answer:1. The incremental contribution margin per container is calculated as follows: Incremental sales revenue per container = 7.60 (selling price) - 3.80 (raw honey cost for 0.75 pounds) = 4.75 Incremental variable costs per container = 3.35 (variable manufacturing) + 0.38 (variable selling expenses) = 3.73 Incremental contribution margin = 4.75 - 3.73 = 1.02 2. To find the break-even point in terms of candy containers, we use the relevant costs and the incremental contribution margin: Avoidable fixed costs = Master candy maker's salary (4,280) + Salesperson's fixed salary (2,166) = 6,446 Break-even point in units = Avoidable fixed costs / Incremental contribution margin per unit Break-even point in units = 6,446 / 1.02 ≈ 6,320 containers Therefore, the company must sell at least 6,320 containers of honey drop candies each month to justify processing honey into candies.

answer:The Jacobian matrix of a vector-valued function mathbf{r}(x, y, z) = langle f(x, y, z), g(x, y, z), h(x, y, z) rangle is a matrix whose entries are the partial derivatives of the component functions f, g, and h. frac{partial}{partial x} [log(x)] = frac{1}{x} frac{partial}{partial y} [log(x)] = 0 frac{partial}{partial z} [log(x)] = 0 frac{partial}{partial x} [sqrt{y}] = 0 frac{partial}{partial y} [sqrt{y}] = frac{1}{2sqrt{y}} frac{partial}{partial z} [sqrt{y}] = 0 frac{partial}{partial x} [cos(x - y)] = -sin(x - y) frac{partial}{partial y} [cos(x - y)] = sin(x - y) frac{partial}{partial z} [cos(x - y)] = 0 The Jacobian matrix of mathbf{r}(x, y, z) is given by: J(mathbf{r}(x, y, z)) = begin{bmatrix} frac{partial}{partial x} [log(x)] & frac{partial}{partial y} [log(x)] & frac{partial}{partial z} [log(x)] frac{partial}{partial x} [sqrt{y}] & frac{partial}{partial y} [sqrt{y}] & frac{partial}{partial z} [sqrt{y}] frac{partial}{partial x} [cos(x - y)] & frac{partial}{partial y} [cos(x - y)] & frac{partial}{partial z} [cos(x - y)] end{bmatrix} = begin{bmatrix} frac{1}{x} & 0 & 0 0 & frac{1}{2sqrt{y}} & 0 -sin(x - y) & sin(x - y) & 0 end{bmatrix}

answer:The velocity and time of a freely falling object can be calculated using the following equations: [ v = sqrt{2gh} ] [ t = sqrt{frac{2h}{g}} ] where: - ( h ) is the initial height (48 feet) - ( g ) is the acceleration due to gravity (32 feet per second squared, ( text{ft/s}^2 )) Given: [ h = 48 text{ ft} ] a) The velocity of the man just before hitting the ground is: [ v = sqrt{2gh} = sqrt{2 times 32 times 48} text{ ft/s} approx 55 text{ ft/s} ] b) The time taken for the man to fall to the ground is: [ t = sqrt{frac{2h}{g}} = sqrt{frac{2 times 48}{32}} text{ s} approx 1.7 text{ s} ] Thus, the man hits the ground with a velocity of approximately 55 feet per second and reaches the ground in about 1.7 seconds.

answer:It is of paramount importance for the judicial branch to have the authority to review laws for several compelling reasons. Firstly, this power serves as a vital check and balance on the legislative and executive branches, ensuring that laws passed by these branches comply with the Constitution. The Constitution is the supreme law of the land, and it sets forth the fundamental principles and rights that govern our society. By having the ability to review laws, the judicial branch can ensure that laws do not violate these principles and rights. Secondly, the judicial branch's power to review laws helps to protect the rights of individuals and minorities. Laws that are passed by the legislative branch may sometimes be influenced by special interests or political considerations, which can lead to laws that unfairly target or discriminate against certain groups of people. The judicial branch, through its power of review, can strike down such laws and protect the rights of those who are affected. Thirdly, the judicial branch's power to review laws promotes the rule of law and ensures that laws are applied fairly and consistently. Without this power, the legislative and executive branches could potentially enact laws that are arbitrary or discriminatory, leading to uncertainty and instability in the legal system. The judicial branch's ability to review laws helps to ensure that laws are based on sound legal principles and that they are applied equally to all citizens.