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2006009 | What is the probability that the sample mean would differ from the true mean by more than 2.2 dollars if a sample of 83 5-gallon pails is randomly selected, given that the cost of 5 gallons of ice cream has a standard deviation of 7 with a mean of 25 dollars during the summer? Round your answer to four decimal places. | 0.00424 | Float | Mathematics | University | [
"0.0042",
"True"
] | False | True |
1724502 | Solve the initial value problem
{eq}\displaystyle 2\left(\sin(t)\frac{dy}{dt}+\cos(t)y\right)=\cos(t)\sin^6(t),
{/eq}
for {eq}0 < t< \pi
{/eq} and {eq}\displaystyle y\left(\frac{\pi}{2}\right)=19.
{/eq} | y(t)=(1/14)sin^6(t)+ (265/14)csc(t) | Expression | Mathematics | University | [
"y(t) = \\frac{\\sin^6(t)}{14} + \\frac{265}{14\\sin(t)}",
"True"
] | False | True |
327473 | Which of the following is a part of the Federal Reserve System's monetary policy toolkit?
a. The income tax rate
b. The reserve requirement
c. Open market operations | c | Multiple Choice | Economics | Senior High School | [
"c",
"True"
] | True | True |
198485 | Given that {eq}i{/eq} is a double root of {eq}2x^6 + x^5 + 2x^3 - 6x^2 + x - 4 = 0{/eq}, find all the other roots of the equation. | $\frac{-1 \pm \sqrt{33}}{4}$ | List | Mathematics | University | [
"\\frac{-1\\pm\\sqrt{33}}{4}, i, i, -i, -i",
"False"
] | False | True |
1471185 | Prove or disprove: $$ \int_{0}^{\pi}\!{{\rm e}^{x}}\sqrt {\sin \left( x \right) }\,{\rm d}x= {\frac {{\pi}^{3/2}{{\rm e}^{\pi/2}}}{2^{3/2}\;\Gamma \left( 5/4+ i/2 \right) \Gamma \left( 5/4-i/2 \right) }} $$ May we conjecture that $$ \int_{0}^{\pi}\!{{\rm e}^{x}} \left( \sin \left( x \right) \right) ^{ n}\,{\rm d}x={\frac {\pi\,{{\rm e}^{\pi/2}}\Gamma \left( n+1 \right) }{{2}^{n}\Gamma \left( n/2+1+i/2 \right) \Gamma \left( n/2+1-i/2 \right) }} $$ holds for all complex numbers $n$ except the negative integers? | $\int_0^\pi e^{i\beta x}\sin^{\nu-1} x\;dx =\frac{\pi e^{i\,\beta\,\pi/2}}{2^{\nu-1}\,\nu\,\displaystyle\operatorname{B}\left(\frac{\nu+\beta+1}{2},\frac{\nu-\beta+1}{2}\right)} ,\quad\operatorname{Re}\;\nu > -1$ | Expression | Mathematics | PhD | [
"True",
"False"
] | False | False |
1693345 | In a proton accelerator used in an elementary particle physics experiments, the trajectories of protons are controlled by bending magnets that produce a magnetic field of 2.40 T. What is the magnetic-field energy in a {eq}\rm 12.0 \ cm^3
{/eq} volume of space where B = 2.40 T ? | 27.51 J | Float | Physics | Senior High School | [
"27.5",
"True"
] | False | True |
313079 | The rate constant for a reaction involving {eq}\rm
NO_2
{/eq} is {eq}\rm
7.45 \times 10^2\ M/s
{/eq} at {eq}\rm
300 ^\circ C
{/eq}. How long (in seconds) would it take for the concentration of {eq}\rm
NO_2
{/eq} to decrease from {eq}\rm
2.15\ M
{/eq} to {eq}\rm
1.28\ M
{/eq}? | 1.17e-3 s | Float | Chemistry | University | [
"** 1.17 \\times 10^{-3}",
"True"
] | False | True |
1877757 | In this example, we will determine the range of angular deviations that a particular grating produces in the visible range of wavelengths. The wavelengths of the visible spectrum are approximately 400 nm (violet) through 700 nm (red). Find the first-order diffraction angles corresponding to the minimum and maximum wavelengths of the visible spectrum that are produced by a plane grating with 600 lines per millimeter. What is the angular width of the first-order diffraction maxima if white light is passed through the grating?
SOLUTION
The first-order spectrum corresponds to {eq}m=1
{/eq}. The grating has 600 lines per millimeter, so the grating spacing (the distance d between adjacent lines) is
{eq}d=\frac{1 \ mm}{600} = 1.67 \times 10^{-6} \ m
{/eq}
With {eq}m=1
{/eq}, the angular deviation of the violet light {eq}\theta_v
{/eq}, is given by
{eq}\sin\theta_v =\frac{m\lambda}{d}=\frac{(1)(4.00 \times 10^{-7} \ m)}{(1.67 \times 10^{-6} \ m)}=0.240
{/eq}
So that {eq}\theta_v=13.9^{\circ}
{/eq}
The angular deviation of the red light is given by
{eq}\sin\theta_r= \frac{(1)(7.00 \times 10^{-7} \ m)}{(1.67 \times 10^{-6} \ m)}=0.420
{/eq}
Thus, {eq}\theta_r=24.8^{\circ}
{/eq}
Therefore, the angular width of the first-order visible spectrum is {eq}24.8^{\circ}-13.9^{\circ} = 10.9^{\circ}
{/eq}
Conclusion: Increasing the number of lines per millimeter in the grating increases the angular width of the spectrum, but the grating spacing {eq}d
{/eq} can?t be less than the wavelengths of the spectrum being observed. Do you see why?
Problem:
If the angular width of the first-order visible spectrum is instead {eq}16.7^{\circ}-9.4^{\circ} = 7.2^{\circ}
{/eq}, how many lines per millimeter are there in the grating? | 411 lines per millimeter | Integer | Physics | Senior High School | [
"406",
"False"
] | False | False |
446856 | The demand, {eq}D(x)
{/eq}, and the supply, {eq}S(x)
{/eq}, functions for a certain type of multipurpose printer are as follows. Find the equilibrium point. Assume that {eq}x
{/eq} is the price in dollars.
