Consider the function

$$f ( x ) = - \frac { 1 } { 2 } x + 5$$

Use composition to show that f(x) and the equation you wrote are inverses.

Use your calculator to find the value of the following, recording the entire display: a.

$$2 ^ { 9 }$$

b.

$$( - 5 ) ^ { 5 }$$

c.

$$- 3 ^ { 5 }$$

d.

$$7 ^ { 5 }$$

e.

$$8 ^ { 3 }$$

f.

$$( - 9 ) ^ { 4 }$$

g.

$$- 9 ^ { 4 }$$

h.

$$1.16 ^ { 11 }$$

i.

$$- 0.981 ^ { 14 }$$

j.

$$( - 1.14 ) ^ { 23 }$$

Evaluate the expression.

$$8 ^ { - 4 / 3 }$$

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

$$\theta$$

.

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 slope and y-intercept (if possible) of the equation of the line. Sketch the line. y - 3 = 0

a. What is the major product obtained from the reaction of propene and

$$Br_2$$

plus excess

$$Cl^-$$

? b. Indicate the relative amounts of the stereoisomers that are obtained.

Use any analytical method to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. You do not need to use the definition of the Taylor series coefficients.

Write <, =, or > to make a true sentence. -6 + 5 $\underline{?}$ -5 + 7

What is the purpose of the AC adapter on the end of the cord used for mobile phones?

Consider the function

$$f ( x ) = - \frac { 1 } { 2 } x + 5$$

Is the inverse of f(x) a function? Explain.

Prove the validity of the second-derivative test in the case that $f^{\prime\prime}(c)<0$.

In aqueous solution , hydrogen sulfide reduces $\mathrm { Br } _ { 2 }$ to $\mathrm { Br } ^ { - }$ In all cases, under appropriate conditions, the product is elemental sulfur. Write a balanced net ionic equation for each reaction.

Let $X$ and $Y$ each have support $(0,1)$ marginally, and suppose that the joint PDF $f_{X,Y}$ of $X$ and $Y$ is positive for $0 < x < y$ and 0 otherwise. (a) What is the support of the conditional PDF of $Y$ given $X = x$? (b) Show that $X$ and $Y$ can’t be independent.