what is the maximum number of roads that can be closed while still making sure that for any two buildings in the city, there still exist roads that people can use to travel from one to the other?graph theory math stack math.stackexchange

Set x = 0 and solve for y to find the y-intercept. The main point will be (0,y).

The point on the line where it intersects the y axis is known as the y intercept.

In analytic geometry, a y-intercept or vertical intercept is a point where the graph of a function or relation intertwines the y-axis of the coordinate system, with the horizontal axis representing a variable x and the vertical axis representing a variable y. As a result, these points satisfy the x = 0 condition.

An intercept is a point on the y-axis through which the slope of a line passes. It is the y-coordinate of a y-axis point at which a straight line or a curve interferes. This is represented by the straight line equation,

y = mx+c,

where m denotes the slope and c is the y-intercept

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The statement that is true about the Random Variable X is P(X ≥ 4) = 0.522  , the correct option is (a) .

In the question ,

it is given that ,

the possible values of the random variable X is 1, 2, 3, 4, and 5 .

given that , 2 is twice as likely as 1 , that means

p(2) = 2p(1)

3 is one-third as likely as 2 , that means

p(3) = 1/3 p(2)

4 is four times as likely as 3 , which is

p(4) = 4/3 p(2)

and 5 is half as likely as 4 , that means

p(5) = 2/3 p(2)

We know that ,

p(1) + p(2) + p(3) + p(4) + p(5) = 1

Substituting the values in the above equation , we get

1/2 p(2) + p(2) + 1/3 p(2) + 4/3 p(2) + 2/3 p(2) = 1

So , p(2) = 6/23

hence ,

P(X ≥ 4) = P(X=4) + P(X=5)

= (4/3) × (6/23) + (2/3) × (6/23)

On simplifying further ,

we get ,

= 0.522

Therefore , the value of P(X ≥ 4) is 0.522    .

The given question is incomplete , the complete question is

Let X be a random variable with possible values 1, 2, 3, 4, and 5. Assume that 2 is twice as likely as 1, 3 is one-third as likely as 2, 4 is four times as likely as 3, and 5 is half as likely as 4. Which of the following is true (to the nearest three decimals)

(a) P(X ≥ 4) = 0.522

(b) P(X = 1 or X = 5) = 0.329

(c) P(X ≤ 2) = 0.367

(d) P(X = 2 or X = 3) = 0.293

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The slope-intercept form of the equation of the line through the given point and parallel to the given line is y=x−14.

In the given question we have to write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

The given points are (–2, –16).

The given equation of line is y = x – 5.

Standard equation of line is y=mx+c.

After comparing to the standard equation.

Slope m(1) = 1

The line passes through (−2,−16), so the point will satisfy the equation y=mx+c. So

−16=−2*1+c

Simlifying

−16=−2+c

Add 2 on both side, we get

c = −16+2

c = −14

As we know that if line is parallel then

m(1)=m(2)

So the value of solpe m = 1

Now the equation of line

y=1*x+(−14)

y=x−14

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The right answer is:

How do you write the slope-intercept form of the equation of the line through the given point and parallel to the given line?

Point (−2,−16), y = x – 5

The given inequality is simplified to t+1≥ t-8.

The given inequality is 3t-2(t-1) ≥ 5t-4(2 + t).

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality can be solved as follows:

3t-2(t-1) ≥ 5t-4(2+t)

⇒ 3t-2t+1 ≥ 5t-8-4t

⇒ t+1≥ t-8

Therefore, the given inequality is simplified to t+1≥ t-8.

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Answer: 6

Step-by-step explanation: n-3x6-6=6

The ph of a buffer that contains 0.41 m propanoic acid and 0.22 m propanoate is 5.505.

In the given question we have to calculate the ph of a buffer.

The ph of buffer contains 0.41 m propanoic acid and 0.22 m propanoate.

The value of ka for propanoic acid is 1.3 x 10^{-5}.

Since, we have to calculate the pH after 0.16 mole of solid NaOH is added to 1.00 L.

Moles of excess NaOH = 0.16-0.041 = 0.119

pH = P(ka)+log(salt/acid)

pH = -log(1.3×10^{-5})+log[(0.88+0.16)/(0.41-0.16)

pH = 4.886+log(1.04/0.25)

pH = 4.886+0.619

pH = 5.505

Hence, the ph of a buffer that contains 0.41 m propanoic acid and 0.22 m propanoate is 5.505.

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Three angles are 36° , 36° , 180°.

Let us denote first, second, third angle by a, b, c respectively.

It is given that second angle is the same as first angle which implies that,

⇒ b = a

And third angle is three times the first which implies that,

⇒ c = 3a

We know that sum of the angle of triangle is 180°.

