For many of us, the thought of snow brings hopes of snow days, sledding or skiing. For others it means traffic jams and shoveling. Unfortunately for Roger's father, he is in this second category. It usually takes Roger's father 35 minutes to get to work. However, after the snowstorm it took him an hour and 15 minutes to get to work. What was the percent increase in his commute time to work? Express your answer to the nearest whole number.

114%

Step-by-step explanation:

From the question, we are informed that it usually takes Roger's father 35 minutes to get to work but that after the snowstorm it took him an hour and 15 minutes to get to work.

We should first convert 1 hour, 15 minutes to minutes. Since 60 minutes = 1 hour; Therefore, 1 hour, 15 minutes = 60 minutes + 15 minutes = 75 minutes.

The percent increase in his commute time to work will then be:

= [(75 - 35) / 35] × 100

= 40/35 × 100

= 114.28571%

= 114%

The percentage increase is 114%.

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.