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Dovator [93]
2 years ago
6

A science class helped to estimate the population of various species in their local woods. Initially they tagged various numbers

of 3 different species. The
class then returned several weeks later to count each of the species that they had originally tagged. For each species, they kept track of the total
counted, and the number with tags. Here are their results:
Species
Number Initially
Tagged
Total Number
Counted
Number Counted with
Tags
Quail
43
51
29
Owl
37
18
7
Lynx
9
4
Based on the data samples collected, which statement shows a reasonable estimate?
There are about 87 owls in the woods.
There are more owls than quails in the woods.
There are approximately twice as many owls as lynxes.
The species that was tagged the most has the highest population
Mathematics
1 answer:
Morgarella [4.7K]2 years ago
8 0

Answer:

67

Step-by-step explanation:

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Explain how to find each root, with its multiplicity, for the polynomial y=x^5-27x^2.
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The roots of y = x^{5}-27\cdot x^{2} are 0 (multiplicity 2), -3 (multiplicity 1), -\frac{3}{2}+i\,\frac{3\sqrt{3}}{2} (multiplicity 1) and -\frac{3}{2}-i\,\frac{3\sqrt{3}}{2} (multiplicity 1).

The characteristics of the polynomial can be derived from algebraic techniques. Roots and multiplicity can be found by <em>factoring</em> the polynomial. The multiplicity is represented by a power binomial of the form:

(x-r_{i})^{m},\,m \le n (1)

Where n is the grade of the polynomial.

Now we proceed to factor the formula:

y = x^{5}-27\cdot x^{2}

y = x^{2}\cdot (x^{3}-27)

y = x^{2}\cdot (x^{2}+3\cdot x +9)\cdot (x-3)

Please notice that x^{2}+3\cdot x + 9 have two complex roots.

y = x^{2}\cdot \left(x+\frac{3}{2}-i\,\frac{3\sqrt{3}}{2}  \right)\cdot \left(x+\frac{3}{2}+i\,\frac{3\sqrt{3}}{3}  \right)\cdot (x-3)

The roots of y = x^{5}-27\cdot x^{2} are 0 (multiplicity 2), -3 (multiplicity 1), -\frac{3}{2}+i\,\frac{3\sqrt{3}}{2} (multiplicity 1) and -\frac{3}{2}-i\,\frac{3\sqrt{3}}{2} (multiplicity 1).

We kindly invite to see this question on polynomials: brainly.com/question/1218505

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Answer:

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Step-by-step explanation:

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Answer:

The answer is A. (-2,-2 and (2,2)

Step-by-step explanation:

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