instruction_seed stringlengths 31 2.65k | source stringclasses 1
value |
|---|---|
a couple married in 1980 had two children , one in 1982 and the other in 1984 . their combined ages will equal the years of the marriage in ? Let's program in Python in the response. | tiger_lab_math |
a single reservoir supplies the petrol to the whole city , while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume . when the reservoir is full and if 40,000 liters of petrol is used daily , the suply fails in 90 days . if 32,000 liters of petrol is used daily , it fails ... | tiger_lab_math |
Of the three-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
Answer Choices: (A) 24 (B) 36 (C) 72 (D) 1 (E) 216 | tiger_lab_math |
a man covers a certain distance q in a train . if the train moved 4 km / hr faster , it would take 30 min less . if it moved 2 km / hr slower , it would take 20 mins more . find the distance ? Let's program in Python in the response. | tiger_lab_math |
15 times a positive integer is more than its square by 56 , then the positive integer is ? Let's write a Python program to solve it. | tiger_lab_math |
A flagpole stands vertically on a hill. If the angle of elevation of the top of the flagpole from a point on the hill is 30 degrees and the angle of elevation of the bottom of the flagpole from the same point is 15 degrees, find the height of the flagpole. Given that the distance between the point on the hill and the f... | tiger_lab_math |
in a coconut grove , ( x + 4 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 4 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x . Let's write a program. | tiger_lab_math |
Consider a conformal map, $f(z) = \frac{2z+1}{z-2}$, that maps the unit circle $|z|=1$ onto a new region in the complex plane. Find the area of this new region. | tiger_lab_math |
frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 480 square feet . how many feet offence does frank use ? Please respond by writing a program in Python. | tiger_lab_math |
Find the greatest natural number $n$ such that $n\leq 2008$ and $(1^2+2^2+3^2+\cdots + n^2)\left[(n+1)^2+(n+2)^2+(n+3)^2+\cdots + (2n)^2\right]$ is a perfect square.
Let's write a Python program. | tiger_lab_math |
in a certain pond , 60 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the p... | tiger_lab_math |
"statement 1": Mac has £ 3 more than Ken , but then Ken wins on the horses and trebles his money , so that he now has £ 2 more than the original amount of money that the two boys had between them, "statement 2" :Mac has £ less than 5 more than Ken , but then Ken wins on the horses and trebles his money , so that he no... | tiger_lab_math |
on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salar... | tiger_lab_math |
A crate weighing 1000 N is being lifted up a building by a rope that is 50 meters long. The rope is initially at ground level and it's being pulled so that the crate moves along the side of the building that is 30 meters high. If the force required to pull the crate is constant at 200 N, calculate the work done by the ... | tiger_lab_math |
a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500,000 ? Please write a program to solve it | tiger_lab_math |
How many distinct ordered pairs of positive integers $(m,n)$ are there so that the sum of the reciprocals of $m$ and $n$ is $\frac14$? | tiger_lab_math |
In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Answer Choices: (A) 5/21 (B) 5/27 (C) 5/97 (D) 5/22 (E) 5/39 | tiger_lab_math |
What is the smallest positive integer n such that there exists a computer program that can determine whether any other given computer program will eventually halt or run forever, in at most n steps? | tiger_lab_math |
a scuba diver descends at a rate of 30 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 2400 feet below the sea level . . how long will he take to reach the ship ? Let's write a Python program. | tiger_lab_math |
Find the sum of the values of $x$ such that $\cos^3 3x+ \cos^3 5x = 8 \cos^3 4x \cos^3 x$, where $x$ is measured in degrees and $100< x< 200.$
Let's program in Python in the response. | tiger_lab_math |
the average of 10 numbers is 0 . in those 10 , at the least , how many may be greater than or equal to zero ? Please respond by writing a program in Python. | tiger_lab_math |
a company organzied a help desk . there have been done 24 hrs work on software , 17 hrs on help user nd 40 % on other services . find the total no . of hrs have been worked on that day ? Let's write a Python program. | tiger_lab_math |
What is the perimeter of the Koch island after the 4th iteration if the original side length of the equilateral triangle is 1 unit? (Note: Each iteration of the Koch island involves replacing each line segment with four segments of equal length, where the middle two segments form an equilateral triangle.) | tiger_lab_math |
A ladder is leaning against a wall and sliding down at a rate of 5 ft/s. Initially, the bottom of the ladder is 12 feet away from the wall and 16 feet long. What is the rate of change of the height of the top of the ladder when the bottom is 9 feet away from the wall? Using the product rule, differentiate the equation ... | tiger_lab_math |
rajan and rakesh started a business and invested rs . 20,000 and rs . 25,000 respectively . after 4 months rakesh left and mukesh joined by investing rs . 15,000 . at the end of the year there was a profit of rs . 4,600 . what is the share of rajan ? Let's write a program. | tiger_lab_math |
Suppose that a pendulum is oscillating with a frequency of 2 Hz in a chaotic motion. The Poincaré map shows that after every full swing, the pendulum rotates by an angle of 0.5 radians. Find the first two return times to the same position of the pendulum after it starts oscillating. | tiger_lab_math |
s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is ? Let's write a program. | tiger_lab_math |
A rectangular rug with side lengths of 4 feet and 6 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
Answer Choices: (A) A.3/16 (B) 1/4 (C) C.1/2 (D) 5/8 (E) 7/8 | tiger_lab_math |
Let A be a set with 6 elements and its complement has 4 elements. Determine the number of elements in the universal set and prove that the union of A and its complement is the universal set using set theory. | tiger_lab_math |
Let A and B be two sets with cardinalities 3 and 4 respectively. Find the number of second-order definable subsets of the Cartesian product A × B. | tiger_lab_math |
Nina did a running drill to get in shape for soccer season . First , Nina ran 0.08 mile . Then she ran 0.08 mile and 0.67 mile. In total , Nina ran _____ miles . Please respond by writing a program in Python. | tiger_lab_math |
Let U be the universal set, and let A be a subset of U such that A is divisible by 3 and U has 50 elements. If the complement of A has 20 elements, prove that the union of A and its complement is equal to U. | tiger_lab_math |
Suppose we have a complex algebraic curve given by the equation $y^2 = x^3 - x + 1$.
(a) Determine the degree of the curve.
(b) Compute the Hodge numbers of the curve.
(c) Find the dimensions of the spaces of holomorphic differentials and harmonic forms on the curve.
(d) Show that the curve admits a non-constan... | tiger_lab_math |
Find all distinct groups of order 20 up to isomorphism, and state which ones are cyclic, which ones are dihedral, and which one is non-abelian. | tiger_lab_math |
a bag contains 5 green balls and 9 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ? Please respond by writing a program in Python. | tiger_lab_math |
the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 8 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ? Let's write a program. | tiger_lab_math |
Consider the following Riemannian metric on the surface of a sphere of radius 3:
$$
ds^2 = 9d\theta^2 + 9\sin^2(\theta) d\phi^2.
$$
Find the symbols $\Gamma_{ij}^k$ of the Levi-Civita connection. | tiger_lab_math |
A triangle has two sides that are equal, and they are 13 cm each. The angle opposite the equal sides is 45 degrees. What is the length of the third side? | tiger_lab_math |
the salary of a , b , c , d , e is rs . 10000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is ? Let's write a program. | tiger_lab_math |
Five kids were walking down the street. At a shop, they saw three brands of chocolates viz. Cadbury, Nestle and Ferrero being displayed. The shopkeeper has three chocolates which are of three different flavors of each brand. The kids bought all the chocolates available and decided to play a game. The chocolates will be... | tiger_lab_math |
Prove that the difference between any two odd numbers is an even number. | tiger_lab_math |
Let A be a set with 5 elements. Find the size of the power set of A and show that it is larger than the size of set A itself, thus proving that the power set of a set is always larger than the set itself. | tiger_lab_math |
Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2:3, then find the number of pens that D gets?
Answer Choices: (A) 16 (B) 76 (C) 75 (D) 88 (E) 52 | tiger_lab_math |
the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach ( b ) to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent... | tiger_lab_math |
the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 1400 per sq . metre . Please respond by writing a program in Python. | tiger_lab_math |
In triangle $ABC$, the angle bisectors are $AD$, $BE$, and $CF$, which intersect at the incenter $I$. If $\angle ACB = 38^\circ$, then find the measure of $\angle AIE$, in degrees. | tiger_lab_math |
a bag contains 4 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is ? Let's write a Python program. | tiger_lab_math |
Find the product of all integer divisors of $105$ that also divide $14$. (Recall that the divisors of an integer may be positive or negative.) Let's write a Python program to solve it. | tiger_lab_math |
Let A = {1, 2} and B = {3, 4}. Find A x B and B x A and show that they are not equal, proving that the Cartesian product of two sets is not commutative. | tiger_lab_math |
alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1111 . find the cost of each ice - cream cup ? Let's write... | tiger_lab_math |
a 6000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ? Please write a pro... | tiger_lab_math |
Determine the equation of the line that passes through points P(3,4) and Q(5,1) and intersects the elliptic curve E: y^2 = x^3 + x + 1 at a third point R. Find the coordinates of point R. | tiger_lab_math |
What is the linking number of two different knots, A and B, in 4-dimensional Euclidean space?
Suppose that knot A has 5 crossings, and its projection diagram can be represented as (3,1,-2,-4,-5). Knot B has a different projection diagram that can be represented as (1,2,-3,-5,-4). Find the linking number between these ... | tiger_lab_math |
question : a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 180 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 195 for the p... | tiger_lab_math |
A plane is uniquely determined by three non-collinear points. What is the maximum possible number of planes that can be determined by 12 points in space? | tiger_lab_math |
Evaluate the expression \[ \frac{a+2}{a+1} \cdot \frac{b-1}{b-2} \cdot \frac{c + 8}{c+6} , \] given that $c = b-10$, $b = a+2$, $a = 4$, and none of the denominators are zero. Let's program in Python in the response. | tiger_lab_math |
pavan travelled for 11 hours . he covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph . find the distance travelled by pavan ? Let's program in Python in the response. | tiger_lab_math |
A rectangular garden is to be fenced using 40 meters of fencing material. One side of the garden will be against the wall of the house and so doesn't need any fencing. What are the dimensions of the garden that will maximize its area? | tiger_lab_math |
12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 6 . Please write a program to solve it | tiger_lab_math |
A mass-spring system has a mass of 0.5 kg attached to a spring with a spring constant of 10 N/m. If the mass is displaced from its equilibrium position by 0.2 meters and released, find the equation of motion and the time period of oscillation. Assume that there is no damping present in the system. | tiger_lab_math |
there are 200 female managers in a certain company . find the total number t of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers . Let's write a Python program to solve it. | tiger_lab_math |
A Koch island is created by starting with an equilateral triangle with sides of length 1. In the first iteration, each side of the triangle is replaced by a longer line segment made up of four segments of equal length, forming a shape that looks like a three-pointed star. In each subsequent iteration, each segment of t... | tiger_lab_math |
a sum of rs . 2795 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ? Please respond by writing a program in Python. | tiger_lab_math |
the population of 6 villages is 803 , 9001100 , 1023945 and 980 . what is the population of the seventh village if the average population of the 7 villages is 1000 ? Let's write a Python program. | tiger_lab_math |
a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 66000 . what is the share of c ? Please write a program to solve it | tiger_lab_math |
Samantha's investment portfolio consists of three stocks: a railway, a bank, and a computer company. In the month of February, the price of the railway's stock rose by 10%, that of the bank decreased by 15% and that of the computer company also decreased by 15%, but the overall value of her portfolio increased. If Sama... | tiger_lab_math |
income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 18000 , then find his savings ? Let's write a program. | tiger_lab_math |
a starts business with rs . 4500 and after 7 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ? Please respond by writing a program in Python. | tiger_lab_math |
the area of a rectangular field is equal to 800 square meters . its perimeter is equal to 120 meters . find the width of this rectangle . Let's program in Python in the response. | tiger_lab_math |
Find the Morse-Smale complex for the function f(x,y) = x^2 - y^2 on the region D={(x,y)| x^2+y^2<=1}, and determine the number of critical points, the index of each critical point and the number of connected components in the complex. | tiger_lab_math |
A sphere is inscribed in a cube with an edge length of 6 cm. Find the volume of the sphere. | tiger_lab_math |
when the no . 7 y 86038 is exactly divisible by 11 , then the smallest whole no . in place of y ? Let's write a Python program. | tiger_lab_math |
maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 74 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he me... | tiger_lab_math |
Let A be a set such that A = {1, 2, 3, 4, 5}. Write out the complement of the set A and calculate the intersection between set A and its complement. Show that the intersection is equal to the empty set. | tiger_lab_math |
a light has a rating of 86 watts , it is replaced with a new light that has 18 % higher wattage . how many watts does the new light have ? Let's write a Python program. | tiger_lab_math |
a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ? Let's write a Python program to solve it. | tiger_lab_math |
When three positive integers are divided by $47$, the remainders are $25$, $20$, and $3$, respectively.
When the sum of the three integers is divided by $47$, what is the remainder? | tiger_lab_math |
A right triangle has a hypotenuse of length 13 and one leg of length 5. Find the length of the other leg. | tiger_lab_math |
Consider the power series representation of the function $f(z) = e^z$ at $z=0$. Determine the radius of convergence of the power series and find the sum of the power series at $z = 1$. | tiger_lab_math |
Consider a graph with 6 vertices and the following edges: (1,2), (2,3), (3,4), (4,5), (5,6), (6,1), (2,4), (4,6). Find the Hamiltonian cycle in the graph if one exists, otherwise state that it doesn't exist. | tiger_lab_math |
a number x is 3 times another number y . the percentage that y is less than x is ? Let's program in Python in the response. | tiger_lab_math |
Find the number of positive integers $n \le 1000$ such that $15n$ is a perfect square. Please respond by writing a program in Python. | tiger_lab_math |
For two real values of $n$, the equation $4x^2+nx+25=0$ has exactly one solution in $x$. What is the positive value of $n$? | tiger_lab_math |
What is the largest positive integer with only even digits that is less than $10,000$ and is a multiple of $9$? Let's write a program. | tiger_lab_math |
sum of the squares of 3 no . is 252 and the sum of their products taken two at a time is 116 . find the sum ? Let's program in Python in the response. | tiger_lab_math |
on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 140 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ? Let's write a Python program. | tiger_lab_math |
The numbers in the sequence $101$, $104$, $109$, $116$,$\ldots$ are of the form $a_n=100+n^2$, where $n=1,2,3,\ldots$ For each $n$, let $d_n$ be the greatest common divisor of $a_n$ and $a_{n+1}$. Find the maximum value of $d_n$ as $n$ ranges through the positive integers.
Let's write a Python program to solve it. | tiger_lab_math |
a cycle is bought for rs . 600 and sold for rs . 1080 , find the gain percent ? Please write a program to solve it | tiger_lab_math |
the area of a triangle will be when a = 1 m , b = 2 m , c = 5 m , a , b , c being lengths of respective sides ? Let's write a program. | tiger_lab_math |
Consider the algebraic curve given by the equation:
y^2 = x^3 + 2x + 1.
Find the rational points on the curve, meaning points with rational coordinates (i.e., coordinates that can be expressed as fractions). | tiger_lab_math |
a car drives 60 miles on local roads at 30 mph , and 65 miles on the highway at 65 mph , what is the average speed of the entire trip ? Let's write a program. | tiger_lab_math |
In a Traveler's Dilemma game between two players, Player A claims that the price of an item lost during traveling is $400 while Player B claims it is $500. Both players are told that if their claims are within $50 of the actual price, they will be reimbursed with their claimed amount; otherwise, they will receive only ... | tiger_lab_math |
a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is ? Please respond by writing a program in Python. | tiger_lab_math |
If $a,b,c>0$, find the smallest possible value of
\[\left\lfloor{\frac{a+b}{c}}\right\rfloor+\left\lfloor{\frac{b+c}{a}}\right\rfloor+\left\lfloor{\frac{c+a}{b}}\right\rfloor.\](Note that $\lfloor{x}\rfloor$ denotes the greatest integer less than or equal to $x$.) | tiger_lab_math |
a 1000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ? Let's write a prog... | tiger_lab_math |
the probability that a number selected at random from the first 50 natural numbers is a composite number is - . Please write a program to solve it | tiger_lab_math |
a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 14 white mice in the experiment , how many brown mice are in the experiment ? Let's write a Python program to solve it. | tiger_lab_math |
in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 60 per square m ? Please respond by writing a program in Python. | tiger_lab_math |
An ellipse has its foci at $(-1, -1)$ and $(-1, -3).$ Given that it passes through the point $(4, -2),$ its equation can be written in the form \[\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\]where $a, b, h, k$ are constants, and $a$ and $b$ are positive. Find $a+k.$ | tiger_lab_math |
Ms. Hatcher teaches 20 third-graders and a number of fourth-graders that is twice the number of third-graders. Her co-teacher asked her to substitute for her fifth-grade class that has half as many students as the number of third-graders. How many students did Ms. Hatcher teach for the day? | tiger_lab_math |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.