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an uneducated retailer marks all his goods at 50 % above the cost price and thinking that he will still make 15 % profit , offers a discount of 15 % on the marked price . what is his actual profit on the sales ? | tiger_math |
Given the equation \( 2r = 4s^2 + 4s + 1 \), where \( r \) and \( s \) are non-negative integers, how many distinct pairs \((r, s)\) satisfy this equation? | automath |
In a hypothetical universe where a constant jerk \( j \) acts downward instead of a constant acceleration due to gravity, an object is launched from the ground with an initial velocity \( v_0 \) at an angle \( \theta \) from the horizontal, and its initial acceleration is zero. If the object eventually hits the ground,... | automath |
In the context of Stokes' Theorem, if we consider a smooth surface \( S \) bounded by a positively oriented curve \( C \) and a vector field \( \vec{F} \), does the normal vector \( \vec{n} \) in the surface integral
\[
\iint_S \text{curl} \, \vec{F} \cdot \vec{n} \, dS
\]
necessarily have to be a unit vector, and i... | automath |
Find the sum of the first five terms in the geometric sequence $\frac13,\frac19,\frac1{27},\dots$. Express your answer as a common fraction. | nvidia_math |
Determine the number of distinct positive factors of $2024$ that are multiples of $4$. | tiger_math |
"statement 1": Elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used, "statement 2" :Elena ’ s bread recipe calls for less than 7 ounces of butter for each 4 cups of flour used, "options: " Entailment or contradiction or neutral? Please write a program to solve it | tiger_lab_math |
Determine whether the series $$\sum_{n=1}^\infty \frac{n^2}{5n^2 + 4}$$ converges or diverges, and provide a justification for your answer. | automath |
Find the value of m from given 72519 x 9999 = m?
Answer Choices: (A) 455666576 (B) 565476563 (C) 567642887 (D) 725117481 (E) 658899003 Let's write a Python program to solve it. | tiger_lab_math |
Given two classifiers A and B that perform optimally at different threshold levels, how can we mathematically model the true positive rate (TPR) and false positive rate (FPR) of a new classifier C created by randomly selecting between classifiers A and B based on a coin flip? Specifically, if classifier A has a TPR of ... | automath |
In a class, there were 13 female students. There were three times as many male students in this class. How many students were in the class? | tiger_lab_math |
Maria has $1.20. She received $0.75 as a gift from her aunt. On her way home, Maria found $0.25 on the ground. She then bought a book that cost $2.00. How much money in cents does Maria have left? | nvidia_math |
What is the radius of convergence of the series expansion of the function \( f(z) = \frac{2z + 3}{z + 1} \) in powers of \( z - 1 \)? | automath |
At a party, the ratio of the number of children to the number of apples is 5:8. If each child receives either 1 apple or 2 apples, what fraction of the children received 2 apples? | automath |
Alex walked 3 blocks from her apartment to the library in New York. She then rode the subway 15 blocks to the museum to meet her friend. After the meeting, she returned home using the same route. How many blocks did Alex travel in total? | nvidia_math |
Factor the following polynomial: 9x^2 + 15x + 6. | tiger_lab_math |
A set of 12 consecutive integers has a mean that is equal to the mean of a set of 8 consecutive integers. What is the positive difference between the largest numbers in the two sets? | nvidia_math |
You have X dimes and 20 quarters. 50 percent of the value of your money is in quarters. What is the value of unknown variable X? | tiger_math |
Consider a function $g$ defined on the set of positive real numbers, such that $g(y^2) = g(y)^2$ for all $y > 0$, and $g(t) = 4 - t$ for $3 \leq t \leq 5$. Determine the value of $x$ for which $g(x) = g(256)$. | nvidia_math |
What is the value of $\log_{16} 4$? | tiger_math |
Given the vector space \( V \) spanned by the vectors \( (1, 1, 1) \) and \( (2, 1, 0) \), determine the dimension of the nullspace of a \( 2 \times 3 \) matrix \( B \) whose row space is \( V \). What is the basis for the nullspace of the matrix \( B \)? | automath |
what is the greatest of 3 consecutive integers whose sum is 33 ? Let's write a Python program to solve it. | tiger_lab_math |
find the area of trapezium whose parallel sides are 20 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 |
Find the maximum value of
\[x^2 + xy + y^2\]over all real numbers $x$ and $y$ such that $x + y = 1$. | tiger_math |
Ron's baseball team scored 270 points in the year. There are 9 players on the team. If a certain number of them averaged 50 points each, and the remainder averaged 5 points, how many players averaged 50 points each? | tiger_math |
a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 40 miles per gallon , and from town b to town c , the car averaged 50 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through ... | tiger_lab_math |
The average weight of a group of 8 persons is W kg. When two new people join the group, replacing two members weighing 65 kg and 75 kg, the average weight of the group increases by 5 kg. What might be the weights of the two new persons? | tiger_math |
Julia has a parrot and a rabbit. She buys food for both of the animals for $30 in total a week. Julia has the rabbit for 5 weeks, and the parrot for 3 weeks. How much money did Julia already spend on food for her animals, if the weekly cost of the rabbit food is $12? Let's program in Python in the response. | tiger_lab_math |
For the piecewise-defined function
$$f(x) = \begin{cases} x^2 - 4 & \text{if } x \ge -4, \\ x + 3 & \text{otherwise}, \end{cases}$$
determine the number of values of \( x \) such that \( f(f(x)) = 5 \). | automath |
If log 27= 1.431, then the value of log 9 is:
Answer Choices: (A) 0.934 (B) 0.945 (C) 0.954 (D) 0.958 (E) 0.959 | tiger_lab_math |
Mrs. Johnson's science class has 25 girls, and 30 of her students bring their textbooks to class. If 18 of the students who brought textbooks are boys, then how many girls didn't bring their textbooks to class? | nvidia_math |
The bagel shop has enough benches to sit $204_6$ people. If X people are supposed to sit on one bench, The shop has 38 benches. What is the value of unknown variable X? | tiger_math |
Given two \( n \times n \) invertible matrices \( A \) and \( B \) with real entries, determine the maximum number of distinct real values of \( \lambda \) such that the matrix \( C = \lambda A + B \) is invertible. | automath |
A fair six-sided die is rolled three times. What is the probability that the product of the three numbers obtained is even? Express your answer as a common fraction. | nvidia_math |
Given positive integers $a$ and $b$ such that $\frac{1}{3a} + \frac{1}{b} = \frac{1}{11}$, what is the least possible value of $ab$? | nvidia_math |
Consider the optimization problem of maximizing the function f(x) = x^2 + 5x + 6 for the range -5 ≤ x ≤ 5 using Ant Colony Optimization. Suppose there are 10 ants and the initial pheromone level for all edges is 0.5. The ant colony algorithm parameters set are follows: evaporation rate 0.1, alpha value 1.5, and beta va... | tiger_lab_math |
What is the range of the function \( \arcsin(x) \) if the inverse sine function is defined based on the restriction of the sine function to the interval \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)? | automath |
Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 9 cm, what is CD, in centimeters?
Answer Choices: (A) 1 (B) 8 (C) 3 (D) 4 (E) 5 | tiger_lab_math |
Let $a,$ $b,$ and $c$ be positive real numbers such that $a + b + c = 1.$ Find the maximum value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}.$ | nvidia_math |
In a triangle, the sum of the angles \( x \), \( y \), and \( z \) is equal to \( 180^\circ \). What is the value of \( \frac{x + y + z}{45} \)? | automath |
Given a skew-symmetric matrix \( A = \begin{pmatrix} 0 & \frac{\pi}{3} \\ -\frac{\pi}{3} & 0 \end{pmatrix} \), compute the matrix exponential \( e^A \) and find the value of its \( (1, 1) \) entry. What is that value? | automath |
Solve $\log_x 2 + \log_{2x} 4 = 3$. | nvidia_math |
Determine whether the series
$$\sum_{n=1}^{\infty}\frac{1}{n}\sqrt{e^\frac{1}{n} - e^\frac{1}{n+1}}$$
converges or diverges. Justify your answer using the Taylor expansion of the exponential function. | automath |
Roman and Remy took separate showers. Remy used x more gallon than 3 times the number of gallons that Roman used for his shower. Together the boys used 33 gallons of water. How many gallons did Remy use?
If we know the answer to the above question is 25, what is the value of unknown variable x? | tiger_math |
Find the number of moles of CO2 formed on combining 1 mole of HCl and 1 mole of NaHCO3 Let's write a Python program to solve it. | tiger_lab_math |
If x fourth of the engines are defective, and there are 5 batches of 80 engines each. How many engines are not defective?
If we know the answer to the above question is 300, what is the value of unknown variable x? | tiger_math |
How many of the following probability statements can be computed using the provided Standard Normal Probability Table?
i. \( P(Z < 0.5) \) where \( Z \) is an exponential random variable with mean = 1 and variance = 1.
ii. \( P(X > 0.4) \) where \( X \) is a standard normal random variable.
iii. \( P(0 < X < 0.55) \... | automath |
How many ways are there to put 5 balls in 2 boxes if the balls are not distinguishable but the boxes are? | tiger_math |
How many pairs of integers $(a, b)$ satisfy the equation $a^2 + b^2 = 5000$, where $a$ and $b$ are both prime numbers? | nvidia_math |
What two-digit positive integer is one more than a multiple of 2, 3, 4, 5 and 6? | tiger_math |
There are four birds in the aviary. They like cherries, dates, and elderberries. The first bird, which likes cherries, eats 2 times as many cherries as the number of dates eaten by the second bird that likes dates. The bird that likes dates eats 2/3 times as many dates as the number of elderberries eaten by the third b... | nvidia_math |
What is the limit of the sequence defined by \( E_n = 0.9 + 0.09 + 0.009 + \ldots + 10^{-n} \) as \( n \) approaches infinity? | automath |
If there are 6 jaguars in a forest and each jaguar eats 5 snakes per day, how many beetles are consumed in total each day considering that each bird eats 12 beetles and each snake eats 3 birds per day? | tiger_math |
Let a beam be modeled using BEAM188 elements as described in the text, where the beam has a length \( L = 100 \) in and a cross-section of \( 1 \) in. \( \times 1 \) in. If the beam is subjected to a uniformly distributed transverse load \( q_0 = 50 \) lbf/in, determine the maximum deflection \( w_{max} \) of the beam ... | automath |
75 is what percent of 125 ? Please write a program to solve it | tiger_lab_math |
Given a group G with a subgroup H, Statement 1 | The left coset of H in G, denoted as aH, is the same as the right coset Ha. Statement 2 | If H is a normal subgroup of G, then the factor group G/H is commutative if G is commutative. Answer Choices: (A) True, True (B) False, False (C) True, False (D) False, True | tiger_lab_math |
Find the value of $(4^{\frac{1}{6}})^{-18}$. | tiger_math |
In a mystical land, a circular tower is surrounded by a garden. The tower has a radius of 10 meters and the entire garden including the tower has a radius of 30 meters. If the garden has a uniform width all around the tower, what is the area, in square meters, of the garden alone? Express your answer in terms of π. | tiger_math |
What is the greatest integer $x$ for which $\frac79 > \frac{x}{13}$? | nvidia_math |
Consider the following message encoded using Bacon's cipher: "mAY WE plEase love one AnotHer?"
If we denote lower-case letters as 0 and upper-case letters as 1, and take groups of five letters at a time, what is the binary representation of the secret message hidden within this plain message?
