When Andy, Becky, Chad, Dave, Eleanor and Fred line up in a row, what is the probability that Andy and Becky are not standing next to each other? Express your answer as a common fraction.

 Tom buys two shirts and one pair of socks for $15. Sam buys one shirt and two pairs of socks for $12. How much will Jim pay for 15 shirts and 10 pairs of socks?

 Next week, to celebrate 50 years in business, the grocery store is giving away a bag of free groceries to every 150th customer, starting with the 150th customer. If 2000 customers shop at the store next week, what is the percentage of customers who will receive a free bag of groceries? Express your answer to the nearest hundredth.

A square is inscribed in a circle with radius 6 inches. What is the area inside the circle but outside the square? Express your answer to the nearest whole number.

The kettle in Kerry’s kitchen is 80% full of water. After 25% of the water in it has been poured out, there are 1200 ml of water left. How many liters of water does Kerry’s kettle hold when it is full? 

Six friends A, B, C, D, E and F eat dinner at a local restaurant. A eats there every day. B eats there every other day. C eats there every third day. D eats there every fourth day. E eats there every fifth day. F eats there every sixth day. If all six of them eat together at the restaurant on January 15, how many more times will they eat together in that calendar year?

 Each of Jonathan’s bicycle tires revolved 2327 times as he rode three miles. What is the diameter of one of Jonathan’s bicycle tires, in inches? Express your answer to the nearest whole number.

 Let PQRS be an isosceles trapezoid with bases PQ = 100 units and RS = 26 units. Suppose PS = QR = x units and a circle with center on base PQ is tangent to both segments PS and QR. If x is the smallest possible value, then what is the value of x\(^2\) ? 

If a Δ b = \(\dfrac{a-b}{2b+6}\) , what is the value of 3 Δ (5 Δ 3)? Express your answer as a common fraction.  

How many integers n satisfying 3000 ≤ n ≤ 4000 have the product of their digits equal to zero?

On the number line, what percent of the interval –10 ≤ x ≤ 10 satisfies the inequality \(x+2< \dfrac{5}{x-2}\)?

 How many sides does a convex polygon with 20 diagonals have?

At Melville Middle School 73 students are in the band, 65 students are in the chorus and 114 students play sports. Thirty-two are both in the band and play sports, 12 play sports and sing in the chorus, but no one is in both the band and the chorus. Five hundred fifty-eight students do not participate in any of these activities. How many students are there at Melville Middle School? 

The largest angle of a quadrilateral is four times its smallest angle. Another angle is 10 degrees more than twice the smallest. The fourth angle is 60 degrees less than 3 times the smallest. What is the measure of the largest angle? 

 The sum of the digits of a two-digit positive integer is 8. When the digits are reversed, the new integer is 3 more than 4 times the original integer. What is the new integer?  

If f(x) = 5x, and g(x) = f(x) –3x – 7, what is the value of g(8)?

 A circle with a radius of \(4\sqrt{3}\) cm is inscribed inside a regular hexagon. What is the area of the hexagon? Express your answer in simplest radical form.

 A rectangle has been partitioned into nine squares, as shown. If the area of each of the three medium squares is 100 square units, what is the area of the largest square?  

What is the integer closest to \(\sqrt{150}+\sqrt{75}\)?

 A regular hexagon and a regular octagon have the same perimeter. If the side lengths of these polygons are whole numbers and the sum of the perimeters is less than 200, how many different pairs of hexagons and octagons can be made?