{eq}\displaystyle D (x) = q = 470 e^{\displaystyle -0.003 x}\\
S (x) = q = 160e^{\displaystyle 0.005 x}
{/eq} | (135, 313) | List | Economics | Senior High School | [
"(134.69, 313.7)",
"False"
] | False | True |
1353735 | Charge A and charge B are 2.00 m apart, and charge A is +3.90 C and charge B is +4.00 C. Charge C is located between them at a certain point and the force on charge C is zero. How far from charge A is charge C? | 0.99 m | Float | Physics | Senior High School | [
"**\n\nThe distance from charge A to charge C is 1.00 m.",
"False"
] | False | False |
1401284 | How much money should a firm be willing to spend to obtain a perfect market forecast?
A. EVwPIminus-Maximum EMV
B. EVwPIminus-EVPI
C. EVPIminus-Maximum EMV
D. EVPIminus-EMV | C | Multiple Choice | Economics | University | [
"A**",
"False"
] | False | False |
913027 | For the position vector $\mathbf r(t)= \langle t^2,t^3 \rangle$, compute the unit tangent vector $\mathbf{T}(t)$ for $t=5, t=-3$. | {eq}\mathbf{T}(5) = \displaystyle \frac {\langle1,7.5\rangle}{\sqrt{57.25}}, \mathbf{T}(-3)=\frac {\langle1,-4.5\rangle}{\sqrt{21.25}}{/eq} | List | Mathematics | University | [
" $\\mathbf{T}(5)=\\langle \\frac{2}{\\sqrt{229}}, \\frac{15}{\\sqrt{229}} \\rangle$, $\\mathbf{T}(-3)=\\langle -\\frac{2}{\\sqrt{85}}, \\frac{9}{\\sqrt{85}} \\rangle$\n$\\mathbf{T}(5) = \\langle \\frac{2}{\\sqrt{229}}, \\frac{15}{\\sqrt{229}} \\rangle$, $\\mathbf{T}(-3) = \\langle -\\frac{2}{\\sqrt{85}}, \\frac{9}{\\sqrt{85}} \\rangle$",
"False"
] | False | False |
1692728 | A man starts walking north at 4 feet/s from a point P. Five minutes later a woman starts walking south at 7 feet/s from a point 500 feet due east of P. At what rate are the people moving apart 15 minutes after the woman starts walking? | 11 ft/s | Float | Physics | Senior High School | [
"The people are moving apart at approximately 10.99 feet/s.",
"True"
] | False | True |
53567 | If an ergonomic intervention was estimated to increase sales by $80,000 within 2 years, what is the maximum investment if the cost of capital is 15%, the cost of sales is 50%, and the tax rate is 40%? | 20869.57 | Float | Finance | University | [
"** The maximum investment is $39,017.02",
"False"
] | False | False |
1836997 | What is the probability that their first son will have hemophilia? | 25% or 1/4 | Percentage | Biology | Senior High School | [
"1/2",
"False"
] | False | False |
1727217 | What is the specific heat of a substance that absorbs #2.5*10^3# joules of heat when a sample of #1 * 10^4# g of the substance increases in temperature from 10°C to 80°C? | 3.57xx10^(-3)J/(g*''^@C) | Float | Physics | Senior High School | [
"The specific heat of the substance is 0.0036 J/g°C",
"True"
] | False | True |
575033 | Reparametrize the curve $\mathbf r(t)= \langle e^{-t} \cos 3t, e^{-t} \sin 3t, e^t\rangle$ with respect to arclength measured from the point (1,0,1) in the direction of increasing t. | {eq}s(t) = \int \sqrt { 10e^{-2t} + e^{2t} } \; dt{/eq} | Expression | Mathematics | University | [
" $\\mathbf{r}(s) = \\langle e^{-t(s)} \\cos 3t(s), e^{-t(s)} \\sin 3t(s), e^{t(s)} \\rangle$, where $s = \\int_0^t \\sqrt{10e^{-2u} + e^{2u}} du$.\nWe cannot find an explicit expression for $t(s)$, so let's leave the answer in implicit form.\n\n$\\mathbf{r}(s)=\\langle e^{-t(s)} \\cos 3t(s), e^{-t(s)} \\sin 3t(s), e^{t(s)}\\rangle$, where $t(s)$ is the inverse function of $s(t) = \\int_0^t \\sqrt{e^{2u}+10e^{-2u}} du$.",
"True"
] | False | True |
36062 | How to say they in Spanish | ellos (masculine) or ellas (feminine) | String | Other | Primary School | [
"ellos/ellas/ustedes",
"False"
] | False | False |
432438 | Tommy Harris Company produced 1,200 units of its only product last month. The company's employees were paid a total of $221,400 for working 20,500 hours. The standard wage rate is $10.50 and the standard time to produce a single unit is 17.50 hours.
