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for each color copy , print shop x charges $ 1.20 and print shop y charges $ 1.70 . how much greater is the charge for 40 color copies at print shop y than at print shop x ? Let's write a program. | tiger_lab_math |
in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 49 as quotient . what is the correct quotient ? Let's write a program. | tiger_lab_math |
Let $A$ equal the number of four digit odd numbers. Let $B$ equal the number of four digit multiples of 5. Find $A+B$. | tiger_lab_math |
Consider a Morse-Smale complex with 7 critical points, where 4 critical points are minima and 3 critical points are saddles. Let the indices of the minima be 0,1,2,3 and the indices of the saddles be 4,5,6. Suppose the attaching matrix of the Morse-Smale complex is given by:
$\begin{pmatrix}
1 & 0 & 0 & 0 & 0 & 0 & 0\... | tiger_lab_math |
set # 1 = { a , b } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ? Let's write a Python program. | tiger_lab_math |
A particle in a one-dimensional potential well has a potential function given by:
V(x) = {4, 0 < x < 1; 0, x ≥ 1}
If the particle is in the ground state with energy E1, find the probability that the particle is found in the right half of the well (1 ≤ x ≤ 2). | tiger_lab_math |
income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 19000 , then find his savings ? Let's write a program. | tiger_lab_math |
Let S be a set with 3 elements. Compute the number of elements in the power set of S and prove that this number is always greater than the number of elements in S itself. | tiger_lab_math |
There are 7.75 gallons of water in Becky 's fish tank. If Becky adds 7 gallons more , In all , there will be _____ gallons . Let's write a Python program to solve it. | tiger_lab_math |
jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 36 / 49 , what... | tiger_lab_math |
A point $(x,y)$ is a distance of 12 units from the $x$-axis. It is a distance of 10 units from the point $(1,6)$. It is a distance $n$ from the origin. Given that $x>1$, what is $n$? | tiger_lab_math |
a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 56 marks . the maximum marks are ? Let's write a program. | tiger_lab_math |
paul completes a piece of work in 80 days , rose completes the same work in 120 days . if both of them work together , then the number of days required to complete the work is ? Let's write a program. | tiger_lab_math |
A triangle has a base of 12 cm and two other sides that measure 9 cm and 15 cm. Find the perimeter of the triangle, using trigonometry. | tiger_lab_math |
if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 12 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ? Let's write a Python program to solve it. | tiger_lab_math |
Each of 435 bags contains at least one of the following three items: coconut, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only coconut and peanuts. Th... | 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.) Please write a program to solve it | tiger_lab_math |
In a national park, the number of redwoods is 20% more than the number of pines. If there are 600 pines in the national park, calculate the total number of pines and redwoods that are there. | tiger_lab_math |
a grocer is storing soap boxes in cartons that measure 30 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ? Please respond by writing a program in Python. | tiger_lab_math |
Given that $\mathbf{a}$ and $\mathbf{b}$ are nonzero vectors such that $\|\mathbf{a} + \mathbf{b}\| = \|\mathbf{a} - \mathbf{b}\|,$ find the angle between $\mathbf{a}$ and $\mathbf{b},$ in degrees. | tiger_lab_math |
A group of people contains men, women, and children. The number of men is twice the number of women, and the number of women is 3 times the number of children. If the number of children is 30, how many people does this group contain? | tiger_lab_math |
A wooden beam of length 10 meters is fixed at both ends. The beam is initially at rest, but suddenly a force of 100 N is applied to the midpoint of the beam. Using the Fourier transform, determine the displacement of the beam at any time t, assuming that the beam has a uniform cross-sectional area and is made of a mate... | tiger_lab_math |
Let A be a set such that A = {1, 2, 3, 4, 5, 6} and let U be the universal set such that U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Using set theory, prove that the intersection of set A and its complement is the empty set. | tiger_lab_math |
If x < y < 0, which of the following must be true?
Answer Choices: (A) x+y is a positive integer (B) x+y is a negative integer (C) xy is a negative integer (D) x/y is a negative integer (E) 2x/y is a negative integer | tiger_lab_math |
The product of the digits of 3214 is 24. How many distinct four-digit positive integers are such that the product of their digits equals 12? Please respond by writing a program in Python. | tiger_lab_math |
the area of a rectangle is 63 sq m . the width is two meters shorter than the length . what is the width ? Please write a program to solve it | tiger_lab_math |
A cylindrical tank with a radius of 5 feet is filled with water to a height of 12 feet. The water is then drained through a hole in the bottom of the tank with a radius of 0.5 feet. The velocity of the water leaving the hole is 8 feet per second. Use Navier-Stokes equations to determine the rate at which the water leve... | tiger_lab_math |
What percent of the positive integers less than or equal to $100$ have no remainders when divided by $5?$ | tiger_lab_math |
the l . c . m . of two numbers is 42 . the numbers are in the ratio 2 : 3 . then sum of the number is : ? Let's write a program. | tiger_lab_math |
there are two cars . one is 300 miles north of the other . simultaneously , the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 60 miles per hour . how many miles apart are the cars after 5 hours ? Let's write a program. | tiger_lab_math |
a , b and c can do a piece of work in 30 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ? Let's write a program. | tiger_lab_math |
the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 130 visitors who did not enjoy the painting also d... | tiger_lab_math |
a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 18 , what is the total amount ? Please respond by writing a program in Python. | tiger_lab_math |
For a polynomial $p(x),$ define its munificence as the maximum value of $|p(x)|$ on the interval $-1 \le x \le 1.$ For example, the munificence of the polynomial $p(x) = -x^2 + 3x - 17$ is 21, since the maximum value of $|-x^2 + 3x - 17|$ for $-1 \le x \le 1$ is 21, occurring at $x = -1.$
Find the smallest possible m... | tiger_lab_math |
a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat ( in still water ) and the stream is : ? Let's write a program. | tiger_lab_math |
in the coordinate plane , points ( x , 1 ) and ( 5 , y ) are on line k . if line k passes through the origin and has slope 1 / 5 , then what are the values of x and y respectively ? Please write a program to solve it | tiger_lab_math |
Consider the manifold given by the equation f(x,y,z) = x^2 + y^2 + z^2 = 5, determine the symmetries of the manifold. Specifically, find the number and nature of isometries of the manifold. | tiger_lab_math |
the compound interest on $ 2000 at 10 % per annum is $ 662 . the period ( in years ) is ? Let's write a Python program. | tiger_lab_math |
the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area t of that hemisphere ? Let's program in Python in the response. | tiger_lab_math |
Let X be a topological space and let Y be a connected space. Prove that if there exist continuous functions f: X to Y and g: X to Y such that f(x) ≠ g(x) for all x in X, then X is also connected.
Furthermore, prove that if X is a path-connected space and there exists a continuous function f: X to Y, then f(X) is also... | tiger_lab_math |
A billiard ball of radius 5 cm is placed on a billiard table with length 3 meters and width 2 meters. The ball is struck in a straight line at an angle of 45 degrees to one of the parallel sides of the table. Assume that the ball follows the law of reflection and that it experiences no friction. What is the length of t... | tiger_lab_math |
Marla has a grid of squares that has 10 rows and 15 squares in each row. She colors 4 rows of 6 squares in the middle of the grid with red. She colors all squares on the first 2 and last 2 rows with blue. Then she colors the rest with green. How many squares does Marla color green? | tiger_lab_math |
before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ? Let's write a Python program ... | tiger_lab_math |
Let R be a noncommutative ring with identity such that R has exactly six two-sided ideals. Find the maximum possible number of idempotent elements in R. | tiger_lab_math |
Consider a beauty contest game where there are three players and each player needs to select a number between 0 and 100. The winner of the game is the player whose number is closest to two-thirds of the average of all three numbers. If all players are rational and understand the rules of the game, what number(s) should... | tiger_lab_math |
A cylindrical container with a radius of 10 cm is filled with water up to a height of 15 cm. The container is then tilted in such a way that the water spills out without leaking from the bottom. What is the maximum distance (in cm) that the water will travel from the container? (Assume the container is tilted at an ang... | tiger_lab_math |
Let A = {1, 2} and B = {3, 4} be two sets. Find the sets (A x B) △ B and A x (B △ A), where △ represents the symmetric difference operator. Show that (A x B) △ B is not equal to A x (B △ A), thereby proving that the Cartesian product of two sets is not associative with respect to symmetric difference. | tiger_lab_math |
The sum of two positive integers multiplied by the larger number is 204. The difference multiplied by the smaller number is 35. The larger number is
Answer Choices: (A) 8 (B) 9 (C) 10 (D) 11 (E) 12 | tiger_lab_math |
the list price of an article is rs . 70 . a customer pays rs . 59.85 for it . he was given two successive discounts , one of them being 10 % . the other discount is ? Let's write a program. | tiger_lab_math |
the average salary per head of the entire staff of an office including the officers and clerks is rs . 90 . the average salary of officers is rs . 600 and that of the clerks is rs . 84 . if the number of officers is 2 , find the number of officers in the office ? Let's program in Python in the response. | tiger_lab_math |
Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. six years from today, the difference between the ag... | tiger_lab_math |
julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 126 from the simple interest account and the compound interest account respectively . if the interest rates for both account... | tiger_lab_math |
Consider a graph G with 6 vertices and the following edges:
{(1,2), (1,3), (1,6), (2,4), (2,6), (3,5), (3,6), (4,5), (4,6), (5,6)}.
Find all the possible Hamiltonian cycles in the graph. | tiger_lab_math |
a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9 . in all papers together , the candidate obtained 60 % of the total marks . then the number of papers in which he got more than 50 % marks is ? Let's prog... | tiger_lab_math |
Find the Fourier series expansion of the piecewise-defined function
$f(x) =
\begin{cases}
x^2 & \text{if } -\pi \leq x < 0\\
\sin(x) & \text{if } 0 \leq x \leq \pi
\end{cases}
$
and use it to solve the boundary value problem:
$$
\frac{d^2y}{dx^2} + y = f(x), \quad y(-\pi) = y(\pi), \quad \frac{dy}{dx}(-\pi) = \frac... | tiger_lab_math |
A square has an area of $25.$ A rectangle has the same width as the square. The length of the rectangle is double its width. What is the area of the rectangle? Let's write a program. | tiger_lab_math |
mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture . Let's write a program. | tiger_lab_math |
Given that $\sum_{k=1}^{35}\sin 5k=\tan \frac mn,$ where angles are measured in degrees, and $m$ and $n$ are relatively prime positive integers that satisfy $\frac mn<90,$ find $m+n.$
| tiger_lab_math |
Five hundred people attended the band concert. For that concert, the band gets 70% of the ticket price. If each ticket costs $30 and there are 4 members of the band, how much did each band member get from that concert? | tiger_lab_math |
A palindrome is an integer that reads the same forward and backward, such as 3663. What percent of the palindromes between 100 and 500 contain at least one 5? | tiger_lab_math |
in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 1 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ? Let's write a program. | tiger_lab_math |
A particle of mass 0.5 kg is moving in one dimension with a potential energy function of V(x) = 2x^2 J/m. If the wave function of the particle is given by
Ψ(x) = Ae^(-ax^2)
where A and a are constants, find the value of A and a such that the wave function is normalized. | tiger_lab_math |
a sum of money deposited at c . i . amounts to rs . 3650 in 2 years and to rs . 4015 in 3 years . find the rate percent ? Please respond by writing a program in Python. | tiger_lab_math |
a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 6 gallons of water and 12 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ? Let's write a Python program. | tiger_lab_math |
Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Two years from today, the difference between the ag... | tiger_lab_math |
What is the Hausdorff dimension of the Koch curve, constructed by starting with an equilateral triangle of side length 1, dividing each side into three equal parts and replacing the middle section with two sides forming an equilateral triangle of length 1/3, and iterating the process infinitely many times? | tiger_lab_math |
A long, cylindrical pipe has a radius of 5 cm and a length of 10 m. If the electric potential at the surface of the pipe is 1000 V and the electric potential at the center of the pipe is 0 V, what is the electric potential at a distance of 2 cm from the center of the pipe? Assume that the pipe is made of a homogeneous ... | tiger_lab_math |
A math student is asked to find the residues of the function f(z) = (z^2-2)/(z^2-1)^2 at each of its singularities and evaluate the integral of the function around a closed contour that encloses the singularities.
Let the contour C be the unit circle centered at the origin. What is the value of the integral, with pos... | tiger_lab_math |
in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 1000 m ? Let's write a program. | tiger_lab_math |
Consider the reaction-diffusion equation:
$\frac{\partial u}{\partial t}=D\frac{\partial^2 u}{\partial x^2}+f(u)$
where $u(x,t)$ represents the concentration of a chemical at location $x$ and time $t$, $D$ is the diffusion coefficient, and $f(u)$ is a function that describes the chemical reaction.
Assume $D=1$, $f... | tiger_lab_math |
The hexagon with the R is colored red. Each hexagon is colored either red, yellow or green, such that no two hexagons with a common side are colored the same color. In how many different ways can the figure be colored?
[asy]
path a=(0,0)--(10,0)--(15,8.7)--(10,17.3)--(0,17.3)--(-5,8.7)--cycle;
draw(a);
draw(shift(... | tiger_lab_math |
What is the area of the black region in the Mandelbrot set bounded by the circle with center at (-0.75, 0) and radius 0.25? | tiger_lab_math |
The country of Belize had a 5 lane bridge that had 2000 vehicles passing through it every month. They decided to build a new bridge that had twice the capacity of the old one, and the number of vehicles passing through the new one increased by 60% more than the old bridge. If the bridges work concurrently for a year, c... | tiger_lab_math |
Suppose you intercepted the following ciphertext that was encrypted using Playfair cipher: "HLBBLJBCYAOM". Assuming that the plaintext is a single word consisting of only lowercase English alphabet letters, can you determine the original message? | tiger_lab_math |
A wire carrying a current of 3 A is bent into a circular loop with a radius of 0.2 meters. Find the magnetic flux density at the center of the loop if the four Maxwell's equations are satisfied. Use the equation B = μ₀I/2r for a current-carrying circular loop. | tiger_lab_math |
a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 27000 . a ' s share is ? Let's program in Python in the response. | tiger_lab_math |
a rectangular tiled patio is composed of 96 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 96 tiles , and it will still be rectangular . how many rows are in the tile patio before th... | tiger_lab_math |
Let $M$ be a smooth connected manifold of dimension $n=3$ and suppose that the cohomology group $H^2(M,\mathbb{R})$ is nontrivial. Let $\omega$ be a closed 2-form on $M$. Show that there exists a nontrivial closed 1-form $\alpha$ on $M$ such that $\omega \wedge \alpha$ is a nontrivial element of $H^3(M,\mathbb{R})$. | tiger_lab_math |
the average of 7 consecutive numbers a , b , c , d , e , f and g is 9 . what percent of g is a ? Let's write a Python program. | tiger_lab_math |
a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ? Let's write a Python program. | tiger_lab_math |
"statement 1": Arun obtained 76 , 65 , 82 , 67 and 85 marks ( out in 100 ) in English , Mathematics , Chemistry , Biology and Physics, "statement 2" :Arun obtained more than 56 , 65 , 82 , 67 and 85 marks ( out in 100 ) in English , Mathematics , Chemistry , Biology and Physics, "options: " Entailment or contradiction... | tiger_lab_math |
in august , a cricket team that played 120 matches won 28 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ? Let's write a Python program to solve it. | tiger_lab_math |
two isosceles triangles have equal vertical angles and their areas are in the ratio 4 : 9 . find the ratio of their corresponding heights . Let's program in Python in the response. | tiger_lab_math |
a hen leaps 3 leaps for every 2 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ? Let's write a program. | tiger_lab_math |
Find all $a,$ $0^\circ < a < 360^\circ,$ such that $\cos a,$ $\cos 2a,$ and $\cos 3a$ form an arithmetic sequence, in that order. Enter the solutions, separated by commas, in degrees. | tiger_lab_math |
the length of rectangle is thrice its breadth and its perimeter is 112 m , find the area of the rectangle ? Let's program in Python in the response. | tiger_lab_math |
What is the Hausdorff dimension of the Lévy C curve, which is created by iteratively replacing each straight line segment with two segments of length a and b, respectively, where a and b satisfy the equation |a| + |b| = 1? | tiger_lab_math |
A message of 35 characters is being digitally signed using the RSA algorithm. The public key has a modulus of 209 and a public exponent of 5. If the hash of the message is 17, what should be the value of the private key exponent so that the digital signature of the message is valid? | tiger_lab_math |
Here's a complex analysis question for a math student to solve:
Suppose that f(x) is a continuous function for all real numbers x, which is also periodic with period 2π. Define the Fourier transform F(k) of f(x) as:
F(k) = ∫2π0 f(x) e^(-ikx) dx,
where i = √-1 is the imaginary unit. Show that F(k) is a continuous fun... | tiger_lab_math |
Let \[f(x) = \left\{
\begin{array}{cl}
-x - 3 & \text{if } x \le 1, \\
\frac{x}{2} + 1 & \text{if } x > 1.
\end{array}
\right.\]Find the sum of all values of $x$ such that $f(x) = 0$. | tiger_lab_math |
a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 50 paise per sq . metre ? Please write a program to solve it | tiger_lab_math |
Mary is making a model sailboat. She wants to add three sails: a rectangular sail that measures 5 inches by 8 inches and two right triangular sails, one that's 3 inches long at the bottom and 4 inches tall and one that's 4 inches long at the bottom and 6 inches tall. (Remember you can find the area of a triangle by div... | tiger_lab_math |
Ten identical crates each of dimensions $3\mathrm{ft}\times 4\mathrm{ft}\times 6\mathrm{ft}$. The first crate is placed flat on the floor. Each of the remaining nine crates is placed, in turn, flat on top of the previous crate, and the orientation of each crate is chosen at random. Let $\frac {m}{n}$ be the probability... | tiger_lab_math |
Let $S$ be a smooth, closed surface in $\mathbb{R}^3$ with a Hamiltonian flow $X$. Suppose that the De Rham cohomology group $H^1_{DR}(S)$ is isomorphic to $\mathbb{R}^3$ and that the flow $X$ has three periodic orbits with periods $1$, $2$, and $3$.
What is the sum of the indices of the three periodic orbits of $X$ ... | tiger_lab_math |
Find the number of distinct functions that can be defined using second-order logic with two variables and a domain of 3 elements. | tiger_lab_math |
A polynomial with integer coefficients is of the form
\[9x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 15 = 0.\]Find the number of different possible rational roots of this polynomial. | tiger_lab_math |
Let A = {1, 2, 3} and B = {2, 3, 4}. Find (A x B) ∩ (B x A) , where "x" represents the Cartesian product of two sets. Show that this proves the Cartesian product of two sets is not commutative with respect to intersection. | tiger_lab_math |
the “ s - number ” of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ s , where s is the s - number of the result of his die roll , and plots 3 ^ s on a number line ... | tiger_lab_math |
What is the smallest positive integer $n$ such that $5^n\equiv 1\pmod{13}$? | tiger_lab_math |
The expression $y^2+10y+33$ can be written as a combination of a square of a binomial and an integer. Find the integer. | tiger_lab_math |
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