what are the numbers for pie I need to know

Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:

```matlab

a = -2;    % Lower limit

b = 2;     % Upper limit

n = 1000;  % Number of subintervals (increase for higher accuracy)

h = (b - a) / n;   % Step size

x = a:h:b;         % Generate evenly spaced x values

y = 1 ./ (25 + x.^2).^1.5;  % Evaluate the function at x

approximation = h * (sum(y) - (y(1) + y(end)) / 2);  % Trapezoidal Rule approximation

fprintf('Approximation: %.6f\n', approximation);

```

1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).

2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).

3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.

4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.

5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.

The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.

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Answer:

There will be less than 1 gram of the radioactive substance remaining by the elapsing of 118 days

Step-by-step explanation:

The given parameters are;

The half life of the radioactive substance = 45 days

The mass of the substance initially present = 6.2 grams

The expression for evaluating the half life is given as follows;

\(N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}\)

Where;

N(t) = The amount of the substance left after a given time period = 1 gram

N₀ = The initial amount of the radioactive substance = 6.2 grams

\(t_{1/2}\) = The half life of the radioactive substance = 45 days

Substituting the values gives;

\(1 = 6.2 \left (\dfrac{1}{2} \right )^{\dfrac{t}{45}\)

\(\dfrac{1}{6.2} = \left (\dfrac{1}{2} \right )^{\dfrac{t}{45}\)

\(ln\left (\dfrac{1}{6.2} \right ) = {\dfrac{t}{45} \times ln \left (\dfrac{1}{2} \right )\)

\(t = 45 \times \dfrac{ln\left (\dfrac{1}{6.2} \right ) }{ln \left (\dfrac{1}{2} \right )} \approx 118.45 \ days\)

The time that it takes for the mass of the radioactive substance to remain 1 g ≈ 118.45 days

Therefore, there will be less than 1 gram of the radioactive substance remaining by the elapsing of 118 days.

Graph the solution of the inequality 4.5k>18 is equal to  k > 4 ( see image), by using the inequality equation.

Based on the given conditions,

4.5k>18

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

a ≠ b says that a is not equal to b

a < b says that a is less than b

a > b says that a is greater than b

(those two are known as strict inequality)

a ≤ b means that a is less than or equal to b

a ≥ b means that a is greater than or equal to b.

To solve given graph,

We can write,

4.5k>18

4.5k - 18 > 0

4.5k > 18

k > 18/4.5

We can get the division,

k > 4   (We can see image)

Therefore,

4.5k>18 Graph the solution of the inequality is k > 4 ( see image ), by using inequality equation.

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Answer:

depends on how many actives there are and maybe on if they preferred one over another it would get more time

Step-by-step explanation:

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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When Cedric walked into a party, two-thirds of those invited had already arrived. Six more people arrived just after Cedric, bringing the number at the party to of those invited. The total number of invited guests is 18 by Linear equations

What was the total number of invited guests?

There are different methods of solving the problem, and we will use the following steps to get the solution of the problem: Let the total number of invited guests be x.Let's solve the problem with a step-by-step explanation.

Step 1: At the time Cedric arrived, two-thirds of the guests were already present.Let the number of guests present at the party when Cedric arrived be A. Therefore, A = (2/3)x

Step 2: Six more people arrived after Cedric got there. Therefore, the total number of guests after the six people arrived is A + 6.

Step 3: The total number of guests present was also x, which is the total number of guests invited. Therefore A + 6 = x.

Step 4: Substitute A = (2/3)x from Step 1 into A + 6 = x from Step 3 to obtain: (2/3)x + 6 = xStep 5: To solve for x, we will get rid of the fraction by multiplying every term by 3x.

Then we will simplify. 3x * (2/3)x + 3x * 6 = 3x * x Simplifying further  2x + 18 = 3x Subtracting 2x from both sides of the equation 18 = x.