Additionally, given th... | automath |
What is the smallest integer \( n \) such that the set \( A \) contains exactly \( n \) elements, given that \( A = \{ x \mid x \text{ is a positive integer and } x < 5 \} \)? | automath |
The average weight of some boys in a class is 48 kgs. The average weight of the class of 25 students is 45 kgs. The average weight of the 15 girls in the class is 40.5 kgs. How many boys are in the class? | tiger_math |
A farmer needs to package 480 kilograms of apples into baskets that hold 8 kilograms each. However, 1/5 of the apples are rotten and need to be removed before packaging. How many baskets can the farmer fill with the remaining good apples? | nvidia_math |
Jackson is buying school supplies for his third grade class, which has 30 students. Each student needs 5 pens, 3 notebooks, 1 binder and 2 highlighters. Pens cost $0.50, notebooks cost $1.25, binders cost $4.25, and highlighters cost x. If Jackson gets a $100 teacher discount, He spends 260 on school supplies. What is ... | tiger_math |
Compute $\sin 105^\circ$. | nvidia_math |
Consider a fuzzy set A on the domain [0,10], defined by the membership function μA(x) = min(x, 10-x). Determine the degree of membership of the number 6 in A. | tiger_lab_math |
Passage: Nintendogs also had very successful launches in North America and Europe, with first week sales of over 250,000 and 160,000 respectively. Lab & Friends received a "Double Platinum" sales award from the Entertainment and Leisure Software Publishers Association (ELSPA), indicating sales of at least 600,000 copie... | tiger_lab_math |
Given a set of size \( l = 10 \) and \( m = 5 \) subsets, each of size \( n = 4 \), how many ways can these subsets be chosen such that each pair of subsets has an intersection size at most \( d = 2 \)? | automath |
Consider the 3-dimensional manifold M given by the equation x^2 + y^2 + z^2 - 4 = 0. Determine the Ricci curvature of M at the point (1, 1, 1). | tiger_lab_math |
If $y=\frac{8x^4+2x^3+6x^2+2x+5}{2x^4+x^3+7x^2+x+3}$, at what value of $y$ will there be a horizontal asymptote? | nvidia_math |
When the value of $y$ is doubled and then this increased value is divided by 5, the result is 10. What is the value of $y$? | nvidia_math |
In a 60-item exam, Liza got 90% of the items correctly. Her best friend, Rose, got 2 more correct answers than her. How many incorrect answers did Rose have? | tiger_lab_math |
Convert $3206_7$ to a base 10 integer. | nvidia_math |
Find the number of functions $f(n),$ taking the integers to the integers, such that
\[f(a - b) + f(a/b) = f(a) f(b) - 1\]for all integers $a$ and $b,$ where $b$ is nonzero. | nvidia_math |
Jaylen’s dog eats 1 cup of dog food in the morning and 1 cup of dog food in the evening. If she buys a bag that has 32 cups of dog food, how many days can she feed her dog with it? Let's program in Python in the response. | tiger_lab_math |
From a circular piece of paper with radius $BC$, Jeff removes the unshaded sector shown. Using the larger shaded sector, he joins edge $BC$ to edge $BA$ (without overlap) to form a cone of radius 12 centimeters and of volume $432\pi$ cubic centimeters. What is the number of degrees in the measure of angle $ABC$ of th... | nvidia_math |
If it takes Alice 25 minutes to clean her room, how many minutes does it take Bob to clean his room, given that it takes him $\frac{2}{5}$ of the time it takes Alice? | tiger_math |
What is the value of \( Z \) at the point \( (1, 1) \) for the surface defined by the function \( z = x \cdot e^{-x^2 - y^2} \), given that \( x \) and \( y \) are generated using the meshgrid command from -2 to 2 with increments of 0.2? | automath |
The green piece of yarn is 156 cm long. The red yarn is 8 cm more than three times the length of the green yarn. What is the number of centimeters in the total length for the 2 pieces of yarn? | tiger_math |
The cross section for a 2.0-MeV neutron (a typical energy for a neutron released in fission) being absorbed by a U-238 nucleus and producing fission is 0.68 barn. For a pure U-238 sample of thickness 3.2 cm, what is the probability of a 2.0-MeV neutron producing fission? Please write a program to solve it | tiger_lab_math |
Andrew works in a company that provides a generous vacation allotment: for every 10 days worked, you get 1 vacation day. If last year Andrew worked 300 days and took 5 days off in March and twice as many in September, how many more vacation days can Andrew still take? | tiger_lab_math |
Which is better investment: 11% stock at 143 or 9% stock at 117?
Answer Choices: (A) 9 3/4% stock at 119 (B) 9 3/4% stock at 117 (C) 9 3/4% stock at 112 (D) 9 3/4% stock at 118 (E) 9 3/4% stock at 111 | tiger_lab_math |
Every bag of Dummies (a chocolate candy) contains the same number of pieces.
The Dummies in one bag can't be divided equally among $10$ kids, because after each kid gets the same (whole) number of pieces, $8$ pieces are left over.
If the Dummies in three bags are divided equally among $10$ kids, what is the smallest ... | tiger_math |
A right circular cone has a slant height of 15 inches and a base circumference of 20 inches. A curved strip is painted on the cone, starting at the bottom and spiraling up to the top, making exactly one full revolution as it reaches the apex. What is the length in inches of the painted strip? | nvidia_math |
Given that the solubility product \( K_{sp} \) for a salt of the type \( AB \) is \( 4 \times 10^{-8} \), what is the molarity of its standard saturated solution?
(1) \( 4 \times 10^{-4} \, \text{mol/L} \)
(2) \( 2 \times 10^{-4} \, \text{mol/L} \)
(3) \( 16 \times 10^{-16} \, \text{mol/L} \)
(4) \( 2 \times 10^{-... | automath |
The odds against ram solving the problem are 4 to 5 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try?
Answer Choices: (A) 1/4 (B) 5/21 (C) 16/21 (D) 23/28 (E) 22/27 | tiger_lab_math |
What is the correct LaTeX code to format the following piecewise function and differential equation in a way that aligns the equations according to the equal signs and properly utilizes the "align" environment without any extra parentheses?
\[
u_t + 2uu_x = 0, \quad x \in \mathbb{R}, t > 0
\]
with
\[
u(x, 0) = ... | automath |
maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 74 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he me... | tiger_lab_math |
A contractor wants to mix cement, sand, and gravel in the ratio 5:3:7 to make concrete for a building project. If he uses 21 cubic yards of gravel, how many cubic yards of sand should he use? | nvidia_math |
What is the probability that a random outcome from the set of all "even up" card games is a winning outcome, if the total number of possible outcomes is 1214? | automath |
a sum of rs . 2678 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ? | tiger_math |
Given a graph with vertices labeled from 1 to 7, identify the edges connecting these vertices. Determine if the set \( C^* = \{1, 2, 3, 7\} \) is a minimal vertex cover, and justify your answer. Additionally, if a greedy \( 2 \)-approximation algorithm yields the vertex cover \( C = \{1, 2, 3, 4, 5, 7\} \), is this a m... | automath |
A group of 250 students attended a music festival at Summer Sound Camp on Friday night. The next morning, for 3 hours straight, they left the camp at a rate of 30 students per hour. Over the next 5 hours, a new group of students arrived at the camp at a rate of 20 students per hour. Immediately thereafter, the camp gat... | nvidia_math |
Ava and Liam both invest $800 in the stock market. Ava's investment triples in value, while Liam's is reduced to 15% of the initial value. How much more money does Ava have than Liam now? | nvidia_math |
Abby and Bobby type at constant rates of 70 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby?
Answer C... | tiger_lab_math |
In a particular pond, 4/5 of the goose eggs laid hatched successfully, and 3/4 of the goslings that hatched survived the first month. During the next three months, only 7/8 of those goslings survived, and in the following six months, 5/6 of the remaining goslings survived. Of the goslings that survived their first year... | tiger_math |
A car is driving on a straight road, and the driver wants to reach a destination 500 meters away. The car's velocity is given by the differential equation:
v' + kv = u
where v is the car's velocity, u is the driver's control input, and k is a constant. The driver can apply a control input that is either -1 m/s^2 or 1... | tiger_lab_math |
Solve the following system of linear equations:
4x + 6y - 2z = 16
2x + 3y - z = 5
x + y + 4z = -3 | tiger_lab_math |
Alex is training for a marathon and wants to break the record of completing 42 kilometers in 3 hours. After running for 1.5 hours, Alex has covered 18 kilometers. How many kilometers per hour will Alex need to run to at least tie the record? | nvidia_math |
If Jayda spent $400 at the Silverlake Flea Market, and Aitana spent 2/5 times more money than Jayda, what is the total amount of money that they spent together? | tiger_math |
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