rationale
stringlengths 0
4.7k
| target
stringlengths 1
171
| source
stringclasses 13
values | prompt
stringlengths 16
2.02k
|
|---|---|---|---|
A girl implies a young girl, whereas a lady implies someone older. Although she is giving a dog a treat, it does not imply she is giving her dog a rawhide bone.
|
Unknown
|
esnli
|
Context: "A girl is giving a dog a treat."
Hypothesis: A lady is giving her dog a rawhide bone.
Based on the context, is the hypothesis true, false, or unknown?
|
$\dfrac{2\left( x+y\right)}{x}=\dfrac{14}{3}\textbackslash{} \textbackslash{} \Rightarrow\textbackslash{} \textbackslash{} \dfrac{x+y}{x}$~$=\dfrac{7}{3}\textbackslash{} \textbackslash{} \Rightarrow\textbackslash{} \textbackslash{} 1+\dfrac{y}{x}=1+\dfrac{4}{3}$ $\Rightarrow\textbackslash{} \textbackslash{} \dfrac{y}{x}=\dfrac{4}{3}\textbackslash{} \textbackslash{} \Rightarrow\textbackslash{} \textbackslash{} \dfrac{y\times y}{x\times y}=\dfrac{4}{3}$ The area is~$x\times y=27\textbackslash{} \textbackslash{} \Rightarrow\textbackslash{} \textbackslash{} \dfrac{y\times y}{27}=\dfrac{4}{3}\textbackslash{} \textbackslash{} \Rightarrow\textbackslash{} \textbackslash{} y\times y=36\textbackslash{} \textbackslash{} \Rightarrow\textbackslash{} \textbackslash{} y=6$
|
[e]
|
TAL-SCQ5K
|
The ratio of the perimeter of a rectangle to the length of one of its sides is~$14:3$. If the area is 27 square inches, how many inches long is one of the longer sides?
[a] $$3$$
[b] $$4$$
[c] $$5$$
[d] $$7$$
[e] $$6$$
|
Consider the antlers of the Irish elk, (often supposed to be far too large; in deer antler size has an allometric relationship to body size). Obviously, antlers serve positively for defence against predators, and to score victories in the annual rut. But they are costly in terms of resource. Their size during the last glacial period presumably depended on the relative gain and loss of reproductive capacity in the population of elks during that time. As another example, camouflage to avoid detection is destroyed when vivid coloration is displayed at mating time. Here the risk to life is counterbalanced by the necessity for reproduction.Stream-dwelling salamanders, such as Caucasian salamander or Gold-striped salamander have very slender, long bodies, perfectly adapted to life at the banks of fast small rivers and mountain brooks. Elongated body protects their larvae from being washed out by current. However, elongated body increases risk of desiccation and decreases dispersal ability of the salamanders; it also negatively affects their fecundity. As a result, fire salamander, less perfectly adapted to the mountain brook habitats, is in general more successful, have a higher fecundity and broader geographic range.
|
Species a
|
ropes
|
John is a biologist. Last summer, he was studying the evolution of two different salamander species, species A and species B. Species A salamander was Gold-striped salamander while species B salamander was fire salamander. He found it interesting that they took different approaches to adapt to different habitats.
Based on the above, answer the following question:
Which species would do better in mountain brooks, species A or species B?
|
Just because men and women have face paint on, it doesn't mean they are dressed as Native Americans.
|
Unknown
|
esnli
|
Given the statement "A group of men and women with face paint on are huddled around a table as one woman pulls up a cup, with a band with various instruments playing music in the background.", is the statement "A group of men and women dressed as Native Americans are huddled around a table." wrong?
- Yes
- No
- Unknown
|
If Doug, Betty's friend, is 40 years old, and the sum of their ages is 90, Betty is 90-40 = 50 years old.
Since twice Betty's age is the cost of a pack of nuts, a pack of nuts is sold at 2*$50 = $100
If Betty wants to buy 20 packs of the nuts, she'll have to pay 20*$100 = $2000
|
2000
|
gsm8k
|
Twice Betty's age is the cost of a pack of nuts. Doug, Betty's friend, is 40 years old. If the sum of their ages is 90, and Betty wants to buy 20 packs of the nuts, calculate the amount of money she'll pay for the packs of nuts.
|
There is either a black dog who runs on the beach or a golden poodle who sits in the shade. These are two different dogs.
|
No
|
esnli
|
Consider the staetement "A black dog runs on the beach.". Based on this statement, is "A golden poodle sits in the shade by the sea." a true statement? Yes/no/unknown
|
The kitchen took 4 * .5 = 2 hours longer than the bedrooms
So the kitchen took 4 + 2 = 6 hours
The bedrooms took 3 * 4 = 12 hours
So the kitchen and bedrooms combined took 12 + 6 = 18 hours
The living room took 18 * 2 = 36 hours
So everything took a total of 18 + 36 = 54 hours
|
54
|
gsm8k
|
Tom decides to renovate a house. There are 3 bedrooms and each bedroom takes 4 hours to renovate. The kitchen takes 50% longer than each bedroom. The living room took twice as much time as everything else combined. How long did everything take?
|
Several people in yellow and black uniforms are lined up carrying drums but they are not a marching band.
|
Unknown
|
esnli
|
Context: "Several people in yellow and black uniforms are lined up carrying drums."
