Find m < b
Find m < c

Answer:

A = 46.74 mi²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{h}[/tex] (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 8.2 , b₁ = 9 , b₂ = 2.4

then

A = [tex]\frac{1}{2}[/tex] × 8.2 × (9 + 2.4) = 4.1 × 11.4 = 46.74 mi²

Answer:

13 meters.

Step-by-step explanation:

We can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height

We are given that the base area (length x width) of the prism is 54 m², so we can write:

length x width = 54 m²

We are also given that the volume of the prism is 702 m³, so we can write:

Volume = length x width x height = 702 m³

We want to find the height of the prism, so we can rearrange the formula for the volume to solve for height:

height = Volume / (length x width)

Substituting the given values, we get:

height = 702 m³ / 54 m²

Simplifying this expression, we can divide both the numerator and the denominator by the greatest common factor of 54 and 702, which is 18:

height = (702/18) m / (54/18) m = 39 m / 3 m

height = 13 meters

Therefore, the height of the rectangular prism is 13 meters.

Answer: f(4) = 11

Step-by-step explanation: See image below.

Answer: 11

Step-by-step explanation:

you need to put 4 where the X is: f(4)=(2*4)+3 = 11

the particular solution to the differential equation. we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]

To find the particular solution to the differential equation {dy}/{dx} = (x+1) (y+1) with the initial condition y(4) = 3, we can use separation of variables and integration.

First, we can rewrite the equation as:

[tex]{1}/{(y+1)} dy = (x+1) dx[/tex]

Next, we can integrate both sides:

[tex]∫ {1}/{(y+1)} dy = ∫ (x+1) dx[/tex]

[tex]ln|y+1| = 1/2 x^2 + x + C[/tex]

where C is the constant of integration.

To determine the value of C, we can use the initial condition y(4) = 3:

[tex]ln|3+1| = 1/2 (4)^2 + 4 + C[/tex]

[tex]ln|4| = 10 + C[/tex]

[tex]C = ln|4| - 10 = -5.605[/tex]

Therefore, the particular solution to the differential equation with the initial condition y(4) = 3 is:

[tex]ln|y+1| = 1/2 x^2 + x - 5.605[/tex]

Solving for y:

[tex]|y+1| = e^(1/2 x^2 + x - 5.605)[/tex]

[tex]y+1 = \pm e^(1/2 x^2 + x - 5.605)[/tex]

[tex]y = -1 \pm e^(1/2 x^2 + x - 5.605)[/tex]

Since [tex]y(4) = 3[/tex], we can determine which sign to use:

[tex]3 = -1 + e^(1/2 (4)^2 + 4 - 5.605)[/tex]

[tex]3 = -1 + e^(7.395)[/tex]

[tex]4 = e^(7.395)[/tex]

Therefore, we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]

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The statement that is true about rhombus is d. some rhombuses have four right angles.

A rhombus is a parallelogram with equal-length sides, though the angles at the opposing ends need not be equal, nor must the sides be parallel. If a rhombus is also a cube, it can have four right angles. It can be viewed as an equal-sided trapezoid as well.

A parallelogram has two sets of parallel sides, whereas a trapezoid only has one pair of parallel sides. Therefore, it is untrue that a trapezoid has two sets of parallel edges. Not all rectangles are squares, but they are all quadrilaterals with four right angles. A unique variety of parallelogram called a square has equal-length edges. Therefore, it is untrue to say that all circles are squares.

Complete Question:

which statement about a quadrilateral is true?

a. a rhombus has exactly one pair of parallel sides.

b. a trapezoid has two pairs of parallel sides.

c. all rectangles are squares.

d. some rhombuses have four right angles.

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1.143 x 10⁷ ft, or approximately 11.43 million feet is the length of the river.

