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A certain family has 3 sons: Richard is 6 years older than David, and David is some years older than Scott. In 8 years, Richard will be twice as old as Scott. David was 12 years old 2 years ago. How many years older is David than Scott? | tiger_math |
What is the value of $0.\overline{78}-0.\overline{45}-0.\overline{12}?$ Express your answer as a fraction in lowest terms. | tiger_math |
A mosquito sucks 20 drops of blood every time it feeds on someone. If there are 5000 drops per liter and you have to lose 3 liters of blood to die, how many mosquitoes would have to feed on you to kill you? | nvidia_math |
Please find the closest option to 100.0. The options are (A) 60% (B) 70% (C) 80% (D) 90% (E) 100% | tiger_lab_math |
A and B together have $100. If 3/10 of A's amount is equal to 1/5 of B's amount, how much amount does B have?
Answer Choices: (A) $60 (B) $55 (C) $42 (D) $31 (E) $100 | tiger_lab_math |
A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n?
Answer Choices: (A) 8/7 (B) 8 (C) 9/8 (D) 7 (E) ... | tiger_lab_math |
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 15% greater than any other employee, what is the lowest possible salary that any one employee earned?
Answer Choices: (A) $40,000 (B) $41,667 (C) $42,000 (D) $43,750 (E) $60,000 | tiger_lab_math |
The cross-section of a water channel is a trapezium in shape. The channel is 14 meters wide at the top and a certain width at the bottom, and the area of the cross-section is 880 square meters. The depth of the channel is 80 meters. What is the width of the channel at the bottom? | tiger_math |
Ethan has 150 sports cards that he wants to organize in a binder with 40 pages. He can place 5 cards on each of the first 15 pages. Then, he can place 3 cards on each of the next 10 pages. If he wants to distribute the remaining cards evenly across the remaining pages, how many cards can he place on each of the remaini... | nvidia_math |
An inverted conical water tank with a height of 20 meters and a radius of 5 meters is being drained through a hole in the vertex at a rate of 2 cubic meters per hour. What is the rate of change of the water depth when the water is 4 meters deep? | automath |
In triangle $ABC$, $\angle ADB = \angle ACB$ and $BD:DC=1:3$. Point $E$ is on $AC$ such that $AE:EC=2:1$. If the area of $\triangle ABE$ is 12, determine the area of $\triangle BDC$. | nvidia_math |
What is the value of the infinite continued fraction representation for the square root of 10, defined as \( A + \frac{B}{2A + \frac{B}{2A + \frac{B}{2A + \cdots}}} \) where \( A \) is the closest integer to \( \sqrt{10} \) and \( B = 10 - A^2 \)? Calculate the value to four decimal places. | automath |
If a population of women in a town is 30% of men . What is the population of men as a % of population of women ?
Answer Choices: (A) A) 333% (B) B) 100% (C) C) 50% (D) D) 65% (E) E) 110% Please write a program to solve it | tiger_lab_math |
Let $\omega$ be a complex number satisfying $\omega^3 + \omega^2 - \omega - 1 = 0$. Determine the value of
$\omega^{2008} + \omega^{2009}$, given $\omega \neq -1$. | nvidia_math |
a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ? Let's write a Python program. | tiger_lab_math |
Five friends eat at Wendy's and ordered the following: a platter of Taco Salad that cost $10, 5 orders of Dave's Single hamburger that cost $5 each, 4 sets of french fries that cost $2.50, and 5 cups of peach lemonade that cost $x each. How much will each of them pay if they will split the bill equally?
If we know the ... | tiger_math |
In how many a committee of 5 members can be selected from 6 men 5 ladies consisting of 3 men and 2 ladies
Answer Choices: (A) 250 (B) 150 (C) 100 (D) 50 (E) 200 Let's program in Python in the response. | tiger_lab_math |
Find the equation of the line passing through the points (4, 2) and (-2, -1). | nvidia_math |
Mia needs to go to the airport for a flight. A taxi ride to the airport costs $5 more than a shuttle ride. A shuttle ride costs $2 more than a train ticket. The taxi ride costs $35. If Mia takes the train to the airport and buys a snack for 15% of the original cost of the train ticket, what is the total cost of the tri... | nvidia_math |
The expression $\sin x + \sin 5x + \sin 11x + \sin 15x$ can be written in the equivalent form
\[a \sin bx \sin cx \sin dx\]for some positive integers $a,$ $b,$ $c,$ and $d.$ Find $a + b + c + d.$ | nvidia_math |
A man invested Rs. 12,000 in two types of stocks: 12% stock at Rs. 120 and 15% stock at Rs. 125. If he earned a total dividend of Rs. 1,620 from these investments, how much did he invest in the 12% stock?
A. Rs. 4,000
B. Rs. 5,000
C. Rs. 6,000
D. Rs. 7,000 | automath |
Lena purchased seven kittens for a total of $600. Four kittens are priced at $70 each. What is the cost of each of the remaining three kittens if they are equally priced? | nvidia_math |
The average of first 10 even numbers is?
Answer Choices: (A) 8 (B) 92 (C) 83 (D) 11 (E) 12 | tiger_lab_math |
Lucy decided to sell lemonade over the weekend at a local park. On Saturday, she sold twice as many cups as on Sunday, and the total number of cups she sold over both days was 54. How many cups did she sell on Sunday? If the answer to the question is 18, calculate how many more cups she sold on Saturday compared to Sun... | tiger_math |
Cindy had 20 marbles which is 5 more than what Lisa had. If Cindy gave her 12 marbles, how many more marbles does Lisa have now? | tiger_lab_math |
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age 10 years back was:
Answer Choices: (A) 10 years. (B) 14 years. (C) 17 years. (D) 16 years. (E) 12 years. | tiger_lab_math |
The Pinedale bus line travels at an average speed of some km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale mall, which is 5 stops away. The mall is 25 kilometers away from Yahya's house. What is the average speed of the Pinedale bus line? | tiger_math |
The average of two 3-digit positive integers is equal to the decimal number obtained by writing the hundreds digit of one of the three-digit integers before the decimal point and the other two digits of that integer after the decimal point. What is the smaller of the two integers? | tiger_math |
Jerry wakes up one morning and finds the thermostat set to 40 degrees. He set it to double the initial temperature. His dad notices, yells at Jerry, and reducing the temperature by 30 degrees. Later, Jerry's mother reduces the temperature by 30%, before his sister increases it by 24 degrees. What's the final temperatur... | tiger_lab_math |
Triangle $ABC$ is a right triangle with $AC = 7,$ $BC = 24,$ and right angle at $C.$ Point $M$ is the midpoint of $AB,$ and $D$ is on the same side of line $AB$ as $C$ so that $AD = BD = 15.$ Given that the area of triangle $CDM$ may be expressed as $\frac {m\sqrt {n}}{p},$ where $m,$ $n,$ and $p$ are positive integers... | tiger_lab_math |
What are the necessary and sufficient conditions for a subset of \(\mathbb{R}^2\) to ensure that if there exists a loop that cannot be contracted to a point, there must also exist a simple loop that cannot be contracted? | automath |
The average salary of all the workers in a workshop is a certain amount. The average salary of 7 technicians is Rs. 8000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is 7. What is the average salary of all the workers in the workshop? | tiger_math |
There are 25 students in Mr. Johnson's class. If there are three times as many students who like math as those who like science, 8 students who like both math and science, and 5 students who like neither math nor science, how many students like science? | nvidia_math |
There are two cars. One is 300 miles north of the other. Simultaneously, the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 60 miles per hour. How many miles apart are the cars after 5 hours?
Answer Choices: (A) 300 (B) 360 (C) 400 (D) 450 (E) 500 | tiger_lab_math |
A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 930gm. for a kg.His gain is …%.
Answer Choices: (A) 5.26% (B) 5.36% (C) 4.26% (D) 6.26% (E) 7.53% Let's write a Python program. | tiger_lab_math |
The digits 1, 2, 3, 5 and 7 are arranged randomly to form a five-digit number. What is the probability that the number is odd? Express your answer as a common fraction. | tiger_math |
When you press buttons 1, 2, and 3 once, how many different ways can you press them in a different order? | tiger_math |
What is the volume, in cubic inches, of a rectangular box, whose faces have areas of $24$ square inches, $16$ square inches and $6$ square inches? | nvidia_math |
The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time Q will it take to fill the tank now?
