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when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 4 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ? Let's... | tiger_lab_math |
Consider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures $3$ by $4$ by $5$ units. Given that the volume of this set is $\frac{m + n\pi}{p},$ where $m, n,$ and $p$ are positive integers, and $n$ and $p$ are relatively prime, find $m + n + p.$
| tiger_lab_math |
the ratio of the incomes of uma and bala is 8 : 7 and the ratio of their expenditure is 7 : 6 . if at the end of the year , each saves $ 2000 then the income of uma is ? Let's program in Python in the response. | tiger_lab_math |
a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 2 of the mixture is water , and the remaining 8 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ? Let's program in Python in the response. | tiger_lab_math |
In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle? | tiger_lab_math |
Triangle $ABC$ is a right triangle with $AC = 7,$ $BC = 24,$ and right angle at $C.$ Point $M$ is the midpoint of $AB,$ and $D$ is on the same side of line $AB$ as $C$ so that $AD = BD = 15.$ Given that the area of triangle $CDM$ may be expressed as $\frac {m\sqrt {n}}{p},$ where $m,$ $n,$ and $p$ are positive integers... | tiger_lab_math |
a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 4 of th area of the garden . what is the radius of the circular garden ? Let's write a program. | tiger_lab_math |
Which of the following numbers is the biggest => [-2/7 , -7/8 , -9/10 , -12/13 , -34/35]
Answer Choices: (A) A) -2/7 (B) B) -7/8 (C) C) -9/10 (D) D) -12/13 (E) E) -34/35 | tiger_lab_math |
a heap of grapes is divided into groups of 3 , 5 and 7 and each time one coconut is left over . the least number of grapes in the heap is ? a . 31 b . 41 c . 51 d . 61 ? Let's program in Python in the response. | tiger_lab_math |
A string of length 10 meters is fixed at both ends. The wave velocity on the string is 20 m/s and the initial shape of the string is given by the equation y(x,0) = 0.5cos(πx/5). Find the wave equation, y(x,t), that describes the displacement of the string at any time t > 0. | tiger_lab_math |
For positive integer n, if the value of Euler's totient function at n is 32 and n has exactly 3 distinct prime factors, what is the value of n? | tiger_lab_math |
in a certain game of dice , the player ’ s score is determined as a sum of two throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 21 other players ,... | tiger_lab_math |
in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds e in the nature reserve are not hawks , paddyfield - warblers , or k... | tiger_lab_math |
if the simple interest on a certain sum of money for 4 years is one – fifth of the sum , then the rate of interest per annum is ? Let's write a Python program. | tiger_lab_math |
A triangle has a leg of length 5 and a hypotenuse of length 13. Find the length of the other leg using trigonometry. | tiger_lab_math |
For how many non-negative real values of $x$ is $\sqrt{144-\sqrt[3]{x}}$ an integer? | tiger_lab_math |
joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 6 of the remaining paint . how many gallons of paint has joe used ? Let's write a Python program to solve it. | tiger_lab_math |
What is the smallest positive integer $n$ such that $2n$ is a perfect square and $3n$ is a perfect cube? | tiger_lab_math |
A circle with a radius of 2 cm is moving along a straight line that is tangent to its center, and its speed is 3 cm/s. What is the rate at which the angle between the radius vector and the tangent is changing when the circle has rolled 4 cm along the line? | tiger_lab_math |
The hypotenuse of an isosceles right triangle is $4\sqrt{2}$ units. How many square units are in the area of the triangle? | tiger_lab_math |
Determine whether the group G with the following multiplication table is isomorphic to either the cyclic group C16, the dihedral group D8, or the non-abelian group of order 16:
\begin{array}{c|cccccccc}
& e & a & b & c & d & e_1 & f & g \\ \hline
e & e & a & b & c & d & e_1 & f & g \\
a & a & e & c & b & f ... | tiger_lab_math |
every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 54 , how many more green disks than blue disks are in the bag ? Let's write a program. | tiger_lab_math |
if the sum and difference of two numbers are 20 and 10 respectively , then the difference of their square is : ? Let's write a program. | tiger_lab_math |
The following is a problem for the math student to solve, based on Inductive Logic:
A math teacher noticed that the first five students who entered the classroom each had a backpack on. Based on this observation, the teacher made the hypothesis that all students in the class would have backpacks on. Later, when the en... | tiger_lab_math |
on a trip covering 400 km , a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour . what is the average speed , in km per hour , for the entire trip ? Let's program in Python in the response. | tiger_lab_math |
"statement 1": Dacid obtained 96 , 95 , 82 , 87 and 92 marks ( out of 100 ) in English , Mathematics , Physics , Chemistry and Biology, "statement 2" :Dacid obtained less than 96 , 95 , 82 , 87 and 92 marks ( out of 100 ) in English , Mathematics , Physics , Chemistry and Biology, "options: " Entailment or contradicti... | tiger_lab_math |
a drink vendor has 10 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ? Let's program in Python in the response... | tiger_lab_math |
in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation .... | tiger_lab_math |
What is the least positive integer with exactly five distinct positive factors? | tiger_lab_math |
in a certain pond , 50 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 ` s the approximate number of fish in the ... | tiger_lab_math |
On a highway, the total number of vehicles passing is 300. If the number of cars on the highway is twice the number of trucks, find out the total number of trucks on the highway? | tiger_lab_math |
Let $f(z) = \frac{z+2}{z-1}$ be an analytic function defined on the upper half-plane $\mathbb{H} = \{ z \in \mathbb{C} : \operatorname{Im}(z) > 0 \}$.
