What are vertical and adjacent angles? How do you find the measure of an unknown angle using these relationships? Give an example and show your work.

Answer:

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

According triangle inequality theorem the sum of any two sides of a triangle is greater than the third side.

Apply this to our options, add up the two shortest sides and compare with the longest side.

ok i can di it...... ..........

The solution is 28.3 m

The circumference of the circle whose radius is 4.5 m is 28.3 m

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the circumference of the circle be represented as C

Now , the equation will be

The diameter of the circle = 9 m

The radius of the circle r = d/2 = 4.5 m

And , the circumference of the circle C = 2πr

Substituting the values in the equation , we get

Circumference of the circle C = 2 x 3.142 x 4.5

Circumference of the circle C = 28.278 m

Therefore , the value of C is 28.3 m

Hence , the circumference of the circle is 28.3 m

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The probability that detector B goes off is 0.75

In this question we have been given the security system in a house has two units that set off an alarm when motion is detected.

Here, the probability that detector A will not go off is 0.35

And the probability that A will go off and B will not go off is 0.25

We need to find the probability that B goes off

The probability that detector A will go off would be,

1 - P( detector A will not go off )

= 1 - 0.35

= 0.65

And the probability that both A and B will go off would be,

= P(A will go off) - P( A will go off and B will not go)

= 0.65 - 0.25

= 0.40

Now we find the required probability.

P(B goes off) = P(both A and B will go off) + P(detector A will not go off)

                     = 0.40 + 0.35

                     = 0.75

Therefore, the required probability is 0.75

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A sampling technique that is based on the cumulative effect of information that every additional item in the sample adds as it is inspected is called: sequential sampling.

What is sequential sampling?

Sequential sampling is a non-probability sampling strategy where the researcher selects one or more populations within a time frame, conducts his research, evaluates the findings, and then selects further populations as necessary.

An auditor develops a set of three groups of sampling units, where each successive group contains the same number of units to be sampled. The sampling plan is to continue to the next group of sampling units if the preceding group contains at least one deviation

Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are examples of probability sampling techniques.

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Answer:

It seems that you are describing a geometric transformation in which triangle WXY is rotated to form triangle W'X'Y'. The correct statement describing this transformation is: "WXY right-arrow W'X'Y'". In this transformation, the triangle is rotated in some way, resulting in the new triangle W'X'Y'.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer: 40%

Step-by-step explanation:

the pecentage of decrease is 40%

correct me if i'm wrong ;(

HOPE THIS HELPS

The proof is explained below

A column proof is a logical argument that is presented in an organized manner. Every two-column proof has exactly two columns. One column represents our statements or conclusions and the other lists our reasons. In other words, the left-hand side represents our “if-then” statements, and the right-hand side explains.

     Statements                                  Reasons

1) ΔABC & ΔDCB are right                  ∠B =∠C =90°

angle triangle

2) AC=DB                                              Given

3) BC is common                                 Given

to both ΔABC & ΔDCB

4)  By SAS property ΔABC≅ΔDCB          ∠B =∠C =90° , BC is common,                          

                                                                       and AC = DB

5) AB=DC                                                 By CPCT theorem

Hence, proved via two column proof.

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Answer:

Step-by-step explanation:

Let y be the altitude and x the distance the plane travels from the point of the 35600 ft altitude location (x=0 at that point)

y = 35600 - 3200x

It would be nice to use time instad of distance, but there is no speed of the plane give.  It's altitude is espressed only on the basis of miles traveled.  If the elevation change were given in feet per minute, or some other unit of time, we can write an equation with time as the x variable.

This equations says:

1)  the plane starts at 35,600 ft (since x = 0, the result is 35,600 feet).

2) it descends 2,300 ft for every mile traveled from x = 0.

The unit rate of change is 3200 feet/mile.

The graph is attached.

