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Which condition allows us to use a normal distribution when creating a confidence interval for a mean?

Bauen Sie zwei Sätze mit der “Introductory es Not the Real Subject” Konstruktion (wie auf S. 248). Geben Sie eine englische Übersetzung für jeden deutschen Satz.

Identifizieren Sie die beste Definition der unterstrichenen Satzposition. _________________ 448 v. Chr. kam der Perserkrieg zu einem Ende. Kurz darauf beschäftigte sich Perikles mit dem Wiederaufbau der Akropolis.

Stellen Sie die richtige W-Frage zur unterstrichenen Satzposition/zu den unterstrichenen parallelen Satzpositionen. Sie brauchen ein “wo(r)-” Fragewort für diese Frage! _______________________ Das Blut besteht aus dem Blutplasma und den darin verteilten Blutkörperchen.

Bauen Sie zwei Sätze oder Satzkombinationen mit “Da(r)-compounds used to replace a pronoun” (wie oben auf S. 244). Geben Sie eine englische Übersetzung für jeden deutschen Satz.

A hot air balloon is ascending at a rate of +4.00 m/s to a height of 12.0 m above the ground when a package is dropped. In the absence of air resistance, what is the velocity (m/s) of the package just before it hits the ground? NOTE: Use correct rounding and significant figures in the answer Enter numerical answer in proper standard notation, not scientific notation Do not enter units with the answer

A 1.15 kg falcon catches a 0.235 kg dove from behind in mid-air. What is their velocity (units: m/s) after impact if the falcon’s initial velocity is 27.5 m/s and the dove’s initial velocity is 5.15 m/s in the same direction?  NOTE: Use correct rounding and significant figures in the answer Enter numerical answer in proper standard notation, not scientific notation Do not enter units with the answer

Find the local extrema of the function: g ( x ) = x 2 e − x 2 {“version”:”1.1″,”math”:”g(x)=x^2 e^{-x^2}”} State your answers as points and label them as maxima or minima respectively. Select an option from below:

The figure shows the graph of the derivative, f'(x), of a function f(x). Answer the following questions and explain your reasoning. (a) For what values of x does f(x) have a local maximum and/or local minimum?(b) Sketch a graph of f”(x).(c) Sketch a possible graph of f(x) Select an option from below:

Choose one of the following three optimization problems. Pay attention to the points. (a) For 8 points.The ideal dosage of a medication is a tradeoff between the efficacy of the drug and the severity of its side effects. If the side effects of a treatment are too severe, it will have to be discontinued, so it will fail to treat the patient. Similarly, if the dosage of the medicine is too low, its efficacy will not be sufficient to treat the patient. Suppose the probability of an effective treatment that accounts for this tradeoff is given by P(x), given below, where $x$ is the dosage of the medication given to the patient. What is the ideal dosage to maximize the cure?  P ( x ) = x 1 + x {“version”:”1.1″,”math”:”P(x)=\dfrac{\sqrt{x}}{1+x}”} (b) For 10 points.A box with an open top is to be constructed from a rectangular piece of cardboard (5 ft wide and 8 ft long) by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (c) For 12 points.An action movie character that loves to break the fourth wall is escaping from a mob of doppelgangers that want to take his place in the movie. He reaches a bank of a straight river, 3 km wide, with a boat unsuspiciously waiting for him. On the other side of the bank, 8 km downstream, he sees The Rock waving at him ready to fly a helicopter for their escape. At this moment he looks directly at the camera (at you) and asks “How can I move the fastest?” while getting himself on the boat. You know he can row at a speed of 6 km/hr and he can run at a speed of 8 km/hr. Should he go directly across (from A to C) and run the rest of the way (to B)? Should he row directly to the helicopter (from A to B)? or should he row for a bit (from A to D) and then run all that’s left to the helicopter? How long will it take him to reach the rock in the shortest time? He’s still staring at the camera, but the sound of the mob is getting louder, he’s counting on you! Select an option from below: