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