For the following exercise, see the example mentioned.

The number of hours worked in a week for 30 workers selected at random from the 2012 General Social Survey appears in the following frequency table. Find the standard deviation.

Interval	Frequency
0-9	1
10-19	3
20-29	5
30-39	3
40-49	12
50-59	3
60-69	1
70-79	2

Write each number in decimal notation without the use of exponents.

$$3.8 \times 10^2$$

Solve the equation algebraically. Round your result to three decimal places. $x \ln x+x=0$

Write the number in decimal notation. Provide your answer correctly.

$$7.1 \times 10^{14}$$

Write each number in decimal notation without the use of exponents.

$$-7.00001 \times 10^{10}$$

State whether

$$T_N$$

or

$$M_N$$

underestimates or overestimates the integral and find a bound for the error (but do not calculate

$$T_N$$

or

$$M_N).$$

$$\int _ { 0 } ^ { \pi / 4 } \cos x , \quad M _ { 20 }$$

Calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for the following reaction, using values of $\Delta G_f^{\circ}$.

$$\mathrm{CaCO}_3(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_2(g)$$

Write the number in decimal notation. Provide your answer correctly.

$$2.670 \times 10^{-8}$$

$\int_{0}^{3} \sqrt{9-x^{2}} d x=$ (A) $\pi$, (B) $\frac{3}{2} \pi$, (C) $\frac{9}{4} \pi$, (D) $\frac{9}{2} \pi$.

At $425^{\circ} \mathrm{C}, K_{\mathrm{p}}=4.18 \times 10^{-9}$ for the reaction

$$2 \mathrm{HBr}(g) \rightleftharpoons \mathrm{H}_2(g)+\mathrm{Br}_2(g)$$

In one experiment, $0.20 \mathrm{~atm}$ of $\mathrm{HBr}(g), 0.010 \mathrm{~atm}$ of $\mathrm{H}_2(g)$, and $0.010 \mathrm{~atm}$ of $\mathrm{Br}_2(\mathrm{~g})$ are introduced into a container. Is the reaction at equilibrium? If not, in which direction will it proceed?

In this exercise, find the indefinite integral.

$$\int(1+\sec \pi x)^2 \sec \pi x \tan \pi x d x$$

Find the indefinite integral.

$$\int \pi\sin \pi x \ dx$$

Write $\frac { 3.19 \times 10 ^ { - 9 } } { 0.02 \times 10 ^ { - 3 } }$ in decimal notation.

A free isothermal jet of 125 cfm (60 L/s), 6 in. (15 cm) diameter, is discharged vertically from the floor toward a ventilation hood 12 ft (3.7 m) above the floor. Approximately what capacity must the hood exhaust fan have to capture all of the airstream at the entrance to the hood?