Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A farmer wanted to estimate how many moles were living on his property, so he marked $39$ of them with tags. A few weeks later, the farmer drove around his property and noticed $21$ tagged moles out of the $420$ moles he counted. To the nearest whole number, what is the best estimate for the mole population?

View step-by-step help

View step-by-step help

Estimate population size using proportions

Full solution

Q. A farmer wanted to estimate how many moles were living on his property, so he marked

39

of them with tags. A few weeks later, the farmer drove around his property and noticed

21

tagged moles out of the

420

moles he counted. To the nearest whole number, what is the best estimate for the mole population?

Set up proportion: Step $1$ : Set up the proportion based on the capture-recapture method. $\newline$ We know: $\newline$ - Tagged moles found: $21$ $\newline$ - Total moles counted in second capture: $420$ $\newline$ - Moles originally tagged: $39$ $\newline$ Let $M$ be the estimated total mole population. $\newline$ Using the proportion: $\newline$ $(\text{tagged moles found} / \text{total moles counted}) = (\text{moles originally tagged} / \text{estimated total mole population})$ $\newline$ $\frac{21}{420} = \frac{39}{M}$
Solve proportion: Step $2$ : Solve the proportion by cross-multiplying to find $M$ . $\newline$ Cross-multiplying gives: $\newline$ $21 \times M = 39 \times 420$
Continue solving: Step $3$ : Continue solving for $M$ . $21 \times M = 16380$ $M = \frac{16380}{21}$ $M = 780$

More problems from Estimate population size using proportions

Question

Recently, frogs have been disappearing from the wild due to a contagious fungus. To monitor the current population in a certain region, Alan collects

28

frogs, marks them, and releases them. Later, he collects

110

frogs and finds that

11

of them are marked. To the nearest whole number, what is the best estimate for the frog population?

\_\_\_\_

Posted 8 months ago

Question

v

in the proportion.

\frac{v}{6} = \frac{25}{30}

v =

Posted 8 months ago

Question

\newline

\frac{7}{3}x= 21

\newline

x =

Posted 9 months ago

Question

Fabio and Carlos play on a basketball team together. In the last game, Fabio had

7

points less than

2

times as many points as Carlos. Fabio scored

31

points in the game. How many points did Carlos score in the last game?

Posted 7 months ago

Question

Stephanie is twice as old as her sister Rosa. If Stephanie is

\mathbf{1 8}

years old, how old is Rosa?

Posted 2 months ago

Question

Yohan is blowing up a spherical balloon. He blows

108 \pi

cubic centimeters of air with every breath. It takes him

72

breaths to fully inflate the balloon. What is the radius of the balloon in centimeters when it is fully inflated?

Posted 7 months ago

Question

4

gallons of gas in her car. If the fuel efficiency of her car is

23

miles per gallon, how many miles can Nadine drive before running out of gas?

Posted 7 months ago

Question

According to a website where users review their doctors,

116

119

users would recommend Dr. Gutierrez to their friends and family. If the website users are representative of Dr. Gutierrez's

1

293

patients, about how many patients would recommend Dr. Gutierrez to their friends and family?

\newline

(Round your answer to the nearest whole number.)

Posted 10 months ago

Question

12

chicken wings in

3

minutes. She eats the chicken wings at a constant rate.

\newline

How many chicken wings can Bao eat in

12

\newline

Posted 4 months ago

Question

The double number lines show the ratio of cups to gallons.

\newline

How many cups are in

3

\newline

Posted 10 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant