Harmonic mean - math word problems - last page
The harmonic mean is a type of average that is particularly useful for calculating rates, ratios, or situations involving reciprocals.It is calculated as the reciprocal of the arithmetic mean of the reciprocals of a set of numbers.
The harmonic mean is often used when dealing with averages of quantities like speed, where time and distance are inversely related. It tends to be less affected by extremely large values in a dataset, making it more appropriate for skewed distributions compared to the arithmetic mean.
A key property of the harmonic mean is that it is always less than or equal to the arithmetic mean and the geometric mean for any set of positive numbers.
It is commonly applied in finance, such as calculating the average price-to-earnings ratio, and in physics, such as finding equivalent resistance in parallel circuits. The harmonic mean is not suitable for datasets containing zero or negative values, as it is undefined in such cases.
Number of problems found: 186
- Drinking water
A man drinks a keg of water in 36 days, and a woman drinks in 65 days. How many days do they consume a keg together? - Pool
If water flows into the pool through two inlets, it will fill for 20 hours. If the first inlet fills the pool 8 hour longer than the second, how long does it take to fill with two inlets separately? - Cyclist
The cyclist goes uphill 2 km for 7.4 minutes and downhill minutes for 4.8 minutes. Both are applied to the pedals with the same force. How long does he pass 2 km by plane? - Energy saving
They released three different independent inventions saving 15%, 17%, and 16% energy. Some considered that with the use of these inventions, the total savings would be 15% + 17% + 16% = 48%. Is this true? How much will the percent of energy save all three
- Electronics: Resistors in parallel
Concerning calculating the resistance of the parallel combination of resistors: (1)/(R) = (1)/(R1) + (1)/(R2) Calculate the R, if R1 = 17Ω a R2 = 20Ω - Tractors
Fields go plow two tractors with various performances. The first tractor plows the whole field in 20 hours. The second tractor plows the whole field 4 hours kratšie. How long does it take to plow the whole field with two tractors?
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