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After answering the given query, we can state that The Pythagorean formula can also be used to determine the cone's cut-off end's diameter: d = (r2 - y2)/2 = (7.2 - 0.6)/2 = 14.27 inches (approximately)

An item with a level base and a smooth, tapering tip or vertex is referred to as a cone in three dimensions. A cone is formed by joining a succession of line segments, half-lines, or lines that link every point on the base in a plane without vertices. A cone is a three-dimensional construction with a smooth shift from a flat, usually circular base to the vertex or peak, which acts as the base's center's axis. An apparent three-dimensional geometric form with a vertically smoothed curved surface is called a cone.

x/h equals (r + y)/r

(r - (h - x - 3)) = (r - (h - x - 3)) = x/h/r

x = r - y = r - (h - x - 3)

x = (2r - h + 3)/2

V = (1/3)πr^2h

2,034.72 = (1/3)πr^2h

2,034.72 = (1/3)πr^2(h - x - 3)

2,034.72 = (1/3)πr^2(h - ((2r - h + 3)/2) - 3)

After simplifying and finding "r," we arrive at:

7.2 centimeters is r.

The height of the removed portion can now be determined using the calculation for "x":

Inches are equal to x = (2r - h + 3)/2 = (2(7.2) - 24 + 3)/2 = 0.6

The Pythagorean formula can also be used to determine the cone's cut-off end's diameter:

d = (r2 - y2)/2 = (7.2 - 0.6)/2 = 14.27 inches (approximately)

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The equation to model the number of ants, A, Ravi will still have after h hours is: A = 25,000 * (1 - 0.356)^h. This equation represents the initial number of ants, 25,000, multiplied by the decay factor, (1 - 0.356), raised to the power of h, the number of hours that have passed.

To find out how many ants Ravi still has after 3 hours, we can plug in h = 3 into the equation: A = 25,000 * (1 - 0.356)^3 = 25,000 * 0.644^3 = 10,563.91. Round to the nearest ant, Ravi still has 10,564 ants after 3 hours.

To find out how long it will take until all of Ravi's ants are gone, we can set A = 0 and solve for h: 0 = 25,000 * (1 - 0.356)^h. Taking the natural log of both sides and rearranging gives us: ln(0/25,000) = h * ln(1 - 0.356), or h = ln(0/25,000)/ln(1 - 0.356). However, since the natural log of 0 is undefined, we cannot find an exact value for h. This means that it will take an infinitely long time for all of Ravi's ants to be gone.

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For the first question, with 0.200 mol of a compound in a 0.720 M solution, the volume of the solution is approximately 0.278 L. For the second and third questions, the molarities are approximately 0.538 M.

Question 3:

To find the volume (in liters) of a 0.720 M solution containing 0.200 mol of a compound, you can use the formula:

Molarity (M) = moles (mol) / volume (L)

0.720 M = 0.200 mol / volume (L)

Rearranging the formula, we get:

volume (L) = moles (mol) / Molarity (M)

volume (L) = 0.200 mol / 0.720 M

volume (L) ≈ 0.278 L

Therefore, the volume of the solution is approximately 0.278 L.

Question 4:

To find the molarity of a solution with 1.75 mol of sucrose in a total volume of 3.25 L, we can use the formula:

Molarity (M) = moles (mol) / volume (L)

Molarity (M) = 1.75 mol / 3.25 L

Molarity (M) ≈ 0.538 M

Therefore, the molarity of the solution is approximately 0.538 M.

For the third question, the molarity of the solution can be found using the formula:

Molarity (M) = moles (mol) / volume (L)

First, we need to convert the mass of glucose from grams to moles:

moles of glucose = mass of glucose (g) / molar mass of glucose (g/mol)

moles of glucose = 43.7 g / 180.16 g/mol

moles of glucose ≈ 0.242 mol

Now, we can find the molarity of the solution:

Molarity (M) = 0.242 mol / 0.450 L

Molarity (M) ≈ 0.538 M

Therefore, the molarity of the solution is approximately 0.538 M.

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Answer:

Slope: -8

Y intercept: (0,1)

Step-by-step explanation:

^^^^

Answer:

\(\star\mathtt{Ans.\:\#1:\:Slope:-8}\)

\(\star\mathtt{Ans.\:\#2:\:y\:intercept:\:1}\)

Step-by-step explanation:

Hi student, let me help you out.

................................................................................................................

First note that the equation we are working with is in slope intercept form. Do you remember the slope intercept form equation? It's \(\mathtt{y=mx+b}\).

In the slope intercept form equation, "m" denotes "slope" and "b" denotes "y intercept".

Looking back at our equation, let's work out the slope & y intercept.

