what us the value of y?

Based on the differential equation a) Solving the DE subject to P(0) = P0 will yield P = ((kP0 - h)e^(kt) + h)/k. b) For the three cases given (P0 > h/k, P0 = h/k, P0 = 0), the behavior of the population P(t) is will be population will grow without bound, the population will remain constant, and the population will decrease and approach zero as t approaches infinity respectively. c) The fish population will go extinct in finite time if there exists a time T > 0 such that P(T) = 0. At T = (1/k)ln(-h/(kP0 - h)) the fish population will go extinct.

(a) To solve the differential equation (dP/dt) = kP - h subject to P(0) = P0, we need to separate the variables and integrate both sides:

(dP/dt) = kP - h

dP/(kP - h) = dt

∫dP/(kP - h) = ∫dt

ln|kP - h| = kt + C

kP - h = e^(kt + C)

P = (e^(kt + C) + h)/k

Using the initial condition P(0) = P0, we can solve for C:

P0 = (e^(k*0 + C) + h)/k

P0 = (e^C + h)/k

e^C = kP0 - h

C = ln(kP0 - h)

Substituting back into the equation for P, we get:

P = (e^(kt + ln(kP0 - h)) + h)/k

P = ((kP0 - h)e^(kt) + h)/k

This is the solution to the differential equation subject to the initial condition P(0) = P0.

(b) The behavior of the population P(t) for increasing time depends on the initial condition P0:

- If P0 > h/k, then the term (kP0 - h)e^(kt) will be positive and will increase exponentially as t increases, so the population will grow without bound.

- If P0 = h/k, then the term (kP0 - h)e^(kt) will be zero and the population will remain constant at P = h/k for all time.

- If P0 < h/k, then the term (kP0 - h)e^(kt) will be negative and will decrease exponentially as t increases, so the population will decrease and approach zero as t approaches infinity.

(c) The fish population will go extinct in finite time if there exists a time T > 0 such that P(T) = 0. From the equation for P, we can see that this will happen if and only if P0 < h/k:

P(T) = ((kP0 - h)e^(kT) + h)/k = 0

(kP0 - h)e^(kT) = -h

e^(kT) = -h/(kP0 - h)

Since the exponential function is always positive, this equation has no solution for P0 > h/k or P0 = h/k. However, if P0 < h/k, then the term (kP0 - h) is negative and the equation has a solution:

kT = ln(-h/(kP0 - h))

T = (1/k)ln(-h/(kP0 - h))

This is the time at which the fish population will go extinct.

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Answer:

Option 2: 67.014

Step-by-step explanation:

Answer:

thats easy

Step-by-step explanation:

The optimal clutch size is 1.

a)The survivorship of an offspring, S, decreases with the clutch size, C.

Therefore, the formula is given as:

S = 0.5 - 0.1C

We need to find the optimal clutch size for this bird species.

We can do this by differentiating S with respect to C, and equating the result to zero.

That is:S = 0.5 - 0.1C => dS/dC = -0.1

Equating dS/dC to zero gives:-0.1 = 0 => C = 0

This implies that there is no optimal clutch size for this species.

However, since C represents clutch size, it must be a positive integer.

Therefore, we can choose a clutch size of 1, which will result in the highest survivorship of offspring. Hence, the optimal clutch size is

1.b)The optimal clutch size for a species with a survivorship-clutch size relationship of the form S = a - bC can be obtained by following the same procedure as above.

We can differentiate S with respect to C, and equate the result to zero.

That is:S = a - bC => dS/dC = -b

Equating dS/dC to zero gives:-b = 0 => C = 0

This implies that there is no optimal clutch size for this species. However, since C represents clutch size, it must be a positive integer. Therefore, we can choose a clutch size of 1, which will result in the highest survivorship of offspring. Hence, the optimal clutch size is 1.

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As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.

As a quarter of 100, a number can be expressed as a percentage. It is frequently used to describe distinctions or express changes in numbers. The symbol for percentages is %, and they are frequently utilized to describe ratios, rates, and certain other numerical connections. An 80 percent score on a test, for instance, indicates that the student correctly answered 80 of the 100 questions. Similar to this, if a retailer were offering a 20% discount on a $100 item, the sale price would be $80.

given

With P = 10000, r = 0.08 (8% stated as a decimal), n = 12 (compound monthly), and t to be found when A = 20000, the situation is as follows.

When these values are added to the formula, we obtain:

\(20000 = 10000(1 + 0.08/12)^(12t) (12t)\)

By multiplying both sides by 1000, we obtain:

\(2 = (1 + 0.08/12)^(12t) (12t)\)

When we take the natural logarithm of both sides, we obtain:

ln(2) = 12t ln(1 + 0.08/12)

When we multiply both sides by 12 ln(1 + 0.08/12), we obtain:

t = ln(2) / (12 ln(1 + 0.08/12))

Calculating the answer, we discover:

10.24 years is t.

As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.

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The approximate perimeter of the entire shape, given that it is a one - half circle attached to a square, is 32 inches

First, find the perimeter of the one - half of a circle with the formula:

= ( π x diameter ) / 2

The diameter is the same as the side of the square which is:

= ( π x 7 ) / 2

= 11 inches

The perimeter of the square component will be for 3 sides alone as the last side is covered by the semi - circle :

= 3 x 7

= 21 inches

The perimeter is:

= 11 + 21

= 32 inches

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Answer: Choice C.

How many 1/4-meter long pieces of ribbon are needed to have a total of 3 1/2 meters of ribbon.

==========================================================

Explanation:

Let's consider a similar problem without the fractions.

Let's say you want to know how many 2 meter lengths of ribbon you can cut from an overall length of 24 meters. That would be 24 ÷ 2 = 12 pieces total.

So we divide the two values (large ÷ small)

The same idea applies to this problem as well. The larger amount (3 & 1/2 meters) is what we cut up, and each slice is 1/4 of a meter. To find the number of pieces, we would compute 3 1/2÷1/4

Note: it might help to convert the mixed number 3 & 1/2 to the improper fraction 7/2

Answer:

znvipahgvahgv

Step-by-step explanation:

The probability that the second chip drawn is red is 1/3.

The probability of drawing a red chip on the first draw is 6/10, or 3/5. After one chip is discarded, there are 9 chips remaining, 3 of which are red. So the probability of drawing a red chip on the second draw, given that a chip has already been discarded, is 3/9, or 1/3.

Therefore, the probability that the second chip drawn is red is 1/3. This is because the first chip drawn could be either white or red, so there are two possible scenarios. If the first chip drawn is white, there will be 6 red chips and 3 white chips left, so the probability of drawing a red chip on the second draw will be 6/9 or 2/3. If the first chip drawn is red, there will be 5 red chips and 4 white chips left, so the probability of drawing a red chip on the second draw will be 5/9. To get the overall probability of drawing a red chip on the second draw, we need to take the average of these two probabilities, weighted by the probability of the first chip being white or red, respectively.

The probability of the first chip being white is 4/10, or 2/5, and the probability of the first chip being red is 6/10, or 3/5. So the overall probability of drawing a red chip on the second draw is

(2/5) x (2/3) + (3/5) x (5/9) = 4/15 + 1/3 = 3/9 = 1/3.

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97.2% of the standard normal curve lies to the left of z = 2.05, and only 2.8% lies to the right.

To find the value of z such that 97.2% of the standard normal curve lies to the left of z, we need to use the standard normal distribution table or a statistical calculator.

In this case, we are looking for the z-score corresponding to a cumulative probability of 97.2%. This means we are looking for the z-score that separates the top 2.8% of the distribution (since 100% - 97.2% = 2.8%).

Using a standard normal distribution table or a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.9782 (which is 1 - 0.028) is approximately 2.05 (rounded to two decimal places).

Therefore, z = 2.05.

Sketching the area described:

If we draw the standard normal distribution curve, with the mean at the center (0) and the standard deviation of 1, the area to the left of z = 2.05 will represent 97.2% of the total area under the curve. This area will be shaded to the left of the z-score value on the curve.

The sketch will show a normal curve with a shaded area to the left of the point corresponding to z = 2.05, representing the 97.2% of the standard normal curve that lies to the left of z.

The standard normal distribution is a bell-shaped curve that is symmetric around its mean. It is used to analyze and compare data by standardizing it to a common scale. The cumulative probability of a specific z-score represents the proportion of data points that fall to the left of that z-score.

In this case, we are interested in finding the z-score that separates the top 2.8% of the distribution, which corresponds to the area to the left of z. By using the standard normal distribution table or a statistical calculator, we can determine that the z-score is approximately 2.05. This means that 97.2% of the standard normal curve lies to the left of z = 2.05, and only 2.8% lies to the right.

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Answer:

Germany - 90

Step-by-step explanation:

Here are the options to this question

Germany 90

Sweden   78

Japan       63

Canada    75

The appropriate answer should be a multiple of 2, 3, 5, 6, and 9. That is when the number is divided by 2, 3, 5, 6, and 9 it should have a remainder of zero.

