Find n for the given value of $a _ { n }$ in each arithmetic sequence. $a _ { n } = 95$; -1, 3, 7, ...

Differentiate the given function and simplify your answer. $h(s)=(1+\sqrt{3} s)^{5}$

For each of the following statements, prove the statement if it is true or give a counterexample if it is false. a. The midpoint of the common chord of two circles that intersect in two points lies on the line through the centers of the circles. b. If inscribed angle $\angle A B C$ in a circle with center O measures $120^{\circ}$, then central angle $\angle A O C$ measures $120^{\circ}$. c. The angle bisector of any angle inscribed in a circle contains the center of the circle. d. If the line through the midpoints of two chords of a circle contains the center of the circle, then the chords are parallel.

Show that the covariance between $\hat { \alpha }$ and $\hat { \beta }$ is zero.

Use the multiplication table. a. Which numbers from 0 to 150 appear most frequently as entries in the multiplication table?
b. Which numbers from 0 to 150 appear least frequently as entries in the multiplication table?

Find each product.

$$7(-6)$$

Construct the indicated confidence interval for the population mean

$$\mu$$

using the t-distribution.

$$c = 0.99 , \overline { x } = 24.7 , s = 4.6 , n = 50$$

Simplify.

$$\sqrt { 80 }$$

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.

$$y = - 2 \sin \left( 2 x + \frac { \pi } { 2 } \right)$$

What were the characteristics of trench warfare?

NBP Model 760 photocopiers print a mean of 76 pages per minute (ppm) with a standard deviation of 11 ppm. NBP Model S22 can scan 50 ppm with a standard deviation of 5 ppm. A software upgrade was tested on both models. After the upgrade, a prototype photocopier makes 90 copies per minute, while a prototype scanner makes 57 scans. Use percentiles to determine on which machine the upgrade had a bigger impact on performance.

Graph each point on a coordinate plane. B(2,-1)

At

$$20 ^ { \circ } \mathrm { C }$$

(approximately room temperature) the average velocity of

$$N_2$$

molecules in air is 1050 mph. What is the average speed in m/s?

In gel electrophoresis, the shortest DNA fragments travel greater distances than the longest DNA fragments.