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shannon joseph

shannon j.

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(Full marks: 100) Question 1 \begin{equation*} Let \quad V = \left\{ \begin{bmatrix} a - b + c \\ 11b - c \\ 3a + 5b \\ 7c \end{bmatrix} \mid a, b, c \in \mathbb{R} \right\} \text{ be a set in } \mathbb{R}^4. \end{equation*} \begin{equation*} Let \quad S = \left\{ \begin{bmatrix} 1 \\ 0 \\ 3 \\ 0 \end{bmatrix}, \begin{bmatrix} -1 \\ 11 \\ 5 \\ 0 \end{bmatrix}, \begin{bmatrix} 1 \\ -1 \\ 0 \\ 7 \end{bmatrix} \right\} \text{ be a set of three vectors in } \mathbb{R}^4. \end{equation*} Question 1a Determine whether \(S\) is a linearly independent set. (3 marks) Question 1b Show that \(V\) is a subspace of \(\mathbb{R}^4\) and state the dimension of \(V\). (6 marks) Question 1c Does \( \begin{bmatrix} 1 \\ 10 \\ 8 \\ 4 \end{bmatrix} \) belong to \(V\)? Question 1d Explain why \( \left\{ \begin{bmatrix} 1 \\ 0 \\ 3 \\ 0 \end{bmatrix}, \begin{bmatrix} -1 \\ 11 \\ 5 \\ 0 \end{bmatrix}, \begin{bmatrix} 1 \\ -1 \\ 0 \\ 7 \end{bmatrix}, \begin{bmatrix} 1 \\ 10 \\ 8 \\ 4 \end{bmatrix} \right\} \) forms a basis of \(\mathbb{R}^4\). (3 marks) (3 marks)

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If biology were the principal factor in human behavior, around the world we would find that men would act like men and women would act like women regardless of the society in which they lives. a. True b. False

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A change in a nucleotide sequence of a gene is termed an elongation. True False

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QUESTION 9 For the circuit shown in the figure below, the current I is approximately $200\angle0^\circ$ V f = 50 Hz $\circ$ 5 $<0^\circ$ A $\circ$ -5 $<0^\circ$ A $\circ$ 5 $<90^\circ$ A $\circ$ 10 $<0^\circ$ A 40 $\Omega$ j40 $\Omega$ V $I_1$ $I_2$ j40 $\Omega$ -j20 $\Omega$

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Question 12 Given the partial fraction decomposition: \frac{8x}{(x-2)(x^2+4)} = \frac{A}{(x-2)} + \frac{Bx+C}{(x^2+4)} Find the values of A= B= C=

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If an initial shock to autonomous expenditures of 40 led to a shift of 40 in the AD curve, you would know that the corresponding AE curve: A. is horizontal. B. is vertical. C. has a slope of 1. D. has a slope of -1.

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The economy has become very sluggish in recent months. You are an economist working at a newspaper and your editor calls you in and says "The Fed is meeting the next two days. Please write a paragraph or two that explains to our readers 1) exactly what group met, 2) what that group's purpose is, and 3) what the likely outcome of the meeting will be. Too, tell the readers how that outcome is likely to be implemented and who will likely handle the implementation." Please draft your write-up below.

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if you want to inject 110 mcg of epinephrine into the fluids surrounding a strip of smooth muscle, what volume of a 1:2,000 epinephrine would you draw up into a syringe? (include units)

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All retail jobs are not created equal. Just ask Anitha. At a previous job, a store owner bluntly told her, "You're just a number. You can be replaced at any time." Anitha said, "When you are told something like that, why would you want to put any effort in?" Luckily, after landing a job at Flight-001, Anitha started to feel motivated again. Flight-001 co-founder Rishabh frequently visits his various stores to talk with staff about what's happening. While visiting Anitha's Surat-based store, where she had recently been promoted to assistant store manager, Rishabh asked if customers were shopping differently after the airlines had added new fees for checked luggage. Anitha confirmed Rishabh's suspicions and gave him a full report along with recommendations for how they might make adjustments in inventory and merchandising. Anitha is thrilled to have found a place where she can make a contribution and be challenged. "At this company, they make an effort to show you you're appreciated; you have a say in what goes on. You're given compliments and feedback about what you could be better at," she explained.

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Consider a put option with a $50 strike price and maturity equal to 1 year. The underlying stock price is $40 and the volatility of the stock is 25%. The stock is not expected to pay any dividends within the next year. The risk-free rate of return is 5%. Calculate the value of u, d, and the risk-neutral probability p for a two-step tree. Using the Binomial tree approach, find the price of a European put option. What would the price of the option be if it were instead American in nature? Please show all necessary steps.

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