Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 41807.0 / 1000.
Final: {"answer": 41.807, "unit": "kg"}

Answer: 41.807

Prompt: Convert 41807 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 41807.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=84 degrees and keep the unit as newtons.
Final: {"answer": [39.1459, 372.4484], "unit": "N"}

Answer: 39.1459

Answer: 372.4484

Prompt: A vector has magnitude 374.5 N at 84 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=84 degrees and keep the unit as newtons.

[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=451 mg, t=50.5 h, and T_half=88.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 303.6703, "unit": "mg"}

Answer: 303.6703

Prompt: A radioactive sample starts with 451 mg. Its half-life is 88.5 hours. How many mg remain after 50.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=451 mg, t=50.5 h, and T_half=88.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.7 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 486.4212, "unit": "g"}

Answer: 486.4212

Prompt: A sample contains 2.7 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.7 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each registry clinical record from batch 787081 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: target_schema, valid_examples.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [2.45, -21.75], "unit": "dimensionless"}

Answer: 2.45

Answer: -21.75

Prompt: A line passes through points (5.75, -7.6625) and (16.75, 19.2875). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.36 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1145.7922, "unit": "g"}

Answer: 1145.7922

Prompt: A sample contains 6.36 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.36 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 3.8^2 and multiply by 0.5 * 6.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 44.403, "unit": "J"}

Answer: 44.403

Prompt: A body of mass 6.15 kg moves at 3.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.8^2 and multiply by 0.5 * 6.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.99 * 8.314 * 292 / 2.5.
Final: {"answer": 3874.59, "unit": "kPa"}

Answer: 3874.59

Prompt: An ideal gas sample has n=3.99 mol, T=292 K, and V=2.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.99 * 8.314 * 292 / 2.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 565 * 0.925 * 27.
Final: {"answer": 14110.875, "unit": "J"}

Answer: 14110.875

Prompt: A 565 g sample has specific heat 0.925 J/(g*K). How much heat is needed to raise its temperature by 27 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 565 * 0.925 * 27.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.0, -9.75], "unit": "dimensionless"}

Answer: -2.0

Answer: -9.75

Prompt: A line passes through points (-14, 18.25) and (-2.25, -5.25). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.9 * 8.314 * 591 / 70.0.
Final: {"answer": 63.1745, "unit": "kPa"}

Answer: 63.1745

Prompt: An ideal gas sample has n=0.9 mol, T=591 K, and V=70.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.9 * 8.314 * 591 / 70.0.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
import math

def unit_vector_007108(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_007108"}

Answer: python_code

Prompt: Write a Python function unit_vector_007108(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    unit_vector_007108(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=84 mg, t=328.5 h, and T_half=41.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.3479, "unit": "mg"}

Answer: 0.3479

Prompt: A radioactive sample starts with 84 mg. Its half-life is 41.5 hours. How many mg remain after 328.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=84 mg, t=328.5 h, and T_half=41.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=11 mg, t=295.5 h, and T_half=64 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.4482, "unit": "mg"}

Answer: 0.4482

Prompt: A radioactive sample starts with 11 mg. Its half-life is 64 hours. How many mg remain after 295.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=11 mg, t=295.5 h, and T_half=64 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.03 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 545.8727, "unit": "g"}

Answer: 545.8727

Prompt: A sample contains 3.03 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.03 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4250.0 / 100.
Final: {"answer": 42.5, "unit": "m"}

Answer: 42.5

Prompt: Convert 4250 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4250.0 / 100.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.15 * 8.314 * 323 / 95.4.
Final: {"answer": 88.6696, "unit": "kPa"}

Answer: 88.6696

Prompt: An ideal gas sample has n=3.15 mol, T=323 K, and V=95.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.15 * 8.314 * 323 / 95.4.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=45.5 mg, t=3.5 h, and T_half=74 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 44.0325, "unit": "mg"}

Answer: 44.0325

Prompt: A radioactive sample starts with 45.5 mg. Its half-life is 74 hours. How many mg remain after 3.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=45.5 mg, t=3.5 h, and T_half=74 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-8.3, -12.0], "unit": "dimensionless"}

Answer: -8.3

Answer: -12.0

Prompt: A line passes through points (0, -12) and (4.25, -47.275). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def safe_mean_007216(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_007216"}

