The Gray family is putting in a pool in the shape of a rectangular prism. The first plan shows a pool that is 15 feet long, 12 feet wide, and 5 feet deep. The second plan shows a pool with the same length and width, but a depth of 7 feet. How much more water is needed to fill the second pool if both pools are filled to the top?

Indicate whether the following statements are true or false. Explain. When a closed system is at the dead state, it is in thermal and mechanical equilibrium with the exergy reference environment, and the values of the system's energy and thermomechanical exergy are each zero.

Each pair of values is from an inverse variation. Find the missing value. (x,12), (4,1.5)

Find an SVD of the indicated matrix.

$$A = \left[ \begin{array} { r r } { 0 } & { - 2 } \\ { - 3 } & { 0 } \end{array} \right]$$

Lana says there are $4 ^ { 3 }$ eggs in a dozen. Patrick says there are $3 ^ { 4 }$ eggs in a dozen. Is either person correct? Explain your reasoning.

Perform the indicated operations. Where possible, reduce the answer to its lowest terms.

$$\frac { 1 } { 3 } - 5 \left( \frac { 1 } { 2 } + 1 \right)$$

Which one of these statements is true? (a) The atomic spacing in crystals is too fine to produce observable diffraction effects with matter waves. (b) Only charged particles have matter waves associated with them. (c) Identical diffraction patterns are obtained when either electrons or neutrons of the same kinetic energy are incident on a single crystal. (d) Electrons, neutrons, and x-rays of appropriate energies can all produce similar diffraction patterns when incident on single crystals. (e) Wave phenomena are not observed for macroscopic objects such as baseballs because the de Broglie wavelength associated with such macroscopic objects is too long.

Write the fraction or mixed number as a decimal. 10 4/9

Fill in the blank. One _______ is the measure of a central angle that intercepts an arc equal in length to the radius of the circle.

Estimate the value of the linear correlation coefficient r for the given paired data obtained from 50 randomly selected adults. Their pulse rates (x) are measured and their IQ scores are measured (y).

Name the property of real numbers illustrated by each equation. $\frac{2}{5}+\frac{27}{5} \cdot \frac{5}{27}=\frac{2}{5}+1$

A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. Use the analytical method to determine the following: (a) Find his net displacement vector. (b) How far is the restaurant from the post office? (c) If he returns directly from the restaurant to the post office, what is his displacement vector on the return trip? (d) What is his compass heading on the return trip? Assume the +x-axis is to the east.

Test for symmetry with respect to the line $\theta=\pi / 2$, the polar axis, and the pole. $r=4 \csc \theta \cos \theta$

What is the partial pressure of hydrogen gas in a mixture of hydrogen and helium if the total pressure is 600 mmHg and the partial pressure of helium is 439 mmHg?