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the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 91 per day . what was his wage on the 8 th day ? Let's program in Python in the response. | tiger_lab_math |
What is the smallest four-digit palindrome that is divisible by 4? (A palindrome is a number that reads the same forwards and backwards, like 61216.) | tiger_lab_math |
A flagpole is standing vertically on a ground. The length of the flagpole is 15 meters. The wind is blowing horizontally and makes an angle of 30 degrees with the ground. Find the maximum distance of the top of the pole from its original position due to wind gusts. | tiger_lab_math |
a pupil ' s marks were wrongly entered as 83 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ? Let's write a program. | tiger_lab_math |
of the diplomats attending a summit conference , 14 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ? Please respond by writing a program in Python. | tiger_lab_math |
Consider a function f(x) = e^x - 4x. Which of the following statements about the function is true? Answer Choices: (A) The function has no real roots (B) The function has one real root (C) The function has two real roots (D) The function has more than two real roots | tiger_lab_math |
A mass of 2 kg is attached to a spring with a spring constant of 5 N/m. Find the natural frequency of the system of vibrations and determine the displacement of the mass at time t=2 seconds if its initial displacement is 0.1m and initial velocity is 0.5m/s. | tiger_lab_math |
hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and two wrenches is one - third that of 8 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ? Let's write a Python program. | tiger_lab_math |
A circle has a radius of 8 cm. Find the perimeter of the sector with a central angle of 45 degrees. | tiger_lab_math |
a bag contains 3 red , 2 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ? Let's write a Python program to solve it. | tiger_lab_math |
the profit obtained by selling an article for rs . 66 is the same as the loss obtained by selling it for rs . 22 . what is the cost price of the article ? Let's write a program. | tiger_lab_math |
Consider the variety $V\subset\mathbb{A}^3$ with coordinates $(x,y,z)$ defined by the equations $x^2+y^2+z^2=1$ and $x+y+z=0$. Find the equation of the line passing through the two points $P_1=(1,0,0)$ and $P_2=(0,1,-1)$ and intersecting $V$ at a third point $P_3$. | tiger_lab_math |
at a small company , 64 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ? Let's write a Python program. | tiger_lab_math |
rs 3500 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part . Let's program in Python in the response. | tiger_lab_math |
a bag contains 3 red , 2 blue and 4 green balls . if 2 balls are picked at random , what is the probability that both are red ? Let's program in Python in the response. | tiger_lab_math |
the h . c . f . of two numbers is 32 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is : ? Let's write a Python program. | tiger_lab_math |
A 10-by-7 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
Answer Choices: (A) The volume of the cylinder with height 10 is 70/pi cubic inches gre... | tiger_lab_math |
at the end of the first quarter , the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 75 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of... | tiger_lab_math |
Consider a covering space $p: \widetilde{X}\rightarrow X$, where $\widetilde{X}$ is the universal cover of $X$ and $X$ is a path-connected, locally path-connected and semi-locally simply connected space. Let $\gamma: [0,1]\rightarrow X$ be a loop at a basepoint $x_0\in X$ such that $\gamma(t)=x_0$ for all $t\in[0,1/2]$... | tiger_lab_math |
a taxi leaves point a 4 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours . Let's write a program. | tiger_lab_math |
what is the smallest number which , when increased by 7 , is divisible by 8 , 11 , and 24 ? Let's program in Python in the response. | tiger_lab_math |
carolyn bought 17 gumballs , lew bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ? Let's write a program. | tiger_lab_math |
How many triangles with positive area are there whose vertices are points in the $xy$-plane whose coordinates are integers $(x,y)$ satisfying $1\le x\le 4$ and $1\le y\le 4$?
$\text{(A) } 496\quad \text{(B) } 500\quad \text{(C) } 512\quad \text{(D) } 516\quad \text{(E) } 560$
Let's write a Python program to solve it. | tiger_lab_math |
For some real numbers $a$ and $b$, the equation $9x^3 + 5ax^2 + 4bx + a = 0$ has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 4, what is the value of $a$? | tiger_lab_math |
Find all solutions for the equation $\sin^2(x)+\cos^2(x)=1$ in the interval $[0,2\pi]$. | tiger_lab_math |
A rectangular rug with side lengths of 6 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) 7/16 (E) 7/8 | tiger_lab_math |
Let A be a set that contains exactly 3 elements. Determine the cardinality of A and its power set P(A), then use this information to prove that the cardinality of P(A) is always greater than the cardinality of A. | tiger_lab_math |
sonika deposited rs . 8000 which amounted to rs . 11200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ? Let's program in Python in the response. | tiger_lab_math |
in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 5 ohms and y is 6 ohms ? Let's program in Python in the response. | tiger_lab_math |
"statement 1": The average number of shirts with Salman , Ambani and Dalmiya is 60 , if all of them reached a shopping mall in Delhi and purchased 6 shirts each of them then average number of shirt each of them now has, "statement 2" :The average number of shirts with Salman , Ambani and Dalmiya is 70 , if all of them... | tiger_lab_math |
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 10 and 100?
