Find the sum of all the elements of this finite geometric sequence:
1, 2, 4, 8, 16, 32, 64, . . . , 1024.
Two candles are of the same height.
One burns in four hours, while the other burns in five hours.
When is one twice the height of the other?
In Morse code, each symbol is either a dot or a dash.
How many different sequences of 8 symbols are possible?
One apple and one banana together cost $3.
One apple and one carrot together cost $4.
One banana and one carrot together cost $5.
How much does an apple cost?
You have two buckets. The first bucket contains 5 liters of water and the second contains 5 liters of milk.
If you pour 1 liter of the water into the milk and then return 1 liter of the mixture to the water bucket, what are the proportions of milk to water in the first bucket?
I would like to write 1000 as n2 - m2, where n and m are positive integers.
Which number can be a solution for the problem?
A is the set of all points (x,y) in the shaded region.
Find the set B consisting of all points (2x, -y)?
A perfect cube is an integer whose cube root is an integer.
For example, 64 and 125 are perfect cubes.
A and B are perfect cubes.
Which of the following will NOT necessarily be a perfect cube?
100% of 90 girls and 90% of 100 boys have shown up in the concert hall on time.
10 teachers came even earlier.
What percentage of the people were late?
Divide 77 into three parts so that one is 150 percent of each of the other two.
What is the smallest number?
Engineers at a race company make three discoveries.
The first invention saves 50% of fuel, the second 30%, and the third 20%.
If the company uses all three innovations at once, how much fuel does a car consume compared with a normal car?
The average age of all teachers and students in a school is 15.
The average age of the teachers is 33.
The average age of the students is 12.
What is the ratio of teachers to students in the school?
One pipe can empty a pool 5 times faster than a second pipe.
When both pipes are opened, they empty the pool in five hours.
How long would it take to empty the pool if only the faster pipe is used?
The sum of the ages of four sisters is 30.
The sum of their ages four years ago was 15.
How old is the youngest sister?
A retailer offers a 25% discount off the normal price of a wooden puzzle.
She makes a profit of 25% over the cost of the puzzle.
What is her profit if the normal price of the puzzle is $20?
An outlet pipe can drain a full pool in 12 hours.
An inlet pipe can fill the empty pool in 8 hours.
The performance of the pipes does not depend on the water volume in the pool.
If both valves are opened, how long will it take to fill the pool?
A circle of radius 3 is drawn centered at the origin.
How many squares of side length 1 and integer coordinate vertices are inside the circle or intersect it?
Mrs. Smith puts $10,000 into a saving account that earns 2% interest compounded annually.
Which expression can be used to find the value of her money in the account at the end of the third year?
James has scored an average of 10 on his first 10 tests.
What score should he get in his eleventh test, so that his average moves up to 11?
Gerry earns 9% commission for each camera sold.
Today, he earned $44.1 commission.
What was his sales total for today?
In a shop, two liters of water costs $1, two liters of natural syrup cost $21, and two liters of the beverage that includes both costs $2.
The shop does not charge a premium for mixing the beverage.
What part of this beverage is the syrup?
If 15 students occupy 5/6 of the seats in the classroom, how many students would occupy 2/3 of the seats in the classroom?