what theorems, properties, or strategies are common to the proof of the triangle proportionality theorem and the proof of converse of the triangle proportionality theorem?'

The difference of the maximum and minimum values is divided by the number of bins.

1. Identify the maximum and minimum values of the quantitative data

2. Subtract the minimum value from the maximum value to get the difference

3. Divide the difference by the number of bins to get the approximate width of each bin

The width of the bins in a frequency distribution of quantitative data can be estimated by dividing the difference between the maximum and minimum values of the data by the desired number of bins. This will provide an approximate size for each bin, which can then be used to construct the frequency distribution.

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The time complexity is O(1) as the recurrence reduces to a constant.

T(n) = 2T(n/2) + n/log n

T(1) = 1

T(2) = 2T(1) + 2/log 2

= 2 + 2/log 2

T(4) = 2T(2) + 4/log 4

= 2(2 + 2/log 2) + 4/log 4

T(8) = 2T(4) + 8/log 8

= 2(2(2 + 2/log 2) + 4/log 4) + 8/log 8

T(n) = 2^k T(1) + (2^k + 2^(k-1) + ... + 2 + 1)*n/log n

= 2^k + (2^k + 2^(k-1) + ... + 2 + 1)*n/log n

= 2^k + n*Σ_(i=1)^k▒2^i/log n

= 2^k + n/log n*(2^(k+1) - 1)

= 2^k + n/log n*(n/2 - 1)

= (2^k + n/2 - n/log n)*n/log n

= (2n - n/log n)*(log n/n)

= 2 - 1/log n

The time complexity is O(1) as the recurrence reduces to a constant.

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Answer:

Step-by-step explanation:

The rate of change is just the slope of the equation and/or graph.

for the linear function A, y = 2/3x + 5, the slope (therefore rate of change) is 2/3. For B (I can't make it out that clear), 3/2. That gives the answer for C: 3/2 is greater than 2/3.

Answer: 112i + 85.8j

Step-by-step explanation:

Answer:

[tex]\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}[/tex]

Step-by-step explanation:

To find the components of a vector given its magnitude and direction, use the following formula:

[tex]\large\boxed{\vec{u}=\left(||\vec{u}|| \cos(\theta),|| \vec{u}|| \sin(\theta)\right)}[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\vec{H}=\left(85.8 \cos(112^{\circ}),85.8 \sin(112^{\circ})\right)[/tex]

[tex]\vec{H}=\left(-32.1, 79.6\right)[/tex]

Therefore:

[tex]\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}[/tex]

Projab is the projection of vector a onto vector b. It is a vector that is perpendicular to b and has the same magnitude as a, and it is the vector that is closest to a in the direction of b.

In R2, the geometric interpretation is that projab is the vector that is obtained by dropping a perpendicular line from the tip of a onto the line containing b.

In R3, the geometric interpretation is that projab is the vector that is obtained by dropping a perpendicular line from the tip of a onto the plane containing b.

The equation for projab is projab = (a.b/|b|^2)b, where a.b is the dot product of a and b, and |b| is the magnitude of b.

The best estimator's error vector, when seen in terms of mean square errors, is orthogonal to all other feasible estimators, according to the orthogonality principle. The orthogonality principle can be expressed in a variety of ways, but it is most frequently used to describe linear estimators.

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Answer:

2700

Step-by-step explanation:

turn 2% into a decimal and multiply by 135,000.

The coordinate of the point R of the line segment QS will be (-3.8, -0.4). Then the correct option is A.

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

The endpoints are Q(-6, -2) and S(5, 6). And m:n is 1:4. Then the coordinate of the point R is given as,

x = (5 · 1 + (-6) · 4) / (1 + 4)

x = -3.8

y = (6 · 1 + (-2) · 4) / (1 + 4)

y = -0.4

The coordinate of the point R of the line segment QS will be (-3.8, -0.4). Then the correct option is A.

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Answer:

Clockwise 90°, enlargement

Step-by-step explanation:

Rotation:

    Rotation means turning around a center and from the center to any point on the shape stays same.

Here, the ΔABC is rotated clockwise 90°with it center O.

Dilation:

          This means resizing either by compression, enlargement or contraction.

Here, the ΔABC is enlarged to ΔA'B'C'

Answer:

Step-by-step explanation:

4 cookies times 7 bags
4x7=28

Answer:

The height of the lamp posts is 20.49 m and the distance between them is 70.98 m.

Step-by-step explanation:

Draw a diagram using the given information (see attachment).

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

Use the tan trigonometric ratio to create two equations for h.

Triangle ACD:

[tex]\implies \tan 30^{\circ}=\dfrac{h}{x}[/tex]

[tex]\implies h=x\tan 30^{\circ}[/tex]

[tex]\implies h=\dfrac{\sqrt{3}}{3}x[/tex]

Triangle BCD:

[tex]\implies \tan 45^{\circ}=\dfrac{h}{x-15}[/tex]

[tex]\implies h=(x-15)\tan 45^{\circ}[/tex]

[tex]\implies h=(x-15)\cdot 1[/tex]

[tex]\implies h=x-15[/tex]

Substitute the second equation into the first equation and solve for x:

[tex]\implies x-15=\dfrac{\sqrt{3}}{3}x[/tex]

[tex]\implies x-\dfrac{\sqrt{3}}{3}x=15[/tex]

[tex]\implies \dfrac{3-\sqrt{3}}{3}x=15[/tex]

[tex]\implies (3-\sqrt{3})x=45[/tex]

[tex]\implies x=\dfrac{45}{3-\sqrt{3}}[/tex]

[tex]\implies x=35.4903810...[/tex]

To find h, substitute the found value of x into the second equation and solve for h:

[tex]\implies h=x-15[/tex]

[tex]\implies h=35.4903810...-15[/tex]

[tex]\implies h=20.4903810...[/tex]

[tex]\implies h=20.49\; \sf m\;\;(2\;d.p.)[/tex]

As the distance between the two lamp posts is 2x:

[tex]\implies 2x=2 \cdot 35.4903810...[/tex]

[tex]\implies 2x=70.9807621...[/tex]

[tex]\implies 2x=70.98\; \sf m\;\;(2\;d.p.)[/tex]

Therefore:

first off, let's notice that the y-coordinates are the same for both points, meaning is really just a horizontal line, and its slope is 0, however, let's go through the rigamarole

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{5}}} \implies \cfrac{-3 +3}{3} \implies \cfrac{ 0 }{ 3 } \implies \text{\LARGE 0}[/tex]

The ratio of the number of astronauts on Earth to the total number of astronauts is 7 : 30.

A ratio is a mathematical expression that compares two or more values by dividing the size of one value by the size of another.

Ratios can be expressed in several different forms, including fractions, decimals, or percentages, and can be used to compare quantities, measurements, or other values in a meaningful way.

Ratios provide a way to express the relationship between two or more values in a compact and concise format, and can be used in a variety of fields, including mathematics, science, finance, and engineering.

If the space program has 23 astronauts in outer space and 7 astronauts on Earth, then the ratio of the number of astronauts on Earth to the total number of astronauts is:

7 : (23 + 7) = 7 : 30

You can simplify the ratio to 7/30 or approximately 0.23 or 23%.

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The sum of angles p, q, and r is equal to 180 degrees.

A degree is a unit of measurement used in geometry to represent angles.

To prove this, we will use the concept of alternate interior angles. Alternate interior angles are angles that are formed on the inside of the two lines when they are parallel to each other. Since AB || CD, alternate interior angles p and q are equal.

We know that the sum of angles in a triangle is equal to 180 degrees. In this case, we have a triangle ABC with angles p, q, and r. Hence,

=> p + q + r = 180 degrees.

Next, since p and q are equal, we can represent them as p = q. Now, substituting the value of q into the above equation, we get:

=> p + p + r = 180 degrees.

This can be simplified to 2p + r = 180 degrees. But since p = q, we can replace p with q. Hence,

=> 2q + r = 180 degrees.

Finally, substituting the value of p = q into the above equation, we get:

=> 2p + r = 180 degrees.

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The degree of expression will be the highest level of each of the aforementioned individuals' expression, or 6.

It is necessary to multiply, dividing, add, or subtract as mathematics. The following is how an assertion is put together: Number, expression, and mathematical operator The components of a mathematical form include numbers, variable, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible that contrast statements and phrases. An expression, often known like an algebraic expression, is there any mathematical statement that abstract, numbers, and a numerical operation between them. For illustration, the word m in the balanced formula is separated from the parts 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.

given:

6y⁶-4y³ is the given expression.

6 y⁶ has a degree of 6.

3 is the degree of - 4y³.

However, the level of expression will be the greatest level of the individual expression of the aforementioned, i.e. 6.

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Answer:

If 58% of the people surveyed said YES to a YES or NO question, the number of people who said YES is

58/100 * 6700 = 3886.

The number of people who said NO is

6700 - 3886 = 2814.

(a) The probability that the entire system works is  0.3136

(b) The probability that the component a is not working is 0.3

Probability is a scale between 0 and 1 that represents the possibility of an event happening. An event with probability 1 is guaranteed to happen, while an event with probability 0 is impossible. The number of favorable outcomes divided by the total number of potential outcomes in the sample space yields the probability of an event A, commonly denoted as P(A). The sample space, for a fair six-sided die, is the set of all potential outcomes, such as 1, 2, 3, 4, 5, and 6. The probability of rolling a 4 is 1/6. Numerous disciplines employ probability to make predictions, deduce conclusions, and make judgments in the face of uncertainty.

(a) To find the probability that the entire system works, we need to find the product of the probabilities of the individual components working.

For the components connected in series, A and B, the probability that both work is equal to the product of their individual probabilities:

P(A and B) = P(A) * P(B) = 0.7 * 0.8 = 0.56

For the components connected in series-parallel, C, D, and E, the probability that all three work is equal to the product of their individual probabilities:

P(C and D and E) = P(C) * P(D) * P(E) = 0.8 * 0.8 * 0.9 = 0.576

To find the probability of the entire system working, we need to find the product of the probability of A and B working and the probability of C, D, and E working:

P(system works) = P(A and B) * P(C and D and E) = 0.56 * 0.576 = 0.3136

(b) Given that the system works, the probability that component A is not working would be equal to 1 minus the probability that component A is working:

P(A not working | system works) = 1 - P(A working | system works) = 1 - 0.7 = 0.3

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The complete question is

The way that increasing the amount of charge on an object affects the electric force it exerts on another charged object is; The electric force increases because the amount of charge has a direct relationship to the force

The amount of charge on an object due to the effect of the force that is exerted on it can be calculated by using the formula :

F = E × q

Where;

F is the electric force.

E is the energy.

q is the charge.

The electric force between charged particles at rest is known as electrostatic force.

The magnitude of the electric force between point charges is directly proportional to the multiplication of the charges and inversely proportional to the distance between them.

Therefore, we conclude that increasing the amount of charge on an object would increase the electric force because the amount of charge has a direct relationship with the force.

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The sum of the interior angles of polygon A is 1260°.

The sum of angles of the exterior angles of a polygon A is 360°

Polygon A

A polygon with 9 sides is called a nonagon. The sum of interior angles of a Nonagon is 1260°. This can be calculated using the formula (n -2) * 180, where n is the number of sides.

Thus, the sum of the interior angles of polygon A is 1260°.

The sum of the exterior angles of a polygon is 360°.Thus, the sum of angles of the exterior angles of a polygon A is 360°.

Polygon B

Polygon B has 7 sides i.e. n = 7

sum of angles of the interior angles of polygon B = (7-4) * 180 = 900°

Thus, y = 900- 135 - 140 - 150 - 120 - 135 - 120 = 100°

x = 180 - 100 = 80°  (sum of angles on a straight line is 180°)

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Answer: A = 19.6^2 ( 19.6 to the 2nd power )

Step-by-step explanation:

Area of a circle = 3.14 * r^2

A = 3.14 * 2.5^2

A = 19.625

19.625 rounded to the nearest tenth is 19.6

According to the information we can infer that the area of the circle with a radius of 2.5 is approximately 19.63 square units.

The area of a circle is given by the formula A = πr², where A represents the area and r represents the radius.

In this case, the radius is given as 2.5 units. Substituting this value into the formula, we have:

Using an approximate value of π as 3.14159, we can calculate the area:

So we can conclude that the area of the circle with a radius of 2.5 units is approximately 19.63 square units.

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The statements that are true about parallelogram WXYZ:

XD ≅ ZD

∠WXZ ≅ ∠YZX

Consider the following diagram.

The diagonals of parallelogram WXYZ intersect at D.

We know that the property of parallelogram that the diagonals bisect each other.

From this property we get,

XD ≅ ZD

Also, from the definition of parallelogram the opposite sides are equal and parallel.

So, we have

WX and YZ are parallel lines with XY transversal.

So, ∠WXZ ≅ ∠YZX as they are alternate interior angles

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Answer:

Step-by-step explanation:

explain what ? what is the question here ?

to find the intersecting point of both lines ?

if that is the case, then please consider that an intersection point is a point, where both equations deliver the same coordinates. it is the same point for both of them.

in other words, the question is for what pair of (x, y) are both equations true (their left and right sides are equal).

we do this by finding a way to express one variable by an expression in the other variable, and then use that identity in one of the equations to solve for the remaining variable. and then we use that in the other equation to solve for the first variable.

line b gives us such an identity right away.

y = (-1/2)x + 6

we can use that in the line a equation :

2x - ((-1/2)x + 6) = 7

2x + (1/2)x - 6 = 7

2x + (1/2)x = 13

(4/2 + 1/2)x = 13

(5/2)x = 13

5x = 26

x = 26/5 = 5.2

y = (-1/2)×5.2 + 6 = -2.6 + 6 = 3.4

The Adding and Subtracting Rational Expression Calculator is a free online tool that displays the results of rational number arithmetic operations.

A rational expression is nothing more than the product of two polynomials. In other words, it is a fraction with polynomial numerator and denominator. Rational expressions resemble fractions with variable denominators (and often numerators too).

Adding or subtracting rational expressions involves four steps: All fractions must be written as equivalent fractions with a common denominator. Combine the fractions to form a single fraction with a common denominator. Reduce the complexity of the expression at the top of the fraction. Reduce the fraction to its simplest terms.

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Answer:

  (i)  No

  (ii)  The line and curve always intersect in two places

Step-by-step explanation:

You want to know if there are values of k such that the curve y = (k+3)x²-3x lies completely above the line y = x+k. And you want to know the relationship between the line and the curve.

The number of points of intersection between the line and the curve can be found by considering the discriminant of the quadratic equation for the difference of the y-values.

The line and curve will intersect when their y-values are equal:

  (k +3)x² -3x = x +k

  (k +3)x² -4x -k = 0 . . . . . compare to ax²+bx+c=0

The discriminant is the value of b²-4ac, so is ...

  d = (-4)² -4(k+3)(-k) = 16 +4k(k -3)

Writing this in vertex form, we have ...

  4(k² -3k) +16 = d

  4(k² -3k +2.25) +16 -4(2.25) = d . . . . . "complete the square"

  4(k -1.5)² +7 = d

The square is always positive, and it is added to a positive value (7), so the discriminant d is always positive. This means there are always two points of intersection between the curve and the line.

As we saw above, the line and curve will always intersect at two points. This means there are always parts of the curve both above and below the line.

__

Additional comment

For the value k=-3, the "curve" becomes a line with slope -3 through the origin. It will intersect the line y=x-3 at one point. It seems reasonable to exclude that case from consideration.

(8k+k26) after matching, (10k+72k2) because a trinomial cannot be factored 3k2 + 18k - 13

In maths, a coefficient is a cubic, a sequence, or the exponential coefficient of a descriptive word in an expression. Any phrase is acceptable, though digits are frequently used. If the equations are variables, and so the word "parameter" also could refer to the variables themselves. A coefficients is the product of either a number and then a variable. Some occurrences of correlations are: The coefficient as in sentence . The variable is multiplied by it amount when word g has a coefficient of 1. example Since "z" is a factor and the term's interpretation is 6z, the multiplier is 6. The square root of x has a score of one.

given

((8k +  (k2)) -  6) -  ((7 - 10k) -  2k2)

The first term is 3k2 and it has a 3 coefficient.

The coefficient of the middle word, +18k, is 18.

"The constant," the final term, is -13.

Step 1: Add the constant 3 • -13 to the coefficient of the first term to get -39.

Step 2 is to identify two -39 factors whose combined value is equal to the middle term's coefficient of 18, which is 18.

      -39    +    1    =    -38

     -13    +    3    =    -10

     -3    +    13    =    10

     -1    +    39    =    38

(8k+k26) after matching, (10k+72k2) because a trinomial cannot be factored 3k2 + 18k - 13 .

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When constructing a Pareto chart, the second bar would be labeled with the name of the item that has the second highest frequency or impact, as determined by the data being analyzed.

In a Pareto chart, the bars are typically labeled with the names of the items being analyzed, and the height of each bar represents the frequency or the impact of each item. The bars are typically ordered from largest to smallest, with the largest bar appearing on the left and the smallest bar on the right.

It is worth noting that the "rule" you referred to in the book might refer to the 80-20 rule, also known as the Pareto principle. This rule states that roughly 80% of the effects come from 20% of the causes. In the context of a Pareto chart, this means that you might expect the first few bars to represent a large portion of the total frequency or impact, while the later bars represent a much smaller portion.

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Answer:

C

Step-by-step explanation:

You are able to simplify both of the 2/8ths and it comes to be 2/8 + 2/8 = 4/8

The expression 3a² + 10a + 7 can be completely factored as (a + 7)(3a + 1).

The expression 3a² + 10a + 7 can be factored as a product of two binomials.

To factor this expression, we can find two numbers that multiply to 7 and add up to 10. The only pair of numbers that have this property is 1 and 7. So, we can write:

3a² + 10a + 7 = 3a² + 7a + a + 7

= a(3a + 1) + 7(1 + 3a)

= (a + 7)(3a + 1)

Factorization is the process of breaking down a mathematical expression into simpler, more manageable parts. There are various methods to factorize an expression, including:

Grouping: This method involves grouping terms in pairs and then factoring out a common factor.

Difference of Squares: This method involves factoring the expression into the difference of two squares.

Sum or Difference of Cubes: This method involves factoring the expression into the sum or difference of two cubes.

Using Factor Trees: This method involves finding the prime factorization of the expression and then grouping the factors to find the final answer.

Using Identities: This method involves using various mathematical identities to simplify the expression.

It's best to determine the method to use based on the specific expression you're trying to factorize.

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