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QUESTION 69 A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.918 a. 0.0347 b. 0.7200 c. 0.9511 d. 0.5645

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1. (15 points) Consider $$ f(x) = \begin{cases} e^{x^2-9} - a & x < 3 \\ b & x = 3 \\ \frac{\frac{3}{x} - 1}{x-3} & x > 3 \end{cases} $$ where a and b are constants (parameter). Is it possible to choose a value for a and b such that f(x) is continuous at x = 3? Explain your reasoning completely and justify with limit computations.

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A person's Body Mass Index is $I = \frac{W}{H^2}$, where $W$ is the body weight (in kilograms) and $H$ is the body height (in meters). A child has weight $W = 39$ kg and height $H = 1.5$ m. Use the linear approximation to estimate the change in $I$ if $(W, H)$ changes to $(40, 1.52)$. (Use decimal notation. Give your answer to three decimal places.) $\Delta I \approx -0.252$ Incorrect Answer

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Predict the ground-state electron configuration of each ion. Use the abbreviated noble gas notation. $ \mathrm{Ru}^{2+} $ : [Kr] $ W^{3+} $ [Xe] I

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. If ~c is the vector sum of vectors ~a and ~b, what must be true about their directions and magnitudes if |~c| = 0 ?

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A cultural East-West mix, "One country, two systems," and the largest number of scrapers are all used to describe Singapore South Korea Hong Kong Taiwan

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Question 10 (1 point) Which of the following statements about novae is true? A) When a star system undergoes a nova, it brightens as much as a star system undergoing a supernova. B) A star system that undergoes a nova may have another nova sometime in the future. C) A nova involves fusion taking place on the surface of a neutron star. D) A nova can occur on a single, isolated star. E) A nova is the most powerful type of explosion ever seen in the universe.

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The text appears to be free of errors and is presented clearly and coherently.

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4) Groceries arrived in 12 bags. Each bag's weight (in lbs) is an i.i.d Uniform(0, 12) random variable. Let X represent the total weight of the groceries. A) Use Markov's inequality to bound the probability that X is greater than 144 pounds (6 points) B) Use Chebyshev's inequality to bound the probability that X is greater than 144 lbs. (6 points) C) Use the Central Limit Theorem to estimate the probability X is greater than 96 pounds (6 points) D) What is the probability X is greater than 144 pounds? Explain (6 points) Note: Some of the info below may be useful to make calculations slightly less tedious for this question $\Phi(0) = .5$ $\Phi(1/2) = .691$ $\Phi(1/8) = .55$ $\Phi(1) = .841$ $\Phi(1/6) = .566$ $\Phi(2) = .977$ $\Phi(1/4) = .599$ $\Phi(3) = .999$

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2. Use the same reasoning as in Lab 8 with angular variables to make a similar statement about the conditions under which angular momentum is conserved. 3. A person swings a ball of mass $m$ around their head at speed $v$ and radius $R$ as depicted to the right. They then pull the string so that the radius decreases from $R$ to $r < R$. In both cases, there is an angle $\theta$ between the string and the vertical, but it is small enough that we can ignore it for simplicity. When the person pulls the string in, does the force exerted on the string produce any torque on the ball? Explain. 4. Determine the initial angular velocity of the ball $\omega_i$ in terms of $v$ and $R$. 5. Determine the ball's angular momentum $L$ before the person pulls the string in terms of $m$, $v$, and $R$. 6. Once the string is pulled, does the angular velocity change? Explain.

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aaron r.