AndrewZeng/random_syn_ori_query_infer_part_2

finish_reason stringclasses 1 value	input stringlengths 26 1.48k	cum_logprobs float64 -49.99 -0.09
stop	# Question Aaron has 10 bicycles. He gives 2 to his friend Ethan and 1 to his friend Dylan. How many bicycles does Aaron have left? # Solution	-34.865945
stop	# Question The number of pencils in a box is 10 more than the number of pens in a box. If the number of pencils in the box is increased by 25 and the number of pens in the box is increased by 10, then the total number of pencils and pens in the box will be 175. What is the original number of pens in the box? # Solution	-38.110051
stop	# Question The cost of a wedding cake is 80% of the cost of the cake itself. What is the cost of the wedding cake if the total cost is 1200? If we know the answer to the above question is 960, what is the cost of the wedding cake? # Solution	-37.969407
stop	# Question If 40% of a number is 8, what is 60% of the same number? # Solution	-10.766386
stop	# Question The average of two numbers is 5 and their difference is 4. What is the product of the two numbers? # Solution	-13.992796
stop	# Question If a number is subtracted from 12, the result is 2. What is the number? # Solution	-16.601233
stop	# Question What is the prime factorization of 32? # Solution	-7.904069
stop	# Question A pencil is 12 centimeters long. What is the length of the pencil in millimeters? # Solution	-14.788228
stop	# Question If the number of students in a school is 2400, and the number of students that like math is 20% of the total number of students, how many students like math? # Solution	-27.203843
stop	# Question What is the difference between the sum of the first $100$ positive integers and the sum of the first $100$ negative integers? # Solution	-8.035364
stop	# Question If $1+x^2+x^4+x^6+x^8=1+x^3+x^6+x^9+x^{12}$, then $x$ is equal to: # Solution	-22.447071
stop	# Question A line segment is drawn in a circle with radius 10 inches. What is the probability that the chord will be longer than 10 inches? # Solution	-27.702354
stop	# Question A canoeist travels 10 miles upstream in 3 hours. She can paddle the same distance downstream in 2 hours. The speed of the current is 2 mph. Find the speed of the canoe in still water. # Solution	-36.695793
stop	# Question A triangle has sides of length 23, 27, and 32. What is the radius of the circle circumscribing this triangle? # Solution	-22.84134
stop	# Question When I was a kid, I was 11 years younger than my brother. If my brother is now 35 years old, how old am I? # Solution	-23.647888
stop	# Question What is the sum of all integers from 45 to 120, inclusive? # Solution	-12.157606
stop	# Question What is the sum of the digits of the product of all prime numbers less than 10? # Solution	-10.826151
stop	# Question Mary has a total of 240 stamps. She has 14 more stamps than Tiffany, and 12 more stamps than Charles. How many stamps does Mary have? # Solution	-46.997782
stop	# Question If the point with coordinates (1,1) is reflected across the line y=mx+b and the resulting image has coordinates (9,5), what is the value of m+b? # Solution	-3.293381
stop	# Question If the area of a forest is three times the area of a square-shaped street, and the street has a length of 100 meters on one side, with 4 trees per square meter in the forest, what is the total number of trees in the forest? # Solution	-4.079891
stop	# Question A certain school principal must choose 5 teachers to lead a faculty club. If there are 11 teachers eligible to serve as club leaders, how many different groups of 5 teachers could the principal choose? # Solution	-26.493121
stop	# Question 1000 people are asked to pick a number from 1 to 1000. What is the probability that 500 of them will pick the same number? # Solution	-24.592385
stop	# Question A certain kind of pizza has a radius of 6 inches. A pizza of this kind costs $10.00. What is the cost of a slice of pizza with a central angle of 120 degrees? # Solution	-33.01056
stop	# Question An infinite geometric series has a first term of X and a second term of $4.$ A second infinite geometric series has the same first term of $12,$ a second term of $4+n,$ and a sum of four times that of the first series. Find the value of $n.$ If we know the answer to the above question is 6, what is the value of unknown variable X? # Solution	-42.25997
stop	# Question What is the value of $\sin 270^\circ$? # Solution	-8.580045
stop	# Question $216x^2 + 324x + 108 = 0$ # Solution	-22.777901
stop	# Question The local aquarium has 4 dolphins that each require x hours of training daily. The aquarium has 2 trainers and they want to split the hours they spend training the dolphins equally. Each trainer will spend 6 hours training the dolphins. What is the value of unknown variable x? # Solution	-2.776084
stop	# Question There are 1000 bags of rice in a store. 500 bags of white rice, 300 bags of brown rice and 200 bags of black rice. How many bags of rice in total are white? # Solution	-29.523665
stop	# Question A dog is tied to a pole with a 20 foot rope. The rope is tied to a post 6 feet away from the dog. How high is the pole? # Solution	-25.415105
stop	# Question There are 12 people in the room. There are 3 more men than women. How many women are there in the room? # Solution	-18.092175
stop	# Question The average of 4 numbers is 27. If the average of 3 of those numbers is 25, what is the value of the fourth number? # Solution	-20.52179
stop	# Question What is the product of 125 and 126? # Solution	-15.728776
stop	# Question Aaron and Bryan are going to split their 20-dollar lunch budget evenly. Aaron spends 6 dollars less than Bryan. How much does each person spend? # Solution	-44.263536
stop	# Question In the past, the ratio of boys to girls was 4 to 7. There are 120 more boys than girls. How many boys are there? # Solution	-28.326734
stop	# Question Which of the following equations has the same solution as the equation $2x+y=11$? # Solution	-20.326602
stop	# Question What is the probability that the first 4 tosses of a fair coin will result in exactly 3 heads? # Solution	-32.199187
stop	# Question Find the sum of all the real numbers $x$ that satisfy the equation $4\log x=\log x^4$. # Solution	-23.7556
stop	# Question At a store, the price of a jacket was increased 20%. How much money was saved by a customer who paid $33.00 for the jacket? # Solution	-34.067223
stop	# Question What is the value of $11^{2} - 22^{2} + 33^{2} - 44^{2} + 55^{2} - 66^{2} + 77^{2} - 88^{2} + 99^{2} - 10^{2} + 111^{2} - 1111^{2} + 11111^{2}$? # Solution	-25.125585
stop	# Question If the ratio of a to b is 3 to 2, and the ratio of a to c is 2 to 3, then what is the ratio of b to c? # Solution	-17.639504
stop	# Question If a fish tank contains 80 liters of water, how much liters of water does it contain after 3 liters are added to the tank and 15 liters of water are removed from the tank? # Solution	-31.432536
stop	# Question What is the greatest integer less than $\sqrt{17}$? # Solution	-7.96102
stop	# Question The only two people in a room are a man and a woman. The woman is the father of the man’s child. The man is not the biological father of the woman’s child. What is the relation between the man and the woman? # Solution	-40.655112
stop	# Question A farmer has a total of 100 feet of fencing to enclose a rectangular area of 1,000 square feet. What should the dimensions of the rectangle be so that the length is greater than the width? # Solution	-29.16222
stop	# Question A rectangle has a width of 3 and a length of 2x + 5. If the area of the rectangle is 40, what is the value of x? # Solution	-25.316905
stop	# Question Find the solution set of the equation $2x + 1 = x + 2$. # Solution	-20.374998
stop	# Question A furniture store sells a desk for $240. If the store gives a discount of 20% to its most loyal customers, what is the sale price of the desk? # Solution	-27.090264
stop	# Question A 15% discount is offered on a$250 computer. How much will you save? # Solution	-23.477742
stop	# Question At a carnival, there are 300 children who are playing games. There are 200 boys and the rest are girls. If 40% of the girls are wearing pink, how many girls are wearing pink? # Solution	-40.144599
