a right triangle has side lengths of 12 feet and 5 feet. what is the length, in feet, of the hypotenuse?

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{2}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~2 - (-4)~~)^2 + (~~4 - 2~~)^2} \implies PQ=\sqrt{(2 +4)^2 + (4 -2)^2} \\\\\\ PQ=\sqrt{( 6 )^2 + ( 2 )^2} \implies PQ=\sqrt{ 36 + 4 } \implies PQ=\sqrt{ 40 }[/tex]

In experimental research, a control group does not receive the independent variable and is used to determine whether the independent variable influenced change in the dependent variable.

A test sample or the group that undergoes an experimental method is referred to as an experimental group. This group is exposed to modifications in the test's independent variable. The independent variable's values and its effects on the dependent variable are noted. Multiple experimental groups may be present at once during an experiment.

A control group is a subset of the experiment that is kept apart from the other groups so that the independent variable under test cannot affect the outcomes. Isolating the effects of the independent variable on the experiment can help rule out other possible explanations for the findings of the experiment.

control groups can be of two types:

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The given statement that the scatter plot is used to visualize the association (or lack of association) between two quantitative variables is true.

A scatter plot is a graphical representation of the relationship between two quantitative variables. The data points are plotted on a coordinate plane, and the pattern or association between the two variables is visualized.

This can help identify the presence or absence of a relationship, the strength of the relationship, and the direction of the relationship (positive or negative). The scatter plot can also be used to identify any outliers or outliers in the data.

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--The given question is incorrect; the correct question is

"A scatter plot is used to visualize the association (or lack of association) between two quantitative variables.

True

False"--

The matrix of the caps size is

13  36  27

10  15   0

The matrix that shows the total value of each cap size in each location is

247   684   513

190   285   0

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

When represented as a matrix, we have

13  36  27

10  15   0

In (a), we have

13  36  27

10  15   0

Multiply the individual elements by 19

So, we have

247   684   513

190   285   0

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Answer:

Step-by-step explanation:

5 (x + 4) = 6x - 5

5x + 20 = 6x - 5

5x + 20 - 20 = 6x - 5 - 20

5x = 6x -25

x= 25

Answer:

x=25

Step-by-step explanation:

[tex]5(x+4)=6x-5\\5x+20=6x-5\\5x+20-20=6x-5-20\\5x=6x-25\\5x-6x=6x-25-6x\\-x=-25\\\frac{-x}{-x} =\frac{-25}{-x} \\x=25[/tex]

The row of the table that reveals the x-intercept of the function f is given as follows:

Second row.

A function has two intercepts, which are listed as follows:

The definition of each type of intercept is given as follows:

From the second row of the table, we have that when x = -4, f(x) = 0, hence the x-intercept of the function is of x = -4.

The y-intercept is of y = -16, as from the fourth row, when x = 0, y assumes a value of 16.

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A person must be at least 7 years old to join the baseball club the inequality is x ≥ 7  where x is the age of the person

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a condition, a person must be at least 7 years old to join a baseball club, we need to represent the age in terms of an inequality,

If we say, a person who wants to join the baseball club is x years old,

Then, the condition for x is given by inequality,

x ≥ 7

Hence, a person must be at least 7 years old to join the baseball club the inequality is x ≥ 7  where x is the age of the person,

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Answer:C.

Step-by-step explanation:

The value of n  is 4, and the regular n-sided polygon becomes a square.

When a square tile, a regular hexagon tile, and an equilateral triangle tile share a common vertex, the total interior angle between them is 360°.

We can represent the interior angle between the sides of the regular n-sided polygon as 360°/n.

In the given problem, the square tile has an interior angle = 90°

The regular hexagon tile has an interior angle = 120°

The equilateral triangle tile has an interior angle = 60°.

The sum of all these interior angles = 270°.

Now equal the sum of interior angles = 360°

360° - 270° = 90° to the total interior angle.

This can be obtained by considering n=4 for the regular n-sided polygon, as the interior angle between sides of a regular 4-sided polygon is 360°/4 = 90°.

Therefore, the value of n  is 4, and the regular n-sided polygon becomes a square.

Did you mean, A square tile, a regular hexagon tile, an equilateral triangle tile, and a regular n-sided polygon tile share a common vertex? There are no gaps or overlaps between the tiles. What is n?

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Answer:

See below

Step-by-step explanation:

Converting from radians to degrees

[tex]r=\frac{\pi}{180}d^\circ[/tex]

Converting from degrees to radians

[tex]d^\circ=\frac{180}{\pi}r[/tex]

Because [tex]2\pi[/tex] radians is equivalent to [tex]360^\circ[/tex], the measure of a full circle, then 1 radian would be [tex]\frac{360^\circ}{2\pi}=\frac{180^\circ}{\pi}[/tex] degrees. Similarly, 1 degree would be [tex]\frac{2\pi}{360^\circ}=\frac{\pi}{180^\circ}[/tex] radians. This is where the formulas come from!

Based on the information in the graph, we can infer that the missing numbers are: 9, 4, 19, 30, 84, 16, 8, 22, and 40.

To complete the table correctly we must identify the columns or rows with more data. These will be the easiest to complete. First of all, we must fill in those that already have a number in the total box because we can add the available numbers and later subtract them from the total to identify the missing number.

We can also find the numbers in the total cells by adding all the numbers in a column or row to find this result. Finally, the boxes that are being completed serve as clues to complete the others.

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The number of calories in each cake will be 136¹/₅. The correct option is C.

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 Jackson ate 5 of a chocolate cake at his brother's birthday party. If the chocolate cake contained 681 calories.

The number of calories in each cake will be calculated as:-

Amount of calories = 681 / 5

Amount of calories = 136.2

Amount of calories = 136¹/₅

Therefore, there will be 1361/5 calories in each cake. The right answer is C.

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The coefficient of variation for 2012 is 20 %. While the coefficient of variation for 2013 is 15%.Therefor the donations in 2012 shows more dispersed distribution.

Here

for 2012  x=245, s = 49

for 2013 X = 480 ,s=72

CV for 2012 is

CV =S /x* 100% =(49 / 245)*100

CV = 20 %.

of cv for 2013 is

CV= (S /x)*100= (72 /480)*100

CV = 15%

The coefficient of variation for 2012 is 20 %. While the coefficient of variation for 2013 is 15%.Therefor the donations in 2012 shows more dispersed distribution.

The coefficient of variation (CV) is a statistical measurement used to compare the amount of variation in a set of data to the mean of the data. It expresses the variation as a percentage of the mean. The formula for CV is the standard deviation divided by the mean, multiplied by 100. CV is used to determine whether the data has a large or small amount of variation relative to its mean. A low CV indicates that the data is relatively consistent, while a high CV means that the data is more spread out. The CV is useful for comparing data sets with different units of measurement or data sets with different means. CV is commonly used in fields such as finance, economics, and quality control.

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To find the time it took Clare to ride 10 miles, we can use the concept of speed, which is defined as distance divided by time. In this case, Clare's constant speed was 15 miles in 72 minutes, so her speed is 15/72 miles per minute.

Using this speed, we can calculate the time it took her to ride 10 miles by dividing the distance by the speed:

Time = Distance / Speed

Time = 10 miles / (15/72 miles per minute)

Time = 10 * 72 / 15 minutes

Time = 43.2 minutes

So, it took Clare approximately 43.2 minutes to ride 10 miles at her constant speed of 15 miles in 72 minutes.

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The indicated quantity is a zero vector for the given vectors.

A vector is a quantity that has both magnitude and direction (numerical size). The inverse of a scalar, which is a quantity with just magnitude and no direction.

The vectors are given in the question, as follows:

u = <3,3>

v = <-5,1>

The vectors u = (3, 3) and v = (-5, 1) represent points in the x-y plane.

Let

u+v = <-2,4>

Now

(u+v).0 = <-2.0,4.0> = <0,0>

(u+v).0 = 0

Thus, the result is a zero vector.

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The value of the coordinate x will be 1 / 4 for the given unit circle.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that there is a unit circle in the image. The radius of the unit circle is equal to 1. The coordinate has the value of y is 3 / 4.

The value of the x-coordinate will be calculated as:-

x -coordinate = 1 - 3 / 4

x -coordinate = ( 4 - 3 ) 4

x -coordinate = 1 / 4

Therefore, the x-coordinate of the point is  1 / 4.

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Answer:

-7/4

Step-by-step explanation:

The value of y of a quadrilateral is 3.

A rectangle is a quadrilateral with four right angles, meaning that all of its angles measure 90 degrees. Given the information provided, the lengths of the left and right sides of the rectangle are equal to 10 and 2y + 4, respectively.

We also have the lengths of the top and bottom sides equal to 18 and 10 + 2x, respectively. However, we don't need to use the information about x as it does not affect the calculation for y.

To find the value of y, we can use the fact that the length and width of a rectangle must be equal. Therefore, we can set the length equal to the width:

10 = 2y + 4

Now that we have an equation, we can solve for y by subtracting 4 from both sides:

2y + 4 - 4 = 10 - 4

2y = 6

Finally, to find y, we can divide both sides of the equation by 2:

2y / 2 = 6 / 2

y = 3

Therefore, the value of y is 3.

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The base function before the transformation is f ( x ) = x³

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the base function be represented as f ( x )

Now , the equation will be

The transformed function is represented as p ( x )

The value of p ( x ) = ( x + 2 )³

So , we can see that the function p ( x ) has been shifted horizontally by a factor of 2 units to the left

So , the base function would be f ( x ) = ( x )³

On simplifying the equation , we get

The base function is f ( x ) = x³

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Answer:

9/2

Step-by-step explanation:

1 Simplify the expression

2 Subtract 6 from both sides

3 Simplify the expression

4 Divide both sides by the same factor

5 Simplify the expression

Answer:

1/2*4x +1/2*6=12

2x+3=12

2x=12-3

2x=9

x=9/2

The required equation that represents the relationship between students and adults ticket in the 2 graphs is given as a = -3s/5 -300 and s = -2a - 600.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

From the graphs,
Graphs 1
X intercept = (500, 0)
Y-intercept =(0, 300)

The equation is given as,
a - y₁ = (y₂ - y₁) /  (x₂ - x₁) (s - x₁)

Substitute the value in the above expression,
a - 0 = 300/-500 (s -500)
a = -3s/5 -300

Similarly,
The equation for graph 2 is given as,
s = -2a - 600

Thus, the required equation that represents the relationship between students and adults ticket in the 2 graphs is given as a = -3s/5 -300 and s = -2a - 600.

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The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approx b). 0.9428.

The intelligence quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. The standard deviation of the mean of a sample of 50 adults can be calculated as the population standard deviation divided by the square root of the sample size, or 15/√50 = 1.58.

Using a standard normal distribution table, the probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 can be calculated as the area under the standard normal curve between the z-scores corresponding to 98 and 103. These z-scores can be calculated using the formula z = (x - mean) / standard deviation, where x is the value of interest and mean is the population mean. The z-score for 98 is (98 - 100) / 1.58 = -1.27, and the z-score for 103 is (103 - 100) / 1.58 = 2.53.

The area under the standard normal curve between -1.27 and 2.53 can be found using a standard normal distribution table or a calculator with normal distribution functions. The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approximately 0.9228, which is closest to the answer choice b. 0.9428.

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The required stem-and-leaf plot shown below that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s.

A stem-and-leaf plot is a type of data display that helps to show the distribution of a set of numerical data.

here,
For the given data set:

Stem Leaf

0         4

1         1, 3, 3

2         0, 0, 0, 6, 7

3         0, 0, 0, 7

The stem-and-leaf plot shows that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s. The plot makes it easier to see the distribution of the data, rather than just looking at the raw values.

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The required inequality is 8x + 10y ≥ 56 which represents given the situation.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let x represent the number of hours babysitting and y represent the number of hours doing yard work,

The inequality that represents the situation is:

8x + 10y ≥ 56

This means that the total amount earned from babysitting (8x) plus the total amount earned from yard work (10y) must be greater than or equal to the cost of the skateboard ($56).

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The speed that Mr. Blacks used to drive to the friend's house would be = 13.3 mph.

The number of hours used by Mr Black to the friend's house = 2 hours

The speed that was used by Mr Black while returning from the friends house = 20 mph.

The number of hours it took to return = 1+2 = 3hrs

Then, if 20 mph = 3hrs

X. mph = 2 hrs

Make X the subject of formula;

X = 20×2/3

= 40/3

= 13.3 mph

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The equations of the asymptotes of the graph of f(x) = 4/(x + 1) + 11 are;

horizontal asymptote:  y = 11      

vertical asymptote: x = - 1

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.

The function we are given is expressed as;

f(x) = 4/(x + 1) + 11

From the attached graph of the function f(x) = 4/(x+1) + 11, it is clear that function will have two asymptotes which are;

horizontal asymptote:  y = 11      

vertical asymptote: x = - 1

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An equation that represents this situation is 5s + 10a = 3000.