Hypothesis: a marching band
Based on the context, is the hypothesis true, false, or unknown?
|
Fences are normally arranged in straight lines, so a dog running along a fence would be following a linear path.
|
True
|
esnli
|
Context: "A dark brown dog is running along a fence outside." Claim: "A dog is following a linear path."
Considering the context, is the claim true, false, or unknown?
|
Do not if they are out on a hike or that a tree is being observed and that paper is just a piece of it.
|
Unknown
|
esnli
|
Context: "Two people stand in the woods to the right of a large, hollowed-out log while two other people examine a piece of paper behind them." Claim: "Four people are out on a hike and stopped to observe a tree and paper."
Considering the context, is the claim true, false, or unknown?
|
Kissing a little boy as he is being held by a man is a different activity than a boy and a man who take swimming lessons together.
|
False
|
esnli
|
Context: "A man in a white shirt is kissing a little boy as he holds him."
Hypothesis: The man and boy take swimming lessons in the community lake.
Based on the context, is the hypothesis true, false, or unknown?
|
Flowing water can slowly dissolve carbon in sedimentary rock.
Limestone is an organic, sedimentary rock.
Flowing water can slowly dissolve carbon in limestone.
|
dissolve
|
qasc
|
Flowing water can slowly _ carbon in limestone.
- alter
- destroy
- erode
- allow growth
- dissolve
- heat
- a solute
- rain
|
125% of 120% of A = 231
125/100 * 120/100 * A = 231
A = 231 * 2/3 = 154.
|
(c)
|
aqua
|
A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $231 for it, the cost price of the Cricket Bat for A is:
(a) 150
(b) 120
(c) 154
(d) 160
(e) 210
|
In order to face the sun and water, the man must be outdoors. The woman is beside him; so she must be outdoors, as well.
|
Yes
|
esnli
|
Given the statement "A man sits facing the sun and water as a woman kneels beside him facing the man.", what is the statement "A man and woman are outdoors." true?
- Yes
- No
- Unknown
|
A party is not always a friend's birthday. There are many types of parties the people could be celebrating.
|
I don't know
|
esnli
|
Consider the statement "Many people are on a party.". Based on this "Many people attend a party to celebrate a friend's birthday." a true statement? Yes, no, or I don't know?
|
The girl is either looking at postcards or flowers, not both. And she can't be in an alleyway full of shops and garbage bins.
|
Yes
|
esnli
|
Given the statement "Young girl looks at postcards in alleyway full of shops.", is the statement "A young girl looks at the flowers in an alleyway full of garbage bins." wrong?
- Yes
- No
- Unknown
|
According to current definitions, all planets must revolve around stars; thus, any potential "rogue planets" are excluded. In the Solar System, all the planets orbit the Sun in the same direction as the Sun rotates (counter-clockwise as seen from above the Sun's north pole). At least one extrasolar planet, WASP-17b, has been found to orbit in the opposite direction to its star's rotation. The period of one revolution of a planet's orbit is known as its sidereal period or year. A planet's year depends on its distance from its star; the farther a planet is from its star, not only the longer the distance it must travel, but also the slower its speed, because it is less affected by its star's gravity. No planet's orbit is perfectly circular, and hence the distance of each varies over the course of its year. The closest approach to its star is called its periastron (perihelion in the Solar System), whereas its farthest separation from the star is called its apastron (aphelion). As a planet approaches periastron, its speed increases as it trades gravitational potential energy for kinetic energy, just as a falling object on Earth accelerates as it falls; as the planet reaches apastron, its speed decreases, just as an object thrown upwards on Earth slows down as it reaches the apex of its trajectory.Each planet's orbit is delineated by a set of elements:
|
Faster
|
ropes
|
John is an amateur astronomer. Last week he was observing the sky with his telescope. First he pointed his telescope at planet Mars. He noted it as case A. Then he pointed his telescope to planet Jupiter, which is farther form the Sun than Mars is. He noted it as case C. Finally, he pointed the telescope to a faraway planet called WASP-17b. He noted that as case B.
Would case A see faster or slower movement than case C?
|
If a woman is carrying a tan bag along with wearing an outfit she would be carrying just the tan bag as well.
|
Yes
|
esnli
|
Given the statement "A woman wearing sandals and a yellow shirt is carrying a tan bag.", is the statement "A woman carries a tan bag." is true?
- Yes
- No
- I don't know
|
A photo collage is a combination of multiple pictures into one, and the man makes one while building a sand castle.
|
True
|
esnli
|
Context: "man in orange shorts builds a sand castle, combining multiple pictures into one resulting in four copies of him." Claim: "A man makes a photo collage of himself building a sandcastle."
Considering the context, is the claim true, false, or unknown?
|
原方程可变为$$1+\frac{5}{x+1}-\left( 3+\frac{x-2}{{{x}^{2}}+3x+2} \right)+2-\frac{3}{x+2}=0$$， 整理得$$\frac{5}{x+1}-\frac{3}{x+2}-\frac{x-2}{{{x}^{2}}+3x+2}=0$$， 去分母、整理得$$x+9=0$$， 计算得出$$x=-9$$． 经检验知，$$x=-9$$是原方程的根．
|
b
|
TAL-SCQ5K
|
解方程：$$\frac{x+6}{x+1}-\frac{3{{x}^{2}}+10x+4}{{{x}^{2}}+3x+2}+\frac{2x+1}{x+2}=0$$的解为．
a: $$x=9$$
b: $$x=-9$$
c: 无解
d: $$x=-\frac{1}{9}$$
|
A woman who is running a marathon excited to cross the finish line is not necessarily in second place.
|
Unknown
|
esnli
|
Given the statement "A woman who is running a marathon is excited to cross the finish line.", what is the statement "The woman crosses the line in second place." true?
