instruction_seed stringlengths 31 2.65k | source stringclasses 1
value |
|---|---|
a scale 7 ft . 6 inches long is divided into 5 equal parts . find the length of each part . Let's program in Python in the response. | tiger_lab_math |
two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer r between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ? Let's write a Python program to solve it. | tiger_lab_math |
Let $g(n)$ be the product of the proper positive integer divisors of $n$. (Recall that a proper divisor of $n$ is a divisor other than $n$.) For how many values of $n$ does $n$ not divide $g(n)$, given that $2 \le n \le 50$? Let's program in Python in the response. | tiger_lab_math |
Find the number of non-isomorphic groups of order 72 that exist, and list all of them along with their isomorphism types. | tiger_lab_math |
If $x$ is a real number and $x^2 = 16$, what is the sum of all possible values of $x$? Let's write a program. | tiger_lab_math |
What is the units digit of the product of all the odd positive integers between 10 and 110? | tiger_lab_math |
with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity e of the pool ? Let's program in Python in the response. | tiger_lab_math |
Let P(x) be a statement about a natural number x. Express the following statement using quantifiers and logical connectives:
"There exists a natural number x such that for all natural numbers y, P(y) implies x <= y."
Also, show that the negation of the statement is true. | tiger_lab_math |
For how many positive integers $n$ does $\frac{1}{n}$ yield a terminating decimal with a non-zero hundredths digit? | tiger_lab_math |
Find the smallest positive four-digit number that is divisible by each of the four smallest prime numbers. Let's write a Python program to solve it. | tiger_lab_math |
Mark bought a shirt, pants, and shoes for $340. What is the price of the pants knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants? | tiger_lab_math |
3 math classes : x , y , and z , take an algebra test . the average score in class x is 83 . the average score in class y is 76 . the average score in class z is 85 . the average score of all students in classes x and y together is 79 . the average score of all students in classes y and z together is 81 . what is the a... | tiger_lab_math |
a cycle is bought for rs . 450 and sold for rs . 520 , find the gain percent ? Let's write a Python program. | tiger_lab_math |
What is the largest value of $x$ such that the expression \[\dfrac{x+1}{8x^2-65x+8}\] is not defined? | tiger_lab_math |
In a company, it is found that the probability of an accident happening in a particular department is 0.25. If there are 10 departments in the company, what is the probability that at least one department will experience an accident? | tiger_lab_math |
We are allowed to remove exactly one integer from the list $$-1,0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,$$and then we choose two distinct integers at random from the remaining list. What number should we remove if we wish to maximize the probability that the sum of the two chosen numbers is 10? Let's write a Python progra... | tiger_lab_math |
when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.45 , what is the value of y ? Please write a program to solve it | tiger_lab_math |
Assuming a weather system can be modeled mathematically as a chaotic system with a Lyapunov exponent of 0.25, and given that the initial conditions are known to an accuracy of 0.01, estimate how far into the future the weather prediction can be made with an accuracy of 99.9%. | tiger_lab_math |
Let $M$ be a 2-dimensional manifold given by the equation $x^2+y^2+z^2=1$. Find the scalar curvature of $M$ at the point $(0,0,1)$. | tiger_lab_math |
a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is two - thirds of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ? Let's write a Python program. | tiger_lab_math |
in a school of 850 boys , 46 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ? Let's write a Python program. | tiger_lab_math |
Given the Henon-Heiles system with the potential energy function:
V(x,y) = 1/2(x^2+y^2) + λ(x^2y-y^3/3)
If λ=0.12 and the initial conditions are x=0.1, y=0.1 with velocities in the x and y directions equal to zero. Determine the maximum value of x and y over a time period of 100 seconds using a fourth-order Runge-Kutt... | tiger_lab_math |
If $a\equiv 18\pmod{42}$ and $b\equiv 73\pmod{42}$, then for what integer $n$ in the set $\{100,101,102,\ldots,140,141\}$ is it true that $$a-b\equiv n\pmod{42}~?$$ | tiger_lab_math |
Homer scored 400 points on the first try in a Candy crush game, 70 points fewer on the second try, and twice the number of points she scored on the second try on the third try. What's the total number of points that she scored in all tries? | tiger_lab_math |
If $\mathbf{a}$ and $\mathbf{b}$ are vectors such that $\|\mathbf{a}\| = 7$ and $\|\mathbf{b}\| = 11$, then find all possible values of $\mathbf{a} \cdot \mathbf{b}$.
