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A cube has a volume of 512 cubic centimeters. What is the surface area of the cube?
A companys revenue increased from $1.2 million to $1.56 million over one year. What is the percentage increase in revenue?
First, find the increase: $1.56 million - $1.2 million = $0.36 million.
A car travels 120 kilometers in 1.5 hours. If it continues at the same speed, how long will it take to travel 320 kilometers?
On Mars, a new settlement uses a timekeeping system where a Martian day (sol) is divided into 28 Mars-hours. Each Mars-hour is further divided into 75 Mars-minutes. How many total Mars-minutes are there in a Martian day?
To determine the total number of Mars-minutes in a Martian day, we start by analyzing the structure of a sol:
We multiply the number of Mars-hours by the number of Mars-minutes per hour to find the total number of Mars-minutes in a sol:
A venture capitalist is evaluating 12 clean technology startups, each working on a unique renewable energy solution. She plans to invest in exactly 4 of them, but wishes to ensure that no two selected startups are in the same environmental category. If there are exactly 4 categories—solar, wind, geothermal, and hydro—and each startup belongs to one category—how many ways can she choose 4 startups, one from each category?
Since each category has exactly 3 startups, and we must pick one from each, the number of valid combinations is:
This counts one startup selected from each category, with no restriction on order (but since we are choosing one per category, each combination is uniquely determined by category selection).