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prove that for any natural n the value of the expression (4n+5)^2–9 is divisible by 4.

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

Use the second shift theorem to find the inverse laplace transform of (e^−3s) / (s^2 + 2s − 3)

Renee hiked for 6 3 /4 miles. after resting, renee hiked back along the same route for 5 1 /4 miles. how many more miles does renee need to hike to return to the place where she started? represent your answer as a simplified mixed number, if necessary.