The blue-throated hummingbird has a heart rate of about 1,260 beats per minute. Explain how you would calculate the number of times the hummingbird's heart beats in a 24-hour day. Then find the number of beats in a 24-hour day.

Draw the three distinct geometric isomers of 2,4-hexadiene.

Prove that if an $n \times n$ matrix $A$ is not invertible, then $A[adj(A)]$ is the zero matrix.

Aniko left for work at 7.39 am and returned home at 6.43 pm. How long was she away from home?

Make a $3 - \mathrm { D }$ surface plot of the function $z = 0.5 x ^ { 2 } + 0.5 y ^ { 2 } \quad$ in the domain $- 2 \leq x \leq 2$ and $- 2 \leq y \leq 2$ .

Two $n\times n$ matrices $A$ and $B$ are called simultaneously diagonalizable it there exists an invertible matrix $P$ such that both $P^{-1}AP$ and $P^{-1}BP$ are diagonal matrices. Prove that if $A$ and $B$ are simultaneously diagonalizable, then $AB=BA$.

The area of a square is 392 square meters. The area of a second square is half the area of the first square. What is the side length of the second square? A 14 meters, B $\approx 20$ meters, C 196 meters, D 96 meters.

Light in a vacuum is incident on a transparent glass slab. The angle of incidence is

$$35.0^\circ.$$

The slab is then immersed in a pool of liquid. When the angle of incidence for the light striking the slab is

$$20.3^\circ,$$

the angle of refraction for the light entering the slab is the same as when the slab was in a vacuum. What is the index of refraction of the liquid?

Multiply. Write the product in scientific notation. (1.25 × 10^-3)(8 × 10^-5)

In your own words, explain how to solve a literal equation for one of the variables.

In a regular NBA season, each team plays 82 games, some at home and some on the road. Can you afford the price of a ticket? The Web site wiki.answers.com indicates that the low prices are around $10 for the high up sears while the court-side seats are around$2000 to $5000 per game and that the average price of a ticket is$75.50 a game. Suppose that we test this claim by selecting a random sample of n=50 ticket purchases from a computer database and find that the average ticket price is $82.50 with a standard deviation of$75.25. a. Do you think that x, the price of an individual regular season ticket has a mound-shaped distribution? If not, what shape would you expect? b. If the distribution of the ticket prices is not normal, you can still use the standard normal distribution to construct a confidence interval for $\mu$, the average price of a ticket. Why? c. Construct a 95% confidence interval for $\mu$, the average price of a ticket. Does this confidence interval cause you support or question the claimed average price of $75.50? Explain.

For each of the following alkyl halides, indicate the stereoisomer that would be obtained in greatest yield in an E2 reaction. a. 3-bromo-2,2,3-trimethylpentane, b. 4-bromo-2,2,3,3-tetramethylpentane, c. 3-bromo-2,3-dimethylpentane, d. 3-bromo-3,4-dimethylhexane

Solve the system. To do so, substitute a for

$$\frac { 1 } { x }$$

and b for

$$\frac { 1 } { y }$$

and solve for a and b. Then find x and y using the fact that

$$a = \frac { 1 } { x }$$

and

$$b = \frac { 1 } { y }$$

.

$$\left\{ \begin{array} { l } { \frac { 1 } { x } + \frac { 2 } { y } = - 1 } \\ { \frac { 2 } { x } - \frac { 1 } { y } = - 7 } \end{array} \right.$$

Find the multiplicative inverse of each element in Z11, Z13, and Z17.