Given: AD, BE and FC intersect at point P. AD⊥FC.
Write at least 6 algebra equations to relate different pairs of angles. Justify your statements with the correct definition or theorem.

There is a 15.47% chance of selecting a red marble from the urn without looking.

The probability of choosing a red marble from the urn is expressed by the following formula:

P(Red Marble) = Number of Red Marbles / Total Number of Marbles

In this case, we are dealing with 13 red marbles, 33 blue marbles, and 38 yellow marbles. Therefore, the probability of choosing a red marble is 13/84, or 15.47%. We can calculate this by dividing the number of red marbles (13) by the total number of marbles (84). This means that there is a 15.47% chance of selecting a red marble from the urn without looking.

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When the potential costs of production are constant, the cost of creating one thing remains constant regardless of how much of that good is produced. This is also known as continuous returns to scale.

The term "constant" has several meanings in mathematics. It refers to non-variance as an adjective; as a noun, it has two meanings: A constant and well-defined integer or other mathematical object that does not change. A constant is a value or number whose expression never changes; it is always the same.

Here,

In this case, increasing the production of one good will result in a proportionate rise in the overall cost of production rather than an increase or decrease in the opportunity cost of producing that good. For example, if a corporation manufactures chairs and tables and the opportunity cost of manufacturing one chair is always two tables, the cost of making two chairs is four tables, the cost of producing three chairs is six tables, and so on.

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Answer:  In this situation, location should be a point of emphasis for marketing the new doggie day care business. As a new business in a town without a doggie day care facility, it is important for potential customers to be aware of the new facility's location. This will help people find the business and consider using it for their dog care needs. Additionally, the location of the business will likely impact its accessibility and convenience for customers, so it's important to make sure people know where it is. Once people are aware of the location, they can then consider other factors such as features, price, and service when deciding whether to use the business.

Step-by-step explanation:

The right answer is C, which means "number of square feet in area equals number of feet in perimeter."

A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. A rectangle is a quadrilateral with equal and parallel opposite sides. It is a four-sided polygon with four angles of 90 degrees. A rectangular form is two-dimensional. A rhombus is a quadrilateral with all sides the same length and both pairs of opposing sides parallel. The term rhomb is occasionally used instead of rhombus, and a rhombus is also known as a diamond.

Here,

area=6*3

=18 units

perimeter=2*(6+3)

=18 units

area=perimeter

The correct option is C that is "number of square feet in area is equal to number of feet in perimeter."

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[tex]5 \: boxes \: cost \: = \$ 12 \\ \therefore \: 1 \: box \: costs \: = \frac{\$12}{5} \\ \\ \longrightarrow \boxed{1 \: box \: costs \: = \$2.4}[/tex]

hope helpful! ;-;

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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Answer:

20.....

Step-by-step explanation:

Answer:

17.0

Step-by-step explanation:

17 is a whole number, so when rounding to the nearest tenth, it would still be 17.

Answer:

X = -2

Step-by-step explanation:

To find slope, it's

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

You're given two points

First one being (-9, -4) and second one being (x, 7). Both are these are in (x,y) form.

Let's plug it in.

[tex] \frac{11}{7} = \frac{7 - ( - 4)}{x - ( - 9)} [/tex]

^ Solving that, we get...

[tex] \frac{11}{7} = \frac{11}{x + 9} [/tex]

And that's because 7 minus a negative 4 means 7 + 4. Two negatives make a positive.

Now the top is good. 11 = 11.

The bottom says 7 = x + 9

If we were to subtract 9 from both sides... 7-9= -2, so

-2 = x

Hope this helps

The function represents the exponential decay. And the rate of change is 20%.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

y = a (1 ± r)ˣ

The exponent function is given below.

[tex]\rm m(t) = \left ( \dfrac{4}{5} \right)^t[/tex]

Compare the equation with the standard form. Then we have

If the value of the 1 - r is less than 1, then the rate is decaying.

1 - r = 4/5

r = 1 - 4/5

r = 1/5

r = 0.20 or 20%

The function represents the exponential decay. And the rate of change is 20%.

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The correct answer is option 2. Neither one is affected by skewness.

The IQR (Interquartile Range) and standard deviation are both measures of variability in a data set, but they are affected by different aspects of the data. The IQR is affected by the spread of the middle 50% of the data, while the standard deviation is affected by the spread of all the data points.

Skewness, or the asymmetry of a distribution, affects the mean and median of a data set but does not directly affect either the IQR or standard deviation. However, it can indirectly affect the measures if it is severe enough to cause the data to be spread more unevenly.

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Complete Question:

Which is more affected by skewness, the IQR or standard deviation?

we can express a trinomial as,

2x² + 5x + 6.

Where 2, 5, and 6 are non-zero real numbers.

2x², 5x,  and 6 are the three terms.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A trinomial is an expression that contains three on-zero terms separated by + or -.

Example:

ax² + bx + c

Where a, b, and c are non-zero real numbers.

Thus,

Trinomials can be 2x² + 5x + 3.

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Using Algebra, we concluded, there are 36 children.

The study of variables and the procedures for modifying variables in formulas is known as algebra, and it is the subject that underlies almost all of mathematics. All applications of mathematics require knowledge of elementary algebra since it deals with manipulating variables as though they were numbers.

In algebra, the fundamental concepts are numbers, variables, constants, expressions, equations, linear equations, and quadratic equations. Additionally, it requires adding, subtracting, multiplying, and dividing basic arithmetic operations within the algebraic formulas.

If there are X children at first

[tex]\frac{360}{x}+2=\frac{360}{x-6}[/tex]

360(x-6)+2x(x-6)=360x

360x-2160-12x=0

(X+30)(x-36)=0

So,x+30=0  x-36=0

X=-30, x=-36

Because X Great than or equal to 0

X=36

So there are 36 children at first.

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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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Answer:

435 cubic yards.

Step-by-step explanation:

Length x width x height.

Cut the shape into 2 parts.

Calculate the length for each.

13 yd - 5 yd = 8 yd

5 × 5 × 11 = 275

8 × 4 × 5 = 160

275 + 160

435 cubic yards

a) The distance of the boat from its starting point is 20 km.

b. The nearest degree  is 63°

c. The bearing g that the boat should travel on to return to the starting point is 360° - 63° = 297°.

To find the distance of the boat from its starting point, we can use the Pythagorean theorem.

x^2 + y^2 = d^2

Substituting the values for x and y, we get:

12^2 + 16^2 = d^2

d^2 = 144 + 256

d^2 = 400

d = 20

Hence, the distance of the boat from its starting point is 20 km.

b) To find the bearing that the boat should travel on to return to the starting point, we must calculate the angle between the two legs of the journey.

b = arctan (y / x) = arctan (16 / 12) = 63.43°

To the nearest degree  is 63°.

c) The bearing that the boat should travel on to return to the starting point is the opposite direction of the angle formed by the two legs of the journey. Therefore, the bearing is 360° - 63° = 297°.

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The inequality is solved to give n ≤ 530

It is important to note that algebraic expression are expressions that are composed of terms, variables, coefficients, factors and constants.

From the information given, we have that;

Nine less than the product of a number n and 1/5 is no more than 97

This is represented as;

1/5n - 9 ≤ 97

Now, collect like terms, we get;

1/5n ≤ 97 + 9

Add the like terms

1/5n ≤ 106

Now, cross multiply, we get;

n ≤ 106(5)

Multiply the values

n ≤ 530

Hence, the value is n ≤ 530

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Square inches formula is: }\\\\\large\boxed{\mathsf{l}\rm{ength}\times\mathsf{h}\rm{eight} = \mathsf{s}\rm{quare \ inches}}}}}}}[/tex]

[tex]\huge\text{So, your equation should look like:}[/tex]

[tex]\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}[/tex]

[tex]\huge\text{Now let us solve for your answer to this problem:}[/tex]

[tex]\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}[/tex]

[tex]\large\boxed{\mathsf{24\ inches\times 14\ inches = square\ inches^2}}[/tex]

[tex]\large\boxed{\mathsf{336 = square\ inches^2}}[/tex]

[tex]\huge\text{Therefore, your answer SHOULD be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ D. \ 336}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

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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Answer:

Below

Step-by-step explanation:

3/8 h = - 9    multiply both sides of the equation by   8/3

h = - 9 * 8/3 = - 24

The section of the pie showing the "yes" answers would have 162 degrees in a pie chart.

In a pie chart, the size of each section is proportional to the proportion of the data it represents. To calculate the size of the section showing the "yes" answers, we first need to find the proportion of "yes" answers in the total sample.

The proportion of "yes" answers can be calculated as:

(54 YES) / (54 YES + 39 NO + 27 no-opinion) = 54 / (120) = 9/20

In a pie chart, the proportion of each section is represented as a fraction of 360 degrees. So, to find the number of degrees in the "yes" section of the pie chart, we multiply 360 by the proportion of "yes" answers:

360 * (9/20) = 162 degrees

Therefore, the section of the pie showing the "yes" answers would have 162 degrees in a pie chart.

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In complex number,  that x ranges from -5 to -1/2 and the correct option is (-∞, -1/2)

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation [tex]{\displaystyle i^{2}=-1};[/tex]

every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes.

Given that,

|P| = 3x + 2

|Q| = 2x + 1

P+Q = -2

We know that, from Cauchy inequalities

|P| + |Q| > |P+Q|

3x + 2 + 2x + 1 > - 2

5x + 3 > - 2

subtract both side by 3

5x > -5

Divide both side by 5

x > -1 first condition

Note that,

|P| > 0

Then,

3x + 2 > 0

3x > -2

x > -2/3

Also,

|Q| > 0

2x + 1 > 0

2x > -1

x > -1/2

So, comparing the three conditions

We see that x ranges from -5 to -1/2, this range covers all the other ranges

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The probability that he or she has a visa card is 40%.

Probability is a mathematical concept that describes the likelihood of an event happening. In this case, the event is the selected individual having a visa card.

Let's assume that the individual has a total of n cards and v of those are visa cards. The probability of the individual having a visa card is given by the formula:

P(Visa) = v/n

This formula expresses the ratio of the number of successful outcomes (having a visa card) to the total number of possible outcomes (having any type of card).

The probability is expressed as a decimal or a percentage. If the individual has 5 cards and 2 of them are visa cards, then the probability of them having a visa card is

=> 2/5 = 0.4 or 40%.

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One possible pair could be "80 cm and 20 cm" if the side length of one triangle is 100 cm.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.

As we know that a triangle is considered a valid triangle if and only if the sum of the lengths of any two sides is greater than the length of the third side.

Given one side length of a triangle is 100 cm, the possible lengths of the other two sides would be any two numbers that add up to be greater than 100 cm.

Thus, one possible pair could be "80 cm and 20 cm" for the given triangle.

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The transformations are composed so that the sides of triangles are in the ratio of 1/2 and the angles are equal.

Similarity transformations are a sort of mathematical transformation that preserves the length ratios of related lines in a figure. Among these transformations are:

A translation is the movement of a figure in a given direction without affecting its size or shape. The combination of two translations results in a single translation equal to the total of the distances travelled.

A rotation is a transformation that involves turning a figure around a fixed point known as the center of rotation. The combination of two revolutions results in a single rotation equal to the total of the angles of rotation.

A reflection is a transition that occurs when a figure is flipped over a line known as the line of reflection. The combination of two reflections is simply a single 180-degree rotation.

Dilation: A dilation is a transformation that enlarges or reduces a figure by a given scale factor, centered at a fixed point. The product of two dilations is a single dilation equal to the product of the scale factors.

Here,

The sides of triangles are in ratio.

4/8=6/3=1/2

The composition of transformations is the sides of triangles are in ratio of 1/2 and angles are equal.  

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Therefore , the solution of the given problem of equation comes out to be

there Are Countless Solutions.

The equivalent indicator (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors using mathematical techniques, which have served as manifestations of reality. For example, the equal sign divides the number 12 or even the solution y + 6 = 12 in two different halves. How many characters already appear on either side of this symbol can be calculated. Conflicting symbol meanings occur frequently.

Here,

Each set of linear equations can have one of three different sorts of solutions.

Unique Solution are them.

No Answer.

There Are Countless Solutions.

Therefore , the solution of the given problem of equation comes out to be

there Are Countless Solutions.

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Functions f(x) and g(x) has same vertex and axis of symmetry. Therefore, option C and D are the correct answers.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(x)= -1/2 x² and f(x)=x².

Graph of g(x):

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex: (0,0)

Focus: (0,-1/2)

Axis of Symmetry: x=0

Directrix: y=1/2

Graph of f(x):

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0,0)

Focus: (0,1/4)

Axis of Symmetry: x=0

Directrix: y= -1/4

Therefore, option C and D are the correct answers.

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In this study, 60 undergraduate students were recruited to examine the effect of recycling on the amount of wrapping paper used to wrap a gift. The students were randomly assigned to one of two rooms, one with a recycling bin and one with a trash bin.

The researchers, who were secretly interested in measuring the amount of paper used, found that the students in the room with the recycling bin used significantly more paper than those in the room with the trash bin. This experiment suggests that the presence of a recycling bin may not have a significant effect on reducing the amount of wrapping paper used.

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Step-by-step explanation:

24×-1=

-24ans

and that's the answer

Answer:

-3(2x-5y+8)

Step-by-step explanation: