Determine the phases that are present and the compositions for each phase in $\mathrm{Cu}$-$85$ $\mathrm{wt} \% \mathrm{Ag}$ at $800^{\circ} \mathrm{C}$.

For the following problem, write the linear combination of cosine and sine as a single cosine with a phase displacement.

$$y=6 \cos \theta-6 \sin \theta$$

Cite the phases that are present and the phase compositions for the following alloys: (a) 15 wt% Sn–85 wt% Pb at $100^{\circ} \mathrm{C}\left(212^{\circ} \mathrm{F}\right)$ (b) 25 wt% Pb–75 wt% Mg at $425^{\circ} \mathrm{C}\left(800^{\circ} \mathrm{F}\right)$ (c) 85 wt% Ag–15 wt% Cu at $800^{\circ} \mathrm{C}\left(1470^{\circ} \mathrm{F}\right)$ (d) 55 wt% Zn–45 wt% Cu at $600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)$ (e) 1.25 kg Sn and 14 kg Pb at $200^{\circ} \mathrm{C}\left(390^{\circ} \mathrm{F}\right)$ (f) $\text { 7.6 } \mathrm{lb}_{\mathrm{m}} \mathrm{Cu} \text { and } 144.4 \mathrm{lb}_{\mathrm{m}} \mathrm{Zn} \text { at } 600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)$ (g) 21.7 mol Mg and 35.4 mol Pb at $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$ (h) 4.2 mol Cu and 1.1 mol Ag at $900^{\circ} \mathrm{C}\left(1650^{\circ} \mathrm{F}\right)$

Place $\in$ or $\notin$ in each blank to make the resulting statement true. 13 $\{3,5,12,14\}$

Fill in the blank to correctly complete each sentence. The elements of the set of natural numbers are ____.

Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error. 1/1.05

For the following problem, write the linear combination of cosine and sine as a single cosine with a phase displacement.

$$y=-15 \cos \theta+8 \sin \theta$$

Explain the change in bonding when $\mathrm{Al}_2 \mathrm{Cl}_6$ dissociates to form $\mathrm{AlCl}_3$ in the gas phase.

Fill in the blank to correctly complete each sentence. In the term $-6 x^{2} y,-6$ is the ____.

The following null and alternate hypotheses are given. Suppose the population standard deviation is 10. The probability of a Type I error is set at .01 and the probability of a Type II error at .30. Assume that the population mean shifts from 50 to 55. How large a sample is necessary to meet these requirements?

Insert $\in$ or $\notin$ in each blank to make the resulting statement true. $\varnothing$____$\varnothing$

Fill in the blank so that the resulting statement is true.

$x^3-27=(x$ _____ $)(x^2+3x$_____$)$

Complete each identity by filling in the blank. than name the identity. $\sec \theta=$____

Show that a wave function, expressed in complex form, is shifted in phase (a) by $\pi / 2$ when multiplied by $i$ and (b) by $\pi$ when multiplied by $-1$.