pe-nlp/numina_orz_deepscaler_resampled · Datasets at Hugging Face

source string	problem string	answer string
orca_math	Three scenes from an hour-long movie were cut due to multiple copyright issues. The first scene was 3 minutes long, the second scene was 5 minutes and 30 seconds long, and the third scene was 2 minutes and 15 seconds long. What is the final length of the movie (in minutes and seconds)?	49
orca_math	A car travels at a certain speed. It travels 325 miles in 5 hours. What is the speed of the car in miles per hour?	65
cn_k12	For any real numbers $a (a \neq 0)$ and $b$, the inequality $\|a+b\|+\|a-b\|\geqslant \|a\|\cdot\|x-2\|$ always holds. Determine the range of the real number $x$.	[0,4]
orca_math	A grocer has 400 pounds of coffee in stock, some percent of which is decaffeinated. The grocer buys another 100 pounds of coffee, of which 60 percent is decaffeinated. The grocer's stock of coffee is 28.000000000000004 percent decaffeinated by weight. What percent of the initial stock was decaffeinated?	20\%
cn_k12	It is known that $\xi$~$N(0,\sigma^2)$, and $P(-2\leq\xi\leq0)=0.4$. Find the probability of $P(\xi>2)$.	0.1
orca_math	There were some onions on the shelf. Sixty-five were sold, and now there are 33 onions left on the shelf. How many onions were there on the shelf initially?	98
orca_math	Tina saved some money in June, $14 in July, and $21 in August. Then Tina spent $5 on books and $17 on new shoes. Tina has $40 left. How much money did Tina save in June?	\$27
orca_math	A worksheet had some problems on it. If a teacher had 9 worksheets to grade and had already graded 5 of them, she has to grade 16 more problems. How many problems are on each worksheet?	4
orca_math	of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?	1200
orca_math	In a two-digit number, it is known that its unit's digit exceeds its 10's digit by 4 and that the product of the given number and the sum of its digits is equal to a certain value. What is the product of the number and the sum of its digits if the number is 26?	208
orca_math	Lindsey saved $50 in September, $37 in October, and $11 in November. Lindsey's mom said that since Lindsey had saved more than a certain amount, she would give Lindsey $25. After spending $87 on a video game, Lindsey had $36 left. What was the minimum amount Lindsey needed to save for her mom to give her $25?	\$98
cn_k12	Given that the function $y=f\left(x\right)$ is an odd function, defined on $R$, and satisfies $f\left(x+4\right)=f\left(x\right)$. When $x\in \left(0,2\right)$, $f\left(x\right)=2^{x}+\log _{3}(x+2)$, find $f\left(2023\right)$.	-3
orca_math	if the product of two numbers is 987153000 and their h . c . f . is 440 , find their l . c . m .	2243525
orca_math	In Yardley, it snowed 0.12 inches in the early morning, 0.24 inches in the late morning, 0.5 inches in the afternoon, and 0.36 inches in the evening. Calculate the total amount of snowfall accumulated throughout the day.	1.22
orca_math	There are 4 types of stickers on a page: Type A has 5 stickers, Type B has 3 stickers, Type C has 2 stickers, and Type D has 1 sticker. If you have 22 pages of stickers, how many stickers of each type do you have in total?	22
orca_math	Carol was sending out birthday invitations to some friends. If each package of invitations she bought had 2 invitations in it and she needed 5 packs, how many friends is she inviting?	10
orca_math	There are 120 students who have to split 8,365 portfolios of paintings. Each student should get at least one portfolio, but they should all receive the same number of portfolios. Additionally, 15% of the students must each receive 10 more portfolios than the remaining 85% of the students. How many portfolios of paintings will each group of students get and how many portfolios will be left after the distribution process is complete?	25
gsm8k	Mary and Jay are planning a wedding. Of the 240 guests, 60 percent are female. Of the females, 50 percent are from Jay's family. How many female guests are from Jay's family?	72
orca_math	Three friends are about to share a strawberry juice. Seonghwa drank 1/6 of the total and Siyeon drank 2/5 of the rest. And if the amount of juice after Youngmin drank 2/3 of the remaining juice was 120 milliliters (㎖), how many milliliters (㎖) of strawberry juice was there at the beginning?	720
orca_math	Find the mass percentage of Al in Aluminum phosphate.	22.12\%
orca_math	A train moves with a certain speed in kmph. Its speed in metres per second is 37.503. What is the speed of the train in kmph?	135.0108
orca_math	40 multiplied by 30, plus (12 + 8) multiplied by a certain number, divided by 5 equals 1212. What is the number?	3
cn_k12	To understand the physical condition of students in grades 10, 11, and 12, a sample of size $1200$ is randomly selected using stratified sampling. The ratio of the number of students in the three grades is $k:5:3$ respectively. It is known that $240$ students from grade 10 were selected. Find the number of students selected from grade 12.	360
cn_k12	Given the function f(x) = g(x) + $$\frac{2019}{2018}$$x^2, where g(x) is an odd function defined on the set of real numbers, and f(1) = 2, find the value of f(-1).	\frac{1}{1009}
orca_math	A 10000-liter tank, half-full of water, is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains. One drain has a rate of 1 kiloliter every 6 minutes. It takes 60 minutes to fill the tank completely. What is the rate of the other drain?	0.25
orca_math	Tim rides his bike back and forth to work for each of his 5 workdays. His work is 20 miles away. He also goes for a weekend bike ride of 200 miles. If he spends 16 hours biking a week, what is his average biking speed in mph?	25
orca_math	a 900 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?	1050
orca_math	Janet hires six employees. Four of them are warehouse workers who make a certain amount per hour, and the other two are managers who make $20/hour. Janet has to pay 10% of her workers' salaries in FICA taxes. If everyone works 25 days a month and 8 hours a day, Janet owes a total of $22,000 for their wages and taxes for one month. How much do the warehouse workers make per hour?	\$15
orca_math	joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 6 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?	120
orca_math	The pet shop grooms dogs. It takes 30 minutes to groom a poodle. It takes half as much time to groom a terrier as it takes to groom a poodle. They do not groom cats. The pet shop grooms some poodles and 8 terriers, and it takes a total of 210 minutes. How many poodles were groomed?	3
orca_math	John plays paintball 3 times a month. Each time he plays, he buys 3 boxes of paintballs. They cost $25 per box. How much does he spend a month on paintballs?	\$225
orca_math	A buffet offers ranch or caesar dressing. They use a certain ratio of ranch dressing to caesar dressing. If the buffet uses 28 cases of ranch dressing and 4 cases of caesar dressing, what is the ratio of ranch dressing used to caesar dressing used?	7:1
orca_math	A chef served 3 different foods for a banquet: 25 plates lobster rolls, 14 plates of spicy hot noodles and 16 plates of seafood noodles. How many plates of food did the chef make altogether?	55
orca_math	A 50 ml after-shave lotion with a certain percentage of alcohol is mixed with 30 ml of pure water. The percentage of alcohol in the new solution is 18.75%. What is the initial percentage of alcohol in the after-shave lotion?	30\%
orca_math	ratio between two numbers is 3 : 4 and their sum is 420 . find the smaller number ?	180
cn_k12	Let the sequence $\{a_n\}$ satisfy $a_1=7$, and $a_n+a_{n+1}=20$. The sum of the first 50 terms of $\{a_n\}$ is ______.	500
orca_math	Pat is having a picnic with her family. She has 42 cookies. She also has some pieces of candy and 21 brownies. There are 7 people in her family. Each person gets 18 pieces of dessert. How many pieces of candy does Pat have?	63
orca_math	Jane started babysitting when she was 18 years old. Whenever she babysat for a child, that child was a certain fraction of her age at the time. Jane is currently 34 years old, and she stopped babysitting 10 years ago. The current age of the oldest person for whom Jane could have babysat is 25. What is the fraction of Jane's age that the child could be at most?	\frac{5}{8}
orca_math	A pet store had 13.5 Siamese cats and 5.25 house cats. During a purchase, they added 10.75 cats but had to give a special discount of 0.5 cats as a refund for a customer. How many cats do they have left?	29
cn_k12	If the one-variable quadratic equation $3x^{2}-6x+k=0$ has two identical real roots with respect to $x$, then the value of $k$ is ______.	3
orca_math	In a class, there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row, there are some more desks than in the previous row. The maximum number of students seated in the class is 136. How many more desks are in each subsequent row compared to the previous row?	2
orca_math	Dennis lives two floors above Charlie. Charlie lives on a floor whose number is 1/4 of Frank's floor number. Frank lives on a certain floor, and Dennis lives on the 6th floor. What floor does Frank live on?	16th
cn_k12	Simplify first, then evaluate: $a-2(a-b^{2})+3(-a+b^{2})$, where $a=2$, $b=-\frac{1}{2}$.	-\frac{27}{4}
orca_math	If 40% of 3/5 of a number is 36, what is the number?	150
orca_math	If 20% of x is 15 less than 15% of a certain number, then x is 1050. What is the number?	1500
orca_math	Company P had 15 percent more employees in December than it had in January. If Company P had 391.304347826087 employees in January, how many employees did it have in December?	450
orca_math	A company pays 15.5% dividend to its investors. An investor buys some shares and gets 25% on investment. The investor bought the shares at Rs. 31. What is the face value of the shares?	50
orca_math	a bag marked at $ 200 is sold for $ 120 . the rate of discount is ?	40\%
orca_math	Armand is playing a guessing game with his dad where he has to guess a number his dad is thinking of. His dad tells him that the number, when multiplied by 3, is three less than twice a certain number. The number Armand has to guess is 33. What is the certain number?	51
cn_k12	The function $f(x) = x(x - m)^2$ has a local minimum at $x = 1$. Find the value of $m$.	1
orca_math	Darry is a roofer and has to climb ladders multiple times a day. He climbs his largest ladder, which has 20 steps, 12 times today. He also climbs his medium-sized ladder, which has 15 steps, 8 times today, and his smaller ladder, which has 10 steps, 10 times today. Additionally, Darry climbs his smallest ladder, which has 5 steps, 15 times today. He did not climb any steps otherwise. In total, how many times has Darry climbed a step today?	535
orca_math	Ram can do a job in 10 days, and Gohul can do the same job in some days independently. They take 5.999999999999999 days to complete the same job working simultaneously. How many days would Gohul take to complete the job independently?	15
orca_math	A man walks at a rate of 10 mph. After every ten miles, he rests for a certain amount of time. He takes 328 minutes to walk 50 miles. How many minutes does he rest after every ten miles?	7
orca_math	The average weight of some students is 28 kg. By the admission of a new student weighing 4 kg, the average weight is reduced to 27.2 kg. How many students were there initially?	29
orca_math	During a certain two-week period, some percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were a action movies rented, then there were 10a comedies rented during that two-week period. What is the percentage of comedies rented during that two-week period?	62.5\%
cn_k12	To understand whether 236 households affected by demolition are satisfied with the compensation plan, Xiao Ming surveyed 50 of these households over the weekend. Among them, 32 households expressed satisfaction with the plan. In this survey, the sample size is ____.	50
orca_math	In the formula a = (2r)^n, if r is halved, then a is multiplied by 0.125. What is the value of n?	3
orca_math	As a freelancer, Katherine takes 20 hours to develop a website for her clients. Her junior, Naomi, takes some more time to complete creating a similar website. In a particular year, Katherine gave her junior 30 websites to develop. Naomi took a total of 750 hours to create the 30 websites. What is the ratio of the time Naomi takes to the time Katherine takes to develop a website?	5:4
cn_k12	Let $x_1$ and $x_2$ be the two real roots of the quadratic equation in $x$, $x^2 + ax + a = 2$. Then, the maximum value of $(x_1 - 2x_2)(x_2 - 2x_1)$ is.	-\frac{63}{8}
orca_math	Damien jogs 5 miles per day on certain days of the week only. He runs 75 miles over three weeks. On which days of the week does he jog?	15
cn_k12	$ \sin 15^\circ \cos 75^\circ + \cos 15^\circ \sin 75^\circ = $	1
cn_k12	Calculate: $-3^{2}+\sqrt{(-2)^{4}}-\sqrt[3]{-27}$.	-2
cn_k12	Using the digits from 0 to 9, how many unique three-digit numbers can be formed without repeating any digit?	648
orca_math	Nina has five times more math homework, nine times more reading homework, and three times more science homework than Ruby. If Ruby has 12 math problems, 4 reading problems, and 5 science problems, what is the total number of math, reading, and science problems that Nina has to complete?	111
orca_math	A glass was filled with 12 ounces of water, and some amount of water evaporated each day during a 22-day period. 5.5 percent of the original amount of water evaporated during this period. How much water evaporated each day?	0.03
cn_k12	Given the function $f(x)= \sqrt{x-1}$. If $f=3$, then the value of $a=$ ______.	10
orca_math	Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate. She worked 3 8-hour shifts this week and averaged $40 in orders per hour. Jill earned $240 this week. What is the standard tip rate of the cost of the orders she serves?	15\%
orca_math	The toll t, in dollars, for a truck using a certain bridge is given by the formula t = 2.50 + 0.50 (x - 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?	\$4.00
orca_math	a number x is 12 times another number y . the percentage that y is less than x is	91.67\%
orca_math	An article is sold for Rs. 350 and Rs. 340, and the profit percentage is different for each selling price. If the cost of the article is Rs. 200, what is the difference in profit percentage between the two selling prices?	5\%
orca_math	A ship going at the speed of 18 km/hr crosses a lighthouse in 20 seconds. What is the length of the ship in meters?	100
cn_k12	A certain company had a turnover of $1$ million in May and $1.21$ million in July. It is known that the growth rates in June and July are the same. What is the growth rate?	10\%
orca_math	You have collected some crickets. You need to collect 4 more crickets to have 11 crickets. How many crickets have you collected so far?	7
cn_k12	Calculate: $\frac{5}{6} \times [1 \div (\frac{7}{8} - \frac{3}{4})]$.	\frac{20}{3}
cn_k12	(2011•Shandong) In a certain university, there are 150, 150, 400, and 300 students in majors A, B, C, and D respectively. To understand the employment preferences of the students, a stratified sampling method is used to survey 40 students from these four majors. The number of students to be sampled from major C should be __________.	16