Answer:

Below

Step-by-step explanation:

D / 5.2 = 2.4        multiply both sides of the equation by 5.2 to get

D = 12.48

Answer: 360

Step-by-step explanation:

Answer is 360 degrees

a parallelogram can be divided into two triangles

The Sum of the angles of each triangle is 180°

2 x 180 =360

Answer:

360

Step-by-step explanation:

Formula to find the sum of angles of any shape

(n-2)x180

(4-2)x180

2x180=360

Hence the sum of angles of a parallelogram is 360

The formula for R(N) for the function f(x) = (5x)2 on [1, 5] in terms of N is R(N) = [tex]100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}[/tex] and area is 767(approx).

In the given question, we have to find a formula for R(N) for the function f(x) = (5x)^2 on [1, 5] in terms of N.

The given function is f(x) = (5x)^2 on [1, 5].

∆x = (5-1)/N

∆x = 4/N

X = 1+i∆x

X = 1+i4/N

f(x) = 25X^2

f(x) = 25(1+i4/N)^2

f(x) = 25(1+i8/N+16/N^2 i^{2})

R(N) = [tex]\sum_{i=1}^{N}f(X)\Delta x[/tex]

Now putting the value of f(x) and ∆x

R(N) = [tex]\sum_{i=1}^{N}\frac{4}{N}\left[25\left(1+\frac{8}{N}i+\frac{16}{N^2}i^{2}\right)\right][/tex]

R(N) = [tex]\frac{100}{N}\sum_{i=1}^{N}\left(1+\frac{8}{N}i+\frac{16}{N^2}i^{2}\right)[/tex]

R(N) = [tex]\frac{100}{N}\left(\sum_{i=1}^{N}1+\sum_{i=1}^{N}\frac{8}{N}i+\sum_{i=1}^{N}\frac{16}{N^2}i^{2}\right)[/tex]

R(N) = [tex]\frac{100}{N}\left(N+\frac{8}{N^2}\sum_{i=1}^{N}i+\frac{16}{N^3}\sum_{i=1}^{N}i^{2}\right)[/tex]

R(N) = [tex]\frac{100}{N}\left(N+\frac{8}{N^2}\frac{N(N+1)}{2}+\frac{16}{N^3}\frac{N(N+1)(2N+1)}{6}\right)[/tex]

R(N) = [tex]\frac{100}{N}\times N+\frac{100}{N}\times\frac{8}{N^2}\times\frac{N(N+1)}{2}+\frac{100}{N}\times\frac{16}{N^3}\times\frac{N(N+1)(2N+1)}{6}[/tex]

R(N) = [tex]100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}[/tex]

Now finding the area

[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = [tex]\text{lim}_{N\rightarrow \infty}\left[100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}\right][/tex]

[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 100 + 400 + 800/3

[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 766.67

[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 767(approx)

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Answer:

Below

Step-by-step explanation:

"The number of veggie burgers he prepares will depend on the number of his coworkers who attend the picnic."

v is dependent variable (see the quote above)

     c is independent

The range of the middle 50% of the data of scores on the assessment is 10.

Option A is the correct answer.

The range is the difference between the highest value and the lowest value of a given set of data.

We have,

Median = 80

First quartile = 70

Third quartile = 90

The Middle 50% is from the Median to the First quartile.

Range.

= 80 - 70

= 10

Thus,

The range is 10.

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Answer:

D: 3/11

Step-by-step explanation:

3/11 is equal to .2727272727 which is known as a repeating decimal as it is never-ending.

3/5 = .6

3/8 = .375

3/10 = .3

Answer:

y = 4x + 1

Step-by-step explanation:

4x - y = 2 => y = 4x - 2

So slope of the above equation is 4.

Parallel lines should have the same slope

Given m = 4, y = -3, x = -1

y = mx + b

-3 = 4(-1) + b

-3 = -4 + b

b = 1

so y = 4x + 1

Answer: I could be wrong, but I tried my best.

Slope: 1/2

Y-intercept: (0, 6)

Step-by-step explanation:

The polynomial p(x) = x³ + 8 · x² + x - 42 contains the zeros - 7, 2 and - 3.

Polynomials are algebraic expressions, whose standard form is shown below:

p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m}

Where:

And whose factor form is:

p(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., m}

Where:

In this problem we need to find a polynomial whose zeros are only real and represented by r₁ = - 7, r₂ = 2 and r₃ = - 3, respectively. If we know that a = 1, r₁ = - 7, r₂ = 2 and r₃ = - 3, then the factor form of the polynomial is:

p(x) = 1 · (x + 7) · (x - 2) · (x + 3)

p(x) = (x + 7) · (x - 2) · (x + 3)

p(x) = (x + 7) · (x² + x - 6)

p(x) = x³ + x² - 6 · x + 7 · x² + 7 · x - 42

p(x) = x³ + 8 · x² + x - 42

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Answer:

x = 90 Tan 50

107.1

Step-by-step explanation:

Adjacent = 90

Height of the tree(opposite) = x

so what connects adjacent and opposite is TOA

Tanθ = opposite /Adjacent

Tan 50° = x/90

cross multiply

x = 90 Tan 50°

x = 90 × 1.19

x = 107.1m

:- the height of the tree is 107.1m

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The required probability that the spinner and number cube both lands on number 2 is 1/4. Option E is correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Total sample space = 4 × 6 = 24
Favorable event  = (2, 2) = 1
The probability that the spinner and number cube both lands on number 2,
= favorable outcome/sample space
= 1 / 24

Thus, the required probability that the spinner and number cube both lands on number 2 is 1/4. Option E is correct.

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Answer:

-12/3

Step-by-step explanation:

the slope of a linear equation is defined as

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

y is the output so in this case, the y's would be f(n) on the chart

x is the input so in this case the x's would be n on the chart

to keep things simple ill use the first 2 columns of the chart, which give the (x,y) pairs (-3,15) and (0,3)

Simply plug these x's and y's into the above equation to get the slope

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\\frac{3 -15 }{0--3 }\\\frac{-12}{3} \\[/tex]

The volume of the solid cone obtained by rotating the region bounded by the line y=12x, y=0, and x=4 about the x-axis is 38603.89 [tex]unit^{3}[/tex]

We will calculate the volume in the following way,

Given lines are: x=4, y=0, y=12x

First, we make a triangle from the given equation and then rotate it along the x-axis to get the dimensions of the cone.

We, need to put x=4 and y=0 in y=12x to get all the vertices of the triangle.

Points are: (0, 0), (4, 0), and (4, 48).

Now, we rotate this triangle about the x-axis.

Thus, the radius of the cone(r)= 48 and the height of the cone(h)= 4.

Therefore, the formula for the volume of the cone (v)= [tex]\frac{4}{3}*(\pi *r^{2}*h )[/tex]

=[tex]\frac{4}{3} \pi*48^{2}*4[/tex]

=38603.89 [tex]units^3[/tex]

Therefore the volume obtained is 38603.89 [tex]unit^{3}[/tex]

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Answer:

4

Step-by-step explanation:

x + 8 = 12

Subtract 8 from both sides :

x = 12 - 8

x = 4

Hope this helped and have a good day

Therefore the probability that out of ten randomly selected 30 year old in 1970. at least one did not earn more than his or her parents at age 30  is 0.8448

The study of probabilities involves calculating the possibility that an event will occur or that a proposition is accurate. The probability of an event is a number between 0 and 1, where 0 often represents impossibility and 1 typically represents certainty.

Here,

It is found by reading so it says ten so we multiply 0.8300 10 times by one and one example 0.0830,0 0.8300, 0.8300 ,0.8300..... and so forth or else you will not get the correct answer, there is an easier way to put in the calculator but you figure that out

after we found that we get =

1−0.830010^10

Our response is 0.1552, so since it specifies "at least," we deduct 1.