Answer Choices: (A) 1345 (B) 1576 (C) 2475 (D) 2578 (E) 1895 | tiger_lab_math |
find the average of all the numbers between 6 and 34 which is divisible by 5 ? Let's write a Python program. | tiger_lab_math |
a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 14 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could ha... | tiger_lab_math |
Let X be a Hausdorff space and A, B be two disjoint closed subsets of X. Prove that there exist open sets U and V such that A ⊆ U, B ⊆ V, and U ∩ V = Ø.
Suppose X is a Hausdorff space and A, B are two disjoint closed sets. Using separation axioms, prove that there exist open sets U and V such that A is a subset of U,... | tiger_lab_math |
What is the minimum number of colors needed to color the vertices of the graph shown below, such that no two adjacent vertices have the same color?
Graph:
```
A-----B
|\ /|
| \ / |
| C |
| / \ |
|/ \|
D-----E
```
Note: This is a common graph known as a "pentagon" and it represents five vertices (... | tiger_lab_math |
Let U be the universal set, and let A be a subset of U. If U has 100 elements and A has 70 elements, how many elements are in A complement? Use set theory to prove that the union of A and its complement is U. | tiger_lab_math |
Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she ... | tiger_lab_math |
1 , 1 , 2 , 1 , 2 , 3 , 1 , 2 , 3 , 4 , 1 , 2 , __ ? Let's write a Python program to solve it. | tiger_lab_math |
a classroom has 3 electric lamps . from a collocation of 10 electric bulbs of which 6 are good , 3 are selected at random and put in the lamps . find the probability that the room is lighted . Please respond by writing a program in Python. | tiger_lab_math |
If the sum of the first n positive integers is x, then which of the following is the sum of the first 2n even positive integers?
Answer Choices: (A) 2x + 2n^2 (B) 3x + 4n^2 (C) 4x + 2n (D) 4x + n^2 (E) 4x + 2n^2 | tiger_lab_math |
Suppose a manufacturer claims that the mean weight of their cereal boxes is 400 grams with a standard deviation of 10 grams. A sample of 50 cereal boxes is taken from a shipment and the mean weight is found to be 395 grams. Is there evidence to suggest that the mean weight of the cereal boxes in the shipment is differe... | tiger_lab_math |
mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.3 more than the next one below it in size . what was the cost , in dollars , of the largest pot ? Please write a program to solve it | 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 |
Find the sum of the positive divisors of 18. Let's program in Python in the response. | tiger_lab_math |
"statement 1": Drip by drip , Aguilar , 28 , watches as chemo enters her body to fight advanced-stage ovarian cancer ., "statement 2" :Christina Aguilar , 28 , is getting treated for ovarian cancer, "options: " Entailment or neutral? Let's write a program. | tiger_lab_math |
Which of the following CANNOT yield an integer when divided by 7 ?
Answer Choices: (A) The sum of three consecutive integers (B) An integer with only even prime factors (C) The product of two odd integers (D) An integer divisible by 8 (E) An even integer | tiger_lab_math |
difference of two numbers is 1650 . if 7.5 % of the number is 12.5 % of the other number , find the number ? Let's program in Python in the response. | tiger_lab_math |
Facebook decided to award a productivity bonus to all its female employees who are mothers. This productivity bonus will total 25% of Facebook's annual earnings, which was $5,000,000 for the year 2020. It is known that Facebook employs 3300 employees; one-third are men, and of the women, 1200 are not mothers. How much ... | tiger_lab_math |
Consider the metric space $(X,d)$ with $X=\{0\}\cup\{\frac{1}{n}:n\in\mathbb{N}\}$ and $d(x,y)=|x-y|$. Let $f:(X,d)\rightarrow (X,d)$ be defined by $f(x)=\frac{x}{2}$ for $x\in X\setminus\{0\}$ and $f(0)=0$. Show that the sequence $(f^n(1))_{n=0}^\infty$ converges in $(X,d)$ and find its limit. | tiger_lab_math |
Consider the Calabi-Yau variety given by the equation $x^3+y^3+z^3=k$, where $k$ is a constant. Find the critical points of the function $f(x,y,z)=x^2+y^2+z^2$ on the Calabi-Yau variety. | tiger_lab_math |
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 |
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 |
Of the numbers 1, 2, 3, ..., 15, which number has the greatest number of divisors (the dots mean that we are including all the integers between 1 and 15)? Please respond by writing a program in Python. | tiger_lab_math |
Let U be a universal set with 100 elements, and let A be a subset of U with 40 elements. What is the cardinality of the union of A and its complement? | tiger_lab_math |
Let $a$ be the number of positive multiples of $6$ that are less than $30$. Let $b$ be the number of positive integers that are less than $30$, and a multiple of $3$ and a multiple of $2$. Compute $(a - b)^3$. Let's write a Python program to solve it. | tiger_lab_math |
after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6700 . find the actual price of the good . Let's write a Python program. | tiger_lab_math |
Determine whether the following function's Fourier series converges or not:
$$
f(x)=\begin{cases}
-1, & -\pi<x<0 \\
1, & 0<x<\pi
\end{cases}
$$
Find the Fourier coefficients $a_n$ and $b_n$, and then justify whether the series converges or not. | tiger_lab_math |
Prove that there are exactly three non-isomorphic groups of order 16, and determine whether each of these groups is cyclic or non-abelian. | tiger_lab_math |
a grocery shop has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ? 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. Seven years from today, the difference between the ... | tiger_lab_math |
A mountain range contains 8 peaks, where no three peaks are in a straight line. In how many ways can a mountaineer climb the mountain range by starting at the first peak and ending at the last peak, with the restriction that each ascent must be followed by a descent, except for the final descent from the last peak? | tiger_lab_math |
from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 12 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ? Let's... | tiger_lab_math |
A triangle has two sides that measure 5 cm each. What is the length of the remaining side if it is an equilateral triangle? | tiger_lab_math |
In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Answer Choices: (A) 24 (B) 26 (C) 42 (D) 46 (E) none | tiger_lab_math |
A possible numerical problem related to Algebraic surfaces would be:
Consider the algebraic surface defined by the equation $x^2+y^2+z^2-2x-2y-2z+1=0$.
- Show that the surface is a sphere centered at point $(1,1,1)$.
- Find the radius of the sphere.
- Calculate the area of the portion of the sphere that lies above th... | tiger_lab_math |
Mr. Manuel is a campsite manager who's been tasked with checking the number of tents set up in the recreation area. On a particular day, he counted 100 tents in the northernmost part of the campsite and twice that number on the east side of the grounds. The number of tents at the center of the camp was four times the n... | tiger_lab_math |
What is the perimeter of the Koch Island fractal after three iterations, given that the initial perimeter of the triangle is 3? | tiger_lab_math |
x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 14080 ? Please respond by writing a program in Python. | tiger_lab_math |
Say that a complex number $z$ is three-presentable if there is a complex number $w$ of absolute value $3$ such that $z = w - \frac{1}{w}$. Let $T$ be the set of all three-presentable complex numbers. The set $T$ forms a closed curve in the complex plane. What is the area inside $T$? | tiger_lab_math |
there is a train and car . the ratio btw the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 480 km in 8 h . the speed of the bus is 3 / 4 th of the speed of the train . how much distance will the car cover in 6 h ? Please write a program to solve it | tiger_lab_math |
if x / ( 12 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ? Let's program in Python in the response. | 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 . 12375 . what is the share of c ? Let's write a Python program. | tiger_lab_math |
If the point $(3,6)$ is on the graph of $y=g(x)$, and $h(x)=(g(x))^2$ for all $x$, then there is one point that must be on the graph of $y=h(x)$. What is the sum of the coordinates of that point? | tiger_lab_math |
