rationale
stringlengths
0
4.7k
target
stringlengths
1
171
source
stringclasses
13 values
prompt
stringlengths
16
2.02k
Stone iscannot no food and cannot be eaten.
B
senmaking
Of the following two sentences, which one is against common sense? A: "i ate grilled and peppered red meat for dinner yesterday." B: "i ate grilled and peppered red stone for dinner yesterday."
$$\Delta \div 2-2=(222-2)\div 2$$ $$=220\div 2=110$$, 因此$$\Delta =(110+2)\times 2=112\times 2=224$$. 故选$$\text{B}$$.
B
TAL-SCQ5K
若$$(\Delta \div 2-2)\times 2+2=222$$,请问$$\Delta $$代表的数是. A. $$56$$ B. $$224$$ C. $$228$$ D. $$876$$ E. $$884$$
During late adulthood, the risk of developing diseases such as cardiovascular diseases and cancer continues to rise. Most people also have a decline in strength and stamina. Their senses may start failing, and their reflex time typically increases. Their immune system also doesn’t work as well as it used to. As a result, common diseases like the flu may become more serious and even lead to death. The majority of late adults develop arthritis, and as many as one in four develop Alzheimer’s disease.
Michael
ropes
Consider the following text: Robert and his son Michael are going to the doctor for their yearly physical. Robert is currently in the late adulthood phase of his life. Michael, on the other hand, just began adulthood and is still quite young. Both of them want to ask the doctor about their risks for future health problems. Who is less likely to develop a cardiovascular disease?
A man wearing a black suit is surrounded by many people inside a building with busts of people on the wall does not indicate that they are waiting there to get permission to enter the building
Unknown
esnli
Context: A man wearing a black suit is surrounded by many people inside a building with busts of people on the wall. Hypothesis: People are waiting there to get permission to enter the building. Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
That a boy rides a bike implies he has the ability to ride a bike, which is meant by he can ride a bike.
Yes
esnli
Given the statement "A boy rides his bike on a half-pipe.", what is the statement "The boy can ride a bike." true? - Yes - No - Unknown
Gravity pulls objects towards the ground, making it impossible for most objects to rise.
B
senmaking
Which of the following sentences is nonsensical? A) "if you fall, the acceleration is towards the ground" B) "if you fall, the acceleration is towards the sky"
WE have no idea if the dog is watching for other animals, the dog could be looking for any other reason. We also have no idea if there are any other animals present.
Unknown
esnli
Context: "A brown dog is standing in a river with its head turned looking behind." Hypothesis: A dog is standing in the river watching for other animals. Based on the context, is the hypothesis true, false, or unknown?
Noble gases are also used to fill the glass tubes of lighted signs like the one in the Figure below . Although noble gases are chemically nonreactive, their electrons can be energized by sending an electric current through them. When this happens, the electrons jump to a higher energy level. When the electrons return to their original energy level, they give off energy as light. Different noble gases give off light of different colors. Neon gives off reddish-orange light, like the word “Open” in the sign below. Krypton gives off violet light and xenon gives off blue light.
Lower
ropes
A scientist, John, has two containers of the same noble gas. John sends electricity through container A. Just as he is about to activate the electricity for container B, the power goes out, and he is unable to do so. Frustrated, John goes to find the circuit breaker to see if a fuse has blown. Will the gas in container B have a higher or lower energy level than container A?
The vendor is either walking or is stopped on a corner. He is also either selling cotton candy or hot dogs.
No
esnli
Consider the staetement "A vendor is walking down the street selling cotton candy.". Based on this statement, is "The vendor is stopped at a street corner and is selling hot dogs." a true statement? Yes/no/unknown
The people are not outside eating, they are in a restaurant having drinks and playing various instruments.
False
esnli
Context: "These people are in a restaurant, having drinks, and playing various instruments." Hypothesis: The people are outside eating. Based on the context, is the hypothesis true, false, or unknown?
A group implies there is more than one person, conversing is a synonym of talking and Police officers are law enforcement people.
Yes
esnli
Given the statement "Group of Police officers in uniform standing in a parking lot, smiling and talking.", is the statement "More than one person conversing works in law enforcement." is true? - Yes - No - I don't know
There are 60 minutes in an hour
Yes
feasibilityQA
Context: Graham is preparing for his mathematics exam. He has been studying for 2 hours and a few minutes to complete the syllabus. Question: "In total, he could have studied for 126 minutes." -- Is this statement true?
A man walks by a woman talking on a cellphone is equivalent to woman talks on a cellphone while a man passes by.
Yes
esnli
Consider the statement "A dark-skinned man walks by a woman talking on a cellphone.". Based on this "A woman talks on a cellphone while a man passes by." a true statement? Yes, no, or I don't know?
Making these healthy lifestyle choices can also help prevent some types of cancer. In addition, you can lower the risk of cancer by avoiding carcinogens , which are substances that cause cancer. For example, you can reduce your risk of lung cancer by not smoking. You can reduce your risk of skin cancer by using sunscreen. How to choose a sunscreen that offers the most protection is explained below ( Figure below ). Some people think that tanning beds are a safe way to get a tan. This is a myth. Tanning beds expose the skin to UV radiation. Any exposure to UV radiation increases the risk of skin cancer. It doesn’t matter whether the radiation comes from tanning lamps or the sun.
