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F, T, T, F

Step-by-step explanation:

1) F because the die is labeled 1 through 8. Because 1 through 3 are included within the die, it is possible to roll a number less than 4.

2) T because the die is from 1 to 8, meaning 5 through 8 - number 4 and greater - are able to be rolled. Rolling a 4, 5, 6, 7, or 8, has a probability of 5/8 chance of being rolled, making it a likely roll (as 5/8 is over a 50% chance).

3) T as numbers are always either even or odd, meaning it is impossible not to roll an even or odd number. In other words, it is certain to roll an even or odd number.

4) F as it is extremely likely to roll a number less than 7 with a whopping 6/8 chance of being rolled. What would be unlikely is rolling a number greater than 7.

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.

y=20x

: )

hope this