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The answer is: ∠N ≈ 33°

To find ∠N in ΔLMN, we can use the Law of Cosines which states that c² = a² + b² - 2abcos(C), where c is the side opposite angle C.

In this case, side LM (m) is opposite angle ∠N, side LN (n) is opposite angle ∠L, and side MN (x) is opposite the unknown angle.

So, we can write:
m² = n² + x² - 2nxcos(82°)

Substituting the given values:
x² = 35² + 59² - 2(35)(59)cos(82°)

Solving for x, we get:
x ≈ 64.27

Now, using the Law of Sines which states that a/sin(A) = b/sin(B) = c/sin(C), we can find ∠N:

sin(∠N)/35 = sin(82°)/64.27

sin(∠N) ≈ 0.5392

∠N ≈ sin⁻¹(0.857) ≈ 32.6344°

Therefore, ∠N ≈ 33° to the nearest degree.

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The total differential of w is given by dw = (∂w/∂x)dx + (∂w/∂y)dy + (∂w/∂z)dz + (∂w/∂z)(∂z/∂y)dy + (∂w/∂z)(∂z/∂z)dz.

Differentiation is a process of finding the changes in any function with a small change in By differentiation, it can be checked that how much a function changes and it also shows the way of change Differentiation is being used cost, production and other management decisions. It gives the rate of change independent variable with respect to the independent variable.                                                                                                             First, let's get the partial derivatives of w with respect to x, y, and z: ∂w/∂x = 15x^14yz^11, ∂w/∂y = x^15z^11cos(yz), ∂w/∂z = 11x^15y^z^10 + x^15y^11cos(yz). Next, we need to find (∂w/∂z)(∂z/∂y): ∂z/∂y = cos(y)
So, (∂w/∂z)(∂z/∂y) = x^15y^11z^10cos(y). Substituting these values into the formula for the total differential, we get: dw = (15x^14yz^11)dx + (x^15z^11cos(yz))dy + (11x^15y^z^10 + x^15y^11cos(yz))dz + (x^15y^11z^10cos(y))dy
Simplifying, we get: dw = 15x^14yz^11dx + x^15z^11cos(yz)dy + (11x^15y^z^10 + x^15y^11cos(yz) + x^15y^11z^10cos(y))dz.

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Answer:

A is -4.5,2 and B is 0,-3.5

Step-by-step explanation:

Answer:

Coordinates of A: (-4.5, 2), Coordinates of B: (0, -3.5)

Let x be the price of one donut and y be the price of one kolache. Then we have:

6x + 2y = 8.84 4x + y = 5.36

We can solve for y by multiplying the second equation by -2 and adding it to the first equation:

6x + 2y = 8.84 -8x - 2y = -10.72

-2x = -1.88

Dividing both sides by -2, we get:

x = 0.94

This means that one donut costs $0.94

The mean of the dataset, rounded to the nearest hundredth, is approximately 265.86.

Calculate the mean of the dataset from calculator?

The mean, also known as the average, is a measure of central tendency that represents the typical value of a dataset. It is calculated by summing up all the values in the dataset and dividing the sum by the number of values.

To calculate the mean of the dataset from the calculator output, we need to use the following formula:

mean = Σx / n

where Σx is the sum of all the values in the dataset, and n is the number of values in the dataset.

From the calculator output, we can see that:

Σx = 1861

n = 7

Substituting these values into the formula, we get:

mean = 1861 / 7

mean = 265.857142857

However, the problem asks us to round the mean to the nearest hundredth, so we need to round the answer to two output decimal places. To do this, we look at the third decimal place of the answer, which is 7, and we check the next decimal place, which is 1. Since 1 is less than 5, we leave the third decimal place as it is and drop all the decimal places after it. Therefore, the rounded mean is:

mean  ≈ 265.86

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Answer:

if Mr. Kamau wants to give each of his children an equal amount of money, he can either:

Buy 1 item for his son (costing sh. 324) and 0 items for his daughter, giving each child sh. 162.

