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After 6 years the population of goats on the small island reaches 1000.

It is the rate of increases of population per individual in the population. The term related to time period and entire population.

given, initial population of goat on the smallest island, N° =2,

after t years the population of goats on this island, N= 1000

the maximum goat carrying capacity of this island, K= 1500

per capita growth rate, r = 0.5 per year

now, we use logistic growth equation, dN/dt = r×N[(K-N)/K]

                                                           dN/dt = 0.5×1000{1500-1000)/1500}

                                                                    dN/dt= 166.67

                                                             ∫dN/166.67 = ∫dt

                                                         by integrating both sides

                                               N/166.67 = t+c , where c is the

                                                     integration constant

                                                    at time t=0, N°=2

                                                        c= 0.012

                                                 N/166.67 =t+0.12

                                    as N=1000 , t= 5.99 years

hence, after 6 years the population of goat on the island reaches 1000.

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Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .Quadratics can be defined using an equation of a second-degree polynomial.

The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.

here

= 6x² - 5x- 6

= 6x² - 9x + 4x - 6

=  2 ( 2x - 3 ) + 3x ( 2x - 3 )

= (3x+2) ( 2x - 3 )

So , Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .

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Answer:

40 orange marbles

Step-by-step explanation:

We know for every 12 marbles, we have 5 orange marbles and 7 green marbles

Now we have 56 green marbles. To get from 7 to 56, we take 7 times 8.

So, we do the same take 5 times 8 = 40 orange marbles

So, it contains 40 orange marbles!

As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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domains =  all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

domains =  all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)

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Answer:

base x height also A=1/2bh

Step-by-step explanation:

that’s the formula

Answer -

So since there are 3 balls that are in the bag, it makes the denominator 3 and since they get one- one chance each, so the answer will be-

yellow ball - 1/3

Red ball - 1/3

Blue Ball - 1/3

The width of the rectangle is 2 units.

Despite having four sides, a rectangle only has two distinct dimensions since the sides are paired. Though the width is often the shorter of these two dimensions, it is more commonly referred to as the horizontal side when the rectangle is shown lying on its side.

Given the width of rectangle is length of rectangle - 5 units.

Let us suppose that length of rectangle is y and width of the rectange is y-5.

The formula of area of rectangle is l×b where l and b are length and breadth respectively.

So substituting in the equation we get

[tex]y* (y-5) = 14.\\y^2- 5y = 14\\y^2 - 5y - 14 = 0[/tex]

Solving the above quadratic equation we get y as 7 and -2.

As length cannot be a negative quantity we take length as 7 and it gives us the result that the width is 2 units.

The width of the rectangle is 2 units.

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The formula for the volume of cylinder with base area B and height H is V = B × H.

A cylinder is a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Area of a circle which is the base of a cylinder = πr²

Given that;

Plug the given values into the above formula.

V = π × r² × h

V = πr² × h

V = Base area × Height

V = B × H

Therefore, formula for the volume is V = B × H.

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The continuous data that is presented as a frequency distribution makes up the median of the grouped data.

The center number in the set of data, known as the median, is what divides the data set's upper and lower halves. Since the data is divided into class intervals, the middle value is unknown when calculating the median of grouped data.

Let us understand this with the help of a median class example.

Consider the data as 48, 20, 59, 69,73. We have to calculate the median.

Arranging in ascending order we get, 20, 48, 59, 69, 73.

Here the number of observations is n = 5.

To find the median of odd data we will use the formula:

[(n+1)/2] = (5+1)/2 = 3.

Therefore, median = 3rd observation.

Median = 59.

Hence we got the idea of the median with the example of class.

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Answer:

Step-by-step explanation:

(

1

)

.

plugging the

4

into

g

(

x

)

and then putting what you get from that in to

f

(

x

)

(

2

)

.

plug

g

(

x

)

into

f

(

x

)

and then plug in the

4

Option 1:

Plug

4

into

g

(

x

)

:

g

(

x

)

=

−

2

(

4

)

−

6

=

−

8

−

6

=

−

14

Then plug

g

(

x

)

into

f

(

x

)

:

f

(

x

)

=

3

(

−

14

)

−

7

=

−

42

−

7

=

−

49

Option 2:

Plug

g

(

x

)

into

f

(

x

)

:

f

(

x

)

=

3

(

−

2

x

−

6

)

−

7

=

−

6

x

−

18

−

7

=

−

6

x

−

25

Finally plug

4

into our current

f

(

x

)

:

f

(

x

)

=

−

6

(

4

)

−

25

=

−

24

−

25

=

−

49

The solutions or roots of the equation 2x² + 3x - 2 = 0 will be 1 and -2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The quadratic equation is given below.

2x² + 3x - 2 = 0

Factorize the equation, then we have

2x² + 3x - 2 = 0

2x² + 4x - x - 2 = 0

2x(x + 2) - 1(x + 2) = 0

(x - 1)(x + 2)

x = 1, -2

The solutions or roots of the equation 2x² + 3x - 2 = 0 will be 1 and -2.

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The roots of the quadratic equation 2x² + 3x - 2 = 0 are - 2, 1/2.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, A quadratic equation 2x² + 3x - 2 = 0.

Now, Two numbers that multiply to - 4 and add to 3 is 4, - 1.

Therefore,

2x² + 3x - 2 = 0.

2x² + 4x - x - 2 = 0.

2x(x + 2) - 1(x + 2) = 0.

(x + 2)(2x - 1) = 0.

x + 2 = 0 Or 2x - 1 = 0.

x = - 2 Or x = 1/2.

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Answer:

-1 ≤ y ≤ 6

Step-by-step explanation:

The range is the values of y.

In this graph lowest point is -1 and the highest is 6.

The points are filled so that means that we include 6 and -1.

So it would be -1 ≤ y ≤ 6.

You can log into your My.SSS account to see the status of your SSS salary loan.

Your salary loan has been granted if you see the message "SSS Loan Application Has Been Granted." Logging into your My.SSS account will allow you to view the status of your SSS salary loan. Select "Inquiry" first, followed by "Loan Info." Your SSS loan status and other loan information can be found here. If the loan funds have already been credited to your disbursement account, you will also get another SMS message.

The loan must be repaid by the borrower in 24 monthly installments. The second month after the loan's origination date is when the monthly amortization starts.  

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The required three consecutive odd numbers that sum up 57 are 17, 19 and 21.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

So, we can say that the difference between any two consecutive odd numbers is:

= 2k+3 – (2k+1)

=2k+3-2k-1

=2

So, for every two consecutive odd numbers there is a difference of 2.

Now, let us take ‘n’ to be an odd number.

So, an odd number just before n will be (n-2).

And also an odd number just after n will be (n+2).

Since, it is given that the sum of these three consecutive odd numbers is 57. So, we can write the following equation:

n-2+n+n+2=57

3n=57

So, n = 19

The odd number before n will be = n -2 = 19-2 = 17

And the odd number after n will be = n+2 = 19 + 2 = 21

Therefore, The required three consecutive odd numbers that sum up 57 are 17, 19 and 21.

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The original price 1. $ 88.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means)

Given;

The cost of the product was reduced by 20%, leaving $ 70.4 as the final price.

Cost of phone after 80% off= $70.40

So, now we will do a cross-multiplication;

If the percent is 80% =70.40

Let, the original price 100% = x

80x = 70.40. 100

80x = 7040

X = 7040: 80

X = 88

Therefore, the 100 percent value of phone will be $88

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The value of the v is 11.5 units.

What is a Line Segment?

A line segment is a portion of a straight line that is defined by two points. It is a one-dimensional geometric figure with no width or area. Line segments can be drawn in many ways, including straight, curved, or jagged. The length of a line segment is the distance between the two points that define it. Line segments are commonly used to measure distances, form shapes, and construct geometric figures. Line segments can be used to define polygons, circles, and other shapes. Line segments are also used in mathematics to represent vectors and calculate angles. Line segments are a fundamental element of geometry and are used in a variety of applications, including navigation, construction, engineering, and computer graphics.

We have,

PS= RS = 31,

PQ = 2v,

and QR = v + 23,

v = ?

If PS= RS = 31,

then  PQ = QR,

so, 2v = v + 23,

v = 23/2

v = 11.5 unit

Hence, the value of the v is 11.5 units.

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(A) The expression for each plane are as follows;

Plane A; 1300 + 17x

Plane B; 1092 + 21x

B). The equation to show when the two planes would be at the same altitude is; 1300 + 17x = 1092 + 21x.

It follows from the task content that the initial altitudes of plane A and B are 1300 and 1092 respectively.

Since plane A gains altitude at 17 meters per second; The expression for the altitude after x seconds is;

1300 + 17x

Also, since plane B gains altitude at 21 meters per second; The expression for the altitude after x seconds is;

1092 + 21x

Ultimately, at the point when the two planes are at the same altitude; the equation which is true about the situation is;

1300 + 17x = 1092 + 21x.

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The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°.

Parallel lines are straight lines that never meet each other no matter how long we extend them

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).

The fundamental characteristics listed below make it simple to recognise parallel lines.

Parallel lines are defined as straight lines that are always the same distance apart.

No matter how far apart they are from one another, parallel lines can never intersect.

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Answer:

Subtraction

Step-by-step explanation:

The additive inverse of something will use subtraction, basically the opposite

The

tools

used to make a

chart

are  Info-gram, tableau, Grafan, Chartist

What is a chart?

A

chart

can be defined as a

graphical

representation for

data

visualization, such that the data is represented with symbols as bars  lines in line chart, or slices in a pie chart"

It is used to represent tabular numeric data and  functions or other kinds of quality structure, providing different information.

The tools used in a chart includes;

Info-gram

tableau

Grafana

Chartist,

FusionCharts,

Datawrapper

ChartBlocks

Hence, a

chart

is a graphic representation of data.

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chart

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With the help of Trigonometry the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.

What is Trigonometry?

Studying the correlations between triangle side lengths and angles is the subject of trigonometry, a branch of mathematics. From the use of geometry in astronomical research, the field first appeared in the Hellenistic world in the third century BC.

Dimensions are the measure of the length, width and height of a given object. Yes, a rectangular box of length 5 feet and height 2 feet can be stored underneath the ramp.

The measure of the sides of a given object is referred to as its dimensions. This can be with respect to its length, width, and height.

It has been given that the height of the ramp is 39 inches. But,

12 inches = 1 feet

So that,

39 inches = x feet

make x the subject of the formula to have;

x = 3.25 feet

Thus the dimensions of the ramp are ;

length = 12 feet

height = 3.25 feet

Therefore, the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.

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Step-by-step explanation:

the domain of a function is the interval or set of all valid x (input) values.

the range of a function is the interval or set of all valid y (function result) values.

the graph shows us that the x values are continuously between -5 and +3.

and the end points are filled, so, they are to be included as valid points (via the <= or >= signs).

so, the domain is

-5 <= x <= 3

To find the degree of a polynomial function, count the number of terms in the expression. To find the number of turning points, take the degree of the polynomial and subtract 1. The number of turning points will be equal to that number.

To find the degree of a polynomial function, the first step is to count the number of terms in the expression. For example, if the expression is 3x^2 + 4x + 2, then the degree is 2 because there are three terms.The second step is to subtract 1 from the degree of the polynomial. In the example, subtracting 1 from 2 gives us 1. Therefore, the polynomial has 1 turning point.A turning point is a point on the graph of the polynomial where the slope of the tangent line is 0. This means the graph changes direction at the turning point. In the example, the graph changes direction at the point (1, 5).In summary, to find the degree and the number of turning points in a polynomial function, count the number of terms in the expression to find the degree, then subtract 1 from the degree to find the number of turning points.

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The expression x³ 3x² 4x 6 can be expanded to x³ + 3x² - 4x - 6. When this expression is evaluated for x = 3, the result is 24, so the remainder is 0.

The expression x³ 3x² 4x 6 can be expanded to x³ + 3x² - 4x - 6. To find the remainder when this expression is evaluated, we must first substitute in a value for x. For this example, let x = 3. When we substitute 3 for x, the expression becomes 3³ + 3x² - 4(3) - 6. We can simplify this expression by performing the operations in order of operations. First, we can calculate 3³, which is equal to 27. Next, we can calculate 3x², which is equal to 27. Subtracting 4(3) from 27 gives us 15. Finally, subtracting 6 from 15 gives us 9.

The remainder of evaluating

x³ 3x² 4x 6 for x = 3 is 9.

x³ 3x² 4x 6 = 3³ + 3x² - 4(3) - 6 = 27 + 27 - 12 - 6 = 24

Remainder = 24 - 3 = 0

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First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.

By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

The relative minimum of h(x) occurs at x = 2. Integrals can be used to solve a wide range of problems in mathematics and physics, such as finding the area under a curve

An integral is a mathematical concept that involves the concept of integration, which is a way to find the area under a curve or the volume of a solid of revolution. Integrals can be classified into two types: indefinite integrals and definite integrals.

To find the relative minimum of the function h(x), we need to find the value of x that minimizes the value of h(x).

First, let's find the derivative of h(x). We can do this by applying the chain rule to the function inside the integral:

[tex]h'(x) = (-4 * (t - 2)^2 + 8)' = (-4 * (t - 2)^2 + 8)' = -8 * (t - 2)[/tex]

Next, we need to find the points where h'(x) = 0 or is undefined. Setting h'(x) = 0 and solving for t, we find that t = 2. Substituting this value back into the original expression for h(x), we get:

[tex]h(x) = -4 * (2 - 2)^2 + 8 = 8[/tex]

Since h'(x) is undefined at t = 2, we need to check whether the function is increasing or decreasing at that point. To do this, we can take the second derivative of h(x):

[tex]h''(x) = (-8 * (t - 2))' = -8[/tex]

Since the second derivative is negative at t = 2, this means that the function is decreasing at that point.

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The third number in this sequence is 23.

The sum of three consecutive odd numbers can be written as (2n-1) + (2n+1) + (2n+3) = 69, where n is a positive integer. Expanding the left side gives us 6n+1 = 69, which means n = 11. The third number in the sequence is (2n+1) = (2 × 11+1) = 23. Therefore, the third number in the sequence is 23.

In the given sequence, 1, –3, 9, –27, 81,..., each number is multiplied by -3 to get the next one in the sequence. Since the absolute values of the numbers in the sequence are increasing, the sequence is diverging to an infinite value, either positive or negative. Therefore, it can be concluded that the given sequence is a divergent sequence.

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To find the vertical asymptote, take the limit of the function as x approaches infinity or negative infinity. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain.

To find the vertical asymptote of a function, take the limit of the function as x approaches either infinity or negative infinity. This will give the value at which the output of the function approaches infinity or negative infinity, respectively. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain. If the limit of the function as x approaches the endpoint is finite, then the horizontal asymptote is the value of the limit. If the limit of the function as x approaches the endpoint is infinite, then the horizontal asymptote is undefined. If the limit of the function as x approaches the endpoint is undefined, then the horizontal asymptote is undefined.

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