orca_math	A new factory hires some people to make t-shirts. Each person makes on average 20 shirts per day during their 8-hour shift. The employees each get paid $12 an hour plus $5 per shirt they make. The company sells shirts for $35 each. Nonemployee expenses come out to $1000 a day. The company makes $9080 in profits per day. How many people does the factory hire?	20
orca_math	A boy sells a book for Rs. 720 and gets a certain percentage of loss. To gain 10%, the selling price should be Rs. 880. What is the percentage of loss in the original selling price?	10\%
orca_math	Car A runs at the speed of 70 km/hr and reaches its destination in a certain amount of time. Car B runs at the speed of 35 km/h and reaches its destination in the same amount of time. The respective ratio of distances covered by Car A and Car B is 2. How long does it take for both cars to reach their destinations?	2,
cn_k12	If $\sin\alpha = 3\sin(\alpha - 2\beta)$, then $\tan(\alpha - \beta) + 2\tan\beta = \_\_\_\_\_\_$.	4\tan\beta
orca_math	Chloe was unboxing some of her old winter clothes. She found 4 boxes of clothing and inside each box there were 2 scarves and some mittens. Chloe had a total of 32 pieces of winter clothing. How many mittens were in each box?	6
orca_math	Jack received 6 emails and 8 letters in the morning. He then received 2 emails and 7 letters in the afternoon. How many more letters did Jack receive in the morning than in the afternoon?	1
orca_math	Kaleb had 39 pieces of clothing to wash. He put some of them in one load, but decided to split the rest into 5 equal loads with 4 pieces of clothing in each. How many pieces of clothing did Kaleb put in the first load?	19
cn_k12	Given a sequence $\{a_n\}$ that satisfies $a_{s \cdot t} = a_s \cdot a_t$ (where $s, t \in \mathbb{N}^*$), and given that $a_2 = 2$, find $a_8$.	8
orca_math	A can do a work in 6 days. B can do the same work in 12 days. If both A & B are working together, in how many days can they finish the work?	4
orca_math	Tom Sawyer has tricked his friends into whitewashing Aunt Polly's 100-foot fence. His first friend, Ben, whitewashed some feet. His second friend Billy whitewashed a fifth of the remaining fence. A third friend, Johnny, whitewashed a third of the fence that was left after that. There are still 48 feet of the fence that need to be whitewashed. How many feet did Ben whitewash?	10
orca_math	If 2^5, 3^3, and 14^2 are all factors of the product of 936 and a positive integer, what is the smallest possible value of that positive integer?	1764
orca_math	during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets e sold was 25200 , how many of them were sold at full price ?	27000
orca_math	If Harold split 15 apples between 3 people in her class and kept the leftovers, how many apples did each classmate get?	5
orca_math	The average expenditure of a labourer for 6 months was 75, and he fell into debt. In the next 4 months, by reducing his monthly expenses to 60, he not only cleared off his debt but also saved some money. His monthly income is 72. How much money did he save after clearing off his debt?	30
orca_math	In a school with 632 students, the average age of the boys is 12 years and that of the girls is 11 years. The number of girls in the school is 158. What is the average age of the school?	11.75
orca_math	A shipment of 230 smartphones contains 84 that are defective. If a customer buys a certain number of smartphones at random from the shipment, the approximate probability that all phones are defective is 0.13237136890070247. How many smartphones does the customer buy?	2
cn_k12	$-20$ is the $\_\_\_\_\_$ term of the sequence $\{(-1)^{n+1}n(n+1)\}$.	4
orca_math	If 6 / w + 6 / x = 6 / y and wx = y, then the average (arithmetic mean) of w and x is 0.5. What is the value of w?	0.5
orca_math	A woman invested a total of 9,000 dollars in 2 accounts, one earning a certain annual interest rate and the other earning 8% annual interest. After 1 year, her combined interest was 678.87 dollars. She invested 6258.0 dollars in the account paying 8% interest. What was the annual interest rate of the first account?	6.5\%
orca_math	youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 12 minutes more to walk to work than to ride his bike to work , then x equals ?	18
orca_math	Brian ran around the school track in 96 seconds. Todd ran around it in some seconds. It took Todd 8 fewer seconds to run around the track. How many seconds did it take Todd to run around the track?	88
orca_math	Luke had 47 pieces of clothing to wash. He put some of them in one load, but decided to split the rest into 5 equal loads. Each of the small loads had 6 pieces of clothing. How many pieces of clothing did Luke put in the first load?	17
orca_math	96 % of the population of a village is 23040 . the total population of the village is ?	24,000
orca_math	The sale price of sarees listed for Rs. 495 after successive discounts of 15%, 10%, and an additional 5% and 3% is?	348.95
cn_k12	The minimum value of the function $f(x) = 2\sin(2x + \frac{\pi}{6})$ in the interval $[0, \frac{\pi}{12}]$ is ______.	1

