# Week One Assignment

Week One Assignment

Patrick Cain

Mat222: Intermediate Algebra

Joseph Oslakovic

August 27, 2012

Week One Assignment

I will set up two ratios and show an appropriate variable and write the equation. First problem is: Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population? In the Capture-Recapture method we notice that we are supposed to assume that the ratio of the original 50 tagged bears to the entire population is equal to the ratio of the recaptured tagged bears to the size of the sample (Dugopolski, 2012). First, we will set up the ratios. Ratio of original tagged bears tot eh whole population is 50 X The ratio of the recaptured tagged bears are 2

100 50 = 2 This is the proportion ready to solve. I will cross multiply x 100 setting the extremes equal to the means. 100 (50) = 2x 100 and 50 are the two extremes, while x and 2 are the means.

5000 = 2x Divide both sides by 2.

2 2

X = 2500 The bear population in Keweenaw Peninsula is approximately 2500.

For the second problem, we are to solve for y. When looking at the equation, I see that it is a single fraction, or ratio, on both sides of the equal sign, which means it is a proportion that can be solved by cross multiplying the extremes and means. y - 1 = - 3 Given equation.

x + 3 4

4(y-1) = -3(x + 3) Result from cross multiplying. -4 + 4y = -9 + -3x...

References: Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing.

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