Which triangle is similar to triangle PQR using the Pieces of Right Triangles Similarity Theorem?

On solving the provided question, we can say that the coordinates are

(3,2) => y = 5x -3/2 => y = 6

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

here,

the coordinates are

(3,2)

y = 5x -3/2

y = 15-3/2

y = 12/2

y = 6

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The approximate probability that the proportion of individuals in the sample who favor capital punishment will exceed 0.41 is given as follows:

0.1093 = 10.93%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

p = 0.38, n = 400.

Hence the mean and the standard error for the approximation are given as follows:

The probability that the proportion exceeds 0.41 is one subtracted by the p-value of Z when X = 0.41, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.41 - 0.38}{0.0243}[/tex]

Z = 1.23

Z = 1.23 has a p-value of 0.8907.

Hence:

1 - 0.8907 = 0.1093 = 10.93%.

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This is an example study method about:

4. controlled experiment

This is a controlled experiment because the puppies are randomly assigned to two groups: one group receiving the new drug and the other receiving a placebo. This is done to control for any external factors that could affect the outcome of the study, and to ensure that any observed differences in the health of the puppies can be attributed to the drug being tested. Additionally, the veterinarians are monitoring the puppies, which is a key aspect of a controlled experiment.

Controlled experiments are a common and widely used method in many fields, including medicine, psychology, and the natural sciences. They are particularly useful in evaluating the effectiveness of a new treatment or intervention, as they allow researchers to control for other variables that may affect the outcome and isolate the specific effects of the treatment being tested. In many cases, the results of controlled experiments are considered to be the most reliable and valid evidence for determining cause-and-effect relationships.

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Answer:

its b

Step-by-step explanation:

Answer: b

Step-by-step explanation:

The test statistic by the given values is t = -2.

Test statistic is a value calculated from a statistical test of hypothesis. It describes the closeness of the observed data with the expected distribution under the null hypothesis.

Test statistic can be calculated from the formula,

t = (xₐ - μ) / (s/√n)

where xₐ is the sample mean, μ is the population mean, s is the standard deviation and n is the sample size.

Given,

n = 49, xₐ = 50, s = 7

Since null and alternate hypothesis are given, μ = 52.

So the test statistic,

t = (50 - 52) / (7/√49)

 = -2 / (7/7)

 = -2

Hence the test statistic is -2.

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Answer:

30.453

Step-by-step explanation:

n = (3000+45.3)/100

=     n = 3045.3/100

=     n = 30.453

Descartes's number is 30.453

2.5

The volume of a quadrilateral is length times width times height so in order to find the height you must multipy the length and the width of the box then divide your answer (20) by the volume which is 50.

For the given equations the value of x is 3 and the value of y is -7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the system of equation is 5x + 7y = -34 and 10x + 17y = -89​. The value of x and y will be calculated as,

5x + 7y = -34   ........................(1)

10x + 17y = -89​ ........................(2)

Multiply the first equation by 2 and subtract the second equation from the first equation,

10x + 14y = -68

-10x - 17y = +89

____________

0    - 3y = 21

          y = -7

The value of x will be,

5x + (7 x -7 ) = -34

5x - 49 = -34

5x = -34 + 49

5x = 15

x =3

Hence, the values are x = 3 and y = -7.

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Answer:

y = -5x/4 + 9

Step-by-step explanation:

Slope-intercept Form: y=mx+b where m=slope

In order to put the equation into slope-intercept form, solve for y:

10x + 8y = 72

8y = -10x + 72 ==> subtract 10x on both sides to isolate y

y = (-10x + 72)/8  ==> divide both sides by 8 to isolate y

y = -10x/8 + 72/8  ==> divide each term by 8

y = -5x/4 + 9  ==> simplify

The solution is : y = -5x/4 + 9, equation of a line into slope-intercept form, simplifying all fractions.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

we know that,

Slope-intercept Form:

y=mx+b

where m=slope

In order to put the equation into slope-intercept form, solve for y:

10x + 8y = 72

8y = -10x + 72 ==> subtract 10x on both sides to isolate y

y = (-10x + 72)/8  ==> divide both sides by 8 to isolate y

y = -10x/8 + 72/8  ==> divide each term by 8

y = -5x/4 + 9  ==> simplify

Hence, The solution is : y = -5x/4 + 9, equation of a line into slope-intercept form, simplifying all fractions.

