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GarryVolchara [31]
4 years ago
14

The bird population on an island is declining at a rate of 2.2% per year. If the population was 3500 in the year 2009, which is

the best prediction of the population in the year 2014
Mathematics
2 answers:
zalisa [80]4 years ago
8 0

Answer:

The answer above me is correct including their math work!

andreyandreev [35.5K]4 years ago
3 0
In the year 2009 there were 3500 birds on an island. If the bird population is declining 2.2% per year it means that in the year 2014 we will have 3500*(1-0.022^{5})=3500*0.978 x^{5}= 3131.57 birds. 
The best prediction is that in the year 2014 the bird population will be 3132.
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find the coordinates of point Z that splits the segment XY located 3/7 of the way between X(-2,1) and Y(4,5)
Drupady [299]

Answer:

Z(-0.2, 2.2).

Step-by-step explanation:

We will use section formula when a point, say P, divides any segment ,say AB, internally in the ratio m:n.

[x=\frac{mx_2+nx_1}{m+n}, y= \frac{my_2+ny_1}{m+n}]

We have been given the points of segment XY as X at (-2,1) and Y at (4,5) and ratio is 3:7.

(x_1, y_1)=(-2,1)

(x_2, y_2)=(4,5)  

m:n=3:7    

Upon substituting coordinates of our given points in section formula we will get,

[x=\frac{(3*4)+(7*-2)}{3+7}, y= \frac{3*5+7*1}{3+7}]

[x=\frac{12-14}{10}, y= \frac{15+7}{10}]

[x=\frac{-2}{10}, y= \frac{22}{10}]

[x=-0.2, y= 2.2]

Therefore, coordinates of point Z will be (-0.2, 2.2).

7 0
3 years ago
The All-Clean Laundry Company washes towels for a nearby hotel. The function f(x)
IRINA_888 [86]

Answer:

Step-by-step explanation:

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5 0
3 years ago
Graph and label the image of the figure below after a dilation by a factor of 1/2.
neonofarm [45]
Answer:

M' (1.5, -1), F' (2, -1), L' (0.5 -2.5), W' (2.5, -2.5)

see graph below

Explanation:

Given:

The image of a quadrilateral on a coordinate plane

To find:

The coordinates of the new image after dilation of 1/2 have been applied to the original image.

Then graph the coordinates

First, we need to state the coordinates of the original image:

M = (3, -2)

F = (4, -2)

L = (1, -5)

W = (5, -5)

Next, we will apply a scale factor of 1/2:

\begin{gathered} Dilation\text{ rule:} \\ (x,\text{ y\rparen}\rightarrow(kx,\text{ ky\rparen} \\ where\text{ k = scale factor} \\  \\ scale\text{ factor = 1/2} \\ M^{\prime}\text{ = \lparen}\frac{1}{2}(3),\text{ }\frac{1}{2}(-2)) \\ M^{\prime}\text{ = \lparen}\frac{3}{2},\text{ -1\rparen} \\  \\ F\text{ = \lparen}\frac{1}{2}(4),\text{ }\frac{1}{2}(-2)) \\ F^{\prime}\text{ = \lparen2, -1\rparen} \end{gathered}\begin{gathered} L\text{ = \lparen}\frac{1}{2}(1),\text{ }\frac{1}{2}(-5)) \\ L^{\prime}\text{ = \lparen}\frac{1}{2},\text{ }\frac{-5}{2}) \\  \\ W\text{ = \lparen}\frac{1}{2}(5),\text{ }\frac{1}{2}(-5)) \\ W^{\prime}\text{ = \lparen}\frac{5}{2},\text{ }\frac{-5}{2}) \end{gathered}

The new coordinates:

M' (3/2, -1), F' (2, -1), L' (1/2, -5/2), W' (5/2, -5/2)

M' (1.5, -1), F' (2, -1), L' (0.5 -2.5), W' (2.5, -2.5)

Plotting the coordinates:

3 0
1 year ago
Which relationship describes angles 1 and 2?
Mnenie [13.5K]

Answer:

Step-by-step explanation:

1 and 2 are vertical angles

6 0
3 years ago
What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negat
CaHeK987 [17]

Answer:

Reflection over the y-axis and rotation of 180°

Step-by-step explanation:

We have,

Rectangle ABCD with co-ordinates A(-4,2), B(-4,1), C(-1,1) and D(-1,2).

It is transformed to a new rectangle A'B'C'D' with co-ordinates A'(-4,-2), B'(-4,-1), C'(-1,-1) and D'(-1,-2).

The graph of both the triangles is shown below.

we see that,

The rectangle ABCD is reflected about y-axis and then rotated 180° to obtain A'B'C'D'.

                     Reflected about y-axis                     Rotation of 180°

A= (-4,2)                     (4,2)                                              A'= (-4,-2)

B= (-4,1)                      (4,1)                                                B'= (-4,-1)

C= (-1,1)                       (1,1)                                                 C'= (-1,-1)

D= (-1,2)                      (1,2)                                                 D'= (-1,-2)

Hence, the second rectangle is formed by: Reflection over the y-axis and rotation of 180°.

5 0
3 years ago
Read 2 more answers
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