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Internal energy is a state variable and is a sum of the change in heat and work in a system. Using the example of an isothermal free expansion of an ideal gas describe how the sum of two path dependent properties can result in a state variable.

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Google it: According to a recent report, 66% of Internet searches in a particular month used the Google search engine. Assume that a sample of 22 searches is studied. What is the probability that exactly 19 of them used Google? Round the answers to at least four decimal places.

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What are the only human chromosomes that can exist as a trisomy in a human who lives to become an adult? The X and chromosome 22 The X and chromosomes 21 and 22 The X and chromosome 14 Just chromosome 14 The X and chromosome 21 Just chromosome 22 Just chromosome 21 Just the X chromosome

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Consider the space curve $\vec{r}(t) = (5t, 3\cos(t), 3\sin(t))$. a. Find the arc length function for $\vec{r}(t)$. $s(t) = \int_0^t ||\vec{r}'(\tau)|| d\tau =$ b. Find the arc length parameterization for $\vec{r}(t)$. $\vec{r}(s) = (\frac{5s}{\sqrt{34}}, 3\cos(\frac{s}{\sqrt{34}}), 3\sin(\frac{s}{\sqrt{34}}))$.

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A carpenter is building a barn for a client. The barn is going to have walls that are 12 feet tall, they have a 2x4 (1.5" thick) at the top and a special 3 5/8" x 4 beam at the base of the studs. How long do the studs need to be cut to, write your answer as a fraction?

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Problem 2: In an urn, there are 3 white balls and 2 black balls. Two balls are drawn successively without replacement. Calculate the probabilities of the following two events: 1) "Draw two balls of the same color" 2) "Draw two balls of different colors".

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During later adolescence, we can observe development of A. Gender identity B. Internalized morality C. Physical maturation D. A and B E. All of the above

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Isotonic solution H2O Animal cell Plant cell Hypotonic solution Hypertonic solution H2O H2O H2O (A) Normal (B) Lysed (C) Shriveled H2O H2O H2O Plasma membrane H2O (D) Flaccid (E) Turgid (F) Shriveled (plasmolyzed) Figure 5.1. Tonicity and osmotic water movement in animal and plant cells What animal cell is depicted in the upper portion of Figure 5.1?

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Evaluate the following integral. \begin{equation*} I = \int_{\theta=0}^{\pi} \int_{r=0}^{\sin(\theta)} r \, dr \, d\theta \end{equation*} You may find the following identity helpful: $\cos(2A) = \cos^2(A) - \sin^2(A) = 2\cos^2(A) - 1 = 1 - 2\sin^2(A)$

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(1 point) Find the area of the region below $y = x^2 + x - 8$ and above $y = 3$ for $3 \le x \le 5$. Area =

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