stop	# Question The sum of two numbers is 104. If one of the numbers is 58, what is the other number? # Solution	-18.275917
stop	# Question The formula for the area of a square is A = s2. The area of a square with a side length of 3 cm is 9 cm2. What is the area of a square with a side length of 4 cm? # Solution	-23.989798
stop	# Question Pete is x years younger than his brother, and his sister is 2 years older than his brother. Pete's sister is 17 years old. What is the value of unknown variable x? What is the value of unknown variable x? # Solution	-23.628398
stop	# Question Let $x$ be a real number and let $f(x)$ be a function defined by $f(x) = x^2 + 4x - 1$. What is the value of $x$ that satisfies $f(x) = 0$? # Solution	-30.900039
stop	# Question A school has 1000 students. 30% of them are girls. If 10% of the girls are left-handed, 20% of the boys are left-handed. What percent of the student population is left-handed? # Solution	-29.816973
stop	# Question If an artist uses 3 ounces of paint for each large canvas and 2 ounces for each small canvas, and they have completed 3 large paintings and 4 small paintings, what is the total amount of paint they have used? # Solution	-1.640701
stop	# Question A local store is offering a 15% discount on all clothing. At the same time, the store is offering 30% off on all purchases over $75. If Martha spent $100 on clothing, how much did she save? # Solution	-49.265358
stop	# Question A rectangular garden has an area of 320 square feet. Its length is 32 feet more than its width. What is the width of the garden? # Solution	-20.722092
stop	# Question What is the remainder when $2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9$ is divided by 10? # Solution	-18.284686
stop	# Question Suppose we have a bag of 10 marbles, each of which are either red or blue. If we were to randomly select 3 marbles without replacement, what is the probability that all 3 marbles will be blue? # Solution	-26.110774
stop	# Question 30% of the students in a class are girls. 1/3 of the girls and 1/4 of the boys have blue eyes. If there are 25 students in the class, how many have blue eyes? # Solution	-25.401801
stop	# Question What is the 100th digit to the right of the decimal point in the decimal representation of $\frac{13}{90}$? # Solution	-6.628838
stop	# Question If $a = 3$ and $b = 2$, what is the value of $a^2 + b^2$? # Solution	-10.370766
stop	# Question What is the inverse of the matrix \[\begin{vmatrix} 1 & 0 & 1 \\ 2 & 1 & 1 \\ 0 & 1 & 1 \end{vmatrix}?\] # Solution	-15.805738
stop	# Question What is the $y$-intercept of $f(x) = -2(x+4)^2+2$? # Solution	-21.217368
stop	# Question A store sells a sweater that costs $28 and a pair of jeans that costs$40. How much change will Daisy receive if she gives the cashier $80 for a sweater and a pair of jeans? # Solution	-40.693196
stop	# Question If $p(x) = x^2 - x + 1$, then $p(x)p(y) - p(y)p(x) =$ # Solution	-19.497667
stop	# Question Mary's cat weighs 5 pounds less than her dog. Together, they weigh 36 pounds. How much does the cat weigh? # Solution	-25.629693
stop	# Question In a certain store, the price of a T-shirt is $15.00. In addition to that price, there is a 7 percent sales tax. If the sales tax is$1.75, what is the price, in dollars, of the T-shirt? # Solution	-31.469259
stop	# Question 22 is 40% of what number? # Solution	-15.160957
stop	# Question 3/4 of a dog cookie in the morning and before bed. She gets 2 whole cookies during the day. Basil’s cookies are packaged with x cookies per box. How many boxes will she need to last her for 30 days? # Solution	-13.193259
stop	# Question What is the value of $(3!)^3 + (4!)^4 + (5!)^5 + (6!)^6 + (7!)^7$? # Solution	-15.180792
stop	# Question Solve the equation for $x$. # Solution	-10.383092
stop	# Question Find the value of $x$ in the equation $(2x-1)^2 - (x-3)^2 = (x+5)^2 - (x-2)^2$. # Solution	-26.73237
stop	# Question There are 5000 registered voters in a town. 75% of them voted in the last election. How many voters voted in the last election? # Solution	-22.678817