By using the x- and y-intercepts, a graph of the function modeling the total number of tickets sold is shown in the image attached below.

In order to write a linear equation to describe this situation, we would a assign variable to the number of student tickets sold and the adult tickets sold respectively, and then translate the word problem into a linear equation as follows:

Since student are paying $5 while adults are paying $10 for a ticket and the athletic association need to raise $3000 by selling tickets, a linear equation that models the situation is given by:

5s + 10a = 3000

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Complete Question:

The Marshall High School Athletic Association sells tickets for the weekly football games. Students pay $5 and adults pay $10 for a ticket. The athletic association needs to raise $3000 selling tickets to send the team to an out-of-town tournament.

1. Write an equation that represents this situation.

2. Use x- and y-intercepts to graph the function modeling the total number of tickets sold on each coordinate plane.

y = x + 2 is the  other equation if its graph has a slope of 1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If the y-coordinate of the intersection point of the two equations is 2, and one of the equations is y = 3x + 5,

The other equation must be of the form y = mx + b, where m is the slope of the line and b is the y-intercept.

m=1 is the slope of the other equation.

y = mx + b

2 = 1x + b

b = 2 - 1x

b = 2 - x

So the other equation is y = x + 2.

Hence,  y = x + 2 is the  other equation if its graph has a slope of 1.

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The scale factor would be 8, that are required to dilate the trapezoid to have each area

The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them are given.

The formula is: A = ½ (a + b) h

where (A) is the area of the trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b).

We know that,

The scale factor for the area is found by squaring the scale factor for length.

The ratio of areas is the square root of the length.

6400÷ 100 =64

Scale factor of the trapezoid = √64 =8

So, the scale factor would be 8.

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The volume of the cylinder is 6.18 [tex]cm^3[/tex].

The volume of a cylinder—which corresponds to how much material can be transported inside of it or immersed in it—determines its density. The volume of a cylinder is calculated using the formula [tex]r^2h[/tex], where r is the radius of the circular base and h is the height of the cylinder. The material might be any substance that can regularly fill the cylinder with liquid or another substance.

Use the following formula to determine a cylinder's volume:

V = π[tex]r^2h[/tex]

where r is the radius of the cylinder (diameter / 2), h is the height of the cylinder, and π is approximately equal to 3.14.

First, find the radius:

r =[tex]\frac{ 1.26}{ 2}[/tex]

r = 0.63 cm

Next, find the volume:

V = π[tex]r^2h[/tex]

V = π[tex](0.63)^2(5.0)[/tex]

V= π * 0.3969 * 5.0

V= 3.14 * 0.3969 * 5.0

V = 6.18 [tex]cm^3[/tex] (rounded to 2 decimal places).

So, the volume of the cylinder is 6.18 [tex]cm^3[/tex].

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The mixed numbers of hours it takes Elisabeth to read 3/4 of the book is;  5³/₅ hours

A mixed number can be used to represent both a whole number and a lawful fraction. It frequently represents a number that lies either between two whole numbers. Look at the figure; it depicts a fraction that is greater than 1 but less than 2. Therefore, it is a mixed number.

We are informed that she reads 15 of her novels in 112 hours.

As a result, reading a book takes 112–15 hours.

As a result, the number of hours needed to finish reading the first third of the book is 3/4 * 112/15 = 28/5.

53 and 5 hours per book when expressed as a mixed number.

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Elisabeth needs 253 hours and 64/100 of an hour to read 34 books, which is stated as a mixed number in the simplest form as 253 3/5 hours.

In order to calculate the amount of time it takes Elisabeth to read 34 books, we need to calculate the amount of time it takes her to read 1 book first.

Since she reads 15 books in 112 hours, we can divide 112 by 15 to find the amount of time it takes her to read 1 book.

112 / 15 = 7.46

This means that it takes Elisabeth 7.46 hours to read 1 book.

Now we can multiply 7.46 by 34 to find the amount of time it takes her to read 34 books.

7.46 x 34 = 253.64

This means it takes Elisabeth 253.64 hours to read 34 books. Since this is a mixed number, we can convert it to its simplest form by subtracting the whole number from the decimal number and expressing it as a fraction.

253.64 - 253 = 0.64

Therefore, it takes Elisabeth 253 hours and 64/100 of an hour to read 34 books, which can be expressed as a mixed number in simplest form as 253 3/5 hours.

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