A pizza place near your office has small cheese pizzas for $4 and small pepperoni pizzas for $5. You are going to pick up pizzas
1 answer:
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Find the powers
$a^{2}=5+2 \sqrt{6}$
$a^{3}=11 \sqrt{2}+9 \sqrt{3}$
The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.
Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$
so fits with the other answers.
Jake's guesses are illustrations of probabilities.
The probability that Jake's guesses are correct is 1/720
The sample size is:
--- 10 different numbers
The probability that Jake's guesses are correct is as follows:
- 1st guess = 1/10
- 2nd guess = 1/9
- 3rd guess = 1/8
So, the required probability is:
Hence, the probability that Jake's guesses are correct is 1/720
Read more about probabilities at: