message
stringlengths 1
1.07k
| message_type
stringclasses 2
values | message_id
int64 0
1
| conversation_id
int64 0
799
|
|---|---|---|---|
What is the effective rates (between 0 and 1) for 18% compounded quarterly? Return the numeric value.
|
instruction
| 0 | 250 |
0.1925
|
output
| 1 | 250 |
You are interviewing two investment managers. Mr. Wong shows that the average return on his portfolio for the past 10 years has been 14%, with a standard deviation of 8% and a beta of 1.2. Ms. Petrov shows that the average return on her portfolio for the past 10 years has been 16%, with a standard deviation of 10% and a beta of 1.6. You know that over the past 10 years, the US Treasury security rate has averaged 2% and the return on the S&P 500 has averaged 11%. By measuring Jensen’s alpha, Mr. Wong has done the better job. Is this correct? Answer True or False.
|
instruction
| 0 | 251 |
True
|
output
| 1 | 251 |
$H(X_n|X_0)$ is a concave function of n for a stationary Markov process. True or False?
|
instruction
| 0 | 252 |
True
|
output
| 1 | 252 |
Denote m(\cdot) to be Lebesgue measure. Given a point set E. Suppose for any closed set F and open set G with F \subset E \subset G, it holds $\sup _F {m(F)}<\inf _G {m(G)}$. Is set E Lebesgue measurable? Answer 1 for yes and 0 for no. Return the number
|
instruction
| 0 | 253 |
0.0
|
output
| 1 | 253 |
A perceptual audio codec is used to compress an audio signal. The codec groups every 4 barks into a subband and then allocates bits to different subbands according to the result of a spectrum analysis based on a psychoacoustic model. All samples in the same subband are quantized with the same quantizer, and the bit resolution of which is allocated by the codec. (The Bark scale is a psychoacoustical scale proposed by Eberhard Zwicker in 1961.) Fig. Q1a shows the frequency spectrum of a windowed segment of audio signal. The psychoacoustic model shown in Fig. Q1b is used in the audio codec to derive the masking threshold for the audio segment. How many potential maskers in Fig. Q1a?
|
instruction
| 0 | 254 |
7
|
output
| 1 | 254 |
Suppose g(x) is the horizontal asymptote of function f(x) = (\sqrt{36 x^2 + 7}) / (9x + 4). What are possible values of g(2023)?
|
instruction
| 0 | 255 |
[0.6667, -0.6667]
|
output
| 1 | 255 |
30 students from 5 classes solved 40 math problems. Each student must answer at least one question. Every two students in the same class solved the same number of questions. The number of questions answered by any two students in different classes is also different. Question: What's maximum possible number of students who only answered one question?
|
instruction
| 0 | 256 |
26
|
output
| 1 | 256 |
Consider the basis B of R^2 consisting of vectors v_1 = [3,1] and v_2 = [-1, 3]. If x = [10, 10], find the B-coordinate vector of x
|
instruction
| 0 | 257 |
[4, 2]
|
output
| 1 | 257 |
Compute $\int_C dz / (z * (z-2)^2)dz$, where C: |z - 2| = 1. The answer is Ai with i denoting the imaginary unit, what is A?
|
instruction
| 0 | 258 |
-0.3926
|
output
| 1 | 258 |
suppose the sequence a_n satisfies 0<a_n<1, and $(1-a_n)a_{n+1}>1/4$ for all n, what is the limit of a_n as n goes to infinity?
|
instruction
| 0 | 259 |
0.5
|
output
| 1 | 259 |
In how many ways can we form a 7-digit number using the digits 1, 2, 2, 3, 3, 3, 3?
|
instruction
| 0 | 260 |
105
|
output
| 1 | 260 |
Suppose C[0,1] denotes the space of all the continuous functions on the interval [0,1]. Is (C[0,1],\|\cdot\|_1 ) a Banach space? Here $\|f(x)\|_1=\int_0^1 |f(t)|dt$ with $f\in C[0,1]$. Answer 1 for yes and 0 for no.
|
instruction
| 0 | 261 |
0.0
|
output
| 1 | 261 |
Is the conditional entropy $H(X_0|X_n)$ non-decreasing with n for any Markov chain?
|
instruction
| 0 | 262 |
True
|
output
| 1 | 262 |
A gun is designed that can launch a projectile of mass 10 kg at a speed of 200 m/s. The gun is placed close to a straight, horizontal railway line and aligned such that the projectile will land further down the line. A small rail car of mass 200 kg and travelling at a speed of 100 m/s passes the gun just as it is fired. Assuming the gun and the car are at the same level, at what angle upwards must the projectile be fired so that it lands in the rail car?
|
instruction
| 0 | 263 |
60.0
|
output
| 1 | 263 |
What is the total number of colors in RGB color space?
