conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "The duration of a process used to manufacture components is known to be normally distributed with a mean of 30 minutes and a standard deviation of 4 minutes. What is the probability of a time greater than 33 minutes being recorded?"
},
{
"from": "gpt",
"value": "<thi... |
[
{
"from": "human",
"value": "A committee is formed by randomly selecting \\( m \\) members from a group of \\( n \\) people. In how many ways can a committee of \\( m \\) people be formed from \\( n \\) people, where order does not matter?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have ... |
[
{
"from": "human",
"value": "If the original price of a shirt is $25, a discount of 20% is applied. How much will you pay for the shirt after the discount?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the discount amount by calculating 20% of the original price of $25.\n\nN... |
[
{
"from": "human",
"value": "Every day, a certain number of guests arrive at a hotel. On the first day, 2 guests arrive. On the second day, 3 guests arrive. On the third day, 5 guests arrive. And on the fourth day, 8 guests arrive. If this pattern continues, on which day will 101 guests arrive?"
},
{
... |
[
{
"from": "human",
"value": "The manager of a petroleum refinery expects a major shutdown to occur with one hundred percent certainty in either 250 days or 350 days. The manager wishes to determine the probability that the shutdown will occur sooner, that is, in 250 days."
},
{
"from": "gpt",
"v... |
[
{
"from": "human",
"value": "Paco, a wallet manufacturer, makes 2 different models of wallets: Standard and Premium. Each Standard wallet requires 2 units of material A and 3 units of material B. Each Premium wallet requires 3 units of material A and 2 units of material B. Paco has 120 units of material A a... |
[
{
"from": "human",
"value": "The first term of a geometric series is 3, and the common ratio is 2. How many terms are in the geometric series if the sum of the series is 3071?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here about a geometric series. The first term is 3,... |
[
{
"from": "human",
"value": "The average (arithmetic mean) of five distinct non-negative integers is 21. What is the sum of the integer values of the mode, median, and mean of the set?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: The average of five distinct non-neg... |
[
{
"from": "human",
"value": "If $y = 2x^2 - 3x - 1,$ then which of the following is equal to $\\frac{dy}{dx}$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: If y equals 2x squared minus 3x minus 1, then which of the following is equal to dy/dx? Hmm, I need to find th... |
[
{
"from": "human",
"value": "The diagram shows that a triangle is inscribed in a circle and in the triangle, $\\overline{AC}=20$, $\\overline{BC}=7$, and $\\overline{AB}=17$. What is the value of $x$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this geometry problem here where a tria... |
[
{
"from": "human",
"value": "If \\( S \\) is a set such that\n\\[ S = \\{ x \\in \\mathbb{R} \\mid x + 3 \\in \\mathbb{Z} \\} \\]\nwhere \\( \\mathbb{R} \\) denotes the set of real numbers and \\( \\mathbb{Z} \\) denotes the set of integers, then what are the elements of \\( S \\)?"
},
{
"from": "gp... |
[
{
"from": "human",
"value": "If a task requires a force of 50 N and the worker applies a force of 60 N, what is the % efficiency of the worker's action?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to understand the problem. The task requires a force of 50 N, and the worker applied a fo... |
[
{
"from": "human",
"value": "A circular coil of radius 6 cm is placed in a uniform magnetic field B = 3.5 mT. A current of 2.5 mA is passed through the coil. The plane of the coil is perpendicular to the magnetic field. Find the magnitude of the torque experienced by the coil due to the magnetic field."
}... |
[
{
"from": "human",
"value": "The median of the numbers in a data set is 12. If each number in the set is increased by 5, what is the median of the new set of numbers?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: The median of the numbers in a data set is 12. If eac... |
[
{
"from": "human",
"value": "How many possible outcomes are there when you roll two six-sided dice?"
},
{
"from": "gpt",
"value": "<think>\nTo determine the number of possible outcomes when rolling two six-sided dice, I start by considering each die individually. Each die has 6 faces, so there a... |
[
{
"from": "human",
"value": "In the previous problem, we calculated the value of \\( \\lim_{x\\to 0} \\frac{\\sin x}{x} \\) as \\(x\\) approaches 0 from the right. Now, if we consider a similar limit but with \\(x\\) approaching 0 from the left, which of the following statements is true?"
},
{
"from... |
[
{
"from": "human",
"value": "An insurance company has data on the number of claims made by its policyholders. They want to analyze the effectiveness of their fraud detection algorithms in identifying the claims. A random sample of 80 claims is taken, out of which 56 are identified as fraudulent. The insuran... |
[
{
"from": "human",
"value": "Solve the equation $\\frac{3}{4}x + 2 = 10$."
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to isolate the term with \\( x \\) on one side of the equation. To do this, I'll subtract 2 from both sides of the equation.\n\nThis will eliminate the constant term on... |
[
{
"from": "human",
"value": "The physics of a bouncing ball on a rigid surface is pretty simple, but it is also very complex. Consider a ball bouncing on a rigid surface. Let the ball's initial velocity vector be \\(v_{0}\\), the angle of incidence (the angle at which the ball hits the ground) be \\(\\theta... |
[
{
"from": "human",
"value": "A rectangle is inscribed in a circle with a diameter of 14 cm. The length and width of the rectangle are given by $x$ and $y$ respectively. The circumference of the circle is given as $2 \\pi r = 2 \\pi \\cdot 7 = 14 \\pi$ cm."
},
{
"from": "gpt",
"value": "<think>\n... |
[
{
"from": "human",
"value": "A 5kg object is attached to a horizontal massless spring with force constant 100N/m. The object is displaced by 0.2m from its equilibrium position and then released from rest. What is the kinetic energy of the object when it passes through its equilibrium position on its first o... |
[
{
"from": "human",
"value": "The graph of a quadratic function of the form $f(x) = x^2 + bx + c$ has vertex $(0, -4)$ and passes through $(1, -3)$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here about a quadratic function. It says the graph of a quadratic function of t... |
[
{
"from": "human",
"value": "The number of integers of the form $3k+1$, $k\\geq 0$, that are less than $1000$ is the same as the number of integers of the form $7l+3$, $l\\geq 0$, that are less than $1000$. Find $k$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: I ne... |
[
{
"from": "human",
"value": "The local branch of the Regional Culture Association is organizing a fair to promote the art and traditions of the region. They have to set up a number of workshops in a large hall. The workshops are organized in rows. However, they have to set up a small stage for the performan... |
[
{
"from": "human",
"value": "The total number of integers from 1 to 100 that are not divisible by 7 and not divisible by 5 is how many?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the total number of integers from 1 to 100, which is 100.\n\nNext, I'll calculate how many of... |
[
{
"from": "human",
"value": "A food truck is traveling along a straight road. It starts at a speed of 25 miles per hour. Every 30 minutes, the truck accelerates by 5 miles per hour. If the food truck travels for 2 hours, how many miles will it travel?"
},
{
"from": "gpt",
"value": "<think>\nFirs... |
[
{
"from": "human",
"value": "After the lab investigation, you have two solutions: Solution A and Solution B. They contain the same solute and same solvent. However, Solution A has a 10% concentration of solute while Solution B has a 20% concentration of solute. What is the volume percentage concentration of... |
[
{
"from": "human",
"value": "A sphere is inscribed in a cube. What is the ratio of the surface area of the sphere to the surface area of the cube?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: A sphere is inscribed in a cube. What is the ratio of the surface area of ... |
[
{
"from": "human",
"value": "A store sells two different types of cookies: chocolate chip and oatmeal raisin. The chocolate chip cookies sell for $3.49 each, and the oatmeal raisin cookies sell for $2.49 each. If Sara buys a total of 12 cookies (a combination of both types), and she spends a total of $36.06... |
[
{
"from": "human",
"value": "This is a problem from an old exam paper:\n\nGiven a function \\( f(x) = \\frac{x^2}{2} + \\frac{3}{2} \\), find the equation of the tangent line to the curve \\( y = f(x) \\) at the point where \\( x = 2 \\)."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have t... |
[
{
"from": "human",
"value": "A high school has a total of 300 students. The students are divided into 5 classes, and each class has an equal number of students. What is the number of students in each class?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the number of students... |
[
{
"from": "human",
"value": "If $x$ and $y$ are real numbers, such that $x + y = 3$ and $x - y = 1$, then what is $xy$?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I have the two equations: \\( x + y = 3 \\) and \\( x - y = 1 \\).\n\nI can add these two equations together to eliminate \\( y \... |
[
{
"from": "human",
"value": "After a 60% discount, a shirt is on sale for $20. What was the original price of the shirt?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that the sale price of the shirt is $20 after a 60% discount.\n\nThis means that $20 represents 40% of the original ... |
[
{
"from": "human",
"value": "A sailor's distance from a lighthouse is 500 meters. If the sailor is sailing directly towards the lighthouse at a constant speed of 10 m/s, how far will the sailor be from the lighthouse after 200 seconds?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to det... |
[
{
"from": "human",
"value": "If $x$ and $y$ are matrices, then the transpose of the matrix product $xy$ is equal to the product of the transposes of the matrices in reverse order, which is stated mathematically as $\\left(xy\\right)^T = y^Tx^T$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I... |
[
{
"from": "human",
"value": "We are given a rectangular coordinate system with coordinates $x$ and $y$ in the range $0 \\leq x,y \\leq 100$. We have four points, which are located at the following coordinates:\n\\[\nP_1 = (x_1, y_1), P_2 = (x_2, y_2), P_3 = (x_3, y_3), P_4 = (x_4, y_4)\n\\]\nWe are also giv... |
[
{
"from": "human",
"value": "If the height of the space station is increased by 26% and then decreased by 16%, what is the overall change in the height of the space station?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the overall change in the height of the space station w... |
[
{
"from": "human",
"value": "The magnitude of the average velocity of a mass during a given time interval is equal to twice the magnitude of its average speed. What is the ratio of the distance traveled by the mass to the magnitude of its displacement?"
},
{
"from": "gpt",
"value": "<think>\nOka... |
[
{
"from": "human",
"value": "The area of the region enclosed by the polar curve $r = \\theta$ for $0 \\le \\theta \\le 2\\pi$ is"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the area enclosed by the polar curve \\( r = \\theta \\) where \\( 0 \\leq \\theta \\leq 2\\pi \\). Hmm... |
[
{
"from": "human",
"value": "There are two random variables, $X$ and $Y$. The probability of the event $X$ is 0.5 and the probability of the event $Y$ is 0.7. The probability of the joint event $X \\cap Y$ is 0.3. What is the probability of the event $X \\cup Y$?"
},
{
"from": "gpt",
"value": "<... |
[
{
"from": "human",
"value": "A school is giving its students a scholarship to attend a study abroad program. The scholarship will cover all expenses except for a registration fee of $X. The registration fee is 25% of the total expenses. What is the total cost of the study abroad program if the registration ... |
[
{
"from": "human",
"value": "There are 10 people in a room, and each person is either a left-hander or a right-hander. If 60% of the people in the room are right-handers, and if no two people in the room have the same handedness as their neighbor to the immediate right or left, then the maximum number of le... |
[
{
"from": "human",
"value": "The scale drawing of a rectangular swimming pool measures 10 inches by 6 inches. If the scale of the drawing is 1/4 inch to 1 foot, how many square feet are in the actual area of the pool?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem about a s... |
[
{
"from": "human",
"value": "We know that: $a^3+b^3 = 3ab(a+b)$. Use this to evaluate the sum: $1^3+2^3+3^3+4^3+5^3+6^3$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this math problem here: I need to evaluate the sum of cubes from 1Β³ to 6Β³, which is 1Β³ + 2Β³ + 3Β³ + 4Β³ + 5Β³ + 6Β³. The p... |
[
{
"from": "human",
"value": "A car is traveling from City A to City B at a constant speed of 60 km/h. The car travels from City A to City C, which is 2/3 of the distance from City A to City B. How far is City C from City A?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the d... |
[
{
"from": "human",
"value": "If \\(f(x) = 2x + 1\\), what is the value of \\(f(f(f(2)))\\)?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this function f(x) = 2x + 1, and I need to find the value of f(f(f(2))). Hmm, that sounds like I have to apply the function f three times, each time... |
[
{
"from": "human",
"value": "The average price of a gallon of gasoline in the United States is $2.75 . If gas costs $2.25 a gallon in Tulsa and $3.00 a gallon in San Francisco, which city is closer to the national average?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine how mu... |
[
{
"from": "human",
"value": "The height of a rectangular block is 10 cm. The total surface area of the rectangular block is 250 cmΒ². If the rectangular block has a length of 15 cm, what is the width of the rectangular block?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem he... |
[
{
"from": "human",
"value": "A cart filled with rocks is moving on a level track. The track suddenly drops down at an angle of $30^\\circ$. What is the maximum angle between the cart's velocity and the track at this point, assuming that the cart does not leave the track?"
},
{
"from": "gpt",
"va... |
[
{
"from": "human",
"value": "The segment AB is 15cm long. Find the length of its median to the side BC if AB=AC=15cm and angle ABC= 80 degrees and angle ACB= 50 degrees."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this geometry problem here. Let me try to visualize it first. The segm... |
[
{
"from": "human",
"value": "The sum of the interior angles of a nondegenerate triangle is always 180 degrees. In a nondegenerate triangle, the longest side is always opposite the largest angle, the shortest side is always opposite the shortest angle, and the remaining side is opposite the remaining angle."... |
[
{
"from": "human",
"value": "The base of a certain solid is a triangle with vertices A(0,0,0), B(2,0,0), and C(1,2,0). The sides of the base are AB, BC, and CA. The height of the solid is perpendicular to the base and is 3 units. If the density of the solid is 4 units of mass per unit volume, what is the ma... |
[
{
"from": "human",
"value": "In 2021, the number of students in a school is 750. If every day, 10 new students are admitted and the number of students is also increased by 0.25% of the current number of students due to other reasons, how many students will there be at the school after 20 days?"
},
{
... |
[
{
"from": "human",
"value": "The angle between two planes, $\\Pi_1$ and $\\Pi_2$, is defined as the angle between their normal vectors. Given that the equation of $\\Pi_1$ is $x + 2y + 3z = 3$, we can determine its normal vector as $\\mathbf{n}_1 = \\langle 1, 2, 3\\rangle$. Similarly, the equation of $\\Pi... |
[
{
"from": "human",
"value": "A triangle with vertices $A(0,0)$, $B(3,3)$, and $C(6,0)$ is reflected across the line $y=x$. What are the coordinates of the reflected triangle?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem where I need to reflect a triangle with vertices at... |
[
{
"from": "human",
"value": "In a class of 30 students, a student is to be randomly selected to give a presentation. Find the probability that the student selected is a member of a club if there are 10 members of the club in the class."
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to det... |
[
{
"from": "human",
"value": "The intersection of two convex sets $A$ and $B$ satisfies\n\n$$x\\in A\\cap B\\quad \\text{if and only if}\\quad x\\in A, x\\in B, \\text{and}\\quad (x-x_0)\\cdot (x_1-x_0)\\leq 0, \\tag{1}$$\n\nwhere $x_0\\in \\mathbb{R}^n$ and $x_1\\in \\mathbb{R}^n$ are given points. What is ... |
[
{
"from": "human",
"value": "A rectangle has an area of $100\\text{ m}^2$ and a perimeter of $60$ m. Find the length of its diagonal."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: A rectangle has an area of 100 mΒ² and a perimeter of 60 m. I need to find the length of... |
[
{
"from": "human",
"value": "Assume that $x$ is an arbitrary positive real number. Find all real values of $a$ for which the inequality $x + 2 \\geq a \\sqrt{x + 1}$ holds for all positive real numbers $x$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this inequality: \\( x + 2 \\geq ... |
[
{
"from": "human",
"value": "The side of a square is 4.2 cm long. If we double its side, what is the ratio of the new area to the old area?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: The side of a square is 4.2 cm long. If we double its side, what is the ratio of ... |
[
{
"from": "human",
"value": "A set of 30 questions is given to two students. Student A answers 20 questions correctly and student B answers 18 questions correctly. What is the probability that student B will answer at least one more question correctly than student A when given another set of 30 questions?"
... |
[
{
"from": "human",
"value": "The school's chess club ordered 15 boxes of pizza with 12 slices in each box. If 48 students attended the meeting and each student ate \\(\\frac{3}{4}\\) of a pizza, how many slices of pizza did they eat in total?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need... |
[
{
"from": "human",
"value": "Tom is training for a marathon. His current training regimen consists of running 30 miles one week, and then increasing that distance by 5 miles the following week. This pattern continues for 10 weeks, after which Tom will run his marathon. If Tom wants to determine how far he w... |
[
{
"from": "human",
"value": "In this exercise, we will examine the application of the quadratic equation in solving problems involving mathematical modeling. Consider a stone thrown upwards with the initial velocity of 20 m/s from a height of 10 m. The height of the stone above the ground at any time t (in ... |
[
{
"from": "human",
"value": "A company makes a profit of $3 on each of its small boxes of cereal and $2 on each of its large boxes of cereal. How much profit will the company make in a day if it sells 140 small boxes and 90 large boxes of cereal?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I ... |
[
{
"from": "human",
"value": "If $f$ and $g$ are differentiable functions such that $f'(x) = g(x)$ and $g'(x) = 1 - f(x)$, then what is the value of $f(1) + f(2) + g(1) + g(0)$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem where I need to find the value of f(1) + f(2) + g(... |
[
{
"from": "human",
"value": "The cost of making a certain type of garment is $2.50 per unit and the selling price is $4.75 per unit. Write an expression to represent the profit made from selling x units of the garment."
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the profit... |
[
{
"from": "human",
"value": "For the experiment of tossing a fair six-sided die, how many total outcomes are there?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that a standard six-sided die has numbers from 1 to 6.\n\nWhen the die is tossed once, each face represents a possible ou... |
[
{
"from": "human",
"value": "The equation x^3 + 2x^2 - 7x -12 = 0 has three real roots r, s, and t.\nWe are also given that r + s + t = -2, rs + st + tr = -7, and rst = 12.\nWhich of the following is closest to the value of r^3 + s^3 + t^3?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have... |
[
{
"from": "human",
"value": "In a triangle, the first angle is $x$ degrees and the third angle is 5 degrees more than the second angle. If the sum of the angles in the triangle is 180 degrees, what is the value of $x$?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that the sum of th... |
[
{
"from": "human",
"value": "The expression $x + y + (x + y) \\cdot (x + y)$ can also be written in the form\n\n$$a(x + y)^2 + bx + by + c,$$where $a$, $b$, and $c$ are constants. What is $a + b + c$?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I'll start by expanding the original expression ... |
[
{
"from": "human",
"value": "Here is a problem: Let G be a group of order 8 with the following properties: i) G has an element a of order 4, ii) G has an element b of order 2, and iii) all non-identity elements of G have order 2 or 4. What can you say about the structure of G?"
},
{
"from": "gpt",
... |
[
{
"from": "human",
"value": "Charges of +3q, +2q, and +q are placed at the vertices of an equilateral triangle. What is the electric potential at the center of the triangle due to these charges?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem where there are three charges pl... |
[
{
"from": "human",
"value": "What is the value of $x$ in the equation $2^x + 3^x = 10$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this equation here: 2^x + 3^x = 10. Hmm, I need to find the value of x. Let me think about how to approach this. \n\nFirst, I know that equations involv... |
[
{
"from": "human",
"value": "This problem is about a discrete random variable. We need to find the probability of the number of defective units in a certain production process.\nThe production process produces units in batches. Each unit has a 3% chance of being defective. We need to find the probability of... |
[
{
"from": "human",
"value": "When the average price of a kilogram of carrots was 28 pence per kilogram, how much did 200 kilograms of carrots cost?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the cost of 200 kilograms of carrots when the average price is 28 pence per kilog... |
[
{
"from": "human",
"value": "The number of students who registered for a course was about 100, and the number of students who passed the course was about 75. The class average for students who passed was 75, and the class average for students who did not pass was 40. Determine the number of students who fai... |
[
{
"from": "human",
"value": "In the United States, the National Restaurant Association conducts an annual survey of American eating habits. One year, the survey found that, on average, Americans eat out between 4.5 and 5.5 times per week. Using a normal distribution, assume that the number of times people e... |
[
{
"from": "human",
"value": "In a survey of 200 workers, 110 of them said that they were not satisfied with their jobs. How many workers are satisfied with their jobs?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I note that there are 200 workers in total.\n\nOut of these, 110 workers are not ... |
[
{
"from": "human",
"value": "A new video game is developed with 5 different difficulty levels: \"Easy\", \"Normal\", \"Hard\", \"Insane\", and \"Hell\". There are 3 aliens in the game, each representing a different difficulty level. The aliens are randomly assigned to the 5 difficulty levels. Calculate the ... |
[
{
"from": "human",
"value": "If $x$ is a positive integer and $x^2+2x+1=64$, what is the value of $x$?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I notice that the equation \\( x^2 + 2x + 1 = 64 \\) can be rewritten by completing the square. This simplifies the equation to \\( (x + 1)^2 = 65... |
[
{
"from": "human",
"value": "One month after a large earthquake, a relief agency has established a refugee camp with 100 tents, and is providing medical care, food, and shelter to the refugees. The agency has budgeted equally for the first 3 months to provide this care. However, 10% of the tents are uninhab... |
[
{
"from": "human",
"value": "An outpatient surgical center needs to stock Cephalexin antibiotic tablets, which come in a bottle of 50, 20, or 10. The center currently has a need for 250 tablets. What size bottles should the center order?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to d... |
[
{
"from": "human",
"value": "L'Hopital's Rule is frequently used to evaluate the limit of many indeterminate forms of type 0/0. One such limit is the following: \\[\\lim_{x\\to 0} \\frac{x^2 \\sin(1/x)}{x}\\]. With L'Hopital's rule, we proceed as follows:\n\\begin{align*}\n\\lim_{x\\to 0} \\frac{x^2 \\sin(1... |
[
{
"from": "human",
"value": "The incidence of a certain disease is estimated to be 250 persons per 100,000 at risk per year. If 120,000 persons are at risk, how many new cases of the disease can be expected per year?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here about... |
[
{
"from": "human",
"value": "In a random sample of 30 observations, the mean of the squares of the observations is 56, and the mean of the observations is 4. Find the sample variance of the observations."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here where I need to fi... |
[
{
"from": "human",
"value": "The radius of the large circle is $30$, and the radius of the small circle is $10$. The points $A, B, C, D, E,$ and $F$ are on the large circle, and the points $G$ and $H$ are on the small circle. The line segments $\\overline{AB}$ and $\\overline{CD}$ are parallel, and $\\angl... |
[
{
"from": "human",
"value": "Norris's grocery list contains 6 different types of cans: corn, peas, carrots, green beans, tomatoes, and beets. These 6 types of cans are to be packed into 3 boxes such that each of the 3 boxes contains exactly two different types of cans. In how many different ways can the box... |
[
{
"from": "human",
"value": "A trader buys 2000 eggs at $0.50 each and sells them at $1.00 each. If 10 eggs were broken, how much profit did the trader make?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to calculate the total cost the trader incurred by multiplying the number of eggs by... |
[
{
"from": "human",
"value": "A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to understand the snail's daily... |
[
{
"from": "human",
"value": "The effect of gravity on the motion of a particle of mass m through a medium with resistive force proportional to the velocity of the particle can be modeled by the initial value problem:\n\nm * (dv/dt) = m * g - b * v\n\nwhere:\n\n* m is a positive constant representing the mas... |
[
{
"from": "human",
"value": "A cone is placed on the top of a cylinder as shown in the figure. The diameter of the cylinder is 20 cm and the total height of the combined shape is 22 cm. The height of the cone is 3 cm. Find the volume of the combined shape."
},
{
"from": "gpt",
"value": "<think>\... |
[
{
"from": "human",
"value": "The volume of a sphere with radius $r$ is given by the formula $\\frac{4}{3}\\pi r^{3}$. A sphere with radius $6$ is melted and made into a sphere with radius $r$. What is the radius of the new sphere?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this prob... |
[
{
"from": "human",
"value": "A triangle has sides of length 7, 9 and x. The sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. What is the possible range of values for x?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem he... |
[
{
"from": "human",
"value": "A 3kg ball is dropped from rest at a height of 10m. What is its velocity as it hits the ground?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this physics problem here: A 3kg ball is dropped from rest at a height of 10m. What is its velocity as it hits the ... |
[
{
"from": "human",
"value": "The length of a rectangle is 12 cm and the width is 8 cm. What is the length of the diagonal?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: A rectangle has a length of 12 cm and a width of 8 cm. I need to find the length of the diagonal. ... |
[
{
"from": "human",
"value": "Two points, $p$ and $q$, are distinct and are located at a distance $r$ from each other. Consider two spheres, one centered at $p$ and the other at $q$, each with a radius of $r$. Prove that any point $x$ that lies on both spheres must also lie on the line segment connecting $p$... |
[
{
"from": "human",
"value": "The sum of the interior angles of any polygon can be found using the formula 180(n-2), where n is the number of sides. How many sides does a polygon have if the sum of its interior angles is 900 degrees?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this pr... |
[
{
"from": "human",
"value": "The owner of a small bakery decided to increase the price of a chocolate cake from $8 to $9. At the same time, the bakery started to offer a 10% discount on all chocolate cakes sold. How did the price change for each chocolate cake sold compare to before the increase and the dis... |
[
{
"from": "human",
"value": "A $1000 loan has an annual interest rate of 9% and a loan period of 1 year. What is the total amount that will be paid back to the loan shark at the end of the year?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the type of interest calculation m... |
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