What is Tommy Harris' labor rate variance? | $6,150 unfavorable | Float | Business | University | [
"The labor rate variance is $6,150 Unfavorable.**",
"True"
] | False | True |
1297035 | The cost of common equity is represented by the symbol g in the dividend growth equation.
a. True
b. False | b | Boolean | Business | University | [
"b. False",
"True"
] | False | True |
1911070 | Who wrote If Roses Grow in Heaven? | Dolores M. Garcia | String | Other | Primary School | [
"FINAL ANSWER: I cannot answer this question.",
"False"
] | False | False |
1292156 | The decomposition of nitrosyl bromide at {eq}10^{\circ}C
{/eq}
{eq}NOBr \rightarrow NO + \dfrac{1}{2}Br_2
{/eq}
is second order in NOBr with a rate constant of 0.800 {eq}M^{-1} s^{-1}
{/eq}. If the initial concentration of NOBr is 0.423 M, the concentration of NOBr will be {eq}5.63 \times 10^{-2}
{/eq} M after how many seconds have passed? | 19.25 s | Float | Chemistry | University | [
"19.25 s**",
"True"
] | True | True |
1036333 | How would one go about solving a differential equation of the form $$ \frac{d^2x}{dt^2} = K( \frac{1}{x^\gamma})$$ where both K and Gamma are constants? | $x(t) = \left(\frac{1}{2}(1-\gamma)\sqrt{\frac{K'}{\gamma + 1}}t + C_1 \right)^{\frac{2}{1-\gamma}}$ | Expression | Mathematics | University | [
"The solution is given implicitly by $$ \\int \\frac{dx}{\\sqrt{\\frac{2K}{1-\\gamma} x^{1-\\gamma} + C_2}} = \\pm t + C_3 $$, where $C_2$ and $C_3$ are constants determined by initial conditions.",
"True"
] | False | True |
2090370 | Suppose the economy starts off producing Natural Real GDP. Next, aggregate demand rises, ceteris paribus. As a result, the price level rises in the short run. In the long run, when the economy has moved back to producing Natural Real GDP, the price level will be-
(A) higher than it was in short-run equilibrium.
(B) lower than it was in short-run equilibrium but higher than it was originally (before aggregate demand increased).
(C) lower than it was originally (before aggregate demand increased).
(D) equal to what it was originally (before aggregate demand increased). | B | Multiple Choice | Economics | University | [
"(A)**",
"True"
] | False | False |
474442 | Convert the following matrix to reduced row echelon form:
$\left(
\begin{array}{cccccc}
-6 & 4 & 10 & -2 & 2 & 1 \\
6 & 0 & -1 & -4 & 3 & 3 \\
-9 & 5 & -8 & 1 & -7 & -10 \\
\end{array}
\right)$. | \left(\begin{array}{cccccc}
1 & 0 & 0 & -\frac{57}{83} & \frac{142}{249} & \frac{97}{166} \\
0 & 1 & 0 & -\frac{102}{83} & \frac{25}{83} & -\frac{23}{166} \\
0 & 0 & 1 & -\frac{10}{83} & \frac{35}{83} & \frac{42}{83} \\
\end{array}\right) | Matrix | Mathematics | University | [
"\\left(\n\\begin{array}{cccccc}\n1 & 0 & 0 & -181/249 & 15/249 & -152/249 \\\\\n0 & 1 & 0 & -102/83 & 15/83 & 103/166 \\\\\n0 & 0 & 1 & -10/83 & 35/83 & 54/83 \\\\\n\\end{array}\n\\right)",
"False"
] | False | False |
288748 | Suppose that you are willing to pay $20 to see a movie on Saturday night. A ticket costs $10, and the next-best alternative use of your time would be to go to dinner with a friend. The cost of the dinner is $20 and you value the experience of having dinner with your friend at $60. The opportunity cost of seeing the movie is equal to:
a) $50.
b) $30.
c) $20.
d) $10. | a | Multiple Choice | Economics | Senior High School | [
"$30",
"False"
] | False | False |
651953 | Use the shell method to find the volume of the solid generated by revolving the shaded region about the x-axis. | π/2 | Expression | Mathematics | University | [
"π/6",
"False"
] | False | False |
582670 | Sponge Bob will receive a payment of $5,100 per year for 7 years beginning three years from today. At a discount rate of 8 percent, what is the present value of this deferred annuity? | $28,931 | Float | Business | University | [
"**\n\n$22,764.48",
"False"
] | False | False |
1404913 | Blood pressure is the pressure of systolic and diastolic pressure. In which part of brain reflexes for blood pressure are present?
a) Medulla
b) Oblongata
c) Crus cerebri
d) Corpora
e) Quadrigemina
f) Pons varolii | A | Multiple Choice | Biology | Senior High School | [
"a",
"False"
] | False | True |
499556 | Early man was attracted to the delta of the Nile for three reasons. These reasons were:
It was close to Jerusalem
The rich soil
The abundance of water
The warm climate
The great fishing | The rich soil, abundance of water and warm climate | List | History | Junior High School | [
"The rich soil, the abundance of water, the great fishing",
"False"
] | False | False |
2015005 | Behavioral ethics experiments conclude that moral suasion can decrease ethical behavior. Indicate whether the statement is true or false | False | Boolean | Philosophy | University | [
"** True",
"False"
] | False | False |
468074 | How do you determine the characteristic polynomial of a matrix? | det(A - λI) | Expression | Mathematics | University | [
"**\n\nThe characteristic polynomial of a matrix *A* is found by calculating det(*A* - λ*I*), where λ is a variable and *I* is the identity matrix of the same size as *A*. The determinant, when simplified, yields the characteristic polynomial.",
"True"
] | False | True |
63831 | Provide Total Terminal Cash flows:
Kraemer Company is launching a new product. The following information relates to the launch:
1) 4 year project life
2) New equipment cost $(200,000)
3) Equipment ship & install cost $(35,000)
4) Related start up cost as a percent of sales $(5,000) -60%
5) Inventory increase$25,000
6) Accounts Payable increase$5,000
7) Equip. salvage value after tax$15,000
8) Sales for first year$200,000
9) Sales increase per year5%
10) Operating cost:$(120,000)
11) Depreciation expense - SL$(60,000)
12) Tax rate-40%
13) WACC-10% | $35,000 | Integer | Business | University | [
"**\n\nThe total terminal cash flow is $40,000.",
"False"
] | False | False |
253114 | Find a fundamental set of solutions of the first order system of ODEs:
x' = 4y,
y' = -x + 4y. | x1(t) = e^(2t) [[2],[1]] and x2(t) = e^(2t) [[2],[1]] | Matrix | Mathematics | University | [
" $\\left\\{ \\begin{pmatrix} 2e^{2t} \\\\ e^{2t} \\end{pmatrix}, \\begin{pmatrix} (2t-1)e^{2t} \\\\ te^{2t} \\end{pmatrix} \\right\\}$",
