ssume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1800 fish. Absent constraints, the population would grow by 180% per year.

If the starting population is given by
p
0
=
100
, then after one breeding season the population of the pond is given by

p
1
=


After two breeding seasons the population of the pond is given by

p
2
=

The equation solved for the variable x is:

[tex]x = e^{ W(ln(y))}[/tex]

In any equation of the form:

y = f(x), to make x the subject of the equation, we need to isolate x in one of the sides of the equation, then we will get:

x = g(y).

In this case we have:

xˣ = y

And we want to make x the subject of the equation.

We can start by apliying the natural logarithm in both sides to get:

ln(xˣ ) = ln(y)

x*ln(x) = ln(y)

We can rewrite:

[tex]x = e^{ln(x)}[/tex]

Then our equation becomes:

[tex]e^{ln(x)}*ln(x) = ln(y)[/tex]

Now the Lambert W function is defined as:

[tex]W(x*e^x) = x[/tex]

So if we apply this in both sides, we will get:

[tex]W(e^{ln(x)}*ln(x)) = W(ln(y))\\ln(x) = W(ln(y))[/tex]

Now apply the exponential in both sides and get:

[tex]ln(x) = W(ln(y))\\\\e^{ln(x)} = e^{ W(ln(y))}\\x = e^{ W(ln(y))}[/tex]

That is the equation solved for x.

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Complete question:

"How can you make x the subject in the equation? xˣ = y"

Answer:

d is the correct option

Step-by-step explanation:

when powers are raised to powers

they got multiplied

Answer:

Step-by-step explanation:

NOTE:

   [tex](x^p)^q=x^{p\times q}[/tex]

As a result of this law the correct solution is (d). )

Answer:

the clock hands do not form a right angle at 5:00.

Step-by-step explanation:

Answer:

1/4(2^3 + 4^2) = 6

Step-by-step explanation:

I

The answer is approximately 4.08 But again, it's hard to say for certain without more information about what you're trying to do with this equation

Sure, I'd be happy to help!

The equation you've given is a bit tricky to interpret without more context, but here's my best attempt:

It looks like you're trying to find the value of "A" based on an expression involving some kind of radical, and two terms "a" and "b".

Specifically, it seems like you're taking the cube of two coordinate points (1,0) and (0,b), and then adding those cubes together. Finally, you're taking the nth root of the resulting sum (where "n" is some unspecified number).

So if we plug in some values for "a" and "b", and assume that "n" is equal to, say, 2, we might get something like:

A = 3√[(1,0)^3 + (0,4)^3]

= 3√(1 + 64)

= 3√65

. Let me know if there's anything else I can help with!

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Answer: 10/20, 8/20, 4/20, 6/20

Step-by-step explanation:

Black: 10/20

Red: 8/20

White: 4/20

Blue: 6/20

There are 20 marbles in total the amount of colored marbles is the numerator and the denominator is the total.

Have a lovely day!!

The answer of the given question on the listing the critical numbers is  the critical numbers as x = 3, 6, and 9. and the function has an absolute maximum at x = 9. and the function has an absolute minimum at x = 2.

an absolute maximum occurs at the highest point on the graph of a function over its entire domain. It can be a local maximum or a global maximum, depending on whether there are any other points in the domain that have higher function values. Finding the absolute maximum of a function is important in optimization problems, where we want to find the maximum or minimum value of a function subject to certain constraints.

Based on the graph provided, we can approximate the critical numbers as x = 3, 6, and 9.

To determine whether there is relative maximum, relative minimum, absolute maximum, or absolute minimum at each critical number, we need to examine  behavior of function near each critical number.

At x = 3, the function has a relative maximum, since the graph changes from increasing to decreasing at that point.

At x = 6, the function has a relative minimum, since the graph changes from decreasing to increasing at that point.

At x = 9, the function has a relative maximum, since the graph changes from increasing to decreasing at that point.

Since the graph increases without bound as x approaches 10 from the left, but approaches a finite value as x approaches 10 from the right, the function has an absolute maximum at x = 9.

Since the graph decreases without bound as x approaches 2 from the right, but approaches a finite value as x approaches 2 from the left, the function has an absolute minimum at x = 2.

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Answer:

$132

Step-by-step explanation:

Hope this helps!

Answer: 11

Step-by-step explanation:

The three integers are 11, 13, and 15.

Explanation:We shall consider the integers as x, 

(x+2), and (x+4).

The sum of these is 39, so we can write:

x+(x+2)+(x+4)=39

Open the brackets and simplify.

x+x+2+x+4=393x+6=39

Subtract 6 from each side.

3x=33

Divide both sides by 3.

x=11

Therefore: 

(x+2)=13 

and

(x+4)=15

His total annual cost for providing these insurance plans will be $ 5, 659 per employee for the year.

The total annual cost for providing these insurance plans will be $ 12, 500 per employee.

The annual cost of insurance to Bob for the insurance package that he wants to offer his employees is:

= Health Insurance + Dental Insurance + Vision Insurance

= 5, 179 + 360 + 120

= $ 5, 659

The total cost of the insurance plans per employee would be:

= Life Insurance + Disability insurance

= 9, 500 + 3, 000

= $ 12, 500

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The full question is:

Let's say Bob wants to offer an insurance package to his employees that will cover any outpatient surgery charges, tooth sealants, and glasses. His total annual cost for providing these insurance plans will be $ ____ per employee for the year. Let's assume that Schmidt wants to cover his employees' expenses in case of disability. He also wants to ensure that the family of an employee is provided for in the event of an employee's loss of life. The total annual cost for providing these insurance plans will be $ _____ per employee.

To find the median of the data, we need to first arrange the numbers in order from smallest to largest:

65, 65, 124, 129, 180, 190, 228, 285, 285, 316, 370, 370

There are 12 numbers in the sample, so the median will be the middle value. In this case, there are two middle values because there are an even number of data points. To find the median, we take the average of the two middle values:

median = (180 + 190)/2 = 185

So the median number of pieces in the sample of building toys is 185.

Answer:

[tex]P(x)=3x^4-11x^3+71x^2-275x-100[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z=a+bi[/tex], the complex conjugate of the number is defined as  [tex]z*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if P(x) is a polynomial with real coefficients, and 5i is a root of P(x)=0, then its complex conjugate -5i is also a root of P(x)=0.

So the zeros of the function are: 5i, -5i, 4, and -1/3.

The zeros of a function P(x) are the x-values of the function such that the P(x)=0.  According to the Factor Theorem, if P(x) is a polynomial, and P(a)=0, then (x - a)  is a factor of P(x).

Therefore, the factors of the function are:

[tex]x=5i \implies (x-5i)[/tex]

[tex]x=-5i \implies (x+5i)[/tex]

[tex]x=4 \implies (x-4)[/tex]

[tex]x=-\dfrac{1}{3} \implies (3x+1)[/tex]

So the polynomial in factored form is:

[tex]P(x)=a(x-5i)(x+5i)(x-4)(3x+1)[/tex]

As we have not been given a specific leading coefficient, let us assume it is one.

[tex]P(x)=(x-5i)(x+5i)(x-4)(3x+1)[/tex]

To write the polynomial in standard form, expand and simplify.

[tex]\begin{aligned}P(x)&=(x-5i)(x+5i)(x-4)(3x+1)\\&=(x^2+5ix-5ix-25i^2)(3x^2+x-12x-4)\\&=(x^2-25(-1))(3x^2-11x-4)\\&=(x^2+25)(3x^2-11x-4)\\&=3x^4-11x^3-4x^2+75x^2-275x-100\\&=3x^4-11x^3+71x^2-275x-100\end{aligned}[/tex]

a. The y-intercept of the line is 4.

b. The gradient of the line is 2.

The gradient of a line is the steepness of the line, which is determined by how much the line rises or falls for each unit of horizontal distance [m = change in y / change in x], while the y-intercept is the point where the line crosses the y-axis.

a. The line cuts the y-axis at 4, therefore, the y-intercept is 4.

b. Gradient of the line = rise/run = 2/1

Gradient = 2.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]6x+y=-10\implies y=-6x-10\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -6 \implies \cfrac{-6}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-6} \implies \cfrac{1}{ 6 }}}[/tex]

so we're really looking for the equation of a line whose slope is 1/6 and it passes through (1 , 1)

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{6}}(x-\stackrel{x_1}{1}) \\\\\\ y-1=\cfrac{1}{6}x-\cfrac{1}{6}\implies y=\cfrac{1}{6}x-\cfrac{1}{6}+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{6}x+\cfrac{5}{6} \end{array}}[/tex]

Answer

Step-by-step explanation:

what's the question?

Answer: $1.46 less

Step-by-step explanation:

Lets find how much each bottle is first for Store B, to do that divide 29.10 divided by 15 and you should get 1.94 meaning each bottle of juice is $1.94. Next, lets find how much each bottle costs in store A. You can take any number from the total cost and divide it by the bottles and you should get the same thing. Lets do the first one 2.40 divided by 5 equals 0.48. If you want to check you can multiply 0.48 by any number of bottles and you should get the total cost. Now we have to find how much less Store A costs, to do so we subtract store B (1.94) and store A (0.48) and you should get $1.46.

Answer: one inch measured the the map represented 100 feet on the ground

Step-by-step explanation:

Answer:

(0,8)

Step-by-step explanation:

The slope intercept formula is set up as y=mx+b, where b is the y-intercept value. In the equation y=3x+8, we can see that 8 is the y-intercept. So we plug 8 for y in a coordinate, and 0 for x. The answer is (0,8)

The correct classification(s) of the fractional number 15/3 is: whole, integer, rational.

What is fractional number?

A fractional number, also known as a fraction, is a number that represents a part of a whole. It consists of two parts: a numerator and a denominator, separated by a slash (/). The numerator is the number above the line, and the denominator is the number below the line.

The number 15/3 is a fraction. When we simplify this fraction, we divide 15 by 3 to get:

15/3 = 5

Therefore, the number 15/3 is equivalent to the whole number 5.

An integer is a number that can be expressed without fractions or decimals, and can be positive, negative, or zero. The number 5 is also an integer, because it is a positive whole number.

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In this case, 15/3 can be expressed as the ratio of two integers (15 and 3), so it is a rational number.

Therefore, the correct classification(s) of the number 15/3 is:

whole, integer, rational.

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Answer:

look in explanation

Step-by-step explanation:

The formula to find the surface area of a cylinder is as follows: SA= (2*π*r*h) + (2*π*r²)

You need to know the height of the cylinder in order to input the number into the equation.

Also, if you are using nets, you need to know the height of the cylinder because you cannot calculate the area of the rectangle part of the cylinder's net without that measurement.

The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

[tex]Area = \int\limits^b_a {y} \, dy[/tex]

[tex]Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy[/tex]

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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The correct way to report the results of this experiment is t(23)=2.92, p<0.05.

Therefore answer is D.

The notation 't(24)=2.92, p<0.05' indicates the degrees of freedom (24), the value of the test statistic (2.92), and the level of significance (p<0.05).

The notation "t(23)" indicates that the t-value was calculated with 24 degrees of freedom, which is the number of subjects minus 1. The level of significance (p<0.05) means that the probability of obtaining a t-value of 2.92 or greater by chance alone is less than 5%. This indicates that the results are statistically significant and unlikely to be due to random chance.

Option A is incomplete because it does not indicate the degrees of freedom. Option B is incorrect because it states that the degrees of freedom is 24. Option C is incorrect because it incorrectly states that the probability is greater than 0.05, which would mean that the results are not statistically significant. Therefore the correct answer is option D.

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Answer:

y = -5x

Step-by-step explanation:

y = -5x;

[tex]\frac{y}{x}[/tex] = -5;

y:x=-5:1

m∠NOP = 90° is the value of angle .

What does a math angle mean?

An angle is made up of two rays (half-lines) that have a shared termination. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

                                           A figure that is created by two rays or lines that have the same endpoint is known as an angle in plane geometry. The Latin word "angulus," which meaning "corner," is the source of the English term "angle". The vertex, which is the shared terminal of the two rays, is referred to as the side of an angle.

m∠NOP = 90° is the value of angle .

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The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.

A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.

From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).

The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.

Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.

To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.

To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.

Substituting these values into the equation for g(x), we have:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4

Therefore, the exact expression for g(x) is:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.

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There are three coefficients present in the expression: 5 for the x³ ;  2 for the x² and 6 is for x.

The integer or constant quantity put before a variable is known as a coefficient.

Thus, there are three coefficients present in the expression: 5 for the x³ ;  2 for the x² and 6 is for x.

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Complete question-

How many coefficients are in the expression 5x³ + 2x²+6x-4?