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Answer:

19/16 or 1 and 3/16 of an inch

Step-by-step explanation:

In order to add fractions, we must first find a common denominator, which in this case would be 16 because 8 times 2 = 16.

Whatever we do to the denominator must be done to the numerator, so we have to also multiply 7 by 2 to give us the fraction 14/16.

Now we can add the fractions: 5/16 + 14/16 = 19/16 or 1 3/16

Answer:

9/5 ft/s

Step-by-step explanation:

v = v₀ + at

v = 2 f/s + (1.5 f/s²)(5 s) = 9.5 ft/s

Answer:
15%

If this help please set brainly brainliest.

Step-by-step explanation:

To determine the rate of sales tax, you will need to divide the amount of sales tax by the price of the appliance. In this case, the rate of sales tax is $1,620.00 / $10,800.00 = 0.15, or 15%.

Answer:

15%

Step-by-step explanation:

Given:

To find the rate of sales tax, divide the amount of tax by the price of the item:

[tex]\implies \textsf{Rate}=\dfrac{1620}{10800}=0.15=15\%[/tex]

Therefore, the rate of sales tax is 15%.

Answer:

Below

Step-by-step explanation:

Loss of 5.75%     means   ( 1 - .0575)   remains after each year

After 7 years, this much will remain:

3000 km^2  *  ( 1-.0575)^7 = 1981.9 km^2

Triangle JKL is right. Triangle XYZ is acute.

To classify a triangle you need to know the measure of each angle.

For triangle JKL, if we measure the angles, we can see that angle JKL is 90 degrees, which makes it a right triangle.

For triangle XYZ, if we measure the angles, we can see that all angles are less than 90 degrees, which makes it an acute triangle.

Triangle JKL is a right triangle and triangle XYZ is an acute triangle.

Triangle JKL is right. Triangle XYZ is acute.

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Answer: b and a

Step-by-step explanation:

The probability that a student likes either mathematics or social sciences, given the survey on the fourth - grade class is, 68 %.

The probability that a student would like either mathematics or social sciences in the fourth - grade class, is :

= Probability that student likes math + Probability that student likes social sciences - Probability that student likes both math and social sciences

Probability that student likes math = 64 %

Probability that student likes social sciences = 11 %

Probability that student likes both math and social sciences  = 7 %

The probability that a student likes either mathematics or social sciences is :
= 64 % + 11 % - 7 %

= 68 %

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Full question is :

A survey of a fourth-grade class, resulted in the following information:

64% liked mathematics, 11% liked social studies, and 7% liked both mathematics and social studies.

Find the probability that a student likes either mathematics or social sciences. (write the answer in percentage)

We can give the following two conclusions:

From the information provided:

Since GFH and HFJ are adjacent, they share a common side or vertex. This means that the two figures are not only congruent, but they also share at least one common angle.

Since GFH and HFJ are congruent, they have the same size and shape. This means that corresponding angles and sides are equal in measure. It also means that the two figures can be superimposed on each other exactly.

In conclusion, since they are congruent and adjacent, we can say that they are part of a larger geometric figure.

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At Marlins Park, the typical ticket cost during that season was $29.62. Operating the stadium for a single game costs about $300,000.

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Answer:

The two equations are: r^(1/3) * s^2 = k and 1/s^2 = k * r^(1/3) where k is a constant.

Step-by-step explanation:

Two equations that model the relationship "the cube root of r varies inversely with the square of s" are:

r^(1/3) * s^2 = k

1/s^2 = k * r^(1/3) (where k is a constant)

In the first equation, the cube root of r is on one side of the equation and the square of s is on the other side, with a constant k connecting them. This represents the inverse relationship between the two variables.

