Yana, Josh, and Katrina are standing at the vertices of a righi triangle as they
throw a frisbee. Yana and Josh are standing 15 feet apart, Josh and Katrina are
standing 12 feet apart, and Katrina and Yana are standing 9 feet apart.
Tree joins the game and stands between Yana and Josh.
What is the shortest possible distance between Trae and Katrina?

The required length of line segment JK would be 16 units.

The midpoint of a line segment is the point that divides the line segment into two equal parts. So, to find the length of the line segment JK, we can first find the coordinates of point J, which is the other endpoint of the line segment.

Let the coordinate of the point J would be (x, y)

Since the midpoint of the line segment is (2, -3), and point K is located at (-6, -3), we can use the midpoint formula to find the coordinates of point J:

2 = (x+(-6))/2 ; -3 = (y+(-3))/2

4 = x - 6 ; -6 = y -3

x = 10 ; y = -3

So the coordinate of the point J :(10, -3)

Now that we have the coordinates of both endpoints of the line segment, we can use the distance formula to find the length of the line segment:

length = √((10 - (-6))² + (-3 - (-3))²)

= √((10 + 6)² + (-3 + 3)²)

= √(16² + 0)

= √(256)

= 16

Therefore, the length of line segment JK is 16 units.

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The probability that exactly two of the students are juniors is given as follows:

0.270 = 27%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of these parameters for this problem are given as follows:

[tex]N = 60, n = 4, k = 18[/tex]

Hence the probability that exactly two of the students are juniors is calculated as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,60,4,18) = \frac{C_{18,2}C_{42,2}}{C_{60,4}} = 0.270[/tex]

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From the concept of algebra of venn diagram we obtain that
P(A or B) = 0.75.

A set is a collection of well-defined objects.

A subset contains all the elements or few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

From set theory, we know that N(A∪B) = N(A) + N(B) - N(A∩B).

It states that N(A) or N(B) is the sum of N(A) and N(B) minus the common intersecting region N(A∩B) as we have already considered the region in the sum of N(A) and N(B) twice.

Similarly, P(A or B) = P(A) + P(B) - P(A∩B)>

Therefore, P(A or B) = 0.50 + 0.40 - 0.15.

P(A or B) = 0.90 - 0.15.

P(A or B) = 0.75.

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The multiplicity of a number is the number of times a number is a factor of another number.

In general, the multiplicity of a number can be determined by dividing the number by the factor. If the result is a whole number, then the multiplicity of the factor is equal to the result of the division. If the result is a decimal or fraction, then the multiplicity of the factor is 0.

For example, if we wanted to find the multiplicity of 5 in 25, we would divide 25 by 5: 25/5 = 5. This means that the multiplicity of 5 in 25 is 5.

The multiplicity of 5 can also be determined by finding the prime factorization of the number. For example, if we wanted to find the multiplicity of 5 in 30, we would factorize 30: 30 = 2 x 3 x 5. This means that the multiplicity of 5 in 30 is 1, because there is only one 5 in the prime factorization of 30.

In summary, the multiplicity of a number is the number of times a number is a factor of another number. The multiplicity of a number can be found by dividing the number by the factor, or by finding the prime factorization of the number.

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By using the concept of conjugate, it can be calculated that

Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]

What is conjugate?

Conjugating is the process of changing a verb in a sentence to match the person, number, gender, tense, mood, and voice of the subject. For example, the verb "to walk" changes to "walked" when conjugated in the past tense. Conjugation is important in many languages, including English, as it helps to make communication more precise. Conjugation involves making changes to the base form of the verb, such as adding suffixes or prefixes, or changing the spelling of the word. Different languages have different rules for conjugating verbs, so it is important to understand the language’s system of conjugation before attempting to use it.

Here the expression is [tex]x + \sqrt{y}[/tex]

Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]

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Answer:5.6

Step-by-step explanation:

Answer: $1.40/4 = $0.35/apple

The parallel marks the northern limit of the Southern Ocean (though some organisations and countries, notably Australia, have other definitions) and of the Antarctic Treaty System.

Parallel lines are straight lines that never meet each other no matter how long we extend them

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).

The fundamental characteristics listed below make it simple to recognise parallel lines.

Parallel lines are defined as straight lines that are always the same distance apart.

No matter how far apart they are from one another, parallel lines can never intersect.

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(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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Counting to 100 frequently and accurately can be mastered between the ages of three and a half and five and a half, but no later than the age of six.

The series of physical, language, mental, and emotional changes that occur in a kid from birth to the beginning of maturity is referred to as child development. During this phase, a kid moves from being dependent on their parents/guardians to be more self-sufficient.

Most parents will notice their children can count to 100 without any assistance around this age.

So it was apparent that they had a lot of practice time and focused specifically on counting to 100. The average age of parents in the discussion cable ranged from tardily 5 to early 6 years old.

Some parents expressed concern about their children not being able to count to 100 by the age of six, but they were apathetic because it was apparent their child was capable of other developmental goals.

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Answer:

1/ simplify polynomial is x^3 y^2 - x^2 y^3 + xy

2/ Answer is -86

Step-by-step explanation:

x²yxy-xy²xy +xy

Simplify each term, and I get

x^3 y^2 - x^2 y^3 + xy

I may be wrong!

Now let's put -3 in for x and 2 in y and evaluate

(-3)^3  (2)^2 -  (-3)^2  (2)^3  +  (-3 times 2)

(27) (4) - (9) (8) - 6

-86

I may be wrong, but I tried my best to help you since this question has been on for a long time, but no one answered. If I am wrong, I am sorry!

Answer:

Greg is correct

Step-by-step explanation:

To determine which of them is experiencing warmer weather, you need to compare the temperatures in the same unit of measurement. 77°F is equivalent to 25°C, while 30°C is equivalent to 86°F. Therefore, Greg is experiencing warmer weather than Josh.

The difference in the temperatures they reported is due to the fact that they are using different temperature scales. The Fahrenheit scale is used in the United States, while the Celsius scale is used in most other countries. The two scales are related by the equation:

C = (F - 32) / 1.8

To convert from Fahrenheit to Celsius, you can use this equation to determine the temperature in Celsius. To convert from Celsius to Fahrenheit, you can use the equation:

F = C * 1.8 + 32

Using these equations, you can compare temperatures in different scales to determine which is warmer.

If the value x =12 then 2x - 5 = 19 the statement is true if 2x -5 = 19 then x = 12. The correct options are A and D.

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 statements are:-

x = 12, then 2x - 5 = 19.

2x - 5 = 19

(2 x 12 ) - 5 = 19

24 - 5 = 19

19 = 19

If 2x - 5 = 19, then x = 12. The value of x will be calculated as,

2x - 5 = 19

2x = 19 + 5

2x = 24

x = 24 / 2

x = 12

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We can write '8 or more' as [tex]\geq 8[/tex], using the greater-than equal to sign.  

The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. In mathematical writing, the greater-than sign is typically placed between two values being compared and signifies that the first number is greater than the second number.

Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.

Here, we can use an alternate to the 'greater-than' symbol: a 'greater-than equal to' symbol, denoted as ≥.

Using this, we can write:

[tex]\geq[/tex] 8, denotes a number greater-than or equal to 8.

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When the mean is 6, the mean deviation of a given collection of data is 2.4.

The deviation is a metric used in statistics and mathematics to discover the difference between the actual and predicted values of a variable. The deviation is just the distance from the central point. The mean deviation is a statistical metric that computes the average departure from the mean value of a given data collection. Using the following approach, you can simply determine the mean deviation of the data values. We categorize the data and describe the frequency distribution of each group to provide it in a more concise way. These are referred to as class intervals.

Here,

To find out the mean deviation, just follow the steps given below.

Step 1: Find the mean for the given set of values

Step 2: Find the distance. (i.e) Subtract the mean value from each given values, and ignore minus symbol if any

Step 3: Finally, find the mean of the obtained distance, which is called the mean deviation.

=(2+4+6+8+10)/5

=6

mean deviation,

=(4+2+0+2+4)/5

=2.4

The mean deviation of given set of values is 2.4 when mean is 6.

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The symbol that represents an expression in statistics are That is option A , B and C.

Statistics is defined as the area of study that is concerned with the collection, organization, analysis, interpretation, and presentation of data.

The importance of statistics is that it helps in conducting research, evaluating results, developing critical thinking and making informed decisions.

The various symbols use in statistics include the following:

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We will write greater than 20 using Inequality sign as ( > 20).

The first number in every inequality sign tells us how the first and second numbers relate to one another, so  > 20 means "A number is greater than 20."

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than symbol (>) is used when the first number exceeds the second number. The less than symbol (<) is used when the first number is less than the second number.

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A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.

For example, the mode of the set {3, 7, 8, 8, 9}, is 8. Therefore, for a finite number of observations, we can easily find the mode. A set of values may have one mode or more than one mode or no mode at all.

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Omar would most likely use a line graph to show changes in water depth. A line graph would allow him to plot the water depth readings against a timeline and visualize how the depth changes over the duration of the drought.

A line graph is the most appropriate method of displaying data to show changes in water depth over the duration of the drought. A line graph is a type of chart that plots data points on a two-dimensional coordinate system. It is used to show how one set of data changes over a period of time. Omar would plot the water depth readings along the vertical y-axis and the days of the drought along the horizontal x-axis. A line would then be drawn to connect the data points, depicting the changes in water depth over the period of the drought. Additionally, the data points can also be labeled to provide more detailed information about the water depth readings at each point. This would allow Omar to compare the readings over time and monitor the effects of the drought on the water depth.

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The lines p and q are perpendicular in the coordinate plane.

The name of the other number line, which is a vertical one, is called the y-axis. To graph points, lines, and other objects, one can utilize the coordinate plane. A pair of numerical coordinates that uniquely identify each point in a Cartesian coordinate system in a plane are called the coordinates. These numerical coordinates are signed length measurements that represent the separations between two fixed perpendicular oriented lines and the point.

Let the equation of the line is:

y-y'=m₁(x-x')

m₁=2/6

m₁=1/3

Therefore, the equation of a line with the point (3, 4) and slope m₁=1/3

y-4=(1/3)(x-3)

y=(1/3)x-1+4

y=(1/3)x+3

And m₂= -3

The line equation that is passing through (2,7) and m₂= -3

y-7=(-3)(x-2)

y-7= -3x+6

y= -3x+13

m₁×m₂= -1

(1/3)(-3)= -1

So, the lines that are given in the coordinate plane p and q are perpendicular.

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Answer:

Step-by-step explanation:

You want the measures of the numbered angles in the figure comprised of overlapping right triangles.

The acute angles in a right triangle are complementary, as are the two angles into which a right angle is divided.

  ∠1 +35° = 90°   ⇒   ∠1 = 55°

  ∠3 +35° = 90°   ⇒   ∠3 = 55°

The angle marked 70° is exterior to the bottom right triangle, so is equal to the sum of angles 3 and 4.

  ∠3 +∠4 = 70°

  55° +∠4 = 70°   ⇒   ∠4 = 15°

Angle 2 is the other acute angle in the bottom right triangle, so ...

  ∠2 = 90° -∠4 = 90° -15°

  ∠2 = 75°

The factors of  2x² - 7x - 15 are (2x + 3) and (x - 5).

By splitting the middle term and factoring the polynomial,

2x² - 7x - 15

= 2x² - 10x + 3x - 15

= 2x(x - 5) + 3(x - 5)

= (2x + 3)(x - 5)

The factors of  2x² - 7x - 15 are (2x + 3) and (x - 5).

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56.6 years  is the mean of the modes of the given set of numbers.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

The mean is calculated by adding together all the values

                 =  (54+54+54+55+56+57+57+58+58+60+60

                  = 623

                  =  56.6 years.

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Answer:

(D) 1/9

Step-by-step explanation:

9x-2=-3

9x=1

x=1/9

You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).

What are the 4 types of function?

There are 4 types of functions:

Functions with arguments and return values. This function has arguments and returns a value: ...

Functions with arguments and without return values. ...

Functions without arguments and with return values. ...

Functions without arguments and without return values.

A function is a relation that for each input value x takes the unique value of output y.

Consider the table

x y

1 7

4 7

2 2

4 1

3 9

You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).

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Answer: The answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hannah's thought that the original photo is congruent and similar to the final image is false

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

Translation creates congruent and similar shapes

However, dilation only create similar shapes,  but not congruent shapes

This means that the shapes are similar, but not congruent

Hence. Hannah is incorrect

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Answer and Step-by-step explanation:

Lydia must sell at least $680 worth of tacos and burritos each day, and she only has enough supplies to make 115 tacos or burritos. If she sells each taco for $4, then she can make a maximum of 115 tacos * $4/taco = $<<115*4=460>>460 by selling tacos.

Therefore, in order to make at least $680, Lydia must sell burritos in addition to the tacos. The minimum number of burritos she must sell in order to make at least $680 is $680 - $460 = $<<680-460=220>>220.

Since Lydia sells each burrito for $6.75, she must sell at least $220 / $6.75/burrito = <<220/6.75=32.5>>32.5 burritos to make at least $680. Since she only has enough supplies to make 115 tacos or burritos, and she has already accounted for 115 tacos, she must sell a minimum of 32.5 burritos to meet the requirements.

The mean squared error is 4.67. So the option a is correct.

In the given question, demand for a product and the forecasting department's forecast for a product are given.

We have to compute the mean squared error.

Period          Actual        Forecasted      Error       Absolute      Squared

                 Demand(E)    Demand (F)     (E-F)        Error |E-F|    Error |(E-F)|^2

1                12    

2                15                12              3               3             9

3                14                15              -1                1              1

4                18                16              2                2              4

                                                                Total=6        Total=14

Now we finding the mean squared error (MAE)

Mean squared error = ∑|(E−F)|^2/n

Mean squared error = 14/3

Mean squared error = 4.67

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