problem
stringlengths 11
2.6k
| answer
stringlengths 1
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stringclasses 10
values | domain
listlengths 1
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| llama8b_solve_rate
float64 0.11
0.89
|
|---|---|---|---|---|
The teacher's helper was putting cookies onto plates following a certain pattern that mixes the Fibonacci sequence with the square number series. He put 2 cookies on the first plate, 4 cookies on the second plate, 8 cookies on the third plate, 16 cookies on the fourth plate, and 32 cookies on the fifth plate. If this pattern continues, how many cookies will the helper put on the ninth plate?
|
512
|
orca_math
|
[
"Mathematics -> Algebra -> Other"
] | 0.1875
|
In the binomial expansion of $(\sqrt{x} - \frac{1}{x})^{10}$, find the coefficient of the $x^2$ term. Express your answer as a single integer.
|
45
|
big_math
|
[
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.328125
|
A train 250 m long takes 8 sec to cross a man walking at 7 kmph in a direction opposite to that of the train. Find the speed of the train.
|
105.5
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.203125
|
Jack went on a diet 6 months ago when he weighed 222 pounds. He now weighs a certain amount and continues to lose at the same average monthly rate. In approximately 45 months, he will weigh 180 pounds. What is Jack's current weight?
|
216.4
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.125
|
Given an arithmetic sequence {a_n}, with a_6 = 2, calculate the sum of the first 11 terms of this sequence, S_{11}. Express your answer as a single integer.
|
22
|
big_math
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 0.59375
|
Find the solution set of the inequality $\left|\frac{x-2}{x}\right|>\frac{x-2}{x}$. Express your answer as an interval or a union of intervals.
|
(0,2)
|
big_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.140625
|
A charitable woman had some pennies in her purse. She gave one penny more than half of the pennies in her purse to a farmer. Afterwards, she came across a beggar to whom she gave 2 pennies more than half of what she had left in her purse. In the end, she gave a certain amount to a boy and was left with a penny. She had 42 pennies in the beginning. What was the amount she gave to the boy?
|
7
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.546875
|
The degree of the monomial $-\frac{{5a{b^3}}}{8}$ is ______.
|
4
|
cn_k12
|
[
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.78125
|
The terms of the geometric sequence $\{a_n\}$ are all positive, and $a_2 = 8$. If $2a_4$, $a_3$, and $4a_5$ form an arithmetic sequence, find the sum of the first 5 terms of $\{a_n\}$.
|
S_5 = 31
|
cn_k12
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 0.1875
|
Given the plane vectors $\mathbf{a}=(3,5)$ and $\mathbf{b}=(-2,1)$, calculate the resulting vector $\mathbf{a}-2\mathbf{b}$. Express your answer as an ordered pair (x, y).
|
(7,3)
|
big_math
|
[
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 0.328125
|
The school decided to have a fundraiser to collect $750 for new basketball equipment. Families could donate $25, $50, or $100. With one day left in the fundraiser, the school has 10 Bronze Status families, a certain number of Silver Status Families and 1 Gold Status family. They need to raise $50 on the final day to reach their goal. How many Silver Status families are there?
|
7
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.71875
|
If a person walks at 16 km/hr instead of 12 km/hr, he would have walked 20 km more. What is the actual distance traveled by him?
|
60
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.75
|
Let $A,$ $B,$ and $C$ be points on a circle of radius $18.$ If $\angle ACB = 70^\circ,$ what is the circumference of the minor arc ${AB}$? Express your answer in terms of $\pi.$
|
14\pi
|
math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.703125
|
Calculate the number of terms in the expansion of $(x+y+z)^4$. Express your answer as a single integer.
|
15
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Combinatorics -> Other"
] | 0.734375
|
Goran will rent a car for the weekend. He can choose 1 of 2 plans. The first plan has an initial fee of 65 dollars and costs an additional 0.40 dollars per mile driven. The second plan has no initial fee but costs a certain amount per mile driven. If Goran needs to drive 325 miles for the 2 plans to cost the same, what is the cost per mile driven for the second plan?
|
$0.60
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.5625
|
A bank employee is filling an empty cash machine with bundles of $5.00, $10.00, and $20.00 bills. Each bundle has 100 bills in it, and the machine holds 10 bundles of each type. Calculate the total amount of money required to fill the machine. Express your answer in dollars as a whole number.
|
35000
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.390625
|
In triangle $ABC$ , we have that $AB=AC$ , $BC=16$ , and that the area of $\triangle ABC$ is $120$ . Compute the length of $AB$ .
|
17
|
aops_forum
|
[
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.734375
|
Express the number 1997 using 11 fours and arithmetic operations.
|
1997 = 4 \cdot 444 + 44 \cdot 4 + 44 + \frac{4}{4}
|
olympiads
|
[
"Mathematics -> Algebra -> Other"
] | 0.328125
|
An escalator moves towards the top level at the rate of 12 ft/sec and its length is 150 feet. If a person walks on the moving escalator at a certain rate towards the top level, he takes 10 seconds to cover the entire length. What is the speed of the person?
|
3
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.703125
|
Camp Cedar has 80 boys, and the number of girls is 6 times the number of boys minus 40. The camp requires 1 counselor for every 5 boys and 1 counselor for every 12 girls. How many counselors does Camp Cedar need?
|
53
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.84375
|
Excluding stoppages, the speed of a train is 48 kmph, and including stoppages, it is 36 kmph. How many minutes does the train stop per hour?
|
15
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.578125
|
Given the function $f(x)=a^{x}+\sin x+x^{2}-x$ $(a>0$, and $a\neq 1)$, the tangent line of the curve $y=f(x)$ at the point $(0,f(0))$ is parallel to the line $2x-2y+9=0$. Find the value of $a$.
|
e
|
cn_k12
|
[
"Mathematics -> Calculus -> Differential Calculus -> Derivatives"
] | 0.46875
|
If $a^2+ma+\frac{1}{4} = (a-\frac{1}{2})^2$, then $m = \_\_\_\_\_\_$.
|
m = -1
|
cn_k12
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.765625
|
Casey is trying to decide which employee she wants to hire. One employee works for $20 an hour. The other employee works for a certain amount per hour, but Casey would also get a $6/hour subsidy from the government for hiring a disabled worker. Casey would save $160 per week by hiring the cheaper employee, if they both work 40 hours per week. How much does the second employee charge per hour before the subsidy?
|
$22
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.40625
|
A restaurant baked 5 cakes during lunch and sold 6 during dinner today . The restaurant baked 3 cakes yesterday. _____ cakes are left .
|
2
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.578125
|
Find the sum of all positive divisors of 1184. Express your answer as a single integer.
|
2394
|
big_math
|
[
"Mathematics -> Number Theory -> Other"
] | 0.203125
|
In a bee hive, there are 400 worker bees, 75 drone bees, 1 queen bee, and 50 guard bees. One day, 28 worker bees, 12 drone bees, and 5 guard bees leave the hive to collect nectar. Meanwhile, 30 worker bees are reassigned to guard duty. Later, 15 additional worker bees return after an earlier nectar collection trip. Finally, the hive discovers a new flower field, and 5 times the current number of worker bees leave the hive for nectar collection. How many worker bees are in the hive now?
|
0
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.171875
|
A student has to obtain a certain percentage of the total marks to pass. He got 175 marks and failed by 89 marks. The maximum marks are 800. What is the passing percentage?
|
33\%
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.828125
|
Given the equation $a\sqrt{1-b^2}+b\sqrt{1-a^2}=1$, calculate the value of $a^{2}+b^{2}$. Express your answer as a single number.
|
1
|
big_math
|
[
"Mathematics -> Algebra -> Other"
] | 0.171875
|
Given the coordinates of points A(0,1), B(1,3), C(5,2), and D(4,0), calculate the area of quadrilateral ABCD. Express your answer as a single integer.
|
9
|
big_math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.75
|
A train 750 meters long, traveling at 120 km/hr, takes 45 seconds to cross a bridge, while facing a constant wind resistance force slowing it down by 10%. Calculate the length of the bridge.
|
600
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.828125
|
The distance between the lines $3x-4y+1=0$ and $3x-4y+7=0$ is \_\_\_\_\_\_.
|
\dfrac {6}{5}
|
cn_k12
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.78125
|
Given $a = \int_{1}^{e} (x + \frac{1}{x}) dx$, calculate the value of $a$.
|
\frac{1}{2}e^2 + \frac{1}{2}
|
cn_k12
|
[
"Mathematics -> Calculus -> Integral Calculus -> Other"
] | 0.875
|
The solution set of the inequality system $\left\{\begin{array}{l}{x-2≥-5①}\\{3x＜x+2②}\end{array}\right.$ is ______.
|
-3 \leq x < 1
|
cn_k12
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.859375
|
A chord is drawn through the point $(3,1)$ on the circle $(x-2)^{2}+(y-2)^{2}=4$. The length of the shortest chord is \_\_\_\_\_\_.
|
2\sqrt{2}
|
cn_k12
|
[
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.359375
|
Brent received 5 Kit-Kat bars, three times that amount in Hershey kisses, some boxes of Nerds, and 11 lollipops. He also had 10 Baby Ruths and half that amount in Reese Peanut butter cups. After giving his little sister 5 lollipops, he had 49 pieces of candy left. How many boxes of Nerds did Brent receive?
|
8
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.53125
|
Emma bought a loaf of bread that had a certain number of slices. Her little cousin Andy ate 3 slices from the bread at two different points in time, and then Emma decided she would make toast with the remaining slices. She used 2 slices of bread to make 1 piece of toast bread, and after making 10 pieces of toast bread, she had 1 slice of bread left. How many slices were in the original loaf?
|
27
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.65625
|
A watch was sold at a loss of 20%. If it was sold for Rs. 520 more, there would have been a gain of 6%. What is the cost price of the watch?
|
2000
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.875
|
In \\(\triangle ABC\\), the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are \\(a\\), \\(b\\), and \\(c\\) respectively. If \\(\left(a^{2}+b^{2}-c^{2}\right)\tan C=ab\\), then \\(C=\\)_________;
|
\frac{\pi}{6} \text{ or } \frac{5\pi}{6}
|
cn_k12
|
[
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.125
|
Find the number which when multiplied by 15 is increased by a certain amount. The result is 14. What is the amount by which the number is increased?
|
13.0666 (repeating)
|
orca_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.421875
|
Simplify first, then evaluate: $\left(2a-b\right)^{2}+\left(a-b\right)\left(a+b\right)-5a\left(a-2b\right)$, where $a=\frac{1}{2}, b=-1$.
|
-3
|
cn_k12
|
[
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.5
|
The average age of 20 members of a committee is the same as it was 8 years ago, because an old member has been replaced by a young member. Find how much younger the new member is compared to the old member.
|
160
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.203125
|
If it takes 10 people 10 days to shovel 10,000 pounds of coal, what is the ratio of the number of people needed to shovel 40,000 pounds of coal in 80 days to the original number of people?
|
1:2
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.578125
|
Given \( n \in \{3900, 3901, \cdots, 3909\} \), find the values of \( n \) for which the set \( \{1, 2, \cdots, n\} \) can be partitioned into several triples, each containing one number that equals the sum of the other two numbers.
|
3900 \text{ or } 3903
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.359375
|
Cole drove from home to work at an average speed of 80 km/h. He then returned home at an average speed of 120 km/h. If it took Cole 72 minutes to drive to work, how long did the round trip take in hours?
|
2
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.796875
|
A firefighting team is trying to extinguish a large building fire that requires 6000 gallons of water to put out. Each firefighter has a hose with different capacities: firefighter A's hose can deliver 18 gallons of water per minute, firefighter B's hose can deliver 22 gallons per minute, firefighter C's hose can deliver 16 gallons per minute, firefighter D's hose can deliver 20 gallons per minute and firefighter E's hose can deliver 24 gallons per minute. After 20 minutes, due to a problem with the water supply, the water pressure drops by 50% causing all hoses to only deliver half of their initial capacity. How long will it take for the team of firefighters to put out the fire?
|
100
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.46875
|
Let \( f(x) \) be a function defined on \( \mathbf{R} \), such that for any \( x \in \mathbf{R} \), \( f(x+1) = \frac{1}{2} + \sqrt{f(x) - [f(x)]^2} \). Given \( f(-1) = \frac{1}{2} \), find the value of \( f(2007) \). Express your answer as a single value.
|
\frac{1}{2}
|
big_math
|
[
"Mathematics -> Other -> Other"
] | 0.6875
|
Mike has two containers. One container is a rectangular prism with width \( 2 \text{ cm} \), length \( 4 \text{ cm} \), and height \( 10 \text{ cm} \). The other is a right cylinder with radius \( 1 \text{ cm} \) and height \( 10 \text{ cm} \). Both containers sit on a flat surface. Water has been poured into the two containers so that the height of the water in both containers is the same. If the combined volume of the water in the two containers is \( 80 \text{ cm}^3 \), then calculate the height of the water in each container. Express your answer in centimeters (cm), rounded to 1 decimal place.
|
7.2
|
big_math
|
[
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 0.84375
|
A fruit and vegetable merchant installed 15 kg of carrots, 13 kg of zucchini, and 8 kg of broccoli. He sold a certain portion of them, which amounted to 18 kg of vegetables. What is the ratio of the mass of vegetables he sold to the total mass of vegetables he installed?
|
1:2
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.828125
|
Given the function f(x) = x ln(x), find the cosine value of the angle of inclination of the tangent line to the curve y = f(x) at the point x = e.
|
\frac{\sqrt{5}}{5}
|
cn_k12
|
[
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.734375
|
Following an increase in prices, the price of a candy box is now 20 pounds and the price of a can of soda is 6 pounds. The price of a candy box was raised by 25%, and the price of a can of soda was raised by a certain percentage. The price of a box of candy plus a can of soda before prices were raised was 20 pounds. What was the percentage increase in the price of a can of soda?
|
50\%
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.78125
|
A man invests a certain amount of money at a certain interest rate and $800 more than that amount in another account at 4% interest. At the end of one year, he earned $92 in interest and he invested $1000 in each account. What was the interest rate of the first account?
|
0.02,
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.359375
|
Find the equation of the parabola with its focus at the left focus of the ellipse $\frac{x^2}{4} + \frac{y^2}{3} = 1$ and its vertex at the origin.
|
y^2 = -4x
|
cn_k12
|
[
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.109375
|
Given the function $f(x) = x^2 - 4x + 5$, where $x \in [1, 4]$, find the range of the function $f(x)$.
|
[1, 5]
|
cn_k12
|
[
"Mathematics -> Algebra -> Intermediate Algebra -> Quadratic Functions"
] | 0.53125
|
If the sum of the first $3n$ positive integers is $150$ more than the sum of the first $n$ positive integers, then find the sum of the first $4n$ positive integers. Express your answer as a single integer.
|
300
|
big_math
|
[
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0.46875
|
a company has two models of computers , model x and model y . operating at a constant rate , a model x computer can complete a certain task in 72 minutes and a model y computer can complete the same task in 36 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model x computers were used ?
|
24
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.828125
|
Schoolchildren Chukov and Gekov are skating at constant speeds around a closed loop ice rink. If Chukov skates clockwise and Gekov skates counterclockwise, their meetings occur four times more often than the times when one overtakes the other if they skate in the same direction. The speed of one of the schoolchildren is 6 m/s. What is the speed of the other?
|
10 \ \text{m/s} \ \text{or} \ 3.6 \ \text{m/s}
|
olympiads
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.109375
|
Calculate the result of the expression \((19 \times 19 - 12 \times 12) \div \left(\frac{19}{12} - \frac{12}{19}\right)\).
|
228
|
olympiads
|
[
"Mathematics -> Algebra -> Other"
] | 0.84375
|
No matter what value $k$ takes, the line $l: kx - y + 1 = 3k$ always passes through a fixed point. The coordinates of this fixed point are \_\_\_\_\_\_.
|
(3, 1)
|
cn_k12
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.515625
|
If the function $$y= \frac {ax+2}{x+2}$$ is increasing in the interval $(-2, +\infty)$, then the range of $a$ is \_\_\_\_\_\_.
|
(1, +\infty)
|
cn_k12
|
[
"Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives"
] | 0.609375
|
Given is a number with $1998$ digits which is divisible by $9$ . Let $x$ be the sum of its digits, let $y$ be the sum of the digits of $x$ , and $z$ the sum of the digits of $y$ . Find $z$ .
|
9
|
aops_forum
|
[
"Mathematics -> Number Theory -> Other"
] | 0.546875
|
A 300 m long train crosses a platform in 27 sec while it crosses a signal pole in a certain amount of time. The length of the platform is 150.00000000000006 m. How long does it take for the train to cross the signal pole?
|
18
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.875
|
Two players take turns breaking a $6 \times 8$ chocolate bar. On their turn, a player can make a straight break along a groove on any piece of the chocolate. The player who cannot make a move loses. Who will win this game?
|
The first player wins.
|
olympiads
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.140625
|
The ring toss game at the carnival made 120 dollars in the first 20 days and 66 dollars in the remaining days. They made 6 dollars per day in the first 20 days at the carnival. How many days are they referring to?
|
31
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.65625
|
Given the sequence 2008, 2009, 1, -2008, -2009,... this sequence is characterized by the fact that starting from the second term, each term is equal to the sum of the term before it and the term after it. Calculate the sum of the first 2016 terms of this sequence. Express your answer as a single integer.
|
0
|
big_math
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 0.125
|
A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. Find the area of the border. Express your answer in square inches as a whole number.
|
88
|
big_math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Area"
] | 0.78125
|
In a school, there are some boys. 34% are Muslims, 28% are Hindus, 10% are Sikhs, and 238 boys belong to other communities. How many boys are there in the school?
|
850
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.5
|
Find the number of solutions to
\[\frac{1}{\sin^2 \theta} - \frac{1}{\cos^2 \theta} - \frac{1}{\tan^2 \theta} - \frac{1}{\cot^2 \theta} - \frac{1}{\sec^2 \theta} - \frac{1}{\csc^2 \theta} = -3\]in the interval $0 \le \theta \le 2 \pi.$
|
4
|
math
|
[
"Mathematics -> Precalculus -> Trigonometric Functions"
] | 0.203125
|
Find the area of a trapezium whose parallel sides are 20 cm and 18 cm long, the distance between them is 25 cm, and one non-parallel side is slanted at an angle of 60° with the longer parallel side.
|
475
|
orca_math
|
[
"Mathematics -> Geometry -> Plane Geometry -> Area"
] | 0.15625
|
The Lion King cost 10 million to make and earned 200 million at the box office. It earned a profit that was half of what Star Wars made, and Star Wars cost 25 million to make. How many millions did Star Wars earn?
|
405
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.828125
|
Given that $2^m = 5^n = t (t > 0, t \neq 1)$ and $\frac{1}{m} + \frac{1}{n} = 3$, find the value of $t$.
|
\sqrt[3]{10}
|
cn_k12
|
[
"Mathematics -> Algebra -> Other"
] | 0.28125
|
In a geometric sequence of real numbers $\{a_n\}$, it is given that $a_2 + a_6 = 34$ and $a_3 \cdot a_5 = 64$. Find the value of $a_4$.