In the second equation, both sides are equal to a constant k, with the reciprocal of the square of s on one side and the cube root of r on the other. This also represents the inverse relationship between the two variables, because if one variable increases, the other will decrease and vice versa.

These two equations are interchangeable, and they both represent the inverse variation between the cube root of r and the square of s. In both of them, the value of k can be determined by any pair of r and s values.

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The number of managers need to order nearest to the whole number will be 14.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The manager needs 343 table settings. If the placemats come in boxes of 26.

Then the number of managers is calculated as,

⇒ 343 / 26

⇒ 13.19

The number of managers need to order nearest to the whole number will be 14.

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A triangle has three sides, three angles, and seven properties including sum of interior angles, exterior angle theorem, triangle inequality theorem, congruence, isosceles triangle theorem, right triangle theorem, and pythagorean theorem.

1. Sum of Interior Angles: The interior angles of a triangle always add up to 180°.

2. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.

3. Triangle Inequality Theorem: The sum of any two sides of a triangle must be greater than the measure of the third side.

4. Congruence: Triangles are congruent if their corresponding angles and sides are equal.

5. Isosceles Triangle Theorem: If two sides of a triangle are equal in length, then the angles opposite those sides are also equal in measure.

6. Right Triangle Theorem: A triangle with one 90-degree angle is called a right triangle.

7. Pythagorean Theorem: The sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.

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The seven properties of triangle is listed below.

Here we have to list down the seven properties of triangle.

The properties of the triangle are as follows:

1) Angle Sum Property states that the sum of the three interior angles of a triangle is always 180°.

2) Triangle Inequality Property states that the sum of the length of the two sides of a triangle is greater than the third side.

3) The difference property states that the difference between the two sides of a triangle is less than the length of the third side.

4) Pythagoras property states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

5) Exterior Angle Property states that the exterior angle of a triangle is always equal to the sum of the interior opposite angles

6) Similarity property states that if two triangles are said to be similar if their corresponding angles of both triangles are congruent and the lengths of their sides are proportional.

7) Congruence Property states that if two triangles are said to be congruent if all their corresponding sides and angles are equal.

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Answer:

π/4

Step-by-step explanation:

(I cannot attach a unit circle here, sorry :)

Recall the function of the (x,y) values of the unit circle. X represents the cosine value, and y is the sine value.

If you look at a unit circle, π/2 has the coordinates (0,1), so the sine value of π/2 is 1.

To find arctangent, remember that the range of tangent is -π/2 < x < π/2. In terms of the unit circle, these are the minimum and maximum values, and we cannot use -π/2 and π/2 since x is 0, which means it'll be undefined. The angle where the coordinates can be found is the arctangent of the function.

So, find the coordinate where both x and y have the same value (√2/2, √2/2) at π/4. Therefore, the answer for the arctan(sin(π/2)) =  π/4.

the probability possible amounts of time for which they could rent the meeting room  for a maximum of six hours

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

[tex]t = time\\44 + 7.30t < 87.80\\7.30t < 43.80\\t < 6[/tex]

They may reserve the room for a maximum of six hours.

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The number of combinations you have is 36.

Combinations are defined as the arrangement of objects or numbers in a way such that the order of the arrangement does not matter.

First consider the pizza we can buy with two group of specifics.

You can get the pizza on thin crust, traditional crust, or deep-dish.

The toppings you have to choose from are pepperoni, sausage, onions, mushrooms, peppers, and extra cheese.

Each of the crusts, thin crust, traditional crust and deep dish can be topped with 6 toppings

Number of combinations from these two = 6 × 3 = 18

Each of these options have two options,  whether to pick it up or have it delivered.

Total number of combinations = 18 × 2 = 36

Hence you have 36 combinations to choose from.

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The quotient from the model of the number line is 0.05.

A quotient is an outcome of a division process carried out by two numbers in which one is a divisor and the other is a dividend. The divisor is the number that is being used to divide the dividend.

A quotient is the output of a division operation in more generic terms. It is the result of dividing one quantity by another. Aside from its mathematical use, the term "quotient" can also refer to the outcome of any division or separation process.