"True"
] | False | False |
710660 | A ball with a mass of # 3 kg# is rolling at #12 m/s# and elastically collides with a resting ball with a mass of #9 kg#. What are the post-collision velocities of the balls? | v_1^'=-6 m/s, v_2^'=6 m/s | List | Physics | Senior High School | [
"Final Answer: The final velocities are -6 m/s for the 3 kg ball and 6 m/s for the 9 kg ball.",
"True"
] | False | True |
761540 | How do you say ''beautiful city'' in French? | belle ville | String | Other | Primary School | [
"belle ville",
"True"
] | True | True |
133550 | Cullumber Company bought a machine on January 1, 2017. The machine cost $142,000 and had an expected salvage value of $29,000. The life of the machine was estimated to be 5 years. The depreciation expense using the straight-line method of depreciation is {eq}\rule{0.5in}{0.3pt}
{/eq}. | 22,600 | Integer | Business | Senior High School | [
"The depreciation expense using the straight-line method of depreciation is $22,600.",
"True"
] | True | True |
666470 | A force F=F_0exp(-at) acts on a harmonic oscillator of mass m, spring constant k, and damping constant b. Find a particular solution of the equation of motion. | x(t) = \frac{F_0}{m a^2 - b a + k} e^{- a t} | Expression | Physics | University | [
"x_p(t) = \\frac{F_0 e^{-at}}{ma^2 - ba + k}",
"True"
] | False | True |
1466001 | A closely wound rectangular coil of 100 turns has dimensions of 21.0 cm by 47.0 cm. The plane of the coil is rotated from a position where it makes an angle of 39.0° with a magnetic field of 1.80 T to a position perpendicular to the field. The rotation takes 5.00 x {eq}10^{-2}
{/eq} s. What is the average emf induced in the coil? | 79.184 V | Float | Physics | Senior High School | [
"** The average emf induced in the coil is 80.0 V.",
"True"
] | False | True |
598581 | A fair die is rolled 100 times. Let X be the sum of all of the faces of the rolls. E(x) = 350. Find P(X = 100). | 1.5306e-78 | Float | Mathematics | University | [
"**\n```\n(1/6)**100\n```",
"False"
] | False | False |
965937 | If the derivative of $y=x^2$ is $0$ when $x$ is $0$, how does that explain all the other values being greater than zero? If the slope is $0$ when $x$ is $0$, then wouldn't there be two values (one right before and one right after) that are equal to zero as well? And in that case, wouldn't the next very, very small point also be zero, and so on forever? How would the function ever increase in value? | 0 | Other | Mathematics | University | [
"** The derivative being zero at x=0 for y=x^2 simply indicates a turning point (a minimum). As x moves away from 0 in either direction, the derivative becomes non-zero, causing the function to increase. The derivative only describes the instantaneous slope at a specific point, and doesn't dictate the behavior of the function in an interval around that point.",
"False"
] | True | False |
772475 | A sequence of observations that are measured at successive regular time intervals is known as: | a | Multiple Choice | Mathematics | University | [
"Time series data",
"False"
] | False | True |
1438555 | What is the probability that in a sample of 100 full-time female workers, fewer than 49% would rather give up some of their salary for more personal time, given that 43% of all full-time female workers would rather do so? | 0.887 | Float | Mathematics | University | [
"0.8873",
"True"
] | False | True |
1099068 | An investment project has annual cash inflows of $3,700, $4,600, $5,800, and $5,000, for the next four years, respectively. The discount rate is 13 percent.
What is the discounted payback period for these cash flows if the initial cost is $8,500? | 2.3 years | Float | Finance | University | [
"The discounted payback period is approximately 2.41 years.",
"True"
] | False | False |
956528 | Consider the titration of 25.0 mL of 0.281 M {eq}NaNO_2
{/eq} with 0.184 M {eq}HClO_4
{/eq}. Calculate the pH of the solution after 12.8 mL of {eq}HClO_4
{/eq} has been added. | 3.439 | Float | Chemistry | University | [
"** 3.45",
"True"
] | False | False |
1003588 | Assuming that the Waterfront Manufacturing Company is purchasing a production facility at a cost of $21,000,000. The firm expects the project to generate annual free cash flows of $7,000,000 over the next five years. They also expect to sell the facility at the end of five years for an after-tax salvage value of $5,000,000. Its cost of capital is 20 percent. What is the net present value (NPV) of this project? | 1,943,672.84 | Float | Finance | University | [
"**\n\nThe net present value (NPV) of this project is $1,944,290.13.",
"True"
] | False | False |
1850330 | What order is the correct stages in the Creative Process?
1: Evaluation, 2: Possible Solution, 3: Preparation, 4: Incubation
a) 2, 4, 3, 1
b) 3, 2, 4, 1
c) 1, 3, 2, 4
d) 4, 1, 3, 2 | d | Multiple Choice | Psychology | Senior High School | [
"(b)",
"True"
] | False | False |
1283735 | A brick has a mass of {eq}4.0 \ kg
{/eq} and the Earth has a mass of {eq}6.0 \times 10^{27} \ g.
{/eq}
a) What is the mass of {eq}1
{/eq} mole of bricks? | 2.40e+24 kg | Float | Physics | Senior High School | [
"2.4088 \\times 10^{27} \\ g",
"False"
] | False | True |
881686 | Compute the (pseudo)inverse of
$\left(
\begin{array}{ccc}
2 & 0 & 5 \\
-3 & 5 & 1 \\
5 & 2 & 4 \\
\end{array}
\right)$. | \frac{1}{119}\left(
\begin{array}{ccc}
-18 & -10 & 25 \\
-17 & 17 & 17 \\
31 & 4 & -10 \\
\end{array}
\right) | Matrix | Mathematics | University | [
"\\begin{pmatrix} -\\frac{18}{119} & -\\frac{10}{119} & \\frac{25}{119} \\\\ -\\frac{17}{119} & \\frac{17}{119} & \\frac{17}{119} \\\\ \\frac{31}{119} & \\frac{4}{119} & -\\frac{10}{119} \\end{pmatrix}",
"True"
] | True | True |
1582974 | Richards Corporation has the following budgeted sales for the first half of next year:
Cash SalesCredit Sales
January$40,000$140,000
February$45,000$160,000
March$40,000$120,000
April$45,000$140,000
May$55,000$190,000
June$70,000$300,000
The company Is In the process of preparing a cash budget and must determine the expected cash collections by month. To this end, the following information has been assembled:
Collections on credit sales:
40% In the month of sales.
45% In the month of following sales.
15% In the second month following sales.
The accounts receivable balance on January 1 is $61,000. Of this amount, $51,000 represents uncollected December sales and $10,000 represents uncollected November sales.
The total cash collected during January would be:
A. $144,250
B. $204,000
C. $85,000
D. $219,000 | A | Multiple Choice | Business | Senior High School | [
"Final Answer: (Undetermined)",
"False"
] | False | False |
475273 | Given two matrices $A$ and $B$, find an invertible matrix $P$ such that $B = PA$. How is it possible to find $P$? | P = R_2^{-1}R_1 where R_1A = R_2B = E, and E is the common row-echelon form of A and B | Matrix | Mathematics | University | [
"P",
"False"
] | False | False |
1474080 | A truck pulls boxes up an incline plane. The truck can exert a maximum force of #4,800 N#. If the plane's incline is #(2 pi )/3 # and the coefficient of friction is #3/8 #, what is the maximum mass that can be pulled up at one time? | 465kg | Integer | Physics | Senior High School | [
"**\nThe maximum mass that can be pulled up at one time is approximately 721.70 kg.",
"False"
] | False | False |
1873235 | Convert the following matrix to reduced row echelon form:
$\left(
\begin{array}{cccc}
1 & -10 & -3 & 7 \\
-7 & 0 & 1 & -4 \\
3 & -1 & 7 & -8 \\
\end{array}
\right)$. | \left( \begin{array}{cccc} 1 & 0 & 0 & \frac{41}{108} \\ 0 & 1 & 0 & -\frac{7}{27} \\ 0 & 0 & 1 & -\frac{145}{108} \\ \end{array} \right) | Matrix | Mathematics | University | [
"\\begin{pmatrix} 1 & 0 & 0 & 53/108 \\\\ 0 & 1 & 0 & -62/189 \\\\ 0 & 0 & 1 & -13/108 \\end{pmatrix}",
"False"
] | False | False |
763234 | Two capacitors are connected in parallel across the terminals of a battery. One has a capacitance of {eq}\rm 2.13 \ \mu F
{/eq} and the other has a capacitance of {eq}\rm 4.04 \ \mu F
{/eq}. These two capacitors together store {eq}\rm 5.09 \times 10^{-5} \ C
{/eq} of charge. What is the voltage of the battery? | 36.5 V | Float | Physics | Senior High School | [
"8.25",
"False"
] | False | True |
1547107 | A model train with a mass of #2 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #9 cm# to #12 cm#, by how much must the centripetal force applied by the tracks change? | 0.18N | Float | Physics | Senior High School | [
"-0.18 N",
"True"
] | False | True |
920621 | Integrate {eq}\frac{dm}{dt} = \int (-c*D) - L{/eq} | m=-cDt-Lt+K | Expression | Mathematics | University | [
"{eq}m(t) = \\int \\left( \\int (-c \\cdot D) \\right) dt - L \\cdot t + C{/eq}",
"False"
] | False | False |
659747 | Evaluate the integral {eq}\int \frac{du}{u \sqrt {3-u^2}} {/eq} | \frac{\ln \left| \sqrt {3-u^2}-\sqrt{3}\right| }{2\sqrt{3}}-\frac{\ln \left( \sqrt {3-u^2}+\sqrt{3}\right) }{2\sqrt{3}}+C | Expression | Mathematics | University | [
"**\n\n```\n-(1/√3) ln |(√3 + √(3 - u²)) / u| + C\n```",
"True"
] | False | False |
1221122 | Red light of wavelength 644 nm, from a point source, passes through two parallel and narrow slits which are 1.00 nm apart. Determine the distance between the central bright fringe and the third dark interference fringe formed on a screen parallel to the plane of the slits and 1.00 m away. | 2,254 m | Float | Physics | University | [
"The third dark fringe cannot be observed because its location is mathematically beyond the physical limits of the screen. Assuming that the largest possible fringe (m=1) at sin(theta)=1 is observed instead, then the distance between the central bright fringe and the position of the maximum fringe is 3.73 m.",
"False"
] | False | False |
1126370 | Conduct a hypothesis test to determine if the brown trout's mean I.Q. is greater than four, given the sample I.Q.s of 5, 4, 7, 3, 6, 4, 5, 3, 6, 3, 8, 5, a significance level of 5%, and a standard deviation of 1.62. | 0.0389 | Float | Mathematics | University | [
"Reject the null hypothesis. There is sufficient evidence to suggest that the mean I.Q. of brown trout is greater than four.",
"False"
] | False | True |
316742 | How do you solve for k using the Arrhenius Equation? A first order reaction has an activation energy of #"E"_a = "65.7 kJ/mol"# and a frequency factor (pre-exponential factor, #"A"#) of #1.31 xx 10^12 "s"^(-1)#. Calculate the rate constant at #19^@ "C"#. | 2.34 s^(-1) | Float | Chemistry | Senior High School | [
"** The rate constant, *k*, at 19°C is approximately 1.32 s<sup>-1</sup>.",
"False"
] | False | False |
410661 | If a spring has a constant of #3 (kg)/s^2#, how much work will it take to extend the spring by #83 cm #? | 1.03 J | Float | Physics | Senior High School | [
"** 1.0 J",
"True"
] | False | False |
1868512 | Driving in your car with a constant speed of v = 22 m/s, you encounter a bump in the road that has a circular cross-section. If the radius of curvature of the bump is 52 m, find the apparent weight of a 66-kg person in your car as you pass over the top of the bump. | 32 N | Integer | Physics | Senior High School | [
"**\nThe apparent weight of the person is 32 N.",
"True"
] | False | True |
452834 | Write an iterated triple integral in cylindrical coordinates which represents the volume of the solid bounded by the paraboloid {eq}z = x^{2} + y^{2} {/eq} and the plane {eq}z=4 {/eq}. | $\int_{0}^{2\pi }\int_{0}^{2}\int_{r^{2}}^{4}rdzdrd\theta$ | Expression | Mathematics | University | [
"**\n\n```\n∫₀^(2π) ∫₀² ∫_(r²)^4 r dz dr dθ\n```",
"True"
] | False | True |
1757752 | Forces with magnitudes of 250 pounds and 130 pounds act on an object at angles of 45º and -60º, respectively, with the x-axis. Find the direction and magnitude of the resultant of these forces. | The magnitude of the resultant force is 250.013 and the direction angle with the positive x-axis is 14.75 degrees | Float | Physics | Senior High School | [
"The magnitude of the resultant force is approximately 250.16 pounds and its direction is approximately 14.86 degrees with the x-axis.",
"True"
] | False | True |
755441 | Write the ODE {eq}m\frac{d^2x}{dt^2}+c\frac{dx}{dt}+kx=0{/eq} as a system of first order differential equations, where {eq}x{/eq} is displacement from the equilibrium position. | z'=[0, 1; -c/m, -k/m]z | Matrix | Mathematics | University | [
"dx/dt = v, dv/dt = -(k/m)x - (c/m)v",
"True"
] | False | True |
1736652 | An AC generator consists of eight turns of wire, each having area {eq}{\text{A = 0}}{\text{.0870 }}{{\text{m}}^{\text{2}}}
{/eq}, with a total resistance of {eq}{\text{12}}{\text{.8 }}\Omega
{/eq}. The loop rotates in a magnetic field of 0.416 T at a constant frequency of 56.2 Hz. What is the maximum induced current? | 8 A | Integer | Physics | Senior High School | [
"7.96",
"False"
] | False | False |
813781 | How high are air currents? | 4 to 53 miles (6 to 85 kilometers) | String | Physics | Junior High School | [
"Air currents can reach heights of up to approximately 7-18 km (4-11 miles), depending on latitude, the type of air current, and weather conditions.",
"False"
] | False | False |
1058119 | Who invented the first closed-circuit TV (CCTV)? | Walter Bruch | String | History | Junior High School | [
"Therefore, the answer is Walter Bruch.",
"True"
] | False | True |
2004771 | Which of the following statements is false?
(a) If an intangible asset has a finite life, it should be amortized.
(b) The amortization period of an intangible asset can exceed 20 years.
(c) Goodwill is recorded only when a business is purchased.
(d) Research and development costs are expensed when incurred, except when the research and development expenditures result in a successful patent. | d | Multiple Choice | Business | University | [
"FINAL ANSWER: (b)",
"False"
] | False | False |
2064612 | A straight rod of length L extends from x = 0 to x = L. The linear mass density of rod varies with x coordinate as {eq}\lambda = a_0 + b_0x^2
{/eq}. What will be the gravitational force experienced by a point mass m at x = -a? | Gm*(a_0*L/(a*(a+L)) + b_0*(L*(2*a+L)+2*a*(a+L)*(log(a)-log(a+L)))/(a+L)) | Expression | Physics | University | [
"Gm[\\frac{b_0L(L+2a)}{L+a} + \\frac{a_0L}{a(L+a)} - 2ab_0ln(1+\\frac{L}{a})]",
"True"
] | False | False |
1880904 | A hardworking ant must supply {eq}0.00955 \ N
{/eq} to pull a small piece of fruit at constant velocity over a distance of {eq}8.60 \ cm
{/eq} up a small hill to the entrance of the colony. If the coefficient of kinetic friction between the piece of fruit and the {eq}16.2^\circ
{/eq} sloped hill is {eq}0.540
{/eq} , calculate the work done by the ant by pulling the piece of fruit up the hill. | 8.21e-4 J | Float | Physics | Senior High School | [
"** 0.0008213 J",
"True"
] | False | True |
42614 | How do I calculate a normal plane for a given vector and calculate the 3D coordinates of planar 2D coordinates? | P = p0 + R [ x1, y1, 0]T, where P is the 3D coordinate, p0 is a point on the plane, R is the rotation matrix constructed from the normal vector and two perpendicular vectors, and (x1, y1) are the 2D coordinates. | Expression | Mathematics | University | [
"To calculate a normal plane for a given vector, use the vector's components as coefficients in the plane equation `ax + by + cz + d = 0`. Determine 'd' by substituting a known point on the plane into the equation. To calculate the 3D coordinates of planar 2D coordinates (u, v) on this plane, find two orthonormal vectors (U_norm, W_norm) within the plane. The 3D point is then `P = P0 + (u * U_norm) + (v * W_norm)`, where P0 is a known point on the plane.",
"True"
] | False | True |
1674200 | In the case of differentiable manifolds, since they are homeomorphic to $\mathbb{R}^n$, does compactness imply closedness? | Yes | Boolean | Mathematics | University | [
"no",
"False"
] | False | False |
542130 | A 5-year bond with 10% coupon rate and $1000 face value is selling for $1123. Calculate the yield to maturity on the bond assuming annual interest payments. | 7.1% | Percentage | Finance | University | [
"7.103%",
"True"
] | False | True |
1716844 | Let $X_i$ be i.i.d Bernoulli random variables with parameter $1/2$. Find a good bound for $$ \mathbb{P} \left( \sum_{i=1}^{1000} X_i \leq 599 \right) \ .$$ Provide hints towards a suitable strategy, rather than an outright bound. | $\Phi\left(\dfrac{599-\dfrac{1000}{2}}{\sqrt{\dfrac{1000}{4}}}\right)$ | Expression | Mathematics | University | [
"**\n\nBased on the normal approximation with continuity correction, $\\mathbb{P}(S \\leq 599) \\approx \\mathbb{P}(Z \\leq 6.28) \\approx 1$. The Chernoff bound gives something very close to zero. A more precise numerical calculation would be needed for a more refined bound. Based on these methods,\n\n$\\mathbb{P} \\left( \\sum_{i=1}^{1000} X_i \\leq 599 \\right) \\approx 1 $",
"True"
] | False | False |
1056973 | Which of the following is NOT one of the steps in statistical process control? | C | Multiple Choice | Mathematics | University | [
"Arbitrarily changing control limits.",
"True"
] | False | False |
1804573 | Imagine you've started a new pizza restaurant. It costs you about $6 to produce a pizza. Last week you sold 500 pizzas for $12 each. This week you raised your price and sold 375 pizzas for $14 each. What price should you be charging? | A | Multiple Choice | Economics | Junior High School | [
"** $13",
"False"
] | False | False |
1362943 | Why do you do no work on a 25-Kg backpack when you walk a horizontal distance of 100mm? | 0 | Integer | Physics | Senior High School | [
