How many distinct 9-letter words starting with “i” can be formed from the word “committee”?

We have already chosen "i" to be the first letter. This means that we still have 8 letters that we can use as the second letter. Once that letter is chosen, we still have 7 letters that we can use as the third letter, and so on. This means we have

ways of choosing the remaining 8 letters.

However, some of the 8 available letters are equal: we have 2 m's, 2 t's and 2 e's. This means that we overcounted the number of words on the reasoning above. We can correct the counting by dividing three times by 2!, one time for each of the repeated letters.

The final answer is

4x and 6y

im not sure though

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.