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RideAnS [48]
3 years ago
8

And a wildlife preserve 46 ducks are captured tagged and then released. Later to her ducks are examined in four of the 200 ducks

are found to have tags. Estimate the number of ducks in the preserve
Mathematics
1 answer:
docker41 [41]3 years ago
4 0

Answer:

2300

Step-by-step explanation:

We are given that

Out of 200 , four ducks are tagged.

We have to find the number of ducks in the preserve if 46 ducks are tagged.

Let x be the number of ducks in the preserve.

If number of tagged ducks increases then number of preserved ducks also increases.It is in direct proportion.

According to question

\frac{x}{46}=\frac{200}{4}

x=\frac{200\times 46}{4}

x=50\times 46

x=2300

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(1 point) Linear System - Three Variables Solve the following system of equations using Gaussian elimination method. If there ar
EastWind [94]

Answer:

x=\frac{-363}{70} ≈ -5.1857

y=\frac{-192}{35} ≈ -5.4857

z=\frac{313}{84} ≈ 3.7262

Step-by-step explanation:

Rewrite the equation system as:

6x+8y=-75

-3x+6y+6z=5

2x-9y=39

Now, write the system in its augmented matrix form:

\left[\begin{array}{cccc}6&8&0&-75\\-3&6&6&5\\2&-9&0&39\end{array}\right]

applying row reduction process to  its associated augmented matrix:

Swap R1 and R3, and then Swap R1 and R2:

\left[\begin{array}{cccc}-3&6&6&5\\2&-9&0&39\\6&8&0&-75\end{array}\right]

R3+2R1

\left[\begin{array}{cccc}-3&6&6&5\\2&-9&0&39\\0&20&12&-65\end{array}\right]

3R2+2R1

\left[\begin{array}{cccc}-3&6&6&5\\0&-15&12&127\\0&20&12&-65\end{array}\right]

15R3+20R2

\left[\begin{array}{cccc}-3&6&6&5\\0&-15&12&127\\0&0&420&1565\end{array}\right]

Now we have a simplified system:

-3x+6y+6z=5\\0-15y+12z=127\\0+0+420z=1565

-3x+6y+6z=5\hspace{5 mm}(1)\\0-15y+12z=127\hspace{3 mm}(2)\\0+0+420z=1565\hspace{3 mm}(3)

From (3):

z=\frac{313}{84} (4)

Replacing (4) in (2)

y=\frac{-192}{35} (5)

Finally replacing (5) and (4) in (1)

x=\frac{-363}{70}

7 0
3 years ago
A shade of green paint is made by mixing yellow paint and blue paint in the ratio 5:2. Mel has 30 litres of yellow paint and 9 l
vodomira [7]

Answer:

31.5 litres

Step-by-step explanation:

If Mel uses all 30 litres of yellow paint, then:

5 / 2 = 30 / x

5x = 60

x = 12

Mel would need 12 litres of blue paint, but she only has 9 litres.  So the amount of yellow paint she needs is:

5 / 2 = x / 9

2x = 45

x = 22.5

Mel will use 22.5 litres of yellow paint with 9 litres of blue paint to make a total of 31.5 litres of green paint.

4 0
3 years ago
Janet has $75 to spend at the mall. She has already spent $28. She wants to buy games that cost $15 each, including tax. Enter t
serg [7]

Answer:

3 games

Step-by-step explanation:

The computation of the maximum number of games that he could buy is shown below:

= Amount available - already spent

= $75 - $28

= $47

If each game cost $15

So, the maximum no of games is

= $47 ÷ $15

= 3.133

= 3 games

3 0
2 years ago
Given 8x + 2 = 3 - x; x =
schepotkina [342]

Answer:

x = 1/9

Step-by-step explanation:

8x + 2 = 3 - x

Add x to both sides.

9x + 2 = 3

Subtract 2 from both sides.

9x = 1

Divide both sides by 9.

x = 1/9

3 0
3 years ago
Read 2 more answers
1. Find the midpoint of AB<br> given A(-3, -4) and B(1,6)
emmainna [20.7K]

Answer:

-1,1

Step-by-step explanation:

because if you plot the points that is half.

7 0
3 years ago
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