Explain how the quotient of powers was used to simplify this expression. 5 to the 4th power over 25 equals 5 to the 2nd power.
a. by simplifying 25 to 5 to the 2nd power to make both powers base five, and subtracting the exponents.
b. by simplifying 25 to 5 to the 2nd power to make both powers base five, and adding the base exponents
c. by finding the quotient of the bases to be 1/5, and cancelling common factors
d. by finding the quotient of the bases to be 1/5, and simplifying the expression

Marco has $38.43 dollars in his checking account. his checking account is linked to his amazon music account so he can buy music. the songs he purchases cost $1.29. part 1: write an expression to describe the amount of money in his checking account in relationship to the number of songs he purchases. part 2: describe what the variable represents in this situation.

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?