Solve for x.

x = ln e

x =

Mrs. avila is buying a wallpaper border to go on all of her kitchen walls. she wants to buy 5 extra feet of wallpaper border than she needs to be sure she has enough. she buys 55.5 feet of the border. the store owner selling the border uses the width of mrs. avila's kitchen to determine that the length of her kitchen must be 14.5 feet.

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.