A hospital must order the drug Porapill from Daisy Drug Company. It costs $500 to place an order and$30 to review the hospital’s inventory of the drug. Annual demand for the drug is N(10,000, 640,000), and it costs $5 to hold one unit in inventory for one year. Orders arrive one month after being placed. Assume that all shortages are backlogged. a. Estimate R and the number of orders per year that should be placed. b. Using the answer in part (a), determine the optimal (R, S) inventory policy. Assume that the shortage cost per unit of the drug is$100.

The speed of a race car during the first seven seconds of a race is given by :

$$\begin{array} { |c| c | c | c | c | c | c | c | } \hline t(s)&0 & { 1 } & { 2 } & { 3 } & { 4 } & { 5 } & { 6 } & { 7 } \\ \hline v(mi/h)&0 & { 14 } & { 39 } & { 69 } & { 95 } & { 114 } & { 129 } & { 139 } \\ \hline \end{array}$$

List the nucleotide bases present: (a) In DNA: _____ (b) In RNA: _____

Suppose that a nuclear fission power plant and a coal-fired power plant both operate at 40% efficiency. Determine the ratio of the mass of coal that must be burned in 1 day of operating a 1000-MW plant compared to the mass of $^{235} \mathrm{U}$ that must undergo fission in the same plant. The energy released by burning coal is $3.3 \times 10^{7} \mathrm{J} / \mathrm{kg}$. The energy released per $^{235} \mathrm{U}$ fission is 200 MeV.

In this exercise, f(x) is a probability density function for a particular random variable x. Use integration to find the indicated probabilities.

$$f(x)=\left\{\begin{array}{ll}{\frac{1}{3}} & {\text { if } 2 \leq x \leq 5} \\ {0} & {\text { otherwise }}\end{array}\right.$$

a. $P(2 \leq X \leq 5)$ b. $P(3 \leq X \leq 4)$ c. $P(X \geq 4)$

How can an element have an atomic weight that is not an integer?

graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, $y=x^{2} )$ and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. $h(x)=\sqrt{x-2}$

If $\mathbf{u}=2 \mathbf{i}-3 \mathbf{j}$ and $\mathbf{v}=x \mathbf{i}+y \mathbf{j},$ describe the set of points in the plane whose coordinates $(x, y)$ satisfy $\|\mathbf{v}-\mathbf{u}\| \leq 2$.

Write the following in the form $a^{x}$ where a is a prime number and x is rational: $\sqrt[3]{32}$

Tom purchased a new car for $36,000. He has determined that it straight line depreciates over 12 years. When he purchased the car, he made a$6,000 down payment and financed the rest with a 5-year loan where he pays $610 per month. a. Create an expense and depreciation function where x represents the number of months. b. After how many months will the amount invested in the car be equal to the value of the car? Round your answer to the nearest month.

Decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem. If false, provide an example, illustration, or brief explanation of why the statement is false. Each eigenspace of an

$$n \times n$$

matrix is a subspace of

$$\mathbb { R } ^ { n }.$$

Find one solution for each equation. Assume that all angles in which an unknown appears are acute angles. $\cot \left(5 \theta+2^{\circ}\right)=\tan \left(2 \theta+4^{\circ}\right)$

Let $\Sigma=\{0,1\}$ and $A=\{0,01,011,111\} \subseteq \Sigma^{*} .$ For $n \geq 1,$ let an count the number of strings in A* of length n. Find and solve a recurrence relation for an.

Why do you think the Europeans did not invite Africans to the Berlin Conference?