90 / 2 = 45

90 / 3 = 30

90 / 5 = 18

90 / 6 = 15

90 / 9 = 10

Thus, the appropriate number is 90

When 78 is divided by 5 and 9, the remainder is not zero

When 63 is divided by 2, 5 and 6, the remainder is not zero

When 75 is divided by 2, 3, 6 and 9, the remainder is not zero

Types of cardioid are Standard cardioid, Nephroid, Limacon, Deltoid, astroid, hypocycloid, and epitrochoid, each with its own unique properties and applications in mathematics and science.

A cardioid is a geometric shape that is formed by tracing a point on a circle as it rotates around another circle of the same size. There are several types of cardioids, each with its own unique properties and characteristics.

Standard cardioid: This is the most common type of cardioid and is formed by tracing a point on a circle as it rotates around another circle of the same size, with the point always being twice as far from the center of the second circle as it is from the center of the first circle.

Nephroid: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is twice its size. The name "nephroid" comes from the Greek word "nephros," which means kidney, as the shape of the curve resembles a kidney.

Limacon: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is slightly larger than itself. The shape of the curve resembles a figure eight.

Deltoid: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is three times its size. The shape of the curve resembles a triangle.

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Answer:

wrong question

Step-by-step explanation:

\(wrong question\)

If the value of the euro was $1.30 last week and during last week the euro depreciated by 5 percent, the value of the euro today is $1.235.

If the euro was worth $1.30 last week and depreciated by 5%, we can calculate the new value by multiplying the original value by (1 - depreciation rate).

Mathematically, the new value of the euro can be calculated as follows:

New Value = Original Value * (1 - Depreciation Rate)

New Value = $1.30 * (1 - 0.05)

New Value = $1.30 * 0.95

New Value = $1.235

Therefore, the value of the euro today is $1.235.

Depreciation is a term used to describe the decline in the value of a currency relative to another currency or to a basket of currencies. It can occur due to various reasons, such as changes in interest rates, inflation rates, political instability, or economic growth.

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Answer:

\(\dfrac{-7}{2}\)

Step-by-step explanation:

Here we are given a polynomial ,

\(\implies f(x) = 2x^3 + Ax^2 + 4x - 5 \)

And the value of ,

\(\implies f(2) = 5 \dots (i) \)

And we need to find out the value of A . Firstly substitute x = 2 in f(x) , we have ,

\(\implies f(2) = 2(2)^3+ A(2)^2 + 4(2) -5 \)

Simplify the exponents ,

\(\implies f(2) = 2(8) + A(4) + 8 - 5 \)

Simplify by multiplying ,

\(\implies f(2) = 16 + 4A + 3 \)

Add the constants ,

\(\implies f(2) = 19 + 4A \)

Now from equation (i) , we have ,

\(\implies 19 + 4A = 5 \)

Subtracting 19 both sides,

\(\implies 4A = 5-19 \)

Simplify,

\(\implies 4A = -14\)

Divide both sides by 4 ,

\(\implies A =\dfrac{-14}{4}=\boxed{ \dfrac{-7}{2}}\)

Hence the value of A is -7/2.

Answer:

The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph below: A graph titled Motion of a Car is shown with Time in hours labeled on x-axis and Distance from Starting Point in miles labeled on y-axis. The scale on the x-axis shows the numbers and the scale on the y-axis shows the numbers There are three straight lines in the graph. The first line joins ordered pair with . The second straight line joins and and the third straight line joins ordered pair with the ordered pair Which of the following best describes the motion of the car shown? It travels for hours, then stops for hours, and finally travels again for hours. It travels for hours, then stops for hours, and finally travels again for hours. It travels for hours, then stops for hour, and finally travels again for hours. It travels for hours, then stops for hour, and finally travels again for hours. Question (Multiple Choice Worth points) ( LC) The graph below shows the height through which an elevator travels, y, in x seconds: A graph is shown with x axis title as Time in seconds. The title on the y-axis is Height of Elevator Above Ground in feet. The values on the x-axis are from toin increments of for each grid line. The values on the y-axis are from to in increments of 10 for each grid line. A line is shown connecting points at ordered pairs 1,10 and 2, 20 and 3, 30 and 4, 40. The title of the graph is Rate of Ascent. What is the rate of change for the relationship represented in the graph? fraction 1 over 40 fraction 1 over 10 10 40 Question 4(Multiple Choice Worth 1 points) (05.03 MC) Barney wants to rent a tent. He has to pay a fixed base cost plus a daily rate for renting the tent. The table shows the amount of money, y, in dollars, that Barney has to pay for renting the tent for x days: Tent Rental Number of days (x) Rent (dollars) (y)

Answer:

z = -10

Step-by-step explanation:

5/10 = 1/2

1/2 of 10 = 5

Answer:

7/2

Step-by-step explanation:

Calculate the product: 15/2 - 4

Solve: 7/2

Answer:

d)

Step-by-step explanation:

turn 9x + y = 8 to slope intercept form

9x + y = 8

-9x         -9x

y = -9x + 8

m = -9

y intercept = 8

Hope this helped! Have a nice day! Plz mark as brainliest!!!

-XxDeathshotxX

The missing premise is "all dogs are non-cats." Therefore, the argument is true.

The given information and analyze the argument step-by-step.

1. Some non-poodles are not non-cats: This statement means that there are some animals that are not poodles and are also cats.

2. No cats are dogs: This statement means that there is no overlap between cats and dogs.

Now, let's try to determine if "some poodles are dogs" can be concluded from these premises:
Since no cats are dogs, it doesn't matter whether some non-poodles are not non-cats. Poodles are a breed of dog, so it's already a fact that poodles are dogs.

So, the answer is True: some poodles are dogs.

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Answer:

(

−

7

)

(

6

+

5

)

g0gf0g0g0

Step-by-step explanation:

There are  19+ 28 + 21 + 29 = 97 balls total

  19 + 21 = 40  are red or blue

      40 out of 97    is   40 / 97 chance of red or blue

The equation that expresses the law of refraction is known as Snell’s law or the law of refraction.

The law of refraction is used to determine the direction in which light bends when it enters a new medium.

What is the law of refraction?

The law of refraction (also known as Snell's law) is a principle of optics used to explain how light behaves at the boundary between two media with different refractive indexes.

The law of refraction states that when light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.

The equation for the law of refraction is as follows:

$$\frac{\sin \theta_1}{\sin \theta_2}= \frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2}=\frac{n_2}{n_1}$$

Where:θ1 = Angle of incidence

           θ2 = Angle of refraction

           v1 = Velocity of light in medium 1

           v2 = Velocity of light in medium 2

           λ1 = Wavelength of light in medium 1

           λ2 = Wavelength of light in medium 2

           n1 = Refractive index of medium 1

           n2 = Refractive index of medium 2

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Y=15

1. use standard form

2/3y _ 10 = 0

2. Factorization

2/3 (y _ 15) =0

3. solution

y = 60/4

y = 15

To minimize the total area of an equilateral triangle and square, the side length of the square should be 2.167 and the side length of the triangle should be 3.833.

To find the dimensions that minimize the total area, we can set up equations based on the given information. Let's denote the side length of the square as 's' and the side length of the equilateral triangle as 't'. The perimeter of the square is 4s, and the perimeter of the equilateral triangle is 3t. Given that the combined perimeter is 13, we have the equation 4s + 3t = 13.

To minimize the total area, we need to consider the formulas for the areas of the square and equilateral triangle. The area of the square is given by A_square = \(s^2\), and the area of the equilateral triangle is given by A_triangle = (\(\sqrt{(3)}\)/4) *\(t^2\).

To find the values that minimize the total area, we can substitute s = (13 - 3t)/4 into the equation for A_square and solve for t. By finding the derivative of the total area with respect to t and setting it equal to zero, we can find the value of t that minimizes the area.

Similarly, to find the dimensions that maximize the total area, we follow the same process but this time maximize the total area by finding the value of t that maximizes the area.

Performing the calculations, we find that to minimize the total area, the side length of the square is approximately 2.167 and the side length of the triangle is approximately 3.833. To maximize the total area, the side length of the square is approximately 4.333 and the side length of the triangle is approximately 1.667.

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Answer:

$9.75

Step-by-step explanation:

65% of 15 is 9.75

Hope this helps∞<3

Let me know if it right or wrong.

Answer:

$9.75

Step-by-step explanation:

To find the sale price, you multiply the sale percent by the original price.  For this problem, it would be 0.65 * 15, which equals $9.75.

(If you didn't already know, you get the decimal version of a percent by moving the decimal at the end two places to the left.)

Answer:

So, I solved it and I got this:

Simplify the expression.

24 x^ 4

Step-by-step explanation:

hope this helps! have a great day!

The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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The expected value of the discrete distribution, for each case, is given as follows:

a) Amount won by one entry: $0.075.

b) If the cost is the cost of a postage stamp:  -$0.525.

The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's probabillity.

In this problem, the distribution for the prizes is given as follows:

Hence the expected value for the prizes is:

E(X) = 10,000,000 x 1/300,000,000 + 350,000 x 1/150,000,000 + 50,000 x 1/10,000,000 + 20,000 x 1/1,000,000 + 400 x 1/200,000 + 75 x 1/6,000 = $0.075.

The cost of a postage stamp is of $0.6, hence the expected value considering this cost would be of:

0.075 - 0.6 = -$0.525.

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