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MC 10 6 5.50 4.50 2 100 300 Quantity What are the total fixed costs for this firm? 450 350 400 500 ATC AVC

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According to symbolic-interaction analysis, tracking and other forms of labeling in education ________. are linked to the budget concerns of schools can create a self-fulfilling prophecy always improve student performance are generally helpful to disadvantaged categories of students

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the asset of federal reserve banks associated with open market operations is

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4. A hot air balloon is rising straight up from a level field at a constant rate of 50 m/min. An observer is standing 150 m from the point on the ground where the balloon was launched. Let θ be the angle between the ground and the point at which the observer is standing (angle of elevation of the balloon). What is the rate of change of θ (in radians/min) when the height of the balloon is 250 m?

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Q3. Programming. A Green LED is connected at P2.0, a red LED at P2.1, a door sensor at P1.0 and a buzzer at P1.2. (2.75 Marks) Make an 8051 C proAgram where the door sensor can detect if the door is open and will sound the buzzer, turn on the green LED, and turn off the red LED. On the other hand, when the door is closed, the buzzer will be off, the green LED will be on, and the red LED will be off. Draw the circuit, write the Algorithm, draw the flowchart and write the C Language program. Q3.1 CIRCUIT: (0.25 Marks) CLO # 2.2

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9. Consider the vectors $v_1 = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$, $v_2 = \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix}$, and $v_3 = \begin{bmatrix} 1 \\ -2 \\ 1 \end{bmatrix}$, which are orthogonal vectors. a. Express $x = \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}$ as a linear combination of $v_1$, $v_2$, and $v_3$. b. Use $v_1$, $v_2$, and $v_3$ to produce an orthonormal basis for $\mathbb{R}^3$.

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If \sin x = \frac{5}{6}, where x in quadrant II, then find the exact value of each of the following. \sin(2x) = \cos(2x) = \tan(2x) =

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Suppose a firm only uses labor input (L) to produce output (Q). Consider the following Cobb-Douglas production function: $Q = L^{0.7}$ a. Find the marginal product of labor (MPL) which is given by the derivative of the production function with respect to labor (i.e., $MPL = \frac{dQ}{dL}$) b. In economics an important concept is that of elasticity. In our example, the elasticity of output with respect to labor input measures the percent change in output caused by percent chane in labor input. The formula of elasticity is given by: elasticity $= \frac{dQ}{dL} \times \frac{L}{Q}$ Using your answer from part a) and the above formula, show that the elasticity of output with respect to labor in this case equals 0.7.

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For the diagram and threading table below, fill in the blanks for the following questions: Thread length, not including acceleration and deceleration but including face chamfer distance: XXX [A] Total number of passes (whole number, no decimals): XXX [B] Major diameter: XXX [C] Diameter at FINAL threading pass: XXX [D] R0.2 0.8-16-UNF Chamfer 0.95 0.55 0.65 0.80 0.9 1.25 1.55 1.65 1.95 TPI (1/P) 8 10 12 14 16 18 24 Pitch P, in. 0.1250 0.1000 0.0833 0.0714 0.0625 0.0556 0.0417 Thread Height (0.6403P), in. 0.0800 0.0640 0.0534 0.0457 0.0400 0.0356 0.0267 1st 0.0472 0.0394 0.0354 0.0315 0.0315 0.0315 0.0315 Number of 2nd 0.0276 0.0276 0.0236 0.0236 0.0236 0.0236 0.0157 passes and 3rd 0.0236 0.0236 0.0236 0.0197 0.0197 0.0118 0.0062 reduction 4th 0.0200 0.0157 0.0157 0.0118 0.0052 0.0043 in diameter 5th 0.0200 0.0157 0.0083 0.0048 for each 6th 0.0158 0.0060 pass 7th 0.0058

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Apple Production: A Synthesis • Suppose there is a small apple farm with only one apple tree. Labor TP AP MP 1 5 • It hires labor to harvest apples. • Given TP, calculate the AP and MP in the table. 2 12 3 18 4 20 • Is the production function 5 20 constant return to scale, increasing return to scale, or decreasing return to scale? 6 18 7 14 • How many labors should be hired to maximize the outputs? $\Delta$ TP>0 $\sim$ MP >0; $\Delta$ TP<0 $\sim$ MP<0. $\Delta$AP<0 $\sim$ MP<AP; $\Delta$AP>0 $\sim$ MP>AP. CRS: MP=C=AP; $\Delta$TP=C

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