Assume that GHI = LMN . Which of the following congruence statements are correct ? Check all that apply

The evaluation of the equations in the questions are as follows;

10. The equation 18·y - 10 = 2 + 18·y has no solutions

11. x = 0

12. x = 20

13. The consecutive integers are -46 and -45

An equation is a statement which indicates the equivalence between two expressions.

10. 18·y - 10 = 2 + 18·y

18·y - 18·y - 10 + 10 = 2 + 18·y - 18·y + 10

0 = 12

The equation 18·y - 10 = 2 + 18·y is a contradiction with no solution.

11. 2·(6·x - 4) - 16x = 4·(3·x - 2)

2·(6·x - 4) - 16x = 12·x - 8 - 16·x = -8 - 4·x

4·(3·x - 2) = 12·x - 8

2·(6·x - 4) - 16x = -8 - 4·x = 4·(3·x - 2) = 12·x - 8 therefore

-8 - 4·x = 12·x - 8

16·x = 0

x = 0 ÷ 16 = 0

x = 0

12. (3/4)·x + 2 = (3/5)·x + 5

(3/4)·x + 2 - (3/5)·x  - 2 = (3/5)·x + 5 - (3/5)·x - 2

(3/4)·x - (3/5)·x = 5 - 2 = 3

(3/20)·x = 3

x = 3 × 20 ÷ 3 = 20

x = 20

13. The sum of the two integers = -91

Let a represent one of the integers, therefore, based on the details;

The other integer = a + 1

a + a + 1 = -91

2·a = -91 - 1 = -92

a = -92 ÷ 2 = -46

One of the integers, a = -46

The other integer, a + 1 = -46 + 1 = -45

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If Sam needs 2/5 pound turkey to make one sandwich, then to make 7 sandwiches, he will need:

(2/5) x 7 = (2 x 7)/5 = 14/5 = 2.8 pounds of turkey

Therefore, Sam needs 2.8 pounds of turkey to make 7 sandwiches.

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No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.

To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).

The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).

To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:

(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4

Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.

The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.

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Answer:

3915 cubic inches

Step-by-step explanation:

Let's individually find the volume of both, and then combine them. For the triangle, we know that the length of the triangular base is 7 inches, the height is 10 inches, and the length of the prism is 29 inches. Therefore, the area of the triangular prism is 7*10*29/2=1015 cubic inches. For the rectangular prism, you simply need to multiply all of the dimensions together, getting 10*10*29=2900 cubic inches. Adding these together, you get a total of 3915 cubic inches. Hope this helps!

The term which is used for describing the number of voters who casted their votes using the ballots is called as voter turnout.

The process of selecting a candidate for a suitable post who takes care of the policies which will be framed for the people is called as voting. In this process, the members/ citizens casts their vote in the favor of their suitable candidate. Many times voters are not valid and their votes are considered as null and void.

The voter turnout is either the percentage of registered voters, eligible voters, or all voting-age people ( this varies from place to place depending upon the minimum voting age required). The voter turnout is also referred to the number of people who go to it or take part in it. High voter turnout is generally considered a sign of a healthy democracy.

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Answer:

Radius

Step-by-step explanation:

I know the answer

Answer:

Radius

Step-by-step explanation:

The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30. (False)

To determine if a point is feasible for a constraint, we need to substitute the values of the point into the constraint equation and check if the resulting inequality holds true.

In this case, the constraint is 2x1 + 6x2 ≤ 30. Substituting x1 = 3 and x2 = 2 into the equation, we get 2(3) + 6(2) = 6 + 12 = 18. Since 18 is not less than or equal to 30, the inequality is not satisfied.

Therefore, the point (3, 2) is not feasible for the given constraint. Feasible points satisfy the constraint, while infeasible points do not. In this case, any point that lies below the line represented by the constraint equation would be feasible, while points above the line would be infeasible.

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Yes, the square of an odd number is always an odd number.

Here we have the statement:

"The square of an odd number is always odd"

First, a general odd number can be written as (2n + 1) where n is any integer number.

The square of that is written as:

(2n + 1)*(2n + 1)

Expanding that we will get:

(2n)*(2n) + (2n)*1 + 1*(2n) + 1*1

4n^2 + 4n + 1

Now can write this as:

2*(2n^2 + 2n) + 1

The term:

2n^2 + 2n

is an integer, we can write 2n^2 + 2n = k

Then we will get:

2k + 1

This is an odd number again.

So yea, the square of an odd number is always an odd number.

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However, I can explain the process of simplifying the given functions using the Karnaugh Map (K-Map) method and provide you with the minimized SOP and POS forms.

1. For Function 1, we have the following grouped and labeled K-Maps:
  - K-Map for variables a, b, and e (4x4 grid)
  - K-Map for variable d (2x2 grid)
2. To obtain the minimized SOP forms of Function 1, we need to analyze the grouped cells in the K-Maps and write the corresponding Boolean expressions. By applying the K-Map method, we can obtain six possible minimized SOP forms for Function 1.

