in triangle XYZ, X = 32°, x = 9 cm, and y = 15cm. Determine the length of side z. Round to the nearest hundredth. (Hint: check for the number of possible triangles, SSA)

Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

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Answer:

4, 15, 16, 17, 19, 21, 22

Step-by-step explanation:

The mode of the data set is 7

The median is 6

the mean is 5.2

The range is 7

This is the number with the highest frequency or occurrence. This is 7

arrange based on ascending order

1, 2, 3, 4, 5, 7, 7, 7, 8, 8

median = 5 + 7 / 2

= 6

add all the numbers / total number

52 /10

= 5.2

The range = highest - lowest

= 8 - 1

= 7

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Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

The solutions to the system are -1 and 3.

What is system of equations?

equations simultaneously, or a system of equations Multiple equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). There must be an equal number of equations and unknowns for a system to have a singular solution. Even then, a solution may not be assured.

Given : y = x + 5  ... equation 1

           y = x² – x + 2 ...equation 2

Putting  y=x+5 in equation 2

We get, x+5 =  x² – x + 2

             x² - x - x +2 -5 = 0

             x² -2x - 3 = 0

It can written be solved as :

                x² -2x - 3 = 0

                x² -3x +x - 3 = 0

                x ( x-3) + 1(x-3) = 0

                (x+1) (x-3) = 0

So, x = -1 and 3.

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Answer:

Step-by-step explanation:

1500+7y > 4700 can be solved algebraically to find the value of y that satisfies the inequality.

First, we need to isolate the variable y on one side of the inequality by subtracting 1500 from both sides:

1500 + 7y - 1500 > 4700 - 1500

Simplifying the left-hand side:

7y > 3200

Finally, we isolate y by dividing both sides by 7:

y > 3200/7

Therefore, the solution to the inequality is y > 457.14 (rounded to two decimal places).

The Congruency Postulates for each of the given triangle are:

1) SAS Congruency

2) AAS Congruency

3) HL Congruency

4) Not enough Information

5) AAS Congruency

There are different congruency postulates such as;

SSS: Side Side Side Congruency

SAS: Side Angle Side Congruency

ASA: Angle Side Angle Congruency

AAS: Angle Angle Side Congruency

HL: Hypotenuse Leg Congruency

1) We are given two triangles with two congruent sides and the included angle and as such it is congruent by SAS Congruency Postulate.

2) We are given two congruent angles and the included side and as such they are congruent by AAS Congruency Postulate.

3) We are given the hypotenuse and leg as congruent and as such we can say that they are congruent by HL Congruency Postulate.

4) We are given two congruent sides and the non-included angle and as such they are not congruent by any congruency postulate.

5) We are given two congruent angles and the non-included side and as such they are congruent by AAS Congruency Postulate.

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Check the picture below.

The length of the measurements are;

EF = 7. 1 units

DE = 7. 0 units

Using the sine trigonometric identity, we have that;

sin θ = opposite/hypotenuse

Given that;

Opposite side = DE

Hypotenuse = DF

Substitute the values

sin 45 = DE/10

Find the value and substitute

DE = 0. 7071(10)

DE = 7. 0

Using the Pythagorean theorem;

EF² = 10² - 7²

find the square value

EF = √ 51

EF = 7.1

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Therefore, the length of AC is √(145) inches.

A triangle is a three-sided polygon, which means it is a flat shape with straight sides. It is the simplest polygon, consisting of three line segments connected end-to-end. The corners where the sides meet are called vertices, and the line segments themselves are called edges or sides. The interior angles of a triangle always add up to 180 degrees. Triangles can be classified according to the lengths of their sides and the sizes of their angles. Common types of triangles include equilateral triangles, isosceles triangles, scalene triangles, acute triangles, right triangles, and obtuse triangles.

Here,

        A

       / \

      /   \

     /     \

    / B    C

   /_|\___/ \

  D       E   \

Since triangle ABC is right-angled at B, we know that angle BAC is a right angle. We can use this fact to find the length of AC by applying the Pythagorean theorem. Let x be the length of AC:

AC² = AB² + BC² (by the Pythagorean theorem)

AC² = AD² + BD² + BC² (by the definition of right triangles)

AC² = AD² + CD² + BC² (since BCD = DCA)

AC² = AE² + EC² + CD² (since BAE = EAC)

AC² = 9² + EC² + 8² (since AE = 9 inches and CD = 8 inches)

Now we need to find EC. We can use the fact that BAE = EAC to find the relationship between AE and EC. Let y be the length of BE:

AE/BE = AC/BC (by the angle bisector theorem)

9/y = x/(BC-y) (substituting the given values)

9(BC-y) = xy

BCy - y² = (9/ x) y²

Next, we can use the fact that BCD = DCA to find the relationship between BD and DC. Let z be the length of AD:

BD/DC = BA/AC

(BD/DC) = (AB/AC) (since B is the right angle)

BD/8 = (x²)/(x² + 8²)

Now we have two equations with two variables (y and z). We can use substitution to solve for one variable in terms of the other. Let's solve for y in terms of z from the first equation:

BCy - y² = (9/x) y²

BCy = y² (9/x + 1)

y(BC - y) = y² (9/x + 1)

y² (BC - y - (9/x + 1)) = 0

Since y cannot be zero, we must have:

BC - y - (9/x + 1) = 0

BC - y = 9/x + 1

Now let's substitute this expression for y into the second equation:

BD/8 = (x²)/(x² + 8²)

BD = (8x²)/(x² + 64)

Since BCD = DCA, we have:

BD/CD = BC/AC

(8x²)/(x² + 64) / 8 = BC/x

BC = x² / (x² + 64)

Now we can substitute this expression for BC into the equation we derived earlier:

BC - y = 9/x + 1

x²/(x² + 64) - y = 9/x + 1

Substituting the value we derived for BD into the equation, we get:

x²/(x² + 64) - 8x²/(x² + 64) = 9/x + 1

Simplifying, we get:

x² = 145

x = √(145)

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The y-value of the solution of the system of equations is given as follows:

y = -1.

The system of equations for this problem is defined as follows:

Adding the two equations, the value of y can be obtained as follows, as the x-variable is eliminated:

6y = -6

y = -6/6

y = -1.

Hence option F is correct.

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Answer:

A. 2.50x + 85 < 125.

Step-by-step explanation:

Let x be the number of cans of tennis balls that Joseph wants to buy.

The total cost of the tennis racket and x cans of tennis balls is:

Cost = 85 + 2.5x

Joseph wants to make sure that he spends less than $125, so we can set up the inequality:

85 + 2.5x < 125

Simplifying this inequality, we get:

2.5x < 40

x < 16

So Joseph can buy at most 15 cans of tennis balls if he wants to spend less than $125.

However, the question asks for the correct inequality, and the inequality that correctly represents this situation is:

2.50x + 85 < 125

Therefore, your answer is gonna be A. 2.50x + 85 < 125.

Answer: "B"

Step-by-step explanation:

Joseph wants to buy some tennis balls. Which costs 2.50$ and tennis racket costs 85$

then, 2.50x+85<125

The value of y when x=3 is y=7. Point A on the graph corresponds to x=3 and y=7.

What is graph ?

A graph is a visual representation of data or mathematical functions. Graphs are used to display data in a way that is easy to understand and interpret. There are many types of graphs, including line graphs, bar graphs, pie charts, scatter plots, and more. Each type of graph has its own unique features and is used for different purposes. Graphs are commonly used in many fields, including science, economics, finance, and engineering, among others, to visualize data and communicate information in a clear and concise way.

According to the question:

a) If x = 3, then:

y = x² - 2

y = 3² - 2

y = 9 - 2

y = 7

Therefore, when x = 3, y = 7.

b) From the graph, we can see that the point (3,1) corresponds to x = 3 and y = 1. Therefore, point A is the correct point on the graph that corresponds to x = 3 and y = 7.

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The slope m of the first equation is [tex]-\frac{4}{3}\\[/tex] and the y-intercept b is -5 and slope m of the second equation is 1 and the y-intercept b is 2.

The formula for a straight line is y=mx+b where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.

To find the slope-intercept form of the equations and their graphs, we need to solve for y in each equation.

[tex]$$4x+3y=-15$$$$3y=-4x-15$$[/tex]

[tex]$y=-\frac{4}{3}x-5$[/tex]

So the slope m of the first equation is [tex]-\frac{4}{3}\\[/tex] and the y-intercept b is -5.

For the second equation,

24y=24x+48

y=x+2

So the slope m of the second equation is 1 and the y-intercept b is 2.

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Answer:

the slop is 2

Step-by-step explanation:

i just calculated it a minute ago

Answer:

it will cost $520.00 to install the gravel path.

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of the diagonal of the rectangular garden. The Pythagorean theorem states that the square of the length of the hypotenuse (in this case, the diagonal) of a right triangle is equal to the sum of the squares of the lengths of the other two sides. Therefore, we have:

diagonal^2 = 24^2 + 32^2

diagonal^2 = 576 + 1024

diagonal^2 = 1600

Taking the square root of both sides, we get:

diagonal = sqrt(1600)

diagonal = 40 feet

Now, we need to calculate the area of the path that Jorge will install. Since the path is 2 feet wide, the width of the garden is reduced by 4 feet (2 feet on each side). Therefore, the length and width of the garden after the path is installed will be:

length = 24 - 4 = 20 feet

width = 32 - 4 = 28 feet

The area of the path is the difference between the area of the garden before and after the path is installed:

area of path = (24 * 32) - (20 * 28)

area of path = 768 - 560

area of path = 208 square feet

Finally, we can calculate the cost of the gravel path by multiplying the area of the path by the cost per square foot:

cost of path = 208 * 2.50

cost of path = $520.00

Therefore, it will cost $520.00 to install the gravel path.

Therefore, using the rule of 72, it would take approximately 9 years for Sofia's $18,000 investment to double at a rate of 8% in interest.

Percent is a term used to describe a value that is a fraction of 100. It is often represented by the symbol "%".  Percentages are commonly used to express rates, ratios, and proportions in many fields, including finance, science, and everyday life. They are often used to describe changes in value, such as increases or decreases in prices, population, or other quantities over time.

Here,

The rule of 72 is a simple formula used to estimate the time it takes for an investment to double in value based on its rate of return. To use this rule, divide 72 by the annual percentage yield (APY) to get an estimate of the number of years it would take for the investment to double.

In this case, the APY is 8%, so we can apply the rule of 72 as follows:

Number of years to double = 72 / APY

= 72 / 8

= 9 years

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Polynomials consist of variables, constants and exponents.

(6x - 1)/ 6x is not a polynomial.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The expression is given as:

⇒ (6x - 1)/ 6x

Hence, We can Split the expression as;

⇒ (6x - 1)/ 6x

⇒ 6x/6x - 1/ 6x

⇒ 1 - 1/6x

Simplify as;

⇒ 1 - (1/6)x⁻¹

Thus, The smallest exponent of a polynomial is 0.

And, The above expression has a negative exponent of x.

Hence, The expression is not a polynomial.

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Answer:

[tex]71.43[/tex]

Step-by-step explanation:

[tex]5 b+ 2 b\geqslant 500 \\ 7b \geqslant 500 \\ \frac{7b}{7} \geqslant \frac{500}{7} \\ b \geqslant 71.43 \\ [/tex]

[tex] b= 71.43 < \infty [/tex]

Addition of the 3 projections will be: (-2.268, 0.168, -1.536)

A matrix is a rectangular array of values that are defined for addition, subtraction, and multiplication among other mathematical operations. The number of rows and columns in a matrix, also known as the order of the matrix, defines the size of the matrix. The order of a matrix with 6 rows and 4 columns is shown when written as a 6 4 and read as 6 by 4.

To find the projection of b onto a3, we use the projection formula:

proj a3(b) = (b dot a3 / [tex]||a3||^2[/tex]) * a3

where "dot" represents the dot product and "|| ||" represents the magnitude or norm.

We first find the dot product:

b dot a3 = (0)(23) + (3)(-13) + (0)(23) = -39

Next, we find the norm of a3:

[tex]||a3||^2 = (23)^2 + (-13)^2 + (23)^2 = 1388[/tex]

Using these values, we can compute the projection:

proj a3(b) = (-39 / 1388) * (23, -13, 23) = (-0.768, 0.436, -0.768)

Similarly, we can find the projections of b onto a1 and a2:

proj a1(b) = (-3 / 14) * (2, 4, 4) = (-3/7, -6/7, -6/7)

proj a2(b) = (3 / 18) * (-3, 3, 0) = (-1/2, 1/2, 0)

Finally, we add the three projections:

(-3/7, -6/7, -6/7) + (-1/2, 1/2, 0) + (-0.768, 0.436, -0.768) = (-2.268, 0.168, -1.536)

To see why P = a1aT1 +a2aT2 +a3aT3, we note that each projection can be written in matrix form:

proj_a1(b) = a1(aT1b)

proj_a2(b) = a2(aT2b)

proj_a3(b) = a3(aT3b)

where aT represents the transpose of a. Using these expressions, we can write:

P = a1(aT1b) + a2(aT2b) + a3(aT3b)

= [a1 a2 a3] [aT1b aT2b aT3b] (by distributing the dot product)

= [a1 a2 a3] [b] (since the aT's are row vectors that multiply with b to form a scalar)

= abT

where abT is the outer product of a and b, which is a matrix. This matrix is the projection matrix that projects vectors onto the subspace spanned by the columns of A.

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Answer: Para resolver el ejercicio se plantea un diagrama de conjuntos, en el

   cual se representan un conjunto A y B ( Ver dibujo adjunto  ) .

        b +x = 46%           a + x = 60%           a + b = 58%

    Al sumar las dos ecuaciones :

       b + x = 46%

       a + x=  60%

--------------------------

   a + b +2x = 106%

      58% + 2x = 106%

                 2x = 106% - 58%

                 2x = 48%

                   x = 48%/2

                   x = 24%   no leen ninguna de las dos revistas

       c = 63000 personas   que leen A y B

       se llama al total de personas y :

       y * 18% = 63000 personas

       y = 63000 / 18%

       y = 63000/0.18 = 350000 son las personas hay en Trujillo

Se compraron 500 panes, pero solo se utilizó el 75%, lo que significa que se consumió el 100% - 75% = 25% de los panes. Para calcular la cantidad de panes que se consumió, podemos multiplicar la fracción de panes consumidos (25% o 0.25) por el número total de panes:

0.25 x 500 = 125

Por lo tanto, se consumieron 125 panes en el cóctel.

The probability of exactly 5 out of the next 10 children getting Huntington's disease is 0.2461, and the probability of exactly 7 getting the disease is 0.1172.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

This problem can be solved using the probability , where we have a fixed number of trials (10 children) and a fixed probability of success (one-in-two chance of getting the disease).

The probability of getting exactly k successes in n trials, each with probability p of success, is given by the binomial probability formula:

P(k) = (n choose k) * [tex]p^k * (1-p)^{(n-k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of a set of n.

For this problem, we have n = 10, p = 1/2 (since the children have a one-in-two chance of getting the disease), and we want to find P(5) and P(7).

P(5) = (10 choose 5) * ([tex]1/2)^5 * (1/2)^{(10-5)} = 0.2461[/tex] (rounded to four decimal places)

P(7) = (10 choose 7) * [tex](1/2)^7 * (1/2)^{(10-7)} = 0.1172[/tex] (rounded to four decimal places)

Hence, The probability of exactly 5 out of the next 10 children getting Huntington's disease is 0.2461, and the probability of exactly 7 getting the disease is 0.1172.

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Simple interest is based on principal only and Compound interest is based on principal and interest both. Then the correct option is C.

Let P be the principal, r be the rate of interest, and n be the number of years. Then the interest rate is given as,

The formula for simple interest is written as,

I = (P × r × n)/100

The compound interest is given as

A = P(1 + r)ⁿ

Simple interest is computed just on the principle. Compound interest is interest calculated on both the initial principal and any accrued interest.

Thus, the correct option is C.

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The number of different types of movies that Lavar can buy according to the inequality m > 15 is action and comedy.

What is meant by inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. However several inequalities are utilised to compare the numbers, whether it is less than or higher than. An inequality symbol has non-equal expressions on both sides. It indicates that the expression on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

The complete question is given below.

The inequality to be used is m > 15.

Now we will look into each genre to select which movies he could buy.

There are 18 action movies.

m = 18 > 15.

There are 18 comedy movies as well.

m = 18 > 15

There are 12 drama movies.

but m = 12< 15

There are 15 thriller movies.

But the given inequality allows only categories with a number of movies greater than 15 and not equal to 15.

Therefore the number of different types of movies that Lavar can buy according to the inequality m > 15 is action and comedy.

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The coordinates of the image of triangle △TUX after dilation with center at (0,0) and scale factor 4, then applying the transformation (x, y) ⟶ (x − 3, y + 1) are T''(25, 25), U''(-35, 13), and X''(5, 5).

Dilation with center refers to a transformation that involves scaling a geometric shape around a fixed center point. The center of dilation is the fixed point around which the shape is being scaled.

Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes in a coordinate plane. It combines the principles of geometry and algebra, where geometric shapes can be represented using algebraic equations and coordinates.In coordinate geometry, points are located in a two-dimensional plane using a system of Cartesian coordinates, which consists of an x-axis and a y-axis perpendicular to each other.

In the given question,

To find the coordinates of the image of triangle △TUX after dilation with center at (0,0) and scale factor 4, we first need to find the coordinates of the image of each point after the dilation.

The image of a point (x, y) after dilation with center at (0,0) and scale factor 4 can be found by multiplying its coordinates by 4. So:

The image of T(-7, -6) is T'(-74, -64) = (28, 24).

The image of U(-8, 3) is U'(-84, 34) = (-32, 12).

The image of X(2, 1) is X'(24, 14) = (8, 4).

Next, we apply the transformation (x, y) ⟶ (x − 3, y + 1) to find the coordinates of the final image of the triangle.

The image of T' is T'' = (T'x - 3, T'y + 1) = (28 - 3, 24 + 1) = (25, 25).

The image of U' is U'' = (U'x - 3, U'y + 1) = (-32 - 3, 12 + 1) = (-35, 13).

The image of X' is X'' = (X'x - 3, X'y + 1) = (8 - 3, 4 + 1) = (5, 5).

Therefore, the coordinates of the image of triangle △TUX after dilation with center at (0,0) and scale factor 4, then applying the transformation (x, y) ⟶ (x − 3, y + 1) are T''(25, 25), U''(-35, 13), and X''(5, 5).

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The line of equation which passes through (-5, 3) and (-2, -3) is 2x+y+7=0.

A line of equation is an equation that represents a straight line on a coordinate plane.

The Straight line equation is: y = mx + b

Here y is the dependent variable, x is the independent variable, m is the slope of the line, and constant b is the y intercept.

The equation of line is:

[tex]y-y_{1} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} (x-x_{1} )[/tex]

Given that, ([tex]x_{1}, y_{1}[/tex]) = (-5, 3) and ([tex]x_{2}, y_{2}[/tex]) = (-2, -3)

By putting the values in above equation,

[tex]y-3 = \frac{-3-3}{-2+5} (x+5)\\[/tex]

y-3 = -2x-10

2x+y+7 = 0

Therefore the line equation is 2x+y+7 = 0.

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( N c ∩ D ) ∪ ( N ∩ D c ) This set represents the people surveyed who subscribe to exactly one of the two news sources given.

Surveyed means to gather information or feedback from a specific group of people through interviews, questionnaires, or other methods of data collection. Surveying can be used to gain insights into opinions, attitudes, and behaviors of a certain population or group. Surveying helps to provide information on topics such as public opinion, market research, and customer needs.

It is a combination of two sets, the first being the set of people surveyed who do not subscribe to The Daily Informer but subscribe to News Magazine, and the second being the set of people surveyed who subscribe to The Daily Informer but not to News Magazine.

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Answer:

-x.

Step-by-step explanation:

1) the equation of the line in slope-interception form is: y=slope*x+interception;

2) according to the graph and data in the condition slope=-1, interception=0, then the requred equation is:

y=-x.