infinitely differentiable functions $f:(-1,1)\to \mathbb{R}$, such that for every $n \in \mathbb{N}$ the relation $f(\frac 1n)=\frac{3n^2}{(5n+1)^2}$ holds. Find the minimum value of $\frac{f^{1000}(0)}{f^{999}(0)}$ on $\mathbb A$.

$\frac{g^{1000}(0)}{g^{999}(0)}$

Expression

Mathematics

University

656315

a speaker fixed to a moving platform moves toward a wall emitting a steady sound with a frequency of {eq}220\ Hz {/eq}. A person on the platform right next to the speaker detects the sound waves reflected off the wall and those emitted by the speaker. How fast should the platform move, {eq}v_p {/eq}, for the person to detect a beat frequency of {eq}6.00\ Hz {/eq}? Take the speed of sound to be {eq}344\ \dfrac ms {/eq}. Express your answer numerically in meters per second using three significant figures.

4.62 m/s

Float

Physics

Senior High School

1906972

If a soap bubble is 96.7 nm thick, what colour will appear at the centre when illuminated normally by white light? Take n = 1.34 for soap and make use of the table of colour ranges below. colour = __________ {eq}\quad \begin{array}{|c|c|} \hline \rm Colour & \rm Range \\ \hline \rm violet & 400 - 446\ \rm nm \\ \hline \rm blue & 446 - 500\ \rm nm \\ \hline \rm green & 500 - 578\ \rm nm \\ \hline \rm yellow & 578 - 592\ \ \rm nm \\ \hline \rm orange & 592 - 620\ \rm nm \\ \hline \rm red & 620 - 700\ \rm nm \\ \hline \end{array} \, {/eq}

green

String

Physics

Senior High School

1070807

A parallel-plate capacitor of capacitance {eq}\displaystyle \rm C {/eq} is cha a battery whose potential difference is {eq}\displaystyle \rm V {/eq}. The battery is disconnected and a dielectric with constant {eq}\displaystyle \rm k \lambda {/eq} is inserted and completely fills the space between the plates. Find the energy stored in the capacitor.

U'= \frac{1}{k\lambda}\left(\frac{1}{2}CV^2\right)

Expression

Physics

University

1724773

A solution is made containing 22.8 g of magnesium nitrate per 325 g of water, what is the weight or percent by mass of the solute?

6.55%

Percentage

Chemistry

Senior High School

903179

Compute $e^\left( \begin{array}{cccc} -1 & -1 & 0 & 1 \\ 0 & -2 & 0 & 2 \\ 3 & -7 & 2 & 9 \\ 0 & 0 & 0 & 0 \\ \end{array} \right)$.

\left( \begin{array}{cccc} \frac{1}{e} & \frac{1}{e^2}-\frac{1}{e} & 0 & \frac{1}{e}-\frac{1}{e^2} \\ 0 & \frac{1}{e^2} & 0 & 1-\frac{1}{e^2} \\ e^2-\frac{1}{e} & \frac{1}{e^2}+\frac{1}{e}-2 e^2 & e^2 & -1-\frac{1}{e^2}-\frac{1}{e}+3 e^2 \\ 0 & 0 & 0 & 1 \\ \end{array} \right)

Matrix

Mathematics

University

1815101

How much work would it take to push a # 9 kg # weight up a # 1 m # plane that is at an incline of # pi / 4 #?

62.37J

Float

Physics

Senior High School

1457482

Hydrochloric acid reacts faster with powdered zinc than with an equal mass of zinc strips because the greater the surface area of the powdered zinc decreases the frequency of particle collisions

False

Boolean

Chemistry

Junior High School

87206

An unknown liquid fills a square container of sides 10 m. What is the density of a material if the pressure 5 m below the surface is 1.6 atm? Assume g=10 m/s{eq}^2 {/eq} and the pressure at the surface of the liquid is 1 atm. Also assume that 1 atm = {eq}10^5 {/eq} Pa. (Hint: make sure to use the reference surface pressure in solving the problem).

1223.24159 kg/m^3

Float

Physics

Senior High School

1780653

A girl of height 120 cm is walking towards a light on the ground at a speed of 0.6 m/s. Her shadow is being cast on a wall behind her that is 5 m from the light. How is the size of her shadow changing when she is 1.5 m from the light?

160 cm/sec

Float

Physics

Senior High School

1687159

Find {eq}\int_C \overrightarrow f · d \overrightarrow r{/eq} where C is a circle of radius 1 in the plane x + y + 2 = 7, centered at (4, 3, 0) and oriented clockwise when viewed from the origin, if {eq}\overrightarrow F= y\overrightarrow i - 2 x\overrightarrow j+ 3 (y - x)\overrightarrow k \int_C \overrightarrow F · d \overrightarrow r = {/eq}

3\pi

Expression

Mathematics

University

984997

A box of mass 7 kg is pulled up a frictionless 30 degree incline by a force of 381 N which acts parallel to the incline surface. The box has an initial speed of 5 m per s and is pulled 9 m. What is the speed of the box at the end of the 9 m?

31.7 m/s

Float

Physics

Senior High School

1182112

How can I show that $$ P(\{\omega:t\to B_t(\omega) \uparrow \})<1$$ given that the proof is just one line and each independent increment must be increasing and therefore each $B_t − B_{t+1}$ > 0, which has probability $lim_{t \to \infty} \frac{1}{2^t} = 0$?

0

Integer

Mathematics

University

1935088

What groups are organized to back a particular candidate in an election?

Political parties

List

Other

Junior High School

1131812

Depreciation provides a sort of shield against taxes. If there were no taxes, there would be no depreciation tax shields. Does this mean that a project's net present value would be less if there were no taxes?

No, the net present value would be greater without taxes.

Boolean

Business

University

662415

Laura joined a multinational corporation. She expects to get her first salary of {eq}\$100,000 {/eq} one year from today. Also, her salary will grow by {eq}4 {/eq} percent each year, starting next year. Laura is {eq}50 {/eq} years old and plans to work {eq}20 {/eq} years, drawing only twenty salaries. What is the present value of Laura's salary if the discount rate is {eq}8 {/eq} percent?

$1,324,746.24

Float

Finance

University

207143

Assume that today is December 31, 2016, and that the following information applies to Artic Supply: 1. After-tax operating income [EBIT(1 - T)] for 2017 is expected to be $450 million. 2. The depreciation expense for 2017 is expected to be $180 million. 3. The capital expenditures for 2017 are expected to be $400 million. 4. No change is expected in net operating working capital. 5. The free cash flow is expected to grow at a constant rate of 4% per year. 6. The required return on equity is 14%. 7. The WACC is 11%. 8. The market value of the company's debt is $3 billion. 9. 250 million shares of stock are outstanding. Using the corporate valuation model approach, what should be the company's stock price today?

$1.14

Float

Finance

University

1666080

Use the characteristic polynomial to solve the differential equation: 14y"-15iy'-4y = 0.

y = c_1*e^(4/7 x) + c_2*e^(1/2 x)

Expression

Mathematics

University

2105294

An object's two dimensional velocity is given by #v(t) = (3t-sqrtt , 2t-4 )#. What is the object's rate and direction of acceleration at #t=3 #?

The rate of acceleration is 3.14 and the direction is 39.6 degrees

Float

Physics

Senior High School

2042490

In terms of debits and credit, which account below will have the same normal balance? a) assets b) common stock c) revenue

None

Multiple Choice

Business

Senior High School

1924497

Net income for a period appears in all but which one of the following? a. Income Statement debit column of the worksheet. b. Statement of Retained Earnings credit column of the worksheet. c. Statement of retained earnings. d. Balance sheet.

D

Multiple Choice

Business

University

1379578

Which type of loan requires that you pay the interest accumulated during college?

Unsubsidized loan

String

Economics

Senior High School

144787

William Tell shoots an apple from his son's head. The speed of the 142-g arrow just before it strikes the apple is 23.9 {eq}\frac{m}{s}{/eq}, and at the time of impact it is traveling horizontally. If the arrow sticks in the apple and the arrow-apple combination strikes the ground 8.00 m behind the son's feet, how massive was the apple? Assume the son is 1.85 m tall.

119 g

Integer

Physics

Senior High School

1586423

Assume that the power radiated by the television transmitter uniformly fills the upper hemisphere. A UHF television with a single turn circular loop antenna of radius 9 cm requires a maximum induced voltage above 18 mV for operation. The speed of light is {eq}2.99792 \times 10^8 {/eq} m/s. Find the distance d at which reception is lost from a 630 kW transmitter operating at 0.16 GHz. Answer in units of km.

7.4 km

Float

Physics

University

486897

An object is thrown upwards and after 2 seconds is 78 m above where it was initially thrown. Assume no air resistance, and determine the initial speed the object was thrown at.

48.8 m/s

Float

Physics

Senior High School

702977

Nitrogen trifluoride decomposes to form nitrogen and fluorine gases according to the following equation: {eq}\rm \displaystyle 2NF_3 \rightleftharpoons N_2 (g) + 3 F_2 (g) {/eq} When {eq}\rm 2.2400000000000002\ mol {/eq} of {eq}\rm NF_3 {/eq} is placed in a {eq}\rm 4.5-L {/eq} container and allowed to come to equilibrium at {eq}\rm 800\ K {/eq}, the mixture is found to contain {eq}\rm 0.0354\ mol {/eq} of {eq}\rm N_2 {/eq}. What is the value of {eq}\rm K_p {/eq} at this temperature? {eq}\rm \displaystyle (R = 0.082057\ L \cdot atm/mol \cdot K) {/eq}

1.92e-3

Float

Chemistry

Senior High School

1778977

A container in the shape of an inverted pyramid with a square base of 2 m by 2 m and a height of 5 m is filled to a depth of 4 m with corn slurry. How much work is required to pump all the slurry over the top of the container? (The density of corn slurry is {eq}\rho = 17.9 kg/m^3 {/eq}) Round the answer to two decimal places. Assume {eq}g = 9.8 m/s^2. {/eq}

1197.53 J

Float

Physics

University

737223

Integrate: {eq}\int \frac{x-4}{x^2+2x+5}dx

\frac{1}{2}\arctan \left(\frac{1}{2}\left(x+1\right)\right)\left(x-4\right) - \frac{1}{2}\left(x\arctan \left(\frac{1}{2}\left(x+1\right)\right)-\ln \left|x^2+2x+5\right|+\arctan \left(\frac{1}{2}\left(x+1\right)\right)\right)+c

Expression

Mathematics

University

1997668

Let $A:H\rightarrow H$ be a densely defined operator in the set of smooth functions of compact support. Assume $||v||_{H}\le(||v||_{\infty}+1)||Av||_{H}$ for all $v\in C_{o}^{\infty}$, where $||v||_{\infty}$ is the sup norm of $v$. Define $K:A(C_{o}^{\infty})\rightarrow \mathbb{R}$ by $K(Av)=(f,v)_{H}$ where $f\in H$. Can $K$ be extended to $H$ by applying Hahn-Banach? More generally, if the estimate is of the form $||v||_{H}\le (g(v)+C)||Av||_{H}$ where $g(v)$ is a positive function and $C$ a positive constant, can we conclude that we can apply Hahn-Banach to extend $K$ to the whole $H$?

Yes

Boolean

Mathematics

University

1154552

What is the IUPAC name for {eq}(CH_3)_2CHF {/eq}?

2-fluoropropane

String

Chemistry

Senior High School

1166673

Estimate the magnitude of the error involved in using the sum to approximate the sum of the entire series. {eq}\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1} (0.7)^n}{n}

A

Multiple Choice

Mathematics

University

1706478

Let $$x = [1/n, 1/n,\dots, 1/n]$$ and $$y = [y_1, \dots, y_n]$$ be probability vectors on $n$ elements (i.e., $\sum x_i = \sum y_i = 1$ and $x_i,y_i\geq 0$). Is it true that $x$ is always majorized by $y$?

Yes

Boolean

Mathematics

University

70886

The driver of a car, traveling at a constant 25 m/s, sees a child suddenly run into the road. It takes the driver 0.45 s to hit the brakes. As it slows, the car has a steady acceleration of 8.5 m/s{eq}^2 {/eq}. What's the total distance the car moves before it stops?

48 m

Integer

Physics

Senior High School

2030739

Consider a random projection of a deterministic positive $m\times m$ Hermitian matrix $A$, defined as $B:=PUAU^\dagger P$, where $U$ is an $m\times m$ Haar random unitary matrix and $P$ is a fixed $m\times m$ projector with rank $n<m$. Does the spectrum of $B$ typically match approximately (up to normalisation) with the spectrum of $A$ ordered in decreasing order at the first $n$ eigenvalues, as $n,m$ become large enough?

no

Boolean

Mathematics

PhD

1228768

Find the area of the surface obtained by rotating the curve x = 4e^{2y} from y = 0 to y = 2 about the y-axis.

149792.17

Float

Mathematics

University

89705

Two point charges are on the y-axis. 4.5 {eq}\mu {/eq}C is at y = 1.25 cm and -2.24 {eq}\mu {/eq}C at y = -1.80 cm. Find V at the origin.

2.12e6 V

Float

Physics

University

952184

What are the PCR steps after DNA has been cut?

1. Denaturation: The double helix is unwound by separating the two DNA strands. This is done by increasing the temperature to 95 degrees Celsius, which breaks the hydrogen bonds between the nucleotides holding the two strands together. 2. Annealing: The temperature is lowered so that two forms of primers can be attached to the now separated strands. The forward primer attaches to the template DNA at the start codon and the reverse primer attaches the complementary strand at the stop codon. 3. Extension: The primers synthesize new strands of DNA from the original template strands. The Taq polymerase enzyme then allows the union of free DNA nucleotides, whose sequence depends on the sequence in the template DNA strand.

List

Biology

Senior High School

1300806

A 0.1428 g sample of carbonate rock was pulverized and heated in a closed system causing the evolution of {eq}CO_2 {/eq}. {eq}MgCO_3 \rightarrow MgO+CO_2(g) {/eq} A stream of nitrogen was used to sweep the {eq}CO_2 {/eq} into 100.0 mL of 0.05172 M {eq}NaOH {/eq} solution. {eq}CO_2(g)+2NaOH \rightarrow Na_2CO_3+H_2O {/eq} The excess {eq}NaOH {/eq} required 28.14 mL of 0.1788 M {eq}HCl {/eq} for titration. Calculate the amount of carbonate in the sample as % {eq}CaCO_3 {/eq}.

4.94%

Percentage

Chemistry

University

1009046

How do you find the integral of #int (sin(pix))^2*(cos(pix))^5 dx#?

1/pi int (u^2-2u^4+u^6)du

Expression

Mathematics

University

1586340

How do you say 'cleaning' in Spanish?

limpieza (noun), limpiando (verb)

List

Other

Primary School

1360908

The ________ was a german school of art and design that operated in the early twentieth century. the students at the school were immersed in the idea that form follows function.

Bauhaus

String

Other

Senior High School

1036704

How do you convert COGS under LIFO to COGS under FIFO? a. Add the change in the LIFO reserve to COGS under LIFO to yield COGS under FIFO. b. Deduct the change in the LIFO reserve from COGS under LIFO to yield COGS under FIFO. c. Neither of the above.

b

Multiple Choice

Business

University

1908968

A sample of gas is held in a 4506-mL vial at 4.9 atm and 28.6 degrees Celsius. How many moles of gas are there in the vial? Answer in scientific notation using 3 significant figures.

8.92e-1 mol

Float

Chemistry

Senior High School

39367

Evaluate: {eq}\int (x+1)^2(1-x)^5 dx

\frac{2(1-x)^6}{6}- \frac{4(1-x)^7}{7}+ \frac{(1-x)^8}{8}+C

Expression

Mathematics

University

425065

How does one obtain the above bound for the product $|x-x_{0}||x+x_{0}|$, if $x$ and $x_{0}$ are assumed to be points in the closed interval $[a,b]$?

