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jose carlos martin

jose carlos m.

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Consider the function $$f(t) = \begin{cases} 0 & \text{for } t < \frac{5\pi}{2}, \\ 2\sin(2t) & \text{for } t \geq \frac{5\pi}{2}. \end{cases}$$ (a) Rewrite the function $f(t)$ as follows: $$f(t) = A u(t-t_0) \sin(2(t-t_0)).$$ Find the constants $t_0$ and $A$. $t_0 = (5\pi/2)$ $A = $ Hints: 1) Rewrite the $\sin(2t) = \sin(2(t-t_0+t_0))$ for an appropriate $t_0$. 2) Use the trigonometric identity $\sin(\alpha + \beta) = \sin(\alpha) \cos(\beta) + \sin(\beta) \cos(\alpha)$ for $\alpha = 2(t-t_0)$ and $\beta = 2t_0$. (b) Use the form of $f(t)$ found in part (a) to find $F(s) = \mathcal{L}[f(t)]$, the Laplace transform of $f(t)$. $F(s) = $

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The following information pertains to internal controls at company A and company B respectively COMPANY A Controls are Strong COMPANY B Controls are Weak If an audit of these companies is performed according to the PCAOB auditing standards, the auditor will: COMPANY A A Test/evaluate Controls B Not test/not evaluate controls C Test/evaluate Controls D Not test/not evaluate controls COMPANY B Not test/not evaluate controls Test/evaluate Controls Test/evaluate Controls Not test/not evaluate controls C Incurred obligations were recorded in the correct period. D B

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In a combustion reaction, a carbon-containing compounds burns in oxygen from air to produce

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A producer of candy packages hypothesizes that his production does not adhere to the weight standard of 250 grams. As a measure of quality control, he weighs 6 packages and obtains the following results in grams: \[ 238,244,234,243,239,255 \] Is there sufficient evidence to support the claim that the mean weights of candy packages is different from 250 grams ? Assume that the population distribution of the weights is normal and the significance level is 0.1 . 1. The alternative hypothesis \( H_{1} \) : \( \mu \) \( \square \) \( \square \) 2. Compute the statistic: \( 2 \sim \) \( \square \) Note: Choose Z for z.test (using the standard normal distribution), T for t.test (using the Student distributions), and F for F.test (using the Fisher distributions). 3. Determine the acceptance region (the complementary region to the rejection region): \( \square \) \( \square \) Note: Type 00 for Infinity and - -0 for Negative Infinity. 4. Make a conclusion: Select an answer \( \square \)

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28. A rectangular lawn is to be surrounded externally by a path which is 3 m wide. If the dimensions of the then are 35 m and 45 m , find the cost of constructing the path at the rate of ? 100 per \( \mathrm{m}^{2} \). 29. Two crossroads each 2 m wide intersect each other at right angles through the centre of rectume area of dimension \( 75 \mathrm{~m} \times 50 \mathrm{~m} \). These crossroads run parallel to sides of the rectangle crossroads. Date

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if 60 of the 90 students in the band are female, what is the ratio of male to female students in the band? write ratio in lowest terms

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The Federal Reserve's Board of Governors is based in which city?

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A 1200 kg sled is being towed by means of two horizontal cables. One cable is pulling with a force of 60 N in a direction 60 degrees north of west. The second cable pulls in a direction 20 degrees east of north. There is no motion of the sled horizontally. What is the total force applied in the northward direction?

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etermine the average rate of change of W(t) from t = 40 to t = 50 Time (minutes) 0 10 20 30 40 50 Temperature (degrees Fahrenheit) 75 55 40 35 32 30

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8. To convert a number from base-10 to base-2, we have to represent it as a sum of powers of 2. For example, suppose we want to convert 25 from base-10 to base-2. We first note that: 1 25 = 16 + 8 + 1 1.16+1.8+1.1 1 16 + 1 8 + 0 4 + 0 2 + 1 1 = 1 24 + 1 23 + 0 22 + 0 21 + 1 20 (25)1o = (11001)2 You may be familiar with the following algorithm for converting a number from base-10 to base-2: 1. Start with a number n 2. Divide n by 2 and write down the remainder 3. If n = 0, go back to step 1. Otherwise go to step 4 4. Read back the remainders in reverse order For example, to convert 25 from base-10 to base-2 we would do the following: 25 2 = 12 2 + 1 12 2 = 6 2 + 0 6 2 = 3 2 + 0 3 2 = 1 2 + 1 1 2 = 0 2 + 1 (25)10 = (11001)2 Let's use modular arithmetic to understand why this algorithm works. Let n be a positive integer. Suppose there exist values bo,b,...b {0,1} such that n=bo2+b21+..+b2 (a) What is the binary representation of n? (b) Prove that n = bo (mod 2) (c) How do the last two answers relate to the algorithm above?

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