"Because the force you exert on the backpack is vertical, while the displacement is horizontal, the angle between the force and displacement is 90 degrees, and the cosine of 90 degrees is zero, resulting in zero work done.",
"False"
] | False | True |
1938377 | Find the directional derivative of {eq}f(x, y, z) = xz + y^4{/eq} at the point (2, 3, 1) in the direction of a vector making an angle of {eq}-\pi/4{/eq} with {eq}\triangledown f(2, 3, 1){/eq}. | 76.3839 | Float | Mathematics | University | [
"\\frac{\\sqrt{23338}}{2}",
"True"
] | False | True |
39984 | Weatherall Enterprises has no debt or preferred stock it is an all-equity firm and has a beta of 2.0. The chief financial officer is evaluating a project with an expected return of 14%, before any risk adjustment. The risk-free rate is 5%, and the market risk premium is 4%. The project being evaluated is riskier than an average project, in terms of both its beta risk and its total risk. Which of the following statements is CORRECT?
a. The project should definitely be rejected because its expected return (before risk adjustment) is less than its required return. b. Riskier-than-average projects should have their expected returns increased to reflect their higher risk. Clearly, this would make the project acceptable regardless of the amount of the adjustment.
c. The accept/reject decision depends on the firm's risk-adjustment policy. If Weatherall's policy is to increase the required return on a riskier-than-average project to 3% over {eq}r_{S}
{/eq}, then it should reject the project.
d. Capital budgeting projects should be evaluated solely on the basis of their total risk. Thus, insufficient information has been provided to make the accept/reject decision.
e. The project should definitely be accepted because its expected return (before any risk adjustments) is greater than its required return. | c | Multiple Choice | Business | University | [
"{/eq}, then it should reject the project.",
"False"
] | False | False |
1788727 | Balance the redox equation by the ion-electron method: {eq}\displaystyle \rm CIO_3^- + Cl^- \to Cl_2 +CIO_2
{/eq} in acidic solution. | 2ClO_3^-+2Cl^-+4H^+\to 2ClO_2+Cl_2+2H_2O | Expression | Chemistry | Senior High School | [
"The balanced redox equation is $\\displaystyle \\rm 2H^+ + CIO_3^- + 2Cl^- \\to Cl_2 +CIO_2 + H_2O$",
"False"
] | False | False |
1785536 | Marissa Company is preparing a statement of cash flows using the indirect method.
The following data are available:
Net income 30,000
Depreciation expense 18,000
Inventory decrease 5,000
Wages payable decrease 10,000
Accounts receivable decrease 10,000
Accounts payable decrease 7,000
Is Net cash, provided by operating activities, equal to $36,000? | 46000 | Integer | Business | University | [
"Is Net cash, provided by operating activities, equal to $36,000? No",
"False"
] | False | False |
1909257 | How many countries in Africa have had a civil war? | 22 | Integer | History | Junior High School | [
"Approximately 19",
"False"
] | False | False |
948949 | Steam flows steadily through a turbine at a rate of 20,000 kg/h, entering at 7 MPa and 500{eq}^{\circ}
{/eq}C and leaving at 40 KPa as saturated vapor. If the power generated by the turbine is 4 MW, determine the rate of heat loss from the steam. | 307 kW | Float | Physics | University | [
"**\n\nThe rate of heat loss from the steam is 8306.7 kW.\n```\n8306.7 kW\n```",
"False"
] | False | False |
621632 | how much does the kinetic energy change is the speed of an object is tripled and its mass is cut in half | 250% | Percentage | Physics | Senior High School | [
"The kinetic energy changes by a factor of 9/4.",
"False"
] | False | False |
1160741 | Combined Communications is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by {eq}15
{/eq} percent a year for the next {eq}3
{/eq} years and then decreasing the growth rate to {eq}5.5
{/eq} percent per year. The company just paid its annual dividend in the amount of {eq}\$0.65
{/eq} per share. What is the current value of this stock if the required rate of return is {eq}15.5
{/eq} percent? | $8.78 | Float | Business | University | [
"8.69",
"False"
] | False | False |
1808319 | Find the radius and interval of convergence of the series {eq}\sum_{n=1}^\infty \frac{(x-1)^n}{n^33^n}
{/eq} | The radius of convergence is 3 and the interval of convergence is [-2,4]. | List | Mathematics | University | [
"R=3, [-2,4]",
"True"
] | False | True |
2063647 | A particular application calls for {eq}N_2(g)
{/eq} with a density of {eq}1.80 \ g / L
{/eq} at {eq}32 ^\circ \ C
{/eq}. What must be the pressure of the {eq}N_2(g)
{/eq} in millimetres of mercury? | 1,222.92 mmHg | Float | Chemistry | Senior High School | [
"** 1216",
"True"
] | False | False |
1012286 | +1.0 C charged object and a +2.0 C charged object are separated by 60 m. Where should a {eq}\rm -1.0 \times 10^{-3} \ C
{/eq} charged object be located on a line between the positively charged objects (from the +1.0 C charged object) so that the net electrical force exerted on the negatively charged object is zero? | 24.85 m | Float | Physics | Senior High School | [
"** The negatively charged object should be located approximately 24.85 m from the +1.0 C charged object.",
"True"
] | False | True |
446117 | The earth has a vertical electric field at the surface, pointing down, which averages 120 N/C. This field is maintained by various atmospheric processes, including lightning. What is the excess charge on the surface of the earth? | 5.46e5 C | Float | Physics | University | [
"-5.42e5 C",
"False"
] | False | False |
1177994 | How many siblings does Katherine Johnson have? | 3 | Integer | History | Junior High School | [
"FINAL ANSWER: 3",
"True"
] | False | True |
1171209 | Draw all resonance structures for the sulfur trioxide molecule, {eq}SO_3.
