What are the most important differences between each of the measures of center?

Graph each function. $f(x)=-\sqrt{x}-2$

Solve the equation using a bar model. $\frac{3}{4} x=8$

Compare the fractions in each pair. Think about how close the fractions are to $0, \frac{1}{2}, \text { or } 1$. a. $\frac{5}{8} \text { and } \frac{7}{12}$ b. $\frac{14}{15} \text { and } \frac{7}{8}$ c. $\frac{1}{9} \text { and } \frac{1}{23}$

Use the following key to label each of the resources as land, labor, capital, or entrepreneurship. If a resource is land, identify it as either renewable or nonrenewable. If a resource is a capital good, identify it as either physical or human. (Hint: Physical capital is a tangible, human-made resource- such as tools or machinery-used to produce other goods and services. Ld-r = land (renewable), Ld-n = land (nonrenewable), Lbr = labor, C = capital, E = entrepreneurship. lawyer ____________

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, give the solution with y arbitrary. For systems in three variables with infinitely many solutions, give the solution with z arbitrary.

$$\begin{aligned} &\frac{3}{8} x-\frac{1}{2} y=\frac{7}{8}\\ &-6 x+8 y=-14 \end{aligned}$$

Rewrite $\frac{2(x+5)-4}{2}-x$ using the fewest terms possible. Justify each step with a property or operation.

A spacecraft is approaching a space station that is orbiting Earth. When the craft is 1000 km from the space station, reverse thrusters must be applied to begin braking. The time, t, in hours, required to reach a distance, d, in kilometres, from the space station while the thrusters are being fired can be modelled by $t=\log _{0.5}\left(\frac{d}{1000}\right)$. The docking sequence can be initialized once the craft is within 10 km of the station’s docking bay. a) How long after the reverse thrusters are first fired should docking procedures begin? b) What are the domain and range of this function? What do these features represent?

Determine the product of all values of k for which the polynomial equation $2 x^{3}-9 x^{2}+12 x-k=0$ has a double root.

One cycle of a sine function begins at $x=-\frac{\pi}{4}$ and ends at $x=\frac{\pi}{3}$. a) Determine the period of the function. b) Determine the phase shift of the function.

From the data shown, determine the economic service lives of the defender and challenger. (Note: Values in the table are AW values, not individual year-end values.)

$$\begin{array}{ccc} \text { Years Retained } & \text { AW of Defender, } \$ & \text { AW of Challenger, } \$ \\ \hline 1 & -145,000 & -136,000 \\ 2 & -96,429 & -126,000 \\ 3 & -63,317 & -92,000 \\ 4 & -39,321 & -53,000 \\ 5 & -49,570 & -38,000 \\ \hline \end{array}$$

Describe the similarities and differences between the parabola $y=x^{2}$ and power functions with even degree greater than two. Use graphs to support your answer.

Which of the following sequences are the first four terms of an arithmetic sequence? For those that are, write down the value of the common difference. (a) 7 10 13 16 ... (b) 3 5 9 15 ... (c) 1 0.1 0.01 0.001 .. . (d) 4 2 0 -2 ... (e) 2 -3 4 -5 ... (f) p - 2q p - q p p + q ... (g) $\frac{1}{2} a \quad \frac{1}{3} a \quad \frac{1}{4} a \quad \frac{1}{5} a \quad \ldots$ (h) x 2x 3x 4x ...

The Gap has some of its jeans stone-washed under a contract with Vietnam Garment Corporation (VGC). If VGC’s estimated operating cost per machine is $26,000 for year 1 and it increases by$1500 per year through year 5, the equivalent uniform annual cost per machine over years 1 to 5, at an interest rate of 8% per year, is closest to: (a) $30,850 (b)$28,770 (c) $26,930 (d)$23,670