Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Because the words BET and BEE both contain three letters, the number of permutations of the letters in each word is 3!, or 6. ____

373 $\div$ 10

Evaluate the following limits.

$$\lim _ { x \rightarrow 0 } \frac { x } { \sqrt { c x + 1 } - 1 }$$

, where c is a nonzero constant

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A permutation occurs when the order of arrangement does not matter.

In Exercise, find the relative extrema using both the first and second derivative tests.
$f ( x ) = \sin ^ { 2 } x . \quad 0 < x < 2 \pi$

Fill in each blank so that the resulting statement is true. The number of permutations of n items, where p items are identical and q items are identical, is given by ____.

Distinguish between immediate types of allergy and delayed allergic reactions in terms of cause and consequences.

The number of possible permutations if $r$ objects are taken from $n$ items is $_nP_r=$ _______.

Write the second term of the sequence.

$5!$, called $5$ __________, is the product of all positive integers from __________ down through _________. By definition, $0!=$ __________.

Lacey wins a million dollar lottery that is to be paid in equal annual amounts over a period of years. a. Set up and solve a difference equation to find the present value $P_n$ of the payout if the prevailing annual interest rate is 5% and the payments are spread over n years. b. Lacey does the math in part (a) and sues the lottery for false advertising, claiming that she was promised a million dollars but will receive less. The court agrees with her and orders the lottery to make an extra payment of A dollars each year in order to bring the present value up to the promised million dollar level. What must A be if the payout is spread over 20 years?

What is your opinion of the diminutive Lilliputians? Think of three words to describe them and give three examples of their behavior to support your opinion.

Microbes such as bacteria have small positive charges when in solution. Public health agencies are exploring a new way to measure the presence of small numbers of microbes in drinking water by using electric forces to concentrate the microbes. Water is sent between the two oppositely charged electrodes of a parallel-plate capacitor. Any microbes in the water will collect on one of the electrodes. a. On which electrode will the microbes collect? b. How could the microbes be easily removed from the electrodes for analysis?

use the given function value(s) and the trigonometric identities to find the indicated trigonometric functions. sin 30° = 1/2 , tan 30° = √3/3 , cos 30°

Suggest two things a property owner could do to reduce water erosion on soil-covered land that has a steep slope.