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[
{
"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... |
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