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olga55 [171]
3 years ago
11

Arithmetic average of real nonnegative numbers is always smaller than or equal to geometric average. Group of answer choices Tru

e False
Mathematics
1 answer:
noname [10]3 years ago
4 0

Answer:

False

Step-by-step explanation:

Actually, the arithmetic average (or mean) is always greater or equal than the geometric average. This is known as the Arithmetic-Geometric inequality (AM inequality). Let a,b be two real numbers, then the AM inequality states that

\frac{a+b}{2}\geq \sqrt{ab}

To see that the given statement is false, consider a=1, b=3. The arithmetic mean is equal to (1+3)/2=2, and the geometric mean is equal to \sqrt{1\cdot 3}=\sqrt{3} but 2>\sqrt{3}, contrary to the statement (arithmetic>geometric in this case).

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A press release describing the 1986 nonstop, round-the-world trip by the aircraft voyager including the following data:
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Answer:

a.) the average speed of the aircraft in miles per hour

115.76 miles/ hour

b.) the fuel consumption in miles per pound of fuel

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Step-by-step explanation:

A press release describing the 1986 nonstop, round-the-world trip by the aircraft voyager including the following data:

flight distance: 25,012 miles

flight time: 9 days, 3 min., 44 seconds

fuel capacity: nearly 9000 lbs.

fuel remaining at the end of flight: 14 gal.

To the maximum number of significant figure permitted, calculate:

a.) the average speed of the aircraft in miles per hour

Step 1

We convert the time to hours

flight time: 9 days, 3 min., 44 seconds

1 day = 24 hours

9 days =

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60 mins = 1 hour

3 mins =

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1 hour = 60 minutes

1 minute = 60 seconds

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If 3600 seconds = 1 hour

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Total number of hours spent = (216 + 0.05 + 0.0122222222) hours

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b.) the fuel consumption in miles per pound of fuel

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We determine how much fuel is used

We have 14 gallons of fuel left over

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14 gallons =

Cross Multiply

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1 gram / millilitre = 1 kilogram / litre

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37.09706kg =

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25012/8918.2009827 lbs = 2.8046015164 miles/lb of fuel

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