Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

1^2+ 4^2+ 7^2 ++(3n-2)^2 = n(6n^2-3n-1) / 2

A) if $50000 is invested in a bank account that pays 9.3% of interest compounded on a six-monthly basis, how much money will be in the account after 3 and 12 years? b) if matusalen's father had put $2.0 in the bank when he was born and there, how long would matusalen have had to his death (969 years later) if the interest was 7% per year composed each month and weekly?

The cost of turkey is directly proportional to its weight. if a 12-pount turkey costs $27, how much does a 16-pound turkey cost? a. $33.75 b. $36.00 c. $31.00 d. $32.50

Emily is entering a bicycle race for charity. her mother pledges $0.90 for every 0.75 mile she bikes. if emily bikes 18 miles, how much will her mother donate?