The maximum grade (slope) allowed for highways in Ontario is 12%. a) Predict the angle

$$\theta$$

, to the nearest degree, associated with this slope. b) Calculate the value of

$$\theta$$

to the nearest degree. c) Determine the six trigonometric ratios for angle

$$\theta$$

.

Solve the equation. Check for extraneous solutions. log(12x-11)=log(3x+13)

A walkway is made up of rectangular blocks.The volume of a block is 255 cubic inches. The width Is 10 inches and the height is 2 inches. What Is the length of a block? You can sketch the block and label It with the given information.Then you can use the formula $V=l \times w \times h$ to find the value of l.

$$\begin{aligned} V &=l \times w \times h \\ 255 &=l \times 10 \times 2 \\ 255 &=l \times 20 \\ 12 \frac{3}{4} &=l \end{aligned}$$

The length of a block is $12 \frac{3}{4}$ inches. Another block has a volume of 180 cubic inches.The area of the base is 72 square inches. What is the height of the block? Use the formula V = 8h to find the answer.

Balance the following chemical equation by inspection.

Fe(s) + Cd(NO$_{3}$)$_{2}$(aq) $\rarr$ Fe(NO$_{3}$)$_{3}$(aq) + Cd(s)

Evaluate the limit $\lim _{x \rightarrow 0} \frac{\log (\operatorname{CoS} a x)}{\log \cos b x)}$.

Answer “true” or “false” to the following statements: If the conclusion asserts that a certain area contains an X and inspection of the diagram reveals that only half an X appears in that area, the argument is valid.

Calculate the theoretical potential of each of the following cells. Is the cell reaction spontaneous as written or spontaneous in the opposite direction?

(a) $\mathrm{Pt} \mid \ {\mathrm{Cr}^{3+}}\left(1.00 \times 10^{-4} \mathrm{M}\right), \mathrm{Cr}^{2+}\left(2.00 \times 10^{-3} \mathrm{M}\right) \| \mathrm{Pb}^{2+}\left(5.60 \times 10^{-2} \mathrm{M}\right) \mid \mathrm{Pb}$

(b) $\mathrm{Hg} \mid \mathrm{Hg}_2{ }^{2+}\left(2.00 \times 10^{-2} \mathrm{M}\right) \| \mathrm{H}^{+}\left(1.00 \times 10^{-2} \mathrm{M}\right), \mathrm{V}^{3+}\left(3.00 \times 10^{-2} \mathrm{M}\right), \mathrm{VO}^{2-}$ $\left(2.00 \times 10^{-3} \mathrm{M}\right) \mid \mathrm{Pt}$

(c) $\mathrm{Pt} \mid \mathrm{Fe}^{3+}\left(4.00 \times 10^{-2} \mathrm{M}\right), \mathrm{Fe}^{2+}\left(3.00 \times 10^{-5} \mathrm{M}\right) \| \mathrm{Sn}^{2+}\left(5.50 \times 10^{-2} \mathrm{M}\right)$, $\mathrm{Sn}^{4+}\left(3.50 \times 10^{-4} \mathrm{M}\right) \mid \mathrm{Pt}$

Summary information from a company’s job cost sheets shows the following information:

$$\begin{array}{lrrccc} \text { Job } & \text { April } & \text { May } & \text { June } & \text { Completed } & \text { Sold } \\ \text { BB3 } & \$ 3,500 & \$ 1,500 & & \text { May } & \text { Not sold } \\ \text { BB4 } & 9,231 & & & \text { April } & \text { May } \\ \text { BB5 } & & 2,540 & & \text { May } & \text { June } \\ \text { BB6 } & & 3,230 & \$ 1,434 & \text { July } & \text { Not sold } \end{array}$$

What are the balances in the work in process inventory, finished goods inventory, and cost of goods sold for April, May, and June?

Find, by inspection, the sum of each series. $1-\frac{\pi^{2}}{2 !}+\frac{\pi^{4}}{4 !}-\frac{\pi^{6}}{6 !}+\cdots$

Let E denote the set of even integers and O denote the set of odd integers. As usual, let Z denote the set of all integers. Determine each of these sets. a) E ∪ O b) E ∩ O c) Z − E d) Z − O

Explain why

$$\log _ { 0 } 3 \text { and } \log _ { 1 } 3$$

do not exist.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality

$$\frac { x - 2 } { x + 3 } < 2$$

can be solved by multiplying both sides by x + 3 resulting in the equivalent inequality

$$x - 2 < 2 ( x + 3 ).$$

Find the area of the region $S=\left\{(x, y) \mid x \geqslant 0, y \leqslant 1, x^{2}+y^{2} \leqslant 4 y\right\}$.

Use the meaning of the symbols $\in$ and $\notin$ to determine whether the statement is true or false.

$\sqrt{2} \notin\{x \mid x$ is a rational number $\}$