{/eq}
Use the following guidelines.
Explicitly draw all H atoms. Include all valence lone pairs in your answer.
Do not include overall ion charges or formal charges in your drawing.
Do not draw double bonds to oxygen unless they are needed for the central atom to obey the octet rule.
Separate resonance structures using the {eq}\leftrightarrow
{/eq} symbol. | <img src="/cimages/multimages/16/capture192472445498470252479.jpg" alt="Resonance structures of sulfur trioxide."> | Other | Chemistry | Senior High School | [
"{image of resonance structures of SO3: S is central atom, single bond to two O's, and double bond to one O. The double bond rotates between all three O's. Each single bonded O has 3 lone pairs. The double bonded O has 2 lone pairs.}\n\n{eq}\\leftrightarrow\n\n{/eq}\n\n{image of resonance structures of SO3: S is central atom, single bond to two O's, and double bond to one O. The double bond rotates between all three O's. Each single bonded O has 3 lone pairs. The double bonded O has 2 lone pairs.}\n\n{eq}\\leftrightarrow\n\n{/eq}\n\n{image of resonance structures of SO3: S is central atom, single bond to two O's, and double bond to one O. The double bond rotates between all three O's. Each single bonded O has 3 lone pairs. The double bonded O has 2 lone pairs.}",
"True"
] | False | True |
594947 | I need the equation of the tangent plane to the sphere $x^2+y^2+z^2=r^2$ such that the plane contains the points $P=(x_1,y_1,z_1)$ and $Q=(x_2,y_2,z_2)$ and touches the sphere at only one point. | αx+βy+γz=r^2 | Expression | Mathematics | University | [
"x_0 x + y_0 y + z_0 z = r^2",
"False"
] | False | True |
1645885 | Which group of policies aims at discouraging rivals from starting a price war?
(a) Price matching and randomized pricing
(b) Price matching, brand loyalty, and commodity bundling
(c) Randomized pricing, price discrimination, and cross-subsidization
(d) Peak-peak pricing, two-part pricing, and price matching. | a | Multiple Choice | Economics | University | [
"(b)",
"False"
] | False | False |
2103352 | Find a power series representation for {eq}f(x) = \frac{1}{x-2}{/eq} and determine the interval of convergence. | The power series representation is {eq}\sum_{n=0}^{\infty} (3-x)^n{/eq} and the interval of convergence is (2,4) | Expression | Mathematics | University | [
"\\sum_{n=0}^{\\infty} -\\frac{1}{2^{n+1}} x^n, (-2, 2)",
"True"
] | False | False |
1822613 | A permanent scholarship fund is started through a donation of $100000. If five scholarships of $5000 each are awarded each year beginning ten years from now, Calculate the rate of return for the invested money. | 10% | Percentage | Finance | University | [
"The rate of return for the invested money is approximately 10.37%.",
"True"
] | False | False |
236261 | Determine how large is the {eq}\vec E
{/eq} field in an inkjet printer if the {eq}22.0 \ \mu m
{/eq} diameter ink drops have an initial velocity of {eq}34.0 \ ms
{/eq}, and a charge of {eq}q=22.00 \ nC
{/eq}. The drop is deflected upward a distance of {eq}3.0 \ mm
{/eq} as the drop travels through the {eq}x=2.0 \ cm
{/eq} long region between two charged plates. The mass {eq}m_e=8 \times10^{-11} \ kg
{/eq}. (Neglect any effects of gravity on the motion of the drops.) | 62.70 N/C | Float | Physics | Senior High School | [
"** The electric field strength is approximately 63630 N/C.",
"False"
] | False | False |
149356 | Consider the infinite sum $s=1+1/2^2-1/3^2-1/4^2+1/5^2+1/6^2-...$. Why does WolframAlpha give a different answer initially, but then seem to converge when adding more terms? Find an analytical expression for the sum. | \frac{\pi^2}{48} + C | Expression | Mathematics | University | [
"\\frac{\\pi^2}{8}",
"False"
] | False | False |
1968780 | Let duv be the length of the shortest path from u to v in a directed graph. Suppose that the length of a single edge (x, y) decreases from cxy to c'xy. Design an algorithm to recompute all the duv's in O(n2). | d'_{u,v} = min{d_{u,v}, d_{u,x} + c'_{x,y} + d_{y,v}} | Expression | Computer Science | University | [
"The algorithm iterates through all pairs of vertices (u, v), and updates the shortest path distance between them if the path u -> x -> y -> v (using the updated edge weight) is shorter than the original shortest path. The time complexity is O(n^2).",
"True"
] | False | True |
1395526 | What is the percent chance of an offspring having the genotype AabbCc if the parents were AaBbCc and AAbbCC respectively? | 12.5% | Percentage | Biology | Senior High School | [
"12.5",
"True"
] | False | False |
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