pe-nlp/numina_orz_deepscaler_resampled · Datasets at Hugging Face

source string	problem string	answer string
orca_math	In years 1998 and 1999, the profits of three companies A, B, and C were 10 percent, 15 percent, and 8 percent of their respective revenues. In 1999, the revenues of company A fell by 30 percent, the revenues of company B increased by 25 percent, and the revenues of company C remained unchanged. However, their respective profit ratios changed, with company A having a profit ratio of 12 percent, company B having a profit ratio of 10 percent, and company C having a profit ratio of 18 percent in 1999. Calculate the profits of each company in 1999 as a percentage of their profits in 1998.	225\%
orca_math	The average monthly income of P and Q is some amount. The average monthly income of Q and R is Rs. 6250, and the average monthly income of P and R is Rs. 5200. If the monthly income of P is Rs. 4000, what is the average monthly income of P and Q?	5050
orca_math	In an examination, 34% of total students failed in Hindi, 44% failed in English, and 22% failed in both. What is the percentage of students who passed in both subjects?	44\%
orca_math	Lisa and Kay were asked by their mother to clean their room . Lisa can clean the room in 8 hours , Kay can do it in 12 hours and their younger brother, Ben, takes 16 hours to clean the room. How long will it take if they all clean their room together?	3.69
gsm8k	A club is going to get additional members so that they will have 5 more than twice their current number of their members. If the club has 10 members now, how many additional members do they need?	15
orca_math	How much is 60% of 50 greater than 30% of 30?	21
orca_math	Eddy and Freddy start simultaneously from city A and they travel to city B and city C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. The distance between city A and city B is 600 kms and city A and city C is 360 kms. What is the ratio of their average speed of travel? (Eddy : Freddy)	20:9
orca_math	The average age of an adult class is 40 years. 10 new students with a certain average age join the class, therefore decreasing the average by 4 years. The original strength of the class was 10. What was the average age of the new students?	32
orca_math	Annika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 35 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 35 minutes, for how many kilometers total did she hike east?	3.5
orca_math	James does chores around the class. There are some bedrooms, 1 living room, and 2 bathrooms to clean. The bedrooms each take 20 minutes to clean. The living room takes as long as the bedrooms combined. The bathroom takes twice as long as the living room. He also cleans the outside which takes twice as long as cleaning the house. He splits the chores with his 2 siblings who are just as fast as him. He works for 4 hours. How many bedrooms are there to clean?	3
orca_math	The ratio of boys to girls in a math class is 5:8, and the ratio of math to science students is 7:4. If the total number of students in both math and science classes is 458, how many girls are in the math class?	184
orca_math	Find the amount of Ammonium chloride that is required to react with 1 mole of Potassium hydroxide to form 1 mole of Ammonia, 1 mole of Water and 1 mole of Potassium chloride	1
orca_math	If animal (A) and animal (B) are added together, there are 17 animals. If there are 8 (B)s, how many (A)s are there?	9
orca_math	The light glows for every 30 seconds. Between 1:57:58 and a certain time, it glowed a maximum of 165.63333333333333 times. What was the ending time?	4:05:47
orca_math	Lee wants to propose marriage to Sierra. He wants to follow the adage that you should spend two months' salary on the ring. He earns $60,000 per year in salary and can save a certain amount per month. It will take him 10 months before he can propose to Sierra. How much can he save per month?	\$1,000
orca_math	The average mark of the students of a class in a particular exam is some value. If 5 students whose average mark in that exam is 44 are excluded, the average mark of the remaining will be 80. There were 9 students who wrote the exam. What was the initial average mark of the class?	60
orca_math	In the school's library, there are 2300 different books. 80% of all the books are in English. A certain percentage of these English books were published in the country, and there are 736 English-language books published outside the country. What percentage of the English books were published in the country?	59.78\%
cn_k12	Given $3\sin \alpha =\cos \alpha $, then the value of $\tan \left(\pi -\alpha \right)$ is ______.	-\frac{1}{3}
orca_math	He was told by one the pickers that they fill some drums of grapes per day. They would fill 2916 drums of grapes in 9 days. How many drums of grapes do they fill per day?	324
cn_k12	For rational numbers $a$ and $b$, if $\sqrt{a+4}+(b-2)^2=0$, then $a-b=\_\_\_\_\_\_.$	-6
orca_math	a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 5 miles per hour for 3 hours . how many miles in total did she walk ?	53
orca_math	A rod has a certain weight. If the weight of a 6 meters long rod is 6.184615384615385 kg, what is the weight of a 13 meters long rod?	13.4
orca_math	A shopkeeper fixes the marked price of an item 50% above its cost price. What percentage of discount should be allowed to gain a 15% profit, and what will be the final selling price of the item after applying the required discount?	\$115
orca_math	Let the ages of three persons a, b, and c be represented by A, B, and C respectively. Given that the total age of a and b is 11 years more than the total age of b and c, also assume that person d has an age represented by D, and the total age of a, b, and d is 8 years more than the total age of b, c, and d. Determine how many years younger C is when compared to the sum of A and D.	11
cn_k12	Given the sets $A=\{-1, 0, 2\}$ and $B=\{2^a\}$, if $B \subseteq A$, then the value of the real number $a$ is \_\_\_\_\_\_.	1
orca_math	A certain amount of money will earn an interest of $300 in 9 months at an annual rate of 4%. How much money was initially invested?	\$10,000
orca_math	A man can row 6 kmph in still water. When the river is running at a certain speed, it takes him 1 hour to row to a place and back. The total distance traveled by the man is 5.333333333333333 km. What is the speed of the river?	2
orca_math	In a class of some children, 30% of children can speak only English, 20% can speak Hindi and English both, and the rest of the children can speak only Hindi. There are 42 children who can speak Hindi. How many children are there in the class?	60
orca_math	Before work, Hayden spends 5 minutes ironing his button-up shirt and 3 minutes ironing his pants. He does this 5 days a week. Over a certain number of weeks, he spends 160 minutes ironing. How many weeks does this time period cover?	4
orca_math	If x is 11 percent greater than 70, what is the value of x?	77.7
orca_math	Mike took a taxi to the airport and paid a certain amount to start plus $0.25 per mile. Annie took a different route to the airport and paid the same starting amount plus $5.00 in bridge toll fees plus $0.25 per mile. Each was charged exactly the same amount, and Annie's ride was 26 miles. How many miles was Mike's ride if his starting amount was $2.50?	46
orca_math	A carpenter worked alone for 1 day on a job. He and another carpenter completed the job in 2 more days. It would have taken the second carpenter 5 days to do the complete job working alone. How many more days would it have taken the first carpenter to finish the job alone?	4
orca_math	Hanna has twice as many erasers as Rachel. Rachel has some erasers as Tanya has red erasers. Tanya has 20 erasers, and half of them are red. Hanna has 4 erasers. What is the difference between the number of erasers Rachel has and one-half the number of red erasers Tanya has?	5
orca_math	At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. There are a certain number of male associates, and there are 40 female managers. How many male associates are there?	160
orca_math	In a class, some students like to play basketball and 8 like to play cricket. 5 students like to play both basketball and cricket. There are 10 students who like to play basketball or cricket or both. How many students like to play basketball?	7
orca_math	Three times a number minus a second number is a certain value. The sum of the two numbers is 48. The smaller number is 17. What is the value of three times the first number minus the second number?	76
cn_k12	Given the constant $a \in \mathbb{R}$, if the coefficient of the $x^7$ term in the binomial expansion of $({x^2 + \frac{a}{x}})^5$ is $-15$, find the value of $a$.	-3
orca_math	It takes Bryan 5 minutes to walk from his house to the bus station. Then he rides the bus for some minutes. After that, he walks 5 minutes from the bus station to his job. It takes the same amount of time in the morning and the evening. Bryan spends 365 hours per year traveling to and from work, if he works every day. How many minutes does Bryan spend riding the bus one way?	20
orca_math	A man is 28 years older than his son. In two years, his age will be a multiple of the age of his son. The present age of the son is 26 years. What is the ratio of the man's age to his son's age in two years?	2:1
cn_k12	Place 4 identical white balls, 5 identical black balls, and 6 identical red balls into 3 of 4 distinct boxes such that one box remains empty and the other three boxes each contain all three colors. The total number of different ways to do this is ___.	720
orca_math	A case of some rolls of paper towels sells for $9. The cost of one roll sold individually is $1. The percent of savings per roll for the case over the cost of the same number of rolls purchased individually is 25%. How many rolls are in the case?	12
orca_math	If the personal income tax rate is lowered from 46% to 32%, the differential savings for a taxpayer having an annual income before tax of some amount is $5040. What is the taxpayer's annual income before tax?	\$36,000
orca_math	The swimming club went to a swim meet in another town. They took 2 cars and 3 vans. There were 5 people in each car and 3 people in each van. Each car can hold a maximum of 6 people and each van can hold a maximum of 8 people. How many more people could have ridden with the swim team?	17
orca_math	The average expenditure of a labourer for 6 months was 80, 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 30. What is his monthly income?	75
orca_math	What is the least number which when divided by a certain number, 7, 9 and 18 leaves remainder 4 in each case and the number is 130?	126,
cn_k12	The complex number $z$ satisfies $(1+2i)z=5$, then $z=$ \_\_\_\_\_\_.	1-2i
cn_k12	If $$\int_{1}^{a} (2x + \frac{1}{x})dx = 3 + \ln 2$$ (where $a > 1$), then the value of $a$ is \_\_\_\_\_\_.	2
orca_math	Autumn was constantly misplacing her pencils. At the start of the school year, she purchased a pack of 20 pencils. In the first month of school, she misplaced some pencils, broke 3 pencils and had to throw them away, she found 4, and bought 2. Autumn had 16 pencils left. How many pencils did she misplace?	7
orca_math	Ceasar needs to read three different books for his literature class. The first book has a total of 563 pages and he has already read 147 pages. The second book contains 849 pages and he has managed to read 389 pages. The last book is 700 pages long and he's read only 134 pages. How many pages in total does he still need to read from all three books?	1442
cn_k12	Given a sequence $\{a\_n\}$ with the first term $a\_1=1$, and it satisfies $a\_{2n+1}=2a\_{2n-1}$ and $a\_{2n}=a\_{2n-1}+1$, find the value of $S\_{20}$ = \_\_\_\_\_\_.	2056
orca_math	two numbers have a h . c . f of 20 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?	128
orca_math	A hotel has 20 rooms and is currently full. Each room holds a family of 5. If each person receives 3 towels, how many towels does the hotel hand out?	300
orca_math	Renaldo drove 15 kilometers. Ernesto drove 7 kilometers more than one-third of Renaldo's distance. How many kilometers did the 2 men drive in total?	27
orca_math	Find the value of a number when multiplied by 9999, the result is 824777405. What is the number?	82482.5
orca_math	Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by some inches by 5 inches, and the maximum number of cake boxes that can be placed in each carton is 210, what is the width of a cake box?	7.5
cn_k12	Given a complex number $z$ satisfying $\|z\|=1$, find the maximum value of $\|z+1+\sqrt{3}i\|$.	3
orca_math	in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 8 years older than b , the present age of b is	38
orca_math	Ashley wants a champagne toast at her wedding. She wants to serve a certain number of glasses of champagne to each of her 120 wedding guests. 1 bottle of champagne has 6 servings. She will need 40 bottles of champagne. How many glasses of champagne does she want to serve to each guest?	2
orca_math	The sum of 0.75 of a number and two is eight. Find the number.	8
orca_math	Sara picked 45 pears and Sally picked 11 pears from the pear tree. How many pears were picked in total?	56
orca_math	There are 34 dogwood trees currently in the park. Park workers will plant some dogwood trees today. The park will have 83 dogwood trees when the workers are finished. How many dogwood trees will the workers plant today?	49
orca_math	A train travelling at 98 kmph takes 5.142857142857143 seconds to pass an electric pole. The train is of a certain length. What is the length of the train in meters?	140
orca_math	If 25% of x is a certain amount less than 20% of 1000, then x is 680. What is the amount?	30
orca_math	The length of a room is 5.5 m and the width is 3.75 m. The cost of paving the floor by slabs at a certain rate per sq. meter is Rs. 20625. What is the rate of paving the floor per sq. meter?	1000
orca_math	An air-conditioning unit costs $470. In December, there was a discount for Christmas of 16%. After the Christmas discount, the company offered an additional discount for a limited time on energy-efficient models at 7%. 6 months later, the holiday season was over and the company raised the price of the air-conditioning unit by 12%. In addition, due to an increase in production costs, there was an additional 8% increase in the price. In November, the company offers a seasonal promotion with a 10% discount on the final price. How much will an air-conditioning unit cost in November considering all these changes?	\$399.71
orca_math	A lent Rs. 5000 to B for 2 years and some money to C for 4 years on simple interest at the same rate of interest and received Rs. 2640 in all from both of them as interest. The rate of interest per annum is 12%. How much money did A lend to C?	3000
orca_math	Michelle uses some beads in making a necklace. She uses 5 blue beads, 2 times as many red beads as blue beads, the same number of white beads as the blue and red beads combined, and 10 silver beads. How many beads does she use in total?	40
orca_math	how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 4 m x 2 m x 25 cm ?	1186
orca_math	if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 15 . what is the value of f ( 6 ) ?	4
orca_math	When toys are grouped into 12 and 18, always 3 toys remain ungrouped. What is the minimum number of toys to be added so that when they are grouped into 7, no toys will remain ungrouped?	4
orca_math	Shirley sold some boxes of trefoils. She needs to deliver 5 cases of boxes, with 2 boxes in each case. How many boxes of trefoils did she sell?	10
cn_k12	From a group of 3 male students and 2 female students, 2 students are randomly selected to participate in volunteer service. What is the probability that at least 1 of the selected students is female?	\frac{7}{10}
cn_k12	Find the solution set for the inequality $$\frac {1}{x} > 1$$; If the solution set for the inequality $a^2 + b + 2 > 0$ is $x - \frac {1}{2} < x < \frac {1}{3}$, find the value of $a + b$.	10
orca_math	A car is running at a certain speed. It covers a distance of 400 meters in 12 seconds. What is the speed of the car in kmph?	120
