3consider the set x = { 1 , 2 , 3 , 4 , 5 } and suppose you have two holes. also suppose that you have 10 pigeons: the 2 -element subsets of x . can you put these 10 pigeons into the two holes in a way that there is no 3 -element subset s = { a , b , c } ⊂ x for which all pigeons from s go in the same hole? then answer the same question if x = { 1 , 2 , 3 , 4 , 5 , 6 } with 15 = c ( 6 , 2 ) pigeons.

At river bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge. calculate the income earned in one month on the checking account for a customer with an account balance of $1,000. a. $4.25 b. $5.50 c. $6.75 d. $7.25 checking account earnings at baker’s bank are expressed by the equation: i = -0.09x + 10.2. while the earnings at elite bank are modeled by: i = -0.02x + 7.5. in both cases, x is the number of checks written. at what number of checks will elite bank start generating more checking account income than baker's bank? a. 12 b. 25 c. 39 d. 42 emilio’s checking account had a balance of 728.32 at the beginning of the week. he wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. he also deposited his paycheck in the amount of $1,109.90. what is his account balance at the end of the week? a. $1,192.35 b. $1,222.86 c. $1,540.52 d. $1,614.96