The second term of an A.P is 2 and the sixth term is - 14. What is he first term and the 9th term?​

Step-by-step explanation:

the general equation of a parabola is

y = a(x – h)² + k.

(h, k) is the vertex of the parabola.

comparing it to

y = 3(x + 4)² - 2

we see that (h, k) = (-4, -2).

the student made a sign mistake. it is "- h" in the squared factor. so, "+4" indicates "-4" as "h".

but the student simply used "+4".

Answer: option B

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.p-by-step explanation:

The equivalence classes are disjoint, and their union covers all of A. Also, each element in A belongs to exactly one equivalence class.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

a) To show that R is an equivalence relation on A, we need to verify three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any x in A, we have f(x) = f(x) by definition of a function. Therefore, (x,x) is in R for any x in A, which means R is reflexive.

Symmetry: For any (x,y) in R, we have f(x) = f(y). This implies that f(y) = f(x), and hence (y,x) is in R. Therefore, R is symmetric.

Transitivity: For any (x,y) and (y,z) in R, we have f(x) = f(y) and f(y) = f(z). This implies that f(x) = f(z), and hence (x,z) is in R.

Therefore, R is transitive.

b) The equivalence classes of R are the sets of elements in A that have the same function value under f.

In other words, the equivalence class of an element x in A is the set of all elements y in A such that f(x) = f(y). We can write this as:

[x] = {y in A | f(x) = f(y)}

For example, if A = {1,2,3,4,5} and f(x) = x², then the equivalence classes of R are:

[1] = {1, -1}

[2] = {2, -2}

[3] = {3, -3}

[4] = {4}

[5] = {5, -5}

Hence, the equivalence classes are disjoint (i.e., they have no common elements), and their union covers all of A. Also, each element in A belongs to exactly one equivalence class.

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The given characteristic equation has two poles in the right half plane and three poles in the left half plane or on the imaginary axis.

To analyze the stability of the given characteristic equation using the Routh-Hurwitz criterion, we need to arrange the equation in the form:

s^5 + 2s^4 + 24s^3 + 48s^2 - 25s - 50 = 0

The Routh table will have five rows since the equation is of fifth order. The first two rows of the Routh table are formed by the coefficients of the even and odd powers of 's' respectively:

Row 1: 1   24   -25

Row 2: 2   48   -50

Now, we can proceed to fill in the remaining rows of the Routh table. The elements in the subsequent rows are calculated using the formulas:

Row 3: (2*(-25) - 24*48) / 2 = -1232

Row 4: (48*(-1232) - (-25)*2) / 48 = 60325

Row 5: (-1232*60325 - 2*48) / (-1232) = 2

The number of sign changes in the first column of the Routh table is equal to the number of roots in the right half plane (RHP). In this case, there are two sign changes. Thus, there are two poles in the RHP. The remaining three poles are in the left half plane (LHP) or on the imaginary axis (jo poles).

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Answer:

y = 30°         { adjacent angles }

z = 90 - 30° = 60°     { right angle triangle - 90° }

x = 180° - 60° - 60° = 60°  { isosceles, triangle has two sides 60° }

Answer:

140°

Step-by-step explanation:

a regular polygon is equiangular, equal angles.

a nonagon is a 9 sided polygon

the sum of the interior angles of a polygon is

sum = 180° (n - 2 ) ← n is the number of sides

here n = 9 , then

sum = 180° (9 - 2) = 180° × 7 = 1260° , then

each angle = 1260° ÷ 9 = 140°

a. Check the images attached below for LTI system.

b. The block diagram of the LTI system is attached below.

A type of systems known as linear time-invariant systems (LTI systems) is used in signals and systems that are both time-invariant and linear. Systems that provide the same results for a linear combination of inputs and individual reactions to those inputs are said to be linear systems.

(a) The block diagram of the LTI system in direct form is as follows:

Image attached below.

(b) The block diagram of the LTI system in transposed direct form is as follows:

Image attached below.

Note that in the transposed direct form, the delay element (z⁻¹) is placed after the summing junction, and the feedback path is connected directly to the input. This is equivalent to the direct form, but may be more convenient for certain implementations.

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Answer : The term used for statistical techniques that use sample data to draw conclusions about the population from which the sample was obtained is called inferential statistics

Explanation : The term used for statistical techniques that use sample data to draw conclusions about the population from which the sample was obtained is called inferential statistics.

Inferential statistics are used to make generalizations or predictions about a population based on the analysis of a sample.

In conclusion, inferential statistics is a powerful tool that allows us to draw meaningful conclusions about populations based on sample data. It is important to use appropriate statistical methods to ensure that the inferences we draw are valid.

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Answer:

b) 24 rows

Step-by-step explanation:

12 inches = 1 foot

Since we are doing 30 feet, multiply 12 by 30

12 · 30 = 360 inches

Then, divide the total length (360 inches) by the spacing size (15 inches)

360 ÷ 15 = 24 rows total

The sensitivity of the closed-loop system with respect to the parameter k is given by 2/(3+4k)². To find the sensitivity of the closed-loop system T = (1+2k) / (3+4k) with respect to the parameter K, we first need to calculate the derivative of T with respect to K.

dT/dK = (d(1+2k)/dK * (3+4k) - (1+2k) * d(3+4k)/dK) / (3+4k)²
Now, find the derivatives:
d(1+2k)/dK = 2
d(3+4k)/dK = 4
Substitute these values back into the expression for dT/dK:
dT/dK = (2 * (3+4k) - (1+2k) * 4) / (3+4k)²
Simplify the expression:
dT/dK = (6+8k - 4-8k) / (3+4k)²
dT/dK = 2 / (3+4k)²
So, the sensitivity of the closed-loop system T with respect to the parameter K is given by: Sensitivity = dT/dK = 2 / (3+4k)².

The sensitivity of the closed-loop system with respect to the parameter k can be calculated using the formula:
S = (dT/dk) * (k/T)
where T is the transfer function of the closed-loop system.
Substituting T = (1+2k)/(3+4k), we get:
S = [(d/dk)((1+2k)/(3+4k))] * (k/((1+2k)/(3+4k)))
Simplifying the above expression, we get:
S = 2/(3+4k)²
Therefore, the sensitivity of the closed-loop system with respect to the parameter k is given by 2/(3+4k)².

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Answer:

The sensitivity of the closed-loop system with respect to the parameter k is given by 2/(3+4k)². To find the sensitivity of the closed-loop system T = (1+2k) / (3+4k) with respect to the parameter K, we first need to calculate the derivative of T with respect to K.

dT/dK = (d(1+2k)/dK * (3+4k) - (1+2k) * d(3+4k)/dK) / (3+4k)²

Now, find the derivatives:

d(1+2k)/dK = 2

d(3+4k)/dK = 4

Substitute these values back into the expression for dT/dK:

dT/dK = (2 * (3+4k) - (1+2k) * 4) / (3+4k)²

Simplify the expression:

dT/dK = (6+8k - 4-8k) / (3+4k)²

dT/dK = 2 / (3+4k)²

So, the sensitivity of the closed-loop system T with respect to the parameter K is given by: Sensitivity = dT/dK = 2 / (3+4k)².

The sensitivity of the closed-loop system with respect to the parameter k can be calculated using the formula:

S = (dT/dk) * (k/T)

where T is the transfer function of the closed-loop system.

Substituting T = (1+2k)/(3+4k), we get:

S = [(d/dk)((1+2k)/(3+4k))] * (k/((1+2k)/(3+4k)))

Simplifying the above expression, we get:

S = 2/(3+4k)²

Therefore, the sensitivity of the closed-loop system with respect to the parameter k is given by 2/(3+4k)².

Step-by-step explanation:

Answer:

Diagram 5: Not adjacent angles

Diagram 6: Not adjacent angles

Diagram 7: Are adjacent angles

Diagram 8: Are adjacent angles

Step-by-step explanation:

In order for angles to be adjacent, they need to have all of three things:

1. Have a common vertex

2. Have a common side

3. Must not overlap

Diagram 5 does not have a common side between angles 1 and 2, so it is not adjacent.

Diagram 6 does not even have angles 1 and 2 connected in any way so it is not adjacent.

Diagrams 7 and 8 have all three conditions, so those diagrams are adjacent.

(a) The generating functions together r times:\(\(f(x) = (1 + x + x^2 + x^3 + x^4 + x^5)^5\)\)

(b) \(\(f(x) = (x^3 + x^4 + x^5 + x^6)^4\)\)

(c) \(\(f(x) = (\frac{x}{1-x})^{7r}\)\)

(d) \(\(f(x) = (1 + x + x^2 + x^3 + x^4 + x^5)^3\)\)

(a) To build a generating function for selecting r items from five different boxes with at most five objects in each box, we can consider each box as a separate generating function and multiply them together.