orca_math

Three scenes from an hour-long movie were cut due to multiple copyright issues. The first scene was 3 minutes long, the second scene was 5 minutes and 30 seconds long, and the third scene was 2 minutes and 15 seconds long. What is the final length of the movie (in minutes and seconds)?

49

orca_math

A car travels at a certain speed. It travels 325 miles in 5 hours. What is the speed of the car in miles per hour?

65

cn_k12

For any real numbers $a (a \neq 0)$ and $b$, the inequality $|a+b|+|a-b|\geqslant |a|\cdot|x-2|$ always holds. Determine the range of the real number $x$.

[0,4]

orca_math

A grocer has 400 pounds of coffee in stock, some percent of which is decaffeinated. The grocer buys another 100 pounds of coffee, of which 60 percent is decaffeinated. The grocer's stock of coffee is 28.000000000000004 percent decaffeinated by weight. What percent of the initial stock was decaffeinated?

20\%

cn_k12

It is known that $\xi$~$N(0,\sigma^2)$, and $P(-2\leq\xi\leq0)=0.4$. Find the probability of $P(\xi>2)$.

0.1

orca_math

There were some onions on the shelf. Sixty-five were sold, and now there are 33 onions left on the shelf. How many onions were there on the shelf initially?

98

orca_math

Tina saved some money in June, $14 in July, and $21 in August. Then Tina spent $5 on books and $17 on new shoes. Tina has $40 left. How much money did Tina save in June?

\$27

orca_math

A worksheet had some problems on it. If a teacher had 9 worksheets to grade and had already graded 5 of them, she has to grade 16 more problems. How many problems are on each worksheet?

4

orca_math

of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?

1200

orca_math

In a two-digit number, it is known that its unit's digit exceeds its 10's digit by 4 and that the product of the given number and the sum of its digits is equal to a certain value. What is the product of the number and the sum of its digits if the number is 26?

208

orca_math

Lindsey saved $50 in September, $37 in October, and $11 in November. Lindsey's mom said that since Lindsey had saved more than a certain amount, she would give Lindsey $25. After spending $87 on a video game, Lindsey had $36 left. What was the minimum amount Lindsey needed to save for her mom to give her $25?

\$98

cn_k12

Given that the function $y=f\left(x\right)$ is an odd function, defined on $R$, and satisfies $f\left(x+4\right)=f\left(x\right)$. When $x\in \left(0,2\right)$, $f\left(x\right)=2^{x}+\log _{3}(x+2)$, find $f\left(2023\right)$.

-3

orca_math

if the product of two numbers is 987153000 and their h . c . f . is 440 , find their l . c . m .

2243525

orca_math

In Yardley, it snowed 0.12 inches in the early morning, 0.24 inches in the late morning, 0.5 inches in the afternoon, and 0.36 inches in the evening. Calculate the total amount of snowfall accumulated throughout the day.

1.22

orca_math

There are 4 types of stickers on a page: Type A has 5 stickers, Type B has 3 stickers, Type C has 2 stickers, and Type D has 1 sticker. If you have 22 pages of stickers, how many stickers of each type do you have in total?

22

orca_math

Carol was sending out birthday invitations to some friends. If each package of invitations she bought had 2 invitations in it and she needed 5 packs, how many friends is she inviting?

10

orca_math

There are 120 students who have to split 8,365 portfolios of paintings. Each student should get at least one portfolio, but they should all receive the same number of portfolios. Additionally, 15% of the students must each receive 10 more portfolios than the remaining 85% of the students. How many portfolios of paintings will each group of students get and how many portfolios will be left after the distribution process is complete?

25

gsm8k

Mary and Jay are planning a wedding. Of the 240 guests, 60 percent are female. Of the females, 50 percent are from Jay's family. How many female guests are from Jay's family?

72

orca_math

Three friends are about to share a strawberry juice. Seonghwa drank 1/6 of the total and Siyeon drank 2/5 of the rest. And if the amount of juice after Youngmin drank 2/3 of the remaining juice was 120 milliliters (㎖), how many milliliters (㎖) of strawberry juice was there at the beginning?

720

orca_math

Find the mass percentage of Al in Aluminum phosphate.

22.12\%

orca_math

A train moves with a certain speed in kmph. Its speed in metres per second is 37.503. What is the speed of the train in kmph?

135.0108

orca_math

40 multiplied by 30, plus (12 + 8) multiplied by a certain number, divided by 5 equals 1212. What is the number?

3

cn_k12

To understand the physical condition of students in grades 10, 11, and 12, a sample of size $1200$ is randomly selected using stratified sampling. The ratio of the number of students in the three grades is $k:5:3$ respectively. It is known that $240$ students from grade 10 were selected. Find the number of students selected from grade 12.

360

cn_k12

Given the function f(x) = g(x) + $$\frac{2019}{2018}$$x^2, where g(x) is an odd function defined on the set of real numbers, and f(1) = 2, find the value of f(-1).

\frac{1}{1009}

orca_math

A 10000-liter tank, half-full of water, is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains. One drain has a rate of 1 kiloliter every 6 minutes. It takes 60 minutes to fill the tank completely. What is the rate of the other drain?

0.25

orca_math

Tim rides his bike back and forth to work for each of his 5 workdays. His work is 20 miles away. He also goes for a weekend bike ride of 200 miles. If he spends 16 hours biking a week, what is his average biking speed in mph?

25

orca_math

a 900 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?

1050

orca_math

Janet hires six employees. Four of them are warehouse workers who make a certain amount per hour, and the other two are managers who make $20/hour. Janet has to pay 10% of her workers' salaries in FICA taxes. If everyone works 25 days a month and 8 hours a day, Janet owes a total of $22,000 for their wages and taxes for one month. How much do the warehouse workers make per hour?

\$15

orca_math

joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 6 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?

120

orca_math

The pet shop grooms dogs. It takes 30 minutes to groom a poodle. It takes half as much time to groom a terrier as it takes to groom a poodle. They do not groom cats. The pet shop grooms some poodles and 8 terriers, and it takes a total of 210 minutes. How many poodles were groomed?

3

orca_math

John plays paintball 3 times a month. Each time he plays, he buys 3 boxes of paintballs. They cost $25 per box. How much does he spend a month on paintballs?

\$225

orca_math

A buffet offers ranch or caesar dressing. They use a certain ratio of ranch dressing to caesar dressing. If the buffet uses 28 cases of ranch dressing and 4 cases of caesar dressing, what is the ratio of ranch dressing used to caesar dressing used?

7:1

orca_math

A chef served 3 different foods for a banquet: 25 plates lobster rolls, 14 plates of spicy hot noodles and 16 plates of seafood noodles. How many plates of food did the chef make altogether?

55

orca_math

A 50 ml after-shave lotion with a certain percentage of alcohol is mixed with 30 ml of pure water. The percentage of alcohol in the new solution is 18.75%. What is the initial percentage of alcohol in the after-shave lotion?

30\%

orca_math

ratio between two numbers is 3 : 4 and their sum is 420 . find the smaller number ?

180

cn_k12

Let the sequence $\{a_n\}$ satisfy $a_1=7$, and $a_n+a_{n+1}=20$. The sum of the first 50 terms of $\{a_n\}$ is ______.

500

orca_math

Pat is having a picnic with her family. She has 42 cookies. She also has some pieces of candy and 21 brownies. There are 7 people in her family. Each person gets 18 pieces of dessert. How many pieces of candy does Pat have?

63

orca_math

Jane started babysitting when she was 18 years old. Whenever she babysat for a child, that child was a certain fraction of her age at the time. Jane is currently 34 years old, and she stopped babysitting 10 years ago. The current age of the oldest person for whom Jane could have babysat is 25. What is the fraction of Jane's age that the child could be at most?

\frac{5}{8}

orca_math

A pet store had 13.5 Siamese cats and 5.25 house cats. During a purchase, they added 10.75 cats but had to give a special discount of 0.5 cats as a refund for a customer. How many cats do they have left?

29

cn_k12

If the one-variable quadratic equation $3x^{2}-6x+k=0$ has two identical real roots with respect to $x$, then the value of $k$ is ______.

3

orca_math

In a class, there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row, there are some more desks than in the previous row. The maximum number of students seated in the class is 136. How many more desks are in each subsequent row compared to the previous row?

2

orca_math

Dennis lives two floors above Charlie. Charlie lives on a floor whose number is 1/4 of Frank's floor number. Frank lives on a certain floor, and Dennis lives on the 6th floor. What floor does Frank live on?

16th

cn_k12

Simplify first, then evaluate: $a-2(a-b^{2})+3(-a+b^{2})$, where $a=2$, $b=-\frac{1}{2}$.

-\frac{27}{4}

orca_math

If 40% of 3/5 of a number is 36, what is the number?

150

orca_math

If 20% of x is 15 less than 15% of a certain number, then x is 1050. What is the number?

1500

orca_math

Company P had 15 percent more employees in December than it had in January. If Company P had 391.304347826087 employees in January, how many employees did it have in December?

450

orca_math

A company pays 15.5% dividend to its investors. An investor buys some shares and gets 25% on investment. The investor bought the shares at Rs. 31. What is the face value of the shares?

50

orca_math

a bag marked at $ 200 is sold for $ 120 . the rate of discount is ?

40\%

orca_math

Armand is playing a guessing game with his dad where he has to guess a number his dad is thinking of. His dad tells him that the number, when multiplied by 3, is three less than twice a certain number. The number Armand has to guess is 33. What is the certain number?

51

cn_k12

The function $f(x) = x(x - m)^2$ has a local minimum at $x = 1$. Find the value of $m$.

1

orca_math

Darry is a roofer and has to climb ladders multiple times a day. He climbs his largest ladder, which has 20 steps, 12 times today. He also climbs his medium-sized ladder, which has 15 steps, 8 times today, and his smaller ladder, which has 10 steps, 10 times today. Additionally, Darry climbs his smallest ladder, which has 5 steps, 15 times today. He did not climb any steps otherwise. In total, how many times has Darry climbed a step today?

535

orca_math

Ram can do a job in 10 days, and Gohul can do the same job in some days independently. They take 5.999999999999999 days to complete the same job working simultaneously. How many days would Gohul take to complete the job independently?

15

orca_math

A man walks at a rate of 10 mph. After every ten miles, he rests for a certain amount of time. He takes 328 minutes to walk 50 miles. How many minutes does he rest after every ten miles?

7

orca_math

The average weight of some students is 28 kg. By the admission of a new student weighing 4 kg, the average weight is reduced to 27.2 kg. How many students were there initially?

29

orca_math

During a certain two-week period, some percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were a action movies rented, then there were 10a comedies rented during that two-week period. What is the percentage of comedies rented during that two-week period?

62.5\%

cn_k12

To understand whether 236 households affected by demolition are satisfied with the compensation plan, Xiao Ming surveyed 50 of these households over the weekend. Among them, 32 households expressed satisfaction with the plan. In this survey, the sample size is ____.

50

orca_math

In the formula a = (2r)^n, if r is halved, then a is multiplied by 0.125. What is the value of n?

3

orca_math

As a freelancer, Katherine takes 20 hours to develop a website for her clients. Her junior, Naomi, takes some more time to complete creating a similar website. In a particular year, Katherine gave her junior 30 websites to develop. Naomi took a total of 750 hours to create the 30 websites. What is the ratio of the time Naomi takes to the time Katherine takes to develop a website?

5:4

cn_k12

Let $x_1$ and $x_2$ be the two real roots of the quadratic equation in $x$, $x^2 + ax + a = 2$. Then, the maximum value of $(x_1 - 2x_2)(x_2 - 2x_1)$ is.

-\frac{63}{8}

orca_math

Damien jogs 5 miles per day on certain days of the week only. He runs 75 miles over three weeks. On which days of the week does he jog?

15

cn_k12

$ \sin 15^\circ \cos 75^\circ + \cos 15^\circ \sin 75^\circ = $

1

cn_k12

Calculate: $-3^{2}+\sqrt{(-2)^{4}}-\sqrt[3]{-27}$.

-2

cn_k12

Using the digits from 0 to 9, how many unique three-digit numbers can be formed without repeating any digit?

648

orca_math

Nina has five times more math homework, nine times more reading homework, and three times more science homework than Ruby. If Ruby has 12 math problems, 4 reading problems, and 5 science problems, what is the total number of math, reading, and science problems that Nina has to complete?

111

orca_math

A glass was filled with 12 ounces of water, and some amount of water evaporated each day during a 22-day period. 5.5 percent of the original amount of water evaporated during this period. How much water evaporated each day?

0.03

cn_k12

Given the function $f(x)= \sqrt{x-1}$. If $f=3$, then the value of $a=$ ______.

10

orca_math

Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate. She worked 3 8-hour shifts this week and averaged $40 in orders per hour. Jill earned $240 this week. What is the standard tip rate of the cost of the orders she serves?

15\%

orca_math

The toll t, in dollars, for a truck using a certain bridge is given by the formula t = 2.50 + 0.50 (x - 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?

\$4.00

orca_math

a number x is 12 times another number y . the percentage that y is less than x is

91.67\%

orca_math

An article is sold for Rs. 350 and Rs. 340, and the profit percentage is different for each selling price. If the cost of the article is Rs. 200, what is the difference in profit percentage between the two selling prices?

5\%

orca_math

A ship going at the speed of 18 km/hr crosses a lighthouse in 20 seconds. What is the length of the ship in meters?

100

cn_k12

A certain company had a turnover of $1$ million in May and $1.21$ million in July. It is known that the growth rates in June and July are the same. What is the growth rate?

10\%

orca_math

You have collected some crickets. You need to collect 4 more crickets to have 11 crickets. How many crickets have you collected so far?

7

cn_k12

Calculate: $\frac{5}{6} \times [1 \div (\frac{7}{8} - \frac{3}{4})]$.

\frac{20}{3}

cn_k12

(2011•Shandong) In a certain university, there are 150, 150, 400, and 300 students in majors A, B, C, and D respectively. To understand the employment preferences of the students, a stratified sampling method is used to survey 40 students from these four majors. The number of students to be sampled from major C should be __________.

16

orca_math

A new factory hires some people to make t-shirts. Each person makes on average 20 shirts per day during their 8-hour shift. The employees each get paid $12 an hour plus $5 per shirt they make. The company sells shirts for $35 each. Nonemployee expenses come out to $1000 a day. The company makes $9080 in profits per day. How many people does the factory hire?

20

orca_math

A boy sells a book for Rs. 720 and gets a certain percentage of loss. To gain 10%, the selling price should be Rs. 880. What is the percentage of loss in the original selling price?

10\%

orca_math

Car A runs at the speed of 70 km/hr and reaches its destination in a certain amount of time. Car B runs at the speed of 35 km/h and reaches its destination in the same amount of time. The respective ratio of distances covered by Car A and Car B is 2. How long does it take for both cars to reach their destinations?

2,

cn_k12

If $\sin\alpha = 3\sin(\alpha - 2\beta)$, then $\tan(\alpha - \beta) + 2\tan\beta = \_\_\_\_\_\_$.

4\tan\beta

orca_math

Chloe was unboxing some of her old winter clothes. She found 4 boxes of clothing and inside each box there were 2 scarves and some mittens. Chloe had a total of 32 pieces of winter clothing. How many mittens were in each box?

6

orca_math

Jack received 6 emails and 8 letters in the morning. He then received 2 emails and 7 letters in the afternoon. How many more letters did Jack receive in the morning than in the afternoon?

1

orca_math

Kaleb had 39 pieces of clothing to wash. He put some of them in one load, but decided to split the rest into 5 equal loads with 4 pieces of clothing in each. How many pieces of clothing did Kaleb put in the first load?

19

cn_k12

Given a sequence $\{a_n\}$ that satisfies $a_{s \cdot t} = a_s \cdot a_t$ (where $s, t \in \mathbb{N}^*$), and given that $a_2 = 2$, find $a_8$.

8

orca_math

A can do a work in 6 days. B can do the same work in 12 days. If both A & B are working together, in how many days can they finish the work?

4

orca_math

Tom Sawyer has tricked his friends into whitewashing Aunt Polly's 100-foot fence. His first friend, Ben, whitewashed some feet. His second friend Billy whitewashed a fifth of the remaining fence. A third friend, Johnny, whitewashed a third of the fence that was left after that. There are still 48 feet of the fence that need to be whitewashed. How many feet did Ben whitewash?

10

orca_math

If 2^5, 3^3, and 14^2 are all factors of the product of 936 and a positive integer, what is the smallest possible value of that positive integer?

1764

orca_math

during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets e sold was 25200 , how many of them were sold at full price ?

27000

orca_math

If Harold split 15 apples between 3 people in her class and kept the leftovers, how many apples did each classmate get?

5

orca_math

The average expenditure of a labourer for 6 months was 75, and he fell into debt. In the next 4 months, by reducing his monthly expenses to 60, he not only cleared off his debt but also saved some money. His monthly income is 72. How much money did he save after clearing off his debt?

30

orca_math

In a school with 632 students, the average age of the boys is 12 years and that of the girls is 11 years. The number of girls in the school is 158. What is the average age of the school?

11.75

orca_math

A shipment of 230 smartphones contains 84 that are defective. If a customer buys a certain number of smartphones at random from the shipment, the approximate probability that all phones are defective is 0.13237136890070247. How many smartphones does the customer buy?

2

cn_k12

$-20$ is the $\_\_\_\_\_$ term of the sequence $\{(-1)^{n+1}n(n+1)\}$.

4

orca_math

If 6 / w + 6 / x = 6 / y and wx = y, then the average (arithmetic mean) of w and x is 0.5. What is the value of w?

0.5

orca_math

A woman invested a total of 9,000 dollars in 2 accounts, one earning a certain annual interest rate and the other earning 8% annual interest. After 1 year, her combined interest was 678.87 dollars. She invested 6258.0 dollars in the account paying 8% interest. What was the annual interest rate of the first account?

6.5\%

orca_math

youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 12 minutes more to walk to work than to ride his bike to work , then x equals ?

18

orca_math

Brian ran around the school track in 96 seconds. Todd ran around it in some seconds. It took Todd 8 fewer seconds to run around the track. How many seconds did it take Todd to run around the track?

88

orca_math

Luke had 47 pieces of clothing to wash. He put some of them in one load, but decided to split the rest into 5 equal loads. Each of the small loads had 6 pieces of clothing. How many pieces of clothing did Luke put in the first load?

17

orca_math

96 % of the population of a village is 23040 . the total population of the village is ?

24,000

orca_math

The sale price of sarees listed for Rs. 495 after successive discounts of 15%, 10%, and an additional 5% and 3% is?

348.95

cn_k12

The minimum value of the function $f(x) = 2\sin(2x + \frac{\pi}{6})$ in the interval $[0, \frac{\pi}{12}]$ is ______.

1