Question Solved1 Answer The table below provides Big Lake Bob's production possibilities schedule, which describes various combinations of fishing tures and duck decoys he can carve efficiently in a week, Big Lake Bob's Production Possibilities Schedule Fishing Lures 12a 80 60 48 20 Duck Decoys B 6 12 18 24 30 a. Graph Big Lake Bob's production possibilities frontier using the information in the table above. Instructions: Use the tool provided "PPF* to plot the production possibilities frontier point point (6 points total Big Lake Bob's Production Possibilities Frontier 36 Tools 30 PPF 24 Duck Decoys 18 12 < Prev 11 of 13 Next > Check my work 30 a. Graph Big Lake Bob's production possibilities frontier using the information in the table above Instructions: Use the tool provided "PPF" to plot the production possibilities frontier point by point (6 points total), Big Lake Bob's Production Possibilities Frontier 36 Tools 2 30 PPF 24 Duck Decoys 18 12 6 0 20 40 60 80 100 120 Fishing Lures b. Which of the following combinations of fishing lures and duck decoys is unobtainable to Big Lake Bob in one week's worth of carving? 20 fishing lures and 24 duck decoys 50 fishing lures and 10 duck decoys 40 fishing lures and 20 duck decoys 80 fishing lures and 5 duck decoys c. Which of the following combinations of fishing lures and duck decoys is an efficient combirkation? 20 fishing tures and 24 duck decoys 50 fishing lures and O duck decoys 16 fishing lures and 30 duck decoys 10 fishing lures and 40 duck decoys

Assignment 1: Essay paper Step 1 Select one press release on a topic related to macroeconomics (covered in the course materials). Criteria: • The original press release should count at least 800 words and date from the period. • after January 2020. • The article should originate from a high-quality, English-written, newspaper or • magazine. Examples are: The Economist, The Financial Times, The New York Times, • The Wall Street Journal, The Guardian, Bloomberg; National Post; BBC Finance; other. • The topic (including title, author’s name, newspaper/magazine source, date, student • name). • Each student should select a unique article. If two or more students post the same • article, then a first come-first-serve rule will apply: the article will be assigned to the • first student. • Choice and length of the press release will count towards the grade. Step 2 Make a summary of the press release. Criteria: • Number of words: between 300 and 350 words. • Word count must be mentioned. • The summary should be well-structured and fluently written, grammar, vocabulary and punctuation will count. • Graphical analyses are not allowed. Step 3 Write an essay on how the press release is linked to the theory. Criteria: • Number of words: between 1 100 and 1 200 words (about 3-4 pages paper). Word count must be mentioned. • The essay should be well-structured and fluently written, grammar, vocabulary and punctuation will count. • You should cite the article(s) in the theory note (not in the summary!). • The reference(s) need(s) to be included in the bibliography list at the end of the essay. • You do not have to cover all the course subjects that are linked to the press release. • You should select only a few subjects and provide a more in-depth analysis. • Graphical analyses are not allowed. • Both, the essay and summary will be graded. • Make sure to paraphrase the ideas from the original text (no quotes). • The written assignment is an individual work and should thus be done individually.

A truck with 18-in.-diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min: How many revolutions per minute do the wheels make? rad/min rpm A truck with 18-in.-diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min: How many revolutions per minute do the wheels make? rad/min rpm

Exercise 8 (Multiple Choice). Let X be inductively defined as the smallest set of finite number lists (taken from N∗) satisfying the following closure properties: Given any natural number n from N, the set X contains the one-element list [n]. Given any list [x1,x2,x3,...,xn] already in X, the set X also contains the list [x1,x2,x3,...,xn,y] where the additional element y is the product x1 × x2 × x3 × ··· × xn. Which of the following lists is NOT in X? [1,1,1,1,1] [2,4,16,256] (c) [3,3,9,81] (d) [4,4,16,256] Exercise 9 (Multiple Choice). Consider the grammar G (note that ϵ stands for the empty string): ::= aS | T ::= bT | U ::= cU | ϵ Which of the following strings is generated by the grammar G? aba bab (c) ca (d) ccc Which of the following is a derivation of bbc in the grammar G? S → T → U → bU → bbU → bbU → bbc S → bT → bbT → bbU → bbcU → bbc S → T → bT → bbT → bbU → bbcU → bbc S → T → bT → bTbT → bbT → bbU → bbcU → bbc Exercise 10 (Multiple Choice). Which of the following grammars describes the same language as 0m1n where m ≤ n? S ::= 0S1 | ϵ S ::= 0S1 | S1 | ϵ S ::= 0S1 | 0S | ϵ S ::= SS | 0 | 1 | ϵ Exercise 11. Consider the following grammar for abstract syntax of arithmetic expressions: E ::= E+E | E−E | E×E | E/E | 1 | 2 | 3 | 4 with the usual associativity and precedence for the arithmetic operators (all operators are left-associative, × and / have a higher precedence than + and −). (1) Draw an abstract syntax tree for each of the following strings: 1 − 2 + 3 1 × 2 + 3 1 × 2 − 3/4 (2) (Multiple Choice & Short Answer) Which of the following pairs of strings with different parentheses represent the same abstract syntax tree according to the above precedence and associativity? Draw that abstract syntax tree. 2 × 4 − 3 versus 2 × (4 − 3) 1 + 2 + 3 + 4 versus 1 + (2 + (3 + 4)) 2 + 3 × 4/2 versus 2 + ((3 × 4)/2)

