answer:The estimated values for the polyhedron are as follows: - Solid Angle at the first listed point: 1.64 steradians - Volume: 0.13 cubic units - Surface Area: 1.76 square units

answer:The equation -(-x) = x is true for any value of x because the negative sign outside the parentheses negates the negative sign inside the parentheses. This means that the expression -(-x) is equivalent to multiplying x by -1 and then multiplying it by -1 again, which results in x.

answer:Given: - Radius, r = 15 cm = 0.15 m - Tangential acceleration, a = 0.27 m/s² - Initial angular velocity, ω₀ = 0 rad/s Angular acceleration, α = a / r = 0.27 m/s² / (0.15 m) = 1.8 rad/s² (a) Angular displacement, θ, after time t can be calculated using: θ = ω₀t + (1/2)αt² At t = 5 s: θ = (0 rad/s) * (5 s) + (1/2) * (1.8 rad/s²) * (5 s)² θ = 22.5 rad Converting to revolutions: 1 revolution = 2π rad Angular displacement in revolutions = θ / (2π) = 22.5 rad / (2π) ≈ 3.6 revolutions (b) After 5 seconds, the turntable has a constant angular velocity, ω, which is also its angular velocity at 9 seconds: ω = ω₀ + αt At t = 5 s: ω = 0 rad/s + 1.8 rad/s² * (5 s) = 9 rad/s The average angular velocity from t = 5 s to t = 9 s is the final angular velocity, since it is constant: Average angular velocity, ω_avg = 9 rad/s The revised question and answer pair is now formatted consistently and provides complete, accurate information.

answer:Let X be the number of seniors in the sample. Since the number of trials is fixed (15) and the probability of success (being a senior) is constant (0.25), X follows a binomial distribution with parameters n = 15 and p = 0.25. The probability of exactly 5 seniors is given by the binomial probability formula: {eq}P(X = 5) = {}^{15}{C_5}{(0.25)^5}{(0.75)^{10}} approx 0.1651{/eq} Therefore, the probability that exactly 5 of the sampled students are seniors is approximately 0.1651.