answer:To calculate the volume, we multiply the number of moles by the molar volume at STP: Volume = (5.5 mol) x (22.414 L/mol) Volume ≈ 123.3 L

answer:The completing the square method is a technique used to solve quadratic equations by converting them into the form (x + a)^2 = b, where a and b are constants. This allows us to easily find the solutions to the equation by taking the square root of both sides. To solve the equation x^2 + 4x = 21 using the completing the square method, follow these steps: 1. Add and subtract the square of half the coefficient of x, which is (4/2)^2 = 4, to the left-hand side of the equation: x^2 + 4x + 4 - 4 = 21 2. Factor the left-hand side as a perfect square: (x + 2)^2 - 4 = 21 3. Add 4 to both sides of the equation: (x + 2)^2 = 25 4. Take the square root of both sides of the equation: x + 2 = ±5 5. Subtract 2 from both sides of the equation: x = -2 ± 5 6. Therefore, the solutions are x = -2 + 5 = 3 and x = -2 - 5 = -7.

answer:To find the relative extrema of {eq}f(x) = x^3 - 6x^2 + 6{/eq}, we first find its critical points by solving {eq}fprime(x) = 0{/eq}. {eq}fprime(x) = 3x^2 - 12x{/eq} {eq}3x(x - 4) = 0{/eq} {eq}x = 0{/eq} or {eq}x = 4{/eq} These critical points divide the real line into three intervals: {eq}(-infty, 0), (0, 4){/eq}, and {eq}(4, infty){/eq}. We then evaluate the second derivative of {eq}f(x){/eq} at each critical point: {eq}fprimeprime(x) = 6x - 12{/eq} {eq}fprimeprime(0) = -12 < 0{/eq} {eq}fprimeprime(4) = 12 > 0{/eq} By the Second Derivative Test, {eq}(0, 6){/eq} is a relative maximum and {eq}(4, -26){/eq} is a relative minimum.

answer:Given: {eq}mu = 72 sigma = 12 P(X < x) = 0.27 {/eq} Now, {eq}P(frac{X - mu}{sigma} < frac{x-mu}{sigma}) = 0.27 P(Z < z) = 0.27 {/eq} Where, {eq}z = frac{x - mu}{sigma} {/eq} Using Excel function: =NORMSINV(0.27) {eq}z = -0.6128 {/eq} So, {eq}-0.6128 = frac{x-mu}{sigma} -0.6128 = frac{x-72}{12} x = -0.6128 times 12 + 72 x = 64.64 {/eq} Therefore, the value that corresponds to the 27th percentile is {eq}64.64. {/eq}