Consider a species that occupies a large, but fixed, number of islands. The distribution of the species across all islands is maintained by a balance between local extinctions and local colonization events. Devise a model for the relationship between the fraction of islands occupied by the species and time. Be clear to outline the assumptions you make and be sure to describe your key predictions

The correct option regarding the solutions of the system of equations for this problem are given as follows:

The solutions are (-1.19, 4.47) and (2.52, 27.92).

The system of equations for this problem is defined as follows:

Adding the two equations, we can eliminate the variable y, hence:

3x² - 4x - 9 = 0.

Meaning that this is a quadratic equation with the coefficients given as follows:

a = 3, b = -4, c = -9.

Inserting these parameters into a quadratic equation calculator, the solutions for x of the quadratic equation are given as follows:

x = -1.19 and x = 2.52.

When x = -1.19, the solution for y is calculated as follows:

y = 4x² + x = 4(-1.19)² - 1.19 = 4.47.

When x = 2.52, the solution for y is calculated as follows:

y = 4x² + x = 4(2.52)² + 2.52 = 27.92.

Meaning that the correct option is given by the second option.

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The cheapest way of buying exactly 7 litres with no extra is buying 500 ml bottle for £1.40

The amount of buying 7 litres of orange juice at the cheapest buy is £2.52

500 ml bottle for £1.40

Convert ml to liters:

500 ml = 0.5 liters

Unit rate = 0.5/1.40

= £0.36 per liter

2 litre carton for £2.50

Unit rate = 2/2.50

= £0.8 per liter

2 cartons for £4.50

Unit rate = 2/4.50

= $0.44 per carton

3 litre carton for £3.50

Unit rate = 3 / 3.50

= £0.86 per liter

The cheapest buy per liter of the orange juice is buying 500 ml bottle for £1.40.

Therefore, the cost of 7 liters at the cheapest buy

= £0.36 per liter × 7

= £2.52

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[tex]T=2\pi \sqrt{\cfrac{L}{g}}\implies \cfrac{T}{2\pi }=\sqrt{\cfrac{L}{g}}\implies \cfrac{T}{2\pi }=\cfrac{\sqrt{L}}{\sqrt{g}}\implies T\sqrt{g}=2\pi \sqrt{L} \\\\\\ \sqrt{g}=\cfrac{2\pi \sqrt{L}}{T}\implies (\sqrt{g})^2=\left( \cfrac{2\pi \sqrt{L}}{T} \right)^2\implies g=\left( \cfrac{2\pi \sqrt{L}}{T} \right)^2 \\\\\\ g=\cfrac{(2\pi \sqrt{L})^2}{(T)^2}\implies g=\cfrac{4\pi ^2L}{T^2}[/tex]

XY = 6 units  is the length of XY in AXYZ .

What is a right-angle triangle, exactly?

A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees.

                         Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

using the sine ratio in the right triangle and the exact value

  sin30° = 1/2, then

    sin30° = XY/XZ = XY/12 =  1/2  ( cross - multiply)

     2XY = 12  ( divide both sides by 2 )

        XY = 6

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The complete question is -

Use right triangle XYZ to complete the following parts.

Part A

12

XY =

30°

? Question

What is the length of XY in AXYZ?

Type the correct answer in the box. Use numerals instead of words.

units

Answer:

An Ideal solution follows the Raoult's law strictly

A Real solution shows deviation from the Raoult's law.

Step-by-step explanation:

The three type of solubility are highly soluble, sparingly soluble or insoluble.

The term solubility is defined as the maximum amount of a substance that will dissolve in a given amount of solvent at a specified temperature

Here we have to major three types of solubility are defined below.

As we all know that Temperature, pressure and the type of bond and forces between the particles are few among them, that are the 3 factors solubility depends on.

According to the concentration of solute dissolves in a solvent, the solutes are categorized into highly soluble, sparingly soluble or insoluble.

Here we have to know that if a concentration of 0.1 g or more of a solute can be dissolved in a 100ml solvent, then it is said to be soluble.

Where as the concentration below 0.1 g is dissolved in the solvent it is said to be sparingly soluble.  

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Each will get 3/5 cups of nuts by ratio and proportion concepts.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

We have to divide total nuts within 5 people.

so,

3 3/5 : 5

but first convert,

3 3/5 = 15/4

substitute,

15/4 : 5 = 15/20cups of nuts

simplify,

3/5 cups

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The measure of the exterior angle of the triangle is 139°.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

From the two given angles are 75° and 64° and exterior angle is 2.

Now, ∠2=75°+64°

∠2=139°

Therefore, the measure of the exterior angle of the triangle is 139°.

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The equation that represents the situation is

2p + 194.99 = 284.97

Option B is the correct answer.

The price of each game is $44.99.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Game system price = $194.99

Total price = $284.97

194.99 + 2 games = $284.97

Games = p

Now,

The price of each game.

194.99 + 2p = 284.97
2p = 284.97 - 194.99

2p = 89.98

p = 44.99

Thus,

The equation is 194.99 + 2p = 284.97.
The price of each game is $44.99.

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The given equation does not give same solution set.The first equation gives negative number and second equation gives positive number as a solution.

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally,Compare the two values whether it is less than or greater than,then different inequalities are used.

Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number.

Now we solve

5-x>8                            x-5<8

5-5-x>8-5                      x-5+5<8+5

-x>3                                  x<13

Hence given equation does not give same solutions.

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In the above scenario, note that the total distance of the flight is given as: 48.4 miles (approximately). This is solved using the law of Sines to find x.

The connection between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it asserts that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.

Thus, with regard to the problem modeled in the attached triangle, because two angles are given, the missing angle is 180° − (157° + 8°) or 15°. Use the Law of Sines to find x.

Using the law of ins we can state that:

Sin 8°/x = sin 15°/90

90 (Sin 8°) /x = Sin 15°

90 Sin 8° = x Sin 15°

90 Sin 8° / Sin 15° = x

90 (0.13917310096)/ 0.2588190451 = x

Thus,

x = 48.3951213156

x [tex]\approx[/tex] 48.4

Thus, the distance of the flight is approximately 48.4 miles.

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A statement 'The lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.' is True.

We know that the formula for the lateral surface area of cone:

Area = π × radius × slant height

and the formula for the lateral surface area of cylinder:

Area = 2π × (radius) × (height)

Here we have been given a cone A with radius r and slant height 2h.

Using the above formula, the lateral surface area of cone A would be:

A1 =  π × r × 2h

A1 =  2π × r × h                    ..................(1)

Also, we have been given a cylinder B with radius r and height h.

Using the above formula, the lateral surface area of cylinder A would be:  

A2 =  2π × r × h                   ..............(2)

From (1) and (2) we can observe that,

A1 = A2

Therefore, the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.

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Answer:

8,960.66

Step-by-step explanation:

In general, the length of the billing cycle is at least 15 days and no longer than 90 days.

The finance charge for a billing cycle is 960.66.

The new opening balance in the following billing cycle is 8,960.66.

The standard form of the function is f(x) = -x² +4x, The vertex form isf(x) = -(x-2)² + 4

What is a function?

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Given table is

x           f(x)

-1            -5

0             0

1               3

2              4

3               3

4                0

Find the difference to find the degree of the given function

f(x)                 -5           0           3            4         3          0

1st difference        5           3           1            -1          -3

2nd difference              -2          -2        -2          -2

The degree of the function is 2.

The general form of a second-degree function is

f(x) = ax²+bx+c

Putting x = 0 and f(0) =0 in f(x) = ax²+bx+c:

f(0) = a×0²+b×0+c

0 = c

Now putting x = 1 and f(1) =3 in f(x) = ax²+bx+c:

f(1) = a×1²+b×1+0    [since c=0]

3 = a + b ....(i)

Now putting x = 2 and f(2) =4 in f(x) = ax²+bx+c:

f(2) = a×2²+b×2+0    [since c=0]

4 = 4a + 2b ....(ii)

Solve equations (i) and (ii) by using the elimination method:

Multiply equation (i) by 2 and subtract it from (ii)

4a + 2b  = 4

2a  + 2b  = 6

(-)   (-)         (-)

__________

2a = -2

a = -1

Putting a = -1 in equation (i):

-1 + b = 3

b = 3+1

b = 4

The function is f(x) = -x² +4x

Rewrite the given function in vertex form:

f(x) = -(x² - 4x +4-4)

f(x) = -(x-2)² + 4

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Given Expression is equivalent to 5x^2 - 2x + 3 With the Same Variable and exponent we have added or subtracted their constant value.

