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What is the probability that out of a sample of 100 people from a certain demographic group, at least 20 of them will be affected by a particular disease, knowing that the overall prevalence of the disease in the population is 10%? | tiger_lab_math |
the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 1323 sq m , then what is the breadth of the rectangular plot ? Let's write a program. | tiger_lab_math |
Consider the function $f(z)=z^2$ and let $\gamma$ be the positively oriented circle of radius $2$ centered at the origin. Find the value of the integral
$$\int_{\gamma} \frac{\bar{z}}{f(z)} dz$$ | tiger_lab_math |
in a mixture 60 litres , the ratio of milk and water 2 : 1 . if this ratio is to be 1 : 2 , then the quanity of water to be further added is : ? Please write a program to solve it | tiger_lab_math |
Find all real numbers $k$ for which there exists a nonzero, 2-dimensional vector $\mathbf{v}$ such that
\[\begin{pmatrix} 1 & 8 \\ 2 & 1 \end{pmatrix} \mathbf{v} = k \mathbf{v}.\]Enter all the solutions, separated by commas. Let's write a Python program to solve it. | tiger_lab_math |
if x , y , and z are positive integers , and 2 x = 5 y = 6 z , then the least possible value of x + y + z is ? Let's write a program. | tiger_lab_math |
What is the probability of a person from the age group of 25-30 years being affected by a rare disease, given that the prevalence of the disease in the population is 0.5%? Assuming that the age group of 25-30 constitutes 15% of the total population. | tiger_lab_math |
Consider a single item auction with two bidders, where the true valuations of the item by the two bidders are independent and identically distributed from a uniform distribution on [0, 1]. The mechanism used in the auction is a second-price sealed-bid auction, in which the highest bidder wins the item and pays a price ... | tiger_lab_math |
if the sum of two numbers is 22 and the sum of their squares is 404 , then the product of the numbers is ? Please respond by writing a program in Python. | tiger_lab_math |
The product of the positive integer divisors of a positive integer $n$ is 729. Find $n$. Let's write a Python program to solve it. | tiger_lab_math |
anne earned $ 3 an hour baby - sitting , and $ 4 an hour working in the garden . last week she did baby - sitting for 5 hours and garden work for 3 hours . how much more money does she need to buy a game that costs $ 35 ? Let's program in Python in the response. | tiger_lab_math |
There are integers $b,c$ for which both roots of the polynomial $x^2-x-1$ are also roots of the polynomial $x^5-bx-c$. Determine the product $bc$. Let's write a Python program to solve it. | tiger_lab_math |
in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 27 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ? Let's program in Python in the res... | tiger_lab_math |
There is a square playground that has a side length of 12 meters. There is a maintenance building on the playground that measures 8 meters by 5 meters. How many square meters of the playground is not covered by the maintenance building? | tiger_lab_math |
the area of a parallelogram is 200 sq m and its altitude is twice the corresponding base . then the length of the base is ? Let's program in Python in the response. | tiger_lab_math |
Let G be a group of order 27. Using the Sylow theorems, determine the number of Sylow 3-subgroups of G. Then, show that G is isomorphic to either the cyclic group C27 or the non-abelian group of order 27 by constructing the multiplication table of G using the fact that there is either only one or nine Sylow 3-subgroups... | tiger_lab_math |
two 100 multiples of 7 are chosen at random , and 300 multiples of 8 are chosen at random . approximately what percentage of the 500 selected numbers are odd ? Please write a program to solve it | tiger_lab_math |
Evaluate the expression \[ \frac{a+2}{a+1} \cdot \frac{b-1}{b-2} \cdot \frac{c + 8}{c+6} , \] given that $c = b-10$, $b = a+2$, $a = 4$, and none of the denominators are zero. Let's write a program. | tiger_lab_math |
How many ways can 2 men and 3 women be arranged in a line such that the women are standing next to each other? | tiger_lab_math |
There are 84 leaves. There are 139 ladybugs on each leaf. In all , there are _____ ladybugs . Let's write a Python program. | tiger_lab_math |
a girl walking at the rate of 9 km per hour crosses a square field diagonally in 12 seconds . the area of the field is : ? Let's write a program. | tiger_lab_math |
"statement 1": Arun obtained more than 46 , 65 , 82 , 67 and 85 marks ( out in 100 ) in English , Mathematics , Chemistry , Biology and Physics, "statement 2" :Arun obtained 76 , 65 , 82 , 67 and 85 marks ( out in 100 ) in English , Mathematics , Chemistry , Biology and Physics, "options: " Entailment or contradiction... | tiger_lab_math |
dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 54 of gas ? Let's write a program. | tiger_lab_math |
initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many r women are currently in the room ? Please write a program to solve it | tiger_lab_math |
a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 7 / 17 . what was the number erased ? Please write a program to solve it | tiger_lab_math |
a grocer has a sale of rs . 5124 , rs . 5366 , rs . 5808 , rs . 5399 and rs . 6124 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5400 ? Let's write a Python program to solve it. | tiger_lab_math |
Let $C$ be a projective curve in $\mathbb{P}^3$ defined by the intersection of two quadric surfaces given by equations $x^2+y^2+z^2+w^2=0$ and $xw-yz=0$. Find the equation of the line passing through the two points $P=(1:0:0:1)$ and $Q=(0:1:1:0)$ on $C$. | 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 ? Let's write a Python program. | tiger_lab_math |
mary works in a restaurant a maximum of 40 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ? Let's program in Python in the response. | tiger_lab_math |
the present population of a town is 1240 . population increase rate is 4 % p . a . find the population of town after 1 years ? Please write a program to solve it | tiger_lab_math |
if the product of two numbers is 62216 and their h . c . f . is 22 , find their l . c . m . Please write a program to solve it | tiger_lab_math |
the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is : ? Let's program in Python in the response. | tiger_lab_math |
Prove that every group of prime order is cyclic, given that the group has order 17. | tiger_lab_math |
Find the number of ordered pairs of positive integers $(a,b)$ such that $a+b=1000$ and neither $a$ nor $b$ has a zero digit.
Please respond by writing a program in Python. | tiger_lab_math |
5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 75 only . men â € ™ s wages are ? Let's write a Python program to solve it. | tiger_lab_math |
Here is a possible precise numerical problem for the math student to solve:
Consider a Belousov-Zhabotinsky reaction whose evolution is described by the following system of ordinary differential equations (in dimensionless form):
dx/dt = a(y-x) + z,
dy/dt = bx - xy - xz,
dz/dt = -c(z+f(x,y)),
where a,b,c are posi... | tiger_lab_math |
a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter m of liquid a was contained by the can initially ? Let's write a Python program. | tiger_lab_math |
A student must optimize the production of two types of t-shirts, A and B. The cost of producing a t-shirt A is $5 and the cost of producing a t-shirt B is $7. The selling price of t-shirt A is $10 and the selling price of t-shirt B is $12. The student has a total budget of $4200 and wants to maximize the profit. Find t... | tiger_lab_math |
Let G be a cyclic group of order 12, generated by the element a. Find all the subgroups of G and for each subgroup, determine an element that generates it. | tiger_lab_math |
thabo owns exactly 180 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books ... | tiger_lab_math |
Assume that f(z) is a complex function with a pole of order 2 at z=0 and a removable singularity at z=1. If f(z) is analytic elsewhere, determine the residue of f(z) at z=0 using the Laurent series expansion of f(z) around z=0. | tiger_lab_math |
a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 168 , how many hours overtime did he work ? Let's write a Python program. | tiger_lab_math |
if a farmer sells 5 of his goats , his stock of feed will last for 4 more days than planned , but if he buys 10 more goats , he will run out of feed 3 days earlier than planned . if no goats are sold or bought , the farmer will be exactly on schedule . how many goats does the farmer have ? Let's write a program. | tiger_lab_math |
Let $O$ be the origin, and let $(a,b,c)$ be a fixed point. A plane passes through $(a,b,c)$ and intersects the $x$-axis, $y$-axis, and $z$-axis at $A,$ $B,$ and $C,$ respectively, all distinct from $O.$ Let $(p,q,r)$ be the center of the sphere passing through $A,$ $B,$ $C,$ and $O.$ Find
\[\frac{a}{p} + \frac{b}{q}... | tiger_lab_math |
There are 30 students in a school, and they are taking at least one of the following subjects: Mathematics, Science, and History. 20 students are taking Mathematics, 15 are taking Science, and 10 are taking History. If 7 students are taking both Mathematics and Science, 4 are taking both Mathematics and History, 3 are ... | tiger_lab_math |
Find the number of all possible functions from a set A with 4 elements to a set B with 3 elements according to the type theory. | tiger_lab_math |
in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate . Please respond by writing a program in Python. | tiger_lab_math |
Albert starts to make a list, in increasing order, of the positive integers that have a first digit of 1. He writes $1, 10, 11, 12, \ldots$ but by the 1,000th digit he (finally) realizes that the list would contain an infinite number of elements. Find the three-digit number formed by the last three digits he wrote (the... | tiger_lab_math |
of the 3 - digit integers greater than 200 , how many have two digits that are equal to each other and the remaining digit different from the other two ? Let's write a Python program. | tiger_lab_math |
average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 25 % the new mean is $ 850 . what was original rent of friend whose rent is increased ? Please write a program to solve it | tiger_lab_math |
a larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 8 smaller cubes and the surface area of the larger cube , in square inch ? Let's write a program. | tiger_lab_math |
Let $a$ and $b$ be positive real numbers with $a\ge b$. Let $\rho$ be the maximum possible value of $\frac {a}{b}$ for which the system of equations $$
a^2 + y^2 = b^2 + x^2 = (a - x)^2 + (b - y)^2
$$has a solution in $(x,y)$ satisfying $0\le x < a$ and $0\le y < b$. Find $\rho^2.$ | tiger_lab_math |
a sum of money at simple interest amounts to rs . 1717 in 1 year and to rs . 1734 in 2 years . the sum is : ? Let's write a Python program. | tiger_lab_math |
If a and b are positive integers and a/b=0 then which of the following give positive Numbers and CANNOT be zero?
