Construct the causal diagram and the Forrester diagram that models the following system of equations
dX/dt = X (Y + 1/W) - N dY/dt = Y (W/z - XN)

the rate of change of h(x) at x = 4 is 25. This means that if we increase x by a small amount around 4, h(x) will increase by approximately 25 times that amount.

we need to use the chain rule of differentiation, which states that the derivative of a composite function is the product of the derivative of the outer function and the derivative of the inner function.

In this case, the outer function is the square root of 6 plus 5 times f(x), and the inner function is f(x). Therefore, we have:

h(x) = (sqrt6 + 5f(x))      

Using the chain rule, we can find h'(x) as follows:

h'(x) = (d/dx)(sqrt6 + 5f(x))

= (d/dx)(sqrt6) + (d/dx)(5f(x))

= 0 + 5f'(x)

We know that f(4) = 6 and f'(4) = 5, so we can substitute these values into the equation above to get:

h'(4) = 5f'(4) = 5(5) = 25

Therefore, the value of h'(4) is 25.

In other words, the rate of change of h(x) at x = 4 is 25. This means that if we increase x by a small amount around 4, h(x) will increase by approximately 25 times that amount. The chain rule is a powerful tool in calculus that allows us to find the derivative of complex functions, and it is essential in many applications of mathematics and science.

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Answer:

Last option

Step-by-step explanation:

Step 1: Write out equation

x² + 8x - 10 = 0

Step 2: Add 10 to both sides

x² + 8x = 10

Step 3: Complete the Square

x² + 8x + 16 = 10 + 16

(x + 4)² = 26

Step 4: Square root both sides

x + 4 = ±√26

Step 5: Subtract 4 on both sides

x = -4 ± √26

a. Based on the sample data, the mean price in dollars for a gallon of unleaded gasoline in San Francisco is $3.72.

b. The sample standard deviation in dollars is $0.3589.

Standard deviation,

Mean (the simple average of the numbers

Data and Calculations:

Average price of a gallon of unleaded gasoline in U.S. = $3.28

Number of gasoline and convenience stores for the U.S. average price = 90,000

Sample of San Francisco gasoline and convenience stores = 20

Prices of a gallon of gasoline in 20 San Francisco stores are as follows:

S/N.     Prices Difference in Mean  Difference Squared

1.          $3.59             -$0.13                     0.0169

2.           3.39                -0.33                     0.1089

3.           4.79                 1.07                      1.1449

4.           3.56               -0.16                      0.0256

5.           3.35              -0.37                      0.1369

6.           3.71               -0.01                     0.0001

7.           3.85              0.13                     0.0169

8.           3.40              -0.32                     0.1024

9.           3.55              -0.17                      0.0289

10.         3.76             0.04                      0.0016

11.          3.77             0.05                        0.0025

12.         3.39             -0.33                      0.1089

13.         3.75              0.03                       0.0009

14.         3.79              0.07                      0.0049

15.         4.19              0.47                       0.2209

16.        4.15             0.43                      0.1849

17.        3.66              -0.06                      0.0036

18.        3.93              0.21                       0.0441

19.        3.41              -0.31                       0.0961

20.      3.57              -0.15                       0.0225

Total $74.40                                          2.5765

Mean = $3.72 ($74.40/20)                 $0.12885 ($2.27394/20)

Standard deviation = square root of $0.12885

= $0.3589

Thus, in San Francisco, the price per gallon of unleaded gasoline is $0.03589 .

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To find the average price of unleaded gasoline in San Francisco, add up all the given prices and divide by the total number of prices. The standard deviation, indicating spread around this average price, is computed by finding the square root of the average of the squared deviations from the mean.

To estimate the mean price of a gallon of unleaded gasoline in San Francisco, you need to add up all the 20 given prices, then divide by the number of terms (20) in this case. The mean gives us the average value of the data set.

The standard deviation is a measure of how spread out the prices are from the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.

Remember, these calculations provide estimates, as the sample might not represent the entire population of gasoline prices in San Francisco. It's also important to note that external factors, such as changes in crude oil prices or regional taxes, can impact the cost of unleaded gasoline in diverse regions.

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A rule that makes a particular cell is highlighted in yellow only if the value it contains is less than $5000 is an example of conditional formatting.

This is a special feature that can be found in programs such as excel and allows users to automatically apply specific changes or formatting to cells that meet specific criteria.

There are four main types:

In the case of the formatting described, this can be classified as conditional formatting because all cells that meet the criteria (less than $5000) will be automatically highlighted in yellow. Moreover, the type of formatting is a change in the color of the cell.

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ok

Volume of the tank = 50 x 42 x 50

= 105000 cm^2

Volume of 2/3 of the tank = 2/3 x 105000

= 70000 cm^3

Volume of 3/4 of the tank = 3/4 x 105000

= 78750 cm^3

a) Capacity of the tank = 105000 cm^3

b) Volume of the stone = 78750 - 70000

= 8750 cm^3

Answer:

nayan plays for 45 min

Step-by-step explanation:

count up

Answer:

The answer is either 45 minutes or 90 minutes / 1 and a half hours

Step-by-step explanation:

You either add the two times together, as he plays for 45 minutes at one time and another 45 minutes at a later time. I'm not sure if the question is asking for the sum or how much time he plays for as an average because they are both 45 minutes.

An exponential function can represent growth or decay.

The graph represents an exponential growth function is given by  \(y = ab^{x}\).

An exponential function is represented as:

\(y = ab^{x}\)

Where:

a represents any constant value.

b represents the growth or decay rate of the function

When the value of b is greater than 1, then the exponential function represents growth

Graph shown below represents an exponential growth function.

Hence, the graph representing an exponential growth function is graph traced by \(y = ab^{x}\).

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Answer:

A fraction equivalent to \(\frac{1}{2}\) on the number line is \(\frac{3}{6}\).

Drag the dot to \(\frac{3}{6}\) on the number line.

Step-by-step explanation:

3 is half of 6. To check if this is correct multiply \(\frac{1}{2}\) and 3.

\(\frac{1}{2}*3=\frac{3}{6}\)

Hope this helps!

If not, I am sorry.

Answer:

4 triangles and 1 square

Step-by-step explanation:

If we are to make a net of this pyramid, we'd have a net that has 4 triangles, and 1 square.

The base of the pyramid has 4 sides of equal length of 5 in each. A polygon that has 4 right angles and 4 sides that are of equal sizes or lengths is said to be a square.

Therefore, the net of the figure above is made up of 4 triangles and 1 square.

Answer:  4 triangles and 1 square

Step-by-step explanation

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

To find the area of the region bounded by the graphs of y = 32 / (x² - 17x + 72), y = 0, x = 0, and x = 1, we can use definite integration.

The area of the region bounded by the given graphs is approximately 25 square units.

To find the area, we need to integrate the given function over the interval [0, 1]. The integral represents the area under the curve between the limits of integration. Since the region is bounded by the x-axis, we integrate the function with respect to x.

∫[0, 1] (32 / (x² - 17x + 72)) dx

Evaluating this integral gives us the area of the region bounded by the graphs. Using numerical integration methods, we find that the area is approximately 25 square units.

The integral calculation involves finding the antiderivative of the function and then evaluating it at the upper and lower limits of integration. The resulting value represents the area between the curves and the x-axis within the specified interval.

Therefore, the area of the region bounded by the graphs of y = 32 / (x² - 17x + 72), y = 0, x = 0, and x = 1 is approximately 25 square units.

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Answer:

Step-by-step explanation:

Answer:

6+7= 13

Step-by-step explanation:

you replace a with 7

Answer:

33.15 that is the answer

Answer: 30

Step-by-step explanation: anything below 5 rounds down to 30, 40,50,60,ect. anything 5 and up rounds to the next number 40,50,60,70,ect.  

Answer:

0.0625 miles

Step-by-step explanation:

There is a faster way but this way makes more sense

1/4 miles = 440 yards

440/4 (since 4 people)

110 yards per person

Put back into miles

Everyone ran 0.0625 miles

the likelihood of getting two triumphs (i.e., two reddish balls) when drawing three balls from the urn is for the most part 0.1042, or 10.42%. 

To discover the likelihood of two triumphs, we'll utilize the binomial likelihood condition:

P(X = k) = (n select k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is known as the likelihood of getting k triumphs

n is known as  the number of trials (in this case, drawing three balls)

k is known as  the number of triumphs we need to be had (in this case, two)

p is the likelihood of triumph on each trial (in this case, the likelihood of drawing a red ball)

To discover p, we have to calculate the degree of red balls interior the urn:

p = 10/12 = 5/6

By and by arranged to plug interior the values:

P(X = 2) = (3 select 2) * (5/6)^2 * (1 - 5/6)^(3 - 2)

= 3 * (25/36) * (1/6)

= 0.1042

In this way,

the likelihood of getting two triumphs (i.e., two reddish balls) when drawing three balls from the urn is for the most part 0.1042, or 10.42%. 

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Answer:

89%

Step-by-step explanation:

Step-by-step explanation:

The equilibrium constant (Kc) for the reaction ni₂⁺ + 6nh₃ is [Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆.

The given reaction is:

Ni₂+ + 6NH₃ ⇌ [Ni(NH₃)₆]²⁺

The equilibrium constant (Kc) for this reaction can be obtained by the formula given below

[Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆

The equilibrium constant (Kc) for the reaction ni²⁺ + 6nh₃ is given as

[Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆

Thus, the equilibrium constant (Kc) for the reaction ni²⁺ + 6nh₃ is [Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆.

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Answer:

3. Fifteen weeks

Step-by-step explanation:

well if you subtract the 4000 from the 10000 you get 6000 and then divide 6000 by the 400 and you get 15

The best graphical representation to display the given data would be a vertical bar chart.

In the given question, we are given a table that contains the data for the number of purchases made in a pharmacy. In order to display the data effectively, we need to choose an appropriate graphical representation. In order to choose an appropriate graphical representation, we need to consider the nature of the data. In this case, the data is categorical. Categorical data refers to data that is divided into categories or groups, such as the type of item purchased.

Therefore, we need to choose a graphical representation that is suitable for categorical data. The given table can be represented in a bar chart. A bar chart is a graphical representation that uses bars to represent the data. Each bar represents a category or group and the height of the bar represents the value of the data. In this case, we can use a vertical bar chart to display the data.

The x-axis of the bar chart will represent the type of item purchased, and the y-axis will represent the number of purchases. Each bar will represent a category, and the height of the bar will represent the number of purchases made for that category.

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Answer:

3200

Step-by-step explanation:

Answer:

3200

Step-by-step explanation:

one kilometer = 1000

3.2 * 1000

To transform a polar equation to rectangular coordinates, we use the formulas x = r cos(theta) and y = r sin(theta), where r is the radius and theta is the angle in polar coordinates. For the equation theta = 11 pi/6, we can see that the angle is fixed and the radius can vary, so we can choose any value of r. Let's choose r = 1 for simplicity.

Using the formulas above, we get x = cos(11 pi/6) and y = sin(11 pi/6). Evaluating these trig functions, we get x = -sqrt(3)/2 and y = -1/2. Therefore, the rectangular equation corresponding to theta = 11 pi/6 is y = (-1/2) / (sqrt(3)/2) x, or y = (-1/sqrt(3)) x.

To write this equation in slope-intercept form, we need to solve for y. Multiplying both sides by sqrt(3) and simplifying, we get y = (-sqrt(3)/3) x. Therefore, the slope-intercept form of the equation is y = mx + b, where m = -sqrt(3)/3 is the slope and b = 0 is the y-intercept. In summary, the equation theta = 11 pi/6 corresponds to the line y = (-sqrt(3)/3) x in rectangular coordinates. Its slope-intercept form is y = (-sqrt(3)/3) x.

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Using the law of cosines, it is found that the length of side AB is of AB = 13.

The law of cosines states that we can find the angle C of a triangle as follows:

\(c^2 = a^2 + b^2 - 2ab\cos{C}\)

in which:

For this problem, the parameters are:

C = 120, a = 8, b = 7.

Hence:

\(c^2 = a^2 + b^2 - 2ab\cos{C}\)

\(c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}\)

\(c^2 = 169\)

\(c = \sqrt{169}\)

c = 13.

Hence AB = 13.

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All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.

1.1 Formulation:

The problem can be formulated as follows:

Minimize: 0 (since it is a feasibility problem)

Subject to:

α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1

α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2

α1, α2, α3, α4 are unrestricted

β is unrestricted

y_i ≥ 0 for all points in S1

z_i ≥ 0 for all points in S2

The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.

1.2 Finding a feasible solution:

To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.

Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.

For S1:

(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible

(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible

(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible

(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible

For S2:

(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible

(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible

(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible

(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible

Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

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Question:

Triangles PQR and RST are similar right triangles.  Which proportion can be used to show that the slope of PR is equal to the slope of RT?

Answer:

\(\frac{3 - 7}{-4 - (-7)} = \frac{-5 - 3}{2 - (-4)}\)

Step-by-step explanation:

See attachment for complete question

From the attachment, we have that:

\(P = (-7,7)\)

\(Q = (-7,3)\)

\(R = (-4,3)\)

\(S = (-4,5)\)

\(T = (2,-5)\)

First, we need to calculate the slope (m) of PQR

Here, we consider P and R

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\(P(x_1,y_1) = (-7,7)\)

\(R(x_2,y_2) = (-4,3)\)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\) becomes

\(m = \frac{3 - 7}{-4 - (-7)}\) --------- (1)

Next, we calculate the slope (m) of RST

Here, we consider R and T

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\(R(x_1,y_1) = (-4,3)\)

\(T (x_2,y_2)= (2,-5)\)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\) becomes

\(m = \frac{-5 - 3}{2 - (-4)}\) ---------- (2)

Next, we equate (1) and (2)

\(\frac{3 - 7}{-4 - (-7)} = \frac{-5 - 3}{2 - (-4)}\)

From the list of given options (see attachment), option A answers the question

Answer:

x=8.5

Step-by-step explanation:

\(34x+95=3(14x+9)\\34x+95=42x+27\\95-27=42x-34x\\68=8x\\x=68/8\\x=8.5\)

Answer:

Step-by-step explanation:

34x+95=3(14x+9) foil ()

34x+95=42x+27 subtract 27 from both sides

34x+68=42x  subtract 34x from both sides

68=8x  divide by 8

x=17/2 or 8 1/2

19-28/n

n=7

19-28/7

19-4

=15

Answer:

d for the lazy people like me  :D PROPS TO THE PERSON ON TOP OF ME

Step-by-step explanation:

Answer

3π is the answer here is the steps I couldn't write it I'm busy so I just wanted to help I hope it helps