at high temperatures, the partition function for rotational energy of a molecule of nitrogen is , where is the energy as in eq. 6.29.

[tex]a_n = 11n + 91[/tex] is the nth term arithmetic progression for the following term.

The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

For instance, the sequence 1, 2, 3, 4, 5, 6,... The standard progression in mathematics is a, (a + d), (a + 2d), and (a + 3d).

Given that,

the first five terms given in the table with position.

Denoted as: a₁ = 102, a₂ = 113, a₃ = 124, a₄ = 135, and a₅ = 146

Thus, the nth term for the arithmetic sequence is given as:

[tex]a_n = a_1 + (n-1)d[/tex]

here, d = (113-102) = 11

[tex]a_1 = 102[/tex]

d is the common difference

So, [tex]a_n = 102 + (n-1)11[/tex]

or, [tex]a_n = 102 +11n-11[/tex]

or, [tex]a_n = 11n + 91[/tex]

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A) Yes, X is a binomial random variable because all of the requirements for a binomial distribution have been established

B) The mean and standard deviation are respectively; 1.2 and 0.6

C) The probability given as P(X ≥ 2) is 0.34464

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula of binomial probability distribution is;

P(X = x) = nCr * p^(x) * (1 - p)^(n - x)

where;

p = probability of "success"

n = number of trials, or the sample size

x = the number of "successes" in the probability we are trying to calculate.

A) We are told that 6 friends each buy one 12-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize.

Probability of success; p = 1/5

Number of events; n = 6 which is the random variable being binomial random variable:

There are two types of accomplishments: successes and failures.

Candies are unrelated to one another.

There is a set number of buddies available.

In addition, the chance of success is fixed.

Because all of the requirements for a binomial distribution have been established, then it is a binomial probability distribution.

B) The formula for the mean here is;

μ = np

Plugging in the relevant values gives;

μ = 6(1/5) = 1.2

Formula for the standard deviation is;

σ = √(np(1 - p))

Thus;

σ = √(6 * 1/5)(1 - (1/5)))

σ = 0.6

C) The probability P(X ≥ 2) calculated with online binomial probability calculator gives;

P(X ≥ 2) = 0.34464

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The independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels is IV (  Interstate migration ) and DV ( State poverty level ) .

Given :

identify the independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels.

Independent variable :

An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure.

Here in the given statement the independent variable is :

IV = Interstate migration

DV = State poverty level

Unit of Analysis = U.S. states

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The value of the following expression x/19 when x=2 is 0.11.

An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping. A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Mathematicians are proficient in addition, subtraction, multiplication, and division. An expression has the following components: an expression, a number or variable, and a mathematical operator.

Given expression is x/19

When x=2,

Then the value of the given expression is:

x/19=2/19

=0.105

≈0.11

Therefore, The value of the following expression x/19 when x=2 is 0.11.

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The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.

Straight line equation is y = a + bx.

The normal equations are

∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :

The values are calculated using the following table

x y x²             x⋅y

58 62 3364 3596

47 51 2209 2397

84 88 7056 7392

62 66 3844 4092

57 61 3249 3477

72 76 5184 5472

69 73 4761 5037

hence :

∑x = 449

∑y = 477

∑x² = 29667

∑x⋅y = 31463

Substituting these values in the normal equations

7a+449b=477

449a+29667b=31463

Solving these two equations using Elimination method,

7a+449b=477

and 449a+29667b=31463

7a+449b=477→(1)

449a+29667b=31463→(2)

equation(1)×449

⇒3143a+201601b=214173

equation(2)×7

⇒3143a+207669b=220241

Substracting

⇒-6068b = -6068

⇒6068b = 6068

⇒b = 1

Putting b = 1 in equation (1), we have

7a+449(1) = 477

⇒7a = 477  - 449

⇒7a = 28 or a  = 4.

Now Estimate y for x=50

y = a + bx , we get

y = 4 + 1×50

y = 4 + 50

y = 54

At x equals 50 we get the value of y as 54 .

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The number of hours it will take the student to complete the project is 5 / 6 hours.

A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate,  the time it will take the student to complete the project can be calculated as follows:

Therefore,

let

x = time it will take the student to complete the project

Hence

if 4 / 5 x = 2 / 3 hours

x = ? hours

cross multiply

Therefore,

number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x

number of hours to complete the whole math project = 2 / 3 x × 5 / 4x

number of hours to complete the whole math project = 10x / 12x

number of hours to complete the whole math project = 10 / 12

number of hours to complete the whole math project = 5 / 6 hours

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Answer: 36.4

Step-by-step explanation:

Just convert the percentage to decimal and multiply.

70 x 0.52 = 36.4

The height of the pile increasing when the pile is 16 feet high is 5/32 ft/min.

We are given dV/dt=10 cubic ft/min and we want to find dh/dt. Therefore, first we need to write a formula relating v and h.

V=pi*r^2*h/3  since d=h at any moment, we know that r=h/2 at any moment and if we substitute h/2 for r, we get

V=pi(h/2)^2*h/3 and if we simplify this,  we get

V=pi*(h^3)/12

Now we need to take the derivative of both sides with respect to t

dV/dt = pi * ( 3 * h^2 ) */12 * dh/dt

= pi * h^2 / 4 * dh/dt, substitute 40 for dV/dt and 16 for h and solve for dh/dt and we get

40 = pi * 16^2/4*dh/dt

dh/dt = 40 * 4 / ( 256 * pi )

= 40/(256*pi) ft/min,

= 10/64

= 5/32 ft/min

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A savings account with just an APR of 5.2% compounded quarterly on a balance of $2,000 will yield $16.61 more interest than a similar account with just an APR of 4.8% compounded monthly on the same balance.

Assume we had two different sorts of savings accounts, each with a deposit of $2,000 in it.

We must now determine the earnings for both accounts.

The following formula will be used to determine the earning:

Here,

Put the values for Account A now.

5.2 % in decimal form = 5.2/100= 0.052

v = 2000 x ( 1 + (0.052/4) )^(4*2)

v = 2217.71

Total earning for account A =  $ 2217.71.

For Account B:

4.8 % in decimal form = 4.8/100= 0.048

v = 2000*( 1 + (0.048/12) )^(12*2)

v = 2201.10

Total earning for account A = $ 2201.10

We will now deduct B's earnings from A's earnings to see how much more A earned than B.

2217.71 - 2201.10 = $16.61

Consequently, account A made $16.61 more so than account B.

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Eric typed 15 words more than Dae per minute.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

To find the amount of words typed in 1 minute for both;

Dae = 333/9

Dae = 27 words per minute

Eric = 252/6

Eric = 42 words per minute

Therefore 42 - 27 = 15 words per minute

Eric typed 15 more words per minute.

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The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).

The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by  

Here we have

A (-12, 2) and B(-6, 2)

B (-6, 2) and C(-6, -4)

C (-6, -4) and D(6, 2)

D (6, 2) and E(6, 4)

E (6, 4) and F(-12, 4)  

Here we will find the distance between given points to find the point which has 6 units between them.

As we know Distance = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]

For Option A

A (-12, 2) and B(-6, 2)

Distance = √(-6 + 12)² + (2 - 2)²

= √[(6)² + (0)²] = √36 = 6

For Option B

For  B (-6, 2) and C(-6, -4)

Distance = √(-6 - (-6))² + ( - 4 - 2)²

= √[(0)² + (-6)²] = √36 = 6  

For Option C

For C (-6, -4) and D(6, 2)

Distance =√(6 - (-6))² + (2 - (-4))²

= √(12)² + (6)² = √180 = 6√5

For Option D

For D (6, 2) and E(6, 4)

Distance = √(4 - 2)² + ( 6 - 6)²

= √[(2)² + (0)²] = √4 = 2      

For Option E

For E (6, 4) and F(-12, 4)  

Distance = √(-12 - 6)² + (4 - 4)²

= √[(18)² + (0)²] = √18² = 18

Therefore,

The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).

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The equation of the line parallel to the line  7x - 4y = - 5 and passing through (16, - 4) is y = (7/4)x - 32.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know lines parallel to each other have the same slope which is

7x - 4y = - 5 ⇒ - 4y = - 7x - 5 ⇒ y = (7/4)x + (5/4) to our required line will also have the same slope passing through the point  (16, - 4).

Therefore, - 4 = 16(7/4) + b.

- 4 = 28 + b.

b = - 32.

Therefore, y = (7/4)x - 32 is the required line.

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Answer:

5x+x=90

Step-by-step explanation:

5 times the other = 5x

the other piece is x

Answer: the small pipe is 15 inches long

Step-by-step explanation: since the larger pipe is 5 times larger than the small pipe, the 90 inch pipe would have too be divided by 6 to make sure the 5 times of the large pipe and the 1 small pipe. so, you would do 90/6=15. so the small pipe is 15 inches long. the large pipe is 75 inches long.

Answer: NO

Step-by-step explanation:

This is not a function, since there are multiple outputs for ONE input.

Answer:

no

Step-by-step explanation:

to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.

The reasons that complete the statements are:

From the question, we have the following parameters that can be used in our computation:

Triangles = RST, and TUR

From the question, we have the following given parameters

∠SRT ≅ ∠UTR

This means that

Statement 2: ∠SRT ≅ ∠UTR ------ Given

At this point, we have

RS ≅ TU --- Congruent side (S)

∠SRT ≅ ∠UTR ------ Congruent angle (A)

RT ≅ TR --- Congruent side (S)

When these congruent sides and angles are combined, we have

SAS congruence property

The SAS congruent theorem implies that the corresponding sides of the triangles in question are congruent and the angles between the corresponding sides are also congruent

Hence, the additional information on the congruency of the triangles are Given and SAS congruence property

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1. This is not wrong at all, but there is a problem. In this case, the target parameter is not mentioned. Average in this case is not the most valid conclusion.

2. Not FALSE as in option #1, but the same problem occurs if the statement does not express a conclusion about the parameter of interest (mean) in this case.

3. This is not the case at all, as the statement refers to possible samples and not confidence levels or parameters of interest. So it's not the best option in this case.

4. true average number of chocolate chips per cookie.

This is the best interpretation, because confidence levels are used to construct the intervals. The most complete answer in this case, as the result is related to the parameter of interest.

Confidence Interval:

A confidence interval is "a range of values ​​that is likely to encompass the values ​​of a population with some degree of confidence. Often expressed as a percentage. The error bar is the range of values ​​above and below the sample statistic in the confidence interval

Normal Distribution:

"A probability distribution that is symmetric about the mean and indicates that data close to the mean are more common than data far from the mean."

X : represents sample mean

μ: population mean (variable of interest)

s : represents sample standard deviation

n : represents sample size

2) The mean confidence interval is given by the formula:

X ± [tex]t_{\alpha /2} \frac{s}{\sqrt{n} }[/tex]                    --------------------------- (1)

The 95% confidence interval obtained in this case is (18.6; 21.3)

Based on this, the statements can be analyzed individually as :

1: We are 95 years old We believe that each cookie from this brand contains approximately 18.6 to 21.3 chocolate chips.

This is not wrong at all, but there is a problem. In this case, the target parameter is not mentioned. Average in this case is not the most valid conclusion.

2: His 95% of cookies are expected to contain 18.6 to 21.3 chocolate his chips.

Not FALSE as in option #1, but the same problem occurs if the statement does not express a conclusion about the parameters of interest in this case.

3: About 95% of all possible sample means from this population are expected to be between 18.6 and 21.3 chocolate chips. This is not the case at all, as you are not referring to some parameter. So it's not the best option in this case.

4: 95% confident that the confidence interval of 18.6 to 21.3 contains the true average number of chocolate chips per cookie.

This is the best interpretation because of the confidence level used to construct the interval. The most complete answer in this case, as the result is related to the parameter of interest.

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By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.

