The infinite sequence a₁, a₂,…, a_n,… is such that a₁ = 2, a₂ = -3, a₃ = 5, a₄ = -1, and a_n = a_n-4 for n > 4.  What is the sum of the first 97 terms of the sequence?

~$\sqrt{2\sqrt{63}+\frac{2}{8+3\sqrt{7}}}=$~

A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office.  In how many ways can the company assign 3 employees to 2 different offices?

From a group of 3 boys and 3 girls, 4 children are to be randomly selected.  What is the probability that equal numbers of boys and girls will be selected?

A student’s average (arithmetic mean) test score on 4 tests is 78.  What must be the student’s score on a 5th test for the student’s average score on the 5 tests to be 80?

A certain state has a sales tax of 5 percent on the portion of a purchase price that is greater than $100.  If a customer paid a sales tax of $4 on a particular item, what was the purchase price of the item?

In the xy-plane, what is the x-intercept of the line whose equation is 3y – 4x = 15?

A salesperson received a 6-percent commission on the amount of total sales up to and including $10,000, and an r-percent commission on the amount of total sales over $10,000.  If the salesperson received a total commission of $920 on total sales of $14,000, what was the value of r?

If ~$\left ( 2-\sqrt{5} \right )x=-1$~ , then x =

The circle shown has center R.  If arc UST has length 48π, what is the radius of the circle?