Answer:
The quadratic mean of 2 real positive numbers is greater than or equal to the arithmetic mean.
Step-by-step explanation:
x and y Quadratic Mean Arithmetic mean
3 and 3 3 3
2 and 3 2.55 2.5
3 and 6 4.74 4.5
2 and 5 3.8 3.5
2 and 17 12.1 9.5
18 and 28 23.5 23
10 and 48 34.7 29
The quadratic mean is always greater than the arithmetic mean except when x and y are the same.
When the difference between the pairs is small the difference in the means is also small. As that difference increases the difference in the means also increases.
So we conjecture that the quadratic mean is always greater than or equal to the arithmetic mean.
Proof.
Suppose it is true then:
√(x^2 + y^2) / 2) ≥ (x + y)/2 Squaring both sides:
(x ^2 + y^2) / 2 ≥ (x + y)^2 / 4 Multiply through by 4:
2x^2 +2y^2 ≥ (x + y)^2
2x^2 +2y^2 >= x^2 + 2xy + y^2
x^2 + y^2 >= 2xy.
x^2 - 2xy + y^2 ≥ 0
(x - y)^2 ≥ 0
This is true because the square of any real number is positive so the original inequality must also be true.
Answer:
Step-by-step explanation:
Well scientific notation is (something*10^(other thing))
so we count have many zeroes there are, and there are 6, so we move the decimal point 6 times and get
Answer:
The expected cost is $8.75
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Step-by-step explanation:
Given
--- If Bob and Anna meet
--- If Bob and Anna do not meet
Required
The expected cost of Bob's meal
First, we list out all possible time both Bob and Anna can select
We have:
The outcome of them meeting at the same time is:
The probability of them meeting at the same time is:
The outcome of them not meeting:
The probability of them meeting at the same time is:
The expected cost is then calculated as:
Take LCM
<em>The expected cost is $8.75</em>
Answer:
80%
Step-by-step explanation:
1200/1500
12/15 = 0.8
80%
