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Triangle PQR is formed by the three squares A, B, and C: A right triangle PQR is shown. On the side PQ of this triangle is a square. Inside the square is written Square A, Area equal to 9 square units. On the side QR of this triangle is another square. Inside the square is written Square B, Area equal to 16 square units. On the side PR of this triangle is another square. Inside the square is written Square C, Area equal to 25 square units. Which statement best explains the relationship between the sides of triangle PQR?

Answer:

5% significance level indicates the level of risk, error or exactness. It guides our conclusion on which hypothesis a data supports

Level of significance defined as the possibility, probability or chances of rejecting a null hypothesis when it's results is valid.

For every statistical hypothesis, the result has propency or likeliness to be exact or not. That is, it has chances of containing a type of error referred to as level of significance.

Now, a 5% significance level implies that, the statistical results or analysis has 95% reliability or confidence level.

In other words, a 5% significance level indicates that a result has 0.05 RISK level.

The level of significance is needed for every hypothetical test because it indicates validity of each hypothesis data. It gives confidence such that one is at peace to know the hypothesis a particular data supports

Answer: 6m+8

m+m+8m-4m = 6m

5+12-9=8

A. 95     95x50=4750    then you divide 4750 by 50 and you get your answer

To find how long George will take to mop the floor, calculate the area of the court (95 ft x 50 ft = 4,750 ft²) and divide it by his mopping rate (50 ft²/min). The calculation shows it will take George 95 minutes to mop the floor.

To determine how long it will take George to mop the gym floor, we first calculate the area of the rectangular court.

Multiplying the length by the width gives us the total area that needs to be mopped:

Now, since George can mop 50 ft² in 1 minute, we divide the total area by the rate at which George can mop:

Therefore, it will take George 95 minutes to mop the gym floor, which corresponds to option (a).

The required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression.
= x ² + 8x + 12 / x² - 2x -8
= (x + 6)(x + 2) / (x + 2)(x  - 4)

Since, if we put x = -2 and x = 4, the expression will we undefined.

And,
= x + 6 / x -4

Thus, the required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.

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Sure, what do you need help finding?

Answer:

to find a percentage of a number u multiply/divide 100

The flight departing at 3:15 PM MST, after 2 hours and 30 minutes, arrives at an estimated time of 4:45 PM PST considering that PST is one hour behind MST.

The subject of this question revolves around time conversion between different standard global time zones. The departure time is 15:15 or 3:15 PM Mountain Standard Time (MST). A flight taking 2 hours and 30 minutes is added onto this original departure time. Therefore, in MST, the arrival time would be 17:45 or 5:45 PM MST. However, we must consider the time difference to Pacific Standard Time (PST) which is one hour behind MST. This means, to reflect PST, we subtract one hour from the MST arrival time, giving us an estimated arrival time of 16:45 or 4:45 PM PST.

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Answer:

b. AA postulate

Step-by-step explanation:

1) EF = 2 and DF = 4

2) KL = 4√3 and JL = 8

3) ST = 6 and RS = 6√3

4) PQ = 4.5√3 and RQ = 4.5

Step-by-step explanation:

Rules for special triangles 30°,60°,90° :

1) DE = 2√3 is opposite to 60°

⇒ 2√3 = a√3

⇒ a = 2

EF = a which is opposite to 30°.

⇒ EF = 2

DF = 2a which is opposite to 90°.

⇒ DF = 4

2) KJ = 4 is opposite to 30°

⇒ a = 4

KL = a√3 which is opposite to 60°.

⇒ KL = 4√3

JL = 2a which is opposite to 90°.

⇒ JL = 8

3) RT = 12 is opposite to 90°

⇒ 2a = 12

⇒ a = 6

ST = a which is opposite to 30°.

⇒ ST = 6

RS = a√3 which is opposite to 60°.

⇒ RS = 6√3

4) PR = 9 is opposite to 90°

⇒ 2a = 9

⇒ a = 4.5

PQ = a√3 which is opposite to 60°.

⇒ PQ = 4.5√3

RQ = a which is opposite to 30°.

⇒ RQ = 4.5

Answer: z = 280

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable causes an increase in the value of the other variable. Also, a decrease in the value of one variable causes an decrease in the value of the other variable.

The variable z is directly proportional to x. If we introduce a constant of variation, the expression would be

z = kx

When x is 10, z has the value 140. It means that

140 = 10k

k = 140/10

k = 14

The equation becomes

z = 14x

the value of z when x = 20 is

z = 14 × 20

z = 280

Three equations with a solution of x = -1/2:

(2x - 1) = 0

(-x + 3) = 1

(4x + 2) = -3

Here are three equations, each created using the digits 0 – 9, with a solution of x = -1/2:

(2x - 1) = 0

Solution: When you solve for x, you get x = -1/2.

(-x + 3) = 1

Solution: Solving for x, you find x = -1/2.

(4x + 2) = -3

Solution: Upon solving for x, the result is x = -1/2.

In each of these equations, the placement of the digits ensures that when you calculate the value of x, it equals -1/2. This demonstrates that it's possible to use the digits 0 – 9 once to form equations with the specified solution.

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Complete question below :

Using the digits 0 – 9, no more than one time each, place a digit in each box to create three equations with a solution x = -1/2.

Step-by-step explanation:

Start by finding when the populations become equal.

C = R

1000e^(0.1t) = 50e^(0.5t)

Divide both sides by 50.

20e^(0.1t) = e^(0.5t)

Divide both sides by e^(0.1t).

20 = e^(0.4t)

Take natural log of both sides.

ln 20 = 0.4t

Multiply both sides by 2.5

t = 2.5 ln 20

t ≈ 7.5

The population of rabbits first exceeds the population of crickets in the middle of the 7th year after 2016, or 2023.

Answer:

8th year

Step-by-step explanation:

r > C

50(e^0.5t) > 1000(e^0.1t)

(e^0.5t)/(e^0.1t) > 20

e^(0.5t-0.1t) > 20

e^0.4t > 20

ln(e^0.4t) > ln20

0.4t × lne > ln20

t > ln(20)/0.4

t > 7.489330685

Population of rabbits first exceeds the population of crickets during the 8th year

Step-by-step explanation:

[tex]y = - 2x + 3[/tex]

The slope of the above line = -2

slope of the line perpendicular to the above line = 1/2

If it passes through point (4,-3) , it's equation

[tex] \frac{y - ( - 3)}{x - 4} = \frac{1}{2} [/tex]

[tex] \frac{y + 3}{x - 4} = \frac{1}{2} [/tex]

[tex]2(y + 3) = x - 4[/tex]

[tex]2y + 6 = x - 4[/tex]

[tex]x - 4 - 2y - 6 = 0[/tex]

[tex]x - 2y - 10 = 0[/tex]

A = 1, B = -2 and C = -10

A+B+C= 1+(-2)+(-10)

= 1-2-10

= 1-12

= -11

Answer:

A = 1, B = -2 and C = -10

Step-by-step explanation:

Answer:

I have a feeling its B

Step-by-step explanation:

Vicky's Gross Monthly Income for the job at Southside High School is $3708.33.

Gross income of an individual is the income he/she receives before deduction and taxes.

Given that,

Base salary per year = $43,600

Income for coaching JC softball = $900

Free life insurance coverage = $15,000

Health & dental or medical premiums = $78/month

Gross income is the income an employee receives before all the deductions.

Insurance premiums are deducted from the base salary. So it is not included in gross income.

Annual Gross income = $43,600 + $900 = $44,500

Monthly Gross Income = $44,500 / 12 = $3708.33

Hence the monthly gross income is $3708.33.

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The mat adds 3 inches to each side, so the length would be 3+20 = 23 inches. The width would become 3 + 9 = 12 inches.Area = Length x width:

23 x 12 = 276 square inches

Answer:

The plant makes 34,802,178 ball bearings in a single day

Step-by-step explanation:

The total output of a plant in a 5-day week is 4335 pounds

Each ball bearing weighs 0.0113g

We are to calculate the number of ball bearings made per day

First, we ensure both mass are in the same unit

Now 1 pound =453.5924 grams

4335 pounds=453.5924 X 4335 =1966323.054 grams

Number of bearings made in a week therefore

= 1966323.054 /0.0113=174010889.7

≈174010890 (to the nearest whole number)

Since there are 5 days in a week of production,

Daily Production=174010890/5

=34802178

The plant makes 34,802,178 ball bearings in a single da

Answer:

The bottom answer

Step-by-step explanation:

Answer:

10.7°

Step-by-step explanation:

1 mile = 5280 feet

Tan(X) = 1000/5280 = 25/132

X = (tan^-1)(25/132)

X = 10.72444854

Answer:

Step-by-step explanation:

The movement of the forms a right angle triangle with the ground. The vertical distance which the plane moves represents the opposite side of the right angle triangle. The horizontal distance covered by the plane represents the adjacent side of the right angle triangle.

1 mile = 5280 feet

To determine the angle of elevation, θ, we would apply

the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan θ = 1000/5280 = 0.189

θ = Tan^-1(0.189)

θ = 10.7°

Answer:

2 raisins.

Step-by-step explanation:

Let x represent total number of required ingredient.

We have been given that Ren finds 6 peanuts, 4 raisins, 3 cranberries, and 5 chocolate chips in a handful of trail mix. We are asked to find of which ingredient Ren will have 2 pieces for a total of 9 pieces.

First of all, we will find total number of ingredients by adding each ingredient as:

[tex]\text{Total number of ingredients}=6+4+3+5[/tex]

[tex]\text{Total number of ingredients}=18[/tex]

Now, we will use ratio to solve for our given problem as:

[tex]\frac{\text{Required ingredient}}{\text{Total ingredient}}=\frac{2}{9}[/tex]

[tex]\frac{x}{18}=\frac{2}{9}[/tex]

[tex]\frac{x}{18}\cdot 18=\frac{2}{9}\cdot 18[/tex]

[tex]x=\frac{2}{1}\cdot 2[/tex]

[tex]x=4[/tex]

Since there are 4 raisins, therefore, for  every 9 pieces in Ren's handful of trail mix there are 2 raisins.

The measurements of ∠1 = 60°, ∠2 = 30° and ∠3 = 90°.

Solution:

By the property of rectangle,

Opposite sides of rectangle are parallel.

By another property of parallel lines,

If two parallel lines cut by a transversal (diagonal) then alternate interior angles are congruent.

60° and ∠1 are alternate interior angles.

Hence m∠1 = 60°.

In rectangle, all the angles are right angle.

m∠1 + m∠2 = 90°

60° + m∠2 = 90°

Subtract 60° from both sides of the equation.

m∠2 = 30°

In rectangle, all the angles are right angle.

m∠3 = 90°

Hence the measurements of ∠1 = 60°, ∠2 = 30° and ∠3 = 90°.

Answer:

About 8 cans.

Step-by-step explanation:

Given:

She starts with nine cans of tomato sauce.

Then use is 9/10 of the cans for her first batch of calzones

To find:

How many cans of tomato sauce does Hannah use for the first batch of calzones ?

Solution:

She starts with number of cans = 9

Then use is [tex]\frac{9}{10}[/tex] of the cans.

Now, we will find number of cans used for the first batch of calzones by multiplying number of cans she starts with by fraction of  cans she used  for the first batch of calzones .

[tex]\frac{9}{10} of 9 cans = \frac{9}{10} \times9\\\frac{81}{10} = 8.1[/tex]

Therefore,  number of cans used for the first batch of calzones is about 8 cans.

Answer:

The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.

Step-by-step explanation:

2x−5y=−5

x+2y=11

In equation (1), substitution of (10,5)

2x−5y=2(10)-5(5)=20-25=-5

However in equation (2), on substitution of (10,5)

x+2y=10+2(5)=10+10=20 ≠11.

However, the solutions of the simultaneous equations

2x−5y=−5

x+2y=11

are (5,3)

The ordered pair (10, 5) is a solution to the first equation of the system but not the second, which means it is not a solution to the entire system of equations.

To determine if the ordered pair (10, 5) is a solution to the given system of equations, we need to substitute x with 10 and y with 5 into each equation and see if the equations hold true:

Since the ordered pair does not satisfy both equations, it is not a solution to the system of equations. Therefore, the correct statements are:

6/7th of £60 to the nearest penny is £51. 43 penny

Step-by-step explanation:

The amount = £60

The fraction that needs to be decided= 6/7th part

For solving the problem, we need to find out the 6/7th part of £60 and then round off the answer to the nearest 2 digits after decimals.

Thus the amount to the nearest penny= (6/7) *60

Amount= £51.42857714285

When the above amount is rounded off to the nearest penny than the amount becomes= £51.43 meaning 51 pounds and 43 pennies.  

Answer:

c

Step-by-step explanation:

I think you missed attaching the photo, please see my attachment.

And the correct answer is C,

When you look at where the arc meets the parallel lines, if you create a seam between two points, you get a straight line parallel to the horizontal lines  so it makes the corresponding angles are congruent.

The theorem stating that when two lines are intersected by a transversal and the corresponding angles are congruent means the lines are parallel, guides a specific construction method in geometry. This method involves using a transversal to determine if the intersected lines are parallel by comparing corresponding angles.

The theorem 'when two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel' justifies a particular construction of parallel lines in geometry.

This principle is a fundamental aspect of geometric theorems on parallel lines and angles created by a transversal. To construct parallel lines using this theorem, one might follow these steps:

Identify or draw a transversal that intersects two lines.

Measure the corresponding angles created by the intersection of the transversal with these lines.

If the corresponding angles are congruent, then by this theorem, the two lines are determined to be parallel.

This concept is essential in understanding the relationships between angles and lines in a plane, providing a cornerstone for proofs and constructions within geometry.

Answer:

y = [tex]\frac{4}{5}[/tex] x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (5, 1)

m = [tex]\frac{1+7}{5+5}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex], thus

y = [tex]\frac{4}{5}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (5, 1), then

1 = 4 + c ⇒ c = 1 - 4 = - 3

y = [tex]\frac{4}{5}[/tex] x - 3 ← equation of line

Answer:

Therefore the shortest man of 65.6 cm was more extreme.

Step-by-step explanation:

A z-test is a statistic test. It is used to determine whether two population mean are different when the variances of the population are known and the sample size large.

[tex]z=\frac{x- \mu}{\sigma}[/tex]

z= the standarized z score

x = the height of sample

μ = mean  = 172.27 cm

σ = standard deviation = 8.82 cm

For tallest

x = 259

[tex]z= \frac{259-172.27}{8.82}[/tex]

  ≈9.83

For shortest

x= 65.6

[tex]z= \frac{65.6-172.27}{8.82}[/tex]

  ≈ - 12.09

The most extreme value has a z score that the furthest from 0.

Since -12.09 is further from 0 than 9.83.

Therefore the shortest man of 65.6 cm was more extreme.

Answer:

The answer to your question is Ariel is correct, x = 27 ft

Step-by-step explanation:

Data

angle = Ф = 47°

Adjacent side = 25

Opposite side = x

Process

1.- To solve this problem, we must use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is tangent.

            tan Ф = Opposite side / Adjacent side

- Solve for Opposite side

            Opposite side (x) = Adjacent side x tan Ф

-Substitution

                                      x = 25 tan 47

                                     x = 25 (1.0724)

-Result

                                    x = 26.8 ≈ 27 ft

Ariel is correct

Answer:

Incorrect angle; 23 feet

Step-by-step explanation:

She has marked the angle incorrectly

Angle of depression is marked between the line of sight and the hypotenuse

The angle she should use is:

90 - 47 = 43

tan(43) = x/25

x = 25tan(43)

x = 23.31287715

Answer:

0.9815

Step-by-step explanation:

P(head) = 0.55

P(tail) = 1 - 0.55 = 0.45

P(Atleast one head)

= 1 - P(all tails)

= 1 - 0.45⁵

= 0.9815471875

= 0.9815

In probability, the complementary event of 'at least one heads' is 'getting no heads'. Calculate the probability of the complement (getting tails five times) and subtract it from 1. The result is 0.8155.

This type of problem deals with

probability

. The best way to approach it is to consider the complementary event. In this case, the complementary event to getting 'at least one heads' is 'getting no heads'. The probability of getting heads is 0.55, so the probability of getting tails is 1 - 0.55 = 0.45. This is because the sum of the probabilities of all possible outcomes (heads or tails) equals 1. So, the probability of getting tails on all five tosses is (0.45)^5 = 0.1845. Now, we subtract this from 1 to get the probability of the desired event, 'at least one heads': 1 - 0.1845 = 0.8155. Therefore, the probability of getting at least one heads in five coin tosses is 0.8155.

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Answer:  a) 264.3, b) 264.349, c) 265, d) 300, e) 260, f) 264.35.

Step-by-step explanation:

Since we have given that

264.34928 rounded to the nearest tenth.

So, it becomes [tex]264.3[/tex]

264.34928 rounded to the nearest thousandths.

So, it becomes [tex]264.349[/tex]

264.34928 rounded to the nearest one.

So, it becomes [tex]265[/tex]

264.34928 rounded to the nearest hundreds.

So, it becomes [tex]300[/tex]

264.34928 rounded to the nearest tens.

So,it becomes [tex]260[/tex]

264.34928 rounded to the nearest hundredths.

So, it becomes [tex]264.35[/tex]

Hence, a) 264.3, b) 264.349, c) 265, d) 300, e) 260, f) 264.35.

a. 264.34928 rounded to the nearest tenth = 264.3

b. 264.34928 rounded to the nearest thousandth = 264.349

c. 265.34928 rounded to the nearest one = 265

d. 264.34928 rounded to the nearest hundred = 264.35

e. 265.34928 rounded to the nearest ten = 265.3

f. 264.34928 rounded to the nearest hundredth = 264.35

Here are the answers matched with their properly rounded values along with explanations:

a. 264.34928 rounded to the nearest tenth: 264.3

Explanation: The tenths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.3.

b. 264.34928 rounded to the nearest thousandth: 264.349

Explanation: The thousandths digit is 9, which is greater than or equal to 5. So, you round up to 264.349.

c. 265.34928 rounded to the nearest one: 265

Explanation: The nearest one for 265.34928 is simply 265 because it is already a whole number.

d. 264.34928 rounded to the nearest hundred: 264.35

Explanation: The hundredths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.35.

e. 265.34928 rounded to the nearest tens: 270

Explanation: The tens digit is 6, and the digit immediately to the right of it is 5 or greater. So, you round up to 270.

f. 264.34928 rounded to the nearest hundredth: 264.35

Explanation: The hundredths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.35.

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Answer:

he ded

Step-by-step explanation:

\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \tohe no alive  because ⇆ω⇆π⊂∴∨α∈\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to[tex]\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to[/tex]