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Using Simpson's [tex]\frac{1}{3}[/tex] rule with 6 strips, the approximate value of the integral ∫[2.0, 2.8] f(x) dx is -3.8492.

To integrate the function [tex]\begin{equation}y = f(x) = \frac{ax^2}{b + x^2}[/tex] using Simpson's 1/3 rule, we need to divide the interval [2.0, 2.8] into an even number of strips (in this case, 6 strips). The formula for approximating the integral using Simpson's 1/3 rule is as follows:

[tex]\begin{equation}\int_a^b f(x) dx \approx \frac{h}{3} \left[ f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + ... + 2f(x_{n-2}) + 4f(x_{n-1}) + f(x_n) \right][/tex]

Where:

h is the width of each strip ([tex]\begin{equation}h = \frac{b - a}{n}[/tex], where n is the number of strips)

[tex]x_0[/tex] is the lower limit (2.0)

[tex]x_n[/tex] is the upper limit (2.8)

f(xi) represents the function evaluated at each strip's midpoint

Given the values of a = 1.2 and b = -0.587, we can proceed with the calculations.

Step 1: Calculate the width of each strip (h):

[tex]\begin{equation}h = \frac{b - a}{n} = \frac{-0.587 - 1.2}{6} = \frac{-1.787}{6} \approx -0.2978[/tex]

Step 2: Calculate the function values at each strip's midpoint:

x₀ = 2.0

x₁ = x₀ + h = 2.0 + (-0.2978) = 1.7022

x₂ = x₁ + h = 1.7022 + (-0.2978) = 1.4044

x₃ = x₂ + h = 1.4044 + (-0.2978) = 1.1066

x₄ = x₃ + h = 1.1066 + (-0.2978) = 0.8088

x₅ = x₄ + h = 0.8088 + (-0.2978) = 0.511

x₆ = x₅ + h = 0.511 + (-0.2978) = 0.2132

xₙ = 2.8

Step 3: Evaluate the function at each midpoint:

[tex]f(x_0) = \frac{1.2 \times 2^2}{-0.587 + 2^2} = \frac{4.8}{3.413} \approx 1.406 \\\\f(x_1) = \frac{1.2 \times 1.7022^2}{-0.587 + 1.7022^2} \approx 2.445 \\\\f(x_2) = \frac{1.2 \times 1.4044^2}{-0.587 + 1.4044^2} \approx 2.784 \\\\f(x_3) = \frac{1.2 \times 1.1066^2}{-0.587 + 1.1066^2} \approx 2.853 \\\\[/tex]

[tex]f(x_4) = \frac{1.2 \times 0.8088^2}{-0.587 + 0.8088^2} \approx 2.455 \\f(x_5) = \frac{1.2 \times 0.511^2}{-0.587 + 0.511^2} \approx 1.316 \\f(x_6) = \frac{1.2 \times 0.2132^2}{-0.587 + 0.2132^2} \approx 0.29[/tex]

Step 4: Apply Simpson's 1/3 rule formula:

[tex]\begin{equation}\int_{2.0}^{2.8} f(x) dx \approx \frac{h}{3} \left[ f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + 2f(x_4) + 4f(x_5) + f(x_6) \right][/tex]

[tex]\begin{equation}\approx \frac{-0.2978}{3} \left[ 1.406 + 4(2.445) + 2(2.784) + 4(2.853) + 2(2.455) + 4(1.316) + 0.29 \right][/tex]

[tex]\begin{equation}= \frac{-0.2978}{3} \left[ 1.406 + 9.78 + 5.568 + 11.412 + 4.91 + 5.264 + 0.29 \right][/tex]

≈ (-0.09926) * 38.63

≈ -3.8492

Therefore, the approximate value of the integral ∫[2.0, 2.8] f(x) dx using Simpson's 1/3 rule with 6 strips is approximately -3.8492.

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Answer:

option B should be correct

Answer:

B and D.

Step-by-step explanation:

A p e x

The following are among the five basic postulates of Euclidean geometry

The five basic postulates of Euclidean geometry

The five (5) basic postulates are:

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Answer:

. the area decreased by 7 is 14

Each satisfies the wave equation.

We are given the functions as follows:

(a) (x+at)², (b) 2e-(x-at) ², 7 satisfy the wave equation J²u(x, t) Ət² = (c) 5 sin[3 (x - at)] + (x + at).

₂d²u(x, t) dx²

Let us prove that they satisfy the wave equation using the formula of the wave equation. Wave equation is given by;

J²u(x, t) Ət² = ₂d²u(x, t) dx²

Applying the partial derivative to

(a) with respect to time, t, we obtain:

2a(x+at)

The second partial derivative with respect to x is as follows:

2a

By substituting these results into the wave equation, we have:

J²u(x, t) Ət² = ₂d²u(x, t) dx²

(2a(x+at)) = 2aJ²u(x, t) Ət² = 2a

Ət² = 1/J².

Thus, (a) satisfies the wave equation.  

For part (b), let us begin by taking the partial derivative of the function with respect to time, t. This is given by:

-4a e^-(x-at) ²

By taking the second partial derivative with respect to x, we get:4a e^-(x-at) ²

Similar to above, we substitute these results into the wave equation as follows:

J²u(x, t) Ət² = ₂d²u(x, t) dx²

-4a e^-(x-at) ² = 4aJ²u(x, t) Ət² = -4a e^-(x-at) ²/J²

Ət² = -1/J²e^-(x-at) ².

Thus, (b) satisfies the wave equation.

For part (c), let us calculate the partial derivative with respect to t as follows:

5a cos[3(x-at)] + a

The second partial derivative with respect to x is given by:-

15a sin[3(x-at)]

By substituting these results into the wave equation, we have:

J²u(x, t) Ət² = ₂d²u(x, t) dx²

(5a cos[3(x-at)] + a) = -15a

sin[3(x-at)]J²u(x, t) Ət² = -15a

sin[3(x-at)]/(5a cos[3(x-at)] + a)

Ət² = -3 sin[3(x-at)]/(cos[3(x-at)] + 1/5).

Thus, (c) satisfies the wave equation.

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Answer:

I don't see any equations.

Answer:

900 cm = 9 m

Step-by-step explanation:

9 m = 900 cm

Therefore, 9 m equals 900 cm.

Answer:

61

Step-by-step explanation:

Givens

Let the pizzas = x

Let the sodas = y

Equation

y = 3x + 2

Part A

y = 3*8 + 2

y = 24 + 2

y = 26

Part B

Sodas = 26* 1.25 = 32.50

Pizzas =9.50 * 3  = 28.50

Total for both = 32.50 + 28.50 = 61

Answer:

The two triangles are related by angles, so the triangles are similar but not proven to be congruent.

Step-by-step explanation:

Because the triangles have the same angles, they are congruent. The definition of congruence is if you take a shape and scale it up or down (or keep it the same) therefore, they are congruent.

Hope this helped, have a nice day

EDIT: I screwed up, I thought it was supposed to be similar.  These triangles are SIMILAR not congruent. The actual answer is they are related by AAA similarity but they are similar, but they are not proven to be congruent. Hope this clears it up, and sorry.

~cloud

The condition imposed on the constants k₁ and k₂ for k₁Θ⁻₁ + k₂Θ⁻₂ to be an unbiased estimator of θ is that their sum must equal 1.

For k₁Θ⁻₁ + k₂Θ⁻₂ to be an unbiased estimator of θ, its expected value should be equal to θ. In other words, we want to find the conditions on k₁ and k₂ such that E(k₁Θ⁻₁ + k₂Θ⁻₂) = θ.

Given that Θ⁻₁ and Θ⁻₂ are unbiased estimators of θ, we have:

E(Θ⁻₁) = θ

E(Θ⁻₂) = θ

Now, let's calculate the expected value of k₁Θ⁻₁ + k₂Θ⁻₂:

E(k₁Θ⁻₁ + k₂Θ⁻₂) = k₁E(Θ⁻₁) + k₂E(Θ⁻₂)

Since E(Θ⁻₁) = θ and E(Θ⁻₂) = θ, we can substitute these values into the equation:

E(k₁Θ⁻₁ + k₂Θ⁻₂) = k₁θ + k₂θ

To make sure this expression is equal to θ, we need:

k₁θ + k₂θ = θ

This implies that k₁ + k₂ = 1. Therefore, the condition imposed on the constants k₁ and k₂ for k₁Θ⁻₁+ k₂Θ⁻₂ to be an unbiased estimator of θ is that their sum must equal 1.

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Answer:

Answer and work is in the pdf

Step-by-step explanation:

75+75+80+80+80+80+80+80+85+85+90+90+90+90+90+90+95+95+95+100+100+100+100+100+100

=2,425

2+6+2+6+3+8

=27

2,425/27=89.81

The mean is 89.81

Answer:

8.8

Step-by-step explanation:

The given functions f(n) = 11 and g(n) = (3/4)^(n-1) can be combined to create a geometric sequence. The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term is given as 11, and the common ratio is (3/4).

The nth term of a geometric sequence is calculated using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the position of the term. By substituting the values into the formula, we can find the 9th term.

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Answer:

5670 yards

Step-by-step explanation:

Length of first race = 2 miles

Since, 1 mile = 1760 yards

Therefore, 2 miles = 1760 × 2

                               = 3520 yards

Length of second race = 1300 yards

Length of third race = 850 yards

Total distance to be run by the horse = 3520 + 1300 + 850

                                                              = 5670 yards

Answer:

There is no fixed number of trials, so X is not a binomial variable

Step-by-step explanation:

mama

There is no fixed number of trials, so X is not a binomial variable.

This is a specific kind of discrete random variable. A binomial random variable counts how regularly a specific event occurs in a fixed variety of attempts or trials.

The binomial is a form of distribution that has possible effects (the prefix “bi” method two, or twice). as an example, a coin toss has only viable effects: heads or tails, and taking a check may want to have viable outcomes: pass or fail. A Binomial Distribution indicates both success and failure.

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The best estimate for the solution to the system of linear equations among the given ordered pairs is (-4, 2 1/2).

In the context of a system of linear equations, the solution represents the values of the variables that satisfy all the equations simultaneously. To determine the best estimate for the solution, we need to evaluate each ordered pair and see which one satisfies the given system.

By substituting the values of the ordered pairs into the equations of the system, we can determine if they satisfy the equations or not. Among the given options, when substituting (-4, 2 1/2) into the system of linear equations, it is likely to result in a solution that satisfies all the equations.  Therefore, it is important to consider the specific equations and the context of the problem to determine the best estimate for the solution.

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Answer:

18 units to the right.

Step-by-step explanation:

Hope this helps!

Answer:

I think it's 21. .........

Answer: 5

Step-by-step explanation: 21 + 4 = 25

square root of 25  = 5

Answer and Step-by-step explanation:

T = 21

U = 4

[tex]\sqrt{ 21 + 4} \\\\\\\sqrt{25} \\\\\\5[/tex]

5 is the answer to the expression.

#teamtrees #PAW (Plant And Water)

a. The total amount owed for the $525 loan at 9.9% interest for 6 months is approximately $556.19 when rounded to the nearest cent.

b. The total amount owed for the $12,460 loan at 5.6% interest for 30 months is approximately $33,504.80 when rounded to the nearest cent.

a. To calculate the total amount owed for the $525 loan at 9.9% interest for 6 months, we can use the formula for simple interest:

Total amount owed = Principal + (Principal × Interest Rate × Time)

Given:

Principal (P) = $525

Interest Rate (R) = 9.9% = 0.099 (converted to decimal)

Time (T) = 6 months

Plugging these values into the formula, we get:

Total amount owed = $525 + ($525 × 0.099 × 6)

Simplifying the equation:

Total amount owed = $525 + ($31.185)

Total amount owed = $556.185

Therefore, the total amount owed for the $525 loan at 9.9% interest for 6 months is approximately $556.19 when rounded to the nearest cent.

b. To calculate the total amount owed for the $12,460 loan at 5.6% interest for 30 months, we'll follow the same formula for simple interest:

Total amount owed = Principal + (Principal * Interest Rate * Time)

Given:

Principal (P) = $12,460

Interest Rate (R) = 5.6% = 0.056 (converted to decimal)

Time (T) = 30 months

Plugging these values into the formula, we get:

Total amount owed = $12,460 + ($12,460 * 0.056 * 30)

Simplifying the equation:

Total amount owed = $12,460 + ($21,044.8)

Total amount owed = $33,504.8

Therefore, the total amount owed for the $12,460 loan at 5.6% interest for 30 months is approximately $33,504.80 when rounded to the nearest cent.

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Step-by-step explanation: *First, decide which volume formula to use:     v = lwh

*Next, substitute in for what you do know (leave variable for unknown):  288 = 12 · w · 6

*Then simplify the side of the equation with the variable: 288 = 72 · w

*Now divide each side of the equation by 72 to solve for w:

288 ÷ 72 = w

4 in = w

Answer:

3/4 is 0.75 and 1 is 1

Step-by-step explanation:

:\

Answer:

“Mean for both bakeries because the data is symmetric.”

Step-by-step explanation:

This is correct because the numbers shown in this problem is all in the same range. Meaning that on bakery A and B there are no stray numbers, also known as outliers. No outliers means that the data is symmetric. If you search up, you can see that when the data is symmetric, you use “mean.”

also I got it right on my test

Answer:

Mean for both bakeries because the data is symmetric.

Step-by-step explanation:

Tossing of a fair coin infinitely many times. The process X(t) can be defined as follows:

- X(t) = 1 if a head shows up at time t, where t = nT for some positive integer n.

- X(t) = 0 if a tail shows up at time t.

In the given scenario, we are considering the tossing of a fair coin infinitely many times. We want to define a process X(t) that represents the outcome of each toss at different time points.

The process X(t) is defined as 1 when a head shows up at time t, where t is a multiple of T (the fixed time interval between tosses). In other words, X(t) takes the value 1 when t is of the form nT, where n is a positive integer.

Conversely, X(t) is defined as 0 when a tail shows up at time t. This includes all time points that are not of the form nT.

The process X(t) is a representation of the outcome of the coin tosses over time. It takes the value 1 when a head shows up at time t = nT for some positive integer n, and 0 when a tail shows up. This process allows us to track the occurrences of heads at specific time intervals in the infinite sequence of coin tosses.

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Answer:

92/37

Step-by-step explanation:

This indicates that vector 2AB has a length of 165.

Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), and E, let's determine the length of the vector 2AB. To begin, we must determine the distance that separates points A and B. The distance formula is as follows: Equation for distance: We can calculate d as [(x2 - x1)2 + (y2 - y1)2] using the distance formula: Spot = [(6 - (- 2))2 + (16 - 0)2] = [(6 + 2)2 + (16)2] = [(8)2 + (16)2] = [(64 + 256) = 320 = 8] Now, we can deduct the directions of point A from guide B toward decide the vector Stomach muscle:

To find 2AB, simply multiply each part of AB by 2: AB = (6 - (-2)i + (16 - 0)j = 8i + 16j 2AB = 2(8i + 16j) = 16i + 32j. Last but not least, we must ascertain the magnitude of 2AB. The extent recipe is as per the following: Size formula: Using the magnitude formula, we get: ||v|| = (v12 + v22). ||2AB|| = (162 + 322) = (256 + 1024) = (1280 + 165). This indicates that vector 2AB has a length of 165.

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Answer:

33

Step-by-step explanation:

6 * 3 = 18

8-3 = h

h = 5

A = 5 * 3 = 15

Combined:

15 + 18

33

Answer:

10 feets

Step-by-step explanation:

Given that:

Angle, θ = 4π/3

Radius, r = 2.5 feets

To obtain how Far Reagan traveled, we calculate the Length of the arc, s

s = r*θ

s = 2.5 feets * 4π/3

s = 10π/3

s = 10.4719

To the nearest foot ; distance traveled by Reagan is 10 feets