A point object is 10 cm away from a plane mirror, and the eye of an observer (with pupil diameter 5.0 mm) is 20 cm away. Assuming the eye and the object to be on the same line perpendicular to the mirror surface, find the area of the mirror used in observing the reflection of the point.

Donna has four bracelets in her jewelry box. They can all be worn together, but each is different from the others. Before she goes to bed at night, she sets out the outfit she will wear the next day, including her accessories. How many different ways can she choose the following: 0 bracelets? 1 bracelet? 2 bracelets? 3 bracelets? 4 bracelets? a. How do these possible combinations compare to the 4th row (n = 4) of Pascal's Triangle? b. If Donna bought two new bracelets, how many combinations of four bracelets can she choose for her outfit? How can you figure this out without multiplying or using your calculator?

What is the derivative of xe^x?

You show your student identification at a local restaurant in order to receive a 5% discount. You spend $12 for your meal at the restaurant. How much would your meal cost without the discount?

Verify each identity.

$$\tan t + \frac { \cos t } { 1 + \sin t } = \sec t$$

Graph each function. State key features of the graph. $f(x)=\frac{1}{2} \sqrt[3]{x-3}+1$

Suppose that a ball is rolling down a ramp. The distance traveled by the ball is given by the function in each exercise, where t is the time, in seconds, after the ball is released, and s(t) is measured in feet. For each given function, find the ball's average velocity from

$$t _ { 1 } = 3 \text { to } t _ { 2 } = 3.01.$$

$$s ( t ) = 10 t ^ { 2 }$$

Solve the compound inequality. Graph the solution set and write it using interval notation.

$$3 x + 4 < - 2 \text { or } 3 x + 4 > 10$$

Find each sale price. $25 sweater; 15% off.

Find the least common denominator for each set of fractions. 1/2, 2/3, and 3/5

The sum of the measures of the interior angles of a polygon is

$$2160 ^ { \circ }.$$

Find the number of sides of the polygon. F 10 G 14 H 16 J 18

Round 45,621 to each place given below.

a. to the nearest ten ___

b. to the nearest hundred ___

c. to the nearest thousand ___

d. to the nearest ten thousand ___

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In a group of five men and five women, the probability of randomly selecting a man is

$$\frac { 1 } { 2 }$$

so if I select two people from the group , the probability that both are men is

$$\frac { 1 } { 2 } \cdot \frac { 1 } { 2 }$$

Find the first partial derivatives of the following functions. f(x, y)=$x ^ { 2 y }$