- Yes
- No
- Unknown
|
The fact that a photographer relishes capturing a great shot doesn't imply that he likes taking baby pictures.
|
Unknown
|
esnli
|
Consider the statement "A photographer relishes capturing a great shot.". Is the statement "The photographer likes taking baby pictures" false? Yes/no/unknown
|
P = (P*3*R)/100
R = 33 1/3%
|
b
|
aqua
|
In what time a sum of money double itself at 3% per annum simple interest?
a. 33 1/9%
b. 33 1/3%
c. 33 7/3%
d. 33 2/3%
e. 33 8/3%
|
People could be any gender, but guys indicates all male. They are either playing instruments or watching television.
|
False
|
esnli
|
Context: "Several people playing instruments in a room together." Claim: "Some guys watch television and talk."
Considering the context, is the claim true, false, or unknown?
|
Women can be in colorful costumes even if they are aren't going to a party on Halloween. A brown vest may not be part of a costume. Women looking at a little girl in a vest may not like what they see.
|
Unknown
|
esnli
|
Given the statement "Two woman in colorful costumes look at a little girl wearing a brown vest.", is the statement "Some girls are going to a party on Halloween and like a girls costume." wrong?
- Yes
- No
- Unknown
|
At present, the two brothers have a combined age of 8 + 12 = 20 years old.
Therefore, 1 year means an increase in the sum of their ages by 1 * 2 = 2 years.
Adam and Tom need a total of 44 - 20 = 24 more years to be 44 years old together.
So both brothers will be 44 years old together after 24 / 2 = 12 years.
|
12
|
gsm8k
|
Adam and Tom are brothers. Adam is 8 years old and Tom is 12 years old. In how many years will their combined age be 44 years old?
|
Two women are sitting at a table together working on crafts does not imply that they working together on craftsand talking.
|
Unknown
|
esnli
|
Consider the staetement "Two women are sitting at a table together working on crafts.". Based on this statement, is "Two women are sitting at a table together working on craftsand talking." a true statement? Yes/no/unknown
|
It is either one man, or a group, not both. They cannot be waist deep in water if they are at a bar.
|
False
|
esnli
|
Context: "A man is waist deep in water with a fishing net and box." Claim: "A group enjoys drinks at the bar."
Considering the context, is the claim true, false, or unknown?
|
Soil is well developed in the forest as suggested by the thick humus layers, rich diversity of large trees and animals that live there. In forests, precipitation exceeds evapotranspiration which results in an excess of water that percolates downward through the soil layers. Slow rates of decomposition leads to large amounts of fulvic acid, greatly enhancing chemical weathering. The downward percolation, in conjunction with chemical weathering leaches magnesium (Mg), iron (Fe), and aluminum (Al) from the soil and transports them downward, a process known as podzolization. This process leads to marked contrasts in the appearance and chemistry of the soil layers.
|
Frank's
|
ropes
|
Consider the following text:
Brad and Frank are two cousins. they both own land in the same county. Frank's parcel is a pine forest, while Brad's is a nice dry grassland with wild flowers and a few shrubs.
Which parcel has a rich diversity of large trees?
|
Just because the men are preparing to set sail, it does not mean that they are going to travel around the world.
|
Unknown
|
esnli
|
Consider the staetement "Three men prepare to set sail on a sailboat.". Based on this statement, is "Three men prepare to travel around the world on a sailboat." a true statement? Yes/no/unknown
|
We can write
\begin{align*}
\frac{\sin 18^\circ \cos 12^\circ + \cos 162^\circ \cos 102^\circ}{\sin 22^\circ \cos 8^\circ + \cos 158^\circ \cos 98^\circ} &= \frac{\sin 18^\circ \cos 12^\circ + \cos 18^\circ \cos 78^\circ}{\sin 22^\circ \cos 8^\circ + \cos 22^\circ \cos 82^\circ} \\
&= \frac{\sin 18^\circ \cos 12^\circ + \cos 18^\circ \sin 12^\circ}{\sin 22^\circ \cos 8^\circ + \cos 22^\circ \sin 8^\circ}.
\end{align*}Then from the angle addition formula,
\begin{align*}
\frac{\sin 18^\circ \cos 12^\circ + \cos 18^\circ \sin 12^\circ}{\sin 22^\circ \cos 8^\circ + \cos 22^\circ \sin 8^\circ} &= \frac{\sin (18^\circ + 12^\circ)}{\sin (22^\circ + 8^\circ)} \\
&= \frac{\sin 30^\circ}{\sin 30^\circ} = 1.
\end{align*}
|
$1$
|
competition-math
|
Find the numerical value of
\[\frac{\sin 18^\circ \cos 12^\circ + \cos 162^\circ \cos 102^\circ}{\sin 22^\circ \cos 8^\circ + \cos 158^\circ \cos 98^\circ}.\]
|
The gymnast could be demonstrating martial arts without it being a performance for a small group of small children.
|
I don't know
|
esnli
|
Context: Demonstration of martial arts by young female in gymnasium.
