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a boat crossed a lake from north to west at the speed of 5 km / h , entered a river and covered twice as much distance going upstream at 4 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.6 km / h that day , what was its approximate downstream speed ? Let's program in Python ... | tiger_lab_math |
The set $S = \{1, 2, 3, \ldots , 49, 50\}$ contains the first $50$ positive integers. After the multiples of 2 and the multiples of 3 are removed, how many integers remain in the set $S$? | tiger_lab_math |
Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
Answer Choices: (A) 6775 ways (B) 1440 ways (C) 1345 ways (D) 1324 ways (E) 1688 ways | tiger_lab_math |
Given a 2-dimensional manifold represented by the equation x^2 + y^2 - 1 = 0, determine its symmetries. Specifically, find all the isometries that leave the manifold invariant, and determine whether there exist non-isometric symmetries. | tiger_lab_math |
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
Answer Choices: (A) 864 (B) 863 (C) 865 (D) 1728 (E) 890 | tiger_lab_math |
a man sells a car to his friend at 14 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was : ? Let's write a program. | tiger_lab_math |
In a Rail fence cipher with 4 rails, the plaintext "HELLOWORLD" is encrypted as follows:
```
H . . . O . . . R . . .
. E . L . W . O . L . D
. . L . . . O . . . H .
. . . O . . . L . . . .
```
What is the ciphertext generated by encrypting the plaintext "GOODMORNING" using the same Rail fence cipher with 4 rails? | tiger_lab_math |
in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 140 ? Let's write a Python program. | tiger_lab_math |
Let there be a set A = {1,2,3,4} and B = {2,3,6,7}. Define a function f: A→P(B) such that for every element x in A, f(x) is the set of all positive divisors of x that are also in B. Calculate the range of this function f. | tiger_lab_math |
in measuring the sides of a rectangle , one side is taken 10 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements . Let's program in Python in the response. | tiger_lab_math |
What is the smallest Sophie Germain prime that is also a Safe prime?
A safe prime is a prime number of the form 2p + 1, where p is also a prime number. Sophie Germain primes are prime numbers p such that 2p + 1 is also prime. | tiger_lab_math |
A metal bar of length 10 cm is initially at a temperature of 20°C. The ends of the bar are maintained at a fixed temperature of 0°C. At t=0, the temperature of the bar is raised to 100°C and it is left to cool. Using the Fourier series method, determine the temperature distribution of the bar at a time t=2 seconds. Ass... | tiger_lab_math |
"statement 1": Mary played the game , getting at least one score of each of 1 , 2 , 3 , 4 , and 5 , and never getting the same score in consecutive steps, "statement 2" :Mary played the game , getting at least one score of each of 2 , 2 , 3 , 4 , and 5 , and never getting the same score in consecutive steps, "options:... | tiger_lab_math |
The expression $729x^3+8$ can be written as $(ax+b)(cx^2+dx+e)$. Find $a+b+c+d+e$. | tiger_lab_math |
Given a surface defined by the equation z = x^3 + y^3, determine the values of the principal curvatures at the point (-1, -1, -2). | tiger_lab_math |
$f(x)$ is a monic polynomial such that $f(0)=4$ and $f(1)=10$. If $f(x)$ has degree $2$, what is $f(x)$? Express your answer in the form $ax^2+bx+c$, where $a$, $b$, and $c$ are real numbers. | tiger_lab_math |
the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department take... | tiger_lab_math |
A road has four intersections. At the first intersection, there are 40 road signs showing different types of information mounted on the street poles. At the second intersection, 1/4 times more road signs than the first intersection are mounted on the street poles. The number of road signs at the third intersection is t... | tiger_lab_math |
"statement 1": Dacid obtained 73 , 69 , 92 , 64 and 82 marks ( out of 100 ) in English , Mathematics , Physics , Chemistry and Biology, "statement 2" :Dacid obtained more than 53 , 69 , 92 , 64 and 82 marks ( out of 100 ) in English , Mathematics , Physics , Chemistry and Biology, "options: " Entailment or contradicti... | tiger_lab_math |
Six positive integers from a list of nine positive integers are $6, 7, 2, 4, 8, 5$. What is the largest possible value of the median of this list of nine positive integers? | tiger_lab_math |
if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is ? Please respond by writing a program in Python. | tiger_lab_math |
if x is a positive integer , then the least value of x for which x ! is divisible by 100000 is ? can someone please explain intuitively what the question is asking ? Please respond by writing a program in Python. | tiger_lab_math |
the ratio of 3 numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ? Let's program in Python in the response. | tiger_lab_math |
a car gets 27 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 14 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ? Please write a program to solve it | tiger_lab_math |
3 numbers are in the ratio 3 : 5 : 7 . the largest number value is 70 . find difference between smallest & largest number is ? Please write a program to solve it | tiger_lab_math |
in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 15 , what is the greatest possible value of b x a ? Let's write a program. | tiger_lab_math |
Find the minimum value of the function f(x) = x^2 - 4x + 7, where x can be any real number, using simulated annealing method. | tiger_lab_math |
Using predicate logic, express the following statement mathematically:
"There exists a real number x such that x squared is equal to 2."
Then, using this statement, evaluate the truth value of the following assertion:
"For every real number x, if x squared is equal to 2, then x is irrational."
What conclusion ca... | tiger_lab_math |
a company decreased the price of its main product by 75 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ? Please write a program to solve it | tiger_lab_math |
a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 50 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ? Let's write a Pyt... | tiger_lab_math |
Mackenzie bought 142 feet of fencing with which to enclose her rectangular garden. If the numbers of feet in the lengths of the garden's sides are natural numbers, what is the maximum number of square feet that can be enclosed by the fencing? | tiger_lab_math |
the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 80 , and what number ? Let's program in Python in the response. | tiger_lab_math |
Consider a planar graph with 6 vertices and 9 edges. Determine the maximum number of regions that can be created when the graph is drawn on a plane without any edge intersection. | tiger_lab_math |
if m is a positive integer and m ^ 2 is divisible by 54 , then the largest positive integer that must divide m is ? Let's write a program. | tiger_lab_math |
60 men shake hands with each other . maximum no of handshakes without cyclic handshakes . Let's write a program. | tiger_lab_math |
In $\triangle RED$, $\measuredangle DRE=75^{\circ}$ and $\measuredangle RED=45^{\circ}$. $RD=1$. Let $M$ be the midpoint of segment $\overline{RD}$. Point $C$ lies on side $\overline{ED}$ such that $\overline{RC}\perp\overline{EM}$. Extend segment $\overline{DE}$ through $E$ to point $A$ such that $CA=AR$. Then $AE=\fr... | tiger_lab_math |
the distance between west - town to east - town is 20 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in ... | tiger_lab_math |
the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 8 of that total . what was the price of the basic computer ? Let's write a pr... | tiger_lab_math |
There are 50 oysters on the rocks at La Push Park and 72 crabs by the beach. Eric, who loves walking by the beach, makes a note of this and goes home. The next day, he realizes only half the number of Oysters were on the rocks, and only 2/3 the number of crabs as the previous day are on the beach. How many oysters and ... | tiger_lab_math |
there are 2 sections a and b in a class , consisting of 26 and 34 students respectively . if the average weight of section a is 50 kg and that of section b is 30 kg , find the average of the whole class ? Let's program in Python in the response. | tiger_lab_math |
in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 90 % people got computers and 85 % got air - conditionor . how many people ( minimum ) got all these luxury . Let's write a Python program. | tiger_lab_math |
a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year . Please write a program to solve it | tiger_lab_math |
Find the sum of all positive integers less than 196 and relatively prime to 98. Let's write a program. | tiger_lab_math |
In a Centipede game, two players A and B alternate taking turns. The game starts with a pot of $100. Every time a player takes their turn, they can either take 4 points from the pot or pass their turn. However, if a player passes their turn, the other player can take 10 points from the pot. The game ends when one playe... | tiger_lab_math |
What is the probability that out of a sample of 100 individuals from a certain demographic group, at least 20 will be affected by a certain disease, given that the overall proportion of affected individuals in the population from which the sample was drawn is known to be 0.3? | tiger_lab_math |
What is the exact value of the area of the largest circular disk that can be completely enclosed within the main cardioid of the Mandelbrot set? Round your answer to the nearest hundredth. | tiger_lab_math |
Consider a closed 2-manifold M, that is, a compact, boundaryless surface. Suppose M is orientable and has genus 2. Determine the number of non-isomorphic differentiable structures that M can have. | tiger_lab_math |
A right triangle has an angle of 60 degrees and the side opposite to the angle measures 6 cm. Find the lengths of the other two sides and the values of all six trigonometric ratios for this angle. | tiger_lab_math |
How many integers $n$ are there such that $3 \leq n \leq 10$ and $121_n$ (the number written as $121$ in base $n$) is a perfect square? | tiger_lab_math |
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ? Let's program in Python in the response. | tiger_lab_math |
tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 12 even numbers . his mother immediately worked out the answer . how much had he scored in math ? Let's write a Python program. | tiger_lab_math |
a is the average ( arithmetic mean ) of the first 7 positive multiples of 5 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ? Let's write a Python program to solve it. | tiger_lab_math |
p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 20 days to complete the same work . then q alone can do it in ? Please respond by writing a program in Python. | tiger_lab_math |
Suppose that a medical study is conducted to investigate the survival time of patients with a specific disease. The study follows 60 patients for a total of 50 weeks. After the end of the study, it is found that 20% of patients survived for at least 45 weeks.