3. For Function 2, we have the following grouped and labeled K-Maps:
  - K-Map for variables a, b, c, and e (4x4 grid)
  - K-Map for variable d (2x2 grid)
4. To obtain the minimized POS forms of Function 2, we need to analyze the grouped cells in the K-Maps and write the corresponding Boolean expressions. By applying the K-Map method, we can obtain three possible minimized POS forms for Function 2.

Please note that the specific expressions and grouped cells for each function can be obtained by visually examining the K-Maps. It would be best to refer to a resource that allows you to draw and label the K-Maps to get the accurate results for Function 1 and Function 2.

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The length of the base of the parallelogram is 10.25 inches.

given that,

the area of parallelogram=102 1/2 square inches

height=10 inches

The following formula determines the area of a parallelogram:

Base + height = area.

The parallelogram's area and height are provided. By entering these values in the above formula we obtain:

102 1/2 = base × 10

We can divide both sides by 10 to find the base:

102 1/2 ÷ 10 = base

By dividing 1 by 2, we may convert the mixed number 1/2 to a decimal:

102 1/2 ÷ 10 = 102.5 ÷ 10 = 10.25

therefore, the length of the base of the parallelogram is 10.25 inches long.

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The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

Answer:

27

Step-by-step explanation:

\(3^{3}\) is basically just multiplying the number 3, three times. So 3x3x3. 3x3 is 9, and when you multiply 3 more, it is 27.

Answer:

Step-by-step explanation: 3, because when 3 is cubed you get 27.

Answer:

No solution

Step-by-step explanation:

There are no values of  x  that make the equation true.

Answer: No solutions

==========================================

Explanation:

Start things off by subtracting 5 from both sides

|x-1|+5 = 2

|x-1|+5-5 = 2-5

|x-1| = -3

We cannot go any further after this point. The result of any absolute value is never negative. The absolute value represents distance from some number to 0. For example, saying |-7| = 7 means -7 is seven units away from 0 on a number line. Negative distance does not make sense.

So going back to |x-1| = -3 makes no sense as well. There are no numbers we can plug in for x to have |x-1| = -3 be true.

The equation |x-1| = -3 has no solutions, so the original equation doesn't have any solutions either.

Answer:

It is either 7.62m or 10m

Step-by-step explanation:

Eduphoria

Answer:

7.62 m

Step-by-step explanation:

Pythagorean theorem, 3^2+7^2=58

√58 is 7.62

Answer:

48x square miles

Step-by-step explanation:

12x4 48

The total area that he has will be 48x² miles square.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

Gerald has lots of lands that are 12x square miles.

He decides to purchase 4x more lots of land of the same size.

Then the total land that he has will be given by the multiplication of the 12x and 4x.

⇒ 12x · 4x

⇒ 48x²

Then the total area that he has will be 48x² miles square.

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Answer:

Sonnet 18. One of Shakespeare's best known and most loved sonnets, this reading explains that the stability of love will immortalize a partners beauty and youth. 'Shall I compare three to a summers day? And summers lease hath all too short a date.

Step-by-step explanation:

The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.

Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.

A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion.  The test statistic for this test is the z-score, which is calculated as:

\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)

If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.

If we substitute the values, we get:

\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)

The z-score for this assertion is calculated, and we find that it is approximately 2.86.

In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.

Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.

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The critical value of the test statistic t for a one-tailed (upper tail) hypothesis test with a sample size of 26 and a significance level of 0.01 is 2.479. This value is used to determine whether the sample data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

If the calculated test statistic is greater than 2.479, it falls into the critical region, and we reject the null hypothesis. Conversely, if the calculated test statistic is less than 2.479, it does not fall into the critical region, and we fail to reject the null hypothesis. The critical value is determined based on the desired level of significance and the degrees of freedom, which in this case is 26 - 1 = 25. For a one-tailed test with a significance level of 0.01, we need to find the t-value that corresponds to the 0.99 percentile of the t-distribution with 25 degrees of freedom. By consulting the t-distribution table or using statistical software, we find that the critical value is 2.479. This means that the calculated test statistic must be greater than 2.479 for us to reject the null hypothesis in favor of the alternative hypothesis at the 0.01 significance level in the upper tail of the distribution.

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A sample of 60 students were taken.

Out of which only 15 said that they will vote for Madelyn.

There are 140 7-th grade students.

Based on the sample data, we want to know how many might vote for Madelyn.

Well, it's quite simple.

15 out of 60 will vote for Madelyn

That is:

So, 1/4th of total students will vote for Madelyn.

That is:

Based on the sample data, 35 people are expected to vote for Madelyn [out of total of 140 people].

The given data is,A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers.

Of the 60 subjects who participate in the study, 21 prefer the instant coffee. We need to find the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee, let's say p. The formula to calculate the proportion of the population is:

p = (n1 + n2) / (x1 + x2)n1 and n2 are the sample sizes of two categories and x1 and x2 are the number of favorable outcomes from the respective categories. Here, n1 = n2 = 60 and x1 = 39 (since 21 out of 60 prefer instant coffee, the remaining 39 must prefer fresh-brewed coffee).Now, p = (60 + 60) / (39 + 21) = 1.2. Since p is a probability, it must be between 0 and 1. But here, p is greater than 1, which is not possible. Therefore, there is an error in the given data and we cannot proceed with the calculation.

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Answer:

y  = \(\frac{2}{3 }\)x - \(\frac{4}{3}\)

Step-by-step explanation:

-6y + 4x = 8  Subtract 4x from both sides of the equation

-6y = -4x + 8  Divide everything by -6

y  = \(\frac{2}{3 }\)x - \(\frac{4}{3}\)

The number which is express in each of the models as given in the image attached to the task content are as follows;

a). 1.37

b). 1.37

c). 1.37.

It follows from the task content that the models describe that One flat represents 1 whole, One rod represents 1 tenth and one unit represents 1 hundredth.

It therefore follows from the task content that in each of the models, the algebraic sum of flat(s), rods and units as the case may be results in the value; 1.37 as the utmost number represented by the models.

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\(8 + 3x = 1 + 7.9x \\ \\ \implies 3x - 7.9x = 1 - 8 \\ \\ \implies - 4.9x = - 7 \\ \\ \implies \: x = \frac { \cancel{- 7}}{ \cancel{ - 4.9} } \\ \\ \implies \: x = 1.43\)

choti bachi hô kya itne simp question ka answer kon puchta hai xD

The intersection of sets A and B, denoted as A∩B, is the set of elements that are common to both sets. In this case, the intersection of sets A and B is {2, 9, 10}, as these elements appear in both sets.

The elements are listed in increasing order and enclosed in curly braces.The union of sets A and B, denoted as A∪B, is the set of all elements that belong to either set A or set B or both. In this case, the union of sets A and B is {1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 15}, as these elements appear in either set A or set B or both. The elements are listed in increasing order and enclosed in curly braces.

To find the intersection, we compare the elements of set A with the elements of set B and select the common elements. In this case, the common elements are 2, 9, and 10.

To find the union, we combine all the elements from both sets, ensuring that each element is included only once. The resulting set includes all the elements from set A and set B without any repetition.

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Answer:

c I do believe good luck with the answer

B and c

Step-by-step explanation:

B. 300 cm, 400 cm, 500 cm

C. also.

Here

500² = 300 ² + 400²

250000 = 250000

Hope it helps :)❤

The surface area and volume of a pentagonal prism is  5/2 × a² × √(5 + 2√5) + 5ab and (1/4) × (5 + 2√5) × a² × h respectively. We can find the solution in the following manner.

A pentagonal prism is a three-dimensional geometric shape that consists of two parallel pentagons as the top and bottom faces, and five rectangular faces connecting them.

To find the surface area and volume of a pentagonal prism, we need to know its height, the length of the sides of the pentagon, and the length of the rectangular faces.

Let's denote the height of the pentagonal prism as "h", the side length of the pentagon as "a", and the length of the rectangular face as "b".

Surface Area of a Pentagonal Prism:

The surface area of a pentagonal prism is the sum of the areas of its faces. There are two pentagonal faces and five rectangular faces in a pentagonal prism.

Area of each pentagonal face = 5/4 × a² × √(5 + 2√5)

Area of each rectangular face = a × b

Total surface area = 2 × Area of pentagonal face + 5 × Area of rectangular face

= 5/2 × a² × √(5 + 2√5) + 5ab

Volume of a Pentagonal Prism:

The volume of a pentagonal prism is given by the formula:

Volume = (1/4) × (5 + 2√5) × a² × h

Therefore, the surface area and volume of a pentagonal prism can be calculated using the above formulas, given the values of a, b, and h.

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The surface area and volume of a pentagonal prism is sum of the areas of its faces, and (1/4) × (5 + 2√5) × a² × h.

A pentagonal prism is a three-dimensional geometric shape that consists of two parallel pentagons as the top and bottom faces, and five rectangular faces connecting them.

Surface Area of a Pentagonal Prism:

The surface area of a pentagonal prism is the sum of the areas of its faces. There are two pentagonal faces and five rectangular faces in a pentagonal prism.

Total surface area = 2 × Area of pentagonal face + 5 × Area of rectangular face

Volume of a Pentagonal Prism:

The volume of a pentagonal prism is given by the formula:

Volume = (1/4) × (5 + 2√5) × a² × h

Therefore, the surface area and volume of a pentagonal prism can be calculated using the above formulas, given the values of a, b, and h.

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Answer:

No, it is not an infinite solution.

Step-by-step explanation:

4x-4=4              

Add 4 to each side

4x=8

Divide 4 on each side

x=2

Answer:

No

Step-by-step explanation:

An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution.

A subset of a population used by statisticians to make predictions about a population is called a sample.

a sample is a smaller, representative group selected from the larger population. The sample is used to gather data and make inferences about the entire population. By analyzing the sample, statisticians can make predictions about the characteristics, trends, or behaviors of the population without having to study every individual within it. This method saves time, resources, and effort while still providing accurate results.

A sample is a crucial tool in statistical analysis, allowing statisticians to make informed predictions about a population based on the study of a smaller, representative subset.

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