Answer: python_code

Prompt: Write a Python function safe_mean_007216(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    safe_mean_007216([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=222.4 V and R=68 ohm.
Final: {"answer": 727.3788, "unit": "W"}

Answer: 727.3788

Prompt: A resistor has resistance 68 ohm and voltage 222.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=222.4 V and R=68 ohm.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 320.0 / 100.
Final: {"answer": 3.2, "unit": "m"}

Answer: 3.2

Prompt: Convert 320 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 320.0 / 100.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=15 degrees through the sine of 2 theta.
3. Substitute v=47.3 m/s and g=9.81 m/s^2.
Final: {"answer": 114.0311, "unit": "m"}

Answer: 114.0311

Prompt: A projectile is launched on level ground with no air resistance at speed 47.3 m/s and angle 15 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=15 degrees through the sine of 2 theta.
Substitute v=47.3 m/s and g=9.81 m/s^2.

speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.5 * 8.314 * 497 / 74.2.
Final: {"answer": 139.2203, "unit": "kPa"}

Answer: 139.2203

Prompt: An ideal gas sample has n=2.5 mol, T=497 K, and V=74.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.5 * 8.314 * 497 / 74.2.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.95 kg and a = 4.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 87.99, "unit": "N"}

Answer: 87.99

Prompt: A cart has mass 20.95 kg and measured acceleration 4.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.95 kg and a = 4.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 8.65^2 and multiply by 0.5 * 20.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 761.3189, "unit": "J"}

Answer: 761.3189

Prompt: A body of mass 20.35 kg moves at 8.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 8.65^2 and multiply by 0.5 * 20.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.86 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1416.0262, "unit": "g"}

Answer: 1416.0262

Prompt: A sample contains 7.86 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.86 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4785 mL to 4.785 L.
3. Compute M = 1.9 / 4.785.
Final: {"answer": 0.3971, "unit": "mol/L"}

Answer: 0.3971

Prompt: A solution contains 1.9 mol of solute in 4785 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4785 mL to 4.785 L.
Compute M = 1.9 / 4.785.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=34 degrees and keep the unit as newtons.
Final: {"answer": [147.5687, 99.5363], "unit": "N"}

Answer: 147.5687

Answer: 99.5363

Prompt: A vector has magnitude 178 N at 34 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=34 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0038, "unit": "state_units"}

Answer: 0.0038

Prompt: Use explicit Euler on dy/dt = -0.54 y with y(0)=31.5, step size h=1.1, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.9, -26.0], "unit": "dimensionless"}

Answer: 5.9

Answer: -26.0

Prompt: A line passes through points (-17, -126.3) and (-6, -61.4). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.7 * 8.314 * 244 / 9.5.
Final: {"answer": 576.554, "unit": "kPa"}

Answer: 576.554

Prompt: An ideal gas sample has n=2.7 mol, T=244 K, and V=9.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.7 * 8.314 * 244 / 9.5.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=63.2 V and R=165.8 ohm.
Final: {"answer": 24.0907, "unit": "W"}

Answer: 24.0907

Prompt: A resistor has resistance 165.8 ohm and voltage 63.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=63.2 V and R=165.8 ohm.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each registry survey record from batch 276282 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: target_schema, valid_examples.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=606 mg, t=234 h, and T_half=111.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 141.4864, "unit": "mg"}

Answer: 141.4864

Prompt: A radioactive sample starts with 606 mg. Its half-life is 111.5 hours. How many mg remain after 234 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=606 mg, t=234 h, and T_half=111.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=137.2 V and R=157.9 ohm.
Final: {"answer": 119.2137, "unit": "W"}

Answer: 119.2137

Prompt: A resistor has resistance 157.9 ohm and voltage 137.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=137.2 V and R=157.9 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.91 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 345.3804, "unit": "g"}

Answer: 345.3804

Prompt: A sample contains 5.91 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.91 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [-0.071, -0.547, -0.826], "unit": "temperature_units"}

Answer: -0.071

Answer: -0.547

Answer: -0.826

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=-0.45; current interior values are [0.1, -1.25, -0.75]. Use r=0.38. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.38 and add it to the current value.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1245 mL to 1.245 L.
3. Compute M = 4.085 / 1.245.
Final: {"answer": 3.2811, "unit": "mol/L"}

Answer: 3.2811

Prompt: A solution contains 4.085 mol of solute in 1245 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1245 mL to 1.245 L.
Compute M = 4.085 / 1.245.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.6422, "unit": "state_units"}

Answer: 0.6422

Prompt: Use explicit Euler on dy/dt = -0.29 y with y(0)=45, step size h=1.75, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-0.25, -23.75], "unit": "dimensionless"}

Answer: -0.25

Answer: -23.75

Prompt: A line passes through points (-9.25, -21.4375) and (2.25, -24.3125). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def center_values_007396(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_007396"}

Answer: python_code

Prompt: Write a Python function center_values_007396(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    center_values_007396([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 680 * 1.905 * 84.
Final: {"answer": 108813.6, "unit": "J"}

Answer: 108813.6

Prompt: A 680 g sample has specific heat 1.905 J/(g*K). How much heat is needed to raise its temperature by 84 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 680 * 1.905 * 84.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 675 mL to 0.675 L.
3. Compute M = 4.685 / 0.675.
Final: {"answer": 6.9407, "unit": "mol/L"}

Answer: 6.9407

Prompt: A solution contains 4.685 mol of solute in 675 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 675 mL to 0.675 L.
Compute M = 4.685 / 0.675.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 8.2^2 and multiply by 0.5 * 7.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 260.555, "unit": "J"}

Answer: 260.555

Prompt: A body of mass 7.75 kg moves at 8.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 8.2^2 and multiply by 0.5 * 7.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [0.55, -28.0], "unit": "dimensionless"}

Answer: 0.55

Answer: -28.0

Prompt: A line passes through points (5.5, -24.975) and (10.25, -22.3625). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.75 kg and a = 14.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 138.9375, "unit": "N"}

Answer: 138.9375

Prompt: A cart has mass 9.75 kg and measured acceleration 14.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.75 kg and a = 14.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3390.5 / 100.
Final: {"answer": 33.905, "unit": "m"}

Answer: 33.905

Prompt: Convert 3390.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 3390.5 / 100.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.9, 19.25], "unit": "dimensionless"}

Answer: 6.9

Answer: 19.25

Prompt: A line passes through points (-20, -118.75) and (-7.25, -30.775). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.55 kg and a = 1.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 8.88, "unit": "N"}

Answer: 8.88

Prompt: A cart has mass 5.55 kg and measured acceleration 1.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.55 kg and a = 1.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=23 degrees through the sine of 2 theta.
3. Substitute v=28.6 m/s and g=9.81 m/s^2.
Final: {"answer": 59.9787, "unit": "m"}

Answer: 59.9787

Prompt: A projectile is launched on level ground with no air resistance at speed 28.6 m/s and angle 23 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=23 degrees through the sine of 2 theta.
Substitute v=28.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=347 degrees and keep the unit as newtons.
Final: {"answer": [190.0022, -43.8655], "unit": "N"}

Answer: 190.0022

Answer: -43.8655

Prompt: A vector has magnitude 195 N at 347 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=347 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=996 mg, t=270 h, and T_half=22 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.2013, "unit": "mg"}

Answer: 0.2013

Prompt: A radioactive sample starts with 996 mg. Its half-life is 22 hours. How many mg remain after 270 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=996 mg, t=270 h, and T_half=22 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.74 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 674.5864, "unit": "g"}

Answer: 674.5864

Prompt: A sample contains 6.74 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.74 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.32 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 95.8398, "unit": "g"}

Answer: 95.8398

Prompt: A sample contains 5.32 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.32 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2115 mL to 2.115 L.
3. Compute M = 2.68 / 2.115.
Final: {"answer": 1.2671, "unit": "mol/L"}

Answer: 1.2671

Prompt: A solution contains 2.68 mol of solute in 2115 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2115 mL to 2.115 L.
Compute M = 2.68 / 2.115.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 9655.0 / 1000.
Final: {"answer": 9.655, "unit": "kg"}

Answer: 9.655

Prompt: Convert 9655 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 9655.0 / 1000.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.45 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 376.938, "unit": "g"}

Answer: 376.938

Prompt: A sample contains 6.45 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.45 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4340 mL to 4.34 L.
3. Compute M = 1.86 / 4.34.
Final: {"answer": 0.4286, "unit": "mol/L"}

Answer: 0.4286

Prompt: A solution contains 1.86 mol of solute in 4340 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4340 mL to 4.34 L.
Compute M = 1.86 / 4.34.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1270 mL to 1.27 L.
3. Compute M = 2.815 / 1.27.
Final: {"answer": 2.2165, "unit": "mol/L"}

Answer: 2.2165

Prompt: A solution contains 2.815 mol of solute in 1270 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1270 mL to 1.27 L.
Compute M = 2.815 / 1.27.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 13.45 kg and a = 2.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 29.59, "unit": "N"}

Answer: 29.59

Prompt: A cart has mass 13.45 kg and measured acceleration 2.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 13.45 kg and a = 2.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=31 degrees through the sine of 2 theta.
3. Substitute v=34.9 m/s and g=9.81 m/s^2.
Final: {"answer": 109.6268, "unit": "m"}

Answer: 109.6268

Prompt: A projectile is launched on level ground with no air resistance at speed 34.9 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=31 degrees through the sine of 2 theta.
Substitute v=34.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=710.5 mg, t=161 h, and T_half=115.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 270.3625, "unit": "mg"}

Answer: 270.3625

Prompt: A radioactive sample starts with 710.5 mg. Its half-life is 115.5 hours. How many mg remain after 161 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=710.5 mg, t=161 h, and T_half=115.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 13.3 kg and a = 6.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 89.775, "unit": "N"}

Answer: 89.775

Prompt: A cart has mass 13.3 kg and measured acceleration 6.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 13.3 kg and a = 6.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=334.5 mg, t=77.5 h, and T_half=116.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 210.9309, "unit": "mg"}

Answer: 210.9309

Prompt: A radioactive sample starts with 334.5 mg. Its half-life is 116.5 hours. How many mg remain after 77.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=334.5 mg, t=77.5 h, and T_half=116.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. density times acceleration times height gives kg/(m*s^2), or pascal
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In field worksheet case 804736, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
density times acceleration times height gives kg/(m*s^2), or pascal
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.25, -18.75], "unit": "dimensionless"}

Answer: -7.25

Answer: -18.75

Prompt: A line passes through points (1.75, -31.4375) and (3.25, -42.3125). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.55^2 and multiply by 0.5 * 10.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9625.2577, "unit": "J"}

Answer: 9625.2577

Prompt: A body of mass 10.15 kg moves at 43.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.55^2 and multiply by 0.5 * 10.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=690 mg, t=289 h, and T_half=20.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0394, "unit": "mg"}

Answer: 0.0394

Prompt: A radioactive sample starts with 690 mg. Its half-life is 20.5 hours. How many mg remain after 289 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=690 mg, t=289 h, and T_half=20.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=272 degrees and keep the unit as newtons.
Final: {"answer": [0.6456, -18.4887], "unit": "N"}

Answer: 0.6456

Answer: -18.4887

Prompt: A vector has magnitude 18.5 N at 272 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=272 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 835 * 2.09 * 103.
Final: {"answer": 179750.45, "unit": "J"}

Answer: 179750.45

Prompt: A 835 g sample has specific heat 2.09 J/(g*K). How much heat is needed to raise its temperature by 103 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 835 * 2.09 * 103.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.7)=-15.88 and f(11.3)=-58.12.
3. The interval width is 6.6.
Final: {"answer": -244.2, "unit": "area_units"}

Answer: -244.2

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.4x+14.2 from x=4.7 to x=11.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.7)=-15.88 and f(11.3)=-58.12.
The interval width is 6.6.

(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.05, 13.0], "unit": "dimensionless"}

Answer: 7.05

Answer: 13.0

Prompt: A line passes through points (-17, -106.85) and (-14.25, -87.4625). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 5.1^2 and multiply by 0.5 * 29.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 380.3962, "unit": "J"}

Answer: 380.3962

Prompt: A body of mass 29.25 kg moves at 5.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.1^2 and multiply by 0.5 * 29.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=524 mg, t=179.5 h, and T_half=113 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 174.2394, "unit": "mg"}

Answer: 174.2394

Prompt: A radioactive sample starts with 524 mg. Its half-life is 113 hours. How many mg remain after 179.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=524 mg, t=179.5 h, and T_half=113 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 221.0 / 100.
Final: {"answer": 2.21, "unit": "m"}

Answer: 2.21

Prompt: Convert 221 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 221.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=128 degrees and keep the unit as newtons.
Final: {"answer": [-44.0198, 56.3428], "unit": "N"}

Answer: -44.0198

Answer: 56.3428

Prompt: A vector has magnitude 71.5 N at 128 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=128 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.48 and add it to the current value.
Final: {"answer": [-0.028, 1.256, 1.81], "unit": "temperature_units"}

Answer: -0.028

Answer: 1.256

Answer: 1.81

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=2.8; current interior values are [0.5, 0.8, 2.05]. Use r=0.48. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.48 and add it to the current value.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 11.6 kg and a = 9.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 109.04, "unit": "N"}

Answer: 109.04

Prompt: A cart has mass 11.6 kg and measured acceleration 9.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 11.6 kg and a = 9.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=67 degrees through the sine of 2 theta.
3. Substitute v=64.3 m/s and g=9.81 m/s^2.
Final: {"answer": 303.1706, "unit": "m"}

Answer: 303.1706

Prompt: A projectile is launched on level ground with no air resistance at speed 64.3 m/s and angle 67 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=67 degrees through the sine of 2 theta.
Substitute v=64.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=984.5 mg, t=165 h, and T_half=68.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 185.3988, "unit": "mg"}

Answer: 185.3988

Prompt: A radioactive sample starts with 984.5 mg. Its half-life is 68.5 hours. How many mg remain after 165 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=984.5 mg, t=165 h, and T_half=68.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def normalize_007792(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_007792"}

Answer: python_code

Prompt: Write a Python function normalize_007792(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

out = normalize_007792([2, 3, 5]); assert len(out) == 3

try:
    normalize_007792([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=73 degrees through the sine of 2 theta.
3. Substitute v=81.2 m/s and g=9.81 m/s^2.
Final: {"answer": 375.8415, "unit": "m"}

Answer: 375.8415

Prompt: A projectile is launched on level ground with no air resistance at speed 81.2 m/s and angle 73 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=73 degrees through the sine of 2 theta.
Substitute v=81.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=89 mg, t=85.5 h, and T_half=71 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 38.6262, "unit": "mg"}

Answer: 38.6262

Prompt: A radioactive sample starts with 89 mg. Its half-life is 71 hours. How many mg remain after 85.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=89 mg, t=85.5 h, and T_half=71 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In quality-control check case 779641, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
volt squared divided by ohm is watt
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.8 kg and a = 9.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 55.39, "unit": "N"}

Answer: 55.39

Prompt: A cart has mass 5.8 kg and measured acceleration 9.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.8 kg and a = 9.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 29.95^2 and multiply by 0.5 * 29.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 13387.7623, "unit": "J"}

Answer: 13387.7623

Prompt: A body of mass 29.85 kg moves at 29.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.95^2 and multiply by 0.5 * 29.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4559.0 / 100.
Final: {"answer": 45.59, "unit": "m"}

Answer: 45.59

Prompt: Convert 4559 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4559.0 / 100.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 10.8^2 and multiply by 0.5 * 13.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 772.74, "unit": "J"}

Answer: 772.74

Prompt: A body of mass 13.25 kg moves at 10.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10.8^2 and multiply by 0.5 * 13.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=72 degrees through the sine of 2 theta.
3. Substitute v=81.2 m/s and g=9.81 m/s^2.
Final: {"answer": 395.0588, "unit": "m"}

Answer: 395.0588

Prompt: A projectile is launched on level ground with no air resistance at speed 81.2 m/s and angle 72 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=72 degrees through the sine of 2 theta.
Substitute v=81.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=138.4 V and R=17.2 ohm.
Final: {"answer": 1113.6372, "unit": "W"}

Answer: 1113.6372

Prompt: A resistor has resistance 17.2 ohm and voltage 138.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=138.4 V and R=17.2 ohm.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=236 degrees and keep the unit as newtons.
Final: {"answer": [-12.0226, -17.8243], "unit": "N"}

Answer: -12.0226

Answer: -17.8243

Prompt: A vector has magnitude 21.5 N at 236 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=236 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. coulomb per second is ampere
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 877605, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
coulomb per second is ampere
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.4 kg and a = 10.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 174.66, "unit": "N"}

Answer: 174.66

Prompt: A cart has mass 16.4 kg and measured acceleration 10.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.4 kg and a = 10.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.14 and add it to the current value.
Final: {"answer": [-1.195, -0.897, 0.277], "unit": "temperature_units"}

Answer: -1.195

Answer: -0.897

Answer: 0.277

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.75, right=0.25; current interior values are [-1.3, -1.1, 0.55]. Use r=0.14. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.14 and add it to the current value.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [2.8, -8.5], "unit": "dimensionless"}

Answer: 2.8

Answer: -8.5

Prompt: A line passes through points (-1.75, -13.4) and (-0.5, -9.9). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def threshold_flags_007900(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_007900"}

Answer: python_code

Prompt: Write a Python function threshold_flags_007900(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

assert threshold_flags_007900([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_007900([], 5) == []

assert threshold_flags_007900([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=64 degrees through the sine of 2 theta.
3. Substitute v=64.1 m/s and g=9.81 m/s^2.
Final: {"answer": 330.0496, "unit": "m"}

Answer: 330.0496

Prompt: A projectile is launched on level ground with no air resistance at speed 64.1 m/s and angle 64 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=64 degrees through the sine of 2 theta.
Substitute v=64.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.34 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 428.9496, "unit": "g"}

Answer: 428.9496

Prompt: A sample contains 7.34 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.34 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.08 and add it to the current value.
Final: {"answer": [0.246, 0.634, 0.336], "unit": "temperature_units"}

Answer: 0.246

Answer: 0.634

Answer: 0.336

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.85, right=2.4; current interior values are [-0.05, 0.75, 0.1]. Use r=0.08. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.08 and add it to the current value.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.42 and add it to the current value.
Final: {"answer": [1.564, 1.161, 1.484], "unit": "temperature_units"}

Answer: 1.564

Answer: 1.161

Answer: 1.484

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.25, right=2.45; current interior values are [2.95, 1.35, -0.7]. Use r=0.42. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.42 and add it to the current value.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=59 degrees through the sine of 2 theta.
3. Substitute v=22.8 m/s and g=9.81 m/s^2.
Final: {"answer": 46.7881, "unit": "m"}

Answer: 46.7881

Prompt: A projectile is launched on level ground with no air resistance at speed 22.8 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=59 degrees through the sine of 2 theta.
Substitute v=22.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.85, -18.5], "unit": "dimensionless"}

Answer: 6.85

Answer: -18.5

Prompt: A line passes through points (6.5, 26.025) and (16.25, 92.8125). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.26 and add it to the current value.
Final: {"answer": [2.018, 1.06, 0.548], "unit": "temperature_units"}

Answer: 2.018

Answer: 1.06

Answer: 0.548

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.8, right=2.5; current interior values are [1.55, 2.1, -1.35]. Use r=0.26. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.26 and add it to the current value.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.75 kg and a = 14.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 207.2375, "unit": "N"}

Answer: 207.2375

Prompt: A cart has mass 14.75 kg and measured acceleration 14.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 14.75 kg and a = 14.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a allocation scoring problem with 4532 items and budget 21255, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: recurrence, objective, tie_breaking_rule.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.25 kg and a = 0.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 14.175, "unit": "N"}

Answer: 14.175

Prompt: A cart has mass 20.25 kg and measured acceleration 0.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.25 kg and a = 0.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.51 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 452.1916, "unit": "g"}

Answer: 452.1916

Prompt: A sample contains 2.51 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.51 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 450 mL to 0.45 L.
3. Compute M = 2.61 / 0.45.
Final: {"answer": 5.8, "unit": "mol/L"}

Answer: 5.8

Prompt: A solution contains 2.61 mol of solute in 450 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 450 mL to 0.45 L.
Compute M = 2.61 / 0.45.