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[(-)/(4) Points] SCALCET9 9.3.046. (a) Formulate a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency into circulation. (dx)/(dt)=◻ x(0)= (b) Solve the initial-value problem found in part (a). x(t)= (c) How long will it take for the new bills to account for 90% of the currency in circulation? (Round your answer to the nearest hundredth of a year.) years

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A shuttle company has a policy of overbooking because based on past research, only 90% of people who buy their tickets actually show up to ride the shuttle. Their shuttles seat 24 passengers. If they sell 25 tickets, what is the probability that there will not be enough seats for the passengers? The probability of not enough seats will be (round your answer to 3 decimal places). Interpret this answer. Which of the following statements is true? OA. The shuttle company wants this number to be big. That way they can decrease their profit and regularly inconvenience their customers. OB. The shuttle company wants this number to be big. That way they can increase their profit, but do not regularly inconvenience their customers. OC. The shuttle company wants this number to be small. That way they can increase their profit, but do not regularly inconvenience their customers. OD. The shuttle company wants this number to be small. That way they can decrease their profit and regularly inconvenience their customers.

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Using an interest rate of 3% per year (APY--no interest rate conversion needed), what is the present value of 35 annual payments of $3,500 if the first payment begins15 years from today?

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The art in scientific thinking—whether in physics, economics, or engineering—is a. the ability to make an abstract subject easy to understand. b. not something in which scientists have to be skilled. c. the design and implementation of laboratory experiments. d. deciding which assumptions to make.

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A 40 kg, 16.5 m long thin rod spins about a point 3.4 m from one end at 5.8 rpm. AGES NOTES DISCUSS UNITS STATUS

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True or false? A computer with only one single core processor can benefit from multi-threading.

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11. STOCKING A LAKE WITH FISH A lake is stocked with 500 fish, and the fish population increases according to the logistic curve $P = \frac{10,000}{1 + 19e^{-t/5}}, t \ge 0$ where $t$ is the time (in months). (a) Use a graphing utility to graph the logistic curve. (b) Find the fish population after 5 months. (c) After how many months will the fish population reach 2000?

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Question 2 (25 marks) a) Find the z-transform of the following sequences: i) $\{n+2\}u[n]$ ii) $\{n^3\}u[n]$ b) Find the inverse z-transform of the following: i) $Z^{-1}\left[\frac{z|2|\sin 3}{z^2 - (2|2|\cos 3)z + |2|^2}\right]\ ii) \(Z^{-1}\frac{z(z^2 + 4z + 1)}{(z - 1)^4}$ iii) $Z^{-1}\frac{z(z + 1^4)}{(z - 1^3)^3}$

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Consider a paramagnet with 6 dipoles, in the energy macrostate $U = 3$. (a) What is the multiplicity of this macrostate? (b) What is the probability that the paramagnet has three adjacent spins pointing upward, if it's in this macrostate? (Enumerating the possible microstates might be easiest.)

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Question 2: (10 marks) From a sample of size 31, SAS gives the following information: Variable Estimate Standard Error Intercept -1.0208 1.3443 $X_1$ -0.6465 0.0288 $X_2$ 0.5555 0.2204 $X_3$ 0.2448 0.1156 a. (5 marks) If only one explanatory variable is to be dropped from the model, which one should be dropped? Why? b. (5 marks) Given the estimated covariance of $\beta_1$ and $\beta_3$ is 0.5. Obtain a 99% Bonferroni confidence interval of ($l_1$, $l_2$) where $l_1 = (\beta_1 + \beta_3)/2$ and $l_2 = \beta_2$.

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jennifer m.