stop	# Question How many squares are there in a $3\times 3$ chessboard? # Solution	-14.321687
stop	# Question For a certain class, there are $16$ girls and $20$ boys. If a group of $6$ students is formed, what is the probability that there will be at least $2$ girls in the group? # Solution	-34.543767
stop	# Question What is the result of $144^{1/2} + 4^{1/2} - 49^{1/2} + 3^{1/2}$? # Solution	-28.302415
stop	# Question The temperature in a room is 20 degrees Celsius. The temperature starts to drop at a rate of 3 degrees Celsius per hour. If x represents the time elapsed in hours, how many degrees Celsius is the temperature after x hours? If we know the answer to the above question is 60 degrees Celsius, what is the value of unknown variable x? # Solution	-42.740888
stop	# Question The population of a certain city is 50000. The number of people increases by 2% every year. What is the population of the city after 3 years? # Solution	-27.547117
stop	# Question What is the value of the following expression? # Solution	-6.945852
stop	# Question If 24 apples are bought for $12.00, what would be the cost of 40 apples? # Solution	-27.121818
stop	# Question The area of a triangle is $4$ square inches. If the base of the triangle is $2$ inches, then what is the height of the triangle? # Solution	-19.884791
stop	# Question A student's math test had 20 questions, and the student answered 16 of them. What is the percentage of questions the student answered incorrectly? # Solution	-27.648315
stop	# Question Find $3^{-1} \pmod{35}$, as a residue modulo 35. (Give an answer between 0 and 34, inclusive.) # Solution	-5.02133
stop	# Question The total cost to produce 100 units of a product is $41000. If the total cost to produce 200 units of the product is$65000, what is the total cost to produce 300 units of the product? # Solution	-26.610656
stop	# Question In the quadratic $ax^2 + bx + c$ expressed as $2(x - 4)^2 + 8$, what is the value of $h$ in the quadratic $3ax^2 + 3bx + 3c$ expressed as $n(x - h)^2 + k$? # Solution	-4.877073
stop	# Question For each of the following questions, choose the correct answer. # Solution	-15.971084
stop	# Question A rectangle has a length of 12 inches and a perimeter of 40 inches. What is the area of the rectangle? # Solution	-17.605747
stop	# Question If 10% of a number is 12, what is 20% of that number? # Solution	-14.953539
stop	# Question What is the range of the function $f(x) = x^2 - 4$? # Solution	-8.887465
stop	# Question In a certain class, 20% of the students are seniors, and the rest are juniors. Among the seniors, 50% wear glasses, and the remaining do not. Among juniors, 40% wear glasses, and the remaining do not. If a student is chosen at random, what is the probability that he or she wears glasses? # Solution	-35.422495
stop	# Question If a rectangle has an area of 12 square units and a perimeter of 18 units, what is the length of one of its sides? # Solution	-17.786689
stop	# Question An equilateral triangle is inscribed in a circle of diameter 12 cm. What is the area of the triangle? # Solution	-10.448418
stop	# Question What is the product of 25% and 18? # Solution	-19.825361
stop	# Question Find the points on the hyperbola $y^2 - x^2 = 1$ that are closest to the point $(0,6)$. # Solution	-20.204726
stop	# Question If a circle has a radius of 10 units, what is the area of the circle? # Solution	-13.164522
stop	# Question A hedge fund sells 1000 shares of a stock for $22 each. If the fund has a 10% profit margin, how much would each share cost? # Solution	-42.708006
stop	# Question The price of a pair of shoes was decreased by 20%. By how much did the price of the pair of shoes decrease? The original price was $50. 20 # Solution	-33.084085
stop	# Question A store sells 150 pencils a day for $0.10 each. It also sells 300 pens a day for$0.20 each. How many pens does the store sell in 10 days? # Solution	-30.2956
stop	# Question How many different four-digit numbers are there whose digits are in strictly ascending order? # Solution	-17.690844

stop

# Question Aaron has 10 bicycles. He gives 2 to his friend Ethan and 1 to his friend Dylan. How many bicycles does Aaron have left? # Solution

-34.865945

stop

# Question The number of pencils in a box is 10 more than the number of pens in a box. If the number of pencils in the box is increased by 25 and the number of pens in the box is increased by 10, then the total number of pencils and pens in the box will be 175. What is the original number of pens in the box? # Solution

-38.110051

stop

# Question The cost of a wedding cake is 80% of the cost of the cake itself. What is the cost of the wedding cake if the total cost is 1200? If we know the answer to the above question is 960, what is the cost of the wedding cake? # Solution

-37.969407

stop

# Question If 40% of a number is 8, what is 60% of the same number? # Solution

-10.766386

stop

# Question The average of two numbers is 5 and their difference is 4. What is the product of the two numbers? # Solution

-13.992796

stop

# Question If a number is subtracted from 12, the result is 2. What is the number? # Solution

-16.601233

stop

# Question What is the prime factorization of 32? # Solution

-7.904069

stop

# Question A pencil is 12 centimeters long. What is the length of the pencil in millimeters? # Solution

-14.788228

stop

# Question If the number of students in a school is 2400, and the number of students that like math is 20% of the total number of students, how many students like math? # Solution

-27.203843

stop

# Question What is the difference between the sum of the first $100$ positive integers and the sum of the first $100$ negative integers? # Solution

-8.035364

stop

# Question If $1+x^2+x^4+x^6+x^8=1+x^3+x^6+x^9+x^{12}$, then $x$ is equal to: # Solution

-22.447071

stop

# Question A line segment is drawn in a circle with radius 10 inches. What is the probability that the chord will be longer than 10 inches? # Solution

-27.702354

stop

# Question A canoeist travels 10 miles upstream in 3 hours. She can paddle the same distance downstream in 2 hours. The speed of the current is 2 mph. Find the speed of the canoe in still water. # Solution

-36.695793

stop

# Question A triangle has sides of length 23, 27, and 32. What is the radius of the circle circumscribing this triangle? # Solution

-22.84134

stop

# Question When I was a kid, I was 11 years younger than my brother. If my brother is now 35 years old, how old am I? # Solution

-23.647888

stop

# Question What is the sum of all integers from 45 to 120, inclusive? # Solution

-12.157606

stop

# Question What is the sum of the digits of the product of all prime numbers less than 10? # Solution

-10.826151

stop

# Question Mary has a total of 240 stamps. She has 14 more stamps than Tiffany, and 12 more stamps than Charles. How many stamps does Mary have? # Solution

-46.997782

stop

# Question If the point with coordinates (1,1) is reflected across the line y=mx+b and the resulting image has coordinates (9,5), what is the value of m+b? # Solution

-3.293381

stop

# Question If the area of a forest is three times the area of a square-shaped street, and the street has a length of 100 meters on one side, with 4 trees per square meter in the forest, what is the total number of trees in the forest? # Solution

-4.079891

stop

# Question A certain school principal must choose 5 teachers to lead a faculty club. If there are 11 teachers eligible to serve as club leaders, how many different groups of 5 teachers could the principal choose? # Solution

-26.493121

stop

# Question 1000 people are asked to pick a number from 1 to 1000. What is the probability that 500 of them will pick the same number? # Solution

-24.592385

stop

# Question A certain kind of pizza has a radius of 6 inches. A pizza of this kind costs $10.00. What is the cost of a slice of pizza with a central angle of 120 degrees? # Solution

-33.01056

stop

# Question An infinite geometric series has a first term of X and a second term of $4.$ A second infinite geometric series has the same first term of $12,$ a second term of $4+n,$ and a sum of four times that of the first series. Find the value of $n.$ If we know the answer to the above question is 6, what is the value of unknown variable X? # Solution

-42.25997

stop

# Question What is the value of $\sin 270^\circ$? # Solution

-8.580045

stop

# Question $216x^2 + 324x + 108 = 0$ # Solution

-22.777901

stop

# Question The local aquarium has 4 dolphins that each require x hours of training daily. The aquarium has 2 trainers and they want to split the hours they spend training the dolphins equally. Each trainer will spend 6 hours training the dolphins. What is the value of unknown variable x? # Solution

-2.776084

stop

# Question There are 1000 bags of rice in a store. 500 bags of white rice, 300 bags of brown rice and 200 bags of black rice. How many bags of rice in total are white? # Solution

-29.523665

stop

# Question A dog is tied to a pole with a 20 foot rope. The rope is tied to a post 6 feet away from the dog. How high is the pole? # Solution

-25.415105

stop

# Question There are 12 people in the room. There are 3 more men than women. How many women are there in the room? # Solution

-18.092175

stop

# Question The average of 4 numbers is 27. If the average of 3 of those numbers is 25, what is the value of the fourth number? # Solution

-20.52179

stop

# Question What is the product of 125 and 126? # Solution

-15.728776

stop

# Question Aaron and Bryan are going to split their 20-dollar lunch budget evenly. Aaron spends 6 dollars less than Bryan. How much does each person spend? # Solution

-44.263536

stop

# Question In the past, the ratio of boys to girls was 4 to 7. There are 120 more boys than girls. How many boys are there? # Solution

-28.326734

stop

# Question Which of the following equations has the same solution as the equation $2x+y=11$? # Solution

-20.326602

stop

# Question What is the probability that the first 4 tosses of a fair coin will result in exactly 3 heads? # Solution

-32.199187

stop

# Question Find the sum of all the real numbers $x$ that satisfy the equation $4\log x=\log x^4$. # Solution

-23.7556

stop

# Question At a store, the price of a jacket was increased 20%. How much money was saved by a customer who paid $33.00 for the jacket? # Solution

-34.067223

stop

# Question What is the value of $11^{2} - 22^{2} + 33^{2} - 44^{2} + 55^{2} - 66^{2} + 77^{2} - 88^{2} + 99^{2} - 10^{2} + 111^{2} - 1111^{2} + 11111^{2}$? # Solution

-25.125585

stop

# Question If the ratio of a to b is 3 to 2, and the ratio of a to c is 2 to 3, then what is the ratio of b to c? # Solution

-17.639504

stop

# Question If a fish tank contains 80 liters of water, how much liters of water does it contain after 3 liters are added to the tank and 15 liters of water are removed from the tank? # Solution

-31.432536

stop

# Question What is the greatest integer less than $\sqrt{17}$? # Solution

-7.96102

stop

# Question The only two people in a room are a man and a woman. The woman is the father of the man’s child. The man is not the biological father of the woman’s child. What is the relation between the man and the woman? # Solution

-40.655112

stop

# Question A farmer has a total of 100 feet of fencing to enclose a rectangular area of 1,000 square feet. What should the dimensions of the rectangle be so that the length is greater than the width? # Solution

-29.16222

stop

# Question A rectangle has a width of 3 and a length of 2x + 5. If the area of the rectangle is 40, what is the value of x? # Solution

-25.316905

stop

# Question Find the solution set of the equation $2x + 1 = x + 2$. # Solution

-20.374998

stop

# Question A furniture store sells a desk for $240. If the store gives a discount of 20% to its most loyal customers, what is the sale price of the desk? # Solution

-27.090264

stop

# Question A 15% discount is offered on a$250 computer. How much will you save? # Solution

-23.477742

stop

# Question At a carnival, there are 300 children who are playing games. There are 200 boys and the rest are girls. If 40% of the girls are wearing pink, how many girls are wearing pink? # Solution

-40.144599

stop

# Question The sum of two numbers is 104. If one of the numbers is 58, what is the other number? # Solution

-18.275917

stop

# Question The formula for the area of a square is A = s2. The area of a square with a side length of 3 cm is 9 cm2. What is the area of a square with a side length of 4 cm? # Solution

-23.989798

stop

# Question Pete is x years younger than his brother, and his sister is 2 years older than his brother. Pete's sister is 17 years old. What is the value of unknown variable x? What is the value of unknown variable x? # Solution

-23.628398

stop

# Question Let $x$ be a real number and let $f(x)$ be a function defined by $f(x) = x^2 + 4x - 1$. What is the value of $x$ that satisfies $f(x) = 0$? # Solution

-30.900039

stop

# Question A school has 1000 students. 30% of them are girls. If 10% of the girls are left-handed, 20% of the boys are left-handed. What percent of the student population is left-handed? # Solution

-29.816973

stop

# Question If an artist uses 3 ounces of paint for each large canvas and 2 ounces for each small canvas, and they have completed 3 large paintings and 4 small paintings, what is the total amount of paint they have used? # Solution

-1.640701

stop

# Question A local store is offering a 15% discount on all clothing. At the same time, the store is offering 30% off on all purchases over $75. If Martha spent $100 on clothing, how much did she save? # Solution

-49.265358

stop

# Question A rectangular garden has an area of 320 square feet. Its length is 32 feet more than its width. What is the width of the garden? # Solution

-20.722092

stop

# Question What is the remainder when $2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9$ is divided by 10? # Solution

-18.284686

stop

# Question Suppose we have a bag of 10 marbles, each of which are either red or blue. If we were to randomly select 3 marbles without replacement, what is the probability that all 3 marbles will be blue? # Solution

-26.110774

stop

# Question 30% of the students in a class are girls. 1/3 of the girls and 1/4 of the boys have blue eyes. If there are 25 students in the class, how many have blue eyes? # Solution

-25.401801

stop

# Question What is the 100th digit to the right of the decimal point in the decimal representation of $\frac{13}{90}$? # Solution

-6.628838

stop

# Question If $a = 3$ and $b = 2$, what is the value of $a^2 + b^2$? # Solution

-10.370766

stop

# Question What is the inverse of the matrix \[\begin{vmatrix} 1 & 0 & 1 \\ 2 & 1 & 1 \\ 0 & 1 & 1 \end{vmatrix}?\] # Solution

-15.805738

stop

# Question What is the $y$-intercept of $f(x) = -2(x+4)^2+2$? # Solution

-21.217368

stop

# Question A store sells a sweater that costs $28 and a pair of jeans that costs$40. How much change will Daisy receive if she gives the cashier $80 for a sweater and a pair of jeans? # Solution

-40.693196

stop

# Question If $p(x) = x^2 - x + 1$, then $p(x)p(y) - p(y)p(x) =$ # Solution

-19.497667

stop

# Question Mary's cat weighs 5 pounds less than her dog. Together, they weigh 36 pounds. How much does the cat weigh? # Solution

-25.629693

stop

# Question In a certain store, the price of a T-shirt is $15.00. In addition to that price, there is a 7 percent sales tax. If the sales tax is$1.75, what is the price, in dollars, of the T-shirt? # Solution

-31.469259

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# Question 22 is 40% of what number? # Solution

-15.160957

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# Question 3/4 of a dog cookie in the morning and before bed. She gets 2 whole cookies during the day. Basil’s cookies are packaged with x cookies per box. How many boxes will she need to last her for 30 days? # Solution

-13.193259

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# Question What is the value of $(3!)^3 + (4!)^4 + (5!)^5 + (6!)^6 + (7!)^7$? # Solution

-15.180792

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# Question Solve the equation for $x$. # Solution

-10.383092

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# Question Find the value of $x$ in the equation $(2x-1)^2 - (x-3)^2 = (x+5)^2 - (x-2)^2$. # Solution

-26.73237

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# Question There are 5000 registered voters in a town. 75% of them voted in the last election. How many voters voted in the last election? # Solution

-22.678817

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# Question How many squares are there in a $3\times 3$ chessboard? # Solution

-14.321687

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# Question For a certain class, there are $16$ girls and $20$ boys. If a group of $6$ students is formed, what is the probability that there will be at least $2$ girls in the group? # Solution

-34.543767

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# Question What is the result of $144^{1/2} + 4^{1/2} - 49^{1/2} + 3^{1/2}$? # Solution

-28.302415

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# Question The temperature in a room is 20 degrees Celsius. The temperature starts to drop at a rate of 3 degrees Celsius per hour. If x represents the time elapsed in hours, how many degrees Celsius is the temperature after x hours? If we know the answer to the above question is 60 degrees Celsius, what is the value of unknown variable x? # Solution

-42.740888

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# Question The population of a certain city is 50000. The number of people increases by 2% every year. What is the population of the city after 3 years? # Solution

-27.547117

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# Question What is the value of the following expression? # Solution

-6.945852

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# Question If 24 apples are bought for $12.00, what would be the cost of 40 apples? # Solution

-27.121818

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# Question The area of a triangle is $4$ square inches. If the base of the triangle is $2$ inches, then what is the height of the triangle? # Solution

-19.884791

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# Question A student's math test had 20 questions, and the student answered 16 of them. What is the percentage of questions the student answered incorrectly? # Solution

-27.648315

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# Question Find $3^{-1} \pmod{35}$, as a residue modulo 35. (Give an answer between 0 and 34, inclusive.) # Solution

-5.02133

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# Question The total cost to produce 100 units of a product is $41000. If the total cost to produce 200 units of the product is$65000, what is the total cost to produce 300 units of the product? # Solution

-26.610656

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# Question In the quadratic $ax^2 + bx + c$ expressed as $2(x - 4)^2 + 8$, what is the value of $h$ in the quadratic $3ax^2 + 3bx + 3c$ expressed as $n(x - h)^2 + k$? # Solution

-4.877073

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# Question For each of the following questions, choose the correct answer. # Solution

-15.971084

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# Question A rectangle has a length of 12 inches and a perimeter of 40 inches. What is the area of the rectangle? # Solution

-17.605747

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# Question If 10% of a number is 12, what is 20% of that number? # Solution

-14.953539

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# Question What is the range of the function $f(x) = x^2 - 4$? # Solution

-8.887465

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# Question In a certain class, 20% of the students are seniors, and the rest are juniors. Among the seniors, 50% wear glasses, and the remaining do not. Among juniors, 40% wear glasses, and the remaining do not. If a student is chosen at random, what is the probability that he or she wears glasses? # Solution

-35.422495

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# Question If a rectangle has an area of 12 square units and a perimeter of 18 units, what is the length of one of its sides? # Solution

-17.786689

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# Question An equilateral triangle is inscribed in a circle of diameter 12 cm. What is the area of the triangle? # Solution

-10.448418

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# Question What is the product of 25% and 18? # Solution

-19.825361

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# Question Find the points on the hyperbola $y^2 - x^2 = 1$ that are closest to the point $(0,6)$. # Solution

-20.204726

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# Question If a circle has a radius of 10 units, what is the area of the circle? # Solution

-13.164522

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# Question A hedge fund sells 1000 shares of a stock for $22 each. If the fund has a 10% profit margin, how much would each share cost? # Solution

-42.708006

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# Question The price of a pair of shoes was decreased by 20%. By how much did the price of the pair of shoes decrease? The original price was $50. 20 # Solution

-33.084085

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# Question A store sells 150 pencils a day for $0.10 each. It also sells 300 pens a day for$0.20 each. How many pens does the store sell in 10 days? # Solution

-30.2956

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# Question How many different four-digit numbers are there whose digits are in strictly ascending order? # Solution

-17.690844