Buy 1 item for his son (costing sh. 324) and 1 item for his daughter (costing sh. 220), giving each child sh. 272.

Step-by-step explanation:

Let x be the number of daughter items that Mr. Kamau will buy for his daughter. Since the son's item costs sh. 324, we know that each child should receive sh. (324 + 220x)/2.

We want to find how many items each child will buy, so we need to solve for x in the equation:

(324 + 220x)/2 = 220

Multiplying both sides by 2, we get:

324 + 220x = 440

Subtracting 324 from both sides, we get:

220x = 116

Dividing both sides by 220, we get:

x = 0.527

Since we can't buy a fraction of an item, Mr. Kamau should buy either 0 or 1 daughter item for his daughter. If he buys 0 daughter items, he can give his son sh. (324 + 2200)/2 = sh. 162. If he buys 1 daughter item, he can give each child sh. (324 + 2201)/2 = sh. 272. Therefore, the possible scenarios are:

Mr. Kamau buys 0 daughter items. His son buys 1 item and his daughter buys 0 items.

Mr. Kamau buys 1 daughter item. His son buys 1 item and his daughter buys 1 item.

The expression that represents the length of rope that needs to be lowered is 30 - -20

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Length of rope = helicopter - canyon

So, we have

Length of rope = 30 - -20

Evaluate

Length of rope = 50

Hence, the length of rope is 50 feet

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The volume of the triangular prism is 171 cubic inches.

To find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism. In this case, the base of the prism has an area of 18 square inches and the height is 9.5 inches. So, the volume of the prism can be calculated as follows:

Volume = Base Area x Height
Volume = 18 sq. in. x 9.5 in.
Volume = 171 cubic inches

Therefore, the volume of the triangular prism is 171 cubic inches.

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Answer:

4/5 or 0.8 Waffles per person

Step-by-step explanation:

Divide the 4 waffles among 5 people, 4/5

0.8 waffle.

We have shown that if r is both symmetric and antisymmetric, then r is a subset of the diagonal relation on s, i.e., r ⊆ diagonal.

If the relation r on s is both symmetric and antisymmetric, then for any elements a and b in s, we have:

If (a, b) is in r, then (b, a) must also be in r because r is symmetric.

If (a, b) and (b, a) are both in r, then a = b because r is antisymmetric.

Now, we want to show that r is a subset of the diagonal relation on s, which is defined as:

diagonal = {(a, a) | a ∈ s}

To prove this, we need to show that for any pair (a, b) in r, (a, b) must also be in the diagonal relation. Since r is a relation on s, (a, b) ∈ s × s, which means that both a and b are elements of s.

Since (a, b) is in r, we know that (b, a) must also be in r, by the symmetry of r. Therefore, we have:

(a, b) ∈ r and (b, a) ∈ r

By the antisymmetry of r, this implies that a = b. Therefore, (a, b) is of the form (a, a), which is an element of the diagonal relation.

Therefore, we have shown that if r is both symmetric and antisymmetric, then r is a subset of the diagonal relation on s, i.e., r ⊆ diagonal.

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Answer:

∠ D = 38°

Step-by-step explanation:

given Δ ABC and Δ DEF are similar, then corresponding angles are congruent, so

∠ A and ∠ D are corresponding , so

∠ D = ∠ A = 38°

Answer:

I think you get 0.65 inches of pizza for 1 dollar

Step-by-step explanation:

$13 divided by 20 inches = 0.65

The area of the ring is 1,462.81 square feet, under the condition that a circle is circumscribed around a regular octagon with side lengths of 10 feet.

The area of the ring formed by the two circles can be evaluated using the formula for the area of a ring which is

Area of ring = π(R² - r²)

Here
R = radius of the larger circle
r = smaller circle radius

The radius of the larger circle is equal to half the diagonal of the octagon which is 10 feet. Applying Pythagoras theorem, we can evaluate that the length of one side of the octagon is 10/√2 feet.
Radius of the larger circle is

R = 5(10/√2)
= 25√2/2 feet
≈ 17.68 feet

Staging these values into the formula for the area of a ring,

Area of ring = π(17.68² - 10²) square feet

Area of ring ≈ 1,462.81 square feet
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There were 28 members in the Northview Swim Club on Monday before any new members joined or any current members left.

The equation "m+22-17=33" represents the situation where "m" is the number of members in the Northview Swim Club on Monday.

To solve the equation, we can start by simplifying it:

m + 5 = 33

Next, we can isolate "m" on one side of the equation by subtracting 5 from both sides:

m = 33 - 5

m = 28

Thus, the solution of the equation for the Northview Swim Club on Monday before any new members joined is determined as 28 members.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.

Check the picture below.

The values of the variables are:

c = 86 degrees

d = 168 degrees

a = 57 degrees

b = 94 degrees

Since the polygon is inscribed in a circle, the opposite angles of the polygon are supplementary. Thus, we have:

The top and bottom angles of the polygon are supplementary to angle "d":

c + 92 + 123 = 180 + d

The left and right angles of the polygon are supplementary to angle "c":

c + 94 = 180, so c = 86

The angle "a" is supplementary to angle "d":

a + 123 = 180 + d

The angle "b" is supplementary to angle "c":

b + 86 = 180

Substituting the values of "c" and solving the system of equations, we get:

d = 168

a = 57

b = 94

Therefore, the values of the variables are:

c = 86 degrees

d = 168 degrees

a = 57 degrees

b = 94 degrees

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The correct statement regarding the perimeter of the rectangle is given as follows:

Both are correct.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The rectangle in this problem has:

Hence the perimeter is given as follows:

2 x 10 + 2 x n = 2 x (10 + n) = 20 + 2n = 2n + 20 cm.

Hence both are correct.

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The z-score of the customer that just turned 25 years old is  -1.45. The z-score for an age of 75 years is approximately 2.17, which is greater than 2,  Since a z-score greater than 2 represents a considerable deviation.

(a)

To find the z-score for a customer that just turned 25 years old :

z-score = (x - mean) / standard deviation

Plugging in the values, we get:
z-score = (25 - 45) / 13.8 = -1.45, where x = 25 years, mean  = 45 years, and standard deviation = 13.8 years.
Rounding to the nearest hundredth, the z-score is -1.45.

(b)

To find an example of a customer age with a z-score greater than 2, we need to identify an age that deviates significantly from the mean given the standard deviation. Since a z-score greater than 2 represents a considerable deviation, let's consider an age of 75 years.

Using the same formula as before:

z = (x - μ) / σ

where:

   x is the customer's age (75 years),

   μ is the mean of the distribution (45 years),

   σ is the standard deviation of the distribution (13.8 years).

Calculating the z-score:

z = (75 - 45) / 13.8

z = 2.17

The z-score for an age of 75 years is approximately 2.17, which is greater than 2, fulfilling the requirement of the question.

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The investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.

To solve this problem, we need to use the formula for continuous compound interest:
A = Pe^(rt)

Where A is the amount after t years, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.

Using the given information, we can fill in the table as follows:

Interest Rate | Amount after 4 years
--------------|---------------------
2%            | $4,493.29
3%            | $4,558.56
4%            | $4,625.05
5%            | $4,692.79
6%            | $4,761.81

To find the amount after 4 years at each interest rate, we plug in the values of P, r, and t into the formula and simplify:

2%: A = $4000 * e^(0.02*4) = $4,493.29
3%: A = $4000 * e^(0.03*4) = $4,558.56
4%: A = $4000 * e^(0.04*4) = $4,625.05
5%: A = $4000 * e^(0.05*4) = $4,692.79
6%: A = $4000 * e^(0.06*4) = $4,761.81

Therefore, the investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.

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Based on the given information, we need to determine whether the Mean Value Theorem can be applied to the dosed interval [100-V2, 14:21].

The Mean Value Theorem states that for a function that is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), there exists at least one point c in (a, b) where the slope of the tangent line to the function at c is equal to the average rate of change of the function over the interval [a, b].

In this case, we do not have enough information about the function or its continuity on the interval [100-V2, 14:21]. Therefore, we cannot determine whether the Mean Value Theorem can be applied or not.

However, we do know that for the Mean Value Theorem to be applicable, the function must be continuous on the closed interval. If the function is not continuous on the closed interval, then the Mean Value Theorem cannot be applied.

Therefore, the answer to the question is B. No, because we do not have enough information about the function's continuity on the dosed interval [100-V2, 14:21].

I understand you're asking about the Mean Value Theorem and whether it can be applied to a given interval. Due to some typos in your question, I'm unable to identify the specific interval and function. However, I can provide general guidance.

The Mean Value Theorem can be applied to a function if:
A. The function is continuous on the closed interval [a, b]
B. The function is differentiable on the open interval (a, b)

If the given function meets these two conditions, then the Mean Value Theorem can be applied. Otherwise, it cannot be applied.

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To find the particular solution to this differential equation using undetermined coefficients, we first need to guess the form of the particular solution. Since the right-hand side of the equation is a sinusoidal function, our guess will be a linear combination of sine and cosine functions with the same frequency:

y_p(t) = A sin(2t) + B cos(2t)

We can then find the derivatives of this guess:

y'_p(t) = 2A cos(2t) - 2B sin(2t)
y''_p(t) = -4A sin(2t) - 4B cos(2t)

Substituting these into the differential equation, we get:

(-4A sin(2t) - 4B cos(2t)) + 41(2A cos(2t) - 2B sin(2t)) - 53(A sin(2t) + B cos(2t)) = -580 sin(2t)

Simplifying and collecting terms, we get:

(-53A + 82B) cos(2t) + (82A + 53B) sin(2t) = -580 sin(2t)

Since the left-hand side and right-hand side of this equation must be equal for all values of t, we can equate the coefficients of each trigonometric function separately:

-53A + 82B = 0
82A + 53B = -580

Solving these equations simultaneously, we get:

A = -23
B = -15

Therefore, the particular solution to the differential equation is:

y_p(t) = -23 sin(2t) - 15 cos(2t)

Adding this to the complementary solution (which is just a constant, since the characteristic equation has no roots), we get the general solution:

y(t) = C - 23 sin(2t) - 15 cos(2t)

where C is a constant determined by the initial conditions.
To solve the given differential equation using the method of undetermined coefficients, we need to identify the correct form of the particular solution.

Given the differential equation:
y'(t) + 41y(t) - 53 = -580sin(2t)

We can rewrite it as:
y'(t) + 41y(t) = 53 + 580sin(2t)

Now, let's assume the particular solution Y_p(t) has the form:
Y_p(t) = A + Bsin(2t) + Ccos(2t)

To find A, B, and C, we will differentiate Y_p(t) with respect to t and substitute it back into the differential equation.

Differentiating Y_p(t):
Y_p'(t) = 0 + 2Bcos(2t) - 2Csin(2t)

Now, substitute Y_p'(t) and Y_p(t) into the given differential equation:
(2Bcos(2t) - 2Csin(2t)) + 41(A + Bsin(2t) + Ccos(2t)) = 53 + 580sin(2t)

Now we can match the coefficients of the similar terms:
41A = 53 (constant term)
41B = 580 (sin(2t) term)
-41C = 0 (cos(2t) term)

Solving for A, B, and C:
A = 53/41
B = 580/41
C = 0

Therefore, the particular solution is:
Y_p(t) = 53/41 + (580/41)sin(2t)

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To find the rate of change of the temperature difference between the two spacecraft, we need to first find the temperature at each spacecraft's position at time t=4.

For the first spacecraft, rt sin(t) = r4sin(4) and t=4, so its position is (4sin(4), 4, 0). Using the temperature function, we have T(4sin(4), 4, 0) = (4sin(4))(4)(5-2) = 48.08.

For the second spacecraft, rz cos(t) = r3cos(4) and t=-4/3, so its position is (3cos(4), -4/3, 7). Using the temperature function, we have T(3cos(4), -4/3, 7) = (3cos(4))(-4/3)(5-2) = -9.09.

Therefore, the temperature difference D between the two spacecraft at time t=4 is D = 48.08 - (-9.09) = 57.17.

To find the rate of change of D with respect to time, we use the Chain Rule. Let x = 4sin(t) and y = 4, so D = T(x, y, 0) - T(3cos(t), -4/3, 7). Then,

dD/dt = dD/dx * dx/dt + dD/dy * dy/dt

We already know that D = 48.08 - 9.09 = 57.17, so dD/dx = dT/dx = y(5-2x) = 4(5-2(4sin(4))) = -31.64.

We also have dx/dt = 4cos(4) and dy/dt = 0, since y is constant.

To find dD/dy, we take the partial derivative of T with respect to y, holding x and z constant: dT/dy = x(5-2y) = (4sin(4))(5-2(4)) = -28.16.

Putting it all together, we get:

dD/dt = dD/dx * dx/dt + dD/dy * dy/dt
= (-31.64)(4cos(4)) + (-28.16)(0)
= -126.56

Therefore, the rate of change of the temperature difference between the two spacecraft at time t=4 is -126.56.
Given the paths of the two spacecraft: r1(t) = (t sin(t), t, 0) and r2(t) = (t cos(t), -t, 7), and the temperature function T(x, y, z) = x * y * z^2, we want to determine the rate of change of the temperature difference D at time t=4 using the Chain Rule.

First, let's find the temperature for each spacecraft at time t:

T1(t) = T(r1(t)) = (t sin(t)) * t * 0^2
T1(t) = 0

T2(t) = T(r2(t)) = (t cos(t)) * (-t) * 7^2
T2(t) = -49t^2 cos(t)

Now, find the temperature difference D(t) = T2(t) - T1(t) = -49t^2 cos(t)

Next, find the derivative of D(t) with respect to t:

dD/dt = -98t cos(t) + 49t^2 sin(t)

Now, we need to evaluate dD/dt at t=4:

dD/dt(4) = -98(4) cos(4) + 49(4)^2 sin(4) ≈ -104.32

Thus, the rate of change of the temperature difference D at time t=4 is approximately -104.32 (in decimal notation, rounded to two decimal places).

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Answer:

Step-by-step explanation:

The volume of the pool can be calculated as:

Volume = length x width x height

Volume = 10 ft x 20 ft x 5 ft

Volume = 1000 cubic feet

The mass of the water in the pool can be calculated as:

Mass = Volume x Density

Mass = 1000 cubic feet x 60 pounds/cubic foot

Mass = 60,000 pounds

Therefore, the approximate mass of water in the pool is 60,000 lb , which corresponds to option D.

Step-by-step explanation:

$20-$3-$15= $2

the amount of money spent on the bouncy ball is $2

We want to use properties to write expressions for the length of the other sides of the square.

Remember that the length of all the sides in a square is the same, so we only need to rewrite the above expression in two different ways.

First, we can use the distribute property in the first term:

[tex]\sf 6\times(3x + 8) + 32 + 12\times x[/tex]

[tex]\sf = 6\times3x + 6\times8 + 32 +12\times x[/tex]

[tex]= \sf 18\times x + 48 + 32 + 12\times x[/tex]

So this can be the length of one of the sides.

Now we can keep simplifying the above equation:

[tex]= \sf 18\times x + 48 + 32 + 12\times x[/tex]

To do it, we can use the distributive and associative property in the next way:

[tex]\sf 18\times x + 48 + 32 + 12\times x[/tex]

[tex]= \sf 18\times x + 12\times x + 48 + 32[/tex]

[tex]= \sf (18\times x + 12\times x) + (48 + 32)[/tex]

[tex]= \sf (18 + 12)\times x + 80[/tex]

[tex]= \sf 30\times x + 80[/tex]

This can be the expression to the other side.

The 99% confidence interval for the population mean is between 39.18 and 62.82, assuming that the population is normally distributed.

To construct a confidence interval for the population mean, we need to make certain assumptions about the distribution of the sample data and the population. In this case, we assume that the population is normally distributed, the sample size is small (less than 30), and the standard deviation of the population is unknown but can be estimated from the sample data.

Using these assumptions, we can calculate the confidence interval as:

CI = X ± tα/2 * (s/√n)

Where X is the sample mean, tα/2 is the critical value of the t-distribution with degrees of freedom (n-1) and a confidence level of 99%, s is the sample standard deviation, and n is the sample size.

Plugging in the values from the provided data, we get:

CI = 51 ± 2.898 * (17/√18)

CI = (39.18, 62.82)

Therefore, with 99% confidence, we can estimate that the population mean is between 39.18 and 62.82 based on the provided data.

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The admission price that will yield maximum revenue is $6.

To determine the admission price that will yield maximum revenue, we'll first find the linear demand function using the given data points: ($7, 1000) and ($6, 1200).

Let x represent the admission price and y represent the number of customers per day. We can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given data points:

m = (1200 - 1000) / (6 - 7) = 200 / (-1) = -200

Now, we have the slope and a point, so we can use the point-slope form to find the linear demand function:

y - y1 = m(x - x1)

Using the point ($7, 1000):

y - 1000 = -200(x - 7)

Now, let's rewrite the equation to the slope-intercept form (y = mx + b):

y = -200x + 2400

The revenue (R) is equal to the product of the admission price (x) and the number of customers (y):

R = xy

Substitute the linear demand function (y = -200x + 2400) into the revenue equation:

R = x(-200x + 2400)

To maximize the revenue, we need to find the vertex of the parabola represented by this equation. The x-coordinate of the vertex is given by:

x_vertex = -b / 2a

In this case, a = -200 and b = 2400:

x_vertex = -2400 / (2 * -200) = 6

The admission price that will yield maximum revenue is $6.

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The volume of the solid generated when the right triangle below is rotated about side IK is: 37.7 units²

The three-dimensional figure that is formed by rotating a triangle about it's height is called a Cone.

Where:

The triangle base length will be seen to become the radius of the cone

The triangle height will be seen to become the height of the cone

The formula for the volume of a cone is expressed as:

V = ¹/₃πr²h

Where:

r refers to the radius

h refers to the height

Therefore, we can say that the volume will be expressed as:

V = ¹/₃ * π * 2² * 9

V = 37.7 units²

Thus, that is the  volume of the solid generated when the right triangle below is rotated about side IK.

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The average rate of change for the number of shares from 2 minutes to 4 minutes is 25 shares per minute.

To find the average rate of change for the number of shares from 2 minutes to 4 minutes, we need to know the initial number of shares at 2 minutes and the final number of shares at 4 minutes. Once we have those values, we can use the formula:

average rate of change = (final value - initial value) / (time elapsed)

Let's say the initial number of shares at 2 minutes was 100 and the final number of shares at 4 minutes was 150. The time elapsed between 2 minutes and 4 minutes is 2 minutes. Plugging these values into the formula, we get:

average rate of change = (150 - 100) / 2
average rate of change = 50 / 2
average rate of change = 25

Therefore, the average rate of change is 25 shares per minute.

More on change rate: https://brainly.com/question/30597272

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Answer:

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Step-by-step explanation:

34.16

[tex] \frac{3416}{100} [/tex]