Tom
ropes
Consider the following text: Two friends had different lifestyles. Tom adopted a healthy lifestyle choice to prevent cancer, but Bill didn't. Bill was diagnosed with cancer a year later. Which of the two friends made healthier choices to prevent cancer
In one scenario, two women are at the store window while a third woman is at the glass. In the other scenario, there is just one woman and she is about to throw a brick through the window.
False
esnli
Context: "Two women are smiling in a store window, holding cleaning supplies, while a third woman presses her face against the glass." Hypothesis: A woman is about to throw a brick through a store window Based on the context, is the hypothesis true, false, or unknown?
A pentagon has five diagonals
Yes
feasibilityQA
Context: Adam in his class was asked a question about the name of figure which has a total of five diagonals. Question: "The figure could be a pentagon." -- Is this statement true?
A sandbar is formed by water moving sediment downstream. Sandbars are preferred nesting habitat. Sediment moved downstream by water can create nesting habitat.
[8]
qasc
What type of habitat can be formed by sediment moved downstream by water? [1] watershred [2] caves [3] desert [4] coral reef [5] savannah [6] streams [7] loose soil [8] nesting
20 minutes is 20/60=1/3 of an hour. Ms. Warren ran 6/3=2 miles. 30 minutes is 30/60=1/2 of an hour. Ms. Warren walked 2/2=1 mile. Ms Warren ran and walked 2+1=3 miles in total.
3
gsm8k
Ms. Warren ran at 6 mph for 20 minutes. After the run, she walked at 2 mph for 30 minutes. How many miles did she run and walk in total?
Everybody usually does not refer to only two beings. Either the group are having a conversation or they are silent. They cannot do both simultaneously.
No
esnli
Given the statement "Two men are having a conversation at a meeting.", is the statement "Everybody is silent." is true? - Yes - No - I don't know
A cyclist that is smiling would suggest that there is a group of people, in this case a crowd, looking on.
Yes
esnli
Given the statement "A cyclist smiling in front of a crowd.", what is the statement "There is a cyclist smiling" true? - Yes - No - Unknown
In a day, the total number of new pins is 10*20= 200. There will be 30*200 = 6000 new pins after a month. The total number with old pins present is 6000+1000 = 7000 pins If the owner deletes five pins every week, the total number of deleted pins in a week is 5*20 = 100 pins. After a month, the number of deleted pins will be 100*4 = 400 The number of pins after the old pins are deleted is 7000-400 = 6600 pins
6,600
gsm8k
Reese joined a Pinterest group where members contributed an average of 10 pins per day. The group owner deleted older pins at the rate of 5 pins per week per person. If the group has 20 people and the total number of pins is 1000, how many pins would be there after Reese had been a member for a month?
Seventeen minutes after $$13:45$$ is $$14:02$$.
$$14:02$$
TAL-SCQ5K
Sam\textquotesingle s exam was meant to begin at $$13:45$$ but started $$17$$ minutes late. At what time did it begin?  - $$13:28$$ - $$13:38$$ - $$13:56$$ - $$14:02$$ - $$14:06$$
The number of cows and foxes in the yacht is 20+15 = 35 Mr. Bodhi also has three times as many zebras as foxes in the yacht, equal to 3*15 = 45 zebras. The number of animals in the yacht so far is 35+45 = 80 To balance the yacht, Mr. Bodhi needs to add 100-80= 20 sheep
20
gsm8k
Mr. Bodhi is transporting some animals using a yacht across a river. He has 20 cows, 15 foxes and three times as many zebras as foxes. To balance the yacht to ensure a smooth sail across the river, the total number of animals in the yacht needs to be 100. If he decides to add sheep to the yacht to make the yacht sail-worthy, how many sheep did he add to the yacht?
Woman and men are people, they have headdress, and since they are talking and existing in the background, they go through life.
True
esnli
Context: "Two woman with headdress talking in the foreground with two men in a different kind of headdress in the background." Hypothesis: People in headdress go through life. Based on the context, is the hypothesis true, false, or unknown?
You can't "blow" an elbow the same way you would a nose.
(1)
senmaking
One of the following sentences is nonsensical. Which one is it? (1) "i blew my elbow into a tissue." (2) "i blew my nose into a tissue."
The people could be any gender, not necessarily men. The police might not chase them away just because they are sleeping outside.
I don't know
esnli
Context: One person is wearing a green shirt while sleeping on the sidewalk while another person wearing black pants is sleeping on the stairs. Hypothesis: A couple of homeless men are trying to catch a few minutes of sleep before the police chase them away. Given this context, is the hypothesis true (Yes/No/I don't know)?
To put your best foot forward typically means to try to act as an ideal version of oneself, but in this context it is used to make a terrible first impression
No
FLUTE
Given the statement "So when you do finally have the chance to meet him, it's allowing you to make a terrible first impression to secure his interest..", what is the statement "So when you do finally have the chance to meet him, it's allowing you to put your best foot forward to secure his interest.”" true? - Yes - No - Unknown
David was very angry when Paul invited his new girlfriend to dance and it looked like he was staring at Paul with daggers in his eyes.