A percentage is a component of a total amount, and the three-step rule is used to relate the measurements.

The percentage of voters who select Candidate J is:

60% of x are voters are female

30% of (1 - x), who vote are male

If the total of these percentages is larger than 50% = 0.5, Candidate J will be elected; therefore:

0.6x + 0.3(1 - x) > 0.5

0.6x + 0.3 - 0.3x > 0.5

0.3x > 0.2

x > 2/3

x > 0.667

x > 67%

By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.

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Answer: To simplify the expression (x - 4)(4x^2 + x - 6), you can use the distributive property, which states that you can multiply a number or expression by each term inside a set of parentheses.

Here is the process for simplifying the expression:

Multiply the first term, "x - 4", by the first term inside the second set of parentheses, "4x^2": (x - 4)(4x^2) = 4x^3 - 16x^2

Multiply the first term, "x - 4", by the second term inside the second set of parentheses, "x": (x - 4)(x) = x^2 - 4x

Multiply the first term, "x - 4", by the third term inside the second set of parentheses, "-6": (x - 4)(-6) = -6x + 24

Add the three products together: 4x^3 - 16x^2 + x^2 - 4x - 6x + 24 = 4x^3 - 16x^2 + x^2 - 10x + 24 = 4x^3 - 15x^2 - 10x + 24

The simplified expression is: 4x^3 - 15x^2 - 10x + 24

So, (x - 4)(4x^2 + x - 6) = 4x^3 - 15x^2 - 10x + 24.

The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24

Centroid is the point in a triangle where all the medians of the triangle intersects.

Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,

1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,

Therefore, 40°+y = 90°

y = 50°

x+y = 90°

x = 90°-50°

x = 40°

z = 180°-50° (linear pair)

z = 130°

2) we know that, the centroid divides the medians into 2:1

AY = 2YP

AY = 16

IY = TY/2

IY = 9

FG = GY+YF   (segment addition postulate)

GY = YF/2

GY = 10

FG = 10+20 = 30

PA = AY+YP  (segment addition postulate)

PA = 8+16

PA = 24

Hence. the measures are x, y and z are 40°, 50° and 130° and  AY = 16, IY = 9, FG = 30, AP = 24

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The value of y is 21.3333. And from the options, 21.3333 is closest to 22.

So, the correct option is C. 22.

A term is composed of one mathematical expression. A single variable (a letter), a single integer (positive or negative), or a number of variables that have been multiplied but never added or subtracted are all examples of single variables. There is a number in front of certain words that are variables. When a phrase is used, a coefficient is given.

We have the expression,

y = 2 · 32 ÷ 3

Simplifying,

y = 2 x 32 ÷ 3

To solve for y:

Using PEMDAS,

the abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations.

P is for "parentheses,"

E is for "exponents,"

M is for "multiplication,"

D is for division,

A is for addition,

and S is for subtraction.

y = 2 x 32 ÷ 3

Firstly, we multiply the number,

y = 64 ÷ 3

Now, the division,

y = 21.3333

Therefore, the value of y is 21.3333.

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The p-value for the z-distribution table is 0.4854.

What is  z-distribution?

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardise it. Z scores provide the number of standard deviations from the mean that each value falls within.

Given that the z statistic to be 2.19 standard deviation above the population mean.

2.19 can be written as 2.1 + 0.09

Z₂.₁₉ = Z₂.₁₊₀.₀₉ =  0.4854

Therefore p-value is  0.4854.

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The following conditions must be met in order to test hypotheses using proportions: np ≥ 5 and nq ≥ 5

To test hypotheses using proportions, the following requirements are necessary:

np ≥ 5 and nq ≥ 5: It is necessary to have a sufficient number of samples in each group being compared.

The rule of thumb is to have at least 5 observations in each group, where n is the sample size and p is the proportion in that group.

This ensures that the sampling distribution of the proportion is approximately normal, which is necessary for hypothesis testing.

Hence, the correct answer would be an option (A).

