Forest habitat is cleared to build a new shopping complex. what does this scenario represent? a loss of biodiversity due to a climate change a gain in biodiversity due to an invasive species a loss of biodiversity due to human activity a loss in biodiversity due to a catastrophic event

Answer:

(a) dp/dx = 90/(x+2)

(b) $2.25

(c) approx = $2.25

    exact = $2.22

Step-by-step explanation:

\(p = 20 + 90 \ln(2x + 4)\)

(a) To find the rate of change, differentiate \(p\) with respect to \(x\) :

\(\implies \frac{d}{dx}(p) = \frac{d}{dx}(20) + \frac{d}{dx}(90 \ln(2x + 4))\)

\(\implies \frac{dp}{dx}=0+90\times\dfrac{1}{2x+4}\times2\)

\(\implies \frac{dp}{dx}=\dfrac{180}{2x+4}\)

\(\implies \frac{dp}{dx}=\dfrac{90}{x+2}\)

(b)  Find  \(\frac{dp}{dx}\)  when \(x=38\) :

\(\implies \frac{dp}{dx}=\dfrac{90}{38+2}\)

\(\implies \frac{dp}{dx}=\dfrac{90}{40}\)

\(\implies \frac{dp}{dx}=2.25\)

(c)  Approximate price increase associated with the number of units supplied changing from 38 to 39 is  \(\frac{dp}{dx}\)  when \(x=38\)

\(\implies \$2.25\)

Exact price increase:

\(\implies \left. p \right_{x=39}-\left. p \right_{x=38}\\\\\implies [20 + 90 \ln(2 \times 39 + 4)]-[20 + 90 \ln(2\times38 + 4)]\\\\\implies 416.6047323...-414.3823972...\\\\\implies 2.222335133...\\\\\implies \$2.22\)

Answer:

The expression for the number of bacteria after t hours is \(P(t) = 50e^{0.2922t}\)

Step-by-step explanation:

When introduced into a nutrient broth, the culture grows at a rate proportional to its size.

This means that the size of the population, after t hours, is modeled by the following differential equation:

\(\frac{dP}{dt} = rP\)

In which R is the growth rate.

The solution of this differential equation is:

\(P(t) = P(0)e^{rt}\)

In which P(0) is the initial population.

A culture of the bacterium Salmonella enteritidis initially contains 50 cells.

This means that \(P(0) = 50\), and so:

\(P(t) = P(0)e^{rt}\)

\(P(t) = 50e^{rt}\)

After 1.5 hours, the population has increased to 775.

This means that \(P(1.5) = 775\). We use this to find r. So

\(P(t) = P(0)e^{rt}\)

\(500e^{1.5r} = 775\)

\(e^{1.5r} = \frac{775}{500}\)

\(\ln{e^{1.5r}} = \ln{\frac{775}{500}}\)

\(1.5r = \ln{\frac{775}{500}}\)

\(r = \frac{\ln{\frac{775}{500}}}{1.5}\)

\(r = 0.2922\)

The expression is:

\(P(t) = 50e^{rt}\)

\(P(t) = 50e^{0.2922t}\)

The expression for the number of bacteria after t hours is \(P(t) = 50e^{0.2922t}\)

Answer: search

Step-by-step explanation: look up the question on your browser and the answer will pop up

39x - 11 = 17x + 6

Answer is A

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.

What is a value function?

The value function represents the optimal payoff of the system over the interval [t, t1] when started at the time- t state variable x(t)=x.

What is a variable?

A quantity that could take on any of a number of different values. : a sign that denotes a variable. : anything has a range. : a variable that might alter in a scientific experiment.

Here, we have

x = -4 and y = 3

then by putting the value of a function in a given equation, we get

1/2*(-4) + 3*(-4)*(3)²

= -110

Hence, If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.

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Answer: C

Step-by-step explanation:

Answer:

1) -0.016 pounds per square inch per cubic inch.

2) \(\displaystyle V'(P)=-\frac{800}{P^2}\)

Step-by-step explanation:

We are given the equation \(PV=800\).

Part A)

We want to determine the average rate of change of P as V increases from 200 cubic inches to 250 cubic inches.

To find the average rate of change between two points, we find the slope between them.

Rewrite the given equation as a function of V:

\(\displaystyle P(V)=\frac{800}{V}\)

Hence, the average rate of change for V = 200 and V = 250 is:

\(\displaystyle \begin{aligned} m &= \frac{P(250) - P(200)}{250 - 200} \\ \\ & = \frac{3.2 - 4}{250 - 200} \\ \\ & = -0.016\end{aligned}\)

Therefore, the average rate of change is -0.016 pounds per square inch per cubic inch.

Part B)

We want to express V as a function of P. This can be done through simple division:

\(\displaystyle V(P)=\frac{800}{P}\)

We want to show that the instantaneous change of V with respect to P is inversely proportional to the square of P. So, let's take the derivative of both sides with respect to P:  

\(\displaystyle \frac{d}{dP}\left[V(P)\right]=\frac{d}{dP}\left[\frac{800}{P}\right]\)

Differentiate. Note that 1/P is equivalent to P⁻¹. This allows for a simple Power Rule:

\(\displaystyle \begin{aligned} V'(P) & = 800\frac{d}{dP}\left[ P^{-1}\right] \\ \\ & = -800(P^{-2}) \\ \\ & = -\frac{800}{P^2}\end{aligned}\)

Therefore, the instantaneous change of V is indeed inversely proportional to the square of P.

Here, the given equation is :-

y= 6x -4

then ,

at (0,-4) : y = 6x - 4

or, -4 = 6(0) -4

or -4 = -4. ( this is true )

so (0,-4) satisfies the given equation.

The same process is to be repeated for each and every points and if the LHS = RHS then the point satisfies the equation .

Answer:

The said friend's grade in Professor Ivy's class is 85.7.

Step-by-step explanation:

Assuming the question asks for your friend's grade in Professor Ivy's class.

0.05(95) + 0.25(89) + 0.25(80) + 0.45(86) = 85.7

A minimum population size of approximately 7373 to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100.

To calculate the minimum population size required to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100, we can use the following formula:

n = [(z-value × SD) / ME]²

Where:

n = the minimum sample size required

z-value = the critical value for the desired confidence level (99% in this case)

SD = the known standard deviation (100 in this case)

ME = the desired margin of error (3 in this case)

First, we need to determine the z-value for a 99% confidence level. Using a standard normal distribution table, we find that the z-value for a 99% confidence level is approximately 2.576.

Substituting the values into the formula, we get:

n = [(2.576 × 100) / 3]²

Simplifying this expression, we get:

n = 7373.08

Therefore, we would need a minimum population size of approximately 7373.

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4 units, 6.93 units, 9.801 units, and 6.93 units are the missing lengths.

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Triangles are the focus of trigonometry, or more specifically, the connection between a right-angled triangle's angles and sides. A triangle has three sides: Hypotenuse, Adjacent, and Opposite. Trigonometric Ratio refers to the ratio between these sides based on the angle between them.

Here,

cos 60°=b/8

0.5=b/8

b=4 units

sin 60°=p/8

0.866*8=p

p=6.93 units

sin 45°=6.93/h

h=6.93/0.707

h=9.801 units

cos 45°=b/9.801

0.707*9.801=b

b=6.93 units

The missing lengths are 4 units, 6.93 units, 9.801 units and 6.93 units.

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Answer:

Dimensions are 2 and 4

Step-by-step explanation:

Area= a*b=8

Perimeter=2(a+b)=12 => a+b = 12/2. a+b = 6

a+b=6 =>a=6-b

If a=2=>b=4 so 4+2=6 , 4*2=8 and 4*2+2*2=12

If a=4=>b=2 so 4+2=6 , 4*2=8 and 4*2+2*2=12

Dimensions are 2 and 4

The possible dimensions of the table are -

L = 2, B = 4.

or

L = 4, B = 2.

Given is a rectangular table top has an area of 8 ft and a perimeter of 12 ft.

Let the dimensions of the rectangular table be {x} ft and {y} ft respectively.

We can write -

xy = 8                               ....... Eq(1)

2(x + y) = 12

x + y = 6                                 ....... Eq(2)

y = (6 - x)

Then, we can write -

x(6 - x) = 8

- x² + 6x = 8

x² - 6x + 8 = 0

(x - 2)(x - 4) = 0

We get -

x = 2 and x = 4

Now,

For x = 2, y = 4.

For x = 4, y = 2.

Therefore, the possible dimensions of the table are -

L = 2, B = 4.

or

L = 4, B = 2.

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The probability that the sum of the two dice is less than 4 is 3/36, which simplifies to 1/12.

Dice probability refers to the likelihood of a certain outcome when rolling one or more dice. The probability of rolling a particular number on a fair six-sided die, for example, is 1 in 6 or approximately 16.67%. The probability of rolling any number from 1 to 6 on a single die is always the same since each face has an equal chance of landing face up.

Given by the question.

To finds the probability that the sum of the two dice is less than 4, we need to list all the possible outcomes when Cindy throws one red and one blue dice, and then count the number of outcomes that satisfy the condition.

Possible outcomes when throwing two dice:

Red Blue

1 1

1 2

1 3

1 4

1 5

1 6

2 1

2 2

2 3

2 4

2 5

2 6

3 1

3 2

3 3

3 4

3 5

3 6

4 1

4 2

4 3

4 4

4 5

4 6

5 1

5 2

5 3

5 4

5 5

5 6

6 1

6 2

6 3

6 4

6 5

6 6

There are 36 possible outcomes when throwing two dice.

Outcomes where the sum of the two dice is less than 4:

Red Blue

1 1

1 2

2 1

There are 3 outcomes where the sum of the two dice is less than 4.

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Answer:

9 laps takes 5 minutes 25 seconds.

Step-by-step explanation:

Here is given:

4 laps takes 6 minutes 12 seconds.

We have to find how long 1 lap takes.

4/4 6/4 12/4 --> 1 lap takes 2 minutes 33 seconds.

Now, multiply each by 9 because you want to find 9 laps, so:

1x9 2x9 33x9 --> 9 laps takes 5 minutes 25 seconds.

Hope this helps :)

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

The 12.3 package

Step-by-step explanation:

Answer:

$8.96

Step-by-step explanation:

To find the total amount, multiply the percentage of the tip (20%) as 0.20 with 7.47

(7.47×0.20=1.494)

Add $1.49 to $7.47

(1.49+7.47=8.96)

And there is your total amount with a 20% tip!

$8.96

Answer:

no

Step-by-step explanation:

equate the two equations (make them equal to each other)

-2/5x - 7 = 2/5x - 3

get rid of the fractions by multiplying everything by 5

5(-2/5x - 7 = 2/5x - 3)

-2x - 35 = 2x - 15

solve

-2x - 35 = 2x - 15

-2x - 2x = -15 + 35

-4x = 20

x = -5

plug in "x" to one of the starting equations (I'm using the second one)

y = 2(-5) - 15

y = -10 - 15

y = -25

an easier way would be to plug in the point for "x" and "y"

-5 = 2(-5) - 15

-5 = -10 - 15

-5 = -25            FALSE

9514 1404 393

Answer:

  $9.86

Step-by-step explanation:

The numbers in your problem statement are somewhat garbled. We understand the problem to be ...

Given:

  earnings: $11.60 per hour

  1/10 of earnings donated

  8 1/2 hours worked

Find:

  the amount donated

Solution:

The amount donated will be the product of the given numbers:

  ($11.60 /hour)×(8.5 hours)×(1/10) = $9.86

Kendra donated $9.86 to the charity last week.

Answer: the answer is C

Step-by-step explanation:

Answer:

The answer is C or 44/12

Step-by-step explanation:

1/2 is equivalent to 3/6

1 4/6 is equivalent to 1 4/6 or 10/6

1 2/4 is equivalent to 1 3/6 or 9/6

When you add all of these together you get 22/6

Then you multiply 22/6 by 2 to get 44/12

Answer:Can somebody also help me with this. i'm confused please hurry!

Step-by-step explanation:

Answer:

n = 26/45

Step-by-step explanation:

If the 9⅓ and 27⅘ are supposed to be \(9^{1/3}\)  and \(27^{4/5}\), then

\(9^{1/3}\) × \(27^{n}\) = \(27^{4/5}\)

=> \((3^{2})^{1/3}\) × \((3^3)^{n}\) = \((3^3)^{4/5}\)

=> \(3^{2/3}\) × \(3^{3n}\) = \(3^{12/5}\)

=> \(3^{3n+\frac{2}{3}}\) = \(3^{12/5}\)

=> 3n+2/3 = 12/5

=> 45n + 10 = 36

=> 45n = 26

=> n = 26/45