Marcus currently has $42 and plans to save an additional $5 each week to buy a pair of shoes. he made a table showing the total amount of money he will have saved for different weeks. number of weeks 0 2 5 8 total amount of money ($) 42 52 67 82 write an equation in standard form that represents the relationship between the number of weeks and the total amount of money marcus will have saved. a. −x+5y=42 b. x+5y=42 c. −5x+y=42 d. 5x+y=42

Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

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.

In a coastal town, the humidity, measured in grams of water per kilogram of air, increases by 43% for every 1 degree celsius increase in temperature. a scientist observes that the humidity on monday morning is 5.75 grams per kilogram. he wants to know how much the temperature must increase for the humidity to reach at least 49.17 grams per kilogram. let t represent the increase in temperature, in degrees celsius, from monday morning's observation. write an inequality to represent the situation, and use it to determine the desired temperature increase.