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1. If four times a certain number is decreased by 5, the result is 25. What is the number?

2. For every integer m greater than 1, let ?m? be defined as the sum of the integers from 1 to m, inclusive. For instance, .

What is the value of

3.

If the circumference of the circle above is 10π, then what is the value of a^{2}+b^{2}?

4. A, B, C, D

How many different three-letter arrangements of the letters above are possible if no letter may be repeated? (An arrangement like ABC is distinct from an arrangement like BCA.)

5. If , then

6. Every term in a certain sequence is one less than three times the previous term. If the fourth term of this sequence is 95, what is the first term of the sequence?

7. If , what is the value of

8. Admission to a museum is $10 for each adult and $5 for each child. If a group of 30 people pays a total of $175 in admission, how many adults are in the group?

9.

The perimeter of the isosceles triangle above is 24. If the ratio of a to b is 2 to 3, what is the value of b?

10.

In the figure above, , , and . What is AD?