To find the length of the river, we need to use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the diagonal line connecting the two endpoints of a right triangle) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the length of the southward flowing part of the river "a" and the length of the southeastward flowing part of the river "b". Then we have:

a = 1.1 x 10⁷ ft

b = 3.2 x 10⁶ ft

The length of the river is given by the hypotenuse of a right triangle with sides a and b. Therefore, we can calculate the length of the river, c, as follows:

c² = a² + b²

c² = (1.1 x 10⁷ ft)² + (3.2 x 10⁶ ft)²

c² = 1.21 x 10¹⁴ ft² + 1.024 x 10¹³ ft²

c² = 1.3104 x 10¹⁴ ft²

c = √(1.3104 x 10¹⁴ ft²)

c = 1.143 x 10⁷ ft

Therefore, the length of the river is 1.143 x 10⁷ ft, or approximately 11.43 million feet

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Hence, the value of y is 23 when x = 7.

Describe equation?

A mathematical equation is a formula that uses the equals symbol (=) to denote the equality of two expressions.

A formula would be 3x - 5 = 16,

for instance. We may determine the value of the variable x by solving this equation: x = 73.

The slope-intercept representation of the equation can be used to determine the equation of a line running through the points (x1, y1) and (x2, y2):

y - y1 = m(x - x1) (x - x1)

where m is the line's slope. The following formula can be used to determine the line's slope:

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

Now put the x and y value in this:

slope of the line using the points (1, 5) and (3, 11):

m = (11 - 5) / (3 - 1) = 6 / 2 = 3

We can use the slope of the line to determine the equation of the line now that we know it:

y - y1 = m(x - x1) (x - x1)

y - 5 = 3(x - 1) (x - 1)

y - 5 = 3x - 3 = 3x + 2

In light of this, the equation for the line connecting points (1, 5) and (3, 11) is y=3x+2

To determine the value of y for x = 7, we can utilize the equation of the line we discovered earlier:

y = 3x + 2

y = 3(7) + 2

y = 21 + 2

y = **23**

Graph calculation given below:

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The stratified random sampling is a method of various strata are selected from the sample. So, the right choice for answer is option(c).

The four probability sampling methods mainly applied in research methods include simple random sampling, cluster sampling, stratified sampling, and systematic sampling. In certain situations, we need to remove the sampling bias, and for that, we opt for stratified random sampling. Here we talking about stratified random sampling. A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub populations) and random samples are drawn from each. Therefore, the required choice is option (c), that is various strata are selected from the sample.

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Answer:

[tex]x {}^{2} - 5[/tex]

The triple integral evaluates to 8/15.

To evaluate the triple integral f 1 dv where f = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 4 − x^2, 0 ≤ z ≤ 4 − x²},

Set up the triple integral
The triple integral is written as ∭(1) dV, with the limits of integration for x, y, and z as given in the problem.

Integrate with respect to z
∫(∫(∫(1) dz) dy) dx
The limits for z are 0 to 4-x², so integrate with respect to z:
∫(∫[(z)|from 0 to 4-x²] dy) dx

Substitute the limits for z
∫(∫[(4-x²)] dy) dx

Integrate with respect to y
∫[(4-x²)y|from 0 to 4-x²] dx

Substitute the limits for y
∫[(4-x²)²] dx

Integrate with respect to x
Integrate the function with respect to x:
∫(16 - 16x² + x⁴) dx from 0 to 2

Substitute the limits for x
[4x³/3 - 16x³/3 + x⁵/5]|

from 0 to 2

Calculate the final result
(4(2)³/3 - 16(2)³/3 + (2)⁵/5) - (0) = (32/3 - 128/3 + 32/5) = 8/15

So, the triple integral evaluates to 8/15.

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Answer:

Option D.

Step-by-step explanation:

According to this survey results:

Students: 80 like viking and 20 like patriot.

Teachers: 5 like viking and 15 like patriot.

In Option A it is given that patriot is more popular in students while viking is more popular in teachers which is not correct.

In option C patriot is equally popular in students and teachers, which is also not correct. because patriot is popular in 20% of students but 80% in teachers, which is not correct.

In option B there is no difference between students and teachers, this statement is also not correct because there is lots of differences in their choices.

In Option D it is said that viking is more popular in students but patriot is more popular in teachers. this is correct.

Answer:

To find A+3B, we need to first find A and B. A = 1 + r + 7r^2 B = 1 - r^2 Now we can substitute these expressions into A+3B: A+3B = (1 + r + 7r^2) + 3(1 - r^2) Simplifying this expression, we get: A+3B = 1 + r + 7r^2 + 3 - 3r^2 A+3B = 4 + r + 4r^2 So the expression that equals A+3B in standard form is 4 + r + 4r^2.

The number completes the number sentence 3m= 5g.

The m refers the meatball which prices $2.50

so for 3m = 3*2.50

          3m = $7.5

g refers to grilled cheese which prices $1.50

so we have to find for how many grilled cheese which equals $7.5

On dividing we get, 7.5/1.50 = 5

Hence 3 meatballs equal 5 grilled cheese, 3m = 5g

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The sample's standard deviation is equal to 12. Thus, choice B is the right choice.

The variance of a sample of 144 observations equals 576.

Variance S² = 144

The standard deviation is a measure of how spread out a set of data is. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The standard deviation can be used to measure the amount of variation or dispersion of a set of data values from the mean.

Standard Deviation = √Variance

Standard Deviation = √144

Standard Deviation = 12

The standard deviation of the sample equals 12. So the option B is correct.

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The complete question is:

The variance of a sample of 144 observations equals 576. The standard deviation of the sample equals:

A. 441

B. 12

C. 63,504

D. 21

Answer:

3/8 - 1/16 simplifies to 5/16.

Step-by-step explanation:

To subtract two fractions, we need to find a common denominator. In this case, the least common multiple of 8 and 16 is 16.

So, we need to rewrite 3/8 and 1/16 with a denominator of 16:

3/8 = 6/16

1/16 = 1/16

Now we can subtract:

6/16 - 1/16 = 5/16

AnswerAns

5/6

Step-by-step explanation

3/8 - 1/16 = (3×2 -1)÷16 = 5/16

Answer:

--------------------------

Standard form for the equation of a circle is:

Convert the given equation into standard form:

Its center is ( 1, 0) and radius is r = 3.

Let's verify the statements:

Answer:

See below

Step-by-step explanation:

To find:-

Answer:-

The given equation of the circle is ,

[tex]\longrightarrow x^2+y^2-2x-8 = 0 \\[/tex]

For finding the correct statements , we need to convert this equation into standard form for a circle.

The standard equation of circle is given by,

[tex]\boxed{\begin{tabular}{c}\textbf{\underline{ \red{Standard\ equation\ of \ circle }}} \\ \\ \text{ The standard equation of a circle is given by:-} \\\\ \longrightarrow \underline{\underline{ (x-h)^2+(y-k)^2 = r {}^{2}}} \\\\ \text{where} , \\\\ \bullet\text{ (h,k) is the centre of the circle.}\\\\\bullet\text{ "r" is the radius of the circle. }\\\end{tabular}}[/tex]

Now for that we need to complete the square for "x" . This can be done by ,

Rearrange the terms,

[tex]\longrightarrow x^2-2x + y^2-8 = 0 \\[/tex]

Add and subtract 1² .

[tex]\longrightarrow ( x^2 -2x +1^2 ) - 1^2 + y^2-8=0 \\[/tex]

Simplify,

[tex]\longrightarrow (x^2-2(1)x+1^2) - 1-8 + y^2=0 \\[/tex]

Notice that the terms inside the small brackets are in the form of a² - 2ab + b² , which is the whole square of (a-b) . So we can write it as,

[tex]\longrightarrow (x-1)^2 +y^2 - 9 = 0 \\[/tex]

Add 9 on both the sides ,

[tex]\longrightarrow (x-1)^2 + y^2 = 9\\[/tex]

This can be written as,

[tex]\longrightarrow \underline{\underline{ \boldsymbol{(x-1)^2+(y-0)^2 = 3^2}}} \\[/tex]

On comparing it to the standard form, we have;

[tex]\longrightarrow\boxed{ \text{Center = (1,0) }} \\[/tex]

[tex]\longrightarrow\boxed{ \text{ Radius = 3 \ units}} \\[/tex]

Let's check the given statements ,

Statement 1: The radius of the circle is 3 units.

