Male Rana catesbeiana bullfrogs are known for their loud mating call. The call is emitted not by the frog's mouth but by its eardrums, which lie on the surface of the head. And, surprisingly, the sound has nothing to do with the frog's inflated throat. If the emitted sound has a frequency of 260 Hz and a sound level of 75 dB (near the eardrum), what is the amplitude of the eardrum 's oscillation? The air density is

$$1.21 kg/m^3$$

.

Decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem. If false, provide an example, illustration, or brief explanation of why the statement is false. There are the same number of permutations of {1, 2, 3, 4} of even parity as there are of odd parity.

True or False: A right triangle has one right angle, one obtuse angle, and one acute angle. If false, explain why.

Suppose a Carnot engine can be operated between two reservoirs as either a heat engine or a refrigerator. How is the coefficient of performance of the refrigerator related to the efficiency of the heat engine?

Having which of the following makes it easier for oligopolies to coordinate on raising prices? A. a large number of firms B. differentiated products C. buyers with bargaining power D. identical perceptions of fairness E. complex pricing schemes

Determine the general solution to the linear system

$$\mathbf { x } ^ { \prime } = A \mathbf { x }$$

for the given matrix A.

$$\left[ \begin{array} { r r } { 3 } & { 13 } \\ { - 1 } & { - 3 } \end{array} \right].$$

What is the Ratio Test inconclusive for summation n=1 to infinite (-3)^n-1/n^1/2 (that is, it fails to give a definite answer)?

If c and d are different positive integers and

$$4c + d = 26,$$

what is the sum of all possible values of c?

$$A \ 6 \\ B \ 10 \\ C \ 15 \\ D \ 21$$

Find general solutions of the differential equation. Primes denote derivatives with respect to $x$.

$$4 y ^ { \prime \prime } + 8 y ^ { \prime } + 3 y = 0$$

Acid or subtract. $\frac { 6 r s } { r ^ { 2 } s ^ { 2 } } + \frac { 18 r } { r ^ { 2 } s ^ { 2 } }$

Of the seventeen students in Angela's class, eight play in the school band. What fraction of the total number of students in Angela's class are in the band?

Evaluate or simplify each expression without using a calculator.

$$\log 10 ^ { 7 }$$

Find the positive radian measure of the angle that the second hand of a clock moves through in the given time.

$$4 \text { minutes and } 25 \text { seconds }$$

What must be the relative speed between source and receiver if the wavelength of an EM wave as measured by the receiver is twice the wavelength as measured by the source? Are source and observer moving closer together or farther apart?