given the relation of this table what is the rule for this relation

a. The time at which the population is at a maximum is 25 hours. b. The maximum population is 1,182,500.

A polynomial function of degree 2 is a quadratic function, while one of degree 1 is a linear function. The formula for a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and an is not equal to 0. A parabola, a U-shaped curve, is the graph of a quadratic function. Depending on the sign of the leading coefficient, the function's minimum or maximum value is located at the parabola's vertex.

a) The highest value of the population function, which is a quadratic function with a negative leading coefficient, occurs near the parabola's vertex.

Thus, t = -b/2a.

Substituting the values  a = -1698, b = 85,000, and c = 10,000 we have:

t = -85000 / 2(-1698) = 25

Therefore, the time at which the population is at a maximum is 25 hours.

b) To determine the maximum population we substitute the value of t = 25.

p(25) = -1698(25)² + 85,000(25) + 10,000 = 1,182,500

Therefore, the maximum population is 1,182,500.

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Answer:

your awnser is C if im wrong message me but I'm positive that I'm right

Let, cost of 1 hot dog and 1 drink is x and y respectively.

Carl bought 4 hot dogs and 6 drinks and paid $23.80.

4x + 6y = 23.80  ....1)

Susan purchased 4 hot dogs and 2 drinks and was charged $15.40.

4x + 2y = 15.40  ....2)

Subtracting equation 2 by 1, we get :

(4x + 6y) - (4x + 2y) = 23.80 - 15.40

4y = 8.4

y = $2.1

4x + 6×2.1 = 23.80

4x = 23.80 - 12.2

4x = 11.6

x = 2.9

Therefore, the  cost of 1 hot dog and what is the cost of 1 drink is $2.9 and $2.1 respectively.

Hence, this is the required solution.

The expression that represents the relationship between the step number n and the total number of small squares in the pattern is this: (n-1)^2.

From the given information, we can see that the pattern starts with 0 squares at step 1, and each subsequent step adds a square to the pattern. However, the lower right square is always missing. Therefore, the total number of small squares in the pattern at step n can be represented by the expression: (n-1)^2

The reason we subtract 1 from n is that we started counting from step 1, whereas the expression (n-1)^2 assumes that we start counting from 0. Then we square (n-1) to account for the number of squares in the pattern, excluding the missing square in the lower right corner.

Complete Question:

Which expression represents the relationship between the step number n and the total number of small squares in the pattern?

A pattern of small squares. Step 1 has 0 squares. Step 3 has 3 squares: 2 by 2 but missing the lower right square. Step 3 has 8 squares: 3 by 3 but missing the lower right square.

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To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.

To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:

Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).

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Answer:

1,4.560

Step-by-step explanation:

I am not so sure.

Answer:

um we cant hear the sound part so

Step-by-step explanation:

Answer:

I think it is supplementary

The total number of muffins were 40 and the equation which represnts the given scenarion is (7/10)x = 28.

Let the total number of muffins be x.

According to the given question.

The number of muffins which blew away by wind = 28

And 28 muffins are the 7/10 part of the total muffins.

Therefore, the linear equation in one variable which represents the above scenario is given by

(7/10)   ×  x = 28

⇒ 7x = 280        (multiplying both the sides by 10)

⇒ x = 280/7          (dividing both the sides by 7)

⇒ x = 40

Hence, the total number of muffins were 40 and the equation which represnts the given scenarion is (7/10)x = 28.

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Answer:

Step-by-step explanation:

Given points

Midpoint formula

Midpoint is (2, 2)

Answer:

r = 106

Step-by-step explanation:

113 + 38 = 151

151 - 45 = 106

r = 106

Answer:

\(\boxed{BC = 11.62}\)

Step-by-step explanation:

Tan 54 = \(\frac{opposite}{adjacent}\)

Where opposite = 16, Adjacent = BC

1.376 = \(\frac{16}{BC}\)

BC = 16/1.376

BC = 11.62

Answer:

11.62468045 or 11.6 to 1 decimal place

Step-by-step explanation:

→ We need to utilise trigonometry. The first step would be to list out the formula triangles

Tan = Opposite ÷ Adjacent

Sin =  Opposite ÷ Hypotenuse

Cos = Adjacent ÷ Hypotenuse

→ Now we need to know which triangle to use, we do that by identifying the side or length we are not given in the triangle and then finding a formula without the name of the given side. First let's identify all the sides.

Opposite = AC = 16

Adjacent = BC = We need to find this out

Hypotenuse = AB = No given value

→ Now we look for a formula with hypotenuse

Tan = Opposite ÷ Adjacent

→ The (Tan = Opposite ÷ Adjacent) is the formula we are going to be using. Since we want to find out the adjacent, we have to rearrange to get adjacent as the subject

Adjacent = Opposite ÷ Tan

→ Now we identify the Opposite and the Tan

Opposite = 16

Tan = 54°

Side note ⇒ Sin, cos and tan will always be the angles

→ Substitute in the values in the formula

Adjacent = Opposite ÷ Tan ⇔ Adjacent = 16 ÷ Tan (54) ⇔ Adjacent = 11.6

→ The adjacent is 11.6 to 1 decimal place

The pros and cons of Kernel Density Estimation (KDE) over histogram has been compared and advantage and disadvantage to each has been given.

Kernel Density Estimation (KDE) and histograms are both methods used for visualizing and estimating probability density functions.

KDE offers advantages such as its ability to capture smooth and continuous distributions, while histograms have benefits like simplicity and ease of interpretation.

However, KDE can be computationally intensive, and histograms may suffer from binning bias.

Kernel Density Estimation (KDE) is a non-parametric method used to estimate the probability density function of a random variable. It offers several advantages over histograms.

Firstly, KDE is able to capture smooth and continuous distributions, providing a more accurate representation of the underlying data.

Additionally, KDE does not rely on binning, allowing for a more precise estimation of the density at any point.

Furthermore, KDE can handle missing or irregularly spaced data.

On the other hand, histograms have their own advantages. They are simple and intuitive, making them easy to understand and interpret.

Histograms also tend to be less computationally intensive compared to KDE, making them suitable for large datasets.

Moreover, histograms can reveal the presence of outliers or gaps in the data due to the discrete nature of the bins.

However, there are also drawbacks to consider. KDE can be computationally intensive, especially for large datasets, requiring more processing power and time compared to histograms.

This can be a limitation when dealing with real-time or interactive applications. In contrast, histograms suffer from binning bias, where the choice of bin size can affect the visual representation and interpretation of the data.

Selecting an inappropriate bin size can lead to either over-smoothing or over-detailing the data distribution.

In summary, KDE offers advantages in capturing smooth distributions and avoiding binning bias, but it may be computationally intensive.

Histograms, on the other hand, are simple and computationally efficient but can suffer from binning bias.

The choice between KDE and histograms depends on the specific characteristics of the data and the objectives of the analysis.

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Answer: no , the correct answer is 3x+2

Step-by-step explanation:

Remove parentheses.

x−1+2x+3

Collect like terms.

(x+2x)+(−1+3)

Simplify.

3x+2

Answer:

y= -1/3x-3

Step-by-step explanation:

The slope is -1/3 because the equation is rise/run. The rise is 1, and the run, or horizontal length, is 3. Because the line is slanting toward the left, the slope will be negative.

y=mx+b is the equation for a linear line.

y= -1/3x+b (substitute the slope in)

choose any point on the line, for example, (0,-3).

-3= -1/3(0)+b   (0 is the x, and -3 is the y)

b= -3

Your equation will be y= -1/3x-3

9514 1404 393

Answer:

  y = -1/4x -3

Step-by-step explanation:

The slope is found by counting grid squares between grid crossing points. The line crosses grid points at (0, -3) and again at (4, -4). That is, for 4 units to the right, it drops 1 unit, so the slope is ...

  m = rise/run = -1/4

The crossing at (0, -3) tells you the y-intercept is b = -3, so the slope-intercept equation is ...

  y = mx +b

  y = -1/4x -3

This indicates that the average number of hours worked by the part-time employees is 17.5 hours per week.

This indicates that the average number of hours worked by the part-time employees is 17.5 hours per week.

17.5 hour

Mean = (5x0.15) + (15x0.28) + (20x0.31) + (25x0.26) = 17.5 hours

The mean of the variable is calculated by multiplying the value of each individual category with its probability, and then summing the resulting values. In this case, the mean is calculated as (5x0.15) + (15x0.28) + (20x0.31) + (25x0.26) = 17.5 hours. This indicates that the average number of hours worked by the part-time employees is 17.5 hours per week.

the complete question is :

Consider the following table of hours worked by part-time employees. These employees must work in 5 hour blocks.Weekly hours worked Probability5 0.1515 0.2820 0.3125 0.26Find the mean of this variable.

Weekly hours   worked Probability

5                              0.15

15                            0.28

20                           0.31

25                           0.26

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The total amount of money that Mike made during summer by solving the equation formed is $3360. And the time that Mike worked whole summer at Six flags was 360 hours.

An equation, like 6 x 4 = 12 x 2, is used to demonstrate that two amounts or values are equal. Numerical noun An equation is a circumstance in which two or more components must be taken into account in order to perceive or comprehend the circumstance as a whole.

a) Let's denote the number of hours that Milk worked at Six Flags as x. Then, the amount of money he earned from Six Flags is given by:

9x

The amount of money he earned from babysitting his sister is given by:

120

Therefore, the total amount of money he made over the summer is:

9x + 120= $3360

b) We are given that the total amount of money Milk earned over the summer is $3,360. Setting this equal to the equation for the total amount of money he made above, we get:

9x + 120 = 3360

Subtracting 120 from both sides:

9x = 3240

Dividing both sides by 9:

x = 360

Therefore, Mike worked 360 hours at Six Flags over the summer.

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A pie chart is commonly used to compare relative parts of a whole. It is a circular chart that is divided into sectors, where each sector represents a proportionate part of the whole.

The size of each sector is proportional to the value it represents, and the whole circle represents the total value. Pie charts are frequently used in business, finance, and statistics to show the relative sizes of different categories or data points. They are easy to understand and can quickly convey complex information in a simple visual format. However, it's important to note that pie charts are not always the most effective way to display data and should be used appropriately depending on the type of data being presented.

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The Critical z-values are -1.96 and 1.96 option second is correct.

It is given that the teachers were allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes.

It is required to find the critical z-values.

It is defined as the area region enclosed by the standard normal curve or bell curve. It gives an idea about every variable, and what value of probability the variables acquire.

We are assuming the data given below:

x = 3.5

\(\mu =3.3\)

\(\sigma = 0.6\)

n = 40

We know the formula for the Z score:

\(\rm Z = \frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }\)

\(\rm Z = \frac{3.5-3.3}{\frac{0.6}{\sqrt{40} } }\)

Z = 2.10

The area under the normal distribution curve:

P(Z= 2.10)  = 0.9821   ( from the z table)

We have null hypothesis H0: in the two groups, the level of job satisfaction is the same ie. with no difference.

H1: There is a significant difference in levels of job satisfaction.

The above hypothesis defined that the test is two-tailed which means there will be two rejection regions.

The critical z-values are:

-1.96 and 1.96  (from the critical value calculator at a 5% significance level with two-tailed)

Thus, the Critical z-values are -1.96 and 1.96 option second is correct.

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The Fourier sine series of the derivative of a function with a jump discontinuity can be expressed in terms of the Fourier cosine series coefficients of the original function.

Let's consider the function f(x) with a jump discontinuity at x = x₀, where f(-x₀) = α and f(+x₀) = β. Since f(x) is continuous except for the jump discontinuity, it can be represented by a Fourier cosine series:

f(x) = A₀ + Σ(Aₙ*cos(nωx))

where A₀ represents the DC component, Aₙ are the Fourier cosine coefficients, and ω is the fundamental frequency.

Now, we want to determine the Fourier sine series of the derivative of f(x), denoted as df/dx. We know that the derivative of the cosine term Aₙcos(nωx) is given by -nωAₙsin(nωx). Thus, the derivative of f(x) can be written as:

df/dx = Σ(-nωAₙ*sin(nωx))

To express df/dx in terms of the Fourier cosine series coefficients, we need to find the Fourier sine series coefficients. These coefficients can be obtained by integrating df/dx over one period and dividing by the appropriate factor. However, since df/dx has jump discontinuity at x = x₀, we need to consider two separate integrals for x < x₀ and x > x₀.

By evaluating the definite integrals, we can express the Fourier sine series of df/dx in terms of the Fourier cosine series coefficients of f(x). This relationship allows us to determine the Fourier sine series representation of the derivative when the original function has a jump discontinuity.

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Answer:

-2w+-14

3d+3

-7y+-16

Step-by-step explanation:

Remove ()-     2w+-9+-4w+-5

2w+-4w = -2w

-9+-5 = -14

-2w+-14

Remove ()-    6d+5+-2+-3d

6d+-3d = 3d

5+-2 = 3

3d+3

Remove ()-   4+-5y+-2y+-16

-5y+-2y = -7y

4+-16 = -12

-7y+-12

PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction. The solution to the Expression (3^0 * 8^2)^-2 is 1/4096.

The expression (3^0 * 8^2)^-2, the order of operations, which is typically referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Simplify the exponent expressions within the parentheses:

(3^0 * 8^2) = (1 * 64) = 64

Step 2: Rewrite the expression with the simplified value:

(64)^-2

Step 3: Apply the exponent rule for a negative exponent:

(64)^-2 = 1 / (64)^2

Step 4: Evaluate the expression within the parentheses:

(64)^2 = 64 * 64 = 4096

Step 5: Rewrite the expression with the simplified value:

1 / 4096

Therefore, the solution to the expression (3^0 * 8^2)^-2 is 1/4096.

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Lee has 9/14 hours left to play the game

Lee's mom said he could play video games for 1 1/2 hours

He has already played the video games for 6/7 hour

The number of time left to play the video games can be calculated as follows

= 3/2 - 6/7

= 21-12/14

= 9/14

Hence Lee has 9/14 hours left to play the video games

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Answer:

The solution is −6+10.

Step-by-step explanation: