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kotegsom [21]
3 years ago
15

for breakfast, Clarissa can choose from oatmeal, cereal, French toast, or scrambled eggs. She thinks that if she selects a break

fast at random, it is likely that it will be oatmeal. Is is she correct? Explain your reasoning.
Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
5 0
I think she is wrong because she can choose each one equally. Imagine it being a spinner with 4 equal sections each one can be chosen at te same rate.
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Solve equation, check for extraneous solutions
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Start with

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We observe that both fractions are not defined if n=0. So, we will assume n \neq 0.

We multiply both numerator and denominator of the first fraction by 3 and we sum the two fractions:

1=\dfrac{3}{3n^2}+\dfrac{n^2-4n-5}{3n^2} = \dfrac{n^2-4n-2}{3n^2}

We multiply both sides by 3n^2:

n^2-4n-2=3n^2

We move everything to one side and solve the quadratic equation:

2n^2+4n+2=0 \iff 2(n^2+2n+1)=0 \iff 2(n+1)^2=0 \iff n+1=0 \iff n=-1

We check the solution:

1=\dfrac{1}{1}+\dfrac{1+4-5}{3} \iff 1 = 1+0

which is true

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