(a) Using the Schwarz reflection principle, find an explicit expression for $f(z)$ in the lower half-plane $\mathbb{H}' = \{ z \in \mathbb{C} : \operatorname{Im}(z) < ... | tiger_lab_math |
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Answer Choices: (A) 22 (B) 73 (C) 99 (D) 42 (E) 11 | tiger_lab_math |
Let $n$ represent the smallest integer that satisfies the following conditions:
$\frac n2$ is a perfect square.
$\frac n3$ is a perfect cube.
$\frac n5$ is a perfect fifth.
How many divisors does $n$ have that are not multiples of 10?
| tiger_lab_math |
It takes exactly 74 colored beads on a string to make a necklace. The beads are strung in the following order: one red, one orange, two yellow, one green, and one blue. Then the pattern repeats starting again with one red bead. If the first bead of the necklace is red, what is the color of the last bead used to make th... | tiger_lab_math |
p , q and r together earn rs . 1800 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ? Let's write a program. | tiger_lab_math |
if i equals the sum of the even integers from 2 to 224 , inclusive , and k equals the sum of the even integers from 8 to 80 , inclusive , what is the value of i - k ? Please write a program to solve it | tiger_lab_math |
The school band is going to a competition. Five members play the flute. There are three times as many members who play the trumpet. There are eight fewer trombone players than trumpeters, and eleven more drummers than trombone players. There are twice as many members that play the clarinet as members that play the flut... | tiger_lab_math |
How many ways are there to arrange the letters of the word "COMBINATORICS" such that the vowels and consonants appear in alternate positions? | tiger_lab_math |
Let E be an elliptic curve over the field of complex numbers. Show that there are at most finitely many non-trivial torsion points in E. | tiger_lab_math |
Sure, here's a precise numerical problem:
Let f(z) be an entire function that satisfies the inequality |f(z)| ≤ 5|z|² for all z in the complex plane. Prove that f(z) is a polynomial of degree at most 2. | tiger_lab_math |
a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 17000 left with him . find salary . . Let's write a program. | tiger_lab_math |
Consider the surface given by the equation z = x^2 - 2y^2. Determine the values of the principal curvatures at the point (1,-1,1). | tiger_lab_math |
reema took a loan of rs 800 with simple interest for as many years as the rate of interest . if she paid rs . 632 as interest at the end of the loan period , what was the rate of interest . Let's write a program. | tiger_lab_math |
In a colony of 50 residents, the ratio of the number of men and women is 3:2. Among the women, the ratio of the educated to the uneducated is 1:3. If the ratio of the number of education to uneducated persons is 4:6, then find the ratio of the number of educated and uneducated men in the colony?
Answer Choices: (A) 1:1... | tiger_lab_math |
a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 25 miles per gallon , and from town b to town c , the car averaged 30 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through ... | tiger_lab_math |
What is the smallest positive integer $x$ such that $2^x \equiv 17 \pmod{67}$? | tiger_lab_math |
Here's a precise numerical problem on Wilson's theorem for you to solve:
Find the smallest positive integer value of n such that (n-1)! + 1 is divisible by n, where n is a prime number. | tiger_lab_math |
"statement 1": Jill , who lives in City C , plans to visit 5 different cities , M , L , S , N , and O, "statement 2" :Jill , who lives in City C , plans to visit more than 5 different cities , M , L , S , N , and O, "options: " Entailment or contradiction or neutral? Let's write a Python program to solve it. | tiger_lab_math |
Find the maximum value of
\[\sin \frac{\theta}{2} \cdot (1 + \cos \theta)\]for $0 < \theta < \pi.$ | tiger_lab_math |
Consider a group of order 12. Prove that it is isomorphic to one of the following groups: C12, A4, or D6. Show all the steps of the proof and determine which group the given group is isomorphic to. | tiger_lab_math |
two trains are approaching each other at 60 mph each . the length of each train is 1 / 6 miles . when the two locomotives ( engines ) meet , how many seconds will it take for them to pass each other completely ? Let's program in Python in the response. | tiger_lab_math |
There are 10 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?
Answer Choices: (A) 7/17 (B) 5/12 (C) 4/11 (D) 3/10 (E) 2/9 | tiger_lab_math |
a man can row upstream at 32 kmph and downstream at 48 kmph , and then find the speed of the man in still water ? Let's program in Python in the response. | tiger_lab_math |
In a race where 18 cars are running, the chance that car X will win is 1/8, that Y will win is 1/12 and that Z will win is 1/6. Assuming that a dead heat is impossible, find the chance that one of them will win.
Answer Choices: (A) 1/140 (B) 1/180 (C) 3/12 (D) 3/8 (E) 57/120 | tiger_lab_math |
a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 64 , find the sum of money ? Let's program in Python in the response. | tiger_lab_math |
There are 360 balls in the ball pit. If a quarter of the balls in the ball pit are red and a fifth of the remaining balls are blue. How many of the balls are neither red nor blue? | tiger_lab_math |
a , b , c hired a car for rs . 520 and used it for 7 , 8 and 11 hours respectively . hire charges paid by b were ? Let's write a Python program to solve it. | tiger_lab_math |
Let X be a topological space and A, B be two disjoint closed subsets of X. If X is normal, prove that there exist two open subsets U and V of X such that A ⊆ U, B ⊆ V, and U ∩ V = ∅.
As an example, let X be the closed interval [0, 1], A = [0, 1/3] and B = [2/3, 1]. Prove that there exist two open subsets U and V of X... | tiger_lab_math |
rahim bought 4 pillows with the average cost of $ 5 . if rahim also buys the fifth pillow with the price of $ 10 , what is the average ( arithmetic mean ) price of those 5 pillows ? Let's program in Python in the response. | tiger_lab_math |
Consider a graph with 9 vertices and 14 edges. Determine the minimum number of edges that need to be removed to disconnect the graph. | tiger_lab_math |
What is the Hausdorff dimension of the Sierpinski triangle?
Solution: The Sierpinski triangle is a geometric fractal that can be created by subdividing a triangle into smaller triangles and removing the center triangle repeatedly. The Hausdorff dimension of the Sierpinski triangle is given by the formula:
D = log(3) ... | tiger_lab_math |
what least number should be added to 1056 , so that the sum is completely divisible by 23 ? Let's write a Python program to solve it. | tiger_lab_math |
Let A = {1, 2, 3} and B = {2, 3, 4}. Prove that the intersection of set A and set B is a subset of both sets A and B. | tiger_lab_math |
a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 10.50 less , he would have gained 30 % . find the cost of the article . Let's write a program. | tiger_lab_math |
In a certain lottery drawing, two balls are selected at random from a container with 50 balls, numbered from 1 to 50, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cas... | tiger_lab_math |
on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor ? Please write a program to solve it | tiger_lab_math |
a certain manufacturer increased its gross profit on a product from 10 percent of the cost of the product to 15 percent of the cost by changing the selling price . if the new selling price was $ 92.00 and the cost of the product remained the same , what was the old selling price ? Let's write a Python program. | tiger_lab_math |
Suppose that you have two bags of marbles, bag A and bag B. Bag A has 6 blue marbles and 4 red marbles, while bag B has 3 blue marbles and 7 red marbles. You draw a marble from one of the bags at random, and it turns out to be blue. What is the probability that the marble came from bag A, given that it is blue? | tiger_lab_math |
Suppose $f(z)$ is an entire function such that $|f(z)|\leq e^{\pi|z|}$ for all $z\in\mathbb{C}$. Compute the value of the integral $\int_{-\infty}^{\infty}\frac{f(x)}{x^2+1}dx$. | tiger_lab_math |
a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 19000 left with him . find salary . . Let's write a Python program. | tiger_lab_math |
a certain hospital has a policy that for every 50 patients there should be 2 doctors . if the number of patients visiting the hospital every day is 400 , how many doctors are there in the hospital ? Let's write a Python program. | tiger_lab_math |
a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 250 more than a : ? Let's write a Python program to solve it. | tiger_lab_math |
the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ? Let's write a Python program. | tiger_lab_math |
there are 15 slate rocks , 20 pumice rocks , and 10 granite rocks randomly distributed in a certain field . if 2 rocks are to be chosen at random and without replacement , what is the probability that both rocks will be slate rocks ? Let's write a Python program. | tiger_lab_math |
in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is theprobability that the extracted ball would turn onto be white , if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ? Please write a program to solve it | tiger_lab_math |
The product $N$ of three positive integers is $6$ times their sum, and one of the integers is the sum of the other two. Find the sum of all possible values of $N$.
