When a 0.80-kg crown is submerged in water, its apparent weight is measured to be 7.3 N. Is the crown pure gold?

Which end of the muscle typically moves?

Use Stokes’ Theorem to evaluate

$$\mathbf{F}(x,y,z)=(x+y^2-2)\mathbf{i}+2xy\mathbf{j}+(x^2+yz^2)\mathbf{k};$$

S is the part of the paraboloid z = 4 - x squared - y squared above the xy-plane with an outward normal

A merchant in Katmandu sells you a solid gold 1-kg statue for a very reasonable price. When you get home, you wonder whether or not you got a bargain, so you lower the statue into a container of water and measure the volume of displaced water. Show that, for pure gold, the volume of water displaced will be $51.8 \mathrm{~cm}^3$.

What is the chance that the next person I meet will be different from me? The diversity index, from 0 (no diversity) to 100, measures the chance that two randomly selected people are of a different race or ethnicity. The diversity index in the United States varies widely from region to region, from as high as 81 in Hawaii to as low as 11 in Vermont. The bar graph at the top of the next column shows the national diversity index for the United States for four years the period from 1980 through 2010.

The data in the graph can be modeled by the formula

$$D=0.7 x+34 \text {, }$$

where $D$ is the national diversity index for the United States $x$ years after 1980.

How well does the formula model the national diversity index for 2010?

Write an algebraic expression for each verbal expression.

$k$ squared minus 11

A merchant in Katmandu sells you a solid gold 1-kg statue for a very reasonable price. When you get home, you wonder whether or not you got a bargain, so you lower the statue into a container of water and measure the volume of displaced water. What volume will verify that it's pure gold?

Suppose we have a repository of 1000 documents, and we wish to build an inverted index with 10,000 words. A block can hold ten word-pointer pairs or 50 pointers to either a document or a position within a document. The distribution of words is Zipfian; the number of occurrences of the $i$ th most frequent word is $100000 / \sqrt{i}$, for $i=1,2, \ldots, 10000$.

a) What is the averge number of words per document?

b) Suppose our inverted index only records for each word all the documents that have that word. What is the maximum number of blocks we could need to hold the inverted index?

c) Suppose our inverted index holds pointers to each occurrence of each word. How many blocks do we need to hold the inverted index?

d) Repeat (b) if the 400 most common words ("stop" words) are not included in the index.

e) Repeat (c) if the 400 most common words are not included in the index.

Write the rational number as a decimal. Then tell whether the decimal is a terminating or a repeating decimal.

$$\frac{4}{12}=$$

Major home appliances purchased in the United States are now labeled with bright yellow "Energy Guide" tags showing anticipated energy consumption. The tag on a recently purchased washing machine indicated the anticipated energy use would be $940 \mathrm{~kW}$-h per year. Calculate the anticipated annual energy use in kilojoules. (See Question 8 for a definition of a kilowatt-hour.) At 8 cents/ kW-hr, how much would it cost per month to operate this machine?

How do negative signs on residuals affect the sum of squared residuals?

One industrial process has an energy consumption of $18.5 \mathrm{kWh} / \mathrm{kg}$ of $\mathrm{Mg}$. How many joules are required per mole $(1 \mathrm{kWh}=1$ kilowatt-hour $=$ $\left.3.6 \times 10^6 \mathrm{~J}\right)$? How does this energy compare with the energy of the following process?

$$\begin{align*} \mathrm{MgCl}_2(\mathrm{~s}) \rightarrow \mathrm{Mg}(\mathrm{s})+\mathrm{Cl}_2(\mathrm{~g}) \end{align*}$$

Consider a $15-\mathrm{cm} \times 20-\mathrm{cm}$ printed circuit board $\mathrm{(PCB)}$ that has electronic components on one side. The board is placed in a room at $20^{\circ} \mathrm{C}$. The heat loss from the back surface of the board is negligible. If the circuit board is dissipating $8 \mathrm{~W}$ of power in steady operation, Find the average temperature of the hot surface of the board, assuming the board is $(a)$ vertical; $(b)$ horizontal with hot surface facing up; and $(c)$ horizontal with hot surface facing down. Take the emissivity of the surface of the board to be $0.8$ and assume the surrounding surfaces to be at the same temperature as the air in the room.

Evaluate each expression. a. 2^4 b. 5^3 c. 8.3^2 d. 1^9 e. 13^1 f. 56.8^0 g. 10^5 h. 100^2 i. 0^12 j. eleven squared k. one and three-tenths cubed l. seven squared times two cubed m. three to the fifth power n. four squared cubed