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Junior has x rabbits. On Monday, he bought 6 toys for his rabbits. On Wednesday, he bought twice as many toys as he did Monday. On Friday, he bought four times as many toys as he did on Monday, and on the next day he bought half as many toys as he did on Wednesday. If he split all the toys evenly between the rabbits, E... | tiger_math |
In what time will a train 150 m long cross an electric pole, if its speed is 220 km/hr? | tiger_math |
Find the point of tangency of the circle $x^2+y^2=25$ and the line $y=2x-3$.
Note: The problem requires finding the point where the line touches the circle, which involves using the concept of tangency and the properties of circles, rather than just finding the intersection of two lines. | nvidia_math |
What is the product of the first 5 positive odd integers? | nvidia_math |
Gretchen read that you should spend 10 minutes walking for every 90 minutes you spend sitting. If Gretchen spends 6 hours working at her desk, how long will she spend walking? | tiger_lab_math |
Simplify $\frac{7}{\sqrt{343}}$ by rationalizing the denominator. | nvidia_math |
Skyler is a composer. He wrote 25 hit songs that made it on the top 10 charts; ten more songs that made it on the top 100 charts than the hit songs; 5 fewer songs than the hit songs that were never released. How many songs did Skyler write in all? | tiger_math |
For the number \( a = 875952 \), what is the remainder when \( a \) is divided by 1000? Additionally, is \( a \) divisible by 1000? | automath |
Consider an ellipse defined by the equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\). If the lengths of the semi-major and semi-minor axes are \(a = 5\) and \(b = 3\), respectively, determine the distance between the foci of the ellipse. Express your answer in simplest form. | automath |
Evaluate \begin{align*} (3x^2 - 7x + 2)(4x - 5) \end{align*} when $x = -\frac13$. | tiger_math |
Emily loves to collect stuffed animals. She has 8 pandas, twice as many kittens, and a tiger. Her grandmother decided to give her three more pandas for every two kittens she has. How many stuffed animals Emily has in total? | nvidia_math |
Suppose we have an algebraic surface defined by the equation 4x^2 + y^2 + z^2 = 16. Calculate the equation of the tangent plane to this surface at the point (1, 2, 2). | tiger_lab_math |
Problem:
The graph of the parabola $x = 2y^2 - 6y + 3$ has an $x$-intercept $(a,0)$ and two $y$-intercepts $(0,b)$ and $(0,c)$. Find $a + b + c$.
New Problem:
The graph of the function $f(x) = \sqrt{3x - 2}$ intersects the graph of the function $g(x) = x^2 - 2x + 1$ at two points, $(p, q)$ and $(r, s)$. Find $p + r$.... | nvidia_math |
"statement 1": After they have worked together for 12 days peter stops and Peter completes the remaining work in 10 days, "statement 2" :After they have worked together for less than 32 days peter stops and Peter completes the remaining work in 10 days, "options: " Entailment or contradiction or neutral? Let's write a... | tiger_lab_math |
Prints a page 50 pg per min .If the printed for 2 hours except 15 min.Where there
was an paper jam,how many page did it print
Answer Choices: (A) 10,880 (B) 12,880 (C) 5,250 (D) 8,880 (E) 18,880 | tiger_lab_math |
Find the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n^2 + 2n + 1}$ and then use this result to compute $\lfloor \frac{1}{S^2} \rfloor$. | nvidia_math |
What is the smallest positive multiple of $23$ that is $4$ more than a multiple of $89$? | nvidia_math |
There are 250 scraps. For each 11 cutting one extra can be obtained. How much maximum is possible, if one cut by one unit?
Answer Choices: (A) 271 (B) 272 (C) 273 (D) 274 (E) 275 | tiger_lab_math |
Given a sphere with center \( P(x_0, y_0, z_0) \) and radius \( r \), how many points with integer coordinates \( (x, y, z) \) satisfy the inequality \( (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 \leq r^2 \) if \( r = 5 \) and the center \( P \) is at \( (1, 2, 3) \)? | automath |
What is the maximum number of non-overlapping circles of area 1 that can be packed onto the surface of a sphere with a radius of 1? | automath |
In a survey, a certain number of students read book A and book B. 20% of those who read book A also read book B, and 50% of those who read book B also read book A. If each student read at least one of the books, the difference between the number of students who read only book A and the number of students who read only ... | tiger_math |
If Jack currently has $43 in his piggy bank and receives a weekly allowance of $10, and he saves half of his allowance in his piggy bank every week, how much money will Jack have in his piggy bank after 8 weeks? | tiger_math |
Given that \( a \), \( b \), and \( i \) are integers, determine whether the equation \( 2b + 1 = a \) holds true.
(1) When \( i \) is divided by 4, the quotient is \( a \) and the remainder is 3.
(2) When \( i \) is divided by 8, the quotient is \( b \) and the remainder is 7.
Is it sufficient to conclude wheth... | automath |
Given a horizontal force of \( \vec{F} = 400 \) lbs acting at point A of a structure, determine the angle \( \phi \) such that the component of \( \vec{F} \) along line AB has a magnitude of \( 600 \) lbs. What is the value of \( \phi \)? | automath |
What is the value of the Legendre polynomial \( P_n(1) \) for any non-negative integer \( n \), and how does this relate to the generating function for Legendre polynomials? | automath |
If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
Answer Choices: (A) 100 (B) 10 (C) 0.01 (D) 0.0001 (E) 0.0001 | tiger_lab_math |
C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If B of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goa... | tiger_lab_math |
What is the value of the limit \( L = \lim_{n \to \infty} \left| \frac{b_{n}}{b_{n-1}} \right| \) for the series \( \sum_{n=1}^{\infty} b_{n} \) where \( b_{1} = 5 \) and \( b_{n} = \frac{(-1)^{n} n b_{n-1}}{3n+1} \) for \( n \geq 2 \), and what does this limit imply about the convergence or divergence of the series? | automath |
Ammonia is a compound consisting of one nitrogen atom and three hydrogen atoms. What is the molecular weight of Ammonia? | tiger_math |
A stream cipher generates a pseudorandom binary sequence (PRBS) that is combined with the plaintext message using an exclusive OR (XOR) operation to generate the ciphertext. Imagine that you have a PRBS of length 32 and the plaintext message "11001100". Find the ciphertext generated by the stream cipher if the initial ... | tiger_lab_math |
a is the average (arithmetic mean) of the first some positive multiples of a number and b is the median of the first 3 positive multiples of positive integer n. The value of a^2 - b^2 is zero, and the value of n is 14. What is the number whose multiples are used to find the average? | tiger_math |
When flipping a fair coin three times, what is the probability that the first two flips are both heads and the third flip is tails? Express your answer as a common fraction. | tiger_math |
A scientist is studying the growth of a special type of bacteria in a laboratory. The number of bacteria doubles every hour. If the scientist starts with an initial count of bacteria represented by $n$, and after 5 hours the lab records a total of 320 bacteria, what was the initial number of bacteria? | tiger_math |
Four prime numbers are randomly selected without replacement from the first ten prime numbers. What is the probability that the sum of the four selected numbers is odd? Express your answer as a common fraction. | tiger_lab_math |
"statement 1": Jerry travels 8 miles at an average speed of 40 miles per hour , stops for 12 minutes , and then travels another 20 miles at an average speed of 60 miles per hour, "statement 2" :Jerry travels more than 3 miles at an average speed of 40 miles per hour , stops for 12 minutes , and then travels another 20... | tiger_lab_math |
Lily puts 5 sweaters in a storage container. She adds three times as many scarves as sweaters in the container. She also adds a quarter as many hats as scarves in the container. In total, how many items is Lily storing? | nvidia_math |
Simplify $\sqrt[4]{27x^6y^8z^{13}}$ and find the product of the exponents of the variables outside the radical. | nvidia_math |
In triangle $ABC$, points $D$ and $E$ are on sides $AB$ and $AC$ respectively, such that $\angle BCD = 2\angle A$ and $\angle CBE = 2\angle A$. If $\angle BAC = 40^\circ$, find the measure of angle $A$ in degrees. | nvidia_math |
A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?