The generating function for selecting objects from the first box is:

\(\(1 + x + x^2 + x^3 + x^4 + x^5\)\)

Similarly, for the second, third, fourth, and fifth boxes, the generating functions are the same:

\(\(1 + x + x^2 + x^3 + x^4 + x^5\)\)

To select r items, we need to choose a certain number of items from each box.

Therefore, we multiply the generating functions together r times:

\(\(f(x) = (1 + x + x^2 + x^3 + x^4 + x^5)^5\)\)

(b) To build a generating function for selecting r items from four different boxes with between three and six objects in each box, we need to consider each box individually.

The generating function for selecting objects from the first box with three to six objects is:

\(\(x^3 + x^4 + x^5 + x^6\)\)

Similarly, for the second, third, and fourth boxes, the generating functions are the same:

\(\(x^3 + x^4 + x^5 + x^6\)\)

To select r items, we multiply the generating functions together r times:

\(\(f(x) = (x^3 + x^4 + x^5 + x^6)^4\)\)

(c) To build a generating function for selecting r items from seven different boxes with at least one object in each box, we need to subtract the case where no items are selected from the total possibilities.

The generating function for selecting objects from each box with at least one object is:

\(\(x + x^2 + x^3 + \ldots = \frac{x}{1-x}\)\)

Since we have seven boxes, the generating function for selecting from all seven boxes with at least one object is:

\(\((\frac{x}{1-x})^7\)\)

To select r items, we multiply the generating function by itself r times:

\(\(f(x) = (\frac{x}{1-x})^{7r}\)\)

(d) To build a generating function for selecting r items from three different boxes with at most five objects in the first box, we can consider each box separately.

The generating function for selecting objects from the first box with at most five objects is:

\(\(1 + x + x^2 + x^3 + x^4 + x^5\)\)

For the second and third boxes, the generating functions are the same:

\(\(1 + x + x^2 + x^3 + x^4 + x^5\)\)

To select r items, we multiply the generating functions together r times:

\(\(f(x) = (1 + x + x^2 + x^3 + x^4 + x^5)^3\)\)

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Answer:

Step-by-step explanation:

Stephan can run

3 miles in 15.75 minutes

1 miles in 15.75/3 minutes

1 miles in 5.25 minutes

Kelsha can run

5 miles in 226 minutes

1 miles in 226/5 minutes

1 miles in 45.2 minutes

Stephan can run faster, since 5.25 < 45.2

Stephan can run faster, than Kelsha since 5.25 < 45.2.

Speed is defined as the ratio of the distance traveled by the body to the time taken by the body to cover the distance. The unit of speed is measured in a meter per second, Miles per second, etc. Speed is a scalar quantity and does not require direction.

The speed for Stephan will be calculated as below:-

3 miles in 15.75 minutes

1 mile in 15.75/3 minutes

1 mile in 5.25 minutes

The speed for Kelsha will be calculated as below:-

5 miles in 226 minutes

1 mile in 226/5 minutes

1 mile in 45.2 minutes

Therefore, Stephan can run faster, than Kelsha since 5.25 < 45.2.

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-4y-1

Step-by-step explanation:

If you subtract \({ \green{ \tt{8y + 7}}} \)from \({ \red{ \tt{4y - 8}}}\) then the resultant answer will be as follows

\( \: \: \: \: \: { \red{ \tt{4y - 8}}} \\ - \ \: { \green{ \tt{8y + 7}}} \\ = -{ \blue{ \tt{ 4y - 1}}}\)

Answer:

No

Step-by-step explanation:

It does not because 5 times the sum of p and 11 is written like this :-

So, it's not the same.

To get 5p + 11, the correct statement should be :-

Answer:

B. 5a + 10

Step-by-step explanation:

Given:

5(a+2)

Open parenthesis

5(a+2)

= 5a + 10

A. 5a + 2

Wrong option

B. 5a + 10

Correct option

C. a + 10

Wrong option

D. 5 + (a + 2)

= 5 + a +2

= a + 7

Wrong option

The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test

Given: Independent group and ordinal data. To find which test to use.

What's the Kruskal Wallis test?

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.

How to calculate the Kruskal Wallis test?

The computation of the Kruskal- Wallis statistic requires

Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.

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We can use the Kruskal Wallis test when we have an independent group design and ordinal data.

We are given an independent group design and ordinate data.

We need to tell which test to use on them.

The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.

The null hypothesis for the Kruskal- Wallis test tells us that:

There are no methodical or harmonious differences among the treatments being compared.

Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.

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All the value of of that satisfy the condition cos θ = - 1/2 ,

where 0 ≤ θ <360° are,

⇒ 120°, 240°

Given that;

Expression is,

cos θ = - 1/2

where 0 ≤ θ <360°

Since, cos θ = - 1/2

Hence, It belong in second and third quadrant.

So, cos θ = - 1/2

cos θ = 120°

cos θ = 240°

Thus, All the value of of that satisfy the condition cos θ = - 1/2 ,

where 0 ≤ θ <360° are,

⇒ 120°, 240°

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The correct option when Triangle ABC is transformed to triangle A′ B′ C is A.The measure of angle BCA = The measure of angle C prime A prime B prime.

Triangle ABC is changed into triangle A′B′C′ and on the x- and y-axes, a coordinate grid ranging from -4 to -4 to 4 is displayed. A is at ordered pair negative 1, 3, B is at ordered pair 0, 1, and C is at ordered pair negative 3, 0 in the triangle ABC.

A triangle Primes A, B, and C have A prime is at ordered pair minus 1, minus 3, B prime is at ordered pair minus 0, and C prime is at ordered pair minus 3, 0.

A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.

Therefore,

<BAC = <B'A'C'

<ABC = <A'B'C'

<ACB = <A'C'B'

In this case, the correct option is A.

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Answer:

The coordinates of the vertices of the original triangle are (-4, 2), (2, 4), and

(-2, -2).

To obtain the new triangle, subtract 2 from each x-coordinate, and subtract 4 from each y-coordinate. So the coordinates of the vertices of the new triangle are (-6, -2), (0, 0) and (-4, -6). Draw the new triangle.

The 95% confidence interval for the difference between the proportion of the population who would survive at least 15 years can be used to estimate the range within which the true difference lies.

It provides a measure of uncertainty around the point estimate. The confidence interval can be interpreted as follows: we are 95% confident that the true difference in proportions of the population who would survive at least 15 years falls within the calculated interval. To construct the confidence interval, we first need to obtain sample data from the population. Let's assume we have collected data from two independent samples. From Sample 1, we find that out of n1 individuals, x1 survive at least 15 years. Similarly, from Sample 2, we have n2 individuals, with x2 surviving at least 15 years. To calculate the confidence interval, we use the formula: CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)) Where p1 = x1 / n1 and p2 = x2 / n2 are the sample proportions, and Z is the critical value corresponding to the desired confidence level (in this case, 95%). The critical value is determined based on the standard normal distribution. Once we have the confidence interval, let's say [lower limit, upper limit], we can interpret it as follows: We are 95% confident that the true difference in proportions between the two populations who would survive at least 15 years lies between the lower limit and the upper limit. In other words, there is a high likelihood that the actual difference falls within this range. The confidence interval allows us to make inferences about the population based on our sample data. It provides a range of plausible values for the difference in proportions, taking into account the variability of the sample. The wider the confidence interval, the greater the uncertainty in our estimate. Conversely, a narrower interval indicates a more precise estimation.

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Ann must take out at least 36 fruits from the basket.

Here, we are given that a large basket of fruit contains apples, oranges, and peaches.

Ann has to take out fruits from the basket such that she chooses at least 10 apples, or at least 12 oranges, or at least 14 peaches.

We need to find the least number of fruits that she must take out.

Now, let us assume that she take out 10 fruits. In order to satisfy the condition given, all the 10 fruits must be apples but this may not be always the case.

Thus, the number of fruits is definitely greater than 10.

Similarly, we can notice that the number of fruits is also greater than 12 and 14.

Now, let us say Ann takes out 12 + 14 + 10 = 36 fruits.

In this case, if either all are oranges, apples or peaches, the condition is satisfied. And similarly, you will notice that any combination of fruits will always satisfy the given condition.

Hence, Ann must take out at least 36 fruits from the basket.

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Answer:

34

Step-by-step explanation:

So you have to think of the worst case scenario, let's say Ann gets really unlucky and picks out 9 apple, 11 oranges, and 13 peaches, which equals 33 fruit in total, the next fruit she picks out will satisfy the condition, so therefore the answer is 34

No , it is not possible to form a triangle with side lengths 3.5, 3.5, and 9 , because of the rule that sum of any two sides must be greater than other side. So, Option D is correct.

A triangle is a two-dimensional shape formed by three line segments connecting three points. In order to form a triangle, a necessary and sufficient condition is that the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.

