This scenario relates to binomial probability, where the results can either be a success or a failure. A success indicates that a selected adult possesses a bachelor's degree. Consequently, the success probability, denoted as p, is 20/100 = 0.2. The number of adults in the sample, represented as n, equals 100, and x, the count of successes, is 60. The probability of having more than 60 adults with a bachelor's degree, represented as P(x >60), can be noted internally as P(x < 60) = binomcdf (100, 0.20, 60). The function binompdf would indicate P(x = 60).
To find the total distance Isla walked, multiply 3/4 of a mile by 2 since it was a round trip. The result is 1.5 miles.
The cubic equation formed is L^3 - 52L +144 = 0. Dimensions: Length = 4 inches, Width = 2 inches, Height = 3 inches. To determine this, let L be the length, W the width, and H the height. The box volume is 24 cubic inches, and its total surface area is 52 sq. inches. Setting W = L/2 leads to Volume = L * W * H, thus substituting W gives us the equation 0.5L^2 * H = 24 resulting in H = 48/L^2. The surface area equation simplifies to (L*W) + (L+H) + (W+H) = 26. Introducing W = 0.5L yields 0.5L^2 + 1.5LH = 26. Substituting H into this gives 0.5L^2 + 72/L = 26. Multiplying throughout by L to eliminate denominators yields 0.5L^3 - 26L + 72 = 0. After multiplying through by 2: L^3 - 52L +144 = 0. Testing L=4 confirms a factor, thus Length (L) = 4 inches, and subsequently, W and H calculate to 2 inches and 3 inches respectively.
Answer:
Step-by-step explanation:
1) True. This stems from the fact that the divergence of F is 1, indicating that F is a linear function. The orientation is outward from the surface. Integrating a linear function over a surface with outward orientation leads to the volume enclosed by that surface.
2) True. This is fundamentally what the Divergence theorem states.
3) False. Had F been specified as 3/pi instead of div(F), this claim would have held true.
4) False. The gradient of divergence can vary. The curl of the divergence of a vector function is 0, contradicting the notion of the gradient of divergence being 0.
5) False. While calculating divergence, derivatives are computed for different variables. Since the derivative of constants is 0, both vector functions F and G can contain distinct constant components even when their divergences are equal.