= 1−0.1552

and our answer is :

= 0.8448

Therefore, the probability that out of ten randomly selected 30 year old in 1970. at least one did not earn more than his or her parents at age 30  is 0.8448

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The probability that you flip 'heads' and roll a number less than 5 is 1/3.

The probability of flipping heads is 1/2, and the probability of rolling a number less than 5 is 4/6.

The probability of both occurring is the product of the two probabilities, or 1/2 multiplied by 4/6, which is equal to 1/3.

This means that the probability of flipping heads and rolling a number less than 5 is 1/3.

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When the point N is dilated, the coordinate of N changes to N' ,the coordinate of point N is (8,12).

What is dilation?

In arithmetic, a dilation may be a perform f from a mathematical space M into itself that satisfies the identity d=rd for all points x, y \in M, wherever d is that the distance from x to y and r is a few positive imaginary number.

Main body;

How to determine the coordinate of N

The given parameters are:

N' = (10,15)

k = 5/4

To calculate the coordinate of N, we make use of:

N * k = N'

So, we have:

N * 5/4 = (10,15)

Multiply both sides by 4

N * 5 = (40,60)

Divide both sides by 5

N = (8,12)

Hence, the coordinate of point N is (8,12)

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Answer: 5

Step-by-step explanation:

(5^2) - (4 x 5)

The slope of the line as per the given points will be equal to 7/10.

It is possible to determine a line's direction and steepness by looking at its slope.

Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the given information in the question,

The given points are (25, 24) and (15, 17)

Use the formula to find the slope,

m = (y₂ - y₁)/(x₂ - x₁)

Substitute the values in the above formula,

m = (17 - 24)/(15 - 25)

m = -7/-10

m = 7/10

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Step-by-step explanation:

10.

-2 < 6x - 2 < 46

0 < 6x < 48

0 < x < 8

so the line goes (with empty dots because of "<") from 0 to 8.

11.

4 + 9r <= 58 or 7r - 3 >= 46

9r <= 54 or 7r >= 49

r <= 6 or r >= 7

the line goes (with filled dots because of ">=" and "<=") from 6 all the way to the left, and from 7 all the way to the right.

12.

filled dot at -4, empty dot at +3.

connecting line between both dots.

-4 <= x < 3

13.

filled dots at -1 and at +6.

lines going away left and right.

x <= -1 or x >= 6

14.

empty dots at +3 and +4.

lines going away left and right.

x < 3 or x > 4

15.

filled dot at +6, empty dot at +8.

connecting line between both dots.

6 <= x < 8

Probability that any one of three outcomes will occur: P(A, B, C), plus P(A, B, C'), plus P(A, B', C);

What is the probability that 3 people have different birthdays?

Since there are 363 days still “unused” out of 365, we have p = 363÷365 = about 0.9945. Multiply that by the 0.9973 for two people and you have about 0.9918, the probability that three randomly selected people will have different birthdays.

Poisson Way. The probability of same-birthdays triplet is 1 / (365 * 365), which is very small, and there are C(n, 3) triplets, which is a big number for the moderately high values of n (~>20).

Calculating the likelihood of three events

Probability that at least one of the three events occurs: Probability that each of the three occurrences will occur: P(A, B, C);

Probability that any one of three outcomes will occur: P(A, B, C), plus P(A, B, C'), plus P(A, B', C);

P() is the likelihood that none of the events will occur.

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Answer:

y-intercept: (0,4)

y-intercept in the coordinate form: (0,4)

The equation in slope-intercept form: y=7x+4

Step-by-step explanation:

The slope is rise/run

We see that the y increase by 28 and the x increase by 4, so the slope is 28/4 = 7

m = 7

We know that the y-intercept is at (0,4)

So the slope-intercept equation will be

y = 7x + 4

Answer:

y- intercept = 0.4

y- intercept in the coordinate = 0.4

so the equation is : y=7x+4