If the sum of the lengths of any two sides is less than or equal to the length of the third side, then the three line segments will not be able to form a closed shape, and therefore cannot form a triangle.

In the case of the triangle with side lengths 3.5, 3.5, and 9, the sum of the lengths of the first two sides is 7, which is less than the length of the third side, 9. Hence, these three side lengths do not satisfy the triangle inequality theorem, and therefore cannot form a triangle.

In general, to determine the type of triangle that can be formed with three given side lengths, it is necessary to compare the lengths of the sides and check if any two sides are equal in length (isosceles), or if all three sides are equal in length (equilateral). If none of the sides are equal, then the triangle is called scalene.

In this case, since it is not possible to form a triangle with the given side lengths, it is not possible to determine the type of triangle that would be formed.

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1. Another word for mean is average.

2. The measure of central tendency that is affected by outliers is the mean.

3. You could calculate an expected value when your data points have various probabilities of occurring.

In statistics, the mean is a measure of central tendency, commonly referred to as the average. It is calculated by adding up all the values in a dataset and then dividing the sum by the number of values.

Outliers are extreme values that are significantly different from the other values in the dataset, and when they are present, they can pull the mean in their direction.

The median is less affected by outliers, as it only depends on the order of the values in the dataset, rather than their magnitude. The mode is the least affected by outliers, as it only depends on the most frequently occurring value in the dataset, regardless of any extreme values.

The expected value, also known as the expectation or the mean of a probability distribution, is the long-run average value of a random variable, weighted by its probability of occurrence. In other words, it represents the average outcome that we can expect to see over a large number of repetitions of a random experiment.

The problem seems incomplete, it must have been...

"1. Another word for mean is _____.

margin

centric statistic

average

product

2. Which measure of central tendency is affected by outliers?

mean

median

both mean and median

mean, median, and mode

3. When would you calculate an expected value?

When your data points occur on different dates

When your data points have various probabilities of occurring

When you only have one data point

When you need to know the exact outcome of a event"

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Using proportions, it is found that the swing set at Marquette Park is 680m long.

A proportion is a fraction of total amount, and the measures are related using a rule of three.

In this problem, each two centimeters of the model corresponds to one meter of the park, and we want to find how many meters will correspond to 1360 cm.

The rule of three is:

2 cm - 1 m

1360 cm - x m

Applying cross multiplication:

\(2x = 1360\)

\(x = \frac{1360}{2}\)

\(x = 680\)

The swing set at Marquette Park is 680m long.

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The value is used for the term p^2 in the equation p^2+ 2pq + q^2 = 1 is 0.16.

According to the statement

we have given that the allele frequency of the dominant allele is 0.4, and we have to find that the value of p^2 in the equation p^2+ 2pq + q^2 = 1.

So, For this purpose, we know that the

The allele frequency represents the incidence of a gene variant in a population. Alleles are variant forms of a gene that are located at the same position, or genetic locus, on a chromosome.

And here

allele frequency is the 0.4 and represent the value of P.

So, The value of p is 0.4 and the

Then p^2 = (0.4)^2

so, the value becomes

p^2 = (0.4)^2

p^2 = 0.16.

So, The value is used for the term p^2 in the equation p^2+ 2pq + q^2 = 1 is 0.16.

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a) The flowchart for the congruency of triangles is given below.

b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.

What is congruency?

The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.

In the given diagram, it can be seen that -

Line segment DQ = Line segment XZ.

Similarly, Line segment PQ = Line segment XY.

Since, the two sides of the triangle are equal, hence the third side must also be equal.

Line segment PD = Line segment ZY.

Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.

Therefore, the triangles PDQ and ZXY are equal and congruent.

The flowchart for the same is given below.

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Numbering starts from the leftmost figure.

\(.\)

1) Opposite sides are equal $\implies$ quadrilateral is a parallelogram. (Can be proven using basic congruency theorems)

2)

Opposite sides are parallel $\implies$ trapezium.

But the other pair of sides are not parallel, hence in the general case this is not a parallelogram but is a trapezium with two equal sides.

3) One pair of opposite sides are congruent and parallel $\implies$ this is a parallelogram.

Proof: Join two vertices and you get that the two triangles formed are congruent.

4)

Diagonals are bisected at their intersections $\implies$ Quadrilateral is a parallelogram.

Show that the two opposite little triangles are congruent by using SAS test (or whatever you call it)

So the figure which is not a parallelogram is 2.

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg