<em>Answer:</em>
<em>There would be 173,535 lionfish after 6 years.</em>
<em>Step-by-step explanation:</em>
<em>Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:</em>
<em></em>
<em>A)</em>
<em>8000 x 1.67 ^ n = f </em>
<em>B)</em>
<em>8000 x 1.67 ^ 6 = X</em>
<em>8000 x 21.691961596369 = X</em>
<em>173,535.692770952 = X </em>
<em>C)</em>
<em>(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f</em>
<em>Therefore, there would be 173,535 lionfish after 6 years.</em>
Answer:
see explanation
Step-by-step explanation:
A translation of 4 units down means subtract 4 from the y- coordinate of the original point and a translation of 3 units left means subtract 3 from the original x- coordinate, thus translation rule is
(x, y ) → (x - 3, y - 4 )
Thus
C(8, 3 ) → C'(8 - 3, 3 - 4 ) → C'(5, - 1 )
Since the direction is not specified, it can be safe to assume that the direction of rotation is counterclockwise.
300 degrees is 60 degrees less than 360 degrees, which is a full rotation. Thus, 300 degrees counterclockwise is the same as 60 degrees clockwise.
Note that this shape is a hexagon. Thus, we can divide a hexagon into 6 equilateral triangles, each with measures of 60 degrees. Just move OQ to the adjacent clockwise equilateral triangle and see what it overlaps with.
OQ is the altitude of the equilateral triangle, so our answer will be the altitude of the adjacent clockwise equilateral triangle.
The answer is OF.
Answer:
(b) 1.95
Step-by-step explanation:
One of the easiest ways to evaluate an arithmetic expression of almost any kind is to type it into an on-line calculator. Many times, typing it into a search box is equivalent.
<h3>Application</h3>
See the attachment for the search box input (at top) and the result. This calculator has the benefit that it <em>always follows the Order of Operations</em> when evaluating an expression. (Not all calculators do.)
ln(7) ≈ 1.95
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<em>Additional comment</em>
If your math course is asking you to evaluate such expressions, you have probably been provided a calculator to use, or given the requirements for a calculator suitable for use in the course.
There are some very nice calculator apps for phone and tablet. Many phones and tablets already come with built-in calculator apps. For the purpose here, you need a "scientific" or "graphing" calculator. A 4-function calculator will not do.
As with any tool, it is always a good idea to read the manual for your calculator and work through any example problems.
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Years ago, handheld calculators were not available, and most desktop calculators were only capable of the basic four arithmetic functions. Finding a logarithm required use of a table of logarithms. Such tables were published in mathematical handbooks, and extracts of those often appeared as appendices in math textbooks used in school.