What common fraction is equal to the sum \(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{512}\)?

Ron and Martin are playing a game with a bowl containing 39 marbles. Each player takes turns removing 1, 2, 3 or 4 marbles from the bowl. The person who removes the last marble loses. If Ron takes the first turn to start the game, how many marbles should he remove to guarantee he is the winner?

The effectiveness of Donovan’s cold medication decreases geometrically, retaining one-fourth of its original effectiveness after four hours. If Donovan takes 500 mg of medication every four hours beginning at 8:00 a.m., how much effective medication remains in his body at 6:00 p.m.? Express your answer as a mixed number.

The first three terms of an arithmetic sequence are 17x + 20, 18x – 3 and 20x + 1, in that order. What is the value of x?

Laree notices that the current mileage on her car is a multiple of 1000 and is a perfect cube. She does some calculations and determines that she will have to drive another 4921 miles before the number of miles on her car is a perfect cube again. What is Laree’s current mileage?

If the15 teams in a soccer league each play eight games in a season, what is the total number of games played during the season?

When an integer is doubled and increased by 3, the result is 5 less than the square of the integer. What is the sum of all such integers?

Starting at the origin of a coordinate plane, an ant crawls 1 unit to the right, 2 units up, 3 units to the right, 4 units up, 5 units to the right and 6 units up. How far from the origin is the ant currently located?

Thomas learned to count in a base other than 10. Instead of writing 163, which is in base 10, Thomas writes 431. What base is Thomas using?

If today is Friday, what day of the week will it be 101 days from today?

Two distinct numbers are selected at random from the set {1, 2, 3, 4, 5, 6}. What is the probability that their product is an odd number? Express your answer as a common fraction.

GG’s shipping company ships golf balls in three different box sizes. The small box contains a dozen golf balls. The medium box is similar to the small box, but each dimension is doubled. The large box also is similar to the small box, but each dimension is tripled. If Jake orders one box of each size, how many golf balls will he receive?

A restaurant offers an incentive by giving a $5 coupon for every $40 spent during a calendar year. If Roberto spends $639 at the restaurant in a year, what is the total dollar value of the coupons he can expect to receive?

A pile of clay can be molded to form a solid cube with edges of length 10 cm. How many solid rectangular prisms with dimensions 2 × 4 × 5 cm can be made from the same amount of clay?

Every day, a cafeteria offers pizza, chicken and salad as lunch entrées. This comes with a choice of milk, juice, water or tea to drink and a cookie or brownie for dessert. If a different combination of one entrée, one drink and one dessert is tried every day, how many days does it take to try every combination?

Zoey has $2.90 in quarters, dimes and nickels. The number of nickels is one more than six times the number of quarters, and the number of dimes is four times the number of quarters. What is the total number of coins Zoey has?

Thirty percent of 80% of 20 is the same as what percent of 60% of 40?

To cater a party, Fancy Caterers charges a certain amount per guest plus a fixed delivery fee. The total cost for a party with 25 guests is twice the cost of a party with 10 guests. If the cost of a party with n guests is twice the cost of a party with 25 guests, what is the value of n?

What is the minimum number of people that must be in a room to guarantee that at least one person has a birthday whose day is a single digit, assuming that no two people have the same birthday?

The mean of the first five terms of an arithmetic sequence is 27, and the mean of the first eight terms of the same sequence is 39. What is the absolute difference between the first and second terms of this sequence?