Answer Choices: (A) 33 (B) 13 (C) 88 (D) 77 (E) 12 Please write a program to solve it | tiger_lab_math |
What are the necessary conditions for a convex body \( K \subseteq \mathbb{R}^n \) to have its circumscribed ellipsoid of minimum Hilbert-Schmidt norm represented as a ball, in relation to the Löwner ellipsoid of \( K \)? | automath |
What are the possible isomorphism types of groups of order 36, and how many non-abelian groups of this order exist? | automath |
For a school bake sale, 25 students were asked to bring in 15 cupcakes each. 18 students were asked to bring in 20 muffins each and 12 students were asked to bring in 18 cookies each. If they sell everything for $1.50 each, how much money will they raise? | nvidia_math |
The ratio of the measures of the two acute angles of a right triangle is $3:5$. In degrees, what is the measure of the largest angle of the triangle? | nvidia_math |
Seven months ago, Emily earned 8 times more money than David. If her salary has increased by 25 percent now, and David's salary then was $1200, calculate Emily's salary now. | nvidia_math |
Given the vector space \(\mathbb{R}^3\), consider the set of all linear combinations of the vectors \((1, 0, 0)\), \((0, 1, 0)\), and \((0, 0, 1)\). What is the dimension of this vector space, and what is a basis for it? | automath |
Five identical rectangles are arranged to form a larger rectangle $ABCD$, as shown. The area of $ABCD$ is $3000$. If the width of each rectangle is half of its length, what is the length of each rectangle, rounded to the nearest integer? | tiger_math |
Let $a,$ $b,$ and $c$ be positive real numbers such that $a + b + c = 2.$ Find the minimum value of
\[\frac{ab + bc + ca}{abc}.\] | nvidia_math |
one night 16 percent of the female officers on a police force were on duty . if 160 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ? | tiger_math |
The townspeople requested that he makes a chocolate cake. He will need 306 lbs. of cocoa powder. The mayor already gave him some amount of cocoa powder. He still needs 47 lbs. of cocoa powder. How much cocoa powder did the mayor give him? | tiger_math |
In the equation 2x – cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 5 ?
Answer Choices: (A) −9/2 (B) -1 (C) -3 (D) 4 (E) 9/2 | tiger_lab_math |
Let the line \(3x + 4y = 2\) be given. If the point \((2, -1)\) is on this line, find the coordinates of the point on the same line that is exactly 5 units away from \((2, -1)\). | automath |
There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with a certain number of other amateurs, the total number of chess games possible to be played in the tournament is 40. How many other amateurs does each chess amateur play with? | tiger_math |
x , a , z , and b are single digit positive integers . x = 1 / 6 a . z = 1 / 6 b . ( 10 a + b ) – ( 10 x + z ) could not equal ? Please write a program to solve it | tiger_lab_math |
during a sale , the price of a pair of shoes is marked down 13 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ? | tiger_math |
Given the following sequence of goals scored by a team in 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3, calculate the mean, median, and mode of these scores. What is the most frequently occurring score? | automath |
Given that $b$ is a multiple of $324$, find the greatest common divisor of $5b^4+2b^3+6b+81$ and $b$. | tiger_math |
A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $30000 was awarded in $1250 scholarships, how many $4000 scholarship... | tiger_lab_math |
A garrison of 2000 men has provisions for 54 days. At the end of 21 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
Answer Choices: (A) 1977 (B) 1893 (C) 1979 (D) 1900 (E) 1300 | tiger_lab_math |
the rear – most end of a 66 foot truck exits a 330 foot tunnel exactly 6 seconds after the front – most end of the truck entered the tunnel . if the truck traveled the entire tunnel at a uniform speed , what is the speed of the truck in miles per hour ( 1 mile = 5,280 feet ) ? Please respond by writing a program in Pyt... | tiger_lab_math |
3/5 of the mangoes on a mango tree are ripe. If Lindsay eats x% of the ripe mangoes, calculate the number of ripe mangoes remaining if there were 400 mangoes on the tree to start with. The answer is 96. What is the value of unknown variable x? What is the value of unknown variable x? | tiger_math |
What is the relationship between the sectional curvature and the scalar curvature in Riemannian geometry, and can you provide a specific example of a manifold where this relationship can be explicitly calculated? | automath |
Given two points on a line, (2, 7) and (2, -6), what is the slope of the line that passes through these points? | automath |
A bag contains 100 marbles, numbered consecutively from 0 to 99. Another bag contains 60 marbles, numbered consecutively from 90 to 149. If one marble is chosen at random from each bag, what is the probability that the two chosen marbles have the same number? Express your answer as a reduced fraction. | automath |
Let \( A = \{ a, b, c, d \} \) and consider the relation \( R_1 = \{ (a,a), (b,b), (c,c), (d,d) \} \). Determine whether \( R_1 \) is reflexive, symmetric, and transitive. Provide a clear justification for each property based on the definitions of reflexivity, symmetry, and transitivity of relations. | automath |
Solve the following intuitionistic logic problem:
Consider the proposition P = "There exists a natural number that is both even and odd."
1. Is P true or false in classical logic?
2. Is P true or false in intuitionistic logic? | tiger_lab_math |
The maximum load that a horizontal beam can carry is directly proportional to its width. If a beam 1.5 inches wide can support a load of 250 pounds , find the load that a beam of the same type can support if its width is 3.5 inches? | tiger_math |
Let $a,$ $b,$ $c$ be the roots of $x^3 - 5x^2 + k = 0,$ where $k$ is a constant. Find the value of $k$ such that $a,$ $b,$ $c$ are in arithmetic progression. | nvidia_math |
After receiving $2000 from the bank, Emma purchased $400 worth of furniture and gave 3/4 of the remaining amount to her friend Anna. How much money does Emma have left? | tiger_math |
Here's a precise numerical problem for a math student to solve in the Discrete logarithm problem of Number theory:
Find the discrete logarithm of 5 modulo 11. | tiger_lab_math |
Let $f(n)$ return the number of distinct ordered pairs of positive integers $(a, b)$ such that for each ordered pair, $a^2 + b^2 = n$. Note that when $a \neq b$, $(a, b)$ and $(b, a)$ are distinct. The smallest positive integer $n$ for which $f(n) = X$ is 50. What is the value of unknown variable X? | tiger_math |
What is the total number of distinct arrangements of the letters in the phrase "MATHS IS THE BEST" if all consonants must be grouped together? | automath |
Kyle knows that $4 = 2^{5r+1}$. What is the value of $r$? Express your answer as a common fraction. | nvidia_math |
Given the vertices \( A = (0, 0) \) and \( B = (6, 0) \) of a triangle, and the centroid \( P = (4, 2) \), find the coordinates of the third vertex \( C \). | automath |
A triangular array of squares has one square in the first row, two in the second, and in general, $k$ squares in the $k$th row for $1 \leq k \leq 11.$ With the exception of the bottom row, each square rests on two squares in the row immediately below (illustrated in the given diagram). In each square of the eleventh ro... | nvidia_math |
If \( 2 \sin{2\theta} = \cos{2\theta} \), find all the possible values of \( \theta \) in the interval \( [0, 2\pi) \). | automath |
A circular table is divided into 16 equal sectors, and 8 identical pieces of paper are placed on the table so that each piece covers one or more sectors. If the entire table cannot be covered, what is the largest number of sectors that can be covered? | nvidia_math |
A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase?
Answer Choices: (A) 9 (B) 10 (C) 11 (D) 12 (E) 13 Let's write a Python program to solve it. | tiger_lab_math |
A right triangle has legs of length 14 cm and 8 cm. In centimeters, what is the perimeter of the triangle if its hypotenuse is 9 cm? | tiger_math |
Emily has six packets with twelve stickers in each packet. Her friend gave her three packets with nine colorful stamps. If she decides to give 75 stickers and stamps to her siblings, how many does she have left? | nvidia_math |
What is the probability of drawing at most 2 defective floppy disks when randomly selecting 10 from a lot of 100 disks, where 20 are known | automath |
Matt is playing basketball. In the first quarter, he made 2-point shots four times and 3-point shots twice. How many points did he score for that quarter? | tiger_lab_math |
Consider an infinite plane with a uniform charge density \(\sigma\). According to Gauss's law, what is the magnitude of the electric field (\(E\)) produced by this infinite sheet of charge at a distance \(d\) from the sheet? Express your answer in terms of \(\sigma\) and constants. | automath |
the average runs scored by a batsman in 22 matches is 28 . in the next 13 matches the batsman scored an average of 15 runs . find his average in all the 35 matches ? Let's write a Python program to solve it. | tiger_lab_math |
Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Answer Choices: (A) 12, 9 (B) 10, 5 (C) 12, 7 (D) 11, 6 (E) 14, 3 | tiger_lab_math |
What is the value of $2^2\times3^2\times5^3\times7$? | tiger_math |
A bag contains 6 red marbles, 4 blue marbles, and 2 green marbles. If 3 marbles are drawn from the bag at random without replacement, what is the probability that exactly 2 of them are blue? | nvidia_math |
Find the smallest positive integer k such that k!, when divided by the square of its highest prime factor, is a perfect square.
Solution:
7 (which gives k = 7) | nvidia_math |
Emily purchased 5 new pens for her art class. 3 of them are blue, one is red, and the other one is purple. The total cost was $30. If the red pen cost $8, and the purple one cost $5, how much did the blue pens cost each? | nvidia_math |
What is the approximate value of the real root of the cubic polynomial \( x^3 - 2x - 5 = 0 \) accurate to six decimal places? | automath |
Compute: $\frac{1}{7} + \frac{2}{7} + \frac{3}{7} + \dots + \frac{13}{7} + \frac{14}{7}$. | nvidia_math |
Sofia ran 24 kilometers, which was three times as far as her brother ran. How many kilometers did Sofia and her brother run in total? | nvidia_math |
In a triangle $DEF$, the angles satisfy the equation
\[\sin 2D + \sin 2E + \sin 2F = \frac{1}{2}.\]Given that two sides of the triangle have lengths 8 and 15, find the minimum length of the third side. | nvidia_math |
Consider the function f(x) = 2x^3 - 9x^2 + 12x + 5. Find the maximum and minimum values of this function on the interval [-3, 4]. | tiger_lab_math |
Given an elliptic curve \( E \) with a point \( P \), suppose \( \mathscr{O}_E(2P) \) has a global section \( s \) that vanishes at \( P \) with order 2, and another section \( t \) in \( \mathscr{O}_{\mathbb{P}^1}(1) \) that pulls back to \( s \). What can be said about the preimage of the zero of \( t \) under the ma... | automath |
The ages of five siblings are consecutive integers. If the sum of their ages is 80, what is the age of the middle child? | nvidia_math |
In a Cartesian coordinate system, a circle with a radius of 5 units is centered at the origin (0,0). A line is drawn from the origin to a point (a,b) on the circle. Another line is drawn from the origin to a point (c,d) on the circle. The two lines form an angle of 60 degrees. Determine the value of a + b + c + d. | nvidia_math |
s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. There are a certain number of digits in s(99). How many perfect squares are attached to form s(99)? | tiger_math |
How many different license plates can be created using three letters followed by three digits, with the condition that no two adjacent letters or digits can be the same? | tiger_math |
Evaluate the expression $(120 \div 6) \div 5$. | tiger_math |
A canoeist paddles upstream at a speed of 5 km/h relative to the water. When paddling downstream, his speed is 3 km/h faster than when paddling upstream. If the speed of the current is 1.5 km/h, what is the canoeist's average speed for a round trip of 20 km? | nvidia_math |
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