The only combinations with at least one boy are: BBB, BBG, BGB, GBB, BGG, GBG, GGB. Out of these, all combinations except BBB have at least one girl. Thus, P(At least one girl | At least one boy) = 6/7.

The only scenario where there are no girls is if all are boys. The probability of at least one girl given at least one boy is 3/4.

For total internal reflection to occur in a fiber optic cable, the core must have a higher refractive index than the cladding.

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.5/1.6) ≈ 38.7°.

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.4/1.5) ≈ 42.0°.

For total internal reflection, the core must have a higher refractive index than the cladding, so it must be greater than 1.45.

The cladding has a lower refractive index than the core, ensuring that light is kept within the core through total internal reflection.

The cladding has a lower refractive index than the core, ensuring that light remains within the core by total internal reflection.

Angular momentum is conserved; it remains constant, but her angular velocity increases.

By conservation of angular momentum, if the moment of inertia decreases, the angular velocity must increase.

By conservation of angular momentum, pulling arms in decreases moment of inertia, thus increasing angular velocity.

Angular momentum remains the same; however, her angular velocity increases due to a decrease in moment of inertia.

Pulling her arms in decreases her moment of inertia, causing her rotational speed to increase to conserve angular momentum.

Using Poiseuille's law, the flow rate Q = (π * r^4 * ΔP) / (8 * η * L). Assuming L = 1 m, Q = (π * (0.05)^4 * 1000) / (8 * 0.1 * 1) = 0.01 m³/s.

Shear stress = viscosity × (velocity/radius) = 0.1 × (1/0.05) = 2 Pa.

Using the formula for shear stress, τ = (4 * η * Q) / (π * r^3), we find τ = 0.4 Pa.

Using the equation ω_f = ω + αt, where α = τ/I, we get ω_f = ω + (τ/I)t.

From Newton's second law for rotation, τ = Iα, thus α = τ/I.

First convert rpm to rad/s: 1000 rpm = (1000 * 2π)/60 rad/s. Then use α = (ωf - ωi)/t = (0 - (1000 * 2π)/60) / 10.

Angular deceleration α = (final angular speed - initial angular speed) / time = (0 - 20 rad/s) / 5 s = -4 rad/s².

Using τ = Iα, we find α = τ/I. Assuming I = 1 kg·m², α = 5 rad/s². Time to stop = ω/α = 20 rad/s / 5 rad/s² = 4 s.

Using τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration. Assuming I = 25 kg·m², α = τ/I = 5/25 = 0.2 rad/s².

Angular deceleration = (final angular velocity - initial angular velocity) / time = (0 - 15) / 3 = -5 rad/s², so the magnitude is 5 rad/s².

Angular acceleration α = Torque/I. Assuming I = 6 kg·m², α = 3 N·m / 6 kg·m² = 0.5 rad/s².

Angular deceleration α = (ω_f - ω_i) / t = (0 - 20 rad/s) / 5 s = -4 rad/s², so the magnitude is 4 rad/s².

The angular deceleration α = (ω_final - ω_initial) / time = (10 - 20) / 5 = -2 rad/s². Torque τ = Iα = 4 kg·m² * (-2 rad/s²) = -8 N·m, so the magnitude is 8 N·m.

Maximum possible value = measured value + uncertainty = 100 + 2 = 102 N.

Percentage uncertainty = (absolute uncertainty / measured value) * 100 = (1 / 50) * 100 = 2%.

Percentage uncertainty = (absolute uncertainty / measured value) * 100 = (2 / 50) * 100 = 4%.

Relative uncertainty = (absolute uncertainty / measured value) = 2 / 50 = 0.04 or 4%.