conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "The area of a rectangle is 40 square units. The length is 5 units. What is the width?"
},
{
"from": "gpt",
"value": "<think>\nTo determine the width of the rectangle, I start with the formula for the area of a rectangle, which is the product of its length and width.\... |
[
{
"from": "human",
"value": "The area of a rectangle is increasing at a rate of 2 square meters per second. The length of the rectangle is increasing at a rate of 1 meter per second. Is the width of the rectangle increasing or decreasing, and at what rate?"
},
{
"from": "gpt",
"value": "<think>\... |
[
{
"from": "human",
"value": "A researcher is studying the effect of a new drug on the levels of a certain protein in the blood. The researcher administers the drug to a group of 10 patients and measures the protein levels in the blood before and after the administration of the drug. The data is as follows:\... |
[
{
"from": "human",
"value": "A closed container has a volume of 0.02 cubic meters. The container is filled with a gas at an initial temperature of 25°C and an initial pressure of 1.25 atm. If the container's volume is kept constant, and the temperature is increased to 85°C, what is the final pressure of the... |
[
{
"from": "human",
"value": "A bag contains 5 red marbles, 5 blue marbles, and 5 green marbles. When 3 marbles are drawn from the bag without replacement, what is the probability that the first marble drawn is red, the second marble drawn is blue, and the third marble drawn is green?"
},
{
"from": "... |
[
{
"from": "human",
"value": "The number of real solutions of \\[x^7 + 4x^5 - 5x^3 - 4x^2 - 1 = 0\\] is 1. Using this information, determine the number of nonreal solutions of the given equation."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this equation: \\(x^7 + 4x^5 - 5x^3 - 4x^2 - ... |
[
{
"from": "human",
"value": "If $f(x)=\\frac{1}{x}$ and $g(x)=1+x^2$, find $(f \\circ g)(x)$.\n\\begin{align*}\n\\text{My work so far: }\n(f \\circ g)(x) &= f(g(x))\\\\\n&= f(1+x^2)\\\\\n&= \\frac{1}{1+x^2}\\\\\n\\end{align*}\nIs my work correct?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so ... |
[
{
"from": "human",
"value": "If \\(f(x) = 2x + 5\\) and \\(g(x) = x^2 - 1\\), find \\((f \\circ g)(-3)\\)."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here where I need to find \\((f \\circ g)(-3)\\). The functions given are \\(f(x) = 2x + 5\\) and \\(g(x) = x^2 - 1\\). ... |
[
{
"from": "human",
"value": "The points (3, -2), (4, 2), and (5, 8) are on the graph of the quadratic equation y = ax^2 + bx + c. Find the values of a, b, and c."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem where I need to find the values of a, b, and c for the quadratic ... |
[
{
"from": "human",
"value": "If we assume a 4.5% annual growth rate of the global economy, what is the projected number of years before the global economy doubles in size based on the rule of 72?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that the Rule of 72 is a quick method to ... |
[
{
"from": "human",
"value": "There are 10 people at a party, and they all shake hands with each other. How many handshakes are there?"
},
{
"from": "gpt",
"value": "<think>\nTo determine the number of handshakes at the party, I start by considering that each of the 10 people can shake hands with... |
[
{
"from": "human",
"value": "During the first two weeks, the average rainfall in City A was 2.2 inches per day. During the next two weeks, the average rainfall in City A was 1.8 inches per day. What was the total amount of rainfall in City A during the four-week period?"
},
{
"from": "gpt",
"val... |
[
{
"from": "human",
"value": "The function \\( f(x) = \\frac{x^3 + 2}{5x - 3} \\) has a horizontal asymptote. Find the equation of the horizontal asymptote."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the horizontal asymptote of the function \\( f(x) = \\frac{x^3 + 2}{5x - 3} ... |
[
{
"from": "human",
"value": "This problem requires a fundamental understanding of particle physics. The problem is stated as follows:\n\nA neutral kaon, which has a mean lifetime of 52 picoseconds (ps), decays into a pion of type π+ with a momentum of 230 MeV/c in the rest frame of the kaon. We can find the... |
[
{
"from": "human",
"value": "In a certain city, there are 5 statues of a famous historical figure. These statues are located in the city's central park, and each statue is unique in terms of its design and appearance. The local government wants to create a brochure that showcases the statues, and they need ... |
[
{
"from": "human",
"value": "A person has a certain number of cats but no more than 5. The probability that they have 0 cats is 10%, the probability that they have 1 cat is 20%, the probability that they have 2 cats is 30%, and the probability that they have 4 cats is 20%. What is the probability that the p... |
[
{
"from": "human",
"value": "A group of 5 friends, Alex, Ben, Charlie, David, and Emily, want to go on a road trip together. They have 5 cars, but each car can only hold 4 people. How many ways can they select 4 people to go in each car, and then arrange the selected people in the 5 different cars?"
},
... |
[
{
"from": "human",
"value": "A base-4 number $1232_4$ can be converted to base-10 by evaluating the expression $1(4^3)+2(4^2)+3(4^1)+2(4^0)$. Using the same method, we can convert a base-5 number $234_5$ to base-10 as $2(5^2)+3(5^1)+4(5^0)$. Now, let's define a new base-$k$ number $pqrs_k$ such that $p$, $q... |
[
{
"from": "human",
"value": "A man is on a mission to check the integrity of the books in his bookcase. He notes that there are 5 shelves. The following books are placed on each shelf:\n\n- Shelf 1: 2 books\n- Shelf 2: 5 books\n- Shelf 3: 3 books\n- Shelf 4: 1 book\n- Shelf 5: 4 books\n\nHow many books are ... |
[
{
"from": "human",
"value": "The total population of a small town is 50000 people. 1/5 of the population are men, and 2/3 of the men are married. What is the number of married men in the town?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the total number of men in the town.... |
[
{
"from": "human",
"value": "The discovery of hidden patterns among seemingly unrelated phenomena is a hallmark of science. One example is the relation between the time it takes for a cup of coffee to cool down and the time it takes for a person to forget a newly learned poem. Although the specific numerica... |
[
{
"from": "human",
"value": "A cylinder with radius 4 cm and height 10 cm is externally tangent to a larger cylinder with an unknown radius and height 20 cm, and to a small cone with radius 4 cm and height 8 cm. What is the radius of the larger cylinder?"
},
{
"from": "gpt",
"value": "<think>\nO... |
[
{
"from": "human",
"value": "The hypotenuse of a right-angled triangle is 10 inches long. One of the other sides is 6 inches long. What is the length of the third side?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here about a right-angled triangle. The hypotenuse is 10 i... |
[
{
"from": "human",
"value": "The sum of the interior angles of any convex polygon can be found by using the formula: 180 (n-2), where n is the number of sides of the polygon. Find the number of sides of a polygon with a sum of interior angles of 720 degrees."
},
{
"from": "gpt",
"value": "<think... |
[
{
"from": "human",
"value": "The Olympic Committee is planning to introduce a new sport to the Olympic Games. The sport requires a triangular area with a specific perimeter length. The perimeter length can be any value between 100m and 150m inclusive. The designer wishes to create a triangular area with the... |
[
{
"from": "human",
"value": "What is the smallest possible value for the product of two positive integers whose sum is 20?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: \"What is the smallest possible value for the product of two positive integers whose sum is 20?\" ... |
[
{
"from": "human",
"value": "The diameter of a semicircular arch is \\(14\\) m. The height of the arch is \\(1.6\\) m. Find the height of the centre of the arch above the ground. Find also the length of the chord joining the two ends of the arch."
},
{
"from": "gpt",
"value": "<think>\nOkay, so ... |
[
{
"from": "human",
"value": "The natural numbers less than 100 that are divisible by 5 or 7 are 5,7,10,14,15,21,25,28,30,35,40,42,45,49,50,56,60,63,65,70,75,77,80,84,85,90,95, and 98. How many of these numbers between 1 and 99 are also divisible by 3?"
},
{
"from": "gpt",
"value": "<think>\nOkay... |
[
{
"from": "human",
"value": "In the diagram below, the triangle $ABC$ is a right triangle with $\\angle C = 90^\\circ$. Point $D$ is the midpoint of $\\overline{AC}$, and point $E$ is the midpoint of $\\overline{BC}$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem about a r... |
[
{
"from": "human",
"value": "The sum of all the numbers in a certain set is 70, and the sum of the squares of all the numbers in this set is 600. What is the average of the squares of all the numbers in this set?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: The sum ... |
[
{
"from": "human",
"value": "Does any linear combination of the vectors $v_1 = \\left( \\begin{array}{c} 1 \\\\ 1 \\\\ 1 \\end{array} \\right)$, $v_2 = \\left( \\begin{array}{c} 1 \\\\ 2 \\\\ 3 \\end{array} \\right)$ and $v_3 = \\left( \\begin{array}{c} 2 \\\\ 3 \\\\ 4 \\end{array} \\right)$ equal the vecto... |
[
{
"from": "human",
"value": "A car increases in speed from 20 km/h to 60 km/h in 6 seconds. What is the average acceleration of the car?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to identify the initial and final speeds of the car. The initial speed is 20 km/h, and the final speed is... |
[
{
"from": "human",
"value": "Find the maximum value of the expression $x^2y^5$, given that $x^2 + y^2 = 1$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem: I need to find the maximum value of the expression \\( x^2y^5 \\) given that \\( x^2 + y^2 = 1 \\). Hmm, that seems li... |
[
{
"from": "human",
"value": "The magnetic dipole moment of a circular coil is given by the formula $m = IA$, where $I$ is the current flowing through the coil and $A$ is the area of the coil. The current through the coil is given by the formula $I = \\frac{E}{R}$, where $E$ is the electromotive force (EMF) ... |
[
{
"from": "human",
"value": "The area of a rectangle is 50 square centimeters and the width is 5 centimeters. What is the length of the rectangle?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that the area of a rectangle is calculated by multiplying its length by its width.\n\nGive... |
[
{
"from": "human",
"value": "Norbert has been saving money for a new bike and has $120 in his savings account. He wants to buy a bike that costs $216. What fraction of the cost of the bike has Norbert already saved?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the fraction ... |
[
{
"from": "human",
"value": "If an object’s weight is 30 N in air, and it is submerged in water, it experiences an upward buoyant force of 20 N. What is its apparent weight in the water?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this physics problem here. It says that an object's w... |
[
{
"from": "human",
"value": "In the following problem, a student is charged different amounts by their credit card company for different types of transactions. The student's credit card company charges:\n* 1% + 0.1 dollars per domestic transaction.\n* 1% + 1.5 dollars per international transaction.\n* 2% + ... |
[
{
"from": "human",
"value": "Q: A car is traveling at a constant acceleration of 3 m/s\\({}^{2}\\). If the car accelerates from a starting velocity of 0 m/s to a final velocity of 30 m/s in 10 seconds, is the information given in the problem inconsistent?"
},
{
"from": "gpt",
"value": "<think>\n... |
[
{
"from": "human",
"value": "The length of rectangle $ABCD$ is 4 and width is 3. What is the length of diagonal $AC$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: There's a rectangle ABCD with a length of 4 and a width of 3. I need to find the length of the diagonal... |
[
{
"from": "human",
"value": "The sum of the squares of the two smallest positive integer solutions to the equation \\( x^2 + 4x + 4 = 3x + 5 \\) is 40. Find the sum of the two solutions."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this equation here: \\( x^2 + 4x + 4 = 3x + 5 \\). Th... |
[
{
"from": "human",
"value": "In a standard game of bridge, a player has 13 cards. Two cards are drawn randomly. What is the probability that the cards drawn are the same suit?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: In a standard game of bridge, a player has 13... |
[
{
"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": "Given the vectors \\( \\mathbf{a} = \\begin{pmatrix} 2 \\\\ 3 \\\\ -1 \\end{pmatrix} \\) and \\( \\mathbf{b} = \\begin{pmatrix} 4 \\\\ -2 \\\\ 5 \\end{pmatrix} \\), find the component of vector \\( \\mathbf{a} \\) along the direction of vector \\( \\mathbf{b} \\)."
},
{
... |
[
{
"from": "human",
"value": "A manufacturer produces 2,500 units of a product every day. It produces units at a rate of 10 units per minute. How many minutes does the manufacturer take to produce 2,500 units?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine how many minutes it ... |
[
{
"from": "human",
"value": "A ship must be at least 10 nautical miles from a certain island in order to avoid shallow waters around it. If the ship is sailing due west and is currently 7 nautical miles from the island, what is the minimum distance the ship must travel to avoid the shallow waters and pass s... |
[
{
"from": "human",
"value": "This problem is about the composition of water molecules. A water molecule is made up of two hydrogen atoms and one oxygen atom, and its formula is H2O. How many hydrogen atoms are contained in one mole of water?"
},
{
"from": "gpt",
"value": "<think>\nTo determine t... |
[
{
"from": "human",
"value": "The power $P$ in a direct current (DC) electrical circuit is given by $P=VI$, where $V$ is the voltage and $I$ is the current. Find $P$ when $V=25$ volts and $I=0.5$ amperes."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here about finding the ... |
[
{
"from": "human",
"value": "The length of a rectangular garden is 10 feet longer than its width. If the area of the garden is 375 square feet, what are the dimensions of the garden?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I'll define the width of the garden as \\( w \\) feet. Since the l... |
[
{
"from": "human",
"value": "A retailer offers a 15% discount on a shirt that originally costs $80. 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 15% of the original price of the shirt... |
[
{
"from": "human",
"value": "A photo shoot for a catalog is being planned. The photographer will take pictures of 5 different outfits on 8 different models. How many different combinations of outfits and models are possible?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem he... |
[
{
"from": "human",
"value": "The population of a city is 350,000. If the population increases by 60,000 in 2 years, at what rate is the population increasing per year?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the total population increase over the two years, which is 60... |
[
{
"from": "human",
"value": "The first term of an arithmetic progression is \\( \\frac{1}{2} \\) and the fourth term is \\( 2 \\frac{1}{2} \\). What is the common difference?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here about an arithmetic progression. The first term... |
[
{
"from": "human",
"value": "The average height of a group of people in a room is 175 cm. If 5 people leave the room and the average height of the remaining people is 178 cm, what is the average height of the 5 people who left the room?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to de... |
[
{
"from": "human",
"value": "Dr. Patel is planning a party for her daughter's birthday. She has $120 to spend on party favors, gifts, and decorations. She wants to spend $20 on decorations and $40 on party favors. How much can she spend on gifts?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I ... |
[
{
"from": "human",
"value": "After a certain period of time, the total volume of a comet's tail is increasing at a rate of 0.6 cubic kilometers per hour and its radius is increasing at a rate of 20 kilometers per hour. What is the rate of change of its height at that instant, given the formula for the volum... |
[
{
"from": "human",
"value": "A system of linear equations has the following coefficient matrix:\n$\\begin{pmatrix} 6 & 3\\\\ 2 & -4 \\end{pmatrix}$.\nFind the determinant of this $2\\times 2$ matrix."
},
{
"from": "gpt",
"value": "<think>\nTo find the determinant of the given 2x2 matrix, I will ... |
[
{
"from": "human",
"value": "A mass \\(m\\) is attached to a spring with a spring constant \\(k\\). The mass is displaced by a distance \\(x\\) from its equilibrium position and then released from rest. The equation of motion for this system is given by the second-order differential equation:\n\\[m\\frac{d^... |
[
{
"from": "human",
"value": "The area of a rectangle is 48 square centimeters. If the length is five centimeters more than the width, what are the dimensions of the rectangle?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I'll define the width of the rectangle as \\( w \\) centimeters. Since th... |
[
{
"from": "human",
"value": "In an experiment, the speed of light in a glass slab is measured to be $2 \\times 10^8 \\textrm{ m/s}$. Given that the speed of light in vacuum is $3 \\times 10^8 \\textrm{ m/s}$, find the refractive index of the glass.\nThe refractive index can be calculated using the formula\n... |
[
{
"from": "human",
"value": "The function f ( x ) = sin(4 x ) is periodic with period T . Find the value of T ."
},
{
"from": "gpt",
"value": "<think>\nTo determine the period \\( T \\) of the function \\( f(x) = \\sin(4x) \\), I start by recalling the general form of the sine function, which is... |
[
{
"from": "human",
"value": "If you can measure the density of a sample of a pure substance, you can calculate its molar volume. How does the molar volume of a sample change when the sample is heated, using only the relationship between density and molar volume (d = M/V)?"
},
{
"from": "gpt",
"... |
[
{
"from": "human",
"value": "The sum of the interior angles of a triangle is always equal to 180°. If your triangle has angles measuring 30°, 60°, and x°, what is the value of x?"
},
{
"from": "gpt",
"value": "<think>\nTo determine the value of \\( x \\), I start by recalling that the sum of the... |
[
{
"from": "human",
"value": "The equation \\( \\frac{2x}{x-3} = \\frac{3}{x+2} \\) can be solved by first cross-multiplying to get \\( 2x(x+2) = 3(x-3) \\). Expanding and simplifying, we obtain \\( 2x^2 + 4x = 3x - 9 \\), which simplifies further to \\( 2x^2 + x - 9 = 0 \\). This equation can be factored or... |
[
{
"from": "human",
"value": "The probability that a randomly selected customer will place an order over the phone is 0.15. If the store receives 100 phone calls in a day from potential customers, what is the expected number of customers who will place an order over the phone?"
},
{
"from": "gpt",
... |
[
{
"from": "human",
"value": "In triangle $ABC$, point $P$ is on side $\\overline{AC}$ and point $M$ is the midpoint of $\\overline{BC}$. Given that $AC = 60$, $AP = 15$, and $PM = 10$, we need to find the length of $\\overline{AM}$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this ge... |
[
{
"from": "human",
"value": "The CEO of a company has at least 100 shareholders. He wants to send a group of $k$ shareholders (where $1 \\le k \\le 100$) to a conference. There are seven executives in the company, and they can only send two executives at a time to any conference. How many different combinat... |
[
{
"from": "human",
"value": "A circle of radius 4 is inscribed in a square. What is the area of the square?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: \"A circle of radius 4 is inscribed in a square. What is the area of the square?\" Hmm, let me try to visualize t... |
[
{
"from": "human",
"value": "A plane is flying at a velocity of 500 mph. As it flies over a town, it releases a package. From the perspective of an observer on the plane, the package falls straight down and lands right below the plane. However, from the perspective of an observer on the ground, the package ... |
[
{
"from": "human",
"value": "A six-sided die is rolled. What is the probability that the number of dots showing is less than 4?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: \"A six-sided die is rolled. What is the probability that the number of dots showing is less ... |
[
{
"from": "human",
"value": "The surface area of a cube can be calculated using the formula 6s^2, where s is the length of one side of the cube. If a cube has a surface area of 384, what is the length of one side of the cube?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that the su... |
[
{
"from": "human",
"value": "A new skate shop, \"The Board Room\", is opening and the owner, Alex, wants to order boards that will appeal to local skaters. After researching local skate parks and talking to experienced skaters, Alex decides on a mix of 110 standard (S) and 90 specialty (T) skateboards to st... |
[
{
"from": "human",
"value": "The document consists of 20 pages. If 8 pages are removed, what percentage of the document remains?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine how many pages remain after removing 8 pages from the original 20 pages.\n\nSubtracting the removed ... |
[
{
"from": "human",
"value": "The manager of a company has $100,000 to spend on bonuses. A total of 15 employees are eligible, and each employee will get a bonus of (8000 + 100r) dollars, where r is the employee's rating on a scale of 1 to 5. What is the total bonus paid to all employees if the rating distri... |
[
{
"from": "human",
"value": "The area of a triangle with vertices \\((x_1,y_1)\\), \\((x_2,y_2)\\), and \\((x_3,y_3)\\) can be calculated using the formula:\n\n\\[\n\\text{Area} = \\frac{1}{2} \\lvert x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \\rvert\n\\]\n\nGiven the vertices \\((0,5)\\), \\((-2,-3)... |
[
{
"from": "human",
"value": "A circle of radius $5$ is inscribed in a circle of radius $12$. A radius of the smaller circle and a radius of the larger circle are drawn to the point of tangency. What is the length of the line segment between the centers of the two circles?"
},
{
"from": "gpt",
"v... |
[
{
"from": "human",
"value": "In a particular week, the total rainfall in Woodville was 15 inches. During the first 5 days of the week, some days had no rain, and the total rainfall for those days was 3 inches. The rainfall on the last 2 days of the week was 4 times the rainfall in the first 5 days. How much... |
[
{
"from": "human",
"value": "A doctor has scheduled two surgeries, one at 9:00 a.m. and another at 1:00 p.m. A third surgery has been added and must be scheduled between the first two surgeries. The total time required for the three surgeries is 7 hours. The second surgery requires 2 hours more than the fir... |
[
{
"from": "human",
"value": "What is the coefficient of $x^{2}$ in $(5 + x)^{4}$?"
},
{
"from": "gpt",
"value": "<think>\nTo find the coefficient of \\( x^{2} \\) in \\( (5 + x)^{4} \\), I can use the Binomial Theorem. The theorem states that \\( (a + b)^{n} = \\sum_{k=0}^{n} \\binom{n}{k} a^{n ... |
[
{
"from": "human",
"value": "A box contains 5 red balls and 3 blue balls. What is the probability of drawing 2 blue balls in succession without replacement?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this probability problem here: there's a box with 5 red balls and 3 blue balls. I n... |
[
{
"from": "human",
"value": "On an arithmetic sequence, the 8th term is 112 and the 10th term is 118. Find the common difference and the first term of the arithmetic sequence."
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that in an arithmetic sequence, each term is obtained by addi... |
[
{
"from": "human",
"value": "A local restaurant desires to make a profit of 15% on their menu prices. If a dish costs them $10 to make, what should be the selling price of the dish?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to determine the desired profit, which is 15% of the cost. T... |
[
{
"from": "human",
"value": "A bakery sells a total of 405 bread loaves per day. The bakery sells two types of bread loaves, namely, whole wheat and white bread. For every 3 whole wheat bread loaves sold, 5 white bread loaves are sold. What is the number of whole wheat bread loaves sold per day?"
},
{
... |
[
{
"from": "human",
"value": "A right triangle has legs of length 3 and 4. Calculate the length of the hypotenuse."
},
{
"from": "gpt",
"value": "<think>\nTo determine the length of the hypotenuse of a right triangle with legs measuring 3 and 4 units, I can use the Pythagorean theorem. This theor... |
[
{
"from": "human",
"value": "The point $(0,1)$ is reflected over the line $x = 2y$. Find the coordinates of the reflected point."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the reflection of the point (0,1) over the line x = 2y. Hmm, reflecting a point over a line... I rememb... |
[
{
"from": "human",
"value": "The distance between the vertices of two lattices is defined as the minimum distance between any pair of vertices on the respective lattices. We are given two lattices in three-dimensional space, one with lattice points \\( (x,y,z) \\) where \\( x,y,z \\) are even integers, and ... |
[
{
"from": "human",
"value": "A triangle has vertices at (0,0), (3,0), and (1.5, √3). What is the area of this triangle?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here where I need to find the area of a triangle with vertices at (0,0), (3,0), and (1.5, √3). Hmm, let me ... |
[
{
"from": "human",
"value": "In a town, there are 9000 people. A survey was conducted to find the number of people who like to read books and watch movies. The survey showed that 60% of the people like to read books, 70% like to watch movies, and 30% like to do both. How many people like to read books or wa... |
[
{
"from": "human",
"value": "The volume of a sphere is \\( V = \\frac{4}{3}\\pi r^3 \\), where \\( r \\) is the radius of the sphere. If the volume of a sphere is \\( 36\\pi \\) cubic units, what is the radius of the sphere?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem he... |
[
{
"from": "human",
"value": "After 5 years of service, an employee is eligible for a 2-week paid vacation. Furthermore, for every year of service after the initial 5 years, the employee earns an additional day of paid vacation. If an employee has 12 years of service, how many days of paid vacation is the em... |
[
{
"from": "human",
"value": "What is the value of the sum of the digits of the number 123456?"
},
{
"from": "gpt",
"value": "<think>\nTo determine the sum of the digits of the number 123456, I will first identify each individual digit. The number 123456 consists of the digits 1, 2, 3, 4, 5, and ... |
[
{
"from": "human",
"value": "In the figure, $O$ is the center of the circle with radius $r$. Chord $AB$ has length $2r\\sin\\alpha$, and chord $BC$ has length $2r\\sin\\beta$. What is the length of chord $AC$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this geometry problem here. Le... |
[
{
"from": "human",
"value": "Assuming a standard deck of 52 cards, if you are dealt 7 cards, what is the probability of getting exactly 2 aces?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the probability of getting exactly 2 aces when I'm dealt 7 cards from a standard d... |
[
{
"from": "human",
"value": "This problem involves independent random variables. Let \\(X\\) and \\(Y\\) be independent and identically distributed (i.i.d.) random variables. Let \\(f_{X}(x)\\) be the probability mass function (pmf) of \\(X\\) and \\(Y\\), and let \\(f_{X|Y}(x|y)\\) be the conditional proba... |
[
{
"from": "human",
"value": "The sum of the first n natural numbers is given by the formula Sn = n(n+1)/2. Find the value of n for which the sum of the first n natural numbers is 253."
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that the sum of the first \\( n \\) natural numbers i... |
[
{
"from": "human",
"value": "When solving linear congruences of the form $ax \\equiv b \\pmod{m}$, where $\\gcd(a,m) = d$, then we can divide both sides of the congruence by $d$ to get a new congruence of the form $\\frac{a}{d}x \\equiv \\frac{b}{d} \\pmod{\\frac{m}{d}}$. But, when $\\gcd(a,m) \\neq 1$, we ... |
[
{
"from": "human",
"value": "This problem appears in a french book (\"Algèbre et Géométrie\" by M. Bataille, 1992). The exercice has been assigned to me by my son. I have to admit I do not know how to solve it. The problem is stated as follows:\n\n\"Un triangles rectangle $ABC$ a un angle droit en $B$ dont ... |
[
{
"from": "human",
"value": "In a study, it was found that the average response time of participants in a visual reaction task was 410 milliseconds. Suppose we want to estimate the true mean response time from a sample of 49 participants’ response times. Assuming the sampling distribution of the mean respon... |
[
{
"from": "human",
"value": "A natural number $N$ is multiplied by $2$ and then $5$ is added to the product. If the result is $2$ more than four times $N$, what is the value of $N$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this math problem here: A natural number N is multiplied b... |
[
{
"from": "human",
"value": "In a particular surgical operation, two procedures A and B are performed simultaneously. Procedure A takes $a$ minutes and procedure B takes $b$ minutes. The first surgeon finishes the operation in $t$ minutes and the second surgeon finishes the operation in $y$ minutes. It is k... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.