Answer Choices: (A) 50% less time (B) 50% more time (C) 75% less time (D) 75% more time (E) 100% more time | tiger_lab_math |
Paul goes fishing every Saturday. Last week he was able to catch 5 fish for every 2 hours he was fishing. How many fish did he catch when he was fishing for 12 hours? | tiger_lab_math |
Given a vector \( x \in \mathbb{R}^2 \) representing the normal direction to a line through the origin, find a unit vector \( v \in \mathbb{R}^2 \) such that the reflection map \( \sigma_x \), defined by
\[
\sigma_x(v) = v - 2 \frac{x \cdot v}{x \cdot x} x,
\]
is equal to the reflection map \( \sigma_a \) on the lin... | automath |
Is there a polynomial-time algorithm to determine the existence of a Hamiltonian cycle in a subgraph \( G \) of the \( k \)-th power of the cycle graph \( C_n^k \) for a constant \( k \), and if so, what is the time complexity of such an algorithm? | automath |
John takes 10 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the... | tiger_lab_math |
A box contains 5 red balls and 3 blue balls. I randomly draw two balls from the box without replacement. What is the probability that the first ball is red and the second ball is blue? | nvidia_math |
Mia had 48 ounces of trail mix. She gave 8 ounces to her friend. Then she divided the rest equally into 4 bags. How much does each bag weigh? | nvidia_math |
Solve $\log_{2x} (x^2 + 1) + \log_{x^2 + 1} (2x) = 2$. | nvidia_math |
A deck of 52 cards is shuffled, and a card is drawn randomly. What is the probability that the drawn card is either a king or a heart? | nvidia_math |
In a complex equation, Emily calculated that $m = 8 + 15i$ and $n = 6$. If the equation is given by \[2n - m = 100\] what is the value of $i$? | tiger_math |
Suppose we cover each rational number \( q \) in \( \mathbb{Q} \) with an open interval of the form \( (q - \epsilon_q, q + \epsilon_q) \), where \( \epsilon_q \) is a positive number that may depend on \( q \). If the total length of all these intervals is finite, does their union necessarily cover all of \( \mathbb{R... | automath |
In base 8, a bird claims to have flown $267_8$ miles. How many miles did it fly in base 10? | tiger_math |
Ashley works as a pet sitter and earns $8.00 for every dog she walks. She walks 3 dogs for her friend's family, 2 dogs for her teacher, and 4 dogs for a neighbor, and then walks the same number again for another family on the block. How much money did Ashley earn? | nvidia_math |
If the first three terms of a geometric series are expressed in terms of \( k \) as \( (k-8), (k+4), \) and \( (3k+2) \), determine the values of \( k \) for which these terms form a geometric series. Subsequently, find the sixth term of the series and the sum of the first 10 terms when \( k = 16 \) and \( k = -1 \). | automath |
Factor the expression $\frac{x^2-2x-15}{x^2-25}$. | nvidia_math |
What is the probability \( P(X < a < Y) \) in terms of the joint cumulative distribution function \( F_{XY}(x,y) \) of two dependent random variables \( X \) and \( Y \) when \( X \) is continuous at \( a \)? | automath |
In an examination, there were 2000 candidates, out of which some candidates were girls and the rest were boys. If 28% of the boys and 32% of the girls passed, then the total percentage of failed candidates is 70.2%. How many candidates were girls? | tiger_math |
A drawer contains 11 different colored socks. A pair of socks is formed by selecting 2 socks from the drawer. What is the probability that a pair of socks randomly selected from the drawer will be a pair of matching socks (i.e., both socks have the same color)? Express your answer as a common fraction. | nvidia_math |
Let $P(x) = (x-1)(x-2)(x-3)$. For how many polynomials $Q(x)$ does there exist a polynomial $R(x)$ of degree 3 such that $P\left(Q(x)\right) = P(x)\cdot R(x)$? | nvidia_math |
Suppose a continuous-time control system has a specified settling time of \( T_{settling} = 0.5 \) seconds and must achieve a percent overshoot of 25%. What is the minimum required damping ratio \( \zeta \) for this system? | automath |
A sock drawer contains four socks, each one a different solid color. The colors of the socks are green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
Answer Choices: (A) 2400 (B) 240 (C) 1,024 (D) 2,520 (E) 24 | tiger_lab_math |
A landscape designer is planning a triangular flower bed in a large garden. If the lengths of two sides of the triangular flower bed are 4 meters and 7 meters, and the included angle between these two sides is 60 degrees, what is the area of the triangular flower bed? | tiger_math |
a fellow borrowed a certain sum of money at 5 % per annum at simple interest and in 5 years the interest amounted to rs . 2250 less than the sum lent . what was the sum lent ? Let's write a Python program. | tiger_lab_math |
Find the value of $(x-2)^3 + 2(x-2)$ when $x = 5$? | tiger_math |
A cone has a base radius of 7 cm and a height of 12 cm. What is the volume of the cone? | tiger_lab_math |
"statement 1": Jill has 35 gallons of water stored in quart , half - gallon , and one gallon jars, "statement 2" :Jill has 85 gallons of water stored in quart , half - gallon , and one gallon jars, "options: " Entailment or contradiction or neutral? Please respond by writing a program in Python. | tiger_lab_math |
If $\gcd(a,b)=c$ and $\gcd(x,y)=z$, where $a, b, c, x, y, z$ are positive integers, what is the smallest possible value of $\gcd(ax,by)$? | nvidia_math |
The sum of ages of 4 children born 1 years different each is 38 years. What is the age of the Elder child?
Answer Choices: (A) 8 (B) 11 (C) 10 (D) 16 (E) 17 | tiger_lab_math |
p is able to do a piece of work in some days and q can do the same work in 20 days. If they work together for 4 days, the fraction of work left is 0.5333333333333333. How many days does it take for p to do the work alone? | tiger_math |
What is the value of Cohen's d for Mr. Brown's students, and how would you interpret this effect size based on the standard interpretation criteria? | automath |
Given that the product of all unique positive divisors of a positive integer \( n \), which is not a perfect cube, equals \( n^2 \), what is the product of all the unique positive divisors of \( n^2 \)?
(A) \( n^3 \)
(B) \( n^4 \)
(C) \( n^6 \)
(D) \( n^8 \)
(E) \( n^9 \)
Provide a verifiable reasoning for ... | automath |
There are some numbers with an average of zero. Of them, at the most, 29 may be greater than zero. How many numbers are there in total? | tiger_math |
Let $x,$ $y,$ $z$ be positive real numbers such that $x + y + z = 4.$ Find the minimum value of
\[\frac{1}{2x + y} + \frac{1}{2y + z} + \frac{1}{2z + x}.\] | nvidia_math |
A water tank can hold 2400 liters of water. A pump can fill the tank at a rate of 0.5 liters per second, but it only works for 4 hours a day. If 1200 liters of water are already in the tank, how many days will it take to fill the tank completely? | nvidia_math |
If $p, q,$ and $r$ are three non-zero integers such that $p + q + r = 27$ and $\frac{1}{p} + \frac{1}{q} + \frac{1}{r} + \frac{405}{pqr} = 1$, find $pqr$. | nvidia_math |
Mary is making a spinach quiche. She takes 40 ounces of raw spinach and cooks it until it's 20% of its initial volume. If she mixes the spinach with 6 ounces of cream cheese and 4 ounces of eggs, what is the total volume of the quiche? | tiger_lab_math |
Peggy buys 3 folders, one each in the colors red, green, and blue. She puts ten sheets of paper in each folder, and then, she puts star-shaped stickers on each sheet of paper. In the red folder, each sheet of paper gets 3 stickers. In the green folder, each sheet of paper gets 2 stickers, and in the blue folder, eac... | tiger_lab_math |
Ava and her brother Liam enjoyed collecting sports cards. Ava had a total of 95 cards in her collection, while Liam had 81 cards in his collection. For their holiday gifts, their aunt gave them 30 sports cards each. How many combined cards did they have? | nvidia_math |
Vlad is 6 feet, 3 inches tall. His younger sister is 2 feet, x inches tall. Vlad is 41 inches taller than his sister. What is the value of unknown variable x? | tiger_math |
rs 80000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 9000 find money given by 10 % ? Let's write a Python program. | tiger_lab_math |
Ryan earns $600 for a standard 45-hour workweek and gets an extra $25 for every hour of overtime. If he worked 55 hours last week, calculate his total income. | nvidia_math |
Emily purchased 72 cookies. She wants to set aside 12 for her sister and then equally divide the remaining cookies among herself and her 5 classmates. How many cookies will each of them receive? | nvidia_math |
A water tank has a circular base with a diameter of 20 meters. A pipe with an inside diameter of 5 centimeters is used to fill the tank. If the pipe is open for 24 hours and the water flows at a constant rate of 10 meters per second, how high will the water level in the tank rise? | tiger_math |
jill has 35 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ? Let's write a Python program to solve it. | tiger_lab_math |
Johnny makes his signature crab dish 40 times a day. It uses 1.5 pounds of crab meat. Crab meat sells for $8 per pound. How much does he spend in a week if he is closed 3 days a week? | tiger_math |
Seven years ago the average age of a family of 2 members was 26 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
Answer Choices: (A) 25years (B) 29years (C) 30years (D) 35years (E) 40years | tiger_lab_math |
