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3 years ago

Compare.write <,> 7/8 23/24

Mathematics

1 answer:

Alisiya [41]3 years ago

8 0

7/8 < 23/24, because 7/8 is .875 and 23/24 is .958

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Write the equation of the line that passes through the given points in slope intercept form

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Answer:

y=3x

Step-by-step explanation:

To put this in slope intercept form, let’s first find the slope

To find slope, use the equation Y2-Y1/X2-X1

When we do this, we get 0-6/0-2

This simplifies out into -6/-2 which is 3

So our slope is 3. Our equation becomes y=3x+b

Now, we find our b

We don’t have to do any solving for this, since we have the point 0,0 listed for us, it goes through the origin and that is our y-intercept or b

So our final equation is y=3x

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1. The number of rabbits on an island is increasing exponentially.

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Answer:

<em>There are approximately 114 rabbits in the year 10</em>

Step-by-step explanation:

<u>Exponential Growth </u>

The natural growth of some magnitudes can be modeled by the equation:

$P=P_o(1+r)^t$

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We are given two measurements of the population of rabbits on an island.

In year 1, there are 50 rabbits. This is the point (1,50)

In year 5, there are 72 rabbits. This is the point (5,72)

Substituting in the general model, we have:

$50=P_o(1+r)^1$

$50=P_o(1+r)\qquad\qquad[1]$

$72=P_o(1+r)^5\qquad\qquad[2]$

Dividing [2] by [1]:

$\displaystyle \frac{72}{50}=(1+r)^{5-1}=(1+r)^{4}$

Solving for r:

$\displaystyle r=\sqrt[4]{\frac{72}{50}}-1$

Calculating:

r=0.095445

From [1], solve for Po:

$\displaystyle P_o=\frac{72}{(1+r)^5}$

$\displaystyle P_o=\frac{72}{(1.095445)^5}$

$P_o=45.64355$

The model can be written now as:

$P=45.64355(1.095445)^t$

In year t=10, the population of rabbits is:

$P=45.64355(1.095445)^{10}$

P = 113.6

$P\approx 114$

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Answer:

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