true or false: a linear programming problem can have an optimal solution that is not a corner point. select one: true false

"It can vary - it really depends on the distribution of the variable."

The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.

Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.

Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.

The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.

While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.

In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.

A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.

Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.

There is no established guideline, however 8–10 intervals are typically utilized.

A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.

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The coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

The circumference of the coin can be calculated as follows to determine the number of turns it makes:

C = πd

where C is the circumference, d is the diameter, and π is the mathematical constant pi (approximately equal to 3.14159).

So, for the given $2 coin with a diameter of 25.75 mm, the circumference is:

C = πd = 3.14159 x 25.75 mm ≈ 80.926 mm

Divide the distance traveled by the coin's circumference to determine the number of turns it makes when rolled on its edge for 1.34 meter:

Number of turns = distance traveled / circumference of the coin

Number of turns = 1.34 m / 0.080926 m

Number of turns ≈ 16.53

Therefore, the coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

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Answer:

To find the values of f(g(x)) for the given values of x, we need to first evaluate g(x) for each value of x, and then plug the result into f(x).

Using the given functions:

g(x) = 2x - 5

f(x) = √(x+1)

Therefore, we have:

f(g(x)) = √(g(x) + 1) = √(2x - 5 + 1) = √(2x - 4) = 2√(x - 2)

So, we can complete the table as follows:

x f(g(x))

4 2

10 4

20 6

34 8

52 10

Therefore, the completed table is:

x f(g(x))

4 2

10 4

20 6

34 8

52 10

Answer:

The amplitude is 1/2, the period is 2π/4 = π/2, and the phase shift is π/2.

Step-by-step explanation:

The given function is:

f(t) = -1/2(4t - 2π)

We can rewrite this function in the form:

f(t) = A cos(B(t - C)) + D

where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Comparing this with the given function, we can see that:

A = 1/2

B = 4

C = π/2

D = 0

Therefore, the amplitude is 1/2, the period is 2π/4 = π/2, and the phase shift is π/2.

Note that the negative sign in front of the function does not affect the amplitude, period, or phase shift. It simply reflects the function across the x-axis.

Step-by-step explanation:

rotate the triangle in your mind (or as actual picture on your phone or computer), so that the right angle is the bottom right or bottom left, and C being the opposite bottom angle.

then we see

28 = cos(C) × 35

21 = sin(C) × 35

and so,

sin(C) = 21/35 = 3/5

cos(C) = 28/35 = 4/5

tan(C) = sin(C)/cos(C) = 3/5 / 4/5 = 3/4

Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.

The total cost of renting a small car with insurance is:

$465 = $25x + $21x

Simplifying and solving for x, we get:

$465 = $46x

x = 10.11

Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.

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For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.

We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%

The percentage of students win a jump rope = 16%

The percentage of students win a t-shirt

= 6%

The winning amount for stuffed toy game = $ 3.60

The winning amount for jump rope game = $1.20

The winning amount for t-shirt game

= $7.90

The remaining students do not win a prize. Now, total number of students play the game at the booth = 150

So, number of students who win stuffed toy = 22% of 150 = 33

Number of students who win jump rope = 16% of 150 = 24

Number of students who win stuffed toy

= 6% of 150 = 9

For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6

= 218.7

Hence required value is $218.70.

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Answer:

$481

Step-by-step explanation:

37×$17=$481

he made $481

Answer:√2/2

Step-by-step explanation:

Let's label the sides of the right triangle as follows:

The side adjacent to the angle θ (cosine is adjacent/hypotenuse): 6

The hypotenuse (the longest side): 6√2

The side opposite to the angle θ (sine is opposite/hypotenuse): 6√3

Using the Pythagorean theorem, we can find the length of the missing side:

a² + b² = c²

6² + (6√3)² = (6√2)²

36 + 108 = 72

144 = 72

√144 = √72

12 = 6√2

Now that we know the length of all three sides, we can use the cosine ratio to find the value of cos(θ):

cos(θ) = adjacent/hypotenuse = 6/6√2 = √2/2

Therefore, the value of cos(θ) in the right triangle with sides of 6, 6√2, and 6√3 is √2/2.

Step-by-step explanation:

18-2x<3(2x-1)-3

21-2x<6x-3

24<8x

3<x

Interval notation

(3, ∞)

The estimated regression equation for the given data is y = -30.7 + 3.409x

To develop an estimated regression equation for the given data, we need to use the method of least squares.

The formula for the slope of the regression line is given by:

b = ∑(xi - x)(yi - y) / ∑(xi - x)²

where xi and yi are the individual values of the two variables, x and y are their respective means.

The formula for the intercept of the regression line is given by:

a = y - b × x

where a is the intercept and b is the slope.

Using the given data, we can calculate the values of x, y, b, and a as follows

x = (6 + 11 + 15 + 18 + 20) / 5 = 14

y = (7 + 9 + 12 + 21 + 30) / 5 = 15.8

∑(xi - x)(yi - y) = (6 - 14)(7 - 15.8) + (11 - 14)(9 - 15.8) + (15 - 14)(12 - 15.8) + (18 - 14)(21 - 15.8) + (20 - 14)(30 - 15.8) = 306.8

∑(xi - x)² = (6 - 14)² + (11 - 14)² + (15 - 14)² + (18 - 14)² + (20 - 14)² = 90

b = ∑(xi - x)(yi - y) / ∑(xi - x)² = 306.8 / 90 = 3.409

a = y - b × x = 15.8 - 3.409 × 14 = -30.7

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The given question is incomplete, the complete question is:

Given are data for two variables, x and y. Develop an estimated regression equation for these data.

Given statement: The rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.

Given statement is True.

The reason for this rule of thumb is that tasks often take longer than initially estimated due to unforeseen challenges, dependencies, and other factors that can cause delays.

By estimating the time of completion as 1.5 times the original estimate, you are accounting for these potential delays and allowing for a more realistic timeline.

This rule of thumb is not a hard and fast rule, and there will be cases where tasks take less or more time than 1.5 times the original estimate. However, it can be a helpful guideline for project planning and resource allocation, as it helps to ensure that sufficient time and resources are allocated to complete tasks within a realistic timeframe.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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Answer:

5x

6xy

2x3y

hope it's helpful

a) Any value outside of Q1 - 1.5(IQR) and Q3 + 1.5(IQR) can be considered a potential outlier.

b) This will give us a visual representation of the distribution of income among the full-time students.

c) It is important to analyze outliers carefully to ensure that they are not artificially skewing the results of our analysis.

(a) To check for outliers in the data set, we can use the box-and-whisker plot or the z-score method. However, since we do not have the exact data, we cannot use these methods. One way to identify potential outliers is to calculate the quartiles (Q1, Q2, and Q3) and the interquartile range (IQR).

(b) To draw a histogram of the data, we can use the frequency distribution table given in the question. The x-axis should represent the income ranges (e.g. $0-$100, $100-$200, etc.) and the y-axis should represent the frequency (i.e. the number of students who earned income within each range).

(c) If there are any outliers in the data set, we need to investigate them further to determine the reason for their unusual values. Possible reasons for outliers could be data entry errors, extreme values due to high- or low-income jobs, or unique situations such as unexpected windfalls or emergencies.

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The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.

The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The

null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative

relationship does not exist, hence the term "null".

In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative

hypothesis represents the effect or relationship the researcher is interested in demonstrating.

The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in

favor of the alternative hypothesis.

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The bigger engine is larger than the smaller one by 235.4724 cubic centimeters.

We know that 1 inch=2.54 centimeters

Then 1 cubic inches-(2.54)^3 cubic centimeters

We have that:

⇒ 1 cubic inches=(2.54)3 = 16.3870 cubic centimeters

⇒350 cubic inches= 350 x 16.3870 = 5735.4724 cubic centimeters

Since, the other displaces 5,500 cubic centimeters  and 5735.4724< 5500. The difference between them is:

= 5735.4724 - 5500

= 235.4724

Hence, the bigger engine larger than the smaller one by 235.4724 cubic centimeters.

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[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank A} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1810)(0.025)(5) \implies I = 226.25 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank B} }{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]A = 1810\left(1+\frac{0.025}{12}\right)^{12\cdot 5} \implies A \approx 2050.73~\hfill \underset{ interest }{\stackrel{2050.73~~ - ~~1810 }{\approx 240.73}} \\\\[-0.35em] ~\dotfill\\\\ 240.73~~ - ~~226.25 ~~ \approx ~~ \text{\LARGE 14.48}[/tex]

The process time of the system is 32 min/unit.

Answer:

f(x) is the blue graph, g(x) is the red graph.

x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2

16 - x^2 = 0 when x = -4, 4

So the area between these two graphs is (using the TI-83 graphing calculator):

fnInt (16 - x^2, x, -4, 4) = 85 1/3

The distribution in which variable x has binomial distribution are as follow,

Option A) When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

Option D) When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

This variable X follows a binomial distribution .