An incompressible (p = constant) liquid flows steadily through a conduit of circular cross-section and increasing diameter. At location 1, the diameter is 2.5 cm and the velocity is 2 m-s-l; at location 2, the diameter is 5 cm. (a) What is the velocity at location 2? (b) What is the kinetic-energy change (J-kg-l) of the fluid between locations 1 and 2?

Multiple choice 1) Consider the total function f(x) = 3x + 2 Which of the following inductive definitions are equivalent to the above f? (a) f(x + 1) = f(x) + 2 (b) f(x + 1) = f(x) + 3 (c) f(0) = 3 f(x + 1) = f(x) + 2 (d) f(0) = 2 f(x + 1) = f(x) + 3 2) Recall that a natural number x is even whenever it is double another natural number (that is to say, there is some other natural number n such that x = 2n). A natural number x is odd whenever it is one more than an even number (that is to say, there is a natural number n such that x = 2n + 1). Consider the partial function h(x) = x 2 if x is even where h(x) is undefined for odd numbers x. Which of the following inductive definitions are equivalent to the above h? (a) h(x + 2) = h(x) + 1 (b) h(0) = 0 h(x + 2) = h(x) + 1 (c) h(1) = 1 h(x + 2) = h(x) + 1 (d) h(0) = 0 h(1) = 1 h(x + 2) = h(x) + 1 3) Let X be inductively defined as the smallest set of finite number lists (taken from N ∗ ) satisfying the following closure properties: • Given any natural number n from N, the set X contains the one-element list [n]. • Given any list [x1, x2, x3, . . . , xn] already in X, the set X also contains the list [x1, x2, x3, . . . , xn, y] where the additional element y is the product x1 × x2 × x3 × · · · × xn. Which of the following lists is NOT in X? (a) [1, 1, 1, 1, 1] (b) [2, 4, 16, 256] (c) [3, 3, 9, 81] (d) [4, 4, 16, 256] 4. Consider the grammar G (note that ϵ stands for the empty string): S ::= aS | T T ::= bT | U U ::= cU | ϵ (1) Which of the following strings is generated by the grammar G? (a) aba (b) bab (c) ca (d) ccc (2) Which of the following is a derivation of bbc in the grammar G? (a) S → T → U → bU → bbU → bbU → bbc (b) S → bT → bbT → bbU → bbcU → bbc (c) S → T → bT → bbT → bbU → bbcU → bbc (d) S → T → bT → bTbT → bbT → bbU → bbcU → bbc 5) . Which of the following grammars describes the same language as 0 m1 n where m ≤ n? (a) S ::= 0S1 | ϵ (b) S ::= 0S1 | S1 | ϵ (c) S ::= 0S1 | 0S | ϵ (d) S ::= SS | 0 | 1 | ϵ 6) Consider the following grammar for abstract syntax of arithmetic expressions: E ::= E+E | E−E | E×E | E/E | 1 | 2 | 3 | 4 with the usual associativity and precedence for the arithmetic operators (all operators are left-associative, × and / have a higher precedence than + and −). (1) Draw an abstract syntax tree for each of the following strings: (a) 1 − 2 + 3 (b) 1 × 2 + 3 (c) 1 × 2 − 3/4(Multiple Choice & Short Answer) Which of the following pairs of strings with different parentheses represent the same abstract syntax tree according to the above precedence and associativity? Draw that abstract syntax tree. (a) 2 × 4 − 3 versus 2 × (4 − 3) (b) 1 + 2 + 3 + 4 versus 1 + (2 + (3 + 4)) (c) 2 + 3 × 4/2 versus 2 + ((3 × 4)/2)

5. Test whether the following expression is a valid pdf. If it is a valid pdf, obtain the CDF and its mean. \[ g(x)=\frac{1}{6} \exp \left(-\frac{x}{2}\right)+\frac{2 x}{12} \exp \left(-\frac{x^{2}}{8}\right), x \geq 0 \]