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The pairs of angles formed when a transversal crosses two parallel lines are categorized into four types:

1. Corresponding angles: Corresponding angles are marked with an "f" shape. They are located in matching corners when a transversal intersects two parallel lines. The key property of corresponding angles is that their measures are equal.

2. Alternate interior angles: Marked with a "Z" shape, alternate interior angles are interior angles that lie on opposite sides of the transversal and between the parallel lines. They have equal measures, making them congruent to each other.

3. Alternate exterior angles: Alternate exterior angles are marked with a "U" shape. These angles are located on opposite sides of the transversal but outside the parallel lines. Similar to alternate interior angles, alternate exterior angles have equal measures.

4. Same-side interior angles: Same-side interior angles are marked with a "C" shape. These angles are located on the same side of the transversal and between the parallel lines. The key characteristic of same-side interior angles is that they are supplementary, meaning their measures add up to 180 degrees.

The corresponding angles have equal measures, alternate interior and exterior angles are congruent, and same-side interior angles are supplementary.

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A rectangular \($12\text{ cm}\times 20\text{ cm}$\) waffle is divided into \($1\text{ cm}\times 1\text{ cm}$\) squares.An ant crawls along a straight path from one corner to the opposite corner.The ant crosses through 31 squares of the waffle.

To determine the number of squares the ant crosses through, we can visualize the path from one corner to the opposite corner of the rectangular waffle. The ant's path consists of several diagonal segments that pass through the individual squares.

The diagonal of the rectangular waffle is equivalent to the ant's path. Using the Pythagorean theorem, we can calculate the length of the diagonal. The length of the diagonal is given by \(\sqrt{(12^2 + 20^2)}= \sqrt{(144 + 400)} = \sqrt{544 }\approx23.32 $cm$.\)

Since each side of the square measures 1 cm, the ant will cross through approximately 23 squares along the diagonal path. However, we need to consider that the ant will also pass through the corners of the squares. Along the diagonal path, the ant will cross through the corner of each square it encounters, except for the endpoints.

Considering the endpoints, we add 1 to account for the square at the starting point and 1 to account for the square at the endpoint. Therefore, the ant crosses through a total of 23 + 2 = 25 squares.

Hence, the ant crosses through 31 squares of the waffle.

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Answer:

C. mental set

Step-by-step explanation:

A mental set generally refers to the brain's tendency to stick with the most familiar solution to a problem and stubbornly ignore alternatives. This tendency is likely driven by previous knowledge (the long-term mental set) or is a temporary by-product of procedural learning (the short-term mental set).

The prices of the two stocks will be the​ same after 3 hours from noon.

A stock, also known as equity, is a security that represents the ownership of a fraction of the issuing corporation.

Given that, The price of Stock A at 9 A.M. was $12.71. Since​ then, the price has been increasing at the rate of $0.12 each hour. At noon the price of Stock B was $13.46. It begins to decrease at the rate of $0.13 each hour.

Let the hours when they equalize at h, then we have:

12.71 + 0.12h = 13.46 - 0.13h

0.25h = 0.75

h = 3

Hence, the prices of the two stocks will be the​ same after 3 hours from noon.

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Answer:

\(\tt b=20\)

Step-by-step explanation:

Use the Pythagorean theorem

\(\tt b^2+15^2=25^2\)

\(\tt b^2+15* 15=25*25\)

\(\tt b^2+225=625\)

\(\tt b^2=625-225\)

\(\tt b^2=400\)

\(\tt b^2=20*20\)

\(\tt b^2=20^2\)

\(\tt b=20\)

Answer:

A

Step-by-step explanation:

Rewritten as decimals, the numbers are 3.66, 3.50, 3.25, 3.20

Answer:

c

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

the probability it would snow is 0.07 or 7%. this is quite low. so, it is unlikely that it would snow

Answer:

Step-by-step explanation:

C

The equivalent equation that can be used to find the amount Jalisa earned babysitting yesterday is d = 71.25 - 22.50.

To find the amount Jalisa earned babysitting yesterday, we need to subtract the additional amount she earned today from her total earnings. The equation given, d + 22.50 = 71.25, represents the relationship between the amount she earned yesterday (d) and the total amount she earned today (71.25).

To rearrange the equation and isolate the value of d, we can subtract 22.50 from both sides of the equation. This gives us d + 22.50 - 22.50 = 71.25 - 22.50. Simplifying, we get d = 71.25 - 22.50.

Thus, the equivalent equation that can be used to find the amount Jalisa earned babysitting yesterday is d = 71.25 - 22.50. By substituting the values into this equation, we can calculate that Jalisa earned $48.75 babysitting yesterday.

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We have drawn the right-angled triangle by using the given data.

What is trigonometry?

Trigonometry is a branch of mathematics that studies the relationships between triangle side lengths and angles. The field arose in the Hellenistic world during the third century BC from geometric applications to astronomical studies.

Given that sinθ =√3/2

So as we know

      sinθ = √3/2

then

     \(\theta=sin^{-1}(\frac{\sqrt{3}}{2} )\\\\\theta = 60^o\)

     sinθ = opposite side/ hypotenuse

     sin60° = BC/AC

     If one of the angles is 60° and the other is 90° then the remaining angle will be 30°.

Now

   cosθ = adjacent side/hypotenuse

   cos60° = AB/AC
    1/2 = AB/AC

Now we can draw the ΔABC as

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The ability to order items in a sequence, such as longest to shortest, is known as Seriation.

Seriation is a cognitive skill that involves arranging objects, events, or ideas in a particular order or sequence. It is a crucial aspect of cognitive development and is typically acquired during early childhood. Seriation is the ability to mentally order objects along a quantitative dimension, such as size, weight, or length.

Seriation involves comparing and ordering items based on specific criteria. For example, if given a group of objects of different lengths, a child who has developed seriation skills will be able to arrange the objects in order from shortest to longest. Similarly, if given a group of numbers, a child who has developed seriation skills will be able to arrange them in order from smallest to largest.

Seriation is an important cognitive skill that is used in various areas of life, including academic, professional, and personal domains. It allows individuals to organize information and ideas in a logical and meaningful way, which can facilitate more efficient processing and understanding of complex concepts.

Overall, seriation is a fundamental cognitive skill that plays a crucial role in various aspects of life, including problem-solving, decision-making, and organization. It is an essential skill that supports the development of higher-order thinking skills, such as analysis, evaluation, and synthesis.

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Answer:

b

Step-by-step explanation:

give other person brainliest

The mistake lies in step -(66/5)/(22/5) → -(66/5)(22/5) where he didn't take the reciprocal of the divisor while dividing the two fractions.

The step would have been like this:

-(66/5)/(22/5) = -(66/5)(5/22) = -(3).

A fraction is a portion of a whole or, more broadly, any number of equal pieces.

It is written in the form p/q, read as "p by q", where p is called the numerator and q is called the denominator, and the fraction p/q represents p number of equal parts from q number of equal parts.

Fractions are of two types:

Fractions are divided by multiplying the dividend by the reciprocal of the divisor

Suppose we are asked to divide a fraction a/b by x/y.

This is written as (a/b) ÷ (x/y) or (a/b)/(x/y), and calculated as:

(a/b)*(y/x).

In the question, we are informed that last night, the temperature fell from 0°F to Negative 13 and one-fifth °F in 4 and two-fifths hours. Alan calculated the average temperature change per hour.

He followed the following steps:

-(13 1/5)/(4 2/5)

= -(66/5)/(22/5)

= -(66/5)(22/5)

= -(1452/25).

The mistake lies in step -(66/5)/(22/5) → -(66/5)(22/5) where he didn't take the reciprocal of the divisor while dividing the two fractions.

The step would have been like this:

-(66/5)/(22/5) = -(66/5)(5/22) = -(3).

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Answer:

The perimeter of the new space used for the playground is 108 feet.

The perimeter of the space used for the new playground is 150 feet.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

The current space is rectangular and has a length of 24 feet and a width of 26 feet.

and, the new space is 36 feet long.

let the width of new space is x.

Since, the two space are similar then the scale factor will be

= 36/24 = 1.5

So, the width of new space = 1.5 x 26 = 39 feet

Thus, the Perimeter of new space

= 2(l +w)

= 2 (36+ 39)

= 150 feet

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It will take Daquin 63min to finish rest of his homework which is 70% of the total homework, if 30% is done in 27 minutes.

Daquin has completed 30% of his work.

Remaining work will be 100-30 = 70%

Means 70% of the total work is remaining to do by Daquin.

By applying unitary method:

Since, to do 30% of the homework it take 27 minutes.

Therefore, To do 1% of the homework it will take 27/30 minutes.

So, To do 70% of the homework it will take (27/30)×70 min

= 63 min

Hence, It will take him 63min to finish rest of his homework.

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Answer:

Using the given recursive formula, we can find the value of H(3) as follows:

H(3) = H(1) x H(2)

H(3) = 9 x 3

H(3) = 27

Therefore, H(3) = 27.

Step-by-step explanation:

Answer:

The sequence you provided is a recursive sequence where each term is defined using the two previous terms. Given that H(1) = 9 and H(2) = 3, we can find H(3) by multiplying H(1) and H(2): H(3) = H(1) x H(2) = 9 x 3 = 27.

Answer:

The equation of the straight line passing through the point ( 3,1 )

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Step-by-step explanation:

Step(i):-

The equation of the straight line passing through the point ( 3,1 )

                      \(\frac{x}{a} + \frac{y}{b} = 1\)

                     \(\frac{3}{a} + \frac{1}{b} = 1\)

                    3b + a = ab ...(i)

Given the difference of length is  4

                      a-b = 4

                       b =  a - 4 ...(ii)

Step(ii):-

substitute b=a-4 in equation (i) , we get

                3( a-4 ) + a = a (a-4)

               3a - 12+ a =  - 4 a + a²  

                 a² - 8 a + 12 =0

Find the factors of 'a'

                 a² - 6a -2a +12 =0

                a (a-6) -2(a-6) =0

             a =2 and a=6

                  we know that a-b =4

             put       a = 2

                          2 - b =4

                            b = -2

The equation of the straight line whose intercepts on the axes

                    \(\frac{x}{a} + \frac{y}{b} = 1\)

                   \(\frac{x}{2} + \frac{y}{-2} = 1\)

The equation of the straight line

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Verification:-

The equation of the straight line passing through the point (3,1)

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Put x =3 and y=1

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

                 1 = 1

∴  The point (3,1) is satisfies the equation

There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

Answer:

the answer is -120

so the answer is -120

Answer: C (The Last One)

Step-by-step explanation:

The answers correct because, If the range and median is 13 that means that the highest and lowest point equal 13 and the middle/the line in the graphs should be on 13. A doesn't have the line/median on 13 so it is not that answer. But B and C have the line/median on the line so we just have to check the range. The range of B is: 9, The range of C is: 13. So based off that we know that the answer is C.

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The value of 2 is at the 0.1 percentile is the answer.

The percentile rank refers to the percentage of the distribution that falls at or below a given score. In statistics, percentiles are used to compare measurements, ranking, and scoring between different entities.

In this scenario, z=2 is what percentile is the question to be answered.

To solve the problem, the Z-score formula is used, which is given by; $$Z = (x - μ) / σ$$ where; Z is the standard score, x is the value of interest, μ is the mean, and σ is the standard deviation of the population.

For instance, assume a normal distribution with a mean of 10 and a standard deviation of 2.5.

Using the z-score formula, we get: Z = (2 - 10) / 2.5 = -3.2

Therefore, Z = -3.2 corresponds to the .1 percentile.

This implies that the value of 2 is greater than 0.1% of the population, meaning that it is close to the lowest score of the distribution.

The value of 2 is at the 0.1 percentile.

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Answer:

s / ( 2 pi * h) = r

Step-by-step explanation:

s = 2 * pi * r * h

Divide each side by 2 * pi * h

s / 2 pi h= 2 * pi * r * h/ ( 2 pi h)

s / ( 2 pi * h) = r

Answer:

s over 2×pie×h

Step-by-step explanation:

To get the variable r by itself you need to divide the 2×pie×hr by 2×pie×h. You need to divided both sides to keep the equation true, so divide both sides by 2×pie×h to get: s/2×pie×h.

Answer:

12,750

Step-by-step explanation:

After investing for 10 years at 4.31% interest, your $8,361 investment will have grown to $12,750

The two necessary instance variables for representing a fraction would be the numerator and the denominator.

The numerator represents the top part of the fraction indicating the number of equal parts being considered. The denominator represents the bottom part of the fraction indicating the total number of equal parts the whole is divided into.

These two variables are crucial for accurately representing and performing operations on fractions such as addition, subtraction, multiplication, and division. They allow for precise manipulation and comparison of fractional values within a programming class.

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Answer:

2x+3

or

2N + 3

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

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

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Answer:

16

Step-by-step explanation:

I had this on my test and got correct