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Two linear polarizing filters are placed one behind the other, so that their transmission directions are parallel to one another. A beam of unpolarized light of intensity $I_0$ is directed at the two filters. What intensity of the light will pass through both filters? 0 $0.5I_0$ $I_0$ $2I_0$ $0.25I_0$

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On 1 June 20X6, Santander acquired 70% of the equity of Madrid in exchange for CU760,000 cash and 100,000 Santander shares. At this date the fair value of the identifiable net assets of Madrid was CU850,000 and the market value of Santander shares was CU2.50. On 31 December 20X8, Santander acquired a further 10% of the equity of Madrid at a cost of CU105,000. On this date the identifiable net assets of Madrid were CU970,000. Santander measures the non-controlling interest using the proportion of net assets method. Requirement (a) What goodwill is recorded in the consolidated statement of financial position at 31 December 20X8, assuming that there is no impairment? (b) What journal adjustment is required on the acquisition of the further 10% of shares?

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b. Identify the data collection method. Are there any potential biases in the method used? Identify the data collection method. Choose the correct answer below. A. The data collection method used was a survey. A random-digit telephone dialing procedure was used to collect the sample. B. The data are from a published source. The researchers randomly selected data by using the telephone numbers in the source. C. The data were collected observationally. The researchers asked for the participant's phone number after making their observation. D. The data are from a designed experiment. A random-digit telephone dialing procedure was used to collect the sample.

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The demand curve for a particular good or service is perfectly elastic. If the supply curve were to decrease what would happen?

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For the function $f(x) = \frac{x-3}{x+6}$, find $f'''(x)$, the third derivative of f, and $f^{(4)}(x)$, the fourth derivative of f. f'''(x) = f^{(4)}(x) =

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6. (5 points) An investor is considering the following stocks. Stock X has a market capitalization of $7 billion, pays a relatively high dividends with little increase in earnings, and has a PE ratio of 11. Stock Y has a market capitalization of $62 billion, but does not currently pay a dividends, and has a PE ratio of 39. Stock Z is a housing company and has a market capitalization of $800 million and a PE of 18. a. How would you classify these stocks according to their market cap? Which one would be large-cap, which one mid-cap and small-cap? b. Which of these stocks would you classify as a growth stock? Why? c. Which of these stocks would you classify as an income stock and why? d. Which one would an aggressive (risk-taking) investor prefer? Why?

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Book Problem 31 Find a function $f$ and a positive number $a$ such that $f(x) = 15x^4$ $a = \frac{3}{4}$ $2 + \int_a^x \frac{f(t)}{t^2} dt = 5x^{-2}, \quad x > 0$

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Compute the directional derivative of the function $g(x,y) = \sin(\pi(x - y))$ at the point $P(-1, -3)$ in the direction $\begin{pmatrix} \frac{5}{13} \\ \frac{12}{13} \end{pmatrix}$. Be sure to use a unit vector for the direction vector. The directional derivative is $oxed{ }$. (Type an exact answer, using $\pi$ as needed.)

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1. (7 pts) The lifetime of a printer costing $300 is exponentially distributed with mean 4 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a one-half refund if it fails during the second year. If the manufacturer sells 100 printers, how much should it expect to pay in refunds? 2. (7 pts) An insurance policy pays for a random loss $X$ subject to a deductible of $C$, where $0 < X < C$. The loss amount is modeled as a continuous random variable with the probability density function $f(x) = \begin{cases} 2x & 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$ Given a random loss $X$, the probability that the insurance payment is less than 0.5 is equal to 65%. Calculate $C$. 3. (7 pts) One company propose to cover a loss, $X$, where $X$ has a uniform distribution on $[0, 1200]$. At what level must a deductible be set in order for the expected payment to be 25% of what it would be with no deductible?

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Describe four different ways resource data can be used, including the method each will be collected and why each is important.

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