First, try to learn what is an expression.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4x+ 15, for instance, the terms 4x and 15 are separated from the variable x by the arithmetic sign +.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The following components make into a mathematical expression:

Constant, Variables, Terms, Operators.

Given expression is  (2x^2-4) - (-3x^2+2x-7)

let's Multiply - sign inside the bracket.

2x^2 - 4 + 3x^2 - 2x + 7

With the Same Variable and exponent and their constant value, we can perform mathematical operations like addition, multiplication, and subtraction.

2x^2 + 3x^2 = 5x^2

5x^2 - 2x + 3.

Given Question is  incomplete complete question here.

Which expression is equivalent to  

[tex](2x^2-4)-(-3x^2+2x-7)[/tex]

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Answer:

x = 2

y = 4

Step-by-step explanation:

Answer:

x= 43

Step-by-step explanation:

The angles are corresponding angles which mean that they are equal to each other.

3x + 5 = 134  Subtract 5 from both sides

3x + 5 - 5 = 134 - 5

3x = 129  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{129}{3}[/tex]

x = 43

Answer:3/4 is the answer

Step-by-step explanation:

Answer:(s)

1/4  -  7/1  =  - 27/4  

Decimal:   - 6.75

Mixed number:  - 6 3/4

Step-by-step explanation:

1/4  -  7/1  =  - 27/4  or - 6.75 or  - 6 3/4

LCM:   4, 1  = 4

Adjust Fraction Based On LCM:

1/4 - 28/4

Apply The Fraction Rule:

a/c - b/c  =  a - b/c

1 - 28/4

Subtract the numbers:

1  -  28   =  - 27

             =  -27/4

Apply Fraction Rule:

- a/b  =  - a/b

Thus:

1/4 - 7/1  =  - 27/4  

Decimal:   - 6.75

Mixed Number Form  - 6 3/4

I hope that helps you!!!

Answer: −2<x<0

Step-by-step explanation: 2<x+4<4 2+−4<x+4+−4<4+−4 −2<x<0

The HCF of the polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1 is 1

When we divide the polynomials f(x) / g(x) then we get f(x) = g(x) × q(x) + r(x). Assuming the degree of g(x) > degree of r(x).

If the remainder r(x) is zero, then q(x) is the highest common factor of polynomials.

Here, we have been given two polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1

Let  f(x) = x^6 + 3x^4 + 3x^2 + 1 and  g(x) = x^3 + 3x^2 + 3x + 1

We can write these polynomials as:

f(x) = x^6 + 3x^4 + 3x^2 + 1

f(x) = (x² + 1)^3

The factors of polynomial  f(x) = x^6 + 3x^4 + 3x^2 + 1: 1 and  (x² + 1)^3

And g(x) = x^3 + 3x^2 + 3x + 1

g(x) = (x + 1)^3

And the factors of g(x) = x^3 + 3x^2 + 3x + 1 : (x + 1)^3 and 1

Therefore, the HCF of the polynomials f(x) and g(x) = 1

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A shape with 1 trillion sides is called a teragon. A teragon is a polygon that has an infinite number of sides, the most famous example of teragon is the Koch snowflake.

Typically, a teragon will be bounded by one or more self-similar fractal curves, which are formed by replacing each line segment in an initial figure with multiple interconnected parts, then substituting each of those parts with the same pattern of segments, then repeating the process an infinite number of times for every line segment in the figure.

Another example of a teragon is the horned triangle which is formed by pitching a series of smaller triangles on one corner of an equilateral triangle. It is also an example of a reptile, or shape that can be completely examined into smaller copies of itself.

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4x - 6 = x + 9

4x - x = 9 + 6

3x = 15

[tex]x = \frac{15}{3} \\ [/tex]

x = 5 ...

Answer:

[tex]x =5[/tex]

Step-by-step explanation:

[tex]4x - 6=x+9[/tex]

Subtract x from both sides

[tex]4x -6-x=x+9-x[/tex]

[tex]3x-6=9[/tex]

Add 6 to both sides

[tex]3x-6+6=9+6[/tex]

[tex]3x=15[/tex]

Divide both sides by 3

[tex]\frac{3x}{3} = \frac{15}{3}[/tex]

[tex]x = 5[/tex]

The net of the display consists of one rectangle and two right triangles.  168 ft² is needed to make a display case. Hence option D is the correct option.

What is surface area?

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The surface area of the triangular prism is the display area of the glass.

The surface area of a triangular prism consists of one rectangle and two right triangles.

The length of the rectangle is (10ft + 6 ft + 8ft) = 24ft.

The width of the rectangle is 5 ft.

The area of a rectangle is the product of length and width.

The area of the rectangle is 24ft × 5ft = 120 square ft

The length of the base of the triangle is 8 ft and the height is 6ft

The area of the triangle is 1/2 × base × height = 1/2 × 8 × 6 = 24 square ft

The display area is 120 square ft + 2 ×24 square ft = 120 + 48 = 168 ft².

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Answer: There are three 0s

240 x 25 = 6000 and there are three 0s in 6000

A system that has no solution is classified as inconsistent.

A system that has one and only one solution is classified as  independent

The system of equation graphed is consistent and independent.

The equations given by the graph are expressed as;

3x - 4y = 32

3x + 5y = 24

Now, if we subtract eq 1 from eq 2, we will get;

5y - (-4y) = 24 - 32

9y = -8

y = -8/9

Put 8/9 for y in eq 2 to get;

3x + 5(8/9) = 24

3x = 24 - 40/9

3x = 176/9

x = 176/27

Now, to classify solution to equations, we say that;

1) When there is no solution, it is inconsistent.

2) When there is one and only one solution, it is independent

Since we have a solution and only one solution, then we can say that the system of equation graphed is consistent and independent.

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The range for the following set of scores: 6, 12, 9, 17, 11, 4, and 14 is 13.

In statistics, the range is a measure of dispersion that describes the difference between the largest and smallest values in a dataset. The range is used to describe the spread of a dataset and can be a simple way to identify outliers or unusually large or small values. It is a simple measure of statistical dispersion and is most useful for interval and ratio data.

It is calculated by subtracting the minimum value from the maximum value among the data set.

range = maximum value - minimum value

Plug in the necessary values and solve for the range.

range = 17 - 4

range = 13

Therefore, the range for the following set of scores is 13.

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The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and and the common multiple of 16 and 40 could be 2 .

What is prime factor ?

prime factor can be defined as the number which is divisible by that number and the number should be prime.

The prime factor tree for 16 as follows

16 = 2*8 = 2* 2 * 4 = 2*2*2*2

                16

            2         8

                     2    4

                         2     2

The prime factor tree for 40 as follows

40 = 2*20 = 2*2*10 = 2*2*2*5

                40

           2            20

                      2        10

                              2      5

Hence, The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and the common multiple of 16 and 40 could be 2 .

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Answer:

Tamicca made 12 monthly payments of $115, for a total payment of 12*$115 = $<<12*115=1380>>1380.

She bought a computer for $1200, so the finance charge that she paid is $1380-$1200 = $<<1380-1200=180>>180.

Therefore, the finance charge that Tamicca paid was $180, rounded to the nearest cent.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A karate studio offers a 6 week session for

$175. How much would you expect to pay for

a 9 week session?

175 : 6 = 29.16

29.16 x 9 = 262.5

or

175 : 6 = x : 9

x = 175 x 9 : 6

x = 262.5