True
FLUTE
Context: "David looked at Paul very angrily when Paul invited his new girlfriend to dance." Hypothesis: David’s eyes were like daggers at Paul when Paul invited his new girlfriend to dance. Based on the context, is the hypothesis true, false, or unknown?
显然$${{x}_{2}}=\frac{1}{2}$$.设$$f\left( x \right)={{\log }_{4}}x-{{\left( \frac{1}{4} \right)}^{x}}$$,则$$f\left( 1 \right)\cdot f\left( 2 \right)\textless{}0$$,所以$$1\textless{}{{x}_{2}}\textless{}2$$.
(a)
TAL-SCQ5K
设方程$${{\log }_{4}}x-{{\left( \frac{1}{4} \right)}^{x}}=0$$与$${{\log }_{\frac{1}{4}}}x-{{\left( \frac{1}{4} \right)}^{x}}=0$$的根分别为$${{x}_{1}}, {{x}_{2}}$$,则 (a) $$0\textless{}{{x}_{1}}{{x}_{2}}\textless{}1$$ (b) $${{x}_{1}}{{x}_{2}}=1$$ (c) $$1\textless{}{{x}_{1}}{{x}_{2}}\textless{}2$$ (d) $${{x}_{1}}{{x}_{2}}\geqslant 2$$
Throwing something doesn't mean she plays fetch with the German shepherd and there is no indication that it is her boyfriends dog.
I don't know
esnli
Consider the statement "Outside by the trees, a woman wearing jeans and red jacket throws something for a German shepherd to chase.". Based on this "a woman plays fetch with her boyfriends dog" a true statement? Yes, no, or I don't know?
A man is either in a black or red hat and he is either loading parcels onto an airplane or the back of horses or donkeys.
No
esnli
Context: A man in a black hat loading parcels on the back of horses or donkeys. Hypothesis: A man in a red hat is loading parcels onto an airplane. Given this context, is the hypothesis true (Yes/No/I don't know)?
- Metal is an electrical / electrical energy conductor - Copper is a kind of metal - Therefore, copper is an electrical conductor - Copper is a kind of metal - Metal is a kind of material - Therefore, copper is a kind of material - Copper is an electrical conductor - Copper is a kind of material - Hence, copper is the material that is an electrical conductor Therefore, copper is the material that is an electrical conductor
Copper
entailment_bank
[Question]Which of these substances conducts electricity the best? [Context]- Metal is an electrical / electrical energy conductor - Copper is a kind of metal - Metal is a kind of material
From where the girl was uni-cycling could not be assumed. She could have been from plenty of organizations besides the local school.
Unknown
esnli
Context: Young girls dressed in red riding unicycles in a parade. Hypothesis: The girl's unicycle club from the local school in the parade. Is the hypothesis incorrect? (Yes, no, or unknown)?
设杰克分到的金币为$$1$$份量,则有 $$\left. \begin{matrix}1+11 1-15 1+20 \end{matrix} \right }\Rightarrow 4+16=280\Rightarrow 1=66\Rightarrow 66+20=86$$
(C)
TAL-SCQ5K
四个海盗杰克、吉米、汤姆和桑吉共分$$280$$个金币.杰克说:``我分到的金币比吉米少$$11$$ 个,比汤姆多$$15$$个,比桑吉少$$20$$个.''那么,桑吉分到了个金币. (A) $$84$$ (B) $$85$$ (C) $$86$$ (D) $$87$$
It would be particularly difficult for a performer to play the electric guitar and piano at once, and all the more difficult if that performer was a cat.
No
esnli
Consider the statement "A young performer singing and playing electric guitar.". Based on this "A cat plays the piano." a true statement? Yes, no, or I don't know?
People are unlikely to be watching movies and watching a tv monitor simultaneously. A tv monitor mounted high on the wall is unlikely to be found in a drive in.
No
esnli
Given the statement "People sitting and watching a tv monitor mounted high on the wall.", is the statement "The people are watching movies in a drive in." is true? - Yes - No - I don't know
People having a conversation and a water bottle falling on the ground doesn't mean that Water got spilled on the ground.
Unknown
esnli
Given the statement "People are having a conversation and a water bottle fell on the ground.", is the statement "Water got spilled on the ground." wrong? - Yes - No - Unknown
To give it a whirl means to try something, and in this sentence the speaker is suggesting trying something new.
No
FLUTE
Consider the statement "Why not give it a try, he said with a wink, whats to lose?". Is the statement "Why not give it a whirl, he said with a wink, whats to lose?" false? Yes/no/unknown
A young boy playing with a yo-yo which is a motor toy and from child's perspective working on his motor skills.
True
esnli
Context: "A young boy is playing with a yo-yo." Claim: "A young boy works on his motor skills." Considering the context, is the claim true, false, or unknown?
Just because the church musicians are practicing for Sunday, it doesn't mean that they are getting ready for their performance on Sunday.
Unknown
esnli
Context: "Church musicians practicing for sunday." Claim: "Church musicians are getting ready for their performance on Sunday." Considering the context, is the claim true, false, or unknown?
maximum is 6+6+6 = 18.
$$22$$
TAL-SCQ5K
Kevin has $3$ regular dice. Each dice has numbers from $1$ to $6$. Which of the following could not be the sum of the numbers on top of the $3$ dice? - $$5$$ - $$13$$ - $$17$$ - $$22$$ - All the above numbers are possible sum
Veins generally carry deoxygenated blood. Veins carry blood to our heart. Deoxygenated blood is carried to our heart.
to our heart
qasc
deoxygenated blood is carried where? to our heart during the day animal transport our planet critical organs mouth of rivers humans organs
There are not necessarily two children playing. The small child could be playing peek-a-boo with and adult.
Unknown
esnli
Consider the staetement "Small child playing peek-a-boo behind a tree in a park.". Based on this statement, is "Two children are playing." a true statement? Yes/no/unknown
Just because workers stand beside equipment it does not mean they observe a moment of silence. Workers do not have to be construction workers.
I don't know
esnli
Context: A half dozen construction workers stand beside a large piece of equipment. Hypothesis: workers observe a moment of silence Given this context, is the hypothesis true (Yes/No/I don't know)?
There are other reasons that a person could be holding a picture of a face in front of their own face other than to make people laugh.
I don't know
esnli
Given the statement "Someone is sitting on a wooden bench holding the picture of a face up in front of their own face.", is the statement "person making people laugh" is true? - Yes - No - I don't know
Mollusks have a circulatory system with one or two hearts that pump blood. Clams, oysters and snails are familiar mollusks. Clams have a circulatory system with one or two hearts.
Clams
qasc
have a circulatory system with one or two hearts - Birds - alpacas - elms - Clams - salmon - animals - toads - complex
Echinoderms have a unique water vascular system with tube feet. All echinoderms are deuterostomes . Deuterostomes can have a water vascular system with tube feet.
H
qasc
What can have a water vascular system with tube feet? A) ducks B) peachleaf willow C) cats D) orchids E) Most plants F) horses G) animals H) deuterostomes
A plank is a piece of wood. If a person is carrying a large plank, then the person in carrying wood.
Yes
esnli
Consider the staetement "Person is carrying a large plank near a body of water while the sun is low in the sky.". Based on this statement, is "A person is carrying wood." a true statement? Yes/no/unknown
G 1/15 + (14/15) * 1/14 = 2/15
D
aqua
What is the probability that Company G's advertisement will be one of the first two be shown during the first commercial break? A. 1/ 225 B. 1 / 30 C. 1 /15 D. 2 / 15 E. 4 /15
In living memory means in a recent enough time as to be remembered by people who are alive today, which is the same as saying it's the hottest summer in recent history.
True
FLUTE
Context: "It's the hottest summer in recent history and, - in these parts, that's a long, long time." Claim: "It's the hottest summer in living memory and, - in these parts, that's a long, long time." Considering the context, is the claim true, false, or unknown?
The solubility of a solid in water increases with an increase in temperature.
No
feasibilityQA
Noah wanted to dissolve salt in water at two different temperatures. At temperature 278 K, the solubility was higher. Question: Is the following statement plausible? The temperature of the other solution could be 281 K.
"A girl has drawn a flower on her hand." paraphrases "A young girl wearing colorful clothing uses henna to draw a flower on her hand."
True
esnli
Context: "A young girl wearing colorful clothing uses henna to draw a flower on her hand." Claim: "A girl has drawn a flower on her hand." Considering the context, is the claim true, false, or unknown?
There is nothing about the man practicing his putting that would imply he's a professional golf player. That he's practicing does not imply he is enjoying the activity.
Unknown
esnli
Given the statement "a man practicing his putting on a portable disc golf basket.", is the statement "A professional golf player is enjoying some portable disc golf." wrong? - Yes - No - Unknown
Just because group of men and women sitting on boxes and buckets in a space with medium light and food does not mean they are about to eat.
I don't know
esnli
Context: Group of men and women sitting on boxes and buckets in a space with medium light and food. Hypothesis: The group is about to eat. Given this context, is the hypothesis true (Yes/No/I don't know)?
Saltiness cannot be judged by smell and salt has no special smell.
A
senmaking
Of the following two sentences, which one is against common sense? A. "salt smells salty." B. "salt tastes salty."
Water vapor cooling causes that water vapor to condense. All carcasses are chilled with cool air for 48 hours. Water vapor chilling causes that water vapor to condense.
G
qasc
What causes water vapor to condense? A. water vapor exploding B. water vapor heating up C. water vapor disappearing D. circulatory systems E. aqueous solution F. Heat energy G. water vapor chilling H. Evaporation
$$26-18=8$$
$$8$$
TAL-SCQ5K
26-18=. - $$8$$ - $$16$$ - $$9$$ - $$12$$ - $$11$$
A surfer whose acronym is he is a guy. Surfing is a rephrasing of when a surfer digs his board deep in the water to cut the wave he is riding.
No
esnli
Given the statement "A surfer digs his board deep in the water to cut the wave he is riding.", is the statement "A guy is surfing." wrong? - Yes - No - Unknown
People being on a slide has no correlation with the ground around them, in this case there was grass instead of sand or mulch.
Unknown
esnli
Context: "Man and child riding down a giant yellow slide." Claim: "THE grass was green" Considering the context, is the claim true, false, or unknown?
If there are n marbles in total, the first player has a winning strategy for all $$n$$ that is not a multiple of $$3$$. For $$n$$ being a multiple of $$3$$, the second player can always win, regardless of what strategy the first player plays. $$16\div (1+2)=5 \textbackslash{} \text{R} 1$$ Rose should take away the remainder, i.e. one marble, to make herself the second player when there is a multiple of $3$ marbles left.
$$1$$
TAL-SCQ5K
Rose and Kylie are playing a game. Here are the rules: 1. There are $$16$$ marbles placed in a row. 2. The players take turns removing either $1$ or $2$ marbles each turn. 3. Whoever picks the last marble wins the game. Rose starts first and is followed by Kylie. To ensure her victory, how many marbles must Rose take away in the first turn? - $$1$$ - $$2$$
An elderly Asian woman wearing a red long-sleeved shirt and other one is with white long sleeved shirt
False
esnli
Context: "An elderly Asian woman wearing a red long-sleeved shirt and carrying a woven purse points to a man she is speaking to who is wearing a red light jacket and carrying a satchel." Hypothesis: An elderly Asian woman has a white long-sleeved shirt Based on the context, is the hypothesis true, false, or unknown?
The pair with the man holding his female partner above his head in the water dance are obviously not asleep.
No
esnli
Given the statement "The strong male partner in the water dancing team held his female partner above his head while she posed acrobatically over his head.", is the statement "The man and woman are in bed asleep." is true? - Yes - No - I don't know
Some of Antarctica has been warming up; particularly strong warming has been noted on the Antarctic Peninsula. A study by Eric Steig published in 2009 noted for the first time that the continent-wide average surface temperature trend of Antarctica is slightly positive at >0.05 °C (0.09 °F) per decade from 1957 to 2006. This study also noted that West Antarctica has warmed by more than 0.1 °C (0.2 °F) per decade in the last 50 years, and this warming is strongest in winter and spring. This is partly offset by autumn cooling in East Antarctica. There is evidence from one study that Antarctica is warming as a result of human carbon dioxide emissions, but this remains ambiguous. The amount of surface warming in West Antarctica, while large, has not led to appreciable melting at the surface, and is not directly affecting the West Antarctic Ice Sheet's contribution to sea level. Instead the recent increases in glacier outflow are believed to be due to an inflow of warm water from the deep ocean, just off the continental shelf. The net contribution to sea level from the Antarctic Peninsula is more likely to be a direct result of the much greater atmospheric warming there.In 2002 the Antarctic Peninsula's Larsen-B ice shelf collapsed. Between 28 February and 8 March 2008, about 570 km2 (220 sq mi) of ice from the Wilkins Ice Shelf on the southwest part of the peninsula collapsed, putting the remaining 15,000 km2 (5,800 sq mi) of the ice shelf at risk. The ice was being held back by a "thread" of ice about 6 km (4 mi) wide, prior to its collapse on 5 April 2009. According to NASA, the most widespread Antarctic surface melting of the past 30 years occurred in 2005, when an area of ice comparable in size to California briefly melted and refroze; this may have resulted from temperatures rising to as high as 5 °C (41 °F).A study published in Nature Geoscience in 2013 (online in December 2012) identified central West Antarctica as one of the fastest-warming regions on Earth. The researchers present a complete temperature record from Antarctica's Byrd Station and assert that it "reveals a linear increase in annual temperature between 1958 and 2010 by 2.4±1.2 °C".
Noah
ropes
Consider the following text: Frank and Noah were two researchers. Noah researched the climate of Antarctica, while Frank researched the climate changes of Madagascar and the Southern tip of Africa. Which researcher observed a stronger warming in winter?
Not all cars that are parked in front of a bank are involved in a bank robbery as a getaway car or any other role.
Unknown
esnli
Consider the statement "Dark colored Mercury car parked in front of PNC Bank.". Is the statement "The Mercury was a getaway car for a bank robbery." false? Yes/no/unknown
Guys is a plural term referring to the two men. The men are near the ocean, the beach is near the ocean. They are watching fireworks.
Yes
esnli
Consider the statement "Two men play with fireworks on the beach.". Based on this "The guys put on a firework show near the ocean." a true statement? Yes, no, or I don't know?
Not all people are children. Face paintings are not always animals. Celebrations are not always a Fall Fest.
Unknown
esnli
Context: People with their faces painted for a celebration. Hypothesis: The children enjoy getting animals painted on their faces for Fall Fest. Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
因为$${{\left[ x+\left( 1-x \right) \right]}^{2020}}$$ $$={{a}_{0}}{{x}^{2020}}+{{a}_{1}}{{x}^{2019}}\left( 1-x \right)+{{a}_{2}}{{x}^{2018}}{{\left( 1-x \right)}^{2}}+\cdots +{{a}_{2020}}{{\left( 1-x \right)}^{2020}}$$ $$=1$$. 且由二项式定理得,当$$0\leqslant k\leqslant 2020$$, 且$$k\in \mathbf{Z}$$时,$${{a}_{k}}=\text{C}_{2020}^{k}$$, 所以$${{a}_{0}}+{{a}_{1}}+\cdots +{{a}_{2020}}$$ $$=\text{C}_{2020}^{0}+\text{C}_{2020}^{1}+\text{C}_{2020}^{2}+\cdots +\text{C}_{2020}^{2020}$$ $$={{2}^{2020}}$$. 故选$$\text{C}$$.
(c)
TAL-SCQ5K
若$${{a}_{0}}{{x}^{2020}}+{{a}_{1}}{{x}^{2019}}\left( 1-x \right)+{{a}_{2}}{{x}^{2018}}{{\left( 1-x \right)}^{2}}+\cdots +{{a}_{2020}}{{\left( 1-x \right)}^{2020}}=1$$,则$${{a}_{0}}+{{a}_{1}}+\cdots +{{a}_{2020}}=$$. (a) $$1$$ (b) $$0$$ (c) $${{2}^{2020}}$$ (d) $${{2}^{2021}}$$
You do not put fuel in your body.
[b]
senmaking
Which of the following sentences is nonsensical? [a] "peoples visit petrol pumbs to refill fuel on their vehicle" [b] "people visit petrol pumps to refill fuel on their stomach"
A man is a person, and tumbling into the water having fallen off a surfboard is generally done outside.
True
esnli
Context: "A man is tumbling into the water having fallen off a surfboard." Hypothesis: A person is outside. Based on the context, is the hypothesis true, false, or unknown?
Just because five people in white coats are standing around sheep does not mean that experiments are the intent.
Unknown
esnli
Given the statement "Two men wearing white coats and standing next to sheet talk to each other while a woman wearing a wicker hat and a white coat stands with sheep looks at a woman in a white coat and a man wearing a white coat and white hat both standing next to sheep.", is the statement "5 people want to do experiments on the sheep." wrong? - Yes - No - Unknown
A white dog is a different animal from a black cat. Also playing in snow is different to playing in water.
No
esnli
Context: A white dog jumps from the grass into water from a hose. Hypothesis: A black cat is playing in the snow. Given this context, is the hypothesis true (Yes/No/I don't know)?
Charging an object by touching it with another charged object is called charging by conduction. By bringing a charged object into contact with an uncharged object, some electrons will migrate to even out the charge on both objects. Charging by conduction gives the previously uncharged object a permanent charge. An uncharged object can also be charged using a method called charging by induction . This process allows a change in charge without actually touching the charged and uncharged objects to each other. Imagine a negatively charged rod held near the knob, but not touching. If we place a finger on the knob, some of the electrons will escape into our body, instead of down the stem and into the leaves. When both our finger and the negatively charged rod are removed, the previously uncharged electroscope now has a slight positive charge. It was charged by induction. Notice that charging by induction causes the newly charged object to have the opposite charge as the originally charged object, while charging by conduction gives them both the same charge.
Case b
ropes
John wanted to charge his electronic gadgets remotely. To that end, he first conducted two experiments, case A and case B. In case A he used conduction, and in case B he used induction. In both cases he used same two objects. Finally, John tried to charge his phone remotely. He called this test as case C. Based on the above, answer the following question: In which case the objcets would have opposite charge, case A or case B?
Eople watching art which represents an invisible man made out of a black suit is a rephrasing of there are three people talking at an airport.
Yes
esnli
Given the statement "Three people are talking in front of an airport", is the statement "There are three people talking at an airport." is true? - Yes - No - I don't know
Many of the worlds people live with water scarcity, and that percentage will increase as populations increase and climate changes.
A
quartz
The population in Milo's city has been decreasing recently. What will happen to the city's level of water scarcity? Options: A: decrease B: increase
Woman refers to an older female, where girl refers to a younger female. One cannot simultaneously play soccer and baseball. Either the field is sand or grass.
False
esnli
Context: "Young woman playing soccer outdoors on a grassy field." Hypothesis: The young girl is playing baseball in the sand. Based on the context, is the hypothesis true, false, or unknown?
Artworks are sold at affordable prices [6] ranging from £5 to £1500. For many of the works, the price goes up as the edition sells out. The edition runs range from 30 to 10,000 editions. Each work comes with a digital certificate that is “signed, numbered and authenticated by the artist” [7][8] Once an edition is sold out, collectors can resell their works in the online marketplace.
Mike's
ropes
The prices of John's paintings started to rise immediately after the edition sold out. they used to cost $10 but now they sell for at least $200. john had 45 paintings in this edition. The prices of Mike's paintings are at $8 a piece, because his edition hasn't sold out yet. Mike's edition run was 250 editions. Which paintings sell for less money today?
If 40% of the guests are females, then there are 40/100*200 = 80 female guests at the party. The number of female guests wearing rabbit ears is 80/100* 80=64 The number of male guests is 200 guests - 80 female guests = 120. If 60% of the male guests are wearing rabbit ears, then there are 60/100 *120 = 72 male guests wearing rabbit ears. The total number of guests wearing rabbit ears is 64+72 = 136
136
gsm8k
At a James Bond movie party, each guest is either male (M) or female (F. 40% of the guests are women, 80% of the women are wearing rabbit ears, and 60% of the males are wearing rabbit ears. If the total number of guests at the party is 200, given all this information, what is the total number of people wearing rabbit ears?
That a man can be seen through a window is the short version of the man is seen through a window with a blue painted top and a red painted bottom
Yes
esnli
Consider the statement "A man stands in the background, seen through a window with a blue painted top and a red painted bottom.". Based on this "A man can be seen through a window." a true statement? Yes, no, or I don't know?
If you stay up late at night, you will be exhausted in the next day.
(b)
senmaking
Choose the sentence that goes against common sense. (a) "a sound sleep helps to improve our working efficiency in the next day." (b) "staying up late helps to improve our working efficiency in the next day."
Insecticide control of aphids is difficult, as they breed rapidly, so even small areas missed may enable the population to recover promptly. Aphids may occupy the undersides of leaves where spray misses them, while systemic insecticides do not move satisfactorily into flower petals. Finally, some aphid species are resistant to common insecticide classes including carbamates, organophosphates, and pyrethroids.For small backyard infestations, spraying plants thoroughly with a strong water jet every few days may be sufficient protection. An insecticidal soap solution can be an effective household remedy to control aphids, but it only kills aphids on contact and has no residual effect. Soap spray may damage plants, especially at higher concentrations or at temperatures above 32 °C (90 °F); some plant species are sensitive to soap sprays.
Mary
ropes
Consider the following text: Pam and Mary were two gardener friends. They both had some aphid infestations, but Mary had more aphids on her farm, so she used every method and insecticide available to get rid of them, with limited success. Which farmer dealt with more aphids resistant to organophosphates?
A man wearing a hula skirt with the ocean behind him with 2 rows of pigs lying on their backs. which means guy wears a grass skirt in front of dead pigs
Yes
esnli
Context: A man wearing a hula skirt stands on the shore with the ocean behind him with 2 rows of pigs lying on their backs. Hypothesis: a guy wears a grass skirt in front of dead pigs Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
One cannot assume that the woman was running late and that is why she painted her nails in the car.
I don't know
esnli
Consider the statement "A passenger in a car painting her nails.". Based on this "The woman was running late so she painted her nails in the car." a true statement? Yes, no, or I don't know?
Just because the dog is walking through a river, it does not mean that he is looking to get a fish.
I don't know
esnli
Given the statement "A white dog is walking through a river that runs through a rocky landscape.", is the statement "A puppy is walking in the river to get a fish." is true? - Yes - No - I don't know
It could have been a man, a woman, a girl or a boy, and that person might not necessarily have been doing a balancing act with it.
Unknown
esnli
Context: "Someone is lying on the ground with a ball on top of their head." Claim: "A boy is doing a balancing act with a ball on his head." Considering the context, is the claim true, false, or unknown?
Seeing the kitchen in a state of disarray would not be a satisfying sight for anyone, considering that it is the place where food is prepared and hence should be kept clean.
No
FLUTE
Given the statement "I can't stand a messy kitchen but my roommate is a pig.", is the statement "I feel satisfied every time I see the kitchen because my roommate never cleans up after himself" is true? - Yes - No - I don't know
The force of water against the seed coat causes a root to emerge from a seed. Germination depends on the seed coat. The force of water causes germination with the emergence of a root.
f
qasc
the force of what causes germination with the emergence of a root Options: a: Light b: gametes c: bamboo d: streams e: wind f: water g: heat h: fibrous
Cholesterol has been implicated in heart disease for decades. Atherosclerosis is a disorder of the arteries in which cholesterol and other materials are deposited on the interior of the arterial wall. These deposits lead to the formation of plaques that can restrict or even block the flow of blood through these blood vessels (see Figure below ). A decrease in the flow of blood can lead to high blood pressure and a lowered oxygen supply to the heart muscle. A complete blockage of blood flow to parts of the heart (a heart attack) can cause significant damage due to oxygen deprivation, in some cases leading to death.
Brad
ropes
Context: Brad and Dale went to the doctor for a check up. Brad did some blood tests and found out he has very high cholesterol levels, while his partner Dale had normal cholesterol levels, and was very healthy. Brad got scared and started worrying. Question: Which friend was at a higher risk of suffering a heart attack?
Annelids have the amazing capacity to regrow segments that break off. Earthworms earthworms are in the phylum annelids. Earthworms have the amazing capacity to regrow segments that break off.
D
qasc
_ have the amazing capacity to regrow segments. A) ferns B) arachnids C) roots D) earthworms E) anthropods F) crustacean G) loose soil H) root growth
Construction workers can work on telephone poles for reasons other than that they're fixing an accident that has taken place.
Unknown
esnli
Given the statement "Construction workers in hard hats and reflection vest are working on a telephone pole.", is the statement "Workers are fixing an accident" wrong? - Yes - No - Unknown
Not being able to keep up with housework can often make people feel like they are not doing enough and result in feelings of guilt and shame
No
FLUTE
Context: I am so behind on my housework. Hypothesis: I feel terrible that I have not been able to keep up with my housework like I wanted to Is the hypothesis incorrect? (Yes, no, or unknown)?
People who eat cakes should not eat more cakes because if they do they will gain weight.
"people who lose weight should eat more cakes"
senmaking
One of the following sentences is nonsensical. Which one is it? Options: - "people who lose weight should eat fewer cakes" - "people who lose weight should eat more cakes"
"A man looks past the camera while a girl sits behind him" is a vague representation of "A man in a gray shirt looks past the camera while a girl in a blue sweatshirt sits behind him to his left.".
True
esnli
Context: "A man in a gray shirt looks past the camera while a girl in a blue sweatshirt sits behind him to his left." Claim: "A man looks past the camera while a girl sits behind him" Considering the context, is the claim true, false, or unknown?
We first note that $\sqrt{3}\times 3^{\frac{1}{2}} = 3^{\frac{1}{2}}\times 3^{\frac{1}{2}} = 3^{\frac{1}{2} + \frac{1}{2}} = 3^1 = 3$ and $4^{3/2} = (2^2)^{\frac{3}{2}} = 2^{2\cdot \frac{3}{2}} = 2^3 = 8$, so \begin{align*} \sqrt{3} \times 3^{\frac{1}{2}} + 12 \div 3 \times 2 - 4^{\frac{3}{2}} &= 3 + 12\div 3 \times 2 - 8\\ &=3 + 4\times 2 - 8\\ &=3+8-8 = 3. \end{align*}
$3$
competition-math
When simplified, what is the value of $\sqrt{3} \times 3^{\frac{1}{2}} + 12 \div 3 \times 2 - 4^{\frac{3}{2}}$?
$$(\vec{c}-\vec{a})\cdot (\vec{c}-\vec{b})=1-\overrightarrow{c}\left( \overrightarrow{a}+\overrightarrow{b} \right)=1-\left\textbar{} \overrightarrow{c} \right\textbar\left\textbar{} \overrightarrow{a}+\overrightarrow{b} \right\textbar\text{cos }\theta \leqslant 1+\sqrt{2}$$,当$$\overrightarrow{c}$$与$$\overrightarrow{a}+\overrightarrow{b}$$的夹角为$$180{}^{}\circ $$时取等号. 故选$$\text{A}$$.
1
TAL-SCQ5K
设$$\vec{a},\vec{b},\vec{c}$$是同一平面内的三个单位向量,且$$\vec{a}\bot \vec{b}$$,则$$(\vec{c}-\vec{a})\cdot (\vec{c}-\vec{b})$$的最大值是(~ ). Options: 1. $$1+\sqrt{2}$$ 2. $$1-\sqrt{2}$$ 3. $$\sqrt{2}-1$$ 4. $$1$$
The total ratio representing the yellow scores that Taylor got is 7+6=13 The difference in the ratio between the number of black and white scores Taylor used is 7-6=1 The fraction representing the difference in the ratio between the number of black and white scores Taylor used is 1/13, representing 1/13*78=6 2/3 of the difference between the number of black and white scores Taylor used is 2/3*6=4
4
gsm8k
To make a yellow score mixture, Taylor has to combine white and black scores in the ratio of 7:6. If she got 78 yellow scores, what's 2/3 of the difference between the number of black and white scores she used?
Woman is a lady. Walks is rephrased as strolls and next to a tree implies she is outside. City implies it is an urban area.
Yes
esnli
Context: A woman in yellow walks next to a tree in the city. Hypothesis: A lady strolls outside in an urban area. Given this context, is the hypothesis true (Yes/No/I don't know)?
Sentence 1: Multiple people around a county fair with several attractions including a fortune telling machine called Grandmas prediction. Sentence 2: A big event is going on with a lot of people in attendance.
Unknown
esnli
Context: Multiple people around a county fair with several attractions including a fortune telling machine called Grandmas prediction. Hypothesis: A big event is going on with a lot of people in attendance. Given this context, determine if the hypothesis is true (Yes, no, or unknown)?
Just because an old woman is in front of a window does not mean that she is watching what is going on.
Unknown
esnli
Given the statement "There is an old woman in front of a window.", what is the statement "The old woman was watching what was happening from the inside." true? - Yes - No - Unknown
When humans dig up and use fossil fuels, we have an impact on the carbon cycle ( Figure below ). This carbon is not recycled until it is used by humans. The burning of fossil fuels releases more carbon dioxide into the atmosphere than is used by photosynthesis. So, there is more carbon dioxide entering the atmosphere than is coming out of it. Carbon dioxide is known as a greenhouse gas , since it lets in light energy but does not let heat escape, much like the panes of a greenhouse. The increase of greenhouse gasses in the atmosphere is contributing to a global rise in Earth’s temperature, known as global warming or global climate change.
Time b
ropes
Greg is an environmental scientist. He wants to know how earth's atmosphere differed in two different time. To that end, he selected two time periods, time A and time B. Time A is set in the year one thousand when using fossil fuels was not very common. Time B is set in the year two thousand when fossil fuels are used in large quantities. In which time more carbon dioxide would be realeased into the atmosphere, time A or time B?
"A man with jacket wears headphones standing in front of a directory" already implies that man stands in front of a directory.
Yes
esnli
Given the statement "A man with a jacket wears headphones standing in front of a directory.", is the statement "A man stands in front of a directory." is true? - Yes - No - I don't know