Lucia is a dedicated dancer. She takes 3 hip-hop classes a week, 2 ballet classes a week, 1 jazz class a week, 1 salsa class every two weeks, and 1 contemporary dance class every three weeks. One hip-hop class costs $10.50, one ballet class costs $12.25, one jazz class costs $8.75, one salsa class costs $15, and one co... | tiger_math |
Let \( G \) be a discrete subgroup of the additive group of real numbers \( \mathbb{R} \). If \( G \) is represented in the form \( G = a\mathbb{Z} \) for some \( a \in \mathbb{R} \), what can be stated about the value of \( a \) if \( G \) is closed? Provide the reasoning behind your answer. | automath |
Given the equation \( x - 3 = 2 - 4x \), determine which of the following equations has the same solution as the original equation:
1. \( 2x - 6 = 4 - 8x \)
2. \( x - 5 = -4x \)
3. \( 2(1 - 2x) = x - 3 \)
4. \( -3 = 2 - 5x \)
Identify all equations that have the same solution as the original equation, and justify you... | automath |
Let $g(x)$ be a function that satisfies the condition $b^2 g(a) = -a^2 g(b)$ for all real numbers $a$ and $b.$ If $g(-1) \neq 0,$ find $\frac{g(-2)+g(1)}{g(-1)}$. | nvidia_math |
a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 7 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces... | tiger_lab_math |
Let \( K \) be a field and \( a_1, \ldots, a_n \in K \). Determine the number of distinct maximal ideals in the polynomial ring \( K[X_1, \ldots, X_n] \) of the form \( (X_1 - a_1, \ldots, X_n - a_n) \). Justify your answer. | automath |
A trapezoidal field is planted uniformly with wheat. The field's dimensions are as follows: the length of the shorter parallel side is 150 meters, the length of the longer parallel side is 300 meters, and the distance between the parallel sides is 200 meters. At harvest, the wheat at any point in the field is brought t... | nvidia_math |
Given the functions \( f_0(x) = 1.0 \), \( f_1(x) = \sin(x^2) \), \( f_2(x) = 3\cos(x) \), \( f_3(x) = \frac{1}{x+1} \), and \( f_4(x) = x^4 \), find the coefficients that minimize the chi-squared error in the fitting function
\[
y = a_0 f_0(x) + a_1 f_1(x) + a_2 f_2(x) + a_3 f_3(x) + a_4 f_4(x)
\]
assuming an obser... | automath |
Rashmi and Rakhi were partners in a business. Rashmi contributed 2/3rd of the capital for 20 months and Rakhi received 3/5th of the total profit. What was the time duration of Rakhi’s investment in the business?
Answer Choices: (A) 60 months (B) 63 months (C) 62 months (D) 30 months (E) 67 months | tiger_lab_math |
Consider the function $f(x) = \sqrt{1 - \cos(x)} + \sin^2(x)$. Determine whether this function is periodic, and if so, find its period. | nvidia_math |
Calculate the percentage gain if a trader bought a bicycle for Rs.440 and sold it for Rs.610?
Answer Choices: (A) 38.64% (B) 39.64% (C) 31.64% (D) 35.64% (E) 34.64% Let's program in Python in the response. | tiger_lab_math |
On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
Answer Choices: (A) 0 Remainder (B) 1 Remainder (C) 2 Remainder (D) 4 Remainder (E) 5 Remainder | tiger_lab_math |
Gail has two fish tanks. The first tank is twice the size of the second tank. There are 48 gallons of water in the first tank. She follows the rule of one gallon of water per inch of fish. If she keeps two-inch fish in the second tank and three-inch fish in the first tank, how many more fish would Gail have in the firs... | tiger_lab_math |
How many numbers from 1 to 250 are not perfect squares or perfect fourth powers? | nvidia_math |
Akira is driving to the beach for a day of surfing. The odometer reads 92,143 when she leaves her house, and it reads 92,219 when she arrives at the beach. Akira's car gets 32 miles per gallon and the price of one gallon of gas is $\$3.92$. What was the cost of the gas that was used for Akira to drive to the beach? (Ex... | nvidia_math |
Ethan is reading a sci-fi book that has 360 pages. He read 40 pages on Saturday morning and another 10 pages at night. The next day he read twice the total pages as on Saturday. How many pages does he have left to read? | tiger_lab_math |
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