Therefore a + b + c = 180°

⇒ a + a + 3a = 180°

              5a = 180°

                 a = 36°

That means b = 26 °

and c = 3a = 3(36°) = 108°

Hence three angles are 36°, 36°, 108°.

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Answer: 310

Step-by-step explanation:

1.Find your constant difference of the sequence by subtracting from left to right which is 9

2. find your fomula by using Tn=bn+C (b is your constant difference you can find C by C=T1 -b ) which will then give us 9n-5

3. T(35)=9n-5=9(35)-5=310

No James' expressions for 23+3 x 9-42 are incorrect

To group numbers or variables, three common grouping symbols are used:

Parentheses are the most widely used grouping symbols.

To make the problem simpler, operations enclosed in parentheses can be carried out before any other operations.

To group the expression correctly using PEMDAS

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

= 23 + 3 x 9 - 42

= 23 + (3 x 9) - 42

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Answer:

2400 cubic inches

Step-by-step explanation:

40 multiply by 30 multiply by 20

= 2400 cubic inches

Answer: 24,000 in³

Step-by-step explanation:

Formula for volume: l * w * h

40 * 30 * 20

= 24,000

Hope this helps!!! :)

After dividing the number, the decimal of 12/16 is 0.75.

In the given question we have to find the 12/16 as a decimal.

The division is shown by the fractional bar between the "part" and the "whole." By dividing the numerator by the denominator, any fractions can be transformed into decimals.

So when we divide 12 by 16 then the result is 0.75.

So the decimal of 12/16 is 0.75.

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The right answer is:

What is 12/16 as a decimal?

The central angle states the property of the center of the circle, So It is called the central angle.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.

An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.

Hence,

The central angle states the property of the center of the circle, So It is called the central angle.

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The Fibonacci series in which 0 does not consider is 1,2,3,5,8,13,21,34,…

A series of numbers known as the Fibonacci sequence is one in which each succeeding number is created by adding the two numbers that came before it. The Fibonacci sequence is named for the Italian mathematician who created it.

The standard Fibonacci series

0,1,1,2,3,5,8,13,21,34,…

When 0 is not considered as Fibonacci number, the series can be rewritten as,

1,2,3,5,8,13,21,34,…

The Fibonacci series where number 0 is excluded is 1,2,3,5,8,13,21,34,…

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The following are the offered rational exponents in expression form:

• (A) the fourth root's tenth root = [tex]\sqrt[10]{4}[/tex]

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: The following rational exponents are expressed in the expression form (Math Operator, Number/Variable, Math Operator): (A) the tenth root of four= [tex]\sqrt[10]{4}[/tex]

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Answer:

Any point with a y coordinate of -3.

Step-by-step explanation:

Because they have the same y coordinate, it is a horizontal line. So any point that has a y coordinate of -3 will be on the same line.

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Answer:

13: 22 < x < 74

14: Side DF, Side DE, side EF

Step-by-step explanation:

So for the first one, you add 26 + 48 which equals 74. Then, you subtract 48 - 26 which equals 22. So the range is 22 < x < 74.

For the second one, the angle corresponds to the side across from it. The smallest side will be across from the smallest angle. So, the order is side DF, side DE , and then side EF.

Hope this helps!!! :)

The margin of error for the true proportion of times the coin would land on heads on a 95% confidence level is 11.

As per the question,

⇒ Confidence interval is calculated by,

                p  ±  z(α/2) × √ ( p × q / n )   =   ( p - E, p + E )

where,     p  =  proportion in a random sample

                q  =  1 - q

                E   =  z(α/2) × √ ( p × q / n )   i.e.  margin of error

⇒  p   =   40 / 50

          =   4 / 5

∴   p   =   0.8

⇒   q  =  1 -  [tex]p^{'}[/tex]  

          =  1 - 0.8

∴    q  =  0.2

⇒  α   =   0.05

⇒ z(α/2)  =  1.94

⇒ Margin of error ( E )   =   z(α/2) × √ ( p × q / n )

                                       =   1.94 × √ ( 0.8 × 0.2 / 50 )

                                       =   1.94 × √ ( 0.16 / 50 )

                                       =   1.94 × √ ( 0.0032 )

                                       =   1.94 × 0.05656

    Margin of error ( E )   =   0.109  ≅  0.11

Therefore, 11 is the Margin of Error ( E ) for the true proportion of times the coin would land on heads at a 95% confidence level i.e option c is correct.

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The complete question is

A trick coin that was purchased at a magic shop was flipped 50 times. The coin landed on heads 40 times. Based on the results, what is the margin of error for the true proportion of times the coin would land on heads? Base your margin of error on a 95% confidence level.

a. 1

b. 10

c. 11

d. 5

The parabolic equation representing the t-shirt's height is given as follows:

y = -16(x - 1)² + 24.

The equation of a quadratic function, representing a parabola, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which the parameters of the function are listed as follows:

Considering the maximum height, the vertex of the parabola is given by the following coordinates:

(1, 24).

Hence:

y = a(x - 1)² + 24.

When x = 0, y = 8, hence the leading coefficient of the equation is obtained as follows:

8 = a + 24

a = -16.

Thus the equation is:

y = -16(x - 1)² + 24.

The team mascot shoots a rolled T-shirt from a special T-shirt cannon to a section of people in the stands at a basketball game. The T-shirt starts at a height of 8 feet when it leaves the cannon and 1 second later reaches a maximum height of 24 feet before coming back down to a lucky winner. If the path of the T-shirt is represented by a parabola, which function could be used to represent the height of the T-shirt as a function of time, t, in seconds?

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The expected value of your profit is -0.25 which is loss, if probability of winning is 0.001.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. In everyday speech, the term "probability" refers to the likelihood that a specific event (or set of events) will take place, expressed as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution.

Given,

Probability of winning = 0.001

probability of losing = 0.999

Expected value of profit can be calculated,

E(x)

= (749 x 0.001) + (-1 x 0.999)

= -0.25

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The percentage decrease in the number of employees would be near around 18%.

What is the percentage decrease?

The difference between the starting and ending values is expressed as a percentage decrease. It displays a percentage loss of value from the original, regardless of unit. The decrease is equal to the original amount minus the final amount.

Percentage Decrease=(Starting Value−Final Value) / |Starting Value|×100

Given data:

The initial number of employees = 116

The final number of employees = 95

Percentage decrease = [tex]\frac{116-95}{116}*100\\[/tex]

                                     = 18.1034% decrease

                                     ≈ 18% decrease

Hence, the percentage decrease in the number of employees would be near around 18%.

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A rational number is a number that can be written in the form p/q where q is not equal to zero and p is an integer.

A root is a value for x that makes the function equal to zero. It is also called a solution.

Hence, a rational root is such a number that makes any polynomial function equal to zero.

let us consider a general polynomial equation-

P(x) = anxn + an− 1xn − 1 + … + a1x1 + a0

hence, the rational roots must be of the form = [tex]\pm[/tex] (factors of a0) / (factors of an).

let us now take an example,

f(x)=[tex]2 x^3-3 x^2-11 x+6[/tex]

here ao = 6, and factors of 6: 1,2,3,6

an = 2 and the factors of 2: 1,2

Hence, we have Possible Rational Roots:

[tex]$$\pm\left\{\frac{1}{1}, \frac{1}{2}, \frac{2}{1}, \frac{2}{2}, \frac{3}{1}, \frac{3}{2}, \frac{6}{1}, \frac{6}{2}\right\}$$[/tex]

removing the duplicate values we have- [tex]$$\pm\left\{1, \frac{1}{2}, 2, 3, \frac{3}{2}, 6\right\}$$[/tex]

In this way, we have the rational numbers which can be possible solutions for our function f(x).

Now we substitute each of these rational numbers one by one to check if it satisfies the equation as follows.

f(1) =[tex]2 (1)^3-3 (1)^2-11 (1)+6[/tex] = 2-3-11+6 = -6 [tex]\neq[/tex] 0.

Hence, it doesn't satisfy the equation, it means it's not the root of the equation.

Similarly, we can check for the rest of the numbers.

we will get f(1/2)=0, f(3)=0 and f(-2)=0

Hence, x=3,1/2 or -2 are the solutions for the equation f(x).

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If the hexagon is changed to an octagon, the area of the shaded portion will be; smaller

We are given;

Diameter of circle = 5 ft

Thus;

radius; r = 5/2 = 2.5 ft

Now, the long diagonal of the hexagon is given as 5ft and we know that if the side of the hexagon is a, then;

a = d/2

where d is the length of the long diagonal

Formula for area of hexagon is;

A = (3/2) * √3 * a²

Thus;

A =  (3/2) * √3 * 2.5²

A = 16.24 ft²

Area of circle is gotten from the formula;

A = πr²

A = π * 2.5²

A = 19.635 ft²

Thus;

Area of shaded portion = 19.635 ft² - 16.24 ft² = 3.395 ft²

If the hexagon is changed to an octagon, the formula for length of diagonal is;

L = a√(4 + 2√2)

where a is side length

Thus;

5 = a√(4 + 2√2)

a = 5/√(4 + 2√2)

Area of octagon is from the formula;

Area = 2a²(1 + √2)

Area = 2(5/√(4 + 2√2))²(1 + √2)

Area = 2(25/(4 + 2√2))(1 + √2)

Area = 17.678 ft²

Area of shaded portion = 19.635 ft² - 17.678 ft² = 1.957ft²

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The central angle is the ratio of arc length and radius.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its centre. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the centre of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's centre subtends is known as the central angle.

According to the central angle, we state that:

An arc's angle at the circle's centre is twice as large as its angle at any other point along the circle's circumference.

OR

The angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the centre of the circle.

Hence,

The central angle is the ratio of arc length and radius.

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7.7%. is  the rate of unemployment.

According to our question-

Unemployment rate = number of unemployed people / total number of unemployed people * 100

Similarly,

Workforce = Employed + Unemployed

Unemployed = 130 million - 120 million. That's 10 million.

For this reason,

Unemployment rate = 10 / 130 * 100

Unemployment = 7.69% or about 7.7%.

Hence, 7.7%. is  the rate of unemployment.

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The vertices of the triangle after the reflection over y = -x are [tex]\left[\begin{array}{ccc}3&-3&-3&-3&-6&-3\end{array}\right][/tex]

The vertices of the triangle are given as

[tex]\left[\begin{array}{ccc}3&6&3&-3&3&3\end{array}\right][/tex]

The transformation rule is given as

Reflection over the line y = -x

Mathematically, this rule is represented as

(x, y) → (-y, -x)

This means that we negate the x-coordinates and the y-coordinates, and then swap the x and the y coordinates

When this rule is applied, we have

[tex]\left[\begin{array}{ccc}3&-3&-3&-3&-6&-3\end{array}\right][/tex]

Hence, the reflection would produce [tex]\left[\begin{array}{ccc}3&-3&-3&-3&-6&-3\end{array}\right][/tex]

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There will be sample Z-test for mean and the confidence interval will be [119.62, 125.38] as well as we are 95% certain that sample mean will fall within the interval.

Any statistical hypothesis test called a t-test has a test statistic that, under the null hypothesis, follows a Student's t-distribution. It is most frequently used when the test statistic would have a normal distribution if the test statistic's scaling term's value were known. A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to see if a procedure or treatment truly affects the population of interest or whether two groups differ from one another.

a. 0.724<p<0.752

E=(0.752-0.724)/2

=0.014

b. n=192

x=129

p=129/192=0.6719

Confidence interval=95%
Z-score= 1.96

E=Z*(√p(1-p)/n)

=1.96*√0.6719*(1-0.6719)/192

=1.96*0.0339

=0.06884

We will do a sample Z-test to determine the mean, and we can be 95% certain that the sample mean will fall within the confidence range of [119.62, 125.38].

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Answer:

Step-by-step explanation:

You have two figures showing expressions for a midline length and the parallel base length. In one case, you want the length of the midline (PQ). In the other case, you want the value of the variable (x).

A midline is the line segment that joins the midpoints of two sides of a triangle. It is parallel to the base, and half the length of the base.

  2PQ = ON

  2(5x -26) = 9x -37 . . . . . use the given expressions

  10x -52 = 9x -37 . . . . . simplify

  x = 15 . . . . . . . . . . . . . add 52 -9x

  PQ = 5(15) -26 = 49

The length of PQ is 49 units.

  2MN = KL

  2(2x+7) = 7x -16 . . . . . . use given expressions

  4x +14 = 7x -16 . . . . . . . . simplify

  30 = 3x . . . . . . . . . . . . . . add 16 -4x

  10 = x . . . . . . . . divide by 3

The value of x is 10.

5 types of angles are formed by the lines cut by the transversal which are mainly corresponding angles, alternate interior angles, alternate exterior angles, co-interior angles, and consecutive interior angles.

Each pair of internal angles on the same side of a transversal that meets two parallel lines is supplementary, or they add up to 180°. The opposing angles that result from the junction of two lines are known as vertical angles or vertically opposed angles.

In geometry, a transversal line intersects two lines in the same plane at two different locations. In the Euclidean plane, transversals help establish the parallelism of two or more other straight lines.

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Example of SMART saving goals is "Viletas de $50 each week in almone market."

SMART financial goals should be Specific, Measurable, Achievable, Relevant, Time-based.

Specific :- Your goal should be specific, not generic or vague.

Measurable :- Make your financial goal measurable by quantifying it so you can evaluate your progress and overall success.

Achievable :- The surest way to improve your financial situation is to take achievable steps.

Realistic :- Setting unrealistic goals usually leads to disappointment and surrender.

Time-based:- Give yourself a time frame to achieve the goal.

By observing all these properties of SMART financial goal the example of this goal will be "Viletas de $50 each week in almone market."

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