orca_math	Amanda's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Amanda $4.60 per pound, and type B coffee costs $5.95 per pound. This month's blend used twice as many pounds of type B coffee as type A. Amanda used 67.52 pounds of type A coffee. What was the total cost of the coffee blend?	\$1114.08
orca_math	A carpenter gave an estimate of 980 dollars to build a cover over a patio. He expects to need 560 dollars in materials and estimates that the job will take 15 hours. What is his hourly rate?	\$28
cn_k12	In the expansion of the algebraic expression $({\sqrt{x}-\frac{1}{{{x^2}}}})^5$, the constant term is ______.	-5
gsm8k	Scarlet saved $80 to spend on jewelry. She bought a pair of earrings that cost $23. Then, she bought a necklace that cost $48. How much of her savings have left?	9
orca_math	The total dining bill for 5 people was $211.00. They added a certain percentage as a tip and divided the bill evenly. Each person's final share was approximately $48.53. What was the percentage of the tip they added?	15\%
gsm8k	Mrs. Oaklyn buys handmade rugs at $40 each and sells them at $60 each. If she bought 20 rugs, calculate the profit she will make from selling the rugs.	400
orca_math	A swimmer can swim in still water at 4 km/h. If the speed of the water current is a certain speed, the swimmer takes 2.5 hours to swim against the current for 5 km. What is the speed of the water current?	2
orca_math	a group of men decided to do a work in 6 days , but 4 of them became absent . if the rest of the group did the work in 12 days , find the original number of men ?	8
orca_math	A person bought 3 different books. The first book was bought for $60 and sold for $78, the second book was bought for $45 and sold for $54, and the third book was bought for $70 and sold for $84. Calculate the overall profit percentage for all three books.	23.43\%
orca_math	There are 92 students altogether. Twenty of them ride the school bus home together, 5/8 of the remaining ride their own bike home, and the rest whose houses are near the school walk home. How many students are walking home?	27
cn_k12	Let the function f(x) = (x - 2)²sin(x - 2) + 3 have its maximum value M and minimum value m in the interval [-1, 5]. Find the value of M + m.	6
orca_math	On his farm, Mr. Mathews has goats and sheep in the ratio of 5:7. He decides to sell half of the goats at a certain price each and 2/3 of the sheep at $30 each. He makes $7200 from the sale of the animals, and the total number of sheep and goats on the farm is 360. How much does he sell each goat for?	\$40
cn_k12	Let the sequence \\(\left\{a_n\right\}\\) have a sum of the first \\(n\\) terms denoted as \\(s_n\\), and \\(s_n = a(2^n - 1)\\). If \\(a_4 = 24\\), then \\(a = \boxed{3}\\).	3
cn_k12	A person shoots once, with a probability of hitting the target being 0.8. If they shoot 4 times, the probability of hitting the target at least 3 times is.	0.8192
cn_k12	Given that the sum of the first $n$ terms of an arithmetic sequence $\{a\_n\}$ is $S\_n$, and $a\_7 = 7a\_4$, find the value of $\frac{S_{13}}{S_{7}}$.	13
orca_math	Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him some tablets asking him to take one tablet every 15 minutes. It took Roy 60 minutes to consume all the tablets. How many tablets did the doctor give Roy?	4
orca_math	Trent walked 4 blocks from his house to the bus stop. He rode the bus 7 blocks to the library. Later, he came home the same way. How many blocks did Trent travel in all?	22
orca_math	The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The typist presently draws Rs. 4180. What was the original salary of the typist?	4000
cn_k12	Given that $\tan (\frac {π}{4}+α)=2,\tan β= \frac {1}{2}$, find the value of $\tan α$ and evaluate the expression $\frac {\sin (α+β)-2\sin α\cos β}{2\sin α \sin β +\cos (α +β )}$.	\frac{1}{7}
orca_math	You are going to divide a number 20. When you mistakenly multiply the number by 10, the answer is 50. What is the correct calculation result?	4
orca_math	On Tuesday, Max's mom gave him $8.5 dollars for a hot dog at the Grand Boulevard park. On Wednesday, his mom gave him 5.5 times as much money as she gave him on Tuesday. On Thursday, his mom gave him 10% more money than she gave him on Wednesday. On Friday, his mom gave him 75% of the money she gave on Thursday. How much more money did his mom give him on Friday than she gave him on Tuesday?	\$30.06875
orca_math	A man traveled a total distance of 900 km. He traveled some part of the whole trip by plane and the distance traveled by train is two-thirds of the distance traveled by bus. He traveled 360 kilometers by bus. What is the ratio of the distance traveled by plane to the total distance?	1:3
cn_k12	Given the sets $A={a,b,c,d}$ and $B={1,2,3,4,5,6}$, how many different mappings from set $A$ to set $B$ can form $f(a)≤f(b)≤f(c)≤f(d)$?	126
orca_math	Trey is raising money for a new bike that costs $112. He plans to sell bracelets for $1 each. On average, he needs to sell 8 bracelets each day. How long does he plan to sell bracelets?	14
orca_math	The Nutty Professor sells cashews for $6.75 per pound and Brazil nuts for $5.00 per pound. To make a mixture that sells for $5.70 per pound, 20 pounds of cashews should be used. How much does the mixture weigh in total?	50
orca_math	a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 390 m long ?	60

orca_math

In years 1998 and 1999, the profits of three companies A, B, and C were 10 percent, 15 percent, and 8 percent of their respective revenues. In 1999, the revenues of company A fell by 30 percent, the revenues of company B increased by 25 percent, and the revenues of company C remained unchanged. However, their respective profit ratios changed, with company A having a profit ratio of 12 percent, company B having a profit ratio of 10 percent, and company C having a profit ratio of 18 percent in 1999. Calculate the profits of each company in 1999 as a percentage of their profits in 1998.

225\%

orca_math

The average monthly income of P and Q is some amount. The average monthly income of Q and R is Rs. 6250, and the average monthly income of P and R is Rs. 5200. If the monthly income of P is Rs. 4000, what is the average monthly income of P and Q?

5050

orca_math

In an examination, 34% of total students failed in Hindi, 44% failed in English, and 22% failed in both. What is the percentage of students who passed in both subjects?

44\%

orca_math

Lisa and Kay were asked by their mother to clean their room . Lisa can clean the room in 8 hours , Kay can do it in 12 hours and their younger brother, Ben, takes 16 hours to clean the room. How long will it take if they all clean their room together?

3.69

gsm8k

A club is going to get additional members so that they will have 5 more than twice their current number of their members. If the club has 10 members now, how many additional members do they need?

15

orca_math

How much is 60% of 50 greater than 30% of 30?

21

orca_math

Eddy and Freddy start simultaneously from city A and they travel to city B and city C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. The distance between city A and city B is 600 kms and city A and city C is 360 kms. What is the ratio of their average speed of travel? (Eddy : Freddy)

20:9

orca_math

The average age of an adult class is 40 years. 10 new students with a certain average age join the class, therefore decreasing the average by 4 years. The original strength of the class was 10. What was the average age of the new students?

32

orca_math

Annika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 35 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 35 minutes, for how many kilometers total did she hike east?

3.5

orca_math

James does chores around the class. There are some bedrooms, 1 living room, and 2 bathrooms to clean. The bedrooms each take 20 minutes to clean. The living room takes as long as the bedrooms combined. The bathroom takes twice as long as the living room. He also cleans the outside which takes twice as long as cleaning the house. He splits the chores with his 2 siblings who are just as fast as him. He works for 4 hours. How many bedrooms are there to clean?

3

orca_math

The ratio of boys to girls in a math class is 5:8, and the ratio of math to science students is 7:4. If the total number of students in both math and science classes is 458, how many girls are in the math class?

184

orca_math

Find the amount of Ammonium chloride that is required to react with 1 mole of Potassium hydroxide to form 1 mole of Ammonia, 1 mole of Water and 1 mole of Potassium chloride

1

orca_math

If animal (A) and animal (B) are added together, there are 17 animals. If there are 8 (B)s, how many (A)s are there?

9

orca_math

The light glows for every 30 seconds. Between 1:57:58 and a certain time, it glowed a maximum of 165.63333333333333 times. What was the ending time?

4:05:47

orca_math

Lee wants to propose marriage to Sierra. He wants to follow the adage that you should spend two months' salary on the ring. He earns $60,000 per year in salary and can save a certain amount per month. It will take him 10 months before he can propose to Sierra. How much can he save per month?

\$1,000

orca_math

The average mark of the students of a class in a particular exam is some value. If 5 students whose average mark in that exam is 44 are excluded, the average mark of the remaining will be 80. There were 9 students who wrote the exam. What was the initial average mark of the class?

60

orca_math

In the school's library, there are 2300 different books. 80% of all the books are in English. A certain percentage of these English books were published in the country, and there are 736 English-language books published outside the country. What percentage of the English books were published in the country?

59.78\%

cn_k12

Given $3\sin \alpha =\cos \alpha $, then the value of $\tan \left(\pi -\alpha \right)$ is ______.

-\frac{1}{3}

orca_math

He was told by one the pickers that they fill some drums of grapes per day. They would fill 2916 drums of grapes in 9 days. How many drums of grapes do they fill per day?

324

cn_k12

For rational numbers $a$ and $b$, if $\sqrt{a+4}+(b-2)^2=0$, then $a-b=\_\_\_\_\_\_.$

-6

orca_math

a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 5 miles per hour for 3 hours . how many miles in total did she walk ?

53

orca_math

A rod has a certain weight. If the weight of a 6 meters long rod is 6.184615384615385 kg, what is the weight of a 13 meters long rod?

13.4

orca_math

A shopkeeper fixes the marked price of an item 50% above its cost price. What percentage of discount should be allowed to gain a 15% profit, and what will be the final selling price of the item after applying the required discount?

\$115

orca_math

Let the ages of three persons a, b, and c be represented by A, B, and C respectively. Given that the total age of a and b is 11 years more than the total age of b and c, also assume that person d has an age represented by D, and the total age of a, b, and d is 8 years more than the total age of b, c, and d. Determine how many years younger C is when compared to the sum of A and D.

11

cn_k12

Given the sets $A=\{-1, 0, 2\}$ and $B=\{2^a\}$, if $B \subseteq A$, then the value of the real number $a$ is \_\_\_\_\_\_.

1

orca_math

A certain amount of money will earn an interest of $300 in 9 months at an annual rate of 4%. How much money was initially invested?

\$10,000

orca_math

A man can row 6 kmph in still water. When the river is running at a certain speed, it takes him 1 hour to row to a place and back. The total distance traveled by the man is 5.333333333333333 km. What is the speed of the river?

2

orca_math

In a class of some children, 30% of children can speak only English, 20% can speak Hindi and English both, and the rest of the children can speak only Hindi. There are 42 children who can speak Hindi. How many children are there in the class?

60

orca_math

Before work, Hayden spends 5 minutes ironing his button-up shirt and 3 minutes ironing his pants. He does this 5 days a week. Over a certain number of weeks, he spends 160 minutes ironing. How many weeks does this time period cover?

4

orca_math

If x is 11 percent greater than 70, what is the value of x?

77.7

orca_math

Mike took a taxi to the airport and paid a certain amount to start plus $0.25 per mile. Annie took a different route to the airport and paid the same starting amount plus $5.00 in bridge toll fees plus $0.25 per mile. Each was charged exactly the same amount, and Annie's ride was 26 miles. How many miles was Mike's ride if his starting amount was $2.50?

46

orca_math

A carpenter worked alone for 1 day on a job. He and another carpenter completed the job in 2 more days. It would have taken the second carpenter 5 days to do the complete job working alone. How many more days would it have taken the first carpenter to finish the job alone?

4

orca_math

Hanna has twice as many erasers as Rachel. Rachel has some erasers as Tanya has red erasers. Tanya has 20 erasers, and half of them are red. Hanna has 4 erasers. What is the difference between the number of erasers Rachel has and one-half the number of red erasers Tanya has?

5

orca_math

At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. There are a certain number of male associates, and there are 40 female managers. How many male associates are there?

160

orca_math

In a class, some students like to play basketball and 8 like to play cricket. 5 students like to play both basketball and cricket. There are 10 students who like to play basketball or cricket or both. How many students like to play basketball?

7

orca_math

Three times a number minus a second number is a certain value. The sum of the two numbers is 48. The smaller number is 17. What is the value of three times the first number minus the second number?

76

cn_k12

Given the constant $a \in \mathbb{R}$, if the coefficient of the $x^7$ term in the binomial expansion of $({x^2 + \frac{a}{x}})^5$ is $-15$, find the value of $a$.

-3

orca_math

It takes Bryan 5 minutes to walk from his house to the bus station. Then he rides the bus for some minutes. After that, he walks 5 minutes from the bus station to his job. It takes the same amount of time in the morning and the evening. Bryan spends 365 hours per year traveling to and from work, if he works every day. How many minutes does Bryan spend riding the bus one way?

20

orca_math

A man is 28 years older than his son. In two years, his age will be a multiple of the age of his son. The present age of the son is 26 years. What is the ratio of the man's age to his son's age in two years?

2:1

cn_k12

Place 4 identical white balls, 5 identical black balls, and 6 identical red balls into 3 of 4 distinct boxes such that one box remains empty and the other three boxes each contain all three colors. The total number of different ways to do this is ___.

720

orca_math

A case of some rolls of paper towels sells for $9. The cost of one roll sold individually is $1. The percent of savings per roll for the case over the cost of the same number of rolls purchased individually is 25%. How many rolls are in the case?

12

orca_math

If the personal income tax rate is lowered from 46% to 32%, the differential savings for a taxpayer having an annual income before tax of some amount is $5040. What is the taxpayer's annual income before tax?

\$36,000

orca_math

The swimming club went to a swim meet in another town. They took 2 cars and 3 vans. There were 5 people in each car and 3 people in each van. Each car can hold a maximum of 6 people and each van can hold a maximum of 8 people. How many more people could have ridden with the swim team?

17

orca_math

The average expenditure of a labourer for 6 months was 80, 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 30. What is his monthly income?

75

orca_math

What is the least number which when divided by a certain number, 7, 9 and 18 leaves remainder 4 in each case and the number is 130?

126,

cn_k12

The complex number $z$ satisfies $(1+2i)z=5$, then $z=$ \_\_\_\_\_\_.

1-2i

cn_k12

If $$\int_{1}^{a} (2x + \frac{1}{x})dx = 3 + \ln 2$$ (where $a > 1$), then the value of $a$ is \_\_\_\_\_\_.

2

orca_math

Autumn was constantly misplacing her pencils. At the start of the school year, she purchased a pack of 20 pencils. In the first month of school, she misplaced some pencils, broke 3 pencils and had to throw them away, she found 4, and bought 2. Autumn had 16 pencils left. How many pencils did she misplace?

7

orca_math

Ceasar needs to read three different books for his literature class. The first book has a total of 563 pages and he has already read 147 pages. The second book contains 849 pages and he has managed to read 389 pages. The last book is 700 pages long and he's read only 134 pages. How many pages in total does he still need to read from all three books?

1442

cn_k12

Given a sequence $\{a\_n\}$ with the first term $a\_1=1$, and it satisfies $a\_{2n+1}=2a\_{2n-1}$ and $a\_{2n}=a\_{2n-1}+1$, find the value of $S\_{20}$ = \_\_\_\_\_\_.

2056

orca_math

two numbers have a h . c . f of 20 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?

128

orca_math

A hotel has 20 rooms and is currently full. Each room holds a family of 5. If each person receives 3 towels, how many towels does the hotel hand out?

300

orca_math

Renaldo drove 15 kilometers. Ernesto drove 7 kilometers more than one-third of Renaldo's distance. How many kilometers did the 2 men drive in total?

27

orca_math

Find the value of a number when multiplied by 9999, the result is 824777405. What is the number?

82482.5

orca_math

Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by some inches by 5 inches, and the maximum number of cake boxes that can be placed in each carton is 210, what is the width of a cake box?

7.5

cn_k12

Given a complex number $z$ satisfying $|z|=1$, find the maximum value of $|z+1+\sqrt{3}i|$.

3

orca_math

in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 8 years older than b , the present age of b is

38

orca_math

Ashley wants a champagne toast at her wedding. She wants to serve a certain number of glasses of champagne to each of her 120 wedding guests. 1 bottle of champagne has 6 servings. She will need 40 bottles of champagne. How many glasses of champagne does she want to serve to each guest?

2

orca_math

The sum of 0.75 of a number and two is eight. Find the number.

8

orca_math

Sara picked 45 pears and Sally picked 11 pears from the pear tree. How many pears were picked in total?

56

orca_math

There are 34 dogwood trees currently in the park. Park workers will plant some dogwood trees today. The park will have 83 dogwood trees when the workers are finished. How many dogwood trees will the workers plant today?

49

orca_math

A train travelling at 98 kmph takes 5.142857142857143 seconds to pass an electric pole. The train is of a certain length. What is the length of the train in meters?

140

orca_math

If 25% of x is a certain amount less than 20% of 1000, then x is 680. What is the amount?

30

orca_math

The length of a room is 5.5 m and the width is 3.75 m. The cost of paving the floor by slabs at a certain rate per sq. meter is Rs. 20625. What is the rate of paving the floor per sq. meter?

1000

orca_math

An air-conditioning unit costs $470. In December, there was a discount for Christmas of 16%. After the Christmas discount, the company offered an additional discount for a limited time on energy-efficient models at 7%. 6 months later, the holiday season was over and the company raised the price of the air-conditioning unit by 12%. In addition, due to an increase in production costs, there was an additional 8% increase in the price. In November, the company offers a seasonal promotion with a 10% discount on the final price. How much will an air-conditioning unit cost in November considering all these changes?

\$399.71

orca_math

A lent Rs. 5000 to B for 2 years and some money to C for 4 years on simple interest at the same rate of interest and received Rs. 2640 in all from both of them as interest. The rate of interest per annum is 12%. How much money did A lend to C?

3000

orca_math

Michelle uses some beads in making a necklace. She uses 5 blue beads, 2 times as many red beads as blue beads, the same number of white beads as the blue and red beads combined, and 10 silver beads. How many beads does she use in total?

40

orca_math

how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 4 m x 2 m x 25 cm ?

1186

orca_math

if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 15 . what is the value of f ( 6 ) ?

4

orca_math

When toys are grouped into 12 and 18, always 3 toys remain ungrouped. What is the minimum number of toys to be added so that when they are grouped into 7, no toys will remain ungrouped?

4

orca_math

Shirley sold some boxes of trefoils. She needs to deliver 5 cases of boxes, with 2 boxes in each case. How many boxes of trefoils did she sell?

10

cn_k12

From a group of 3 male students and 2 female students, 2 students are randomly selected to participate in volunteer service. What is the probability that at least 1 of the selected students is female?

\frac{7}{10}

cn_k12

Find the solution set for the inequality $$\frac {1}{x} > 1$$; If the solution set for the inequality $a^2 + b + 2 > 0$ is $x - \frac {1}{2} < x < \frac {1}{3}$, find the value of $a + b$.

10

orca_math

A car is running at a certain speed. It covers a distance of 400 meters in 12 seconds. What is the speed of the car in kmph?

120

orca_math

Amanda's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Amanda $4.60 per pound, and type B coffee costs $5.95 per pound. This month's blend used twice as many pounds of type B coffee as type A. Amanda used 67.52 pounds of type A coffee. What was the total cost of the coffee blend?

\$1114.08

orca_math

A carpenter gave an estimate of 980 dollars to build a cover over a patio. He expects to need 560 dollars in materials and estimates that the job will take 15 hours. What is his hourly rate?

\$28

cn_k12

In the expansion of the algebraic expression $({\sqrt{x}-\frac{1}{{{x^2}}}})^5$, the constant term is ______.

-5

gsm8k

Scarlet saved $80 to spend on jewelry. She bought a pair of earrings that cost $23. Then, she bought a necklace that cost $48. How much of her savings have left?

9

orca_math

The total dining bill for 5 people was $211.00. They added a certain percentage as a tip and divided the bill evenly. Each person's final share was approximately $48.53. What was the percentage of the tip they added?

15\%

gsm8k

Mrs. Oaklyn buys handmade rugs at $40 each and sells them at $60 each. If she bought 20 rugs, calculate the profit she will make from selling the rugs.

400

orca_math

A swimmer can swim in still water at 4 km/h. If the speed of the water current is a certain speed, the swimmer takes 2.5 hours to swim against the current for 5 km. What is the speed of the water current?

2

orca_math

a group of men decided to do a work in 6 days , but 4 of them became absent . if the rest of the group did the work in 12 days , find the original number of men ?

8

orca_math

A person bought 3 different books. The first book was bought for $60 and sold for $78, the second book was bought for $45 and sold for $54, and the third book was bought for $70 and sold for $84. Calculate the overall profit percentage for all three books.

23.43\%

orca_math

There are 92 students altogether. Twenty of them ride the school bus home together, 5/8 of the remaining ride their own bike home, and the rest whose houses are near the school walk home. How many students are walking home?

27

cn_k12

Let the function f(x) = (x - 2)²sin(x - 2) + 3 have its maximum value M and minimum value m in the interval [-1, 5]. Find the value of M + m.

6

orca_math

On his farm, Mr. Mathews has goats and sheep in the ratio of 5:7. He decides to sell half of the goats at a certain price each and 2/3 of the sheep at $30 each. He makes $7200 from the sale of the animals, and the total number of sheep and goats on the farm is 360. How much does he sell each goat for?

\$40

cn_k12

Let the sequence \$\left\{a_n\right\}\$ have a sum of the first \$n\$ terms denoted as \$s_n\$, and \$s_n = a(2^n - 1)\$. If \$a_4 = 24\$, then \$a = \boxed{3}\$.

3

cn_k12

A person shoots once, with a probability of hitting the target being 0.8. If they shoot 4 times, the probability of hitting the target at least 3 times is.

0.8192

cn_k12

Given that the sum of the first $n$ terms of an arithmetic sequence $\{a\_n\}$ is $S\_n$, and $a\_7 = 7a\_4$, find the value of $\frac{S_{13}}{S_{7}}$.

13

orca_math

Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him some tablets asking him to take one tablet every 15 minutes. It took Roy 60 minutes to consume all the tablets. How many tablets did the doctor give Roy?

4

orca_math

Trent walked 4 blocks from his house to the bus stop. He rode the bus 7 blocks to the library. Later, he came home the same way. How many blocks did Trent travel in all?

22

orca_math

The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The typist presently draws Rs. 4180. What was the original salary of the typist?

4000

cn_k12

Given that $\tan (\frac {π}{4}+α)=2,\tan β= \frac {1}{2}$, find the value of $\tan α$ and evaluate the expression $\frac {\sin (α+β)-2\sin α\cos β}{2\sin α \sin β +\cos (α +β )}$.

\frac{1}{7}

orca_math

You are going to divide a number 20. When you mistakenly multiply the number by 10, the answer is 50. What is the correct calculation result?

4

orca_math

On Tuesday, Max's mom gave him $8.5 dollars for a hot dog at the Grand Boulevard park. On Wednesday, his mom gave him 5.5 times as much money as she gave him on Tuesday. On Thursday, his mom gave him 10% more money than she gave him on Wednesday. On Friday, his mom gave him 75% of the money she gave on Thursday. How much more money did his mom give him on Friday than she gave him on Tuesday?

\$30.06875

orca_math

A man traveled a total distance of 900 km. He traveled some part of the whole trip by plane and the distance traveled by train is two-thirds of the distance traveled by bus. He traveled 360 kilometers by bus. What is the ratio of the distance traveled by plane to the total distance?

1:3

cn_k12

Given the sets $A={a,b,c,d}$ and $B={1,2,3,4,5,6}$, how many different mappings from set $A$ to set $B$ can form $f(a)≤f(b)≤f(c)≤f(d)$?

126

orca_math

Trey is raising money for a new bike that costs $112. He plans to sell bracelets for $1 each. On average, he needs to sell 8 bracelets each day. How long does he plan to sell bracelets?

14

orca_math

The Nutty Professor sells cashews for $6.75 per pound and Brazil nuts for $5.00 per pound. To make a mixture that sells for $5.70 per pound, 20 pounds of cashews should be used. How much does the mixture weigh in total?

50

orca_math

a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 390 m long ?

60