a game has an expected value to you of ​$. it costs ​$ to​ play, but if you​ win, you receive​ $100,000 (including your ​$ ​bet) for a net gain of ​$. what is the probability of​ winning?

a) The logistic equation for this problem is L dP/dt = P(1 - P/L), where L = 2000 and Po = 100.

b)  The maximum reproduction rate is 0.03465 times the current population.

a. The logistic equation for this problem is:

L dP/dt = P(1 - P/L)

where L is the carrying capacity of the lake, P is the current population, and dP/dt is the rate of change of the population over time.

We know that at t = 0, P = 100, and one year later at t = 1, P = 200. So we can use this information to find k, which is the growth rate coefficient:

P(t) = L / (1 + (L / Po - 1) * exp(-kt))

200 = L / (1 + (L / 100 - 1) * exp(-k))

200 = L / (1 + (L - 100) * exp(-k))

200 + 200L - 20000 = L * (1 + (L - 100) * exp(-k))

200L -\(L^2\) * exp(-k) + 200L * exp(-k) - 10000 * exp(-k) = 0

\(L^2\) - 400L + 5000 = (L - 200)^2 - 30000

\((L - 200)^2\) = 35000

L = 200 + sqrt(35000) ≈ 223.6

So L ≈ 223.6, and we can use this to find k:

2000 = 223.6 / (1 + (223.6 / 100 - 1) * exp(-k))

20000 + 2000L - 2236 = L * (1 + (L - 100) * exp(-k))

2236 - \(L^2\)  * exp(-k) + 2236 * exp(-k) - 100 * exp(-k) = 0

\(L^2\) - 4472L + 220000 = 0

(L - 2000)(L - 100) = 0

So either L = 2000 or L = 100. We know that L ≠ 100, since we know that the population stabilizes at 2000 after a long time. Therefore, L = 2000, and we can solve for k:

k = -ln((L / Po - 1) / (1 + (L / Po - 1))) / t

k = -ln((2000 / 100 - 1) / (1 + (2000 / 100 - 1))) / 1

k ≈ 0.0693

Therefore, the logistic equation for this problem is:

L dP/dt = P(1 - P/L)

dP/dt = 0.0693P(1 - P/2000)

b. The maximum reproduction rate occurs when the population is halfway to the carrying capacity, or P = L/2. At this point, the equation becomes:

dP/dt = 0.0693P(1 - 0.5)

dP/dt = 0.03465P

Therefore, the maximum reproduction rate is 0.03465 times the current population. For example, if the current population is 1000, the maximum reproduction rate is 34.65 fish per year.

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Full Question : Logistic Equation: L dP dt P(1-2). P() = L - Po Po 1+ 4e ki Where A 1. Fish population in a lake grows according to the logistic law. The initial population of 100 fish and year later it was 200. After a long time fish population stabilized at 2000.

a. Write down the logistic equation for this problem.

b. What is the maximum reproduction rate (fish/year)?

Answer:

4

Step-by-step explanation:

to evaluate (f ○ g)(3) , evaluate g(3) then substitute the value obtained into f(x) , that is

g(3) = 3 - 5 = - 2 , then

f(- 2) = (- 2)² = 4

Answer:

The fraction is 3/10 = .3

Answer: -1.3

Step-by-step explanation:

The mean is their average so add them up and divide it by the number of values.

(-4) + (-3) + (-1) + ( -1) + (0) + (1) = -8

-8/6 = 1.333....

The correct answer is d. 10 years.

To find out how many years it will take for Jiefei to double her initial investment, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = initial investment
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, Jiefei's initial investment will double, so the final amount (A) will be 2 times her initial investment (P). The interest rate (r) is given as 7.125%, which is equivalent to 0.07125. Since the interest is compounded annually, n = 1.
So the equation becomes:
2P = P(1 + 0.07125/1)^(1*t)
Simplifying the equation:
2 = (1 + 0.07125)^t
Taking the natural logarithm of both sides:
ln(2) = ln(1 + 0.07125)^t
Using the logarithmic property:
ln(2) = t * ln(1 + 0.07125)
Solving for t:
t = ln(2) / ln(1 + 0.07125)
Using a calculator:
t ≈ 9.95 years
Rounding up to the nearest whole number, it will take approximately 10 years for Jiefei to double her initial investment.

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Circle O area = pi * r²

= 64π

Circle A area = π × 4²

= 16π

Circle B area = π × 2²

= 4π

shaded area = Circle O area - Circle A area + Circle B area

= 64π - 16 π + 4π

=52π cm²

A simple linear regression model is appropriate when the response variable is influenced by only one explanatory variable.

A simple linear regression model assumes a linear relationship between the response variable (y) and a single explanatory variable (x).

It is suitable when we want to understand how changes in the explanatory variable affect the response variable.

In the given options, the situation where the response variable y is influenced by one explanatory variable aligns with the requirements of a simple linear regression model.

This means that the relationship between y and x can be adequately described by a straight line.

The model aims to estimate the slope and intercept of this line, allowing us to make predictions and draw conclusions about the impact of the explanatory variable on the response variable.

If the response variable y is influenced by two or more explanatory variables, a multiple linear regression model would be more appropriate.

Multiple linear regression allows for the analysis of the combined effects of multiple predictors on the response variable, accounting for their individual contributions.

Similarly, if the explanatory variable x is influenced by two or more response variables, a different modeling technique, such as multivariate regression, would be more suitable.

Therefore, the situation where the response variable y is influenced by one explanatory variable is the scenario where a simple linear regression model is appropriate.

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Answer:

6 thousandths

Step-by-step explanation:

the 2 is tenths the 3 is hundreths and the 6 is thousandths

Answer:

The 6 is in the thousands place.

Answer:

1. Two points coplanar with the point D are the points A and B which are on the same plane, K, as the point D

2. Another name for the line P is a straight straight angle AEB

3. The intersection of line r and plane K is the point X

4. A point non-coplanar to the plane K is the point W

Step-by-step explanation:

1. Two points collinear to point D are point E and F.

2. Another name of line p is line AB

3. the intersection of line r and plane K is point X

4. Points W and Y are non-coplanar to plane K

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\({ \red{ \boxed{ \sf{ \sqrt{344} \: units}}}}\)

Step-by-step explanation:

Let, (9, 3) = (x1, y1) and (21, 23) = (x2, y2)

By using distance formula, we can find the answer. Let us use the formula and get answer fast.

\({ \sf{d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}\)

Substitute all the values in this above formula.

\({ \sf{d = \sqrt{ {(21 - 9)}^{2} + {(23 - 3)}^{2} }}} \)

\({ \sf{d = \sqrt{ {(12)}^{2} + {(20)}^{2} }}} \)

\({ \sf{d = \sqrt{144 + 200}}} \)

\({ \sf{d = \sqrt{344} \: units}} \)

The average population being studied is people with warts. Specifically, this population includes individuals of all ages who have been diagnosed with any type of wart caused by a virus, such as common warts, plantar warts, and flat warts.

The population being studied is people with warts. Warts are caused by a virus and can occur anywhere on the body. Common warts, plantar warts, and flat warts are the most common types. Common warts are usually found on the hands and fingers, and are usually round and raised. Plantar warts are found on the soles of the feet and can be painful. Flat warts are usually found on the face, arms, and legs, and are generally flat and smooth. People of all ages can be affected by warts, and they are highly contagious and can be spread through contact with an infected person or surface. Treatment options include over-the-counter medicines and prescription medications, as well as cryotherapy and laser treatments. This population is being studied to better understand the causes, risk factors, and treatments for warts.

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The complete question is

what is the population being studied warts and  the prevalence of warts in the population being studied?

Answer:

True

Step-by-step explanation:

The given statement "John Graunt is said to be the first to employ quantitative methods to describe population vital statistics" is true as he was interested in how various factors affected mortality rates and population growth.

Quantitative methods are used to quantify and assess data. These techniques are employed by statisticians and scientists in a variety of fields, including psychology, economics, and public health. Quantitative data can be transformed into statistical analyses to make sense of patterns, patterns, and relationships.

John Graunt was a London haberdasher who lived from 1620 to 1674. He is known as the father of vital statistics, and he was the first to employ quantitative methods to describe population vital statistics.

Graunt was interested in how various factors affected mortality rates and population growth, and he used statistical methods to investigate these issues.

In summary, John Graunt is said to be the first to employ quantitative methods to describe population vital statistics.

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The Solution:

We are to name each of the polynomials based on their number of terms and degrees.

Thus, all the answers are correct as ticked in the above pictures.

Answer:

55%

Step-by-step explanation:

to find percentages:

\(\frac{part}{whole}\) I \(\frac{percent}{100}\)     pretend this is a box

basically just fill this in and it will give you what you want. For example, here, you have the original and part of the original so it will look like this:

\(\frac{99}{180}\) I \(\frac{x}{100}\) then you multiply across and divide top to bottom (doesn't matter in which order), so: \(\frac{99}{180}\) =0.55 · 100 = 55%.

It is 45 because im doing my work right now on Aleks and it just told me

Step-by-step explanation:

Answer:

stop rushing me aaaaaaaaaahhhhhhhh

Step-by-step explanation:

The probability that micah is included in the group of students chosen is ²⁸²⁸²⁸C₃₃₂ / ²⁸²⁸²⁸C₃₃₃

According to the question,

Total number of students in class = 282828

Micha's roll number = 111

Micha's teacher is randomly selecting students

Number of students to be selected = 333

So , Total number of ways to select 333 students from 282828 is

=> ²⁸²⁸²⁸C₃₃₃

Now , We have to find the probability that micah is included in this sample.

So, Lets fixed the place of micah

Number of students left after fixing micah place = 333 - 1

=> 332

Number of ways to select these 332 = ²⁸²⁸²⁸C₃₃₂

Therefore , Probability = ²⁸²⁸²⁸C₃₃₂ / ²⁸²⁸²⁸C₃₃₃

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Answer:

18

Step-by-step explanation:

f(x)=2x and g(x)=x2+3, find (g ∘ f)(−3)

f(x)= 2(-3)= -6

g(x)= (-3)(2) +3= -6+3= -3

(g ∘ f) = -6 x -3= 18

Answer:

\(y = \frac{6}{5} x-\frac{7}{5}\)

Step-by-step explanation:

6x - 5y = 7 is in standard form

-5y = -6x + 7

divide all terms by -5

\(y = \frac{6}{5} x-\frac{7}{5}\)

Answer:

19 bags of chips

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

10.45 ÷ 0.55 = 19

$0.55 x 19 = $10.45

Answer:

0.6376785714275 is the average degrees celcius in the city.

Step-by-step explanation:

In order to find the average, I must add the numbers and divide them by 4.

2.34 + -2/7 + -0.45 + 3/8 = 2.55071428571

2.55071428571/4 = 0.6376785714275

I AM 100% SURE

Can I have Brainliest?

Answer:

0.36

0.0068

0.043

0.00048

Step-by-step explanation:

trust me bro

The value of a/b is  \(\sqrt{6}\) / 2

The area of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.

Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items. Measurements of surface areas required for estimation of painting houses, buildings, etc.

According to the question:-

Side of an equilateral triangle equals a/3.

Therefore, the equilateral triangle's area is equal to (1/2)(a/3)2 sqrt (3) / 2 = a2 [sqrt (3)/ 36].

Hexagonal side equals b / 6.

The area is thus 6 (1/2) (b/6)^2 sqrt (3) / 2 

= b^2 [ 3 sqrt (3) / 72] = b^2 [sqrt (3) / 24]

So

sqrt (3) / 36 a2 = sqrt (3) / 24 b2

So

A2 / B2 = [Sqrt(3)/24] / [Sqrt(3)/36]

a^2 / b^2 = [ 36 / 24 ]

a^2/ b^2 = 3/2

A/ B = Sqrt(3) / Sqrt(2)

=Sqrt(6) / 2

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To determine who has the higher tax burden based on a 7 percent sales tax rate, we need to compare the tax amount paid by different individuals or entities.

The tax burden will be higher for those who make larger purchases or spend more money. The sales tax is typically calculated as a percentage of the purchase price of goods or services. In this case, with a 7 percent sales tax rate, every purchase will have an additional 7 percent added to its price as tax.

To determine who has the higher tax burden, we need to compare the tax paid by different individuals or entities. The tax burden will depend on the amount of money spent on taxable items. Those who make larger purchases or spend more money will pay a higher tax amount and thus have a higher tax burden.

For example, if Person A spends $1,000 on taxable items, their sales tax burden will be 7 percent of $1,000, which is $70. On the other hand, if Person B spends $500 on taxable items, their sales tax burden will be 7 percent of $500, which is $35. In this scenario, Person A has a higher tax burden compared to Person B because they are spending more money and, therefore, paying a higher tax amount.

It's important to note that the sales tax burden can vary depending on individual spending habits, purchasing power, and the type of items being purchased. Individuals or entities with higher incomes or those who make more significant purchases will generally have a higher tax burden compared to those with lower incomes or smaller purchases.

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The correct answer choice:

The student would be able to afford the in-state cost for one year at a public 2-year college.

The correct option is D.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

A student is planning to attend college in 5 years.

The student has saved $1,200 and plans to save another $50 per month over the next 60 months.

The total savings,

= 1200 + (50 x 60)

= $4200

That is equivalent to the cost of one year at a public 2-year college.

Therefore, the saving amount is equivalent to the cost of one year at a public 2-year college.

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The table shows the cost per year of attending different types of colleges.

A student is planning to attend college in 5 years. The student has saved $1,200 and plans to save another $50 per month over the next 60 months.

Based on this information about the student's plan, which statement about the possible choices for a college is true?

Answer choices

The student would be able to afford the cost for one year at a private 4-year college.

The student would be able to afford out-of-state cost for half a year at a 4-year public college.

The student would be able to afford in-state cost for half a year at a public 4-year college.

The student would be able to afford in-state cost for one year at a public 2-year college.

Answer:

x=8 y=2

Step-by-step explanation:

the ratio is 9:6 so it'll be 3:2

complete one by one, pair by pair

\( \frac{4 + x}{3} = \frac{x}{2} \)

then complete for y

\( \frac{4 + y}{3} = \frac{4}{2} \)

Statement (B) The mean lies to the left of the median for a positively skewed distribution because there will be fewer data on the right side is correct.

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

We know on the left side skewed histogram has more data on the right and on the left side, there are fewer data. It is also called a negatively skewed histogram.

On the right side skewed histogram, there is fewer data on the right side and more data on the left side. It is also called a positive histogram.

Thus, statement (B) The mean lies to the left of the median for a positively skewed distribution because there will be fewer data on the right side is correct.

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Answer:

We can determine the roots of the quadratic equation f(x) = x^2 + 4x + 7 by using the quadratic formula, which states that for a quadratic equation of the form ax^2 + bx + c = 0, the roots are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 4, and c = 7. Substituting these values into the quadratic formula, we get:

x = (-4 ± sqrt(4^2 - 4(1)(7))) / 2(1)

Simplifying this expression, we get:

x = (-4 ± sqrt(16 - 28)) / 2

x = (-4 ± sqrt(-12)) / 2

Since the square root of a negative number is not a real number, the roots of the equation f(x) = x^2 + 4x + 7 are complex conjugates. Therefore, the equation has no real roots.

Answer: Devon, Tasha, Liza, Effon

Step-by-step explanation:

From the question, we are informed that four friends race their bikes down the street and that Evan finishes in 6.2 seconds, Devon in 6.0999 seconds, Liza in 6.188 seconds, and Tasha in 6.168 seconds.

The order that shows the friends' times from fastest to slowest is:

• Devon

• Tasha

• Liza

• Effon

Devon used 6.0999 seconds which is the fastest time, after then Tasha comes next with 6.168 seconds, then Liza with 6.188 seconds and lastly Effon with 6.2 seconds

The distance between the skew lines given by the equations \(X = y + 73, z = 0 and 2x - 1 = X = z + 3\) is equal to \(\sqrt{(d^2 - p^2)}\), where d is the distance between the parallel planes that contain the lines, and p is the perpendicular distance between the lines and one of the planes.

To find d, we need to determine the normal vectors of the planes that contain the lines. For the first line, the direction vector is (1, 1, 0), and for the second line, it is (2, -1, 1). Taking the cross product of these two vectors, we obtain the normal vector of the plane containing the first line as (1, -1, -3).

Next, we find the perpendicular distance p between the lines and one of the planes. Substituting the coordinates of any point on the first line into the equation of the second line, we get \(2(y + 73) - 1 = y + 3\), which gives y = -35. Therefore, the perpendicular distance between the lines and the plane is \(|-35 - 0| = 35.\)

Finally, we can calculate the distance between the skew lines:

\(\sqrt{((-35)^2 - 35^2)}\)

\(=\sqrt{(-35^2)}\)

= 35.

Hence, the distance between the skew lines X = y + 73, z = 0 and 2x - 1 = X = z + 3 is 35 units.

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