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Joe runs a small boat factory. He can make ten boats per year. It costs Joe $200,000 for the raw materials (fiberglass, wood, paint, and so on) to build the ten boats. Joe has invested $500,000 in the factory and equipment needed to produce the boats which are now assets that he owns: $200,000 from his own savings where he was earning 5% interest and $300,000 borrowed at 10% interest. Joe can work at a competing boat factory for $80,000 per year. Hint: The funds invested in the factory and equipment ($500,000) are not treated as a cost here because they represent assets of the firm, there is however a cost associated with obtaining these funds.

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A fast car can go from 0 to 90 mph in 7.0 s, and a slow car can go from 0 to 45 mph in 7.0 s. If $P_{fast}$ is the average power of the fast car's engine, and $P_{slow}$ is the average power of the slow car's engine, then which describes the relationship between $P_{fast}$ and $P_{slow}$?

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1. (2 points) Find the solutions to each the system of linear equations: 2x+y+z=-1 x+2y+z=0 3x-2z=5 2. (2 points) Consider the system of linear equations, where a, b, c are some constants: x+2y-z=a 2x+y+3z=b x-4y+9z=c For what values of a, b, c is this system consistent? (Hint: Use row-operations, bring to REF and show that the system is consistent only if c=2b-3a). 3. (2 points) Use row operations to bring the matrix to REF and find the rank: $\begin{bmatrix} 2 & 3 & 3 \ 3 & -4 & 1 \ -5 & 7 & 2 \end{bmatrix}$ 4. (2 points) Write $\vec{v}$ as a linear combination of $\vec{x}$, $\vec{y}$ or show that it is not possible to do so. $\vec{x} = \begin{bmatrix} 2 \ 1 \ -1 \end{bmatrix}$, $\vec{y} = \begin{bmatrix} 1 \ 0 \ 1 \end{bmatrix}$, $\vec{v} = \begin{bmatrix} 0 \ 1 \ -3 \end{bmatrix}$ 5. (2 points) Solve the system of homogeneous linear equations: x_1+2x_2-x_3+2x_4=0 x_1+2x_2+2x_3=0 2x_1+4x_2-2x_3+3x_4=0

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The doctor activates his entry/exit on the LCD screen that is placed on the door of the consultation room. Assume that the room door has four digit infrared (IR) sensors for monitoring the doctor's entry and exit. Both IR sensor modules are connected to the INTO and INT1 pins of 8051 respectively. Whenever the doctor enters the room, an interruption (INTO) will be observed by the IR sensors, then the LCD should display "DOCTOR: IN" and while the doctor exits the room, an interruption (INT1) will be observed by the IR sensors the display should show "DOCTOR: OUT" "Write an Dosi ALP for above system

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For confidence intervals, just write answer from calculator or Statistical Technology Tools 1. Of 800 adults selected randomly from one town, 272 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. Interval: ( ) What is the value of $\hat{p}$ or the point estimate? 2. A sample of the speeds of 10 cars on a local road is listed below: 32 32 33 41 29 23 27 25 28 38 a) Find a 95% confidence level to estimate the average speed of all drivers on this local road. Interval: ( ) b) What is the sample mean? c) What is the sample standard deviation to 2 decimal places? 3. A random sample of 14 seniors from Stat High School showed that the average number of text messages sent daily was 60 with a sample standard deviation of 7. Construct a 95% confidence leve the average number of text messages sent by all seniors at Stat High School. Interval: ( ) From your answers above, fill in the blanks in the following sentence rounding the interval numbers whole numbers: The survey people are % confident that the true of text messages sent by all seniors is between and

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Suppose that $\tan \theta = -\frac{1}{2}$ and $270^\circ < \theta < 360^\circ$. Find the exact values of $\sin \frac{\theta}{2}$ and $\tan \frac{\theta}{2}$.

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Prepare an argument for or against the proposition that the following is ethical behavior. Without telling anyone, your ISP starts tracking every HTTP exchange from all its customers' computers. They use the data to determine heavy traffic routes in order to improve service to frequently accessed sites, such as search engines. Does the argument change if the purpose is to derive revenue by selling the data to advertisers seeking to determine popularity of different sites? Does the argument change if the purpose is to make traffic records available for government analysis?

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The parameter set \{a=3, b=7, c=9, d=6, e=1, f=1\} Consider the following closed-loop transfer function: $T(s) = \frac{s^2 + 9s + 16}{s^6 + as^5 + bs^4 + cs^3 + ds^2 + es + f}$ Part a) Routh Array Part b) (Is the system stable/unstable) Part c) (# of poles on the RHP) Column-1 $s^6$ $s^5$ $s^4$ $s^3$ $s^2$ $s^1$ $s^0$

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2. Consider the following graph G with solid and dotted edges: The solid edges form a spanning tree T of graph G. Each of the solid edges has a weight. Assign weights to the dotted edges, (1,2), (3,8), (6,10), (7,11), (8,12), and (9,10), such that: • Each of the edge weights is a positive INTEGER; • Tree T is a MINIMUM spanning tree of G and NO other tree is a MINIMUM spanning tree of G; • Each of the edge weights of the dotted edges is as small as possible. For instance, if you assign the edge weight 1 to edge (1,2), then replacing edge (1,5) in T with edge (1,2) will give a spanning tree with less weight than T. Thus edge (3,8) must have a weight greater than 1. If you assign the edge weight 4 to edge (1,2), then replacing edge (1,5) in T with edge (1,2) will give a different spanning tree with weight equal to T. This new tree would also be a minimum spanning tree. Thus edge (1,2) must have a weight greater than 4.

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(iv) Use the method of Lagrange multipliers to find the minimum value of f(x, y, z) = 2x^2 + y^2 + 3z^2 subject to the constraint 2x - 3y - 4z = 49. Solution:

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ryan w.