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Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) +             2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

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a. The first term of the arithmetic sequence is 12.

b. The value of n for which the nth term is -33 is 16.

c. The common difference of the arithmetic sequence is -3.

a. The first term, u1, can be found by substituting n=1 into the given formula for the nth term:

u1 = 15 - 3(1) = 12

b. To find the value of n for which the nth term is -33, we set the formula for the nth term equal to -33 and solve for n:

un = 15 - 3n = -33

Adding 3n to both sides, we get:

15 = -33 + 3n

Adding 33 to both sides, we get:

48 = 3n

Dividing both sides by 3, we get:

n = 16

c. The common difference, d, is the difference between any two consecutive terms of the sequence. To find d, we can subtract any two consecutive terms, such as u2 and u1:

u2 = 15 - 3(2) = 9

u1 = 15 - 3(1) = 12

d = u2 - u1 = 9 - 12 = -3

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The condition that will prove the two triangles similar is

side JL = 8 * side ZX

angle L = angle Z

Similar triangles are  triangles which have the  similar shape however not necessarily the equal size. More officially, two triangles are comparable if their corresponding angles are congruent and their corresponding aspects are in proportion.

This means that if we had been to scale one triangle up or down uniformly, the ensuing triangle could be much like the original triangle.

In the figure, the scale is 8

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Answer:

xs7

Step-by-step explanation:

Answer:

8y

Step-by-step explanation:

Lets put these two parts into addition to make it easier.

(y)56x + 16y^2

(8y)7x + 2y^2

8y is the GCF(grates common factor)

They need to sell at least 13 cups to gain profits.

Here, we have,

Givens

The initial cost is $1.20.

Each cup of lemonade costs 6 cents to make.

May's children sell 10 cents a cup.

First, we need to represents the cost of their investment.

0.06x = 1.20, because each cup costs 6 cents, and the initial costs of all is $1.20.

That means,

x= 20

They can produced 20 cups.

However, they already sell a cup for 10 cents. So, how many cups they need to sell to gain profits? We need to establish a similar relation,

0.10 x = 1.20

 x = 12

This means if they sell 12 cups, they will just cover the investment, that is, zero profits.

Therefore, they need to sell at least 13 cups to gain profits.

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complete question

Mary's children decide to run a lemonade stand to earn some extra money.The cost to start the business is $1.20 and each cup of lemonade costs 6 cents to make. If lemonade sells for 10 cents a cup,how many cups must Mary's children sell to make a profit?----Apply systems of equations

The inverse of the function f(x) = x + 4 is given as f⁻¹(x) = x - 4

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, the function given is f(x) = x + 4;

We can find the inverse of the function as;

y = x + 4;

Let's switch the variables by replacing x as y and y as x;

x = y + 4

Solving for y;

y = x - 4

f⁻¹(x) = x - 4

The graph of the function is attached below

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A coefficient is any constant or numerical term that is in front of one or more variables and is defined as a fixed number that is multiplied by a variable. For example, in the expression 3x+2y+4, 3 is the coefficient of x, 2 is the coefficient of y but 4 is not a coefficient, as it is not being multiplied by a variable.

To find the coefficient of x, we can encircle it or underline it. Then, take everything else except for x, i.e. 5y. So, the coefficient of x in the term 5xy is 5y. Similarly, the coefficient of y in the term 5xy is 5x.

(2.x+3)² = (2x+3)(2x+3)

2x(2x+3)+3(2x+3)=

2x(2x+3)+3(2x+3)=

4x²+6x+3(2x+3)=

4x²+12x+9

so if your using the binomial theorem it would equal 4x²+12x+9

if you just want the coefficient of x that would be 4 ↑

As far as a 5/1 ARM is concerned, note that the "1" refers to how often the rate can be adjusted after the initial fixed-rate period ends.

A 5/1 ARM is an adjustable rate mortgage loan (ARM) that has a fixed interest rate for the first five years. Following that, the 5/1 ARM transitions to an adjustable interest rate for the remainder of its term. The terms "variable" and "adjustable" are frequently used synonymously.

If you want a low monthly payment and don't expect to stay in your house for long, a 5/1 adjustable-rate mortgage (ARM) loan may be worth considering. For the first five years, rates on 5/1 ARMs are typically lower than rates on 30-year fixed-rate mortgages.

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If the size of matrix "M" is 9×10, and a scalar "c" is multiplied by matrix, then the size of "cM"  will be 9×10.

We know that when a scalar is multiplied to a matrix, each element of the matrix gets multiplied by that scalar.

In this case, the scalar "c" is multiplied with the Matrix "M";

So if a scalar "c" is multiplied by a matrix "M" of size 9×10, then the resulting matrix "cM" will also have the same number of rows and columns as the original matrix "M".

Therefore, the size of "cM" will also be 9×10.

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The value of x in the trapezoid is 2.

The mid points of a trapezoid is a line that goes across from the middle of one leg to the middle of the other leg.

Using the mid point theorem, let's find the value of x in the trapezoid as follows:

PS = 1 / 2 (QR + TU)

PS = x + 33

QR = -6x + 37

TU = 2x + 41

Therefore,

x + 33 = 1 / 2 (-6x + 37 + 2x + 41)

x + 33 =  1 / 2 (-4x + 78)

x + 33 = -2x + 39

x + 2x = 39 - 33

3x = 6

divide both sides by 3

x = 6 / 3

x = 2

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The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

We have,

To factor x² + 12 using the difference of squares formula, we need to express it as the difference between two squares:

x² + 12 = x² + (2√3)²

Now we can use the difference of squares formula, which states that:

a² - b² = (a + b)(a - b)

In this case, we have a = x and b = 2√3. So we can write:

= x² + 12

= x² + (2√3)²

= (x + 2√3)(x - 2√3)

Therefore,

The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

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The requried area of the shaded shape is 5 square millimeters.

From the figure,
The area of the green shaded area is given by:
The area of a single square is given as = 1 * 1 = 1 square millimeters.
Now there is 5 square in the shaded region, So the area is given as:

= 5 * 1 = 5 square millimeters.

Thus, the requried area of the shaded shape is 5 square millimeters.

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Okay, here are the steps to solve this problem:

1) The height (h) of the rocket t seconds after launch is given as: h = - 3t2 + 0t + 48

2) We want to find the time (t) when the rocket hits the ground (h = 0)

3) Set the formula equal to 0: - 3t2 + 0t + 48 = 0

4) Factor the left side: - 3(t2 - 0t) + 48 = 0

5) Solve for t2 - 0t: t2 - 0t = 16

6) Add 0t to both sides: t2 = 16 + 0t

7) Take the square root of both sides: t = 4

Therefore, the time for the rocket to hit the ground is 4 seconds.

So in this case, t = 4

Let me know if you have any other questions!

Answer:

4 seconds.

Step-by-step explanation:

When the rocket hits the ground, its height will be 0. Therefore, since we are given an expression for the height of the rocket dependent on the time, we can simply set it equal to 0 and solve for the time and find how long the rocket will take to hit the ground. I'm assuming the equation is[tex]h = -3t^{2} + 48[/tex]

Now set this equal to 0

[tex]0 = -3t^2+48[/tex]. Solve for t by isolating it.

[tex]-48 = -3t^2[/tex]

[tex]16 = t^2[/tex]

From here, by taking the square root, we see that t is either equal to 4 or -4 in seconds. Since we can't have negative time, we can clearly see that the answer is 4 seconds.

Hope this helps

Answer:

Muhammad biked 64 miles

Step-by-step explanation:

Olivia biked 8 miles.

Cameron biked 4 times as many miles as Olivia, and Muhammad biked 2 times as many miles as Cameron.

Cameron: 4 x 8 = 32

Cameron biked 32 m.

Muhammad: 32 x 2 = 64

Muhammad biked 64 miles.

The instantaneous rate of change at x = 2 is equal to the derivative, which is 2.

The derivative of f(x) = 2x - 5 with respect to x can be found by applying the power rule of differentiation, which states that the derivative of x^n is n*x^(n-1).

Taking the derivative of f(x) = 2x - 5:

f'(x) = 2 * (d/dx)(x) - (d/dx)(5)

= 2 * 1 - 0

= 2.

The derivative of f(x) with respect to x is a constant, 2, indicating that the function has a constant slope.

Therefore, the instantaneous rate of change at x = 2 is equal to the derivative, which is 2.

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(i). His monthly basic salary is Rs 79,200.

(ii) His taxable income is Rs 1,02,480.​

(i) The monthly basic salary of the married COAS General is given as Rs 79,200, with an additional Rs 2,000 as a dearness allowance.

Total salary = Basic salary + Dearness allowance

Total salary = Rs 79,200 + Rs 2,000

Total salary = Rs 81,200

So his monthly basic salary is Rs 79,200.

(ii)

Total income = Basic salary + Dearness allowance + Dashain allowance

Total income = Rs 79,200 + Rs 2,000 + Rs 79,200

Total income = Rs 1,60,400

From this, we subtract his EPF contribution and life insurance premium:

Taxable income = Total income - EPF contribution - Life insurance premium

Taxable income = Rs 1,60,400 - 10% of Rs 79,200 - Rs 50,000

Taxable income = Rs 1,60,400 - Rs 7,920 - Rs 50,000

Taxable income = Rs 1,02,480

So his taxable income is Rs 1,02,480.

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The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.

