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Is there a sequence of Riemann integrable functions \( \{ f_n \} \) that converges pointwise to a function \( f \) which is not Riemann integrable? If so, please provide an explicit example and compute the integral of the limit function over the interval [-2, 3]. | automath |
Emily has 15 members of her family on her mother's side. Her father's side is 40% smaller. How many people are there in total? | nvidia_math |
The sum of a number and its square is 1406. What is the number?
Answer Choices: (A) 1409 (B) 1402 (C) 1221 (D) 1406 (E) 8828 | tiger_lab_math |
For what values of $b$ is $-2$ not in the range of the function $f(x)=x^2+bx+2$? Express your answer in interval notation. | nvidia_math |
What integer $n$ satisfies $0\le n<{101}$ and $$100n\equiv 72\pmod {101}~?$$ | nvidia_math |
Rick can iron 4 dress shirts in an hour. He can iron x dress pants in an hour. If he spends 3 hours ironing dress shirts and 5 hours ironing dress pants, how many pieces of clothing has he ironed?
If we know the answer to the above question is 27, what is the value of unknown variable x? | tiger_math |
What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers? | nvidia_math |
In a convex quadrilateral ABCD, the diagonals AC and BD intersect at a point E. If the ratio of the length of AE to the length of CE is 2:3, and the ratio of the length of BE to the length of DE is 3:4, determine the ratio of the area of triangle ABE to the area of triangle CDE. | nvidia_math |
$A$, $B$, $C$, and $D$ are points on a circle, and segments $\overline{AC}$ and $\overline{BD}$ intersect at $P$, such that $AP=8$, $PC=1$, and $BD=6$. Find $BP$, given that $BP < DP.$
[asy]
unitsize(0.6 inch);
draw(circle((0,0),1));
draw((-0.3,0.94)--(0.3,-0.94));
draw((-0.7,-0.7)--(0.7,-0.7));
label("$A$",(-0.3,0... | tiger_lab_math |
Determine all real numbers $x$ such that $(2-3i)x$ is equal to its complex conjugate. | nvidia_math |
In MATLAB, I have a function defined as follows:
```matlab
myfun = @(x, z) x' * x + z;
```
If I create a random 500x500 matrix `x`, and compute the output of `myfun(x(:, k), z)` for all columns `k = 1` to `500` and for scalars `z = 1, 2, 3, \ldots, 500`, what will be the total number of distinct outputs produced by t... | automath |
a group of men decided to do a work in 10 days , but 5 of them became absent . if the rest of the group did the work in 12 days , find the original number of men ? Let's write a Python program to solve it. | tiger_lab_math |
When positive integer G is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when G is divided by B?
Answer Choices: (A) 13 (B) 14 (C) 15 (D) 16 (E) 17 | tiger_lab_math |
Look at this series: 404, 369, 334, 299, 264, 229, 194 ... What number should come next?
Answer Choices: (A) 194 (B) 108 (C) 106 (D) 107 (E) 104 | tiger_lab_math |
a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 25 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he ... | tiger_lab_math |
Passage: Following their impressive divisional home win over the Vikings, the Lions flew to Lincoln Financial Field for an intraconference fight with the throwback-clad Philadelphia Eagles. In the first quarter, Detroit trailed early as Eagles RB Brian Westbrook ran 25 yards for a TD. The Lions tied the game on a Kevi... | tiger_lab_math |
Let $f(x) = x - \sin x$ for every real number $x$. If $n$ is a positive integer, define $b_n$ by
\[
b_n = f \Bigl( f \Bigl( f \Bigl( \cdots f \Bigl( \frac{n}{\pi} \Bigr) \cdots \Bigr) \Bigr) \Bigr),
\]where there are $n$ iterations of $f$. For example,
\[
b_4 = f \Bigl( f \Bigl( f \Bigl( f \Bigl( \frac{4}{\pi} \B... | nvidia_math |
The graph of $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ has its vertices at $(\pm 5, 0)$, while the graph of $\frac{x^2}{a^2}-\frac{y^2}{b^2} = 1$ has its asymptotes $y = \pm 3x.$ Compute the value of $|ab|$. | nvidia_math |
A triangle is randomly chosen from all possible triangles with vertices on the points $(0,0)$, $(0,3)$, $(4,0)$, and $(4,3)$. What is the probability that the chosen triangle has a right angle? | nvidia_math |
Fernanda purchased six audiobooks from Audible to listen to from her audible app. If each audiobook was x hours long and she listened to 2 hours of an audiobook each day, It took her 90 total time to finish the six audiobooks. What is the value of unknown variable x? | tiger_math |
What is the area of a circle with a radius of 1, and how does this relate to the definition and properties of the unit circle? | automath |
Container A contains 12 red marbles and 6 blue marbles; containers B and C each hold 4 red marbles and 8 blue marbles. A container is chosen at random and then a marble is randomly chosen from that container. What is the probability that the marble selected is blue? Express your answer as a common fraction. | nvidia_math |
If x/y = 10/4 and y = 18, what is the value of x? | tiger_math |
Grant has worked as a freelance math worker for the last three months. The first month he made 350$. The second month he made 50$ more than double he made the first month. The third month he quadrupled the sum of the first two months. How much did Grant make in his first three months total? Please respond by writin... | tiger_lab_math |
In a village of 100 people where an unknown number are pickpockets, if we can remove any number of villagers each day, and each pickpocket can only pickpocket one person per day, what is the optimal strategy to identify all pickpockets, and what is the maximum number of days required to ensure every pickpocket is ident... | automath |
the sum of all two digit numbers divisible by 5 is
Answer Choices: (A) 945 (B) 3487 (C) 28 (D) 279 (E) 1287 | tiger_lab_math |
An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
Answ... | tiger_lab_math |
Fred wants to order a variety pack of sliced meats for the upcoming game. He can order a 4 pack of fancy, sliced meat for $40.00 and add rush delivery for an additional 30%. With rush shipping added, how much will each type of sliced meat cost? | tiger_lab_math |
Given a triangle ABC, where AB = 5 cm, BC = 6 cm, and AC = 7 cm, find the length of the shortest line segment PQ that is tangent to circles D and E, where D is inscribed in triangle ABC and E is circumscribed around triangle ABC. | nvidia_math |
Socorro is preparing for a math contest. She needs to train for a total of x hours. Each day, she answers problems about multiplication for 10 minutes and then division problems for 20 minutes. It will take her 10 days to complete her training. What is the value of unknown variable x? What is the value of unknown varia... | tiger_math |
Five consecutive two-digit positive integers, each less than 40, are not prime. What is the largest of these five integers? | tiger_math |
What is the relationship between the historical use of infinitesimals in calculus and the modern framework of non-standard analysis, and how do they compare in terms of rigor and applicability in mathematical analysis? | automath |
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 $f^{-1}(-3)+f^{-1}(0)+f^{-1}(3)$. | nvidia_math |
In a class of 25 students taught by Mr. Bolton, 2/5 of the students like math, 1/3 of the remaining students like science, and the rest of the students like history. What is the total number of students who like math and history combined? | tiger_math |
Given a positive integer \( p \) and a nonzero rational number \( r = \frac{a}{b} \), where \( a \) and \( b \) are integers, determine the \( p \)-adic valuation \( v_p(r) \) and explain how it relates to the largest power of \( p \) that divides \( r \). Additionally, if \( r = \frac{2^5 \cdot 3}{5^2} \), compute \( ... | automath |
The rim of a standard basketball hoop is 10 feet above the ground. Additionally, most experts will say that a player must be able to reach at least 6 inches above the rim to dunk a basketball. Suppose a basketball player is 6 feet tall and can reach x inches above their head using the wingspan of their arms. This pla... | tiger_math |
Roberta wants to have a dinner party centered around soufflés. Each savory souffle calls for 8 eggs each and the dessert ones call for 6 eggs each. She wants to make 3 savory soufflés and 5 dessert soufflés for the party. How many eggs will she need? Please write a program to solve it | tiger_lab_math |
A cube has a smaller cube inscribed within it, sharing the same center. The larger cube has side length $10$, while the smaller cube has side length $8$. A sphere is circumscribed around the smaller cube, and a sphere is inscribed within the larger cube. A point $Q$ is chosen at random inside the larger cube. What is t... | nvidia_math |
What is the probability that when we randomly select a 5-letter word from the English language, its letters are not in alphabetical order? | nvidia_math |
Let $g(x) = \begin{cases} \sin x &\text{if } x<m, \\ 2x-m &\text{if }x\ge{m}. \end{cases}$
If the graph $y=g(x)$ has exactly one point of discontinuity, find the smallest possible value of $m$. | nvidia_math |
The local grocery store is having a sale on soda. Each 12-ounce can costs $0.75. If Sarah wants to buy at least 60 ounces of soda, what is the minimum amount of money she needs to spend? | tiger_math |
Find $\tan \frac{9 \pi}{4}.$ | tiger_lab_math |
Each year Dani gets 4 pairs of two pants each as pay winning the best Amazon buyer of the season. If he initially had 50 pants, calculate the number of pants he'll have in 5 years. | nvidia_math |
Find the integer that is closest to $1000\sum_{n=3}^{10000}\frac1{n^2-4}$. | nvidia_math |
If sum of the first 11 terms of arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?
Answer Choices: (A) 0 (B) -1 (C) 1 (D) Not unique (E) None of these | tiger_lab_math |
Emily recently got some new CDs and wants to organize her music collection. After adding the new CDs to her music rack, she finds out that she has enough CDs to completely fill her music rack with 5 CDs left over. Before buying the new CDs, Emily had 30 CDs in her music rack. If her music rack has 3 shelves and can hol... | nvidia_math |
Given two \( m \times n \) data matrices \( A \) and \( B \) with \( n = 2 \), let \( C' = A^T B \) and assume the singular value decomposition of \( C' \) is \( C' = U \Sigma V^T \). If \( R = V U^T \) is the rotation matrix derived from this SVD, how can we verify whether the eigenvalues of the covariance matrix \( C... | automath |
How many ways can we arrange a set of 10 distinct CDs on a shelf, and can you explain the reasoning behind the calculation? | automath |
Calculate the value of $g(g(g(g(2)))), where $g(x)$ is defined as follows: $g(x) = x^3$ if $x > 0$ and $g(x) = -x - 5$ if $x \le 0$. | tiger_math |
For all positive integers m and v, the expression m θ v represents the remainder when m is divided by v. What is the value of ((90 θ 33) θ 17) - (99 θ (33 θ 17))? | tiger_math |
John pays for a candy bar with 4 quarters, x dimes, and a nickel. He got 4 cents back in change. How many cents did the candy bar cost?
If we know the answer to the above question is 131, what is the value of unknown variable x? | tiger_math |
Jonathan's full name contains 8 letters for the first name and 10 letters for the surname. His sister's name has 5 letters for the first name and 10 letters for the second name. What's the total number of letters in their names? | tiger_math |
A bicycle has two wheels with radii of 1.2 meters and 0.3 meters, respectively. If the larger wheel makes 200 revolutions, how many revolutions does the smaller wheel make? | tiger_math |
Caroline can make eleven lassis out of two mangoes. How many lassis can she make out of twelve mangoes? | tiger_math |
There are 30 players on a football team. The coach has 8 liters of water. She pours x milliliters of water for every player so they can get hydrated. Unfortunately, there was a water spill and 250ml of water was spilled. How much water was left over?
If we know the answer to the above question is 1750, what is the valu... | tiger_math |
Consider the functions \( f(x) = \frac{x}{x} \) and \( g(x) = \frac{|x|}{x} \).
1. Determine the domain of each function.
2. Compare the values of \( f(x) \) and \( g(x) \) for \( x < 0 \), \( x = 0 \), and \( x > 0 \).
What can you conclude about the differences in the behavior of these two functions based on your... | automath |
Given three fields \( F \subseteq K \subseteq L \), if the dimension of \( L \) over \( K \) is 3, and the dimension of \( K \) over \( F \) is 2, what is the dimension of \( L \) over \( F \) according to the Tower Law? | automath |
A rocket is launched from Earth's surface with an initial velocity of 400 m/s. The rocket has a mass of 2000 kg and is fueled with a rocket propellant that can provide a thrust of 90,000 Newtons. Assuming that air resistance is negligible, what is the optimal control strategy to maximize the altitude achieved by the ro... | tiger_lab_math |
Kevin has been for a run and wants to calculate how far he traveled. He ran at 10 miles per hour for half an hour, 20 miles per hour for half an hour, then ran at 8 miles per hour for 15 minutes. How many miles has Kevin run? | tiger_math |
a man is 28 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ? Let's write a program. | tiger_lab_math |
Given the radius \( r = 2 \), what is the area of a circle calculated using the gauge mark for \( \pi \) on a slide rule? Provide your answer to two decimal places. | automath |
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. However, if the snail reaches the top of the well, it will stay there. How many days will it take for the snail to reach the top of the well? | nvidia_math |
Given that the sequence described is the Fibonacci sequence, where each term is the sum of the two preceding terms and defined as \( s_1 = 1, s_2 = 1, s_3 = 2, \ldots \), what is the value of \( s_{12} \)? | automath |
Find the monic quadratic polynomial, in $x,$ with real coefficients, which has $3 + 2i$ as a root. | nvidia_math |
Given that the vector $\mathbf{v} = \begin{pmatrix} x \\ y \\ z \end{pmatrix}$ is orthogonal to both $\mathbf{u}_1 = \begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix}$ and $\mathbf{u}_2 = \begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix}$, and that the magnitude of $\mathbf{v}$ is $\sqrt{42}$, determine the value of $x + y + z$. | nvidia_math |
Randy had some money. Smith gave him another $200. Randy then gave Sally $1,200 and kept the rest. If Randy has $2000 left, how much money, in dollars, did Randy have at first? | tiger_math |
Given the function \( y = (p^{x^p})(x^p) \) where \( p > 0 \), compute \( \frac{dy}{dx} \) and find the value of \( \frac{dy}{dx} \) at \( x = 1 \). | automath |
a group of 3 investors and 3 clients recently frequented the chinese luyang restaurant . the total bill for the meal , including 20 % gratuity , came to $ 720 . on average , how much did the meal of each individual cost before gratuity ? Please write a program to solve it | tiger_lab_math |
Consider the elliptic curve defined by the equation: y^2 = x^3 + 2x + 2 over the finite field of order p, where p = 17.
1. Calculate the number of points on the elliptic curve over the field Fp.
2. Find a point G on the curve with the maximum possible order (i.e., order greater than or equal to p).
3. Given a point P ... | tiger_lab_math |
2^46655 mod 9 = ?
Answer Choices: (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 | tiger_lab_math |
Abe finds 4 ants on the sidewalk. Beth sees 50% more ants than Abe. CeCe watches twice as many ants as Abe. Duke discovers half as many ants as Abe. The x children find 20 ants together. What is the value of unknown variable x? What is the value of unknown variable x? | tiger_math |
For a set of 10 different stocks, how many different ways can you list 3 of them in order, where the order of selection matters? | automath |
In a high-tech laboratory, a scientist is working with a specialized robotic arm that can only read and process numbers in hexadecimal (base 16). The arm has collected samples of three different materials, each labeled with a specific mass in hexadecimal: $A3C2_{16}$ grams of silicon, $82B1_{16}$ grams of copper, and $... | nvidia_math |
If m = 3^n, what is the greatest value of n for which m is a factor of 22!
Answer Choices: (A) 8 (B) 10 (C) 9 (D) 14 (E) 16 | tiger_lab_math |
Let $\theta$ be an angle such that $\sin 2 \theta = \frac{1}{3}.$ Compute $\sin^6 \theta + \cos^6 \theta.$ | tiger_lab_math |
if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 2 = 1 / ( ( 10 ) ^ 4 ) , then m = ? Please write a program to solve it | tiger_lab_math |
Bogan laid out 10 maggots for her pet beetle. The beetle only ate 1 and Bogan had to throw out the rest. Later that day, she tried feeding again and the beetle ate 3. If Bogan served 20 maggots in total, how many did she attempt to feed the beetle the second time? | tiger_lab_math |
Tough and Tricky questions: Combinations.
seven contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
Answer Ch... | tiger_lab_math |
Given a circle of radius \( R \) centered at the origin, denote the positive y-intercept of the circle by \( (0, R) \). If the circle is shifted \( n \) units horizontally (to the right), and the positive y-intercept decreases by \( m \) units, what formula can be used to find the radius \( R \) in terms of \( n \) and... | automath |
The parabolas $y=x^2$ and $x=y^2$ intersect at two points. The line passing through these two points intersects the line $y=x$ at a point $(a,a)$. Find the value of $\sqrt{a}$. | nvidia_math |
Two days ago, the temperature in the morning went up 1.5 degrees every 2 hours. If the temperature was 50 degrees at 3 A.M., what was the temperature at 11 A.M.? | tiger_lab_math |
Find the amount of a certain sum of money invested at 9% per annum for 2 2/5 years if the principle is Rs. 921.0526315789474. | tiger_math |
Benjamin has been saving money for a new bike and it took him four months to reach his goal. If he saved 20 dollars the first month and 40 more dollars each subsequent month, how much did he have saved by the end of the fourth month? | nvidia_math |
Given a circle with radius \( r = 5 \) units, how long is the tangent line segment from a point \( P \) that is 13 units away from the center of the circle to the point of tangency? | automath |
Given that \( A \) is a \( 4 \times 4 \) matrix defined as
\[
A =
\begin{bmatrix}
16 & 2 & 3 & 13 \\
5 & 11 & 10 & 8 \\
9 & 7 & 6 & 12 \\
4 & 14 & 15 & 1
\end{bmatrix}
\]
and \( B \) is a \( 4 \times 4 \) matrix with real entries, describe the conditions on \( B \) under which the matrix equation \( AX = B \) c... | automath |
Jake splits 8 shots of vodka with his friend. Each shot of vodka is 1.5 ounces. If the vodka is 50% pure alcohol, how much pure alcohol did Jake drink? Let's program in Python in the response. | tiger_lab_math |
A long cylindrical conductor with radius \( R = 0.1 \, \text{m} \) carries a total current \( I = 10 \, \text{A} \) uniformly distributed over its cross-section. Compute the magnetic field \( B \) at a distance of \( r = 0.05 \, \text{m} \) from the center of the conductor. Then, calculate the magnetic field \( B \) at... | automath |
Find $x$, such that $4^{\log_7x}=16$. | nvidia_math |
Angeli had 90 assorted candies. One-third of the candies were lollipops and the rest were candy canes. She then shared the lollipops equally among the boys such that each boy received 3. She then shared the candy canes equally among the girls such that each received 2. How many boys and girls were given altogether? | tiger_lab_math |
A department store has a discount coupon that can be used on any purchase made on a specific day. The coupon provides a discount of $25\%$ off the original price of the item. If a customer buys a TV priced at $\$500$ with the coupon, how much will they pay after applying the discount? | nvidia_math |
In the equation
$$x^2 - 3ax + a^2 = 0$$
determine $a$ such that the sum of the roots is equal to 4. | nvidia_math |
How many integer values of $m$ satisfy $-75 < m^2 < 75$? | nvidia_math |
A fair six-sided die has its faces labeled 1, 2, 3, 4, 5, and x. If the expected value of rolling the die is 4, what is the value of x? | nvidia_math |
Solve the following system of linear equations using QR decomposition:
x + 2y - z = 5
2x - y + 3z = 0
3x + y + z = 7 | tiger_lab_math |
if the cost price is 82 % of the selling price , then what is the profit percent ? Please respond by writing a program in Python. | tiger_lab_math |
Three siblings, Alice, Bob, and Carol, shared a box of chocolates. There were $\frac{5}{6}$ of the chocolates left in the box. Alice took half of the remaining chocolates, and Bob took $\frac{1}{3}$ of what was left after Alice took hers. How much of the box of chocolates did Carol get? | tiger_math |
Maria is a florist preparing bouquets for a wedding. Each large bouquet requires 5 yards of ribbon to wrap, each medium bouquet requires 3 yards of ribbon, and each small bouquet requires 2 yards of ribbon. Additionally, each bouquet requires 1 yard of ribbon to tie a decorative bow. If Maria made three large bouquets,... | nvidia_math |
What is the greatest integer $x$ for which $\frac79 > \frac{x}{13}$? | nvidia_math |
The mean of one set of five numbers is 13, and the mean of a separate set of six numbers is 24. What is the mean of the set of all eleven numbers? Let's write a program. | tiger_lab_math |
The average fuel efficiency of a certain car model is 35 miles per gallon. However, it is known that the fuel efficiency varies depending on the driving conditions. In a recent study, it was found that 80% of the drivers reported an average fuel efficiency of 32 miles per gallon, while the remaining 20% reported an ave... | nvidia_math |
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