From the number line, we have 20 spaces between 0 to 1. So, it implies that 1 is the dividend and 20 is the divisor.

i.e.

[tex]\dfrac{1}{20}[/tex]

= 0.05  ... The result of this division process is known as the quotient.

Therefore, we can conclude that the quotient that models the division of the number line is 0.05.

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Answer:

$630.69

Step-by-step explanation:

Copnvert 93% into decimal format and multiply by $678.16:

(0.93)*($678.16) = $630.6888, whcih we will round to $630.69.

The property of congruence illustrated in the statement is the transitive property. AB ≅ DE, EF ≅ DE then AB ≅ EF is congruence.

According to the transitive property, if A and B are congruent and if B is congruent with C, then A must also be congruent with C. In other words, two things are congruent to each other if a third object is congruent to them.

Since AB and EF are both congruent to DE in the sentence "If AB DE, EF DE therefore AB EF," AB must likewise be congruent to EF in accordance with the transitive property.

The additional attributes you mentioned don't apply in this situation. According to the symmetric property, if A and B are congruent, then so is B. According to the reflexive quality, each item corresponds to itself. And congruence does not have the property of multiplication.

Your question is incomplete but most probably your full question was

How do you know AB ≅ DE, EF ≅ DE then AB ≅ EF explain?

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The likelihood that the penny and dime both appear is [tex](1/2)^ 4=1/16[/tex]

The likelihood of one is half: It will display heads roughly half the time (all values in this answer will be averages). Only 50% of the time will the second coin reveal heads when the first one displays heads. Now, only 25% of the time remains. Only 50% of the time will the third coin reveal heads when the second coin displays heads. 1/8 of this.

Each coin has a potential for two states (heads or tails). In total, the four coins have 24=16 different permutations (states) that they might be in. Only one of these combinations results in all heads. This results in a result of 1/16. And just 50% of the time will the fourth coin also reveal heads when the third coin also displays heads. 1/16 is one-half of 1/8.

[tex](1/2)^ 4=1/16[/tex]

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Answer:

1/2

Step-by-step explanation:

There are $2^4=16$ possible outcomes, since each of the 4 coins can land 2 different ways (heads or tails). There are 2 possibilities for the penny and the dime: either they're both heads or they're both tails. There are also 2 possibilities for the nickel and 2 possibilities for the quarter. So there are $2 \times 2 \times 2 = 8$ successful outcomes, and the probability of success is $\dfrac{8}{16} = \boxed{\dfrac{1}{2}}$.

The required interval is (105.4, 144.6) about the mean includes 95% of the data.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.

The data is given in the question below as:

X ~ N ( µ = 125 , σ = 10 )

P ( a < X < b ) = 0.95

Dividing the area 0.95 in two parts we get 0.95/2 = 0.475

Since 0.5 area in the normal curve is above and below the mean

The area below the mean is a = 0.5 - 0.475

The area above the mean is b = 0.5 + 0.475

For the probability 0.025 in standard normal table to calculate critical value Z = -1.96

For the probability 0.975 in standard normal table to calculate critical value Z = 1.96

Z = ( X - µ ) / σ

-1.96 = ( X - 125 ) / 10

a = 105.4

1.96 = ( X - 125 ) / 10

b = 144.6

P ( 105.4 < X < 144.6 ) = 0.95

Hence, the required interval is (105.4, 144.6).

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The answer of addition & multiplication are,

101,455,348 + 1,111,419 = 102566767

0.000000612 x 0.00031119 = 1.9044828E-10

297,060 + 0.0004839 =297060.0005

0.000000612 x 0.00031119 =

297,060 + 0.0004839 =

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

101,455,348 + 1,111,419 = 102566767

0.000000612 x 0.00031119 = 1.9044828E-10

297,060 + 0.0004839 =297060.0005

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Answer: Y is 8

Step-by-step explanation:

Add 16 to both sides. y/4 = 2. Multiply both sides by 4 to get y=8.