| tiger_lab_math |
What is the smallest positive integer that satisfies Wilson's theorem? | tiger_lab_math |
a ’ s speed is 25 / 18 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ? Let's program in Python in the response. | tiger_lab_math |
Point $A$ has coordinates $(x,6)$. When Point $A$ is reflected over the $y$-axis it lands on Point $B$. What is the sum of the four coordinate values of points $A$ and $B$? | tiger_lab_math |
jennifer had $ 180 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ? Let's program in Python in the response. | tiger_lab_math |
Brad’s zip code consists of five numbers that add up to 10. The first and second numbers are the same. The third number is zero. The fourth number is double the first number. The fourth and fifth numbers add up to 8. What is Brad’s zip code? | tiger_lab_math |
A triangle has two sides that are equal in length. The length of one of these sides is 5 cm. The angle between these sides is 60 degrees. What is the length of the third side, in centimeters? | tiger_lab_math |
Consider the first-order language L = {0, 1, +, ×}, where 0 is a constant symbol for the additive identity, 1 is a constant symbol for the multiplicative identity, and + and × are binary function symbols for addition and multiplication, respectively. Let T be the set of all sentences in the language L that are true in ... | tiger_lab_math |
Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of... | tiger_lab_math |
Find all prime numbers between 50 and 70, inclusive. | tiger_lab_math |
Consider the system of nonlinear equations:
$$
\begin{cases}
x^2 + y^2 - 9 = 0 \\
\ln(x+1) + e^y - 6 =0
\end{cases}
$$
Using Newton's method, find an approximation of the solution $(x,y)$ such that $|x-x_0|<0.001$ and $|y-y_0|<0.001$, where $(x_0,y_0)=(1,1)$ is the initial guess. | tiger_lab_math |
tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next 5 weeks be to increase his average weekly income t... | tiger_lab_math |
A drawer in a darkened room contains $100$ red socks, $80$ green socks, $60$ blue socks and $40$ black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to guarantee that the selection contains at ... | tiger_lab_math |
the product of two successive numbers is 2652 . which is the smaller of the two numbers ? Please respond by writing a program in Python. | tiger_lab_math |
geetha ' s home has one tap , working alone at its maximum constant rate , can fill a certain sink in 210 seconds . a second tap , working alone at its maximum constant rate , can fill the same sink in 214 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill th... | tiger_lab_math |
A heated rod is modeled as the line segment $L$ from $z=0$ to $z=1+i$ in the complex plane. The ends of the rod are kept at a constant temperature of $0$ degrees and $100$ degrees, respectively. The temperature $u(z,t)$ at position $z$ and time $t$ is given by the solution to the heat equation:
$$u_t(z,t) = u_{zz}(z,... | tiger_lab_math |
the parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ? Please respond by writing a program in Python. | tiger_lab_math |
a bank pays interest to its customers on the last day of the year . the interest paid to a customer is calculated as 10 % of the average monthly balance maintained by the customer . john is a customer at the bank . on the last day , when the interest was accumulated into his account , his bank balance doubled to $ 5080... | tiger_lab_math |
A 'fishbowl' of height 4r/3 is formed by removing the top third of a sphere of radius r=6. The fishbowl is fixed in sand so that its rim is parallel with the ground. A small marble of mass m rests at the bottom of the fishbowl. Assuming all surfaces are frictionless and ignoring air resistance, find the maximum initial... | tiger_lab_math |
two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is : ? Let's write a program. | tiger_lab_math |
a small beaker is 1 / 2 filled with salt water . another beaker , which has 5 times the capacity of the small beaker , is 1 / 5 filled with fresh water . after dumping all of the salt water from the small beaker into the large beaker , to what fraction of its capacity will the large beaker be filled ? Let's write a pro... | tiger_lab_math |
a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , two - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to th... | tiger_lab_math |
in a 100 m race , sam beats john by 3 seconds . on the contrary , if sam allowed john to start 24 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ? Let's program in Python in the response. | tiger_lab_math |
Hartley has 4 puppies that each weigh 7.5 kilograms. The rescue center has 14 cats that each weigh 2.5 kilograms. How many kilograms more do the cats weigh than the puppies? | tiger_lab_math |
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