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3 years ago

How do you find a polynomial and factor it completely?

Mathematics

1 answer:

natulia [17]3 years ago

6 0

a² + 10a + 16

Find two numbers whose product equals 16 and sum equals 10:

Product = 16 Sum = 10

1 * 16 1 + 16 = 17 doesn't work

2 * 8 2 + 8 = 10 THIS WORKS!

4 * 4 4 + 4 = 8 doesn't work

Since 2 & 8 satisfy our requirements, those are the values that go into the parentheses.

Answer: (a + 2)(a + 8)

Note: when there is a coefficient for a², a different method is used to find the factors.

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nata0808 [166]

Answer:

P(0) = 0.055

P(1) = 0.16

P(2) = 0.231

P(3) = 0.224

P(4) = 0.162

P(5 or more) = 0.168

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Here λ = 2.90 is the average number of bacteria colonies per field.

This means that $\mu = 2.90$

Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more.

$P(0) = \frac{e^{-2.9}*(2.9)^{0}}{(0)!} = 0.055$

$P(1) = \frac{e^{-2.9}*(2.9)^{1}}{(1)!} = 0.16$

$P(2) = \frac{e^{-2.9}*(2.9)^{2}}{(2)!} = 0.231$

$P(3) = \frac{e^{-2.9}*(2.9)^{3}}{(3)!} = 0.224$

$P(4) = \frac{e^{-2.9}*(2.9)^{4}}{(4)!} = 0.162$

5 or more:

This is

$P(X \geq 5) - 1 - P(X < 5)$

In which:

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.055 + 0.16 + 0.231 + 0.224 + 0.162 = 0.832$

$P(X \geq 5) - 1 - P(X < 5) = 1 - 0.832 = 0.168$

P(5 or more) = 0.168

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3 years ago