While shopping at a clearance sale, samantha finds a $60.00 dress on sale for 25% off. samantha also has a 50% off coupon. which statement correctly summarizes her savings? samantha will save $45.00 because the two sales will combine for 75% off the original cost. samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction. samantha will save $22.50 because she must first find the 25% sale price before taking the extra 50% reduction. samantha will save $15.00 because the two sales will combine for 75% off the original cost.

It seems most likely that ...

... Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction

In the real world, it seems probable that Samantha will be offered the choice of using the coupon or the sale discount. If she chooses tht 50% coupon, her savings will be $30. If she chooses the marked sale discount, her savings will be $15.

The scenario above assumes she gets 50% off the sale price of $45, so saves $15+22.50 = $37.50 off the original price.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.