Perform the computations. Write answers in scientific notation.

$$\frac{3 \times 10^{20}}{6 \times 10^{-8}}$$

Perform the indicated computations. Write the answers in scientific notation.

$$\frac{5 \times 10^{-6}}{20 \times 10^{-8}}$$

A rock is dropped from a window and falls to the ground below. The height, $s$ (in meters), of the rock above ground is a function of the time, $t$ (in seconds), since the rock was dropped, so $s = f(t)$.

Sketch a possible graph of $s$ as a function of $t$.

Write a sentence explaining how to tell if the domain of a trigonometric function is restricted.

Display the data in a histogram. Describe the shape of the distribution.

$$\begin{matrix} \text{Goals Scored in a Soccer Game} & \text{Frequency }\\ \text{0} & \text{4}\\ \text{1} & \text{8}\\ \text{2} & \text{5}\\ \text{3} & \text{3}\\ \text{4} & \text{1}\\ \text{5} & \text{1}\\ \text{6} & \text{0}\\ \text{7} & \text{1}\\ \end{matrix}$$

If $w=\operatorname{cis}\left(\frac{2 \pi}{n}\right)$ is the nth root of unity with the smallest positive argument, show that: a. the n roots of $z^{n}=1$ are $1, w, w^{2}, w^{3}, \dots \dots, w^{n-1}$ b. $1+w+w^{2}+w^{3}+\ldots \ldots+w^{n-1}=0$ Note: The roots of unity lie on the unit circle, equally spaced around the unit circle.

At the beginning of 2021, Quentin and Kopps (Q&K) adopted the dollar-value LIFO (DVL) inventory method. On that date the value of its one inventory pool was $84,000. The company uses an internally generated cost index to convert ending inventory to base year. Inventory data for 2021 through 2024 are as follows:

$$\begin{array}{lcccc} \begin{array}{c} \text { Year Ended } \\ \text { December 31 } \end{array} & \begin{array}{c} \text { Ending Inventory } \\ \text { at Year-End Costs } \end{array} & \begin{array}{c} \text { Ending Inventory } \\ \text { at Base Year Costs } \end{array} & \text { Cost Index } & \begin{array}{c} \text { Ending Inventory } \\ \text { at DVL cost } \end{array} \\ \hline 2021 & \$ 100,800 & \$ 96,000 & 1.05 & ? \\ 2022 & 136,800 & ? & 1.14 & ? \\ 2023 & 150,000 & 125,000 & ? & ? \\ 2024 & ? & ? & 1.25 & \$ 133,710 \end{array}$$

Determine the missing amounts.

What is the change in entropy of $1.00 \mathrm{m}^{3}$ of water at $0^{\circ} \mathrm{C}$ when it is frozen to ice at $0^{\circ} \mathrm{C} ?$

find a set of parametric equations to represent the graph of the rectangular equation using t = x.

$$y=2-x^2$$

Fill in the blanks.

Medical specialist in kidney treatment $\quad\rule{2cm}{0.15mm}$ / $\rule{2cm}{0.15mm}$ / $\rule{2cm}{0.15mm}$

Estimate using compatible numbers, then perform the computations.

$$\frac{5}{7} \times 44 \frac{1}{2}$$

Evaluate the definite integrals.

$$\int_0^1 8 x\ d x$$

Determine the rectangular coordinates of the vertices of the ellipse whose polar equation is $r=2 /(2-\sin \theta)$.

Shelia's measured glucose level one hour after a sugary drink varies according to the Normal distribution with u = 125 mg/dl and a = 10 mg/di. Let's consider what could happen if we took 4 separate measurements from Shelia. What is the blood glucose level L such that the probability is only 0.05 that the average of 4 measurements is larger than L? (Hint: This requires a backward Normal calculation.)