Identify the reflection rule on a coordinate plane that verifies that triangle a(-2,3), b(-3,-2), c(-10,0) and triangle a'(2,3), b'(3,-2), c'(10,0) are congruent when reflected over the y-axis.

The completed tiles are placed in the appropriate slots to prove that line j is parallel to k, as follows;

Statements         [tex]{}[/tex] Reasons

1. ∠6 ≅∠3 [tex]{}[/tex]          1. Given

2. ∠3 ≅∠2 [tex]{}[/tex]         2. Vertical ∠s ≅

3. ∠6 ≅ ∠2 [tex]{}[/tex]        3. Transitive Property

4. j ║ k       [tex]{}[/tex]         4. Corresponding ∠s ≅, lines ║

Parallel lines are are two lines that continue indefinitely and do not meet, such that they make the same or congruent corresponding angles with a common transversal.

The details of the reasons used to prove that line j is parallel to line k are as follows;

Vertical ∠s ≅

The vertical angles theorem states that vertical angles, which are angles formed by the intersection of two lines and which are located, opposite to each other are congruent.

Transitive property

The transitive property of congruency states that if a is congruent to b and b is congruent to c, them a is congruent to c

Corresponding ∠s ≅

The corresponding angles formed between parallel lines are congruent.

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Answer:

neither

Step-by-step explanation:

line T: m = -2/3

If line U was parallel to T it would have the same slope (-2/3)

If line U was perpendicular to T it would have a slope that is the negative reciprocal of the slope of line T  (3/2)

10 mg of carbon-14 would still be present in the sample after 17,190 years.

The formula: A = A θ * (1/2)(t/t 1/2)

can be used to determine how much carbon-14 is still present in a sample after a specific number of years.

where A is the remaining carbon-14, A 0 is the initial carbon-14 concentration, t is the passing of time, t 1/2 is the carbon-14 half-life (5,730 years), and 1/2 is the decay factor.

By entering the specified values, we obtain:

A = 80 mg * (1/2)^ 5,730 years / 17,190 years

A = 80 mg * (1/2)^3

A = 80 mg * (1/8)

A = 10 mg

Therefore, 10 mg of carbon-14 would still be present in the sample after 17,190 years.

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The area of the billboard is [tex]1,632,400 cm^{2}[/tex], Option (d) is correct.

Since the linear scale factor f=20, then the billboard area:

A = [tex]77.53[/tex]×[tex]20^{2}[/tex]

= [tex]1,632,400 cm^{2}[/tex]

Linear scale Factor:

The size of the enlargement/reduction is represented by the scale factor. For example, a scale factor of 2 means that the new shape is twice the original shape. A scale factor of 3 means that the new shape is three times the size of the original shape.

Therefore, the area of the billboard is [tex]1,632,400 cm^{2}[/tex], and Option (d) is correct.

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The percentage change is 65.38%.

                                [tex]amount of change = \frac{new value - old value }{old value}[/tex]

If the amount of change is positive, it is an increase.

If the amount of change is negative, it is a decrease.

            % of change =amount of change * 100

According to the question,

new quantity = 40

original quantity =23

% change [tex]= \frac{new value - old value}{old value} * 100[/tex]

% change [tex]= \frac{40 - 23}{23} * 100[/tex] = 65.38%

So, the percentage change is 65.38%.

[tex]% change = \frac{new value - old value}{old value} * 100[/tex][tex]% change =\frac{new value - old value }{old value} * 100[/tex]

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The complete two way relative frequency table shown below:

A statistical table called a two-way or contingency table displays the observed quantity or frequency for two variables, with the rows denoting one category and the columns denoting the other. In this case, the gender (male or female) row category. They can opt to have a yes or no column category.

Given:

Color     Car      Truck      Total

Blue       25          16            41

Red        21           13            34

Total       46         29            75

Now, the two way relative frequency table

Blue Car:   25 /75 x 100 = 33.33%

Blue Truck: 16/75 x 100 = 21.33%

Blue total = 41 /75 x 100 = 54.66%

Red car: 21/75 x 100 = 28%

Red Truck: 13/75 x 100 = 17.33%

Red total: 34/75 x 100 = 45.33%

Total car: 46/75 x 100 = 61.33%

Total truck: 29/75 x 100 = 38.66%

Total to total = 75/75 x 100 = 100%

so, the table is

Color     Car               Truck            Total

Blue       33.33%        21.33%       54.66%

Red        28%             17.33%        45.33%

Total       61.33%        38.66%          100%

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Answer:

8890.83

Step-by-step explanation:

trust me this the answer

Students are now at the dance after the additional freshmen arrive 75 students

Let x be the number of freshmen and y be the total number of people attending the dance who ARE NOT freshmen.

So...initially

x  / ( x + y)  =   40     cross-multiply

x = .40x +  .40y

x - .40x  =.40y

.60x  = .40y

y  = (3/2)x

We have that once 15 more freshmen arrive.

(x + 15)  / ( x +  (3/2)x  + 15)  =  .52

(x + 15) / ( 5/2 x  + 15)  = .52     cross-multiply

x + 15  =  .52 ( 5/2x  + 15)

x + 15 =  1.3x  + 7.8

1.3x - x  =  15 - 7.8

3x  =  7.2

3x  = 72

x = 24 =  number of original freshmen

24(3/2)  = 36  = number not freshmen

The initial attendance at the dance was 24 + (3/2)24) = 60 students.

(24) / 60   = ,40  = 40%

After 15 more freshmen arrive.....there are  60 + 15  = 75 students

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Answer: Let's call the number of sandals manufactured in a typical month x, and the number of running shoes manufactured in a typical month y. The total cost for sandals and running shoes in a typical month is $2450, so the following equation represents the cost:

2.5x + 4y = 2450

During the month of April, the company doubled the number of sandals manufactured, so x becomes 2x. The total cost during the month of April is $3700, so the following equation represents the cost:

2.5(2x) + 4y = 3700

Expanding the left side:

5x + 4y = 3700

Subtracting the first equation from the second equation:

5x - 2.5x + 4y - 4y = 3700 - 2450

2.5x = 1250

Dividing both sides by 2.5:

x = 500

Substituting x = 500 into the first equation:

2.5 * 500 + 4y = 2450

Expanding and solving for y:

1250 + 4y = 2450

1250 - 1250 + 4y = 2450 - 1250

4y = 1200

Dividing both sides by 4:

y = 300

So the company makes 500 pairs of sandals and 300 pairs of running shoes during a typical month.

Step-by-step explanation:

The matrix A of T with transformation T: R²→R² and is reflection of the line y = -x is [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

T: IR²→IR² is reflection of the line y = -x.

It is known that e1 = (1,0) and e2 = (0,1) is the standard basis of IR².

So, the transformation is T(e1) = e1' and T(e2) = e2'.

T(e1) = e1' = (0,1)

= 0(1,0) + (-1)(0,1)

= 0 · e1 + (-1) · e2

T(e2) = e2' = (-1,0)

= (-1)(1,0) + 0(0,1)

= (-1) · e1 + 0 · e2

So, now the matrix A becomes [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

Therefore, the new matrix is [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

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Find the matrix A of T for the following transformation. T: R²→R² is a reflection in the line y = -x.

Answer:

16.429

Step-by-step explanation:

x+12.23=28.659

28.659-12.23=16.429

Answer:

Step-by-step explanation:

[tex]\mathrm{x + 12.23 = 28.659}[/tex]

Subtract 12.23 from both sides:-

[tex]\mathrm{x=28.659-12.23}[/tex]

Simplify  :-

[tex]\mathrm{x=16.429}[/tex]

___________________

-Hope this helps!

Answer:

15

Step-by-step explanation:

A linear function has the form y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we can use the formula:

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

Plugging in the given points (3,18) and (9,24):

m = (24 - 18) / (9 - 3) = 6 / 6 = 1

To find the y-intercept (b), we can use either of the given points and the slope. Let's use the point (3,18):

18 = 1 * 3 + b

b = 18 - 3 = 15

So, the linear function rule is:

y = x + 15

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Answer:

800

Step-by-step explanation:

You would actually round 772 to 800. This is because the tens digit, 7, is greater than 5.

Answer:

800

Step-by-step explanation:

because 72 is more than 50

The rate law is an equation that describes the rate of a reaction as a function of the concentrations of the reactants. The rate of a reaction is typically represented as the change in concentration of a reactant or product over time.

a) Rate = k[a]2 - Second Order Rate Law

b) Rate = k[a] - First Order Rate Law

c) Rate = k - No Match

The rate law is an equation that describes the rate of a reaction as a function of the concentrations of the reactants. The rate of a reaction is typically represented as the change in concentration of a reactant or product over time.

a) The rate law equation for a second order reaction is rate = k[a]2, where k is the rate constant and [a] is the concentration of the reactant.

b) The rate law equation for a first order reaction is rate = k[a], where k is the rate constant and [a] is the concentration of the reactant.

c) There is no rate law equation for a reaction with a rate of k.

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Answer:

The expression 2a^2b^2 + 2b^2c^2 + 2a^2c^2 - a^4 - b^4 - c^4 can be factored as:

(2ab^2 + 2bc^2 + 2ac^2)(a^2 - c^2) - (a^2 - b^2)(a^2 - c^2)

= (a^2 + b^2 + c^2)(2ab^2 + 2bc^2 + 2ac^2) - (a^2 - b^2)(a^2 - c^2)

A ray has only one endpoint. A segment has two endpoints.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. In everyday language, a line segment with two points designating its ends is also referred to as a "line."

A ray and a segment are parts of a line.

This line segment has two fixed-length endpoints, A and B. The distance between this line segment's endpoints A and B is its length.

In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length.

A line segment's length can be calculated using either metric units like millimeters or centimeters or conventional units like feet or inches.

Ray has only one endpoint and the other ends go infinity.

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The Intermediate Value Theorem (IVT) states that for any continuous function f(z) and any real number a, if f(a) and f(b) have opposite signs, then there exists a number c in the interval (a,b) such that f(c) = 0.

The IVT states that if a continuous function has different signs (positive or negative) at two points in its domain, then it must have a zero in between those two points. In the case of the function f(z) = 26z^53 + 3, we are asked to find an integer n such that there exists a zero of the function in the interval [n/4, (n + 1)/4].

To find the solution, we can use the IVT by considering two points in the interval with opposite signs. For example, if we take n = 1, then the interval is [1/4, 2/4]. We can evaluate the function at the two endpoints of the interval and look for opposite signs:

f(1/4) = 26 * (1/4)^53 + 3 > 0

f(2/4) = 26 * (2/4)^53 + 3 < 0

Since the function has opposite signs at the endpoints, the IVT guarantees that there exists a zero of the function in the interval [1/4, 2/4]. This means that for n = 1, the IVT is satisfied and the function has a zero in the interval [1/4, 2/4].

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Complete Question:

For which integer n, 0 < n < 3 , does the IVT say that f(z) 26 53 + 3 has & zero in the interval [n/4, (n + 1)/4]?

The limit law used to justify the computation is limₓ⇒ 2[4f(x)] = by constant multiple law of limit, So correct option is A.

In mathematics, a limit is a value that a function approaches as the input approaches a particular value. Limits are used to describe the behavior of functions near certain points and to find the derivative and integral of functions.

The formal definition of a limit is as follows: Let f(x) be a function and c be a real number. The limit of f(x) as x approaches c is L, denoted by

lim x -> c f(x) = L

if for every ε > 0, there exists a δ > 0 such that for all x, 0 < |x - c| < δ implies |f(x) - L| < ε. In other words, as x gets arbitrarily close to c, the values of f(x) get arbitrarily close to L.

The concept of limits is fundamental to calculus and is used in many applications, such as finding the maximum and minimum values of a function, determining the continuity and differentiability of a function, and solving problems in physics, engineering, and economics.

The constant multiple law of limit states that if f(x) approaches L as x approaches c, then k × f(x) approaches k × L as x approaches c, where k is a constant.

In this case, f(x) approaches 6 as x approaches 2, so limₓ⇒2 f(x) = 6.

And, 4 × f(x) = 4 × 6 = 24, so limₓ⇒2 [4f(x)] = 24 by the constant multiple law of limit.

So the answer is A: limₓ⇒2 [4f(x)] = 24 by constant multiple law of limit.

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Point estimators have their drawbacks, such as virtually certain error, lack of capacity to reflect larger sample sizes, and inability to infer population data.

Point estimators are useful for obtaining a single value that estimates a population parameter. However, these estimators are not always accurate as it is virtually certain that the estimate will be wrong. Additionally, point estimators are not able to reflect the effects of larger sample sizes, which means that drawing inferences about a population from a larger sample is not possible. Therefore, when using point estimators, it is important to keep in mind their limitations and use other estimation methods to achieve more accurate results.

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For the function C(t) = {9,          0 ≤ t ≤ 3

                            C(t) = {9 + t,     3 < t ≤ 8

                            C(t) = {20         8 < t < 28

a) If you want to give their pizza a try, in order to get the best price you should buy a large pizza on date(s) February 10, February 11, February 12, and February 13.

b) The cost of large pizza on February 18th will be $17.

c) A large pizza will cost $13 on the date February 14.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given function is C(t) = {9,          0 ≤ t ≤ 3

                                   C(t) = {9 + t,     3 < t ≤ 8

                                   C(t) = {20         8 < t < 28

a) According to the function above, the promotion's lowest price for a large pizza is $9.

When t = 0, t = 1, t = 2, and t = 3, this is how much the pizza will cost.

We are aware that the symbol t stands for the duration since February 10th.

Therefore, t = 0 relates to February 10, t = 1, t = 2, and t = 3 correspond to February 11, February 12, and February 13, respectively.

Therefore, February 10, February 11, February 12, and February 13 are the best dates to test the new pizza joint in order to receive the best price.

b) Eight days after February 10th, or t = 8, is February 18th.

When 3 < t ≤ 8, the function C(t) = 9 + t can be used to calculate the price of a large pizza in dollars.

At that point, C(t) = 9 + 8 = 17 dollars when t = 8.

Therefore, on February 18, a big pizza will cost $17.

c) Because the function above says that for these values of t, C(t) = 9, we know that 13 ≠ 9 and thus a big pizza cannot cost 13 dollars when 0 ≤ t ≤ 3.

Similar to the previous example, it is also known that 13 ≠ 20 indicates that a big pizza cannot cost 13 dollars when 8 < t < 28 because C(t) = 20 for these values.

As a result, it is known that the only circumstance in which a large pizza may cost 13 dollars is when t falls within the range 3t–8 for which C(t) = 9 + t.

Enter 13 as the cost into this equation and solve for t in order to determine the day on which a large pizza will cost 13 dollars -

13 = 9 + t

t = 13 - 9

t = 4

When t = 4, this indicates that a large pizza costs $13.00.

Given that t represents the number of days since February 10, it is known that t = 4 represents February 14.

Therefore, on February 14th, a big pizza will cost $13.

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Answer:

Cheetah A ran at a faster speed than Cheetah B, as it ran 18 miles in 16 minutes while Cheetah B ran 54 miles in 50 minutes.

Step-by-step explanation:

Answer: its A

Step-by-step explanation:

Since Zx and Zy are suplementary angles, Zx is 92°.

Supplementary angles are 2 angles that if added together created a sum of 180°. Supplementary angles have several properties such:

Supplementary angles might come in adjacent and non-adjacent types. Adjacent supplementary angles share a common arm and a common vertex. The adjacent supplementary angles share one common line segment. Non-adjacent supplementary angles do not have a common arm and vertex. They do not share a common line segment with each other.

On the case, we know that:

Zy = 88°

Zy and Zx --> supplementary angles

Then:

Zy + Zx = 180°

88° + Zx = 180°

Zx = 92°

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The car is traveling with the speed of 0.25 miles/min.

For the stated question:

Distance travelled by car ; d =  5 miles

Time taken by the care: t = 20 minuts.

Using the formula for the speed:

speed = distance /time

s = d /t

s = 5 / 20

s = 0.25 miles/min

Thus, the car is traveling with the speed of 0.25 miles/min.

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the correct question is-

A car travels 5 miles in 20 minutes. How fast was it traveling (in miles/min)

The angle in the sector formed in radian is 5/4 π

The length of an arc is defined as the part of the circumference of a circle which is bounded by two radii.

The length of an arc = tetha / 360 × 2πr

where( tetha) is the angle

r is the radius

360° = 2π

therefore :

15π/2 = tetha/2π × 2× 6 × π

15π/2 = 6 tetha

tetha = 15π/2 ÷ 6

tetha = 15/12 π

tetha = 5/4 π

therefore the value of the angle in radian Is 5/4 π

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For any probability distribution, the expected value: 1. represents the location/center of the distribution.

In Mathematics and statistics, an expected value is sometimes referred to as the long-term mean (average) of a discrete random variable, E(X) and it can be calculated by taking the weighted average of all the outcomes of the discrete random variable with respect to their probabilities.

For instance, in a game of dice, the total number of outcomes (expected values) is generally equal to six (6). This ultimately implies that, the probability of rolling each number is p(x) = 1/6.

In conclusion, the location or center of distribution is represented by the expected value in any probability distribution.

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Addition of mixed numbers with different denominators includes converting each mixed number to an improper fraction, addition or subtraction, and simplification to a mixed number.

Here are ten examples:

3 1/4 + 2 3/5 = (3 x 4 + 1) / 4 + (2 x 5 + 3) / 5 = 13/4 + 13/5

4 2/3 + 2 1/4 = (4 x 3 + 2) / 3 + (2 x 4 + 1) / 4 = 14/3 + 9/4

5 1/2 - 3 1/3 = (5 x 2 + 1 ) / 2 - (3 x 3 + 1) / 3 = 11/2 - 10/3

3 3/4 - 1 2/5 = (3 x 4 + 3) / 4 - (1 x 5 + 2) / 5 = 15/4 - 7/5

2 1/3 + 3 2/5 = (2 x 3 + 1) / 3 + (3 x 5 + 2) / 5 = 7/3 + 17/5

Addition of mixed numbers with different denominators includes converting each mixed number to an improper fraction, finding a common denominator, converting to an equivalent fraction. addition or subtraction, and simplification to a mixed number.

additive mixed denominator unequal numbers involves the following steps:

Converts each mixed number to an improper fraction.

Finds the common denominator that is the lowest common multiple of the denominators of two or more improper fractions.

Converts each improper fraction to an equivalent fraction with a common denominator.

Add or subtract the appropriate fraction.

Simplify the result to mixed numbers if necessary.

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Answer:

x = 3 units

Step-by-step explanation:

Given that,

length of the square = a = √(x+6)

area of the square = 3x

We know that, the formula to find the area  of a square is:

Area = a²

3x = (√(x+6))²

3x = x + 6

Subtract x from both sides.

3x - x = 6

2x = 6

Divide both sides by 2.

x = 3

Answer:

0.868

Step-by-step explanation:

you js have to times it not hard hope u have a good day,night

The critical points are y = 0 and y = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

The critical points of the differential equation dy/dx = y^2 - 4y are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:

y² - 4y = 0

y(y - 4) = 0

So the critical points are y = 0 and y = 4.

For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.

At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.

At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.

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The critical points are y = 0 and y = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

The critical points of the differential equation [tex]\frac{dy}{dx} = y^{2} - 4y[/tex] are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:

[tex]y^{2} - 4y[/tex]= 0

[tex]y(y-4)[/tex] = 0

So the critical points are y = 0 and y = 4.

For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.

At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.

At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.

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The denominator is the length of the interval of integration be[tex]$\frac{-\cos x}{\pi/2}$[/tex], between the limits [0, π/2]

The average value of a function throughout its domain is a loose definition of the term "mean" in calculus, and particularly in multivariable calculus. The Average function adds up the values in the given range, divides that total by the number of non-zero cells in the range, and returns the average.

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.

The integral of a function divided by the duration of the interval is the definition of the average value of a function across the interval.

Let the given function be f(x) = sin x on the interval [0, π/2]

Average [tex]$=\frac{\int \sin x d x}{\pi/2}$[/tex], over the interval [0, π/2]

The denominator is the length of the interval of integration.t.

[tex]$=\frac{-\cos x}{\pi/2}$[/tex], between the limits [0, π/2]

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