A bag contains 6 nickels and 14 pennies. What is the ratio, written in lowest terms, of nickels to the total number of coins in
2 answers:
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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>
This is the same as showing the following system of equations doesn't have a solution:
or in matrix form,
The quickest way to check if there is a solution is to check whether the coefficient matrix is invertible. If its determinant is 0, then it is not invertible.
And the quickest way to show that the determinant is 0 is by observing that the third row is a linear combination of the first two rows:
(-2, 9, 6) - (-3, 2, 1) = (-2 + 3, 9 - 2, 6 - 1) = (1, 7, 5)
So there are indeed no such scalars <em>c₁</em>, <em>c₂</em>, and <em>c₃</em>.