Explain why governments provide subsidies, and describe examples of subsidies.

Find the exact value of the expression.

$$\sin 150^{\circ}$$

Tell whether a triangle can have the given angle measures. If not, change the first angle measure so that the angle measures form a triangle.

$$5 \frac{2}{3}^{\circ}, 64 \frac{1}{3} \circ 87^{\circ}$$

Use the graph of f to explain the transformation that yields the graph of g.

$$f(x)=3^x, \quad g(x)=3^{x-4}$$

Sketch the graph of $y=x^n$ and each transformation.

$y=x^5$ $\quad$ (d) $f(x)=-\frac{1}{2}(x+1)^5$

Find the exact value of the expression.

$$\cos (\arccos 0.25)$$

Below are heights of 25 female college students.

$$\overset{1}{54},\overset{2}{55},\overset{3}{56},\overset{4}{56},\overset{5}{57},\overset{6}{58},\overset{7}{58},\overset{8}{59},\overset{9}{60},\overset{10}{60},\overset{11}{60},\overset{12}{61},\overset{13}{61},\overset{14}{62},\overset{15}{62},\overset{16}{63},\overset{17}{63},\overset{18}{63},\overset{19}{64},\overset{20}{65},\overset{21}{65},\overset{22}{67},\overset{23}{67},\overset{24}{69},\overset{25}{73}$$

(a) The mean height is 61.52 inches with a standard deviation of 4.58 inches. Use this information to determine if the heights approximately follow the 68-95-99.7% Rule.

(b) Do these data appear to follow a normal distribution?

It is not possible to give an exact formula for the macromolecules in polythene. Why not?

Find the exact value of the expression.

$$\sin 15^{\circ}$$

Calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for the reaction

$$\mathrm{Ni}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Ni}^{2+}(a q)+2 \mathrm{Ag}(s)$$

Which of the following observations about subsidies is true?

a. Government subsidies must be paid for, typically by taxing individuals and corporations.
b. Subsidies are used to reduce exports from a sector, often for political reasons.
c. Whether subsidies generate national benefits that exceed their national costs is debatable.
c. Subsidies help foreign producers gain a competitive advantage over domestic producers.

Apply the same sequence of interchanges as required in part (a) to the list 1, 2, 3, 4, 5; that is, if it is necessary to interchange the second and third elements at a certain stage in the bubble sort of (a), then interchange the second and third elements at the same stage in the "sort" of 1, 2, 3, 4,5. The final sequence is 2, 4, 1, 5, 3, which describes the order in which the elements of c, a, e, b, d must be taken to list them in order.

Explain why subsidies are not a stable source of funds.

Why do excise taxes and subsidies affect supply differently?