Let's put these two equations together:

\(\mathtt{y=mx+b}\)

\(\mathtt{y=-8x+1}\)

See what I mean? The y intercept of this equation is 1 and the slope is -8.

Hope this helped you out! Ask in comments if any queries arise.

Best wishes from "reflect"!

\(\star\bigstar\underline{\overline{\overline{\underline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star\)

\(\underline{\rule{300}{6}}\)

To solve the given problem first we need to find the equation for line then we have to find the intersection point on circle.

You will pick up a signal from the transmitter in 29% of the drive.

Given:

The radius is 53 mile.

The origin point of transmitter is .

Calculate the slope of line with point  and .

Substitute the value.

Write the general equation of line.

Now we got the equation of line,

Write the transmitter reach the area enclosed by the next circle.

Substitute the value of .

Thus, You will pick up a signal from the transmitter in 29% of the drive.

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(a) The range of c₁ (the objective coefficient of x₁) for which this BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ (the right-hand side of the second constraint) for which this BFS remains optimal is 3 ≤ b₂ < 4.

(c) The dual price of the second constraint is 0.

(a) The optimality condition for a linear programming problem requires that the objective coefficient of a non-basic variable (here, x₁) should not increase beyond the dual price of the corresponding constraint. In this case, the dual price of the second constraint is 0, indicating that increasing the coefficient of x₁ will not affect the optimality of the basic feasible solution. Therefore, the range of c₁ for which the BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ for which the BFS remains optimal is determined by the allowable range of the corresponding dual variable. In this case, the dual price of the second constraint is 0, implying that the dual variable associated with that constraint can vary within any range. As long as 3 ≤ b₂ < 4, the dual variable remains within its allowable range, and thus, the BFS remains optimal.

(c) The dual price of a constraint represents the rate of change in the objective function value per unit change in the right-hand side of the constraint, while keeping all other variables fixed. In this case, the dual price of the second constraint is 0, indicating that the objective function value does not change with variations in the right-hand side of that constraint.

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The number of students in each bus is 21

Given data

Total number of students on the trip = 172

25 students traveled in cars

7 buses were filled

let the number students on each bus be x

number of students on the bus is gotten by

172 - 25 = 147

so 147 students travelled by bus and the total number of buses is 7.

to get the number of students in each bus we solve as follows

147 / 7 = 21

Hence each bus contains 21 students.

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Answer:A

Step-by-step explanation:

Answer:

1,420 grams per 100 baseballs

Step-by-step explanation:

Set up an equation:

Variable x = grams per 100 baseballs

1/14.2 = 100/x

Cross multiply

1 × x = 14.2 × 100

1x = 1420

x = 1420

To get the total surface area: 120 + 260 + 240 = 620 cm^2

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

All triangles are contained in a single plane if all geometry is on the Euclidean plane, but in higher-dimensional Euclidean spaces, this is no longer the case.

The definition of the terminology used to classify triangles can be found on the first page of Euclid's Elements, which dates back more than two thousand years. In modern classification, names are either directly transliterated from Euclid's Greek or translated from Latin.

According to our question-

(24 × 5) ÷ 2

120 ÷ 2 = 60 cm^2

Since there are two triangles:

60 × 2 = 120 cm^2

Dimensions of two similar rectangles:

The two short lines, which indicate that this is an isosceles triangle, show that they are identical. Both of their sides are the same.

A = L × W

Substitute

10 × 13 = 130

Considering there are two:

130 × 2 = 260 cm^2

Dimensions of the rectangle at bottom:

- Don't overlook the rectangle that forms the base of this shape.

A = L × W

Substitute

24 × 10 = 240 cm^2

To determine the overall surface area, add all of these together:

120 + 260 + 240 = 620 cm^2

Hence, To get the total surface area: 120 + 260 + 240 = 620 cm^2

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The sum of the measures of the angle of a triangle is 180 degrees.

The given triangle is a type of triangle and the type of triangle a scalene triangle.

For a scalene triangle, the measure of the three sides are unequal and the sum of the interior angle of a triangle is 180 degrees.

Hence the measure of the angles <A, <B and <C are all less than 90 degrees since they are all acute angles.

We can therefore conclude that:

m<A + m<B + m<C = 180 degrees

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The correct option is A) 9∕8, evaluating the exponent expression with a = -2 and b = 3, we find that the value is -8.

We are given the expression a^b, where a = -2 and b = 3. Substituting these values into the expression, we have (-2)^3.

To evaluate this expression, we raise -2 to the power of 3. When we raise a negative number to an odd power, the result will be a negative number.

So, (-2)^3 will yield a negative value.

Calculating (-2)^3, we multiply -2 by itself three times: (-2) × (-2) × (-2). This equals -8.

Therefore, the correct option is A) 9∕8 and the value of the exponent expression (-2)^3 is -8.

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The solutions to the given system are (4, 3) and (-3, -4).

The given system is,

y = x-1

x²+y² =25

The first equation,

y = x - 1, is a linear-quadratic system.

Substituting y = x - 1 into the second equation, we get:

x² + (x - 1)² = 25

Simplifying this equation, we get:

2x² - 2x - 24 = 0

Dividing by 2, we get:

x² - x - 12 = 0

Factoring this equation, we get:

(x - 4)(x + 3) = 0

So the solutions for x are x = 4 and x = -3.

Substituting these values back into the first equation, we get:

When x = 4, y = 3. When x = -3, y = -4.

Therefore, the solutions to the system are (4, 3) and (-3, -4).

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ANSWER

• 60 feet

• The point is ,(60, 1)

EXPLANATION

As said, x is depth in feet, and f(x) represents the percentage of surface sunlight that reaches a depth of x feet. We have to find the value of x for which f(x) = 1,

Divide both sides by 16,

Take logarithm to both sides to apply the rule of the logarithm of power on the right side,

Divide both sides by log(0.955),

In the graph this is,

Answer: They won 80% and lost 20%.

Step-by-step explanation:

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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Answer:

3:4

Step-by-step explanation:

18:24 —> 9:12–> 3:4

hope this helps :)

Answer:

D Wilhem

Step-by-step explanation:

When solving a algebraic equation You follow these steps: group like factors(adding the 32g+8g-10g=30g) then you divide the numbers.(30g=150, 30/30=0 and the 150/30=5) So(g=5)

Answer:

D: Wilhem

Step-by-step explanation:

The answer to the indices is 1/16. Option C

You should understand that in mathematics and computer programming, index notation is used to specify the elements of an array of numbers. The formalism of how indices are used varies according to the subject, depending on whether one is writing a formal mathematical paper for publication, or when one is writing a computer program

The given question is

[(1/4)⁷ ÷ (1/4)⁶]⁷

⇒[ 1/16384 ÷ 1/4096]²

Simplifying this to have

1/16384 * 4096/1

This implies 4096/16384

⇒ 0.25

Converting this to a fraction we divide by 100 to have

0.25/100 = 25/100

Dividing by 25 to have [1/4]²

Therefore the answer is 1/16

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Step-by-step explanation:

6x^2, and 9x^2 can both be combined

Answer:

5 adult tickets

Step-by-step explanation:

      Let x be adult tickets and y be tickets for children under the age of 12.

      We know the group of 8 people spent a total of 36.50 dollars, so we can create the following system of equations:

             $5.5x + $3y = $36.5

             x + y = 8

      Now we can graph this system to help us answer the question.

-> See attached

-> The point at which the lines intersect answers our question. It means these values satisfy both equations.

      The equations, when graphed, intersect at point (5, 3). In the beginning I said that x is adult tickets, so 5 adult tickets were sold.

Five adults were in the group of 8.

\(Let\ x=#\ adult\ tickets\)            \(5.5x+3(-x+8)=36.5\)

      \(y=#\ child\ tickets\)            \(5.5\times-3x+24=36.5\)

                                              \(2.5x=12.5\)

\(x+y=8\rightarrowy=-x+8\)   \(\nearrow\)              \(x=5\)

\(5.5x+3y=36.5\)

  \(5+y=8\)

  \(y=3\)

I hope this helps you

:)

The t- test test's sizes for samples 1 and 2 are n1 and n2, respectively.

What can you infer from a sample t-test?

df for one sample t-test is n-1

where n is sample size

df for independent sample t-test is n1+n2-2

where n1 and n2 are respective sample sizes for sample 1 and sample 2 .

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Answer:

see attached file

Step-by-step explanation: