An inverting amplifier is built with $R_{2}=47 \mathrm{k} \Omega$ and $R_{1}=2.4 \mathrm{k} \Omega$ using an op amp with an open-loop gain of 100 dB, an input resistance of 300 $\mathrm{k} \Omega$, and an output resistance of 200 $\Omega$. What are the closedloop gain, input resistance, and output resistance for this amplifier? (b) Repeat if the open-loop gain is changed to 94 dB.

Ms. Yoto is putting together bags of fruit that contain 1 pear for every 2 apples. For each ratio given, create a picture module. Then, calculate the answer from your model, and explain your reasoning. a. How many apples are in the bag if there are a total of 9 pieces of fruti? b. How many apples are in the bag if there are a total of 15 pieces of fruit? c. How many pieces of fruit are there if there are 8 apples in the bag?

Graph each quadratic function. Give range. $f(x)=x^{2}+6 x+5$

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.)

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

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 ...