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The option that best describes the shape of the data is the data is bimodal because the park might have more visitors on those days due to special park passes (fourth option)

The given image is that of a histogram. A histogram is a diagram that is used to describe a dataset by showing its frequency distribution. The histogram is made up of rectangles. The height of the rectangle is equal to the frequency and the width is equal to the interval of the dataset.

In this histogram, the number of visits is on the x-axis while the frequency is on the y-axis.

A bimodal data set is a distribution with two clear most frequent values. Intervals 6 - 10 and 21 - 25  both have a frequency of 6. This indicates that the data is bimodal.

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The radius of the sphere B is 3 times greater than the radius of the sphere A or radius of the sphere A is 1/3 times greater than the radius of the sphere B.

A sphere is a three dimensional shape formed by the set of all points which are at equidistance from a point called the center of the sphere.

Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³

Let the volume and radius of sphere A is V₁ and r₁ respectively and the volume and radius of sphere B be V₂ and r₂ respectively.

We have,

V₁ × 27 = V₂

[tex]\frac{4}{3}[/tex] π r₁³ × 27 = [tex]\frac{4}{3}[/tex] π r₂³

Common terms [tex]\frac{4}{3}[/tex] π get cancelled.

⇒ 27r₁³ = r₂³

⇒ r₁³ / r₂³ = 1 / 27

Taking cube root on both sides,

⇒ r₁ / r₂ = 1 / 3

⇒ 3r₁ =  r₂

⇒ r₁ = [tex]\frac{1}{3}[/tex] r₂

Hence the radius of the sphere A is 1/3 times greater than the radius of the sphere B.

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The line AC in the figure is the diameter of the circle also it is a chord.

The chord of a circle is a straight path that connects two locations on the circle's circumference. The chord is one of the line segments whose ends are on the perimeter of a circle that can be drawn.

As per the information obtained from the figure,

The line AC in the given diagram is the diameter of the circle, but it is also a chord of the circle because another definition of diameter is as a chord that runs across the center of the circle.

Note the point that every diameter can be said as a chord, but every chord cannot be the diameter of the circle.

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Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

According to the question given,

Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.

The formula of a confidence interval that we will be using for the solution will be,

p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]

In the above expression,

p = observed population.

n = sample size

[tex]z_{a}[/tex] = critical value of confidence interval

Now the given observations in question = 115

That result in success = 46

The resultant sample proportion = [tex]\frac{46}{115}[/tex]

⇒ 0.40 and it is for both success and failure

Here we can see that the answer for both parts will be identical.

The critical value of z at 90% confidence = 1.64

a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.402

b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.598

Confidence interval = 0.402 to 0.598

Therefore,

Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

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The sum of two forces, one having a magnitude of 9 N acting due east and other having a magnitude of 4 N acting due north is 9.85 N.

One of the forces is of magnitude 9 N acting due east

The second force is of magnitude 4 N acting due north

Therefore, the sum of the two forces (say F1 and F2) will be the resultant of the two forces,

that is: sqrt ( (F1) ^ 2 + (F2) ^ 2)

= sqrt ( (9) ^ 2 + (4) ^ 2) = sqrt (97) = 9.8488 N ≈ 9.85 N

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The 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5

An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.

Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >,,, and. has the connotation "7 is greater than" (or "is less than 7," when read left to right).

Given the incomplete expression

1 1/4 × 2 1/5 _ 5/6 × 2 1/5

We are to fill it with the necessary inequality sign

For the expression:

1 1/4 × 2 1/5 = 5/4 * 11/5

1 1/4 × 2 1/5 = 55/20

1 1/4 × 2 1/5 = 2 3/4

For the expression 5/6 × 2 1/5

5/6 × 2 1/5 = 5/6 * 11/5

5/6 × 2 1/5 = 55/30

5/6 × 2 1/5 = 1 25/30

Since 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5

The complete question is : Select the correct symbol to compare the expressions below.

1 1/4 × 2 1/5 _ 5/6 × 2 1/5

Symbols: <, >, =

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Answer: You must give more points for questions that are this long

sincerely,

A Friend

Step-by-step explanation: