For a business using just-in-time inventory, a delivery of Q items arrives just as the last item is shipped out. Suppose that items are shipped out at a nonconstant rate such that $f(t)=Q-r \sqrt{t}$ gives the number of items in inventory. Find the time T at which the next shipment must arrive. Find the average value of f on the interval [0, T].

Just-in-time inventory assumes all of the following, except: 1. Zero defects. 2. Resources will only be introduced as they are needed. 3. Just-in-time inventory presumes first-in, first-out costing. 4. Production of components only occurs only when requested further downstream in the manufacturing cycle.

Zoom out sufficiently far so that the graph appears as a line. What equation does this line appear to have? (Note that the points at which the function is not continuous are not readily seen when you zoom out.)

$$f(x)=-\frac{x^{3}-2x^{2}+2}{2x^{2}}$$

$$g(x)= -\frac{1}{2}x+1-\frac{1}{x^{2}}$$

Write out and evaluate each sum.

$$\sum_{k=0}^5\left(k^2-2 k+3\right)$$

Carry out the differentiation.
$\displaystyle \frac{d}{dx}\left(\int_x^{x^2} \frac{dt}{1+t^2}\right)$.

Study the entries and answer the question that follows.

The root cant means "sing."

The root clam means "shout."

The prefix in-means "in," "on," or "onto."

The prefix re- means "back."

The prefix ad- means "toward."

The prefix de- means "down from."

The suffix-ment means "result of."

If ex-means "out," then the word means "to shout out suddenly."

Assume all variables are binomial. (Note: If values are not found in Previous Table . use the binomial formula.)
High School Dropouts Approximately $10.3\%$ of American high school students drop out of school before graduation. Choose $10$ students entering high school at random. Find the probability that
No more than $2$ drop out

Wire 1 has a current flowing out of the page, $i_{\text {out, }}$ as shown in the figure. Wire 2 has a current flowing into the page, $i_{\mathrm{m}}$. What is the direction of the magnetic field at point $P$ ? a) upward in the plane b) to the right c) downward in the of the page plane of the page d) to the left e) The magnetic field at point $P$ is zero.

After a collision with a power pole, you are trapped in your car, with a high-voltage line (with frayed insulation) in contact with the hood of the car. If you must get out before help arrives, is it safer to step out of the car one foot at a time or to jump with both feet leaving the car at the same time? Explain your reasoning.

A manufacturer of lightbulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let F(t) be the fraction of the company’s bulbs that burn out before t hours, so F(t) always lies between 0 and 1. What is the value of ^∞∫0 r(t) dt? Why?

For each sentence, if the underlined pronoun is correct write C above it. If it is not correct, cross it out and write the correct form of the pronoun above it.

Example 1. My choice for the student delegate will be $\overset{\textit{\color{#c34632}{she}}}{{\underline{\sout{\text{her}}}}}$.

It wasn’t $\underline{\text{I}}$ who left the baseball equipment out on the field.

The speed, s, in metres per second, of water flowing out of a hole near the bottom of a tank relates to the height, h, in metres, of the water above the hole by the formula $s=\sqrt{2gh}$ . In the formula, g represents the acceleration due to gravity, 9.8 m/$s^2$. At what height is the water flowing out a speed of 9 m/s?

Add parentheses and brackets where they are needed in the following sentences.

Afterward Nigel said, "He Newfie seemed to come out of nowhere!"

A television advertisement shows a lawyer in a bathing suit coming out of a lake. He says, "If you're in over your head because of bad debts, let us bail you out. We're the best firm in the state." Should there be any restrictions on ads like this? If so, what? Should there be other restrictions on ads? If so, what should they be?