Complete the following two column proof

If P(C) = 5/17, then the probability of event C occurring is 5/17.

To find the probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes. The result is a number between 0 and 1 (inclusive) that represents the likelihood of the event occurring.

More formally, the probability of an event A can be calculated using the following formula:

P(A) = number of favorable outcomes for A / total number of possible outcomes

For example, if you roll a fair six-sided die, the probability of rolling a 4 is 1/6 because there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

It's important to note that the above formula assumes that all outcomes are equally likely. In some cases, such as when dealing with biased or weighted dice, the probability of an event may need to be calculated using a different method.

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The sum to infinity of the sequence is 96/13

Every term in a geometric sequence is obtained by multiplying the term before it by the same number. [tex]\mathrm{a_n= a_1 r^{n -1 }}[/tex] is the general term for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the term before it.

Given the nth term of a geometric sequence expressed as:

Tn = Σ12(-5/8)ⁿ

The sum to infinity of the sequence is expressed as;

S∞ = a/1-r

where

a is the first term = 12

r is the common ratio = -5/8

Substitute

S∞ =  12/1-(-5/8)

S∞ = 12/1+5/8

S∞ = 12/(13/8)

S∞ =12 *8/13

S∞ = 96/13

Hence, the sum to infinity of the sequence is 96/13

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The 1 1/2 cups divided by 2 is 0.75  cups

Division is the opposite of multiplication. If 3 groups of 4 are multiplied by 12, then dividing 12 into 3 equal groups yields 4 in each group when divided.

Dividend: The dividend is the number that is being divided in the division process.

Divisor: The number by which the dividend is being divided by is called the divisor.

Quotient: The quotient is a result obtained in the division process.

Remainder: Sometimes, we cannot divide things exactly. There may be a leftover number. That leftover number is called the remainder.

The relationship between these four parts can be expressed as follows:

Dividend = Divisor x Quotient + Remainder

The main purpose of sharing is to see how many equal groups form, or how many people belong to each group, when sharing equitably.

In the above example, to divide the 12 donuts into 3 similar groups, we need to place 4 donuts in each group. So dividing 12 by 3 gives 4.

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Answer:

Below

Step-by-step explanation:

Since it is a QUADRATIC  it should be

3x^2 - 75 = 0    divide through by 3 to get

x^2 - 25 = 0       then

x^2 = 25

x = ±5

Answer: x = 0, Y = 2    

              x = 1, Y = 5

Step-by-step explanation:

Y = −3x^2 + 6x + 2

Y = 3x + 2

We can set the two equations equal to each other, since they both equal Y:

−3x^2 + 6x + 2 = 3x + 2

−3x^2 + 3x = 0

 3x(-x + 1) = 0

This gives us two possible solutions:

x = 0

x = 1

When x = 0, Y = 3(0) + 2 = 2

When x = 1, Y = 3(1) + 2 = 5

Therefore, the solutions to the system of equations are:

x = 0, Y = 2

x = 1, Y = 5

The volumes of the given cube and rectangular prisms in cubic centimeters are:

1) Cube with a side length of 2/5 cm: 8/125 cm^3

2) Rectangular prism with a length, width, and height of 3/5 cm, 4/5 cm, and 3/5 cm respectively: 36/125 cm^3

3) Rectangular prism with a length, width, and height of 1/5 cm, 2/5 cm, and 3.5 cm respectively: 6/125 cm^3

4) Cube with a side length of 1/5 cm: 1/125 cm^3

To find the volume of a cube or rectangular prism, you need to use the formula:

Volume = length x width x height

The length, width, and height represent the three dimensions of the object, which are measured in units such as centimeters, meters, or inches. To find the volume in cubic centimeters, you would use centimeters as your unit of measurement.

For example, let's say we have a cube with a side length of 2/5 cm. To find the volume, we would use the formula:

Volume = length x width x height

Volume = 2/5 cm x 2/5 cm x 2/5 cm

Volume = 8/125 cm^3

So the volume of this cube is 8/125 cubic centimeters.

Similarly, for the other pairs:

Rectangular prism with a length, width, and height of 3/5 cm, 4/5 cm, and 3/5 cm respectively:

Volume = length x width x height

Volume = 3/5 cm x 4/5 cm x 3/5 cm

Volume = 36/125 cm^3

Rectangular prism with a length, width, and height of 1/5 cm, 2/5 cm, and 3.5 cm respectively:

Volume = length x width x height

Volume = 1/5 cm x 2/5 cm x 3.5 cm

Volume = 6/125 cm^3

Cube with a side length of 1/5 cm:

Volume = length x width x height

Volume = 1/5 cm x 1/5 cm x 1/5 cm

Volume = 1/125 cm^3

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The given question is incomplete, the complete question is :

D rag the tiles to the correct boxes to complete the pairs. Find the volume of the cubes or rectangular prisms in cubic centimeter's answers: 6/125 cm^3, 36/125 cm^3, 8/125 cm^3, 1/125 cm^3.the pairing questions are :cube with a side length of 2/5 cm,,,, rectangular prism with a length width and height of 3/5 cm 4/5 cm and 3/5 cm respectively.,,, rectangular prism with a length width and height of 1/5 cm, 2/5 cm, and 3,5 cm respectively and cube with a side length of 1/5cm.

The simplified expression is [tex]4.0 \times 10^{32}[/tex]

A mathematical statement without an equals sign that contains variables, constants, and mathematical operations is known as an algebraic expression. Algebra and other branches of mathematics both employ algebraic expressions to represent mathematical connections.

Simple algebraic expressions include x + 2, which consists of the addition operation, the constant (2), and the variable x. Several variables, constants, and operations can be found in more complicated algebraic formulas, like 2x2 + 3xy - 4.

Whereas constants are fixed values that never change, variables in algebraic expressions indicate unknowable values that can vary or change. Variables and constants are combined using mathematical operations including addition, subtraction, multiplication, and division.

In several academic disciplines, such as physics, chemistry, economics, and engineering, algebraic expressions are employed to solve issues. Moreover, they are used to manipulate and simplify mathematical formulas and equations as well as to mimic actual life circumstances.

By combining like terms, or terms with the same variable raised to the same power, algebraic expressions can be made simpler. For instance, the like words 3x and 2x in the equation 3x + 2x + 5 can be combined to create 5x, resulting in the abbreviated expression 5x + 5.

[tex]2\times 2 \times 10 = 20\times 2[/tex]

Next, we can use the rule that when we multiply two numbers with the same base, we add their exponents. Therefore:

[tex]10^{58} \times 10^{-27} = 10^{(58-27)} = 10^{31}[/tex]

Putting it all together:

[tex](2\times 2 \times 10) \times (10^{58} \times 10^{-27}) = 20\times 2 \times 10^{31} = 40\times 10^{31} = 4.0 x 10^32[/tex]

Therefore, the simplified expression is [tex]4.0 \times 10^{32}[/tex]

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A number z divided by 2 is at least -6 is expressed as z ÷ 2 = ≥ -6

One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal parts. Every day, we might use the division technique in various situations.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.

On a fundamental level, counting the instances in which one number is contained within another is one interpretation of the division of two natural numbers. 7 It's not necessary for this number to be an integer.

The expression to represent this problem is:

z ÷ 2 = ≥ -6

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The number outcomes in the sample space is option (3) 64

In mathematics, combination is a way of selecting a group of objects from a larger set, where the order in which the objects are selected does not matter.

The number of outcomes in the sample space can be calculated by finding the total number of possible combinations of genders for the six children.

For each child, there are two possible genders: male or female. Therefore, the number of possible outcomes for one child is 2.

To find the total number of outcomes for six children, we need to multiply the number of possible outcomes for each child together:

2 × 2 × 2 × 2 × 2 × 2 = 64

Therefore, the correct option is (3) 64

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10m for the 1st floor. 7.32m for the 2nd floor.

What is the Trigonometry?

Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.

Let the point where the man is standing on window be A.

Let the point where the dustbin is there be B.

Let the foot of the building be C.

So, according to the given details,

CB = 10m.

angle (ABC)= 45 degrees.

Let the point of the 2nd floor be P.

We must understand what the angle of depression is: It is the angle measured below the horizontal level.

In triangles ABC and PBC, we use trigonometric ratios as follows:

[tex]tan(45) = AC/BC\\\\AC = BC = 10cm.\\tan(60) = CP/BC\\\\CP = BC\sqrt[2]{3}\\CP = 10\sqrt[2]{3}\\ CP = 17.32m. \\\\2ndfloorheight = CP - AC = 7.32m[/tex]

Hence, 10m for the 1st floor. 7.32m for the 2nd floor.

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True. Rational functions are defined as the division of two polynomials. These functions are limited in their scope and, as a result, have specific properties. One such property is the existence of vertical asymptotes.

Vertical asymptotes occur when the denominator of a rational function approaches zero, resulting in a discontinuity in the graph of the function, or a point at which the function can approach but never reach. This creates a divide in the graph, resulting in two halves with a vertical line at the point where the denominator equals zero. This vertical line is the vertical asymptote of the rational function. In conclusion, all rational functions have vertical asymptotes due to their limited scope and specific properties.

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To divide polynomials by a monomial written in standard form, you can divide each term of the polynomial by the monomial separately. Applying this to the given expression, we get:

(30c^8d^3 - 3bc^6d^2 + 6c^8d) / (12c^2d)

= 30c^8d^3/(12c^2d) - 3bc^6d^2/(12c^2d) + 6c^8d/(12c^2d)

= 2.5c^(8-2)d^(3-1) - 0.25bc^(6-2)d^(2-1) + 0.5c^(8-2)d^(1-1)

= 2.5c^6d^2 - 0.25bc^4d + 0.5c^6

= 5c^6d^2 - 0.5bc^4d + c^6/2

Therefore, the simplified expression is 5c^6d^2 - 0.5bc^4d + c^6/2.

Answer:

An important step in the process of translation is lexical analysis, which involves identifying and analyzing the individual words in a text. Lexical analysis is used to determine the meaning of words in the context in which they are used, allowing a translator to accurately render the text into the target language. Additionally, lexical analysis is used to identify any potential ambiguities in the text, which can be important for ensuring that the translation is as accurate as possible.

[tex]\frac{1}{10}[/tex] of electricity is made up of other resources and it can be found by addition and subtraction of fractions.

Examine the fractions' denominators. Find the LCM of the denominators and rationalise them to make the denominators of the fractions the same. Add the fraction numerators while keeping the denominator constant. To get the final sum, simplify the fraction.

To subtract fractions, first calculate the denominator's LCM. Step 2: Multiply the numerator and denominator by the same number to get the LCM value. Step 3: When the denominator and numerator are equal, subtract the numerator. Step 4: If necessary, simplify the resulting fraction.

[tex]\frac{5}{10} + \frac{2}{10} + \frac{2}{10} + x = 1.\\\frac{9}{10} + x = 1.\\\frac{10x+ 9}{10} = 1\\10x + 9= 10\\x= \frac{1}{10}[/tex]

hence, 1/10 of the electricity is made up of other resources.

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For each point, their position with respect to its location on the circle are as follows;

(4, 0) will be located inside the circle.

(-3, 3) will be located outside the circle.

(-2, -2) will be located on the circle.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

In this exercise, we would use an online graphing calculator to plot the equation of this circle as shown in the image attached below.

(x - 2)² + (y - 1)² = 25

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Refer to the attached image.

The rule for the graph of g is g(x) = -4(x^2-3). This graph is a vertical stretch by a factor of 4 and a reflection in the x-axis of the graph of f(x) = x^2-3.

The volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8 is approximately 1483.6 cubic units.

To find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8, we can use the method of cylindrical shells.

To find the volume of the solid, we need to integrate the area of each cylindrical shell over the height of the solid. Let r be the radius of a cylindrical shell at height y, and let h be the thickness of the shell. Then the volume of the shell is given by:

dV = 2πrh × h

where the factor of 2 comes from the fact that there are two cylindrical shells (one on either side of the line x = 8).

We can express r and h in terms of y:

r = 8 - y

h = e^8 - e^-x

Substituting these expressions into the formula for dV and integrating from y = 0 to y = 1, we get,

V = ∫(0 to 1) 2π(8 - y)(e^8 - e^-x) dy

= 2π ∫(0 to 1) (8e^8 - 8e^-x - ye^8 + ye^-x) dy

= 2π [8e^8 - 8e^-1 - (1/2)e^8 + (1/2)e^-1]

= 2π [15e^8 - 4e^-1]

≈ 1483.6 cubic units

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The given question is incomplete, the complete question is:

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8.

The volume of an aquarium is 2071.875 cubic inches. Below, you will learn how to solve the problem.

The volume of an aquarium can be calculated by multiplying its length, width, and height. In this case, the length is 19 1/2 inches, the width is 8 1/2 inches, and the height is 12 1/2 inches.

To calculate the volume, we need to multiply these three measurements together:

Volume = Length × Width × Height
Volume = (19 1/2) × (8 1/2) × (12 1/2)
Volume = 2071.875 cubic inches

So the volume of the aquarium is 2071.875 cubic inches.

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Calculator with inverse tangent is a calculator with  four basic arithmetic operations and variety of functions such as logarithms, exponents, trigonometric functions etc.

A calculator with inverse tangent, commonly known as a scientific calculator, is a type of electronic calculator designed to perform mathematical calculations beyond basic arithmetic. In addition to the four basic arithmetic operations (addition, subtraction, multiplication, and division), it includes a variety of functions such as logarithms, exponents, trigonometric functions (sine, cosine, tangent), and their inverse functions (arcsine, arccosine, and arctangent).

The inverse tangent function, also known as arctangent, is one of the trigonometric functions that is commonly included in scientific calculators. It is used to determine the angle between the x-axis and a line drawn between the origin and a point on the graph of a function. In other words, it helps to find the angle whose tangent is a given number.

To use the inverse tangent function on a calculator, you will typically need to press the "tan^-1" or "arctan" button, followed by the number you want to find the arctangent of. The calculator will then display the angle in radians or degrees, depending on the mode it is set to.

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The derivative of e²ˣ is 2e²ˣ.

A derivative of any function is the rate of change that will be made on the function if its independent variable changes by a small amount.

Now a function can also have another function in it. Then if we need to find the derivative of that function we need to use the chain rule. This states that for any variable x, if there is a function

f(g(x)) then derivative of f(g(x) will be f'(g(x))⋅g'(x)

this means that we need to first hold the function in it constant and then multiply the function's derivative with respect to x.

Here f(g(x)) = e²ˣ where g(x) is 2x

Now we will first hold 2x as one variable. We know that d/x of eˣ is eˣ

Hence we get

e²ˣ

Now we will differentiate 2x. The derivative of 2x is 2

Hence we get the derivative as

2e²ˣ

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The first term and the last term in the arithmetic progression are -2.5 and 22.5 respectively.

In Mathematics, the sum of a geometric sequence is given by this mathematical expression:

[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]

Where:

Mathematically, the sum of an arithmetic sequence is calculated by using this expression:

Sn = n/2(2a₁ + (n - 1)d)

Where:

Since the sum of all the terms in the geometric progression is equal to the sum of all the terms in the arithmetic progression, we have:

256(1 - 0.5^8)/(1 - 0.5) = 51/2(2a₁ + (51 - 1)0.5)

256(1 - 0.00390625)/(0.5) = 25.5(2a₁ + 25)

255/0.5 = 51a₁ + 637.5

510 = 51a₁ + 637.5

51a₁ = -127.5

a₁ = -2.5

For the last term, we would use the following formula:

aₙ =  a₁ + (n - 1)d

a₅₁ =  -2.5 + (51 - 1)4

a₅₁ =  -2.5 + (50)0.5

a₅₁ = 22.5.

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Answer:

See below

Step-by-step explanation:

1. The sum of two numbers is 72. Lets say the two numbers are x and y:

   x + y = 72

If one number is 3 times the other,

  x = 3y

what is the largest number?

 Substitute the second into the first expression

x + y = 72

3y + y = 72

4y = 72

 y = 18

2.  From 6:30am to noon is 5 1/2 hours.  From noon to 1:30 is another 1 1/2 hours.  The sum is (5.5 + 1.5) = 7 hours

3.  I'm assuming the bottom two angles are the same (diffiuclt to read).  If so, we know that the sum of the interior angles of a triangle is 180 degrees.  

        2x + x + x = 180

        4x = 180

          x = 45 degrees

4.  (1.5 meters)*($22.50/meter) = $33.75

5.  (0.5 L)*(1000 ml/L) = 500 ml

Answer:

true

Step-by-step explanation:

log2(5x+3)=log2(4x-3)

log2(5x+3)/log2(4x-3)

division turns to minus

log2(5x+3-4x-3)

log2(x)

Using the given equation, The weight of a cat when it is 7 months old is 4 kilograms.

Equations describe physical processes and the relationship between different physical quantities. Equations are mathematical and physical statements. Physical quantities are presented using simple variables, and after that, a personal variable, such as your energy, may be indicated.

An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14. Algebraic equations in mathematics frequently have one or more variables.

In this situation, the statement "w(7) = 4" represents that a cat that is 7 months old weighs 4 kilograms.

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On converting the length , 152 centimeter is equivalent to 59.8424 inches .

There are various units of measuring the length , which include , meter (m) , centimeter (cm) , kilometer (km) , inches (in.) ;

In order to convert 152 centimeters (cm) to inches,

We use the conversion factor of 0.3937 inches per centimeter.

So , we multiply the number of centimeters by this conversion factor to get the equivalent length in inches ;

By using this method, we get ;

⇒ 152 cm × 0.3937 inches/cm = 59.8424 inches ;

Therefore, 152 centimeters is equal to approximately 59.8424 inches.

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A box plot is a graphical representation of data that is based on (c) a five number summary

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

Statement: a box plot is a graphical representation of data that is based on__

A box plot (also called a box-and-whisker plot) is a way to display the distribution of a dataset.

It shows the median, quartiles, minimum, and maximum values of the data.

These items are referred to as the five number summary

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Answer:

26 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

26 3/3 - 2/3 = 26 1/3

The initial position is the starting point, and the final position is the endpoint.

We proceed to explain the initial and final position:

For example, if an object starts at the 2 meter mark (initial position) and moves 3 meters to the right, its final position would be at the 5 meter mark.

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