Submit your answer in interval notation. | tiger_lab_math |
Suppose you want to encrypt the plaintext message "101110" using Feistel cipher structure with the key "010101". Each round of the Feistel cipher involves the use of two functions, F and XOR. The F function takes in a 4-bit input and outputs a 4-bit output, and the XOR operation returns the exclusive OR of the two inpu... | tiger_lab_math |
A tree on a farm has 10 branches. Each branch has 40 sub-branches with 60 leaves each. If the total number of trees on the farm is 4 and they have the same number of leaves, calculate the total number of leaves on all the trees. | tiger_lab_math |
Given that the point $(9,7)$ is on the graph of $y=f(x)$, there is one point that must be on the graph of $2y=\frac{f(2x)}2+2$. What is the sum of coordinates of that point? | tiger_lab_math |
a school has 4 section of chemistry in class x having 55 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student . Let's write a Python program. | tiger_lab_math |
What is the value of the maximum number of iterations required to determine the boundary of the Mandelbrot set at a zoom level of 10^13 centered at -0.5 + 0i? | tiger_lab_math |
In how many ways can you partition the number 7 into a sum of positive integers, ignoring the order of the summands? | tiger_lab_math |
if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > – 1 , 3 > x > 0 , and x + 2 < 4 , then x is ? Let's write a Python program. | tiger_lab_math |
The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
Answer Choices: (A) 125 (B) 144 (C) 516 (D) 143 (E) 142 | tiger_lab_math |
Find all the quadratic residues modulo 17. | tiger_lab_math |
Let f(z) be an entire function such that |f(z)| ≤ 4|z| for all z in the complex plane. Prove that f(z) is a polynomial of degree at most 1.
Using Liouville's Theorem from Complex Analysis, if the function f(z) is entire and bounded, it must be a constant function. However, in this case, |f(z)| ≤ 4|z|, which suggests t... | tiger_lab_math |
the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 50 kmph its consumption is 1 litre per hour . if each litre costs $ 50 and other expenses per hous is $ 50 , then what would be the minimum expenditure required to cover a distance of 500 km ? Please write... | tiger_lab_math |
a number , x is chosen at random from the set of positive integers less than 10 . what is the probability that ( 8 / x ) > x ? Let's write a Python program. | tiger_lab_math |
a factory produces 4340 toys per week . if the workers at this factory work 2 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ? Let's program in Python in the response. | tiger_lab_math |
ram - leela has $ 100 in her piggy bank . how much will she have in her bank 52 weeks from now if she puts $ 1 in the bank next week , $ 2 two weeks from now , $ 3 3 weeks from now , and continues to increase the amount that she puts in by $ 1 each week ? Let's write a Python program. | tiger_lab_math |
Find the two numbers whose sum is 45 and such that one is 4 times as large as the other. Find the smaller number. Let's write a Python program to solve it. | tiger_lab_math |
Let M be a smooth manifold of dimension 2. Suppose the tangent bundle of M is nontrivial and has a nonvanishing global section. Prove that the Euler characteristic of M is zero. | tiger_lab_math |
the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 6270 . what was his original salary ? Please write a program to solve it | tiger_lab_math |
A number $x$ is equal to $7\cdot24\cdot48$. What is the smallest positive integer $y$ such that the product $xy$ is a perfect cube? Please respond by writing a program in Python. | tiger_lab_math |
Find all the solutions to
\[\sqrt[3]{2 - x} + \sqrt{x - 1} = 1.\]Enter all the solutions, separated by commas. | tiger_lab_math |
"statement 1": The next day , Cara took the test , and with this grade included , the new average was 77, "statement 2" :The next day , Cara took the test , and with this grade included , the new average was more than 47, "options: " Entailment or contradiction or neutral? Let's write a program. | tiger_lab_math |
A plane intersects a right circular cylinder of radius $1$ forming an ellipse. If the major axis of the ellipse of $50\%$ longer than the minor axis, the length of the major axis is
$\textbf{(A)}\ 1\qquad \textbf{(B)}\ \frac{3}{2}\qquad \textbf{(C)}\ 2\qquad \textbf{(D)}\ \frac{9}{4}\qquad \textbf{(E)}\ 3$
Please writ... | tiger_lab_math |
"statement 1": Store Z : $ 90 , a 20 % sales tax , and $ 10 rebate after tax
Isaac can purchase a certain item in four different ways , as shown in the table, "statement 2" :Store Z : $ more than 60 , a 20 % sales tax , and $ 10 rebate after tax Isaac can purchase a certain item in four different ways , as shown in th... | tiger_lab_math |
120 students represent x percent of the boys at a school . if the boys at the school make up 30 % of the total school population of x students , what is x ? Let's write a Python program. | tiger_lab_math |
Ten adults enter a room, remove their shoes, and toss their shoes into a pile. Later, a child randomly pairs each left shoe with a right shoe without regard to which shoes belong together. The probability that for every positive integer $k<5$, no collection of $k$ pairs made by the child contains the shoes from exactly... | tiger_lab_math |
What is the sum of two prime numbers that equals 46? (This problem pertains to Goldbach's conjecture that every even integer greater than 2 can be expressed as the sum of two prime numbers.) | tiger_lab_math |
Rectangle $ABCD$ and a semicircle with diameter $AB$ are coplanar and have nonoverlapping interiors. Let $\mathcal{R}$ denote the region enclosed by the semicircle and the rectangle. Line $\ell$ meets the semicircle, segment $AB$, and segment $CD$ at distinct points $N$, $U$, and $T$, respectively. Line $\ell$ divides ... | tiger_lab_math |
Find the missing number in the series.
2 , 3 , 6 , 0 , 10, -3 , 14...
Answer Choices: (A) -6 (B) 8 (C) 7 (D) 67 (E) 65 | tiger_lab_math |
at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 35 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at ... | tiger_lab_math |
a line that passes through ( – 1 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ? Let's program in Python in the response. | tiger_lab_math |
A hospital conducted a study on a certain medical condition and found that 25% of the patients who have the symptoms of the condition test positive for it. If 500 patients have the symptoms, how many of them would test positive for the condition according to the probability? | tiger_lab_math |
In a game, Player 1 has a card with a number between 1 and 10 written on it, but Player 2 does not know the number on the card. However, Player 2 knows that the number on the card is an even number. Player 1 tells Player 2, "I will reveal the number on the card if it is greater than 4." After hearing this, Player 2 con... | tiger_lab_math |
an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles... | tiger_lab_math |
a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability e that both selected dogs are not littermates ? Let's program in Python in the response. | tiger_lab_math |
two pipes a and b fill at a certain rate . b is filled at 1020 , 4080 ( 10 in 1 hour , 20 in 2 hours , 40 in 3 hrs and so on ) . if 1 / 16 of b is filled in 17 hrs , what time it will take to get completely filled ? Please respond by writing a program in Python. | tiger_lab_math |
How many positive 3-digit numbers are divisible by 11? | tiger_lab_math |
Find the number of points on the Calabi-Yau variety defined by the equation $xy(x+y-2z)+z^3=0$, where $x, y, z$ are integers between $1$ and $100$ (inclusive). | tiger_lab_math |
a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 110 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello ar... | tiger_lab_math |
a no . when divided by 142 gives a remainder 110 , what remainder will be obtainedby dividingthe same no . 14 ? Let's write a program. | tiger_lab_math |
A triangle has sides with lengths 5 cm, 8 cm and 9 cm. Find the measure of the largest angle in the triangle using the law of cosines. | tiger_lab_math |
find large number from below question the difference of two numbers is 1335 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder ? Let's program in Python in the response. | tiger_lab_math |
a shopkeeper buys two articles for rs . 1000 each and then sells them , making 10 % profit on the first article and 10 % loss on second article . find the net profit or loss percent ? Let's write a program. | tiger_lab_math |
A cube 4 units on each side is composed of 64 unit cubes. Two faces of the larger cube that share an edge are painted blue, and the cube is disassembled into 64 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly two painted f... | tiger_lab_math |
What is the sum of all of the solutions of the equation $\frac{4x}{20}=\frac{5}{x}$? | tiger_lab_math |
ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the number . Please write a program to solve it | tiger_lab_math |
A 2D image has a brightness function defined by the partial differential equation:
$ \frac{\partial u}{\partial t} = k \left(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\right) $
where $u(x,y,t)$ represents the brightness of an image at point $(x,y)$ and time $t$, and $k$ is a constant. If t... | tiger_lab_math |
there are 17 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ? Let's program in Python in the response. | tiger_lab_math |
What is the area of the largest circular disk that can fit entirely inside the Mandelbrot set? | tiger_lab_math |
There are 23 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
Answer Choices: (A) 39 (B) 40 (C) 51 (D) 58 (E) 63 | tiger_lab_math |
two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 2 . find the larger integer . Please respond by writing a program in Python. | tiger_lab_math |
in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 8 , 1 ) , ( 1 , 1 ) , ( 1 , - 7 and ( - 8 , - 7 ) ? Let's write a program. | tiger_lab_math |
two numbers have a h . c . f of 16 and a product of two numbers is 2560 . find the l . c . m of the two numbers ? Let's program in Python in the response. | tiger_lab_math |
Find the value of $x$ if $x$ is positive and $x\cdot\lfloor x\rfloor=70$. Express your answer as a decimal. | tiger_lab_math |
a grocer has a sale of rs . 5921 , rs . 5468 , rs . 5568 , rs . 6088 and rs . 6433 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5900 ? Please write a program to solve it | tiger_lab_math |
Suppose a company produces light bulbs, with a production rate of 10 bulbs each minute. The quality control team has found that, on average, 2% of the bulbs are defective. Suppose you pick one bulb at random from a box. Calculate the probability that it is a defective bulb, using Bayesian statistics with a prior belief... | tiger_lab_math |
An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 64 times the difference between the two numbers. How many coins did the old man have?
Answer Choices: (A) 24 (B) 26 (C) 30 (D) 64 (E) 40 | tiger_lab_math |
Consider the system of nonlinear equations
x^2 + y^2 = 8
x^2 - y^2 = 4
Find the value of (x, y) that satisfies the above system of equations using Newton's method. | tiger_lab_math |
a circular mat with diameter 18 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ? Let's write a Python program. | tiger_lab_math |
the marks obtained by polly and sandy are in the ratio 4 : 5 and those obtained by sandy and willy are in the ratio of 5 : 2 . the marks obtained by polly and willy are in the ratio of . . . ? Please write a program to solve it | tiger_lab_math |
Twenty gremlins and fifteen imps are at the Annual Mischief Convention. The imps have had a lot of in-fighting lately and refuse to shake hands with each other, but they readily shake hands with all of the gremlins. Meanwhile, all the gremlins are quite friendly and shake hands with all of the other gremlins as well as... | tiger_lab_math |
A plane is flying at a speed of 500 km/h and heading towards a destination that is 1200 km away. If the plane encounters a wind with a velocity of 80 km/h blowing at an angle of 30 degrees to its direction of travel, find the new heading of the plane and the time it will take to reach the destination. Use the law of co... | tiger_lab_math |
My mother celebrated her birthday with a total of 60 guests. Half of the guests are women, 15 are men, and the rest are children. In the middle of the celebration, 1/3 of the men and 5 children left. How many people stayed and enjoyed the birthday celebration? | tiger_lab_math |
two pipes a and b can separately fill a cistern in 60 minutes and 80 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ? Please ... | tiger_lab_math |
A rectangular box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 30 cm by 20 cm by cutting out equal squares of side x from each corner and folding up the sides. If the volume of the box has to be 3600 cubic cm, what is the minimum size of the squares that need to be cut out... | tiger_lab_math |
What is the sum of the real values in the Mandelbrot set that correspond to points within the boundary of the Julia set that is generated by the complex number -0.75 + 0.1i? | tiger_lab_math |
find the area of the square , one of whose diagonals is 3.8 m long ? Let's write a Python program. | tiger_lab_math |
a number consists of 3 digit whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is : ? Please respond by writing a program in Python. | tiger_lab_math |
"statement 1": The next day , Dan took the test , and with this grade included , the new average was 76, "statement 2" :The next day , Dan took the test , and with this grade included , the new average was more than 16, "options: " Entailment or contradiction or neutral? Let's program in Python in the response. | tiger_lab_math |
Consider the following partial differential equation for image processing:
𝜕f/𝜕t = 𝜕²f/𝜕x² + 𝜕²f/𝜕y²
where f(x,y,t) is a grayscale image.
Let f(x,y,0) be a square image of size 256x256 with constant intensity of 100.
If the boundary conditions are homogeneous Neumann conditions (∂f/∂x=0, ∂f/∂y=0) for all side... | tiger_lab_math |
a family travelled for 12 hours . they covered the first half of the distance at 35 kmph and remaining half of the distance at 40 kmph . find the distance travelled by the family ? Please respond by writing a program in Python. | tiger_lab_math |
Evaluate the following complex integral:
$$ \int_{\gamma} \frac{1}{z^2+4z+29}dz$$
where $\gamma$ is the positively oriented circle centered at $-3+2i$ with radius $3$. | tiger_lab_math |
How many positive four-digit integers are divisible by $8$? | tiger_lab_math |
Let A = {1, 2, 3} and B = {2, 3, 4}. Find the symmetric difference of A and B, then find the intersection of A and B, and then find the symmetric difference of B and A. Show that the symmetric difference of A and B is not commutative with respect to intersection. | tiger_lab_math |
110 people are attending a newspaper conference . 45 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ? Let's write a Python program. | tiger_lab_math |
john and steve are speed walkers in a race . john is 15 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ? Let's program in Pyth... | tiger_lab_math |
"statement 1": David obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in English , mathematics , physics , chemistry and biology, "statement 2" :David obtained less than 86 , 65 , 82 , 67 and 85 marks ( out of 100 ) in English , mathematics , physics , chemistry and biology, "options: " Entailment or contradicti... | tiger_lab_math |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.