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3 years ago

Factor the trinomial. p2 - 4p - 5 What is the a, b and c?

Mathematics

1 answer:

Mademuasel [1]3 years ago

3 0

Answer:

(p - 5)(p + 1)

Step-by-step explanation:

Given

p² - 4p - 5

Consider the factors of the constant term (- 5) which sum to give the coefficient of the x- term (- 4)

The factors are - 5 and + 1 , since

- 5 × + 1 = - 5 and - 5 + 1 = - 4, then

p² - 4p - 5 = (p - 5)(p + 1) ← in factored form

The standard form of a trinomial is

ax² + bx + c ( a ≠ 0 )

p² - 4p - 5 ← is in standard form

with a = 1, b = - 4 and c = - 5

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Answer:

a) 3354 seconds

b) 6294 seconds

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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(a) The cutoff time for the fastest 5% of athletes in the men's group, i.e. those who took the shortest 5% of time to finish.

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The cutoff for the shortest 5% is the 5th percentile, which is X when Z has a pvalue of 0.05. So X when Z = -1.645.

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$X - 4313 = -1.645*583$

$X = 3354$

Cutoff of 3354 seconds.

(b) The cutoff time for the slowest 10% of athletes in the women's group.

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$1.28 = \frac{X - 5261}{807}$

$X - 5261 = 1.28*807$

$X = 6294$

Cutoff time of 6294 seconds

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