What is the probability that a patient with this disease w... | tiger_lab_math |
points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction d of the area of triangle abc is the area of triangle xyz ? Let's write a Python program. | tiger_lab_math |
a = { 0 , 1 , - 3 , 6 , - 8 , - 10 } b = { - 1 , 2 , - 4 , 7 , 6 , - 9 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab < 0 ? Let's write a program. | tiger_lab_math |
in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many q cents does a liter of kerosene cost ? [ one dollar has 100 cents . ] ? Let's write a Python program. | tiger_lab_math |
A cylindrical tin can is to be made with a volume of 500 cubic centimeters. Find the dimensions of the can with the smallest surface area. | tiger_lab_math |
mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 25 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ? Please write a program to solve i... | tiger_lab_math |
there are 4 red books and 4 blue books on a shelf . if 2 books are selected at random from the shelf , what is the probability that both books selected are red books ? Please respond by writing a program in Python. | tiger_lab_math |
in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 37 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ? Let's program in Python in the response. | tiger_lab_math |
A cable of length 10 meters is cut into two pieces. The first piece is bent into a circle, while the second piece is bent into a square. What are the dimensions of the circle and square that maximize the total area enclosed by the two shapes? | tiger_lab_math |
Kaleb defined a $\emph{clever integer}$ as an even integer that is greater than 20, less than 120, and such that the sum of its digits is 9. What fraction of all clever integers is divisible by 27? Express your answer as a common fraction. Let's write a program. | tiger_lab_math |
Suppose you are trying to estimate the value of pi using the Monte Carlo simulation method. If you generate a million random points inside a circle with radius 1 inscribed in a square with side length 2, how would you estimate the value of pi using the proportion of points that fall inside the circle? | tiger_lab_math |
Consider the following network:
Find the maximum flow from node A to node E, and specify the flow along each edge that achieves this maximum. | tiger_lab_math |
the diagonal of a square is 40 m . the area of the square is : ? Please write a program to solve it | tiger_lab_math |
Consider a car moving on a straight road. The car starts from rest and has to cover a distance of 1000 meters in the minimum possible time. The car is subject to a maximum acceleration of 8 meters per second squared, and a maximum speed of 50 meters per second. Determine the minimum time that the car can take to cover ... | tiger_lab_math |
company t produces two kinds of stereos : basic and deluxe . of the stereos produced by company t last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last... | tiger_lab_math |
the diluted wine contains only 8 liters of wine and the rest is water . a new mixture whose concentration is 30 % , is to be formed by replacing wine . how many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ? Let's write a program. | tiger_lab_math |
A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every two leaps of the hare, the jackal takes three leaps. Find the ratio of the speed of the hare to the speed of the jackal.