Because there are two independent trials two patients.

With a constant probability of success 30%.

And the outcome of one trial doesn't affect the outcome of the other.

When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

This variable X does not follow a binomial distribution.

Because the probability of success is not constant it's the complement of 30%, which is 70%.

Also, the outcome of one trial affects the outcome of the other trials.

As there are only six patients .

Number of patients for whom medicine does not work depends on number of patients for whom it worked.

When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

This variable X follows a binomial distribution.

Because there are six independent trials six patients with a constant probability of success (30%) .

The outcome of one trial doesn't affect the outcome of the other.

When the medicine is tried with two patients, X is the number of doses each patient needs to take.

This variable X does not follow a binomial distribution.

Because it's not a count of successes out of a fixed number of independent trials.

But rather a continuous variable that can take any non-negative value.

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The above question is incomplete, the complete question is:

For a certain type of hay fever, Medicine H has a 30% probability of working.

In which distributions does the variable X have a binomial distribution?

Select EACH correct answer.

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

D. When the medicine is tried with two patients, X is the number of doses each patient needs to take.

In a standard additions method workup the information from the linear regression that is most closely related to the unknown concentration is this:  the intercept of the linear regression line.

In the standard additions method workup, the information that is most closely related to the unknown concentration is the intercept of the linear regression line.

The reason why this is the case is that the intercept represents the y-value of the regression line where the line crosses the y-axis. This y-axis is the value of the dependent variable when the independent variable or concentration is zero. So, by solving for the intercept, we can determine the concentration of the unknown sample.

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Answer:

To determine which ratio is proportional to 80:60, we need to simplify the ratio by dividing both terms by their greatest common factor. In this case, the greatest common factor of 80 and 60 is 20, so:

80/20 = 4

60/20 = 3

Therefore, the simplified ratio is 4:3.

Now we can compare this ratio to the given options to see which one is proportional to 4:3:

16:15 is not proportional

16:12 is proportional (since 16/4 = 4 and 12/3 = 4)

18:15 is not proportional

18:12 is proportional (since 18/3 = 6 and 12/2 = 6)

Therefore, the ratio that is proportional to 80:60 is 16:12.

Point A = (5,4). If you rotated A 90 degrees about the point (2,-1), the coordinates of A' is (-1,2).

Rotation is the process of rotating an object or a point around a fixed point or axis. In mathematics, rotation refers to a transformation that preserves the size and shape of an object while changing its orientation. It is a basic geometric transformation that is used in various fields, including mathematics, physics, engineering, and computer graphics.

In a two-dimensional space, a rotation is typically described by an angle of rotation and a fixed point, which is known as the center of rotation. The angle of rotation represents the amount by which the object is rotated, while the center of rotation is the point around which the object is rotated. In a three-dimensional space, a rotation is described by an axis of rotation and an angle of rotation.

To rotate point A 90 degrees counterclockwise about the point (2,-1), we can use the following formula:

A' = (x', y') = (a + (x - a) cosθ - (y - b) sinθ, b + (x - a) sinθ + (y - b) cosθ)

where (a,b) is the center of rotation and θ is the angle of rotation (90 degrees in this case).

Substituting the given values, we get:

a = 2, b = -1, x = 5, y = 4, θ = 90 degrees

x' = 2 + (5 - 2) cos(90) - (4 + 1) sin(90) = 2 - 3 = -1

y' = -1 + (5 - 2) sin(90) + (4 + 1) cos(90) = -1 + 3 = 2

Therefore, the coordinates of A' are (-1, 2).

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Sampled 200 delinquent credit card accounts instead of 100, the margin of error would decrease.

Sampled 200 delinquent credit card accounts, the margin of error for the sample mean at a 95% confidence level would be $80.164.

Smaller than the margin of error we found earlier for a sample size of 100.

The margin of error for the sample means at a 95% confidence level, we need to use the formula:
[tex]Margin of error = z\times (standard deviation / square root of sample size)[/tex]
[tex]z\times[/tex] is the z-score for the 95% confidence level, which is 1.96.
So, plugging in the given values, we get:
[tex]Margin of error = 1.96 \times  (578 / \sqrt 100)[/tex]
[tex]Margin of error = 1.96 \times 57.8[/tex]
Margin of error = 113.008
Therefore, the margin of error for the sample mean at a 95% confidence level is $113.008.
Repeated samples of 100 delinquent credit card accounts and computed the sample mean each time, we would expect the true population mean to be within $113.008 of our sample mean about 95% of the time.
The margin of error is inversely proportional to the square root of the sample size. So, as the sample size increases, the margin of error decreases.
To see this, let's plug in the new sample size into the margin of error formula:
[tex]Margin of error = 1.96 \times (578 / \sqrt 200)[/tex]
[tex]Margin of error = 1.96 \times 40.9[/tex]
Margin of error = 80.164

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The radius of the water bottle which is in cylindrical shape is approximately 2.12 cm.

A cylinder is a three-dimensional shape that consists of two congruent, parallel circular bases that are connected by a curved lateral surface. The lateral surface of the cylinder is formed by a rectangle that is wrapped around the circular bases.

A cylinder can be thought of as a circular prism, where the bases are circles and the lateral surface is curved. The height of a cylinder is the perpendicular distance between the two bases, and the radius is the distance from the center of the base to the edge of the circular base.

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We can rearrange this formula to solve for the radius:

r = √(V/πh)

Substituting the given values, we have:

r = √(150/π(8.9))

r ≈ 2.12 cm (rounded to two decimal places)

Therefore, the radius of the water bottle is approximately 2.12 cm.

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Answer:  the answer is A. 14.

Step-by-step explanation: In each trial of the reenactment, Scott chooses one card from the stack and records its digit. Based on the given data, a digit of or 1 speaks to a objective scored, and a digit of 2 through 9 speaks to a missed endeavor.

Out of the 5 endeavors per amusement, on the off chance that Scott scores precisely 2 objectives, it implies he missed 3 endeavors. Subsequently, the likelihood of this occasion can be calculated as:

P(exactly 2 objectives) = (0.2)²(0.8)³ = 0.008192

This likelihood can be utilized to discover the anticipated number of diversions in which Scott scores precisely 2 objectives, by duplicating it by the overall number of diversions reenacted:

Anticipated number of recreations = P(exactly 2 objectives) × Add up to number of recreations = 0.008192 × 84 ≈ 0.68

Adjusting to the closest entire number, we get that Scott is anticipated to score precisely 2 objectives in 1 diversion out of the 84 recreated diversions.

Answer:

The correct answer is:

10√2

Explanation:

In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.

In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.

Let's denote the side length of each square as "s" inches.

According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

In this case, the hypotenuse is 20 inches, so we have:

20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)

400 = 2s^2

Dividing both sides by 2, we get:

200 = s^2

Taking the square root of both sides, we get:

s = √200

Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:

√200 = √(100 x 2) = 10√2

So, the side length of each quilt piece is 10√

The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.

This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).

[tex]h = \sqrt{p^2 + b^2}[/tex]

Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.

20 = √2p²  (since p and b are equal, b can be taken as p)

On squaring both sides,

400 = 2p²

p² = 400/2

p² = 200

p = √200

p = 10√2 = b

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The score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.

Let us consider the score that Tim needs to get on his fourth quiz be x.

Score he needs to get in order to have a mean quiz score of 90,

Set up an equation using the formula for the mean ,

(mean score) = (sum of scores) / (number of scores)

If Tim wants his mean quiz score to be 90, then we have,

⇒ 90 = (86 + 92 + 94 + x) / 4

Multiplying both sides by 4, we get,

⇒360 = 86 + 92 + 94 + x

Simplifying this equation, we get,

⇒ x = 360 - 272

⇒ x = 88

Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.

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For all given Quadrilaterals none has enough information provided in the problem to definitively say - if they are a parallelogram.Hence, option E is correct for all.

If a quadrilateral is a parallelogram, it satisfies the following properties:

It is important to note that in order to definitively conclude that a quadrilateral is a parallelogram, all four properties must be satisfied. If only one or some of the properties are met, it does not necessarily guarantee that the quadrilateral is a parallelogram.

Figure 1-: Adjacent angles are 105 and 75 degrees, which satify the condition of opposite angles being equal but except this no other information is provided, Hence, we don't have enough information to say figure 1 is a parallelogram.

Figure 2-: Diagonals bisect each other and make angle 65 degree with each other. Given that Diagonal 1 bisects Diagonal 2 and the opposite sides of the quadrilateral are equal, by using SAS criterion, the congruency of triangles formed by the diagonals can be derived to say that the opposite angles of the quadrilateral are also equal . However, we still need more information about parallelism of sides to definitively say given quadrilateral is a parallelogram.

Figure 3-: One pair of opposite side is equal in length ,while other pair of line is parallel to each other.This information is insufficient to determine if given quadrilateral is a parallelogram.

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