Answer Choices: (A) ab/ba (B) a/b-b/a (C) b/a-a/b (D) (a^2 -b^2) /ab (E) a/b | tiger_lab_math |
Let $a$ and $b$ be angles such that
\[\cos (a + b) = \cos a + \cos b.\]Find the maximum value of $\cos a.$ | tiger_lab_math |
darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the ... | tiger_lab_math |
What are the probability of finding a particle from the Henon-Heiles system in the region $x_1=0.25$, $x_2=0.1$, $y_1=-0.3$, and $y_2=0.3$ after $100$ iterations? Assume that the initial conditions of the system are uniformly distributed in the phase space. | tiger_lab_math |
Consider a graph with 7 vertices and 10 edges. Determine the minimum number of edges that must be removed in order to disconnect the graph. | tiger_lab_math |
the second angle of a triangle is double the first ( 110 ) . the third angle is 40 less than the first ( 15 ) . find the first angle . Let's write a program. | tiger_lab_math |
one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field in meter square ? Let's program in Python in the response. | tiger_lab_math |
The area of a triangle is 600 square feet. Find the altitude, in feet, of the triangle if the length of the corresponding base is 30 feet. | tiger_lab_math |
Find all real numbers $x$ such that
\[\frac{8^x + 27^x}{12^x + 18^x} = \frac{7}{6}.\]Enter all the solutions, separated by commas. | tiger_lab_math |
rs . 120 are divided among a , b , c such that a ' s share is rs . 20 more than b ' s and rs . 20 less than c ' s . what is b ' s share ? Please write a program to solve it | tiger_lab_math |
T = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set T and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
Answer Choices: (A) 0.15 (B) 0.20 (C) 0.25 (D) 0.30 (E) 0.33 | tiger_lab_math |
the perimeters of 2 squares are 60 cm and 48 cm . find the perimeter of a third square whose area is equal to the difference of the areas of the two squares ? Please write a program to solve it | tiger_lab_math |
in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 10 people all together . how many people can sit in a bus ? Let's write a Python program to solve it. | tiger_lab_math |
of 70 players on a football team , 46 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? Let's write a Python program. | tiger_lab_math |
for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 24 , then v = ? Let's write a Python program. | tiger_lab_math |
In a certain lottery drawing, two balls are selected at random from a container with 30 balls, numbered from 1 to 30, 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 |
Consider the projective variety given by the equation $x^2+y^2+z^2 = 1$ in $\mathbb{P}^2(\mathbb{R})$. Find the equation of the line passing through the points $[1:0:1]$ and $[0:1:-1]$, and determine if this line intersects the projective variety at any other points. | tiger_lab_math |
two guys a and b leave point a and point b simultaneously and travel towards point b and point a on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will b take to cover the entire... | tiger_lab_math |
Jason, Ryan, and Jeffery went fishing at the lake. Ryan caught three times the number of fish that Jason caught. Jefferey caught twice the number of fish that Ryan got. If Jeffery caught 60 fish, how many fish did all of them catch in total? | tiger_lab_math |
the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 602 to 700 inclusive ? Please respond by writing a program in Python. | tiger_lab_math |
the population of a village is 15540 . it increases annually at the rate of 28 % p . a . what will be its population after 2 years ? Please write a program to solve it | tiger_lab_math |
The domain of the function $f(x) = \arcsin(\log_{m}(nx))$ is a closed interval of length $\frac{1}{2013}$ , where $m$ and $n$ are positive integers and $m>1$. Find the the smallest possible value of $m+n.$ | tiger_lab_math |
the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.5 kg . the weight of the new student is ? Please write a program to solve it | tiger_lab_math |
find the area of trapezium whose parallel sides are 30 cm and 18 cm long , and the distance between them is 15 cm . Let's write a Python program to solve it. | tiger_lab_math |
The ages of three brothers are consecutive integers with the sum of 96. How old is the youngest brother? | tiger_lab_math |
the concentration of spirit in 3 different vessels a , b and c are 45 % , 30 % and 10 % respectively . if 4 litres from vessel a , 5 litres from vessel b and 6 litres from vessel c are mixed , find the concentration of spirit in the resultant solution . Let's program in Python in the response. | tiger_lab_math |
set x consists of the integers from 1 to 12 , inclusive , while set y consists of the integers from 0 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ? Let's write a program. | tiger_lab_math |
A tank with rectangular shape and no lid is required to hold 50 cubic meters of water. Determine the dimensions of the tank that require the least material to be used in its construction. | tiger_lab_math |
In a community of 500 people, 280 are married and 220 have at least one child. If 180 people are married and have at least one child, what is the probability that a randomly selected person from the community is married or has at least one child? | tiger_lab_math |
A flagpole is standing vertically on a ground. The flag on the top of the pole is at an angle of elevation of 60 degrees from a point 20 meters away from the base of the pole. Find the height of the flagpole. | tiger_lab_math |
the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 30 per cent . the two reductions together are equal to a single reduction of ? Let's program in Python in the response. | tiger_lab_math |
Find the minimum value of
\[x^2 + 2xy + 3y^2 - 6x - 2y,\]over all real numbers $x$ and $y.$ | tiger_lab_math |
A lucky integer is a positive integer which is divisible by the sum of its digits. What is the least positive multiple of 9 that is not a lucky integer? Let's program in Python in the response. | tiger_lab_math |
on dividing 21 by a number , the quotient is 10 and the remainder is 1 . find the divisor . Please write a program to solve it | tiger_lab_math |
A stock price for Company ABC is currently at $50 per share. In the next month, there is a 70% chance that the stock price will increase by $10 per share and a 30% chance that the stock price will decrease by $5 per share. What is the probability that the stock price for Company ABC will be at least $60 per share at th... | tiger_lab_math |
in the science city , kolkata the rate of the ticket is increased by 50 % to increased the revenue but simultaneously 20 % of the visitor decreased . what is percentage change in the revenue . if it is known that the science city collects one revenue only from the visitors and it has no other financial supports : ? Let... | tiger_lab_math |
the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 385 the other is ? Please respond by writing a program in Python. | tiger_lab_math |
There are 39 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
Answer Choices: (A) 39 (B) 40 (C) 55 (D) 58 (E) 63 | tiger_lab_math |
on a purchase of $ 118 , a store offered a payment plan consisting of a $ 18 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ? Let's program in Python in the response. | tiger_lab_math |
three circles of radius 3.5 cm are placed in such a way that each circle touches the other two . the area of the portion enclosed by the circles is ? Let's program in Python in the response. | tiger_lab_math |
A financial firm has identified that the probability of a certain type of fraud occurring on any given day is 0.02. If the firm operates 250 business days in a year, what is the probability that the fraud will occur at least once during the year? | tiger_lab_math |
In a circus performance, there are 10 clowns who could potentially perform a comedy skit. If the chance that any given clown performs is 70%, what is the probability that at least 7 clowns will perform the comedy skit during the performance? | tiger_lab_math |
A cable of length 20 meters is to be cut into two pieces. One piece will be used to hang a sign with one end attached to a building and the other end attached to a post that is 5 meters from the building. The other piece will be used to hang a sign with one end attached to the same building and the other end attached t... | tiger_lab_math |
ele , the circus elephant , is currently 3 times older than lyn , the circus lion . in 15 years from now , lyn the circus lion will be exactly half as old as ele , the circus elephant . how old is ele today ? Let's write a Python program to solve it. | tiger_lab_math |
The numbers $\sqrt{2u-1}$, $\sqrt{2u+1}$ and $2\sqrt{u}$ are the side lengths of a triangle. How many degrees are in the measure of the largest angle? Let's write a Python program. | tiger_lab_math |
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to ... | tiger_lab_math |
Consider the following projective variety defined by the homogeneous polynomial:
*f(x, y, z) = x^3 - 2x^2y + xy^2 + 2y^2z - z^3.*
1. Determine the degree of the projective variety.
2. Identify the singular points of the projective variety.
3. Show that the projective variety is not isomorphic to the projective line.... | tiger_lab_math |
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