Hypothesis: the female is performing in front of a small group of children
Given this context, is the hypothesis true (Yes/No/I don't know)?
|
There is a line of people waiting against a tall iron work fence just means a line of people wait by a fence
|
True
|
esnli
|
Context: "There is a line of people dressed for cool weather waiting against a tall iron work fence."
Hypothesis: a line of people wait by a fence
Based on the context, is the hypothesis true, false, or unknown?
|
There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 16 possibilities (4*4) since each team has 4 players. So there are a total of 48 possibilities (16*3). I hope this method is easier for you to understand.
|
C
|
aqua
|
There are 3 teams each with 4 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
A: 50
B: 23
C: 48
D: 28
E: 45
|
A snowboarder who rides down the slope could not have crashed into a tree. Crashing into the tree would have prevented him from riding down the slope.
|
Yes
|
esnli
|
Given the statement "a snowboarder in red rides down the slope.", is the statement "A snowboarder after he crashed into a tree." wrong?
- Yes
- No
- Unknown
|
Echinoderms lack a centralized nervous system.
Echinoderms are represented by the starfish.
Starfish lack a centralized nervous system.
|
(G)
|
qasc
|
What kind of animal doesn't have a centralized nervous system?
(A) dog
(B) mammals
(C) cows
(D) bird
(E) human
(F) elephants
(G) starfish
(H) a fish
|
The Human Immunodeficiency Virus ( HIV ) is the virus that causes Acquired Immunodeficiency Syndrome ( AIDS ). Most researchers believe that the HIV originated in sub-Saharan Africa during the 20th century. HIV is transmitted by sexual contact and by contact with infected bodily fluids, such as blood, semen, breast milk, and vaginal secretions. It is also passed from mother to fetus. HIV is now a pandemic , with an estimated (as of 2008) 38.6 million people now living with the disease worldwide. It is estimated that AIDS has killed more than 25 million people since it was first recognized in 1981. For further information about HIV/AIDS, see the CDC (Centers for Disease Control and Prevention) web site at http://www.cdc.gov/hiv/resources/factsheets/ .
|
Paul
|
ropes
|
Context: Dean and Paul both went to volunteered in Africa. They had a blood test when they came back. Paul had been infected with the HIV virus while Dean was healthy and clean.
Question: Which friend has a virus that is transmitted by contact with infected semen?
|
There is not necessarily any man, or anyone carrying a cage, or any monkey, or anyone walking past.
|
I don't know
|
esnli
|
Consider the statement "A child is observing a chicken in a cage.". Based on this "A child is looking at a man carry a cage with a monkey inside past him" a true statement? Yes, no, or I don't know?
|
Olaf is 12 years + 3 years = 15 years old.
Shannen is 15 years old - 2 years = 13 years old.
Jack is 5 years + (2 * 13 years) = 31 years old.
The sum of all of their ages is 12 + 15 + 13 + 31 = 71 years old.
|
71
|
gsm8k
|
Beckett is 12 and is three years younger than Olaf, while Shannen is two years younger than Olaf. If Jack is five more than twice as old as Shannen, what is the sum of the ages of all 4 people?
|
A girl cannot wear a pink shirt and red dress at the same time. A girl cannot sit and stand at the same time.
|
Yes
|
esnli
|
Given the statement "A little girl in a pink shirt sitting in a stadium bench.", is the statement "A girl in a red dress standing on a bench." wrong?
- Yes
- No
- Unknown
|
A drunk text message is often regretted after sending and so receiving it back from the boss would create a lot of anxiety and hence not being carefree at all.
|
Yes
|
FLUTE
|
Consider the statement "I drunk texted my boss last night telling him everything that is wrong with his management style and think I'll get fired.". Is the statement "I am really carefree that my boss might have received the drunk text message I sent him last night about his terrible management style" false? Yes/no/unknown
|
Getting the car back from the mechanic with an enormous scratch on it would not make anyone amused and instead be a cause for anger or frustration.
|
No
|
FLUTE
|
Context: I went to pick up my car from the mechanic and found a huge scratch on the side!
Hypothesis: I was amused when I found my car with an enormous scratch on the side after picking it up from the mechanic
Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
|
112 ounces of a substance has a volume of 48 cubic inches
84 ounces of a substance has a volume of (48/112)*84 = 36 cubic inches
|
(2)
|
aqua
|
The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 84 ounces of this substance?
(1) 27
(2) 36
(3) 42
(4) 64
(5) 147
|
Observers are people; staring and looking are not mutually exclusive; a tree could not be described in terms of Christmas unless it were appropriately decorated.
|
True
|
esnli
|
Context: "Observers stare at a giant christmas tree on the sidewalk."
Hypothesis: People are looking at the christmas decorations.
Based on the context, is the hypothesis true, false, or unknown?
|
You can't imply there is food theft while these elderly people get interviewed for the Three News personal.
|
Unknown
|
esnli
|
Context: "Three News personal interviewing a couple of senior citizens, while another person looks on." Claim: "three people interview a couple of seniors about food theft while another person watches"
Considering the context, is the claim true, false, or unknown?
|
The woman handling the underside of one in a row of furry animals can't be running around with them at the same time.
|
Yes
|
esnli
|
Context: A woman in a green apron and rolled-up sleeves is handling the underside of one in a row of furry animals.
Hypothesis: A woman runs around with some furry animals.
Is the hypothesis incorrect? (Yes, no, or unknown)?
|
Any unused energy in food, whether it comes from carbohydrates, proteins, or lipids, is stored in the body as fat. An extra 3,500 Calories of energy results in the storage of almost half a kilogram (1 pound) of stored body fat. People who consistently consume more food energy then they need may become obese. Obesity occurs when the body mass index is 30.0 kg/m 2 or greater. Body mass index (BMI) is an estimate of the fat content of the body. It is calculated by dividing a person’s weight (in kilograms) by the square of the person’s height (in meters). Obesity increases the risk of health problems such as type 2 diabetes and hypertension.
|
Patient b
|
ropes
|
Context:
John is a physician in the local hospital. Today, he is seeing two patients, patient A and patient B. John determines that patient A is obese, and patient B is not obese. He needs to prescribe medicine according to his findings.
Q: Which patient would have lower BMI, patient A or patient B?
|
Thirst is used to make an animal realize that it needs to replenish its bodily water by the body.
Humans are animals too.
Thirst is used to make humans realize they need to replenish bodily water.
|
humans
|
qasc
|
what uses thirst to realize it needs to replenish bodily water?
* Mammal
* humans
* omnivores
* oxygen
* h2o
* bears
* Lobsters
* drinks
|
Someone refers to a human, not a dog. One cannot be suspended high on a wire and asleep simultaneously.
|
No
|
esnli
|
Consider the staetement "Someone suspended high on a wire near a large metal structure.". Based on this statement, is "the dogs are asleep" a true statement? Yes/no/unknown
|
A man with a red shirt on is standing on a skateboard that is resting on a garbage container does not indicate that he is doing tricks on his skateboard.
|
Unknown
|
esnli
|
Context: "A man with a red shirt on is standing on a skateboard that is resting on a garbage container." Claim: "The man is doing tricks on his skateboard."
Considering the context, is the claim true, false, or unknown?
|
While the cowboy is desperately hanging on does not necessarily mean he is 1 ride away from winning the competition
|
Unknown
|
esnli
|
Given the statement "A cowboy desperately tries to hang on to a bucking pinto horse during a rodeo.", what is the statement "the cowboy is 1 ride away from winning the competition" true?
- Yes
- No
- Unknown
|
A valley is formed by a river flowing.
Examples are napa valley and sonoma valley.
Napa and sonoma were formed by a river flowing.
|
(e)
|
qasc
|
what were formed by a river flowing?
(a) Statue of Liberty
(b) body water
(c) swamp vegetation
(d) Rockies
(e) Napa and Sonoma
(f) clouds
(g) Sediment
(h) Calcium carbonate
|
If the people are jumping off a boat, it can not be in a swimming pool. So one or the other must be true, not both.
|
No
|
esnli
|
Consider the statement "A man wearing swim trunks and a woman wearing a bikini are holding hands while jumping off of a boat into the water.". Based on this "Family jumping into swimming pool." a true statement? Yes, no, or I don't know?
|
The first sentence specifies how many men drink out of whatever color cups and in the second there are just men drinking out of cups.
|
No
|
esnli
|
Context: Two men with angry faces drink out of white cups.
Hypothesis: The men are drinking out of cups.
Is the hypothesis incorrect? (Yes, no, or unknown)?
|
Aging occurs as cells lose their ability to divide.
Death is attributed to the infirmities of old age.
Death occurs as cells lose their ability to divide.
|
(D)
|
qasc
|
What occurs as cells lose their ability to divide?
(A) illness
(B) Winter
(C) disease
(D) death
(E) youth
(F) die
(G) black holes
(H) cell growth
|
We can use the coefficient of the $x^3$ term to find $b$. On the right we have $-14x^3$, and on the left, the only $x^3$ terms we will get when we expand are $-3x(ax^2)$ and $5x^2(bx)$.
So we must have
$$-3ax^3 + 5bx^3 = -14x^3$$which means
$$5b - 3a = -14$$To find $a$, we use the same reasoning and look at the $x^4$ terms. On the right we have $15x^4$, and on the left, the only $x^4$ term we will get when we expand is $5x^2(ax^2)$. Then we know that
$$5ax^4 = 15x^4$$which means that $a=3$.
Then $5b -3(3) = -14$ and $b = -1$.
|
$-1$
|
competition-math
|
Find the constant $b$ such that
$$\left(5x^2-3x+\frac{7}{3}\right)(ax^2+bx+c) = 15x^4 - 14x^3 + 20x^2 - \frac{25}{3}x + \frac{14}{3}$$
|
The fact that a grandpa is teaching his grandson how to be a handyman doesn't imply showing his grandson how to use tools.
|
Unknown
|
esnli
|
Given the statement "a grandpa teaching his grandson how to be a handyman", is the statement "A grandpa is showing his grandson how to use tools." wrong?
- Yes
- No
- Unknown
|
There is no oxygen on the moon therefore the horse will not live.
|
[2]
|
senmaking
|
Pick which sentence is not logical.
[1] "a horse live on a farm."
[2] "a horse lives on the moon."
|
One would infer that a man standing at a street vendor that sells vegetables would likely be buying vegetables.
|
True
|
esnli
|
Context: "a man wearing blue shorts, striped shirt, and brown sandals stands at a street vendor selling vegetables engaging with a person working there in a sleeveless shirt." Claim: "a man buying vegetables at street"
Considering the context, is the claim true, false, or unknown?
|
A lot of people fear going to the dentist and so having to go there for a tooth extraction which is a painful process, cannot be considered to be an exhilarating experience.
|
False
|
FLUTE
|
Context: "I am going to the dentist to have a tooth pulled tomorrow." Claim: "I am feeling really exhilarated about the fact that I have to go to the dentist tomorrow to have a tooth pulled"
Considering the context, is the claim true, false, or unknown?
|
Just becsue a man wears camouflage and hides in flowers, it does not mean he is a soldier that spends his time inspecting flowers.
|
Unknown
|
esnli
|
Context: A man in camouflage clothing hides in a bed of roses and other flowers.
Hypothesis: The soldier spends time inspecting flowers.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
|
Biofuel is used to produce electricity by burning.
Biofuels can reduce the greenhouse effect.
Some electricity production reduces greenhouse effect.
|
6
|
qasc
|
what reduces greenhouse effect?
1) Fully cooking the oysters
2) Something made from fermented ricce
3) fuel
4) reusing materials
5) gas
6) some electricity production
7) evaporative cooling
8) cells
|
Double means two times
|
No
|
feasibilityQA
|
Context: Last year 548 people voted for the college election and this year the vote count was more than double the last time.
Question: "950 people could have voted this year." -- Is this statement true?
|
Just because the men are wearing hard hats and yellow construction gear doesn't mean the construction hard hats are yellow
|
Unknown
|
esnli
|
Context: Three men are working on a road wearing hard hats and bright yellow construction gear.
Hypothesis: Guys are wearing yellow construction hard hats.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
|
By Vieta's formulas, $ab = 2.$ Then
\[q = \left( a + \frac{1}{b} \right) \left( b + \frac{1}{a} \right) = ab + 1 + 1 + \frac{1}{ab} = 2 + 1 + 1 + \frac{1}{2} = \frac{9{2}}.\]
|
$\frac{9$
|
competition-math
|
Let $a$ and $b$ be the roots of the equation $x^2-mx+2=0$. Suppose that $a + \frac{1}{b}$ and $b + \frac{1}{a}$ are the roots of the equation $x^2-px+q=0$. What is $q$?
|
Raising the temperature of a chemical reaction usually results in a higher rate of reaction. When the reactant particles are heated, they move faster and faster. This results in a greater frequency of collisions. A more important effect of the temperature increase is that the collisions occur with a greater force and are thus more likely to surmount the activation energy barrier and go on to form products. Increasing the temperature of a reaction increases the number of effective collisions between reacting particles, so the reaction rate increases.
|
Sean
|
ropes
|
Context: Two colleagues read about types of chemical reactions. Sean studied about the influence of temperature on chemical reactions. Gabe studied about other influencing factors.
Question: Which student read more about the activation energy barrier?
|
Just because A lady wearing a white t-shirt and a pink skirt is playing tennis does not mean that is trying to lose weight.
|
Unknown
|
esnli
|
Given the statement "A lady wearing a white t-shirt and a pink skirt is playing tennis.", what is the statement "An woman is trying to lose weight by playing tennis." true?
- Yes
- No
- Unknown
|
Sally made $0.4 * 20=8$ shots originally. Letting $x$ be the number of shots she made, we have $\frac{8+x}{25}=0.52$. Solving for $x$ gives us $x=5$
|
e
|
TAL-SCQ5K
|
After Sally takes $20$ shots, she has made $40 \textbackslash\%$ of her shots. After she takes $5$ more shots, she raises her percentage to $52 \textbackslash\%$. How many of the last $5$ shots did she make? ( adapted from 2004 AMC 8, Question\#6)
a: $$1$$
b: $$2$$
c: $$3$$
d: $$4$$
e: $$5$$
|
There is either a group or Mexican dancers twirling their flowing skirts, or a mariachi band performing for people.
|
No
|
esnli
|
Context: A group of traditional Mexican dancers twirl their flowing skirts.
Hypothesis: A mariachi band is performing for people.
Given this context, is the hypothesis true (Yes/No/I don't know)?
|
Muscle contraction occurs when muscle fibers get shorter.
Movement is based on the contraction of muscles.
Movement happens when muscle fibers get shorter.
|
[6]
|
qasc
|
What do muscle fibers need to do to enable movement?
[1] Bend
[2] strength
[3] exercise
[4] ligt
[5] It expands
[6] shorten
[7] Vibrates
[8] stay warm
|
Walking down the same street does not necessarily imply they are together and having a conversation
|
Unknown
|
esnli
|
Context: Two women walk with purses walk down the street.
Hypothesis: Two women walk together and have a conversation.
Is the hypothesis incorrect? (Yes, no, or unknown)?
|
Another obvious change that occurs during puberty is rapid growth. This is called the adolescent growth spurt . In boys, it is controlled by testosterone. The rate of growth usually starts to increase relatively early in puberty. At its peak rate, growth in height is about 10 centimeters (almost 4 inches) per year in the average male. Growth generally remains rapid for several years. Growth and development of muscles occur toward the end of the growth spurt in height. Muscles may continue to develop and gain strength after growth in height is finished.
|
Tim
|
ropes
|
Two researches studied adolescents during puberty. Tim studied males, while Dan studied females.
Based on the above, answer the following question:
Which researcher observed that growth and development of muscles occur toward the end of the growth spurt in height?
|
672/4 = 168 balloons
168 * (1/2) = 84 balloons
Anya took 84 balloons home.
|
84
|
gsm8k
|
There were 672 balloons that were either green, blue, yellow, or red. They were divided into equal groups and then Anya took half of the yellow ones home. How many balloons did Anya take home?
|
Here, l = 7 and m = 14
Therefore, first number = l/m x 100% of second number = 7/14 x 100% of second number = 50% of second number
|
D
|
aqua
|
If the given two numbers are respectively 7% and 14% of a third number, then what percentage is the first of the second ?
Options:
A. 20%
B. 25%
C. 18%
D. 50%
E. none of these
|
Rainbows are generally used to represent lighthearted and happy subjects, which is contradictory to the serious and tragic subject of disaster victims in need.
|
Yes
|
esnli
|
Consider the statement "A truck passing out food donations to disaster victims in need.". Is the statement "The truck has rainbows on it." false? Yes/no/unknown
|
Many police in shielded helmets are gathered underneath a railway show that they are on on a mission.
|
Yes
|
esnli
|
Given the statement "Many police in shielded helmets are gathered underneath a railway.", what is the statement "The police are on a mission." true?
- Yes
- No
- Unknown
|
Most amphibians breathe with gills as larvae and with lungs as adults.
Frogs are amphibians, iguanas and snakes are reptiles.
Frogs breathe with gills as larvae and lungs as adults.
|
C
|
qasc
|
what breathe with gills as larvae and lungs as adults?
A. fish
B. snakes
C. frogs
D. salmon
E. breathe
F. bats
G. lungs
H. animals
|
It is not directly stated that the man is at a baseball game, therefore it cannot directly be inferred.
|
Unknown
|
esnli
|
Context: A man wearing a blue baseball cap is gazing into the distance.
Hypothesis: The man is at a baseball game.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
|
The two men who play basketball are Paul on the white team with possession of the ball, and number 4 on the blue team who plays defense.
|
True
|
esnli
|
Context: "2 men play basketball, Paul (number 13) on the white team has possession of the ball with his back to us, as number 4 on the blue team plays defense against him."
Hypothesis: Two men play basketball.
Based on the context, is the hypothesis true, false, or unknown?
|
A comet tail—and coma—are features visible in comets when they are illuminated by the Sun and may become visible from Earth when a comet passes through the inner Solar System. As a comet approaches the inner Solar System, solar radiation causes the volatile materials within the comet to vaporize and stream out of the nucleus, carrying dust away with them. Separate tails are formed of dust and gases, becoming visible through different phenomena; the dust reflects sunlight directly and the gases glow from ionisation. Most comets are too faint to be visible without the aid of a telescope, but a few each decade become bright enough to be visible to the naked eye.
|
Not visible
|
ropes
|
Consider the following text:
Stargazers across the world wait for 2020 when newly discovered very bright Neil's comet would start to pass through the inner solar system On December 21, 2020. After December 27, 2020 the comet would leave the inner solar system. Like many other enthusiasts Ken bought a telescope for the event. His friend Mike is interested in that event too, but is too busy to buy a telescope.
Would Neil's Comet be visible or not visible after December 27, 2020?
|
Because richer nations use more fossil fuels, they also cause more air pollution and global warming than poorer nations do.
|
[B]
|
quartz
|
A country like the US burns more fossil fuels than a third world country. This means that a third world country causes _____ pollution than a richer country.
[A] more
[B] less
|
When a hemisphere is tilted away from the sun , that hemisphere receives less direct sunlight.
In winter, the northern hemisphere is tilted away from the sun.
the northern hemisphere gets less sun in the winter.
|
5
|
qasc
|
When does the northern hemisphere experience cooler temperatures?
Options:
1. In the Autumn
2. air cools
3. dry and hot
4. Under 32 degrees
5. In the winter
6. When it's cold
7. In the Spring
8. In the summer
|
Either the woman is dressing a random baby, or the woman is a mother of the baby. She cannot be both related and unrelated simultaneously.
|
No
|
esnli
|
Consider the statement "A woman in green buttons up a baby's dress shirt.". Based on this "A mother dresses her girl." a true statement? Yes, no, or I don't know?
|
A man who tries on a rubber monster mask becomes the man who tried on the rubber monster mask temporally.
|
True
|
esnli
|
Context: "A man in a tuxedo shirt and black sport coat tries on a rubber monster mask." Claim: "The man in the tuxedo shirt tried on the rubber monster mask."
Considering the context, is the claim true, false, or unknown?
|
Snakes are often feared by people and considered to be dangerous, so seeing one in person would not be a exhilarating experience for most.
|
No
|
FLUTE
|
Consider the statement "I was startled the other day by a snake.". Based on this "I was on cloud nine the other day when I saw a snake slither in my backyard" a true statement? Yes, no, or I don't know?
|
Seafloor spreading helps explain continental drift in the theory of plate tectonics. When oceanic plates diverge, tensional stress causes fractures to occur in the lithosphere. The motivating force for seafloor spreading ridges is tectonic plate pull rather than magma pressure, although there is typically significant magma activity at spreading ridges. At a spreading center, basaltic magma rises up the fractures and cools on the ocean floor to form new seabed. Hydrothermal vents are common at spreading centers. Older rocks will be found farther away from the spreading zone while younger rocks will be found nearer to the spreading zone. Additionally spreading rates determine if the ridge is fast, intermediate, or slow. As a general rule, fast ridges have spreading (opening) rates of more than 9 cm/year. Intermediate ridges have a spreading rate of 5–9 cm/year while slow spreading ridges have a rate less than 5 cm/year.
|
Bobby
|
ropes
|
Context: Two geology students had an exam on plate tectonics. Bobby learned more about divergent tectonic plates, while Nate was more confident in explaining everything about Convergent plates.
Question: Which student knew more about seafloor spreading?
|
Not all skateboarders are an athlete let alone mean they are skating mean they are on their way to school
|
Unknown
|
esnli
|
Context: A skateboarder in striped shorts skating down a street.
Hypothesis: An athlete is performing tricks on his way to school.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
|
To get a rise out of someone means to provoke an angry or irritated response, which is what he was trying to do by teasing her.
|
Yes
|
FLUTE
|
Context: He was doing this intentionally; trying to make her angry or irritated by teasing her.
Hypothesis: He was doing this on purpose; trying to get a rise out of her.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
|
Though both occur on a track and field, if someone throws a javelin they are not running on a track.
|
Yes
|
esnli
|
Given the statement "Someone is running on a track at sunset.", is the statement "A man throws a javelin." wrong?
- Yes
- No
- Unknown
|
Three women and one man are also four people around a vehicle with luggage stand or a white minivan.
|
Yes
|
esnli
|
Context: Three women and one man, all with luggage stand around a white minivan on a very sunny day.
Hypothesis: Four people are standing around a vehicle.
Given this context, is the hypothesis true (Yes/No/I don't know)?
|
The boaters could have been rowing and disappointed for a reason unrelated to the boat being broke down.
|
Unknown
|
esnli
|
Given the statement "A man in a cluttered motorboat rows whilst his female passenger has a look of disappointment on her face.", is the statement "The motorboat is broke down." wrong?
- Yes
- No
- Unknown
|
A man is riding a bicycle with a cart full of flowers in the front does not imply he is a vendor on bike selling flowers from his cart.
|
Unknown
|
esnli
|
Context: "A man is riding a bicycle with a cart full of flowers in the front."
Hypothesis: Vendor on bike sells flowers from his cart.
Based on the context, is the hypothesis true, false, or unknown?
|
Not every women who cleans a public seating area is a janitor. Not all public seating areas are bleachers.
|
Unknown
|
esnli
|
Given the statement "A woman with bucket cleaning a public seating area.", what is the statement "A janitor is cleaning the bleachers." true?
- Yes
- No
- Unknown
|
If it is commonplace, then it is not extraordinary or like a new chapter in history
|
No
|
FLUTE
|
Given the statement "It is commonplace for an average person to come into power in this manner.", what is the statement "An ordinary citizen coming to power in this way is like a new chapter in history." true?
- Yes
- No
- Unknown
|
$$7$$级和$$4$$级差了$$3$$级，所以$$7$$级是$$4$$级的$$30\times 30\times 30$$倍.
|
$$30\times 30\times 30$$
|
TAL-SCQ5K
|
已知地震级数每升$$1$$级，地震释放能量大约扩大到原来的$$30$$倍，那么$$7$$级地震释放能量$$4$$级地震的多少倍？．
- $$30\times 3$$
- $$30\times 2$$
- $$30\times 30$$
- $$30\times 30\times 30$$
|
Spin the bottle requires players to crouch or sit on the ground so the group of people cannot be standing and playing spin the bottle at the same time.
|
No
|
esnli
|
Context: Four men and one woman in blue outfits are standing together in a street with onlookers in the background.
Hypothesis: a group of people play spin the bottle
Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
|
If the woman does not believe in getting tattoos, she would not show a tattoo on her body since she would never get one.
|
False
|
esnli
|
Context: "A woman is walking away from the viewer, she is wearing white clothing and has a handbag draped on her left shoulder; her upper back is exposed, showing a tattoo of a winged creature (possibly a fairy)."
Hypothesis: The woman does not believe in getting tattoos on her body.
Based on the context, is the hypothesis true, false, or unknown?
|
Sea level rises if an increase in seafloor spreading rate buoys up the ocean crust, causing the ocean basin to become smaller.
|
b
|
quartz
|
If Milo is measuring the seafloor and he notices the level of spreading has increased, what will happen to the sea level?
Options:
a: it will fall
b: it will rise
|
Often, foreign exchange controls can result in the creation of black markets to exchange the weaker currency for stronger currencies. This leads to a situation where the exchange rate for the foreign currency is much higher than the rate set by the government, and therefore creates a shadow currency exchange market. As such, it is unclear whether governments have the ability to enact effective exchange controls.[1]
|
Not be exchanged
|
ropes
|
Consider the following text:
On March 2015 Japans economy soared. There was a likelihood that the Japanese yen would rise in value. In the wake of this event, Japanese Government adjusted
the price of Japanese Currency Yen in accordance with the going market price. On the other hand, at he same time, UK was having economic downturn. There was a likelihood that the UK Currency Pound Sterling would go down. Fearing public backlash, UK Government kept the price of the Pound Sterling at the same level.
Will Japanese Yen be exchanged or not be exchanged in the black market?
|
It's necessarily true that the kid holding the letter P is the one who holds it up. The young boy may or may not be in class.
|
Unknown
|
esnli
|
Given the statement "A young boy looks at a hand holding the letter P.", what is the statement "a kid holds up a letter in class" true?
- Yes
- No
- Unknown
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.