The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.

To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.

Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.

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Answer:

60

Step-by-step explanation:

180 - 120 = 60

The inverse variation is y = 9/x, using that equation we can see that n = 9.

An inverse variation between two variables x and y can be written as:

y = k/x

Where k is a constant.

We know that this inverse variation contains the point (3, 3), replacing these values we have:

3 = k/3

3*3 = k

9 = k

Then the inverse variation is:

y = 9/x

Now we want to find n such that (1, n) is on the relation above, then we will get:

n = 9/1

n = 9

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Alondra will be able to withdraw approximately $1,427 per month to take withdrawals for 22 years from her retirement account.

To calculate the monthly withdrawal amount, we need to use the present value formula, which is:

PMT = (PV * r) / (1 - (1 + r)⁻ⁿ)

where:

PV = present value = $350,000

r = monthly interest rate = 2.9% / 12 = 0.002417

n = number of months = 22 years * 12 months/year = 264 months

Substituting the values into the formula, we get:

PMT = (350000 * 0.002417) / (1 - (1 + 0.002417)⁻²⁶⁴)

PMT ≈ $1,427.07

This calculation assumes that the interest rate remains constant throughout the 22-year period, which may not be the case in reality.

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1. The equation of the form y = a • bˣ is y = 81 x (¹/₃)ˣ

2. His stamp should be worth approximately $7,851.47 after 6 years.

3. The equation of the form y = a • bˣ is y = (¹/₁₆) x 2²ˣ ⁺ ⁵

1. One will see that y is decreasing by a factor of 3 as x increases by 1. Therefore, we can write the equation as:

y = 81 x (¹/₃)ˣ

2. The increase in value of the stamp can be calculated using the formula:

V = P(1+r)ᵗ

where V is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.

Substituting the given values:

V = 4900(1+0.075)⁶

V ≈ $7,851.47

Therefore, the stamp should be worth approximately $7,851.47 after 6 years.

3. One will see that y is increasing by a factor of 2 as x increases by 1. Therefore, we can write the equation as:

y = (1/16) x 2²ˣ ⁺ ⁵

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In order to understand and prioritize the vaccination strategy for the community health clinic, first accurately assess the demographics of the community based on the data provided.

Calculating the absolute numbers of people in each group: over 65 and immunocompromised, and under 65 and immunocompromised. For this, we'll apply the given percentage to the total population of 50,000.

Knowing the total number of people in each category will help us understand the size of each target group and prioritize accordingly. The clinic's current priority is immunocompromised people over 65, so having the exact figure will aid in planning for vaccine supply and outreach strategies.

Furthermore, the analysis of this data can also aid in projecting the needs for future vaccine campaigns for the remaining community members. Finally, this detailed analysis will help in crafting an effective communication plan that emphasizes the clinic's priority of serving the most vulnerable first, while still acknowledging the needs of all community members.

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The value of sin(θ) is 0.31 and it lies in the third and fourth quadrants. if the value of the cosine of θ is −0.95.

cos(θ) = -0.95

To calculate the value of sin(θ), we can use the Pythagorean theorem:

[tex]sin^{2}[/tex] (θ) +[tex]cos^{2}[/tex] (θ) = 1

We can rearrange the Pythagorean identity to solve for sin(θ):

[tex]sin^{2}[/tex] (θ)= 1 - [tex]cos^{2}[/tex]

sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)---------  (equation 1)

Substitute the value of the cosine of θ = −0.95 in Equation 1

sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)

sin(θ) = ±[tex]\sqrt{(1 - 0.9025)}[/tex]

sin(θ) = ±[tex]\sqrt{0.0975}[/tex]

The positive value determines that the value is in the first and second quadrants, Negative shows the third and fourth quadrants.

sin(θ) = [tex]\sqrt{ 0.0975}[/tex]

sin(θ) = 0.312

Therefore, we can conclude that the value of sin(θ) is 0.312.

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The actual distance from the movie theater to the school is given as follows:

A. 15 miles.

The actual distance from the movie theater to the school is obtained applying the proportions in the context of the problem.

On the map, the grocery store is 2 inches away from the library. The actual distance is 1.5 miles, hence the scale factor is of:

2 inches = 1.5 miles

1 inch = 0.75 miles.

The same map shows that the movie theater is 20 inches from the school, hence the actual distance is given as follows:

20 x 0.75 = 15 miles.

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Answer:

No, it is not a right triangle.

[tex] \sqrt{ {13}^{2} + \ {18}^{2} } = \sqrt{169 + 324} = \sqrt{493} [/tex]

√493 is not equal to 24.

Answer:

it doesn't

Step-by-step explanation:

it doesn't follow pythagoras theorem

a² = b² + c²

Answer:

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Step-by-step explanation:

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