LINEAR ALGEBRA
Some parking meters in downtown Geneva, Switzerland, accept 2 Franc and 5 Franc coins. a. A parking officer collects 51 coins worth 144 Francs. How many coins are there of each kind? b. Find the matrix A that transforms the vector $$ \begin{bmatrix} \textrm{number of 2 Franc coins}\\ \textrm{number of 5 Franc coins} \end{bmatrix} $$ into the vector $$ \begin{bmatrix} \textrm{total value of coins}\\ \textrm{total number of coins} \end{bmatrix}. $$ c. Is the matrix $A$ in part $(b)$ invertible? If so, find the inverse (use Exercise 13). Use the result to check your answer in part $(a)$.
ECONOMICS
Assume that the exchange rate is 1 Swiss franc = $0.80. How many Swiss francs (rounded to the nearest hundredth) will it take to buy one dollar?
PREALGEBRA
Use a ratio box to solve this problem. If Milton can exchange $200 for 300 Swiss francs, how many dollars would a 240-franc Swiss watch cost?
BUSINESS MATH
What is the exchange rate between dollars and Swiss francs if one dollar is convertible into 1/20 ounce of gold and one Swiss franc is convertible into 1/40 ounce of gold?
ACCOUNTING
Boat Belting sells goods for 900,000 Mexican pesos. The foreign-exchange rate for a peso is $0.094 on the date of sale. Boat Belting then collects cash on April 24 when the exchange rate for a peso is$0.099. Record Boat’s cash collection. Boat Belting buys inventory for 21,000 Swiss francs. A Swiss franc costs $1.12 on the purchase date. Record Boat Belting’s payment of cash on October 25, when the exchange rate for a Swiss Franc is$1.14. In these two scenarios, which currencies strengthened? Which currencies weakened?
ADVANCED MATH
A student returning from Europe changes her euros and Swiss francs into U.S. money. If she received $46.58 and received$1.39 for each euro and 91c for each Swiss franc, how much of each type of currency did she exchange?
ADVANCED MATH
Money manager Boris Milkem deals with French currency (the franc) and American currency (the dollar). At 12 midnight, he can buy francs by paying 25 dollars per franc and dollars by paying 3 francs per dollar. Let x1 = number of dollars bought (by paying francs) and x2 = number of francs bought (by paying dollars). Assume that both types of transactions take place simultaneously, and the only constraint is that at 12:01 a.m. Boris must have a nonnegative number of francs and dollars. a. Formulate an LP that enables Boris to maximize the number of dollars he has after all transactions are completed. b. Graphically solve the LP and comment on the answer.
ALGEBRA
On a shopping spree in Europe, Bob spend 100 pounds in England, 150 euros in France, and 200 francs in Switzerland. At the time, a pound is worth $\$1.80$, a euro is worth$\$1.25$ and a Swiss franc is worth $\$0.75$. a. In dollars, how much does Bob spend? b. How does this exercise connect to Exercise 16-18?
ECONOMICS
Assume that the exchange rate is 1 Swiss franc = $0.80. Complete the following table.$ $$ \begin{matrix} \text{ } & \text{Price in dollars} & \text{Price in francs}\\ \text{A Ford Focus car} & \text{17000.00}\\ \text{A McDonalds Big Mac} & \text{4.50}\\ \text{A souvenir coffee mug} & \text{11.00}\\ \text{A picture book of New York} & \text{19.00}\\ \end{matrix} $$ $
PREALGEBRA
Until recently, you needed different types of money (francs, marks, punts, etc.) to travel through Europe. Now all you need to get by in most European countries is the new European currency, the euro. One U.S. dollar buys about 0.81 euros. One French franc was worth about 0.15 euros, and an Irish punt was worth about 1.27 euros. About how many euros were 20 French francs worth? (A) 0.15 euros (B) 3.00 euros (C) 20.00 euros (D) 150.00 euros
PREALGEBRA
Until recently, you needed different types of money (francs, marks, punts, etc.) to travel through Europe. Now all you need to get by in most European countries is the new European currency, the euro. One U.S. dollar buys about 0.81 euros. One French franc was worth about 0.15 euros, and an Irish punt was worth about 1.27 euros. About how many U.S. dollars would you get if you exchanged 15 euros? (A) $12.15 (B)$18.52 (C) $22.50 (D)$27.28
PREALGEBRA
Until recently, you needed different types of money (francs, marks, punts, etc.) to travel through Europe. Now all you need to get by in most European countries is the new European currency, the euro. One U.S. dollar buys about 0.81 euros. One French franc was worth about 0.15 euros, and an Irish punt was worth about 1.27 euros. Which expression shows how many French francs you could get for one Irish punt? (F) 0.15 x 1.27 (G) 0.15/1.27 (H) 0.15 + 1.27 (J) 1.27/0.15
PREALGEBRA
Until recently, you needed different types of money (francs, marks, punts, etc.) to travel through Europe. Now all you need to get by in most European countries is the new European currency, the euro. One U.S. dollar buys about 0.81 euros. One French franc was worth about 0.15 euros, and an Irish punt was worth about 1.27 euros. Hsio came home from a trip with currency worth 20 U.S. dollars. She had 10 euros and the rest in U.S. currency. About how many dollars did she have? (F) $12.35 (G)$11.90 (H) $8.10 (J)$7.65
ENGINEERING
Sketch the root locus for K>0 and K<0 for each of the following: (a) G(s)H(s)=1/s-1, (b) G(s)H(s)=1/(s-1)(s+3), (c) G(s)H(s)=1/s²+s+1, (d) G(s)H(s)=s+1/s² , (e) G(s)H(s)=(s+1)²/s³, (f) G(s)H(s)=s²+2s+2/s²(s-1), (g) G(s)H(s)=(s+1)(s-1)/s(s³+2s+2), (b) G(s)H(s)=(1-s)/(s+2)(s+3).
QUESTION
Prove that if φ: S→S' is an isomorphism of ⟨S, *⟩ with ⟨S', *'⟩ and ψ: S'→S" is an isomorphism of ⟨S', *'⟩ with ⟨S'', *''⟩, then the composite function ψ* ∘ φ is an isomorphism of ⟨S, *⟩ with ⟨S'', *''⟩.
DISCRETE MATH
Determine whether each of these compound propositions is satisfiable. a) (p ∨ q ∨ ¬r) ∧ (p ∨ ¬q ∨ ¬s) ∧ (p ∨ ¬r ∨ ¬s) ∧ (¬p ∨ ¬q ∨ ¬s) ∧ (p ∨ q ∨ ¬s) b) (¬p ∨ ¬q ∨ r) ∧ (¬p ∨ q ∨ ¬s) ∧ (p ∨ ¬q ∨ ¬s) ∧ (¬p ∨ ¬r ∨ ¬s) ∧ (p ∨ q ∨ ¬r) ∧ (p ∨ ¬r ∨ ¬s) c) (p ∨ q ∨ r) ∧ (p ∨ ¬q ∨ ¬s) ∧ (q ∨ ¬r ∨ s) ∧ (¬p ∨ r ∨ s) ∧ (¬p ∨ q ∨ ¬s) ∧ (p ∨ ¬q ∨ ¬r) ∧ (¬p ∨ ¬q ∨ s) ∧ (¬p ∨ ¬r ∨ ¬s)
ENGINEERING
Find f(t) for each of the following functions. a) F(s) = 320/(s²(s + 8)). b) F(s) = (80(s + 3))/(s(s + 2)²). c) F(s) = (60(s + 5))/((s + 1)² (s² + 6s + 25)). d) F(s) = (25(s + 4)²)/(s²(s + 5)²).
ENGINEERING
Given the following functions F(s), find f(t). (a) $\mathbf{F}(s)=\frac{s^{2}+7 s+12}{(s+2)(s+4)(s+6)}$. (b) $\mathbf{F}(s)=\frac{(s+3)(s+6)}{s\left(s^{2}+10 s+24\right)}$. (c) $\mathbf{F}(s)=\frac{s^{2}+5 s+12}{(s+2)(s+4)(s+6)}$. (d) $\mathbf{F}(s)=\frac{(s+3)(s+6)}{s\left(s^{2}+8 s+12\right)}$
ENGINEERING
Given the following functions F(s), find f(t). (a) $\mathbf{F}(s)=\frac{s+1}{s(s+2)(s+3)}$. (b) $\mathbf{F}(s)=\frac{s^{2}+s+1}{s(s+1)(s+2)}$
ENGINEERING
Find the inverse Laplace transform of the following functions: a) $\mathbf{F}(s)=\frac{(s+3) e^{-s}}{s(s+2)}$ b) $\mathbf{F}(s)=\frac{e^{-10 s}}{(s+2)(s+3)}$ c) $\mathbf{F}(s)=\frac{\left(s^{2}+2 s+1\right) e^{-2 s}}{s(s+1)(s+2)}$ d) $\mathbf{F}(s)=\frac{(s+1) e^{-4 s}}{s^{2}(s+2)}$
ENGINEERING
Find f(t) if $\textbf{F}$(s) is given by the following functions: a) $\textbf{F}(s)=\dfrac{2(s+1) e^{-s}}{(s+2)(s+4)}$ b) $\textbf{F}(s)=\dfrac{10(s+2) e^{-2 s}}{(s+1)(s+4)}$ c) $\textbf{F}(s)=\dfrac{s e^{-s}}{(s+4)(s+8)}$
ENGINEERING
Obtain the inverse Laplace transforms of the following functions: (a) X(s) = 3/s²(s + 2)(s + 3) (b) Y(s) = 2/s(s + 1)² (C) Z(s) = 5/s(s + 1)(s² + 6s + 10)
COMPUTER SCIENCE
Explain the difference between s = 0 if x > 0 : s = s + 1 if y > 0 : s = s + 1 and s = 0 if x > 0 : s = s + 1 elif y > 0 : s = s + 1
BIOLOGY
In corn, the allele s causes sugary endosperm, whereas S causes starchy. What endosperm genotypes result from each of the following crosses? a. s/s female x S/S male b. S/S female x s/s male c. S/s female x S/s male
DISCRETE MATH
Define a set S recursively as follows: I. Base: $$ 1 \in S , 3 \in S , 5 \in S , 7 \in S , 9 \in S $$ , II. RECURSION: If $$ s \in S $$ and $$ t \in S $$ then, a. $$ S t \in S $$ , b. $$ 2 s \in S $$ , c. $$ 4 s \in S $$ , d. $$ 6 s \in S $$ , e. $$ 8 s \in S $$ . III. RESTRICTION: Nothing is in S other than objects defined in I and II above. Use structural induction to prove that every string in S represents an odd integer.