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Raj's house has an area equal to 1,110 square feet. It has 4 bedrooms that each measure 11 x 11 feet. There are 2 bathrooms that are 6 x 8 feet each. The kitchen and living area complete the home and they have the same sized area. How many square feet is the area of the kitchen? | tiger_lab_math |
Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base. The areas of the cross sections are $216\sqrt{3}$ square feet and $486\sqrt{3}$ square feet. The two planes are $8$ feet apart. How far from the apex of the pyramid is the larger cross section... | tiger_lab_math |
david obtained 96 , 95 , 82 , 97 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ? Please write a program to solve it | tiger_lab_math |
the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1400 per sq . metre . Let's write a Python program. | tiger_lab_math |
a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ? Please write a program to solve it | tiger_lab_math |
In the engineering department, 70% of the students are men and 180 are women. How many men are there? | tiger_lab_math |
a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 38 now , the son age 5 years back was : ? Let's write a program. | tiger_lab_math |
set # 1 = { a , b , o , d , e } set # 2 = { k , l , m , n , u , 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 to solve it. | tiger_lab_math |
"statement 1": An investor can sell her MicroTron stock for less than 76 $ per share and her Dynaco stock for 48 $ per share , If she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of Dynaco stock has she sold ?, "statement 2" :An investor can sell her MicroT... | tiger_lab_math |
Two quadrilaterals are considered the same if one can be obtained from the other by a rotation and a translation. How many different convex cyclic quadrilaterals are there with integer sides and perimeter equal to 32?
$\textbf{(A)}\ 560 \qquad \textbf{(B)}\ 564 \qquad \textbf{(C)}\ 568 \qquad \textbf{(D)}\ 1498 \qquad ... | tiger_lab_math |
when a student joe , weighing 42 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left an... | tiger_lab_math |
two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 110 kmph , find the rate at which the train b runs . Let's write a program. | tiger_lab_math |
Joan has 180 socks. Two thirds of the socks are white, and the rest of the socks are blue. How many blue socks does Joan have? | tiger_lab_math |
the greater of two numbers is twice the less , and the sum of the numbers is 96 . what are the numbers ? Let's program in Python in the response. | tiger_lab_math |
A curve is defined by the function f(x) = x^2 - 3x. At which point on the curve does the slope of the tangent line equal 4? | tiger_lab_math |
A local park has 70 pigeons that call the park home. Half of the pigeons are black, and 20 percent of the black pigeons are male. How many more black female pigeons are there than black male pigeons? | tiger_lab_math |
In how many ways can 8 beads be arranged on a necklace with 4 beads of one color and 4 beads of another color, considering two arrangements are considered the same if one can be rotated to obtain the other? (Note: Polya's enumeration theorem can be used to solve this problem) | tiger_lab_math |
Let $\triangle ABC$ be a right triangle such that $B$ is a right angle. A circle with diameter of $BC$ meets side $AC$ at $D.$ If $AD = 1$ and $BD = 4,$ then what is $CD$? | tiger_lab_math |
What is the equation of the plane that passes through the intersection of the surfaces given by the equations
$$ x^2 + y^2 - z^2 = 1 $$
and
$$ x + y + z = 3 $$
in 3-dimensional space? | tiger_lab_math |
there were two candidates in an election . winner candidate received 62 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ? Let's write a program. | tiger_lab_math |
A string that is 2 meters long is fixed at both ends. If it is plucked so that it vibrates in its fundamental mode with a frequency of 100 Hz, find the equation that describes the wave motion and determine the amplitude of the wave at the point 0.5 meters from one end of the string. Assume the wave travels at a speed o... | tiger_lab_math |
Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers that could be under the ink stain?