|
instruction
| 0 | 264 |
16777216
|
output
| 1 | 264 |
If polygon ABCDE ~ polygon PQRST, AB = BC = 8, AE = CD = 4, ED = 6, QR = QP, and RS = PT = 3, find the perimeter of polygon ABCDE.
|
instruction
| 0 | 265 |
30
|
output
| 1 | 265 |
Derive the solution y = f(t) to the following IVP. $ty' - 2y = t^5sin(2t) - t^3 + 4t^4$, where $y(\pi) = 3\pi^4/2$. What is y(t) when $t=pi/2$.
|
instruction
| 0 | 266 |
19.095
|
output
| 1 | 266 |
An IPv4 packet contains the following data (in hexadecimal value) in the IP header: 4500 0034 B612 4000 4006 6F80 0A00 008B 5BC6 AEE0 . Does the header contains error?
|
instruction
| 0 | 267 |
False
|
output
| 1 | 267 |
Consider a source X uniform on $\{1,2,\ldots,m\}$ with a distortion measure $d(x, \hat{x})$ that satisfies the following property: all rows and columns of the distortion matrix are permutations of the set $\{d_1, d_2, \ldots, d_m\}$. Then the Shannon lower bound is tight. i.e. $R(D)=H(X)-\phi(D)$. True or False?
|
instruction
| 0 | 268 |
True
|
output
| 1 | 268 |
Calculate the momentum uncertainty of a tennis ball constrained to be in a fence enclosure of length 35 m surrounding the court in kg m/s.
|
instruction
| 0 | 269 |
3e-36
|
output
| 1 | 269 |
A $200-cm^3$ glass flask is filled to the brim with mercury at 20°C How much mercury overflows when the temperature of the system is raised to 100°C. The coefficient of linear expansion of the glass is $0.40 \times 10^{-5} K^{-1}. (Unit: cm^3)
|
instruction
| 0 | 270 |
2.7
|
output
| 1 | 270 |
Consider a 26-key typewriter. Suppose that pushing a key results in printing that letter or the next (with equal probability). Thus A results in A or B, ..., Z results in Z or A. What is the capacity of this channel in bits?
|
instruction
| 0 | 271 |
3.7
|
output
| 1 | 271 |
In how many ways can 10 distinct balls be placed into 4 identical boxes if each box must have at least 1 balls?
|
instruction
| 0 | 272 |
26335
|
output
| 1 | 272 |
If r(t) = (6t+2)i + 5t^2j - 8tk, find the Binormal vector as [xi, yj, zk]. What are x, y, z? Return them as a list.
|
instruction
| 0 | 273 |
[0.8, 0.0, 0.6]
|
output
| 1 | 273 |
Given that $V_A = V_B$, determine the value of $C_2$ (in μF) in the following circuit in the figure.
|
instruction
| 0 | 274 |
0.103
|
output
| 1 | 274 |
For matrix A = [[2, 4, 3], [3, 3, 1], [42, 20, 51]], what is its determinant?
|
instruction
| 0 | 275 |
-376
|
output
| 1 | 275 |
Given a color image of size 28 x 28 x 3 pixels, how many convolutional filters in the first layer of a Convolutional Neural Network if the first layer's output tensor has size 26 x 26 x 64?
|
instruction
| 0 | 276 |
64
|
output
| 1 | 276 |
The cross section for neutrons of energy 10 eV being captured by silver is 17 barns. What is the probability of a neutron being captured as it passes through a layer of silver 2 mm thick?
|
instruction
| 0 | 277 |
0.2
|
output
| 1 | 277 |
Compute $\int_{|z| = 2} (5z - 2) / (z * (z - 1)) dz$. The answer is Ai with i denoting the imaginary unit, what is A?
|
instruction
| 0 | 278 |
31.4
|
output
| 1 | 278 |
Calculate the momentum uncertainty of an electron within the smallest diameter of a hydrogen atom in kg m/s.
|
instruction
| 0 | 279 |
1e-24
|
output
| 1 | 279 |
is 1/4 belongs to Cantor set? Is 1/13 belongs to Cantor set? Return the two answers as a list with 1 for yes and 0 for no. For example, if you think both belong to Cantor set, return [1,1]
|
instruction
| 0 | 280 |
[1, 1]
|
output
| 1 | 280 |
How many ways are there to distribute 13 identical balls into 4 distinct boxes if the boxes are distinguishable and no box can be left empty?
|
instruction
| 0 | 281 |
220
|
output
| 1 | 281 |
What is the value of the integral $\int_2^4 \frac{\sqrt{log(9-x)}}{\sqrt{log(9-x)}+\sqrt{log(x+3)}} dx$?
|
instruction
| 0 | 282 |
1.0
|
output
| 1 | 282 |
What is the order of the element 5 in U_8?
|
instruction
| 0 | 283 |
2
|
output
| 1 | 283 |
suppose $u=\arctan \frac{y}{x}$, what is numeric of $\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}$?
|
instruction
| 0 | 284 |
0.0
|
output
| 1 | 284 |
Consider a file with a size of 350 Kbytes storing in a web server. Client A sends a request to the server to retrieve the file from a remote location. It is known that the link capacity between client A and the server is 10 Mbps and the round trip time (RTT) between the server and client is fixed at 20ms. Assume that the segment size is 20 Kbytes and the client has a receiver buffer of 200Kbytes. Assume that the window size (W) is fixed at 2. How long (in ms) does client A take to receive the whole file from the server after sending a request?
|
instruction
| 0 | 285 |
352
|
output
| 1 | 285 |
H(z) = $\int_0^1 e^{-z^2 t^2} dt$, what is H'(1)?
|
instruction
| 0 | 286 |
-0.3789
|
output
| 1 | 286 |
James (mass 90.0 kg) and Ramon (mass 60.0 kg) are 20.0 m apart on a frozen pond. Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them. When James has moved 6.0 m toward the mug, how far has Ramon moved? (Unit: m)
|
instruction
| 0 | 287 |
1.0
|
output
| 1 | 287 |
The following data related the rubber percentage of two types of rubber plants, where the sample have been drawn independently. Test for their mean difference. Type 1: 6.21 5.70 6.04 4.47 5.22 4.45 4.84 5.84 5.88 5.82 6.09 5.59 6.06 5.59 6.74 5.55, Type 2: 4.28 7.71 6.48 7.71 7.37 7.20 7.06 6.40 8.93 5.91 5.51 6.36. Are there difference between these two rubber plants?
|
instruction
| 0 | 288 |
True
|
output
| 1 | 288 |
Use Green's Theorem to evaluate $\oiint_{s} y^3 dx + x^3dy$ where $C$ is the positively oriented circle of radius 2 centered at origin.
|
instruction
| 0 | 289 |
-75.396
|
output
| 1 | 289 |
suppose the 10-by-10 matrix A has the form: if i \neq j, A_{i,j}=a_i*b_j; if i=j, A_{i,j}=1+a_i*b_j for all 1<=i,j<=10. Here a_i = 1/i, b_i=1/(i+1). Find the determinant of A. return the numeric.
|
instruction
| 0 | 290 |
1.9
|
output
| 1 | 290 |
Calculate the de Broglie Wavelength of a tennis ball of mass 57 g traveling 25 m/s in meters.
|
instruction
| 0 | 291 |
4.7e-34
|
output
| 1 | 291 |
Coloring the edges of a complete graph with n vertices in 2 colors (red and blue), what is the smallest n that guarantees there is either a 4-clique in red or a 4-clique in blue?
|
instruction
| 0 | 292 |
18
|
output
| 1 | 292 |
Consider that the following two signals: $x(t)$ and $v(t)$ $$ x(t)=\left\{\begin{array}{cc} 1 & 0 \leq t \leq 3 \\ 0 & \text { otherwise } \end{array} \quad v(t)=\left\{\begin{array}{cc} 1 & 0 \leq t \leq 2 \\ 0 & \text { otherwise } \end{array}\right.\right. $$ Let $y(\tau)=\int_{-\infty}^{\infty} x(\tau-t) v(t) d t$. Let $\tau=2.5$. Determine $y(\tau)$.
|
instruction
| 0 | 293 |
2
|
output
| 1 | 293 |
Calculate the minimum kinetic energy of an electron that is localized within a typical nuclear radius of 6 x 10^-15 m in MeV.
|
instruction
| 0 | 294 |
15.9
|
output
| 1 | 294 |
A load dissipates 1.5kW of power in an ac series RC circuit. Given that the power factor is 0.75, what is its reactive power $(P_r)$? What is its apparent power $(P_a)$? Represent the answer in a list [$P_r, P_a$] with unit kVA and kVAR respectively.
|
instruction
| 0 | 295 |
[2.0, 1.32]
|
output
| 1 | 295 |
If the sum-product algorithm is run on a factor graph with a tree structure (no loops), then after a finite number of messages have been sent, there will be no pending messages. True or false?
|
instruction
| 0 | 296 |
True
|
output
| 1 | 296 |
For matrix A = [[2, 4, 3], [3, 0, 1], [1, 2, 5]], what is its determinant?
|
instruction
| 0 | 297 |
-42
|
output
| 1 | 297 |
How many ways are there to divide a set of 5 elements into 2 non-empty ordered subsets?
|
instruction
| 0 | 298 |
240
|
output
| 1 | 298 |
In how many ways can 3 students be selected from a class of 20 to form a study group?
|
instruction
| 0 | 299 |
1140
|
output
| 1 | 299 |
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