Answer Choices: (A) 64:25 (B) 8:9 (C) 5:8 (D) 25:64 (E) 4:7 | tiger_lab_math |
find a number such that when 15 is subtracted from 7 times the number , the results is more than twice the number ? Please respond by writing a program in Python. | tiger_lab_math |
Let A and B be two sets such that A = {1, 3, 5} and B = {1, 2, 4}. Let C be the complement of A union B. Find the symmetric difference between (A symmetric difference B) and C. Show that the symmetric difference of two sets is not distributive over complement. | tiger_lab_math |
A company has three workers who can complete a project in 5, 6 and 10 days, respectively. What is the minimum time in which the project can be completed, assuming that the workers can work on the project at the same time? | tiger_lab_math |
Find the smallest positive integer solution to the equation $3^x \equiv 13 \pmod {19}$. | tiger_lab_math |
list i : 3 , 4 , 8 , 19 list ii : x , 3 , 4 , 8 , 19 ? Please write a program to solve it | tiger_lab_math |
The ratio of boys to girls at the dance was 3:4. There were 60 girls at the dance. The teachers were 20% of the number of boys. How many people were at the dance? | tiger_lab_math |
a pharmaceutical company received $ 2 million in royalties on the first $ 12 ; million in sales of generic equivalent of one of its products and then $ 4 million in royalties on the next $ 48 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 12 million in sal... | 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? Let's write a program. | tiger_lab_math |
a man two flats for $ 675958 each . on one he gains 12 % while on the other he loses 12 % . how much does he gain or lose in the whole transaction ? Let's program in Python in the response. | tiger_lab_math |
What is the minimum number of bags required to pack 16 identical tennis balls in such a way that no bag contains more than 3 balls and no two bags have exactly the same number of balls? Determine the treewidth of the resulting graph. | tiger_lab_math |
A factory produces light bulbs, and it is known from historical data that 2% of the bulbs are defective. If a sample of 1000 bulbs is selected at random from this factory’s production, what is the probability that the sample will contain less than 20 defective bulbs? | tiger_lab_math |
a gambler has won 40 % of his 40 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ? Let's write a Python program to solve it. | tiger_lab_math |
Find the number of permutations $(a_1, a_2, a_3, a_4, a_5, a_6)$ of $(1,2,3,4,5,6)$ that satisfy
\[\frac{a_1 + 1}{2} \cdot \frac{a_2 + 2}{2} \cdot \frac{a_3 + 3}{2} \cdot \frac{a_4 + 4}{2} \cdot \frac{a_5 + 5}{2} \cdot \frac{a_6 + 6}{2} > 6!.\] | tiger_lab_math |
a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 40 marks , find the maximum marks set for the test . Please write a program to solve it | tiger_lab_math |
A triangle has sides of lengths 8 cm, 10 cm, and 12 cm. Find the measure of the largest angle of the triangle using the law of cosines. | tiger_lab_math |
The difference equation of a digital system is given by $$ y[n]=8 x[n]+2 x[n-1]-x[n-2], $$ where $x[n]$ and $y[n]$ are, respectively the current samples of the input and the output signals of the system. Determine if the system is a FIR. | tiger_lab_math |
the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 8 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ? Let's program in Python in the response. | tiger_lab_math |
Jake is retrieving the notes on a communal board, putting all of the red notes in the complaints bin and all of the blue notes in the compliments bin. The red notes were in 5 rows with 6 notes in each row. There are 2 blue notes under each of the red notes, as well as another 10 blue notes scattered at the bottom of th... | tiger_lab_math |
sachin borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends money to rahul at 25 / 4 % p . a . for 2 years . find the gain of one year by sachin . Let's program in Python in the response. | tiger_lab_math |
Prove that the sum of two odd numbers is an even number. Then, find two odd numbers and verify this statement. | tiger_lab_math |
of 70 players on a cricket team , 37 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 |
The function f is defined for all positive integers m by the following rule. f(m) is the number of positive integers each of which is less than m and has no positive factor in common with m other than 1. If p is any 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 |
in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 14 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ? Let's write a Python program. | tiger_lab_math |
Six congruent copies of the parabola $y = x^2$ are arranged in the plane so that each vertex is tangent to a circle, and each parabola is tangent to its two neighbors. Find the radius of the circle.
[asy]
unitsize(1 cm);
real func (real x) {
return (x^2 + 3/4);
}
path parab = graph(func,-1.5,1.5);
draw(parab);
d... | tiger_lab_math |
a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a ? Let's program in Python in the response. | tiger_lab_math |
on dividing 136 by a number , the quotient is 9 and the remainder is 1 . find the divisor ? Let's write a program. | tiger_lab_math |
What is the smallest positive integer with exactly 10 positive integer divisors? | tiger_lab_math |
In a race where 16 cars are running, the chance that car X will win is 1/4, that Y will win is 1/12 and that Z will win is 1/7. Assuming that a dead heat is impossible, find the chance that one of them will win.
Answer Choices: (A) 1/140 (B) 10/21 (C) 27/410 (D) 11/21 (E) 57/120 | tiger_lab_math |
a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 900 . find the sum ? Please respond by writing a program in Python. | tiger_lab_math |
At the beginning of an academic year, there were 15 boys in a class and the number of girls was 20% greater. Later in the year, transfer students were admitted such that the number of girls doubled but the number of boys remained the same. How many students are in the class now? | tiger_lab_math |
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