Statement 2: The centre of the circle lies on the x-axis.

Statement 3: The statement of the circle lies on the y-axis.

Statement 4: The standard equation of the circle is (x-1)²+y² = 3

Statement 5: The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The graph for the same has been attached.

To find the total percentage decrease, we first need to find the new values of the stocks in Company A and Company B after the decrease.

The new value of the stock in Company A is: $5800 - (1% \times $5800) = $5742

The new value of the stock in Company B is: $7470 - (20% \times $7470) = $5976

To find the total value after the decrease, we add these two values: $5742 + $5976 = $11718

To find the percentage decrease from the original total value ($5800 + $7470 = $13270) to the new total value ($11718), we use the formula:

percentage decrease = [(original value - new value) / original value] x 100%

percentage decrease = [($13270 - $11718) / $13270] x 100%

percentage decrease = 11.7%

Therefore, the total percentage decrease in the investor's stock account is 11.7%.

a. The sample mean for sample 1 is 9.2, and the sample mean for sample 2 is 7.17.

b. The sample standard deviation for sample 1 is approximately 3.29, and the sample standard deviation for sample 2 is approximately 3.65.

c. The point estimate of the difference between the two population means is 2.03.

d. The 90% confidence interval estimate of the difference between the two population means is [-0.44, 4.50].

a. The sample mean for sample 1 is

(10 + 13 + 9 + 8 + 6) / 5 = 9.2

The sample mean for sample 2 is

(7 + 7 + 8 + 4 + 9 + 8) / 6 = 7.1667 ≈ 7.17

b. The sample standard deviation for sample 1 is:

√[((10-9.2)² + (13-9.2)² + (9-9.2)² + (8-9.2)² + (6-9.2)²) / (5-1)]

= √[10.8] ≈ 3.29

The sample standard deviation for sample 2 is

√[((7-7.17)² + (7-7.17)² + (8-7.17)² + (4-7.17)² + (9-7.17)² + (8-7.17)²) / (6-1)]

= √[13.33] ≈ 3.65

c. The point estimate of the difference between the two population means is:

9.2 - 7.17 = 2.03

d. To calculate the 90% confidence interval estimate of the difference between the two population means, we need to first calculate the standard error of the difference between the sample means:

s.e.(difference between sample means) = √[(s1²/n1) + (s2²/n2)]

= √[(3.29²/5) + (3.65²/6)]

= √[2.60]

≈ 1.61

Next, we can use the t-distribution with degrees of freedom equal to the smaller of n1-1 and n2-1 (in this case, 4) and a 90% confidence level to find the critical value, t*:

t* = 1.533 (from t-distribution table or calculator)

Finally, we can construct the confidence interval estimate:

9.2 - 7.17 ± (t* * s.e.(difference between sample means))

= 2.03 ± (1.533 * 1.61)

= 2.03 ± 2.47

= [ -0.44 , 4.50 ]

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This is reflected in the data as the number of bacteria doubles every two hours, which is a characteristic of exponential growth.

Data that changes or grows at an exponential rate over time is referred to as exponential data. This indicates that the data changes quickly, either increasing or decreasing, and that the pace of change quickens over time. Exponential data frequently consists of numbers that rise steadily over time, with the rate of rise accelerating over time.

a.) exponential function would be the ideal option to model this data. An exponential curve is produced as the quantity of bacteria multiplies at an ever-increasingly rapid rate.

b. One way to determine which function is the best choice is to examine the rate of change of the data. In this case, we may calculate the average rate of change for each time period and see if it is constant. If the rate of change is constant, the data can be represented by a linear function. However, if the rate of change increases or decreases, an exponential or quadratic function might be a better fit.

From 0 to 2 hours: (25-10)/(2-0) = 7.5

From 2 to 4 hours: (50-25)/(4-2) = 12.5

From 4 to 6 hours: (100-50)/(6-4) = 25

c. The distance travelled by an automobile at a constant pace is an illustration of data that would be best characterised by a linear function. Imagine a car driving for four hours at a speed of 60 mph. Below is a list of the distance covered each hour:

After 1 hour: 60 miles

After 2 hours: 120 miles

After 3 hours: 180 miles

After 4 hours: 240 miles

In this case, the distance traveled is directly proportional to the time, so a linear function would be the best fit.

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Answer: it's 1

Step-by-step explanation:

The x in the numerator determines that the x is in absolute value, meaning only positive integers.

That wouldn't matter anyway, because since any value of x would have to be greater than 0 (meaning only positive values), and both x's are the same x, the equation would have to equal one.

For example, you could plug in 2 to both x's. 2/2 is 1.

Or you could plug in 289 to both x's, in which 289/289 is 1.

No matter what number, as long as it's positive, will be 1.

The two column proof is completed as follows

Statement                                               Reason

1. AB || CD                                           Given

2 Construct BE perpendicular to      Construction of side BE

CD  such that point E is on CD

3 Construct CF perpendicular to      Construction of side CF

AB such that point F is on AB

4 ∠ CFB = ∠ BEC = 90°                     All perpendicular angles measure 90°

5 CF = BE                                           Any point on one parallel line is the                          

                                                           same distance from the other line on        

                                                           a perpendicular transversal (1, 2, 3)

6. BC = BC                                         They are measures of the same            

                                                           segment.

7. Δ BCF ≅ Δ CBE                             SAS congruence (4, 6,5)

The SAS congruence theorem, also known as the Side-Angle-Side congruence theorem, states that if two triangles have two sides and the included angle of one triangle congruent to the corresponding parts of another triangle, then the triangles are congruent.

The equality of the included angle is by the alternate interior angles theorem.

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Option D is the correct option i.e., 2.5 hours. Timing is everything when it comes to dining before a fight. Athletes must ingest enough calories to power their efforts without developing gastrointestinal pain or bloating while competing. Typically, a substantial dinner should be eaten two to three hours prior to the game. 

The body needs time to process and assimilate nutrients, which is the cause of this. A big dinner requires the body to divert a lot of blood flow to the digestive system, which can have an impact on an athlete's performance. Athletes' performance can be hampered by sluggishness, gastrointestinal pain, or even vomiting brought on by eating too close to a competition.

In general, it is recommended that athletes experiment with different meal timings and types of food during their training to determine what works best for their individual needs.

They should also consider the length of the event and the intensity of their activity to determine the amount and timing of their meals. A registered dietitian or sports nutritionist can help athletes create a personalized nutrition plan to optimize their performance.

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If ∠1 and ∠2 are vertical angles and m∠22 = 180°, then m∠1 = 90°

Vertical angles are pairs of angles that are opposite to each other when two lines intersect. Vertical angles are always equal in measure. Therefore, if ∠1 and ∠2 are vertical angles, then:

∠1 = ∠2

We are also given that m∠22 has a measure of 180°. Since ∠1 and ∠2 are vertical angles, they form a straight line, and their measures add up to 180°. Therefore:

∠1 + ∠2 = 180°

Since ∠1  = ∠2, we can substitute ∠1 for ∠2 in the above equation:

∠1 + ∠1 = 180°

Simplifying the equation, we get:

2∠1 = 180°

Dividing both sides by 2, we get:

∠1 = 90°

Therefore, ∠1 has a measure of 90°.

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To be 95% confident within a 4% margin of error, the programmer must survey at least 601 computers.

To estimate the percentage of computers that use a new operating system with a 95% confidence level and a 4% margin of error, you must first determine the required sample size. Here's a step-by-step explanation:
Identify the confidence level and margin of error: In this case, the confidence level is 95% and the margin of error is 4%.
Determine the standard value (Z-score) for the desired confidence level: For a 95% confidence level, the Z-score is 1.96. This value can be found using a Z-score table or an online calculator.
Use the formula for sample size calculation:
  n = (Z^2 * p * (1-p)) / E^2
  Where n is the required sample size, Z is the Z-score, p is the estimated proportion of computers using the new operating system, and E is the margin of error.
Since we do not have an estimate for the proportion (p), we will assume the worst-case scenario (p=0.5) to ensure the largest possible sample size:
  n = (1.96^2 * 0.5 * 0.5) / 0.04^2
Calculate the sample size:
  n ≈ (3.8416 * 0.25) / 0.0016
  n ≈ 0.9604 / 0.0016
  n ≈ 600.25
Round up to the nearest whole number: Since we cannot survey a fraction of a computer, we will round up to the next whole number, which is 601.

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72 books were divided up among 18 children means 18 kids and 72 books equal 4 books for each youngster.

An element of a whole is a portion. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a straightforward fraction. A fraction appears in the numerator or denominator of a complicated fraction. The numerator of a perfect fraction is less than the denominator.0

1) 8/3 split by 6/9: To begin, we divide both the numerator and denominator by 3 to reduce 6/9 to 2/3.

8/3 ÷ 2/3 = (8/3) x (3/2) = 4

The fraction we began with is not equivalent to this expression.

2) 8/3 times 2/3: By multiplying the numerators and denominators, we can reduce this expression:

(8/3) x (2/3) = 16/9

The fraction we began with is not equivalent to this expression.

3) 2/9 split by 8/9: We multiply the first fraction by the reciprocal of the second fraction to divide fractions:

(2/9) ÷ (8/9) = (2/9) x (9/8) = 1/4

The fraction we began with is not equivalent to this expression.

4) In order to simplify this equation, let's first reduce 8/2 to 4:

2 x 4 = 8

The fraction we began with is not equivalent to this expression.

The fraction that accurately describes the circumstance cannot be expressed using any of the given expressions.

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In the last 10 softball games, the mode number of runs for Delisa is 3.

Mode is the value that appears most frequently in a given data set. It is one of the three measures of central tendency, along with mean and median.

To find the mode, we need to determine which number appears most frequently in the data set. In this case, the number of runs that Delisa scored in each game.

We have been given the data points,

2,1,3,3,1,3,2,4,3,5

The number 3 appears most frequently, occurring three times. Therefore, the mode number of runs for Delisa is 3.

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Step-by-step explanation:

if it is between 0 and pi/2 (90°), or between 3pi/2 (270°) and 2pi (360°).

for angle = 0, cos = 1. therefore, positive.

0 <= 5pi/12 <= pi/2. therefore, positive.

pi/2 <= 5pi/6 <= pi. therefore, negative.

pi/2 <= 3pi/4 <= pi. therefore, negative.

3pi/2 <= 5pi/3 <= 2pi. therefore, positive.

you do know how to compare fractions, right ?

you need to bring then to the same denominator by multiplying numerator and denominator by the same factor.

e.g. comparing 5pi/12 with pi/2.

to bring them both to .../12, we have to multiply pi/2 by 6/6.

so, we are comparing 5pi/12 and 6pi/12.

and we see, 5pi/12 is smaller.

the others work the same way.

3pi/6 <= 5pi/6 <= 6pi/6

2pi/4 <= 3pi/4 <= 4pi/4

9pi/6 <= 10pi/6 <= 12pi/6

now you see it clearly.

Answer:

can u break that down

Step-by-step explanation: