answer:The curl of a vector field mathbf{F} = f(x,y,z)mathbf{i} + g(x,y,z)mathbf{j} + h(x,y,z)mathbf{k} is given by: nabla times mathbf{F} = left(frac{partial h}{partial y} - frac{partial g}{partial z}right)mathbf{i} + left(frac{partial f}{partial z} - frac{partial h}{partial x}right)mathbf{j} + left(frac{partial g}{partial x} - frac{partial f}{partial y}right)mathbf{k} Plugging in the given functions, we get: begin{split}nabla times mathbf{F} &= left(frac{partial}{partial y}[sin (y z)] - frac{partial}{partial z}[z^5]right)mathbf{i} + left(frac{partial}{partial z}[arctan(x)] - frac{partial}{partial x}[sin (y z)]right)mathbf{j} & quad + left(frac{partial}{partial x}[z^5] - frac{partial}{partial y}[arctan(x)]right)mathbf{k} &= left(z cos (y z) - 5 z^4right)mathbf{i} + (0 - 0)mathbf{j} + (0 - 0)mathbf{k} &= left(z cos (y z) - 5 z^4, 0, 0right). end{split} The answer is nabla times mathbf{F} = left(0, -z cos (y z) + 5 z^4, 0right).

answer:Using the z-score formula, we want to minimize the z-score to make the value least extreme. Since the standard deviation is in the denominator, we should choose the largest value: Therefore: {eq}displaystyle bf {text{d) s = 4}} {/eq}

answer:The location of the testes in the scrotum outside the body provides a cooler environment necessary for temperature-sensitive sperm development.

answer:frac{9}{17}lt frac{n}{n+k} lt frac{8}{15} is equivalent to frac{8}{9}nlt klt frac{15}{16}ntag1 If frac{15}{16}n-frac{8}{9}ngt 2, i.e. ngt 128, then there are at least two ks satisfying (1). So, we have to have nle 128. n=128 is sufficient since (1)iff 112lt klt 113 So, the largest n is color{red}{128}.