a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1760 in all from both of them as interest . the rate of interest per annum is ? Let's program in Python in the response. | tiger_lab_math |
Consider the parallelogram with vertices $(10,45)$, $(10,114)$, $(28,153)$, and $(28,84)$. A line through the origin cuts this figure into two congruent polygons. The slope of the line is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
| tiger_lab_math |
the cost per pound of green tea and coffee were the same in june . in july , the price of coffee shot up by 100 % and that of green tea dropped by 90 % . if in july , a mixture containing equal quantities of green tea and coffee costs $ 3.15 for 3 lbs , how much did a pound of green tea cost in july ? Please write a pr... | tiger_lab_math |
if the area of a triangle with base 6 cm is equal to the area of a square with side 6 cm , then the altitude of the triangle is ? Please respond by writing a program in Python. | tiger_lab_math |
Consider $x(t)$ to be given as, $$ x(t)=\cos (1000 \pi t) $$ . Let the sampling frequency be $2000 \mathrm{~Hz}$. Does aliasing occur? | tiger_lab_math |
Let $a<b<c$ be three integers such that $a,b,c$ is an arithmetic progression and $a,c,b$ is a geometric progression. What is the smallest possible value of $c$? | tiger_lab_math |
the first half of the 20 th century , the population of a particular country increased by 200 percent . in the second half of the century , the population increased by 300 percent . what was the percent increase for the 20 th century as a whole ? Let's write a Python program. | tiger_lab_math |
Jude bought three chairs for his house, all at the same price. He also bought a table that costs $50 and two sets of plates at $20 for each set. After giving the cashier $130, Jude got a $4 change. How much did each of the chairs cost? | tiger_lab_math |
"statement 1": Susan , John , Daisy , Tim , Matt , Jane and Kim need to be seated in 7 identical chairs in straight line so that Susan is seated always left to Tim, "statement 2" :Susan , John , Daisy , Tim , Matt , Jane and Kim need to be seated in more than 1 identical chairs in straight line so that Susan is seated... | tiger_lab_math |
a train 140 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train . Let's program in Python in the response. | tiger_lab_math |
a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 330 . how much does c have ? Let's write a Python program to solve it. | tiger_lab_math |
A message needs to be digitally signed using the RSA algorithm. The prime numbers used in the algorithm are p=17 and q=23, and the public key exponent is e=7. The message to be signed has the numerical value of 123. Find the digital signature to be sent along with the message. | tiger_lab_math |
Find the Fourier series of the function f(x) = |x| on the interval -π < x < π. | tiger_lab_math |
What is the probability that a patient with a specific disease will survive for at least 5 years?
Assuming that the survival time of patients with the disease follows an exponential distribution with a mean of 4 years. | tiger_lab_math |
a person walks from one end to the other of a 80 - meter long moving walkway at a constant rate in 40 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the di... | tiger_lab_math |
Find the number of regions in a planar graph with 12 vertices, where each vertex has degree 3. | tiger_lab_math |
Find the range of the function \[g(t) = \frac{t^2+\tfrac34 t}{t^2+1},\]where $t$ can be any real number. (Give your answer in interval notation.) | tiger_lab_math |
a certain box has 11 cards and each card has one of the integers from 1 to 11 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on... | tiger_lab_math |
A function g(t) has a Fourier transform G(f) such that G(2) = 5 and G(5) = 10. Determine the value of G(10) if the function g(t) is time-limited to the interval [-2,2]. | tiger_lab_math |
A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Answer Choices: (A) 1/5 (B) 1/3 (C) 1/7 (D) 1/9 (E) 1/12 | tiger_lab_math |
Let $f$ be a function satisfying $f(xy) = f(x)/y$ for all positive real numbers $x$ and $y$. If $f(500) = 3$, what is the value of $f(600)$? | tiger_lab_math |
Consider the sets A = {1, 3, 5} and B = {2, 4}. Let C = {2, 3}. Find the following two sets: (A × B) Δ C and A × (B Δ C), where "×" represents the Cartesian product and "Δ" represents the symmetric difference operation. Show that they are not equal and hence prove that the Cartesian product of two sets is not associati... | tiger_lab_math |
each week , harry is paid x dollars per hour for the first 21 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and ja... | tiger_lab_math |
In a social network, there are 10 people who are all friends with each other. How many unique groups of friends can be formed if each group consists of exactly 3 people? | tiger_lab_math |
If x < y < 0, which of the following must be true?
Answer Choices: (A) 2x+y is a negative integer (B) 2xy is a negative integer (C) x-y is a positive integer (D) (-x) + (-y) is positive integer (E) x/y is a negative integer | tiger_lab_math |
Let $f$ be defined by \[f(x) = \left\{
\begin{array}{cl}
2-x & \text{ if } x \leq 1, \\
2x-x^2 & \text{ if } x>1.
\end{array}
\right.\]Calculate $f^{-1}(-3)+f^{-1}(0)+f^{-1}(3)$. | tiger_lab_math |
a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be ? Please respond by writing a program in Python. | tiger_lab_math |
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