Question Portia produces and sells headbands. Her marginal cost for one headband is $6, and her average cost is $4. She gains producer surplus only when she sells headbands at a price above: O $10. $5. $6. $4. (Figure: Supply Curve) The graph shows the supply curve for jars of laundry detergent. Price Supply $20 $5 0 1 18 Quantity If 18 units are sold at a price of $20, what is the producer surplus on the last jar sold? O $15 O $270 $0 $135

**Please answer the following** * Free market economies stimulate greater economic growth, whereas state-directed economies stifle growth. Discuss *A democratic political system is an essential condition for sustained economic progress. Discuss * You are the CEO of a company that has to choose between making $100 million investment in Russia or Poland. Both investments promise the same long-run return, so your choice is driven by risk considerations, Assess the various risks of doing business in each of these nations. Which investment would you favor and why?

Write in a 1 whole sheet of yellow paper. Derive the truth table, simplified Boolean function (equation), and draw the logical diagram. 1. F(A,B,C)= [ (0,1,4,5,6,) 2. F(w,x,y,z) = {(1,3,4,7,10,12,13,15) 3. F(x,y,z) = T (1,3,4,5,7) 4. F(w,x,y,z) = T (0,1,4,5,6,8,9,11,12,14,15) 5. Implement using NAND-NAND, F= B'+CD'(A+B)+A'BC

Solve both please Two ideas pouring where are stacked so that none of the incident unpotarted light is transmitted. A third polarizing sheet is slipped between the first two sheets such at 10 percent of incident light is transmited through the stack. Find the angle of the third polarizing sheet 58 degrees 39 2 egrees 10 6 cegrees 11 5 degrees A block of mass 10 kg is attached to a spring of spring constant 1000 Nm. Block is pulled by 15 cm downwards (Point A) from its equilibrium position and released. In case 1) block now performs a SHM. In case 2) spring is cut when it was at its natural length and the block was moving upwards (during SHM). Find the difference of time taken by the block reaches to point A in case 1 and case 2. (Take g = 10 m/s/s)

Problems 3.2(e,f), 3.4(e,f), 3.5(b,c), 3.6(c,d), 3.10(a,b), 3.11, 3.12(b), 3.15(a,c) 140 Chapter 3 Gate-Level Minimization Problems 141 3.4 Simplify the following Boolean functions, using K-maps: (a) F(x,y, z) (2,3.6,7) (c)' F(A,B,C,D)=Σ(3,7, ll, 13, 14, 15) (e) F (w, x, y, z) = Σ(11, 12, 13, 14, 15) (g) F(w, x, y, z)=E(0.1.4,5,10,1 1,14,15) Simplify the following Boolean functions, using four-variable K-maps: (a)" F (w, x, y, z) = Σ(1, 4, 5, 6, 12, 14, 15) (b)" F (A, B, C, D) = Σ(2, 3, 6, 7, 12, 13, 14) (c) F (w, x, y, z) = Σ(1, 3, 4, 5, 6, 7, 9, 1 1, 13, 15) (d)' F (A, B, C, D) = Σ (0, 2, 4, 5, 6, 7, 8, 10, 13, i5) Simplify the following Boolean expressions, using four-variable K-maps: (a) A'B'C'D AC'D' B'CDA'BCD BCD (by (d)' (f) (h) F (A, B, C, D) = Σ(4. 6, 7, 15) F(w.rry, z)_E(2.3. I2. 13, 14, 15) F (w, x, y, z)-S(8, 10, 12, 13.4) F(w, x, y, z)-E(2.3.6.7.8.9.12,I3) UDP 02467 3.5 FIGURE 3.40 Schematic for Circuit with UDP_02467 3.6 Although Verilog HDL uses this kind of description for UDPs only, other HDLs and computer-aided design (CAD) systems use other procedures to specify digital circuits in tabular form. The tables can be processed by CAD software to derive an efficient gate structurc of the design. None of Verilog's predefined primitives describes sequential logic. The model of a sequential UDP requires that its output be declared as a reg data type, and that a column be added to the truth table to describe the next state. So the columns are organized as inputs: state: next state. (c) A'B'CD AB'D +A'BC ABCD AB'C (d) A'B'C'D' BC'D A'C'D A'BCD +ACD' Simplify the following Boolean expressions, using four-variable K-maps: 3.7 In this section, we introduced the HDLs and presented simple examples to illustrate alternatives for modeling combinational logic. A more detailed presentation of model- ing with HDLs can be found in the next chapter. The reader familiar with combinational circuits can go directly to Section 4.12 to continue with this subject. (c) AB C B'C'DBCD ACD'+ A'B'C+ A BC D Find the minterms of the following Boolean expressions by first plotting each function in a K-map: 3.8 (a) xy yz + xy'z (b) C'D+ABC ABD' +A'B'D (d) A'B A'CD B'CD BC'D VHDL-Truth Tables 3.9 Find all the prime implicants for the following Boolean functions, and determine which are essential: (a)" F(w, x, y, z) = Σ(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) (b), F (A, B, C, D) = Σ(0, 2, 3, 5, 7, 8, 10, 11, 14, 15) (c) F (A, B, C, D) = Σ(2, 3, 4, 5, 6, 7, 9, 11, 12, 13) (d) F(w,x, y, z)=E(1.3, 6, 7, 8, 9, 12, 13, 14, 15) (e) F (A, B, C, D) = Σ(0, 1, 2, 5, 7, 8, 9, 10, 13, 15) (f) F(w, x, y, z)=E(0.1, 2, 5, 7, 8, 10, 15) Simplify the following Boolean functions by first finding the essential prime implicants: (a) F (w, x, y, z) 2(0, 2, 5, 7, 8, 10, 12, 13, 14, 15) (b) F(A, B,C, D) 2(0,2,3,5,7,8,10, 11, 14, 15) (e)* F(A, B,C,D)-(1,3,4,5, 10, 11, 12, 13, 14, 15) (d) F (w, x, y, z) = Σ(0, 1, 4, 5, 6, 7, 9, 11, 14, 15) (e) F (A, B, C, D)-Σ(0.1, 3, 7, 8, 9, 10, 13, 15) (f) F (w, x, y, z) = Σ(0, 1, 2, 4, 5, 6, 7, 10, 15) VHDL does not support truth tables directly. Instead, a truth table has to be converted into a set of Boolean equations, which can be described by signal assignment statements. PROBLEMS (Answers to problems marked with appear at the end of the text.) 3.10 1 Simplify the following Boolean functions, using three-variable K-maps: (a) F(x, y, z) = Σ (0, 2, 4, 5) (c) Fr, y, )-20,1,2,3, 5) (b) F(x,y, z)-2(0, 2, 4, 5, 6) (d) , y, z)=E(1,2,3,7) 2 Simplify the following Boolean functions, using three-variable K-maps: (b)" F(x, y, z) = Σ(1, 2, 3, 6, 7) (d) F(x, y, z) = Σ( 1, 2, 3, 5, 6, 7) (f) F(x, y, z)=E(3, 4, 5, 6, 7) (a)" F(x, y, z) = Σ (0, 1, 5, 7) (c) Fx,y, z) (2,3,4,5) (e) P(x, y, z) = Σ(0,2,4,6) Simplify the following Boolean expressions, using three-variable K-maps: (a)'. F (x.yz) = xy + x'y'z, + χ,yz (c)" F (x, y, z) = x,y + yz' + y,z' 3.11 Using K-maps for Fand F,convert the following Boolean function from a sum-of-prod- 3.3 ucts form to a simplified product-of-sums form. (d) F(x, y, z) = x,yz + xy,z' + xy'z F(w ryz)0,,2, 5,8, 10, 13)

Please help solving problem 1,2 and 3. Thank you very much. For questions 1 - 3, consider the following test results obtained for a surface water sample. lon Concentration (ppm) Ca2+ 36.0 Mg2+ 10.8 Na 12.4 K 5.9 нсоз" 82.1 SO42 32.0 CI 16.9 NO3 7.4 1. Check the accuracy of the analytical measurements. Do you suspect that a constituent of significance has been neglected? If so, is it a cation or an anion? 2. Determine the mole fraction of calcium, magnesium, and sulfate for the water sample given above. 3. Determine this water's hardness and alkalinity in mg/L as CaCO3.

Die-rolling experiment: 1) Acquire any "fair-enough" die. 2) Roll it at least 100 times (each person for themselves). 3) Note what the outcome is overy time. 4) For each group of 5 (go consecutively, i.e. group first five rolls, then the next five rolls, etc.), take the average of the 5 rolls. For example, if the first five rolls are \( 3,6,1 \), 5 , and 3 , Die-rolling experiment: 1) Acquire any "fair-enough" die. 2) Roll it at least 100 times (each person for themselves). 3) Note what the outcome is overy time. 4) For each group of 5 (go consecutively, i.e. group first five rolls, then the next five rolls, etc.), take the average of the 5 rolls. For example, if the first five rolls are \( 3,6,1 \), 5 , and 3 , the average will be \( 18 / 5=3.6 \). 5) You will end up with at least 20 averages. Plot these averages on a \( 2 \mathrm{D} \) column graph. Alternatively, you can do a histogram of your results, which will be a fancier way of doing a 2D column graph. With a histogram though, you can control the bin size and instead of each individual average (e.g. 3.2, 3.4. 3.6, etc.). you can group them together with a bin size of 1 . Bonus credits will be assigned to those showing their results with a histogram of bin size 1 in addition to their regular \( 2 \mathrm{D} \) column graphs. 6) All the probabilities of \( 1,2,3,4,5 \) and 6 are \( 1 / 6 \) with a fair die. Therefore, the probabilities are said to be "uniformly distributed". Then, why is your \( 2 D \) column graph / histogram not looking uniform at all? Speculate / comment on the rationale for this.