|
8
|
cn_k12
|
[
"Mathematics -> Algebra -> Sequences and Series"
] | 0.1875
|
A and B can together finish a work in 40 days. They worked together for 10 days and then B left. After some days, A finished the remaining work. A alone can finish the job in 28 days. For how many days did A work alone after B left?
|
21
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.6875
|
In a video game, each enemy defeated gives you 3 points. Additionally, you receive a 5-point bonus if you defeat both a red enemy and a blue enemy. If a level has 6 enemies total, consisting of 3 red enemies and 3 blue enemies, and you destroy all but 2 of them (leaving one red enemy and one blue enemy undefeated), how many points would you earn if you get hit twice and lose 2 points for each hit?
|
13
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.421875
|
A train that is 300 meters long is running at a certain speed. It will pass a tunnel of 1200 meters length in 100 seconds. What is the speed of the train in km/hour?
|
54
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.875
|
The negation of the proposition "$\forall x\geqslant 1$, $x^{2}\geqslant 1$" is ____.
|
\exists x\geqslant 1, x^{2} < 1
|
cn_k12
|
[
"Mathematics -> Discrete Mathematics -> Logic -> Other"
] | 0.453125
|
Given \\(x > 0\\), \\(y > 0\\), and \\(x+y=4\\), what is the maximum value of \\(2xy\\)?
|
8
|
cn_k12
|
[
"Mathematics -> Calculus -> Applications of Derivatives"
] | 0.859375
|
What is the largest integer \( n \) for which \( 3\left(n^{2007}\right) < 3^{4015} \)? Express your answer as a single integer.
|
8
|
big_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.484375
|
Using the numbers 1, 2, 3, 4, and 5, construct a five-digit number with no repeated digits that is even. How many such numbers can be formed? Express your answer as a whole number.
|
48
|
big_math
|
[
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Permutations"
] | 0.6875
|
Given that \(x^{2} + x - 1 = 0\), calculate the value of \(2x^{3} + 3x^{2} - x\). Express your answer as a single integer.
|
1
|
big_math
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.203125
|
Given vectors $\overrightarrow{a}=(m,2)$ and $\overrightarrow{b}=(-1,n)$ with $n > 0$ and $\overrightarrow{a} \cdot \overrightarrow{b} = 0$, and point $P(m,n)$ lies on the circle $x^2 + y^2 = 5$, find the value of $|2\overrightarrow{a} + \overrightarrow{b}|$.
|
\sqrt{34}
|
cn_k12
|
[
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 0.59375
|
Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is some kmph. The bus stops for 6 minutes per hour. What is the speed of the bus including stoppages?
|
45
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.28125
|
Christina just transferred some money out of her bank account. As a result, the account now has $26,935 left in it. There was $27,004 in the account before the transfer. How much money did Christina transfer out of her bank account?
|
$69
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.875
|
Tom has 50 violet balloons. He gave 2/5 of the balloons to Fred, and then Fred gave 1/4 of the balloons he received to Emily. How many violet balloons does Tom have left now?
|
30
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.59375
|
Solve the equation $4^x - 2^{x+2} - 12 = 0$.
|
\{x | x = 1 + \log_2{3}\}
|
cn_k12
|
[
"Mathematics -> Algebra -> Intermediate Algebra -> Exponential Functions"
] | 0.796875
|
Given a function defined on the real number line f(x) = (x^2 - 5x + 6) * g(x) + x^3 + x - 25, and knowing that the graph of the function y = g(x) is a continuous curve, apply the Intermediate Value Theorem (IVT) to determine the range where the equation f(x) = 0 necessarily has a real root. Express your answer as an interval (a, b).
|
(2, 3)
|
big_math
|
[
"Mathematics -> Calculus -> Other"
] | 0.421875
|
Find all real numbers \( x, y, z \) such that
\[
\begin{aligned}
x^{2} y + y^{2} z + z^{2} &= 0, \\
z^{3} + z^{2} y + z y^{3} + x^{2} y &= \frac{1}{4}\left(x^{4} + y^{4}\right).
\end{aligned}
\]
|
x = y = z = 0
|
olympiads
|
[
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.15625
|
Mary works in a restaurant a maximum of 60 hours per week. For the first 40 hours, she is paid $10 per hour. For the next 10 hours of overtime, she is paid at a rate which is 25% higher than her regular rate. If she works beyond 50 hours but less than or equal to 60 hours, she is paid at a rate which is 50% higher than her regular rate. On weekends, she earns a $50 bonus for each day worked. Additionally, if she works more than 55 hours in a week, she receives a $100 bonus for reaching that milestone. What is the maximum amount Mary can earn in a week, considering all the different pay rates, bonus opportunities, and weekend earnings?
|
$875
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.4375
|
Given the function $f(x) = 2^x + \log_{3}x$ has a root in the interval $(k, k+1)$, find the value of the integer $k$.
|
0
|
cn_k12
|
[
"Mathematics -> Precalculus -> Functions"
] | 0.234375
|
A trader sold an article at a certain price with a 20% profit. If he sold it at a different price, then his profit percentage was 140%. What is the ratio of the second selling price to the first selling price?
|
2:1
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.234375
|
The letter sequence AJHSME has 6 unique letters, and the digit sequence 1989 has 4 unique digits. Each rotation shifts both sequences by one position. What is the minimum number of rotations required for both sequences to return to their original forms simultaneously? Express your answer as a single integer.
|
12
|
big_math
|
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.8125
|
A train speeds past a pole in 50 seconds and a platform of a certain length in 100 seconds. Its length is 500 m. How long is the platform?
|
500
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.75
|
Given vectors $\overrightarrow{a}=(3,4)$, $\overrightarrow{b}=(1,0)$, and $\overrightarrow{c}=\overrightarrow{a}+t\overrightarrow{b}$, find the value of $t$ such that the angle between $\overrightarrow{a}$ and $\overrightarrow{c}$ is equal to the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$. Express your answer as a single number.
|
5
|
big_math
|
[
"Mathematics -> Algebra -> Linear Algebra -> Vectors"
] | 0.375
|
Find the constant term in the expansion of the binomial ${\left(\frac{2}{x}+x\right)}^{4}$.
|
24
|
cn_k12
|
[
"Mathematics -> Algebra -> Polynomial Operations"
] | 0.65625
|
The solution of the equation $\lg x - 2x + 11 = 0$ is $x$. If the inequality $x \leq x$ holds, then the maximum integer value of $x$ is ____.
|
5
|
cn_k12
|
[
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.15625
|
What is the remainder when the number \((\underbrace{999999999 \ldots 999)^{2007}}_{20089 \text{ nines}} - (\underbrace{333333333 \ldots 333}_{20083 \text{ threes}})^{2007}\) is divided by 11? Express your answer as a single integer.
|
0
|
big_math
|
[
"Mathematics -> Number Theory -> Other"
] | 0.203125
|
American carmakers produce a certain number of cars each year. They distribute it to 5 car suppliers. The first supplier receives 1,000,000 cars each. The second supplier receives 500,000 cars more while the third car supplier receives the same number as the first and second suppliers combined. The fourth and the fifth supplier receive an equal number of cars, which is 325,000 cars each. How many cars do American carmakers produce each year?
|
5,650,000
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.203125
|
A can run 4 times as fast as B and gives B a start of some meters. The race course is 84 meters long so that A and B might reach the finish line at the same time. How many meters of a head start does A give B?
|
63
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.296875
|
A real number \( x \) satisfies \( 9^{x} + 3^{x} = 6 \). Compute the value of \( 16^{1/x} + 4^{1/x} \).
|
90
|
olympiads
|
[
"Mathematics -> Algebra -> Exponential Functions"
] | 0.234375
|
A can do a half of certain work in 70 days and B one third of the same in 35 days. How many days will they together need to do the whole work?
|
60
|
orca_math
|
[
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.5625
|
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