$|x| \le |a|+|b|$

Expression

Mathematics

University

241482

An application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared deviations between the _____.

c

Multiple Choice

Mathematics

University

1608030

How do you take the derivative of the Lagrangian functional $L = \int_0^1 f(x)^{1 - \frac{1}{\alpha}}dx - \lambda\int_0^1 g(x) f(x) dx$ with respect to the function $f(x)$, and what are the first-order conditions?

$$ f(x) = \left( \frac{\lambda \alpha}{\alpha-1} g(x)\right)^{-\alpha} $$

Expression

Mathematics

University

204356

Books Brothers' stock was priced at $15 per share two years ago. The stock sold for $15 last year and now, it sells for $20. A $2 dividend was also paid over the last year. What was the total return for owning Books Brothers' stock during the most recent year?

46.67%

Percentage

Finance

Senior High School

1874036

You are deciding whether to purchase some shares of a corporation. You expect that the corporation will not pay any dividends in the first three years. The estimated dividends for years four and five are as follows: End of year four: $1.00 per share End of year five: $1.20 per share The dividends are expected to grow at 5% per year thereafter, in perpetuity. Assuming a required return of 12% per year, calculate the current value of one share of the corporation.

11.53

Float

Business

University

1407787

An inverted conical water tank with a height of 8 feet and radius 4 feet is drained through a hole in the vertex at a rate of 5 cubic feet per second. What is the rate of change of water depth when the water is 2 feet?

1.59 ft/s

Float

Mathematics

University

1561190

Is the equation $ 2 b \cos(t+2r) \sin(a t) - 2 \sin(t) \cos(a t + 2 b (\pi - r - t)) + 2 \sin(t) \cos(a t) - 2 b \cos(t) \sin(a t)$ equivalent to $ \sin(b(\pi-r-t)) \sin(t) \sin(b(\pi - r - t) + a t) - b \sin(r) \sin(a t) \sin(r+t)$ and if so, how was the simplification performed?

-4[b*sin(r)*sin(r+t)*sin(at)+sin(b(π-r-t))*sin(at+b(π-r-t))*sin(t)]

Expression

Mathematics

University

566089

Find the area of the surface given parametrically by the equation {eq}R(u,v)=uvi+2(u-v)j+2(u+v)k \ \ for \ \ u^2+v^2 <= 1{/eq}.

25.9025

Float

Mathematics

University

932485

Consider a project to supply 106 million postage stamps per year to the U.S. Postal Service for the next five years. You have an idle parcel of land available that cost $1,960,000 five years ago; if the land were sold today, it would net you $2,160,000 aftertax. The land can be sold for $2,360,000 after taxes in five years. You will need to install $5.46 million in new manufacturing plant and equipment to actually produce the stamps; this plant and equipment will be depreciated straight-line to zero over the project?s five-year life. The equipment can be sold for $560,000 at the end of the project. You will also need $660,000 in initial net working capital for the project, and an additional investment of $56,000 in every year thereafter. Your production costs are .56 cents per stamp, and you have fixed costs of $1,080,000 per year. If your tax rate is 34 percent and your required return on this project is 12 percent, what bid price should you submit on the contract?

0.59

Float

Finance

University

459162

A company can manufacture a product with off-the-shelf hand tools. Fixed costs will be $1,500 for tools and $1.50 manufacturing cost per unit. As an alternative, an automated system will cost $15,000 with a $0.50 manufacturing cost per unit. With an annual anticipated volume of 5,000 units, the break-even point in years is?

3 years

Integer

Business

Senior High School

144001

A 60.0 kg crate starts from rest on an incline of {eq}28.0 ^\circ {/eq} that is 85.0 meters long. The coefficient of friction is 0.0900 along the incline. If the ground is level at the base of the incline and has the same coefficient of friction, how far will the crate slide horizontally?

368 m

Integer

Physics

Senior High School

1985437

An operator is required to apply 66 ft-lbs of torque to a bolt. The operator can apply a maximum of 37 pounds of force to the end of the wrench. What is the minimum length of torque wrench required, in inches?

21.40 inches

Float

Physics

Junior High School

120534

A particular solution of the differential equation y'' - 2y' + y = sin x is ____.

1/2cosx

Expression

Mathematics

University

1554596

How many partitions of $[n]$ into sequences exist?

The number of partitions of $[n]$ into sequences is given by the $n$th ordered Bell number, which can be calculated as the sum $a_n = \sum_{k=0}^n k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling numbers of the second kind, given by $S(n, k) = \frac{1}{k!} \sum_{j=0}^k (-1)^{k-j} \binom{k}{j} j^n$.

Expression

Mathematics

University

37156

How many Australian soldiers died in the Battle of Fromelles?

2000

Integer

History

Junior High School

415756

The value of equity in a firm is an increasing function of the duration of the debt in the firm (i.e., equity will be more valuable in a firm with longer-term debt than an otherwise similar firm with short-term debt). a. True b. False

b

Boolean

Business

University

239529

A solenoid that is {eq}\displaystyle \rm 54 \ cm {/eq} long has a cross-sectional area of {eq}\displaystyle \rm 17 \ cm^2 {/eq}. The magnetic field inside the solenoid has a magnitude of {eq}\displaystyle \rm 130 \ mT {/eq}. What is the total energy stored by the magnetic field inside the solenoid?

6.2 J

Float

Physics

University

938756

A ball is thrown straight upwards at a speed of 32.3 m/s and from a height of 1.5 m above the ground. How fast is it traveling when it hits the ground? (m/s)

32.752 m/sec

Float

Physics

Senior High School

874676

Convert the following matrix to reduced row echelon form: $\left( \begin{array}{ccccccc} -7 & -6 & -9 & -5 & -8 & -10 & -4 \\ 6 & 8 & 6 & -5 & 7 & 5 & 2 \\ 5 & 4 & -6 & 3 & 1 & -1 & -8 \\ \end{array} \right)$.

\\$ \left( \begin{array}{ccccccc} 1 & 0 & 0 & \frac{23}{7} & \frac{3}{7} & \frac{9}{7} & -\frac{4}{7} \\ 0 & 1 & 0 & -\frac{89}{28} & \frac{23}{84} & -\frac{71}{84} & \frac{1}{42} \\ 0 & 0 & 1 & \frac{5}{42} & \frac{47}{126} & \frac{85}{126} & \frac{55}{63} \\ \end{array} \right) $

Matrix

Mathematics

University

742708

What is the IUPAC name for CH3CH(CH3)CH2CH2-O-CH3

1-methoxy-3-methyl butane

String

Chemistry

Senior High School

859981

The Photo Film Company's bonds have 4 years remaining to maturity. Interest is paid semi annually. The bonds have a $1,000 par value and the coupon interest rate is 8.75%. Would you pay $935 for one of these bonds if you thought that the market rate of interest was 9.5%?

$975.52

Float

Finance

University

868068

{eq}8.7\times10^{24} \space H_2 {/eq} molecules are produced by the reaction of zinc and 30% W/W {eq}H_2SO_4 {/eq} solution of density {eq}1.25\space g/cm^3 {/eq}. For the reaction {eq}Zn(s) +H_2SO_4(aq) \rightarrow H_2(g) + ZnSO_4(s) {/eq} Calculate the volume of sulphuric acid solution used. (Zn = 65, O = 16, S = 32, H = 1 g/mol)

3774.96 cm^3

Float

Chemistry

Senior High School

1459511

Forces with a magnitude of 125 newtons and 300 newtons act on an object. The angle between the two forces is 45 degrees. Find the direction and magnitude of the resultant forces.

398.32 N with a direction of 32.17 ° below the positive x axis (SE direction)

Float

Physics

Senior High School

1676621

Let f(x)=x^3tan^{-1}(2x). Find f'(x)

2x^3/(4x^2+1)+3x^2arctan(2x)

Expression

Mathematics

University

533351

Terry Monson starts a merchandising business on December 1 and enters into the following three inventory purchases. Also, on December 15, Monson sells 15 units for $20 each. Purchases on December 7 10 units @ $6.00 cost Purchases on December 14 20 units @ $12.00 cost Purchases on December 21 10 units @ $14.00 cost Required: Monson uses a perpetual inventory system. Determine the costs assigned to the December 31 ending inventory based on the FIFO method. Perpetual FIFO: Goods Purchased Cost of Goods Sold Inventory Balance Date # of Units Cost Per Unit Goods Purchased # of Units Sold Cost Per Unit Cost of Goods Sold # of Units Cost Per Unit Inventory Balance December 7 ____________________________________________________________________________________________________________________________________________________________________ December 14 ____________________________________________________________________________________________________________________________________________________________________ December 15 ____________________________________________________________________________________________________________________________________________________________________ December 21 Totals ____________________________________________________________________________________________________________________________________________________________________

200

Integer

Business

Senior High School

154837

Determine the upper-tail critical value when 1 - {eq}\alpha{/eq} = 0.95 and n = 16.

1.75

Float

Mathematics

University

384913

Write the net ionic equation for the following reaction. {eq}Hg_2Cl_2(s) + 2NH_3(aq) \to Hg(s) + HgNH_2Cl(s) + NH_4Cl(aq) {/eq}

Hg_2Cl_2(s) + 2NH_3(aq) o Hg(s) + HgNH_2Cl(s) + NH_4^+(aq)+Cl^-(aq)

Expression

Chemistry

Senior High School

1954303

The journal entry to record the issuance of a stock dividend is to: a) debit Common Stock Dividend Distributable (number of shares × par value common stock); credit Common Stock (same). b) debit Common Stock Dividends Distributable (number of shares × market value common stock); credit Common Stock (same). c) debit Retained Earnings (market value × number of shares); credit Common Stock Dividends Distributable (number of shares × par value); credit Paid-in Capital in Excess of Par-Stock Dividend d) debit Common Stock Dividend Distributable (number of shares × par value); credit Cash.

c

Multiple Choice

Business

University

610537

Which of the words printed in italics in the following sentences is most likely to convey a denotative meaning? A. What time did he call? B. Deliver the goods soon, or else. C. The recipe calls for one pint of cream. D. Do you know what the owl signifies?

C

Multiple Choice

Other

Senior High School

730851

Light from a helium-neon laser {eq}(\lambda = 633 \ n m) {/eq} is used to illuminate two narrow slits. The interference pattern is observed on a screen {eq}3.1 \ m {/eq} behind the slits. Eleven bright fringes are seen, spanning a distance of {eq}54 \ mm {/eq}. What is the spacing (in mm) between the slits?

0.36 mm

Float

Physics

Senior High School

1726393

Find the exponential generating function for the number of ways to distribute $r$ distinct objects into five different boxes when $b_1<b_2\le 4$, where $b_1,b_2$ are the numbers of objects in boxes $1$ and $2$, respectively.

$e^{3x}\left(\frac{x}{1!}+\frac{x^2}{2!}+\frac{4x^3}{3!}+\frac{5x^4}{4!}+ \frac{15x^5}{5!}+\frac{15x^6}{6!}+\frac{35x^7}{7!}\right)$

Expression

Mathematics

University

1201004

How do you evaluate the integral #int 1/(xsqrt(2+x^2))#?

#1/sqrt2lnabs(x/(sqrt(x^2+2)+sqrt2))+C#

Expression

Mathematics

University

1191477

Find $\int _0^{\frac{\pi }{6}}\:\sqrt{1+\sin^2\left(x\right)}dx$ to within an accuracy of at least $1/10$. The provided approach involves approximating $\sin x$ using a Taylor series with one term and an error term, analyzing the error, and then calculating $\int _0^{\frac{\pi }{6}}\:\sqrt{1+x^2}dx$. Why is this approach possibly wrong, and what is the correct method to solve this problem?

0.55

Float

Mathematics

University