[asy]
draw((0,0)--(3,0)--(3,3)--(0,3)--cycle);
fill((0,0)--(3,0)-... | tiger_lab_math |
Suppose $f(z)$ is an entire function with $|f(z)| \leq 5$ for all $z\in \mathbb{C}$. Using the maximum modulus principle, prove that $f(z)$ is a constant function. | tiger_lab_math |
the sum of two numbers is 84 , and one of them is 12 more than the other . what are the two numbers ? Let's write a Python program to solve it. | tiger_lab_math |
A bridge is to be constructed with a maximum weight limit of 5000 kg on a span of 20 meters. The bridge will be made of steel and concrete. The concrete costs $500 per cubic meter, and the steel costs $1500 per cubic meter. The cross-sectional area of steel should be at least 10% of the total cross-sectional area of th... | tiger_lab_math |
Let A be a set with 10 elements. Find the complement of set A, and prove that this complement is unique. | tiger_lab_math |
The positive four-digit integers that use each of the four digits $1,$ $2,$ $3,$ and $4$ exactly once are ordered from least to greatest. What is the $15^{\text{th}}$ integer in the list? | tiger_lab_math |
Suppose that a restaurant is considering hiring a new chef. The expected profits of the restaurant will depend on the quality of the food that the chef produces. The restaurant can pay the chef either a low wage of $1,000 per week or a high wage of $1,500 per week. The quality of the chef's work will depend on whether ... | tiger_lab_math |
a number is doubled and 5 is added . if the resultant is trebled , it becomes 135 . what is that number ? Please respond by writing a program in Python. | tiger_lab_math |
Prove that the group G, of order 7 is cyclic. | tiger_lab_math |
A bag contains ten balls, some of which are red and the rest of which are yellow. When two balls are drawn at random at the same time, the probability that both balls are red is $\frac{1}{15}$. How many balls in the bag are red? | tiger_lab_math |
An integer $n$ is said to be square-free if the only perfect square that divides $n$ is $1^2$. How many positive odd integers greater than 1 and less than $100$ are square-free? Let's write a Python program. | tiger_lab_math |
A town has a population of 100,000 people. A disease is spreading throughout the town with a rate of spread proportional to the number of infected people. After one week, there are 500 infected people. How many people will be infected after three weeks? Assume that there are no recovery or death rates during this time ... | tiger_lab_math |
Consider a graph G with 10 vertices and 12 edges. Determine whether G is a connected graph or not. If it is connected, find the minimum number of edges that need to be removed to disconnect the graph. | tiger_lab_math |
8 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire rest of the car , then the share of each of the remaining persons increased by ? Please write a program to solve it | tiger_lab_math |
the ratio of numbers is 3 : 4 and their h . c . f is 5 . their l . c . m is : ? Please write a program to solve it | tiger_lab_math |
an escalator moves towards the top level at the rate of 12 ft . sec and its length is 160 feet . if a person walks on the moving escalator at the rate of 8 feet per second towards the top level , how much time does he take to cover the entire length . Please write a program to solve it | tiger_lab_math |
Two players are playing a game called Nim. The game starts with two piles of stones. On their turn, a player must remove at least one stone from one of the piles, or remove stones from both piles such that the number of stones removed from each pile is the same. The player who removes the last stone(s) wins. If player ... | tiger_lab_math |
Elise had $8. Then she saved $13 from her allowance and bought a puzzle for $18 that got her a $2 discount. Elise is left with $_____ . Let's write a program. | tiger_lab_math |
the length of a rectangle is 3 times its width . if the width of the rectangle is 6 inches , what is the rectangle ' s area , in square inches ? Let's write a Python program. | tiger_lab_math |
Circle $A$ is in the interior of circle $B$. The diameter of circle $B$ is 16 cm. What is the diameter of circle $A$ for which the ratio of the shaded area to the area of circle $A$ is 3:1?
[asy]size(101);
import graph;
pair B = (0,0);
pair A = (1,-3);
filldraw(Circle(B,10)^^Circle(A,5),gray(.6)+fillrule(1),linewidth(... | tiger_lab_math |
Find the steady-state voltage of the Chua circuit given that the values of the initial conditions of the capacitors are C1 = 1µF and C2 = 2µF, the resistance of the resistor is R = 100Ω, and the values of the parameters of the Chua diode are a = 15.6V, b = 28V, c1 = -1/7, and c2 = -8/7. | tiger_lab_math |
There are 261 fishbowls. Each fishbowl has 23 fish. So , there are _____ fishes . Let's write a program. | tiger_lab_math |
Let X be the set of all real numbers and let S be the subset defined by S = {x ∈ X : -2 < x ≤ 3}. Show that the sequence (a_n) = (1/n) converges to zero with respect to the subspace topology on S. | tiger_lab_math |
In a compound, the number of cats is 20% less than the number of dogs. There are also twice as many frogs as the number of dogs in the compound. Calculate the total number of animals present in the compound if there are 160 frogs. | tiger_lab_math |
at a school , 3 - fifths of the male students and two - thirds of the female students speak a foreign language . if the number of males is equal to the number of females , what fraction of the students speak a foreign language ? Let's write a Python program. | tiger_lab_math |
the product of two positive integers is 323 and their difference is 2 . what is the smaller number ? Let's program in Python in the response. | tiger_lab_math |
What is the smallest positive integer that is divisible by 6, 8 and 15? | tiger_lab_math |
the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 15 % profit ? Let's program in Python in the response. | tiger_lab_math |
john makes $ 30 a week from his job . he earns a raise andnow makes $ 40 a week . what is the % increase ? Let's program in Python in the response. | tiger_lab_math |
In a signaling game, there are two players: the sender and the receiver. The sender has two types, A and B, and the receiver only knows the probability that the sender is type A, which is 0.6. If the sender is type A, they will send a signal of "1" with probability 0.8, and if they're type B, they'll send a signal of "... | tiger_lab_math |
there are 50 students in a class . if 12 % are absent on a particular day , find the number of students present in the class . Please respond by writing a program in Python. | tiger_lab_math |
Find the particular solution of the differential equation `[dy/dx = 3x^2]` that passes through the point `(1,4)`. | tiger_lab_math |
Determine a conformal mapping that transforms the unit disk $|z| < 1$ onto the upper half plane $\{z: \mathrm{Im}(z) > 0\}$, and fixes the point $i$. | tiger_lab_math |
Prove that there is no group of order 30 which is isomorphic to the Klein four-group. | tiger_lab_math |
Compute the sum of the geometric series $-1 -3-9-27 -81-243-729$. | tiger_lab_math |
the product z of two prime numbers is between 15 and 36 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24 , then what is z ? Let's write a Python program. | tiger_lab_math |
"statement 1": If Martin returned two packet to the retailer , and the average price of the remaining millk packet was 12 ¢ , then what is the average price , in cents , of the two returned milk packets ?, "statement 2" :If Martin returned two packet to the retailer , and the average price of the remaining millk packe... | tiger_lab_math |
a train with 120 wagons crosses john who is going in the same direction , in 36 seconds . it travels for half an hour from the time it starts ove ( who is also riding on his horse ) coming from the opposite direction in 24 seconds . in how much time after the train has crossed the mike do the john meets to mike ? rtaki... | 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 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if ... | tiger_lab_math |
If $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^3 + bx^2 + 1,$ find $b.$ | tiger_lab_math |
a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 9 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ? Please write a program to ... | tiger_lab_math |
there is a total of 120 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 1 / 3 . what is the probability that the marble will be either red or blue ? Please resp... | tiger_lab_math |
Find all $y \in [0,\pi]$ for which \[\sin(x+y)\leq \sin(x)+\sin(y)\]for every $x$ between $0$ and $\pi$, inclusive. | tiger_lab_math |
The product of two positive integers is 18. The positive difference of these two integers is 3. What is the sum of the two integers? | tiger_lab_math |
in an election between two candidates , the winner has a margin of 20 % of the votes polled . if 1000 people change their mind and vote for the loser , the loser would have won by a margin of 20 % of the votes polled . find the total number of votes polled in the election ? Please respond by writing a program in Python... | tiger_lab_math |
some persons can do a piece of work in 12 days . two times the number of these people will do half of that work in ? Let's write a program. | tiger_lab_math |
The points $(1, 7), (13, 16)$ and $(5, k)$, where $k$ is an integer, are vertices of a triangle. What is the sum of the values of $k$ for which the area of the triangle is a minimum? | tiger_lab_math |
Find $r$ such that $\log_{81} (2r-1) = -1/2$. | tiger_lab_math |
two trains of length 250 m and 120 m are 50 m apart . they start moving towards each other on parallel tracks , at speeds 64 kmph and 42 kmph . after how much time will the trains meet ? Let's write a Python program. | tiger_lab_math |
the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 60 kmph , find the speed of the stream ? Let's program in Python in the response. | tiger_lab_math |
a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 9 : 00 , how many seconds elaps... | tiger_lab_math |
Aaron has four brothers. If the number of Bennett's brothers is two less than twice the number of Aaron's brothers, what is the number of Bennett's brothers? | tiger_lab_math |
A circle has a diameter of 16 cm. Find the perimeter of a sector that has a central angle of 60 degrees. | tiger_lab_math |
if a fills a tank in 30 mins , and b fills the same tank in 20 mins , and c emptys it in 40 min , if a , b , c works together how much time will the tank take to fill ? Let's write a program. | tiger_lab_math |
in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 35 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ? Let's write a Python program. | tiger_lab_math |
Consider the heat equation in complex analysis:
$$\frac{\partial u(x,t)}{\partial t} = k \frac{\partial^2 u(x,t)}{\partial x^2} $$
where $u(x,t)$ is the temperature at position $x$ and time $t$, and $k$ is a positive constant. Suppose the initial temperature is given by:
$$ u(x,0) = \begin{cases} 0 & \text{if } 0 \l... | tiger_lab_math |
the cost per pound of milk powder and coffee were the same in june . in july , the price of coffee shot up by 200 % and that of milk powder dropped by 60 % . if in july , a mixture containing equal quantities of milk powder and coffee costs $ 5.10 for 3 lbs , how much did a pound of milk powder cost in july ? Let's wri... | tiger_lab_math |
What is the smallest positive integer $n$ such that $17n \equiv 1234 \pmod{7}?$ | tiger_lab_math |
What is the smallest positive number that is prime and $10$ less than a perfect square? | tiger_lab_math |
an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 4 ? Let's write a program. | tiger_lab_math |
Consider a graph with 7 vertices and 10 edges. Determine the number of cut vertices and the number of bridges in the graph. | tiger_lab_math |
One red flower, three white flowers and two blue flowers are arranged in a line such that
I. No two adjacent flowers are of the same colour.
II. The flowers at the two ends of the line are of different colours.
In how many different ways can the flowers be arranged?
Answer Choices: (A) 6 (B) 4 (C) 10 (D) 12 (E) 14 | tiger_lab_math |
a man is standing on a railway bridge which is 180 m long . he finds that a train crosses the bridge in 20 seconds but himself in 8 seconds . find the length of the train and its speed . Let's program in Python in the response. | tiger_lab_math |
The number $r$ can be expressed as a four-place decimal $0.abcd,$ where $a, b, c,$ and $d$ represent digits, any of which could be zero. It is desired to approximate $r$ by a fraction whose numerator is 1 or 2 and whose denominator is an integer. The closest such fraction to $r$ is $\frac 27.$ What is the number of pos... | tiger_lab_math |
the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 46 kg , then the weight of b is : ? Please write a program to solve it | tiger_lab_math |
Consider a connected undirected graph with 9 vertices and 18 edges. Determine the minimum number of edges that must be removed in order to disconnect the graph. | tiger_lab_math |
There are ten more newborn elephants than baby hippos. If an entire herd starts with 20 elephants and 35 hippos, and the female hippos, whose number is 5/7 of the total number of hippos, give birth to 5 new baby hippos each, find the number of animals that are there altogether? | tiger_lab_math |
What is the smallest positive integer that satisfies Wilson's theorem? | tiger_lab_math |
A farmer has counted his chickens for 100 days in a row and every time he has found that the number of chickens was greater than the day before. Based on this observation, what is the minimum number of days that the farmer can be sure that the next day will also have more chickens than the previous day? | tiger_lab_math |
Let $M$ be a 2-dimensional manifold with metric $g$, and let $f: M \rightarrow \mathbb{R}$ be a smooth function such that $f(x,y) = x^2 + y^2$ for all $(x,y) \in M$. Determine the Laplacian of $f$ on $M$. | tiger_lab_math |
A particle with mass m = 1 kg is moving in a one-dimensional potential well given by:
$$ V(x) = \begin{cases} 0 & \text{for } 0<x<1 \\ 100 & \text{for } x ≤ 0 \text{ or } x ≥ 1 \end{cases} $$
Assuming that the particle's wave function is given by:
$$ \psi(x,0) = \begin{cases} Ax(1-x) & \text{for } 0<x<1 \\ 0 & \text{ot... | tiger_lab_math |
The function f is defined for all the positive integers n by the following rule: f(a) is the number of positive integers each of which is less than a and has no positive factor in common with a other than 1 . if p is a prime number then f(p)?
Answer Choices: (A) p-1 (B) p-2 (C) (p+1) /2 (D) (p-1) /2 (E) 2 | tiger_lab_math |
a man purchased 3 blankets @ rs . 100 each , 3 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ? Let's program in Python in the response. | tiger_lab_math |
Determine the Fourier transform of the function f(x) = 2xe^{-x^2} for all real values of x. | tiger_lab_math |
tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , ho... | tiger_lab_math |
What is the area of the smallest bulb of the Mandelbrot set with a cardioid boundary?
Hint: The formula for the area of a Cardioid is given by A = (3/8)πr^2 where r is the radius of the cardioid. | tiger_lab_math |
X and Y are two points respectively on sides AB and AC of triangle ABC such that XY is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium XYCB is 25:144 and BC=13 cm, then find the length of XY.
Answer Choices: (A) 12 (B) 13 (C) 14 (D) 11 (E) 5 | tiger_lab_math |
Two-fifths of the seats in an auditorium that holds 500 people are currently taken. It was found that 1/10 of the seats are broken. How many seats are still available? Let's write a program. | tiger_lab_math |
Find all real values of $x$ that satisfy $\frac{x(x+1)}{(x-4)^2} \ge 12.$ (Give your answer in interval notation.) | tiger_lab_math |
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