Two angles across from each other at and intersection of two lines are called ?

Answer:

Step-by-step explanation:

The central angle and the angle between the tangents are supplementary, so

x + 26° = 180° ( subtract 26° from both sides )

26 - 26 = 0

180 - 26 = 154

x = 154°

The value of the x will be 154°.

The central angle and the angle between the tangents are supplementary.

If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to line L.

So,

x + 26° = 180°

Subtract 26° from both sides;

x + 26 - 26 =  180 - 26

x = 154°

Hence, the value of the x will be 154°.

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The statement "the chance of it being a small sale is 0.20" is true. The sum of the probabilities of the three possible sales levels must equal 1, as they represent the complete set of the possible outcomes.

In this case, the probability of a large sale is 0.20 and the chance of the medium sale is 0.60, so the probability of a small sale is 1 - (0.20 + 0.60) = 0.20. This means that the probability of the small sale is also 0.20, so the statement that the chance of it being a small sale is 0.20 is true.

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To plot the function f(x) = -4x^2 + sin(5x) and its derivative, and to save the results in a file named "results.txt" with 2 decimal places.

You can use the following MATLAB code:

```matlab

x = -10:0.5:10; % Generate x values

f = -4*x.^2 + sin(5*x); % Calculate f(x)

df_dx = -8*x + 5*pi*cos(5*x); % Calculate the derivative

% Saving results to file

output = [x', f', df_dx'];

dlmwrite('results.txt', output, 'delimiter', '\t', 'precision', '%.2f');

1. First, we define the range of x values using the vector `-10:0.5:10` to cover the desired interval with a step size of 0.5.

2. Next, we calculate the values of f(x) and its derivative using the defined mathematical expressions.

3. We then plot the function and its derivative using the `plot` function. The red dashed line represents f(x), and the blue solid line represents its derivative.

4. To save the results, we create a matrix `output` that concatenates the x values, f(x), and the derivative column-wise.

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Answer:

rational

Step-by-step explanation:

If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if it cannot be written in this form, then it is irrational.       hope that helped

Answer:

2.72

Step-by-step explanation:

f(x)=g(x)

4.2x=2x+6

2.2x=6

x=2.72

In a group of 62 students, 27 are normal, 13 are abnormal, and 32 are normal-abnormal. We want to find the probability that a student picked at random is either normal or abnormal.

To calculate this probability, we need to consider the total number of students who are either normal or abnormal. This includes the students who are solely normal (27), solely abnormal (13), and those who are both normal and abnormal (32). We add these numbers together to get the total count of students who fall into either category, which is 27 + 13 + 32 = 72.

The probability of picking a student who is either normal or abnormal can be calculated by dividing the total count of students who are either normal or abnormal by the total number of students in the group. Therefore, the probability is 72/62 = 1.1613.

To find the probability of picking a student who is either normal or abnormal, we consider the total number of students falling into those categories. Since a student can only be classified as either normal, abnormal, or normal-abnormal, we need to count the students falling into each category and add them together. Dividing this sum by the total number of students gives us the probability. In this case, the probability is greater than 1 because there seems to be an error in the provided data, where the total count of students who are either normal or abnormal (72) exceeds the total number of students in the group (62).

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Answer:

  ST = 6

Step-by-step explanation:

The segment sum is ...

  QR +RS +ST = QT

  QR +2 +ST = 10 . . . . use given values

Since R is the midpoint of QS, we know QR = RS = 2. Now, we have ...

  ST = 10 -2 -QR = 10 -2 -2 = 6

The length of ST is 6.

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The general solution to the differential equation is y'' + 2y' + 5y = -2e^(-x)cos2x is-

y = c1y1 + c2y2.

Using the formula,y1'

= u1'(x) cos 2x + u2'(x) sin 2x + 2u1(x) sin 2x - 2u2(x) cos 2xy2'

= v1'(x) cos 2x + v2'(x) sin 2x + 2v1(x) sin 2x - 2v2(x) cos 2xand y1''

= (u1''(x) - 4u1(x) + 4u2'(x))cos 2x + (u2''(x) + 4u1'(x) + 4u2(x))sin 2xy2''

= (v1''(x) - 4v1(x) + 4v2'(x))cos 2x + (v2''(x) + 4v1'(x) + 4v2(x))sin 2x.

Substituting the above equations in equation (1),

-2e^(-x)cos2x

= y'' + 2y' + 5y

= [(u1''(x) - 4u1(x) + 4u2'(x))cos 2x + (u2''(x) + 4u1'(x) + 4u2(x))sin 2x] + 2 [(u1'(x) cos 2x + u2'(x) sin 2x + 2u1(x) sin 2x - 2u2(x) cos 2x) + (v1'(x) cos 2x + v2'(x) sin 2x + 2v1(x) sin 2x - 2v2(x) cos 2x)] + 5 [(u1(x) cos 2x + u2(x) sin 2x) + (v1(x) cos 2x + v2(x) sin 2x)] = [(u1''(x) - 4u1(x) + 4u2'(x)) + 2u1'(x) + 5u1(x)]cos 2x + [(u2''(x) + 4u1'(x) + 4u2(x)) + 2u2'(x) + 5u2(x)]sin 2x + [(v1''(x) - 4v1(x) + 4v2'(x)) + 2v1'(x) + 5v1(x)]cos 2x + [(v2''(x) + 4v1'(x) + 4v2(x)) + 2v2'(x) + 5v2(x)]sin 2x

Equating the coefficients of sin 2x and cos 2x, we get:

u1''(x) - 4u1(x) + 4u2'(x) + 2u1'(x) + 5u1(x) = 0    -----(2)

u2''(x) + 4u1'(x) + 4u2(x) + 2u2'(x) + 5u2(x) = -2e^(-x)    -----(3)

v1''(x) - 4v1(x) + 4v2'(x) + 2v1'(x) + 5v1(x)= 0    -----(4)

v2''(x) + 4v1'(x) + 4v2(x) + 2v2'(x) + 5v2(x) = 0    -----(5).

Solving the equations (2), (3), (4), and (5), we getu1(x)

= e^(-x) [c1 cos(2x) + c2 sin(2x) - (1/5) sin(2x) cos(x)]u2(x)

= (1/10) e^(-x) [4c2 cos(2x) - (2/5) (c1 - c2) sin(2x) - 2 cos(2x) cos(x)]v1(x)

= (1/5) e^(-x) [c3 cos(2x) + c4 sin(2x) + sin(2x) cos(x)]v2(x)

= (1/10) e^(-x) [-4c4 cos(2x) + (2/5) (c3 - c4) sin(2x) + 2 cos(2x) cos(x)]

Thus, the general solution to the differential equation-

y'' + 2y' + 5y = -2e^(-x)cos2x is

y = c1y1 + c2y2

where

y1 = u1(x) cos 2x + u2(x) sin 2x and y2

= v1(x) cos 2x + v2(x) sin 2x.

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By using the rotation formula, the image of the point (- 6, 4) after rotating 180° counterclockwise about the origin is equal to point (6, - 4).

In this problem we find the coordinates of the image, which is the result of rotating a point 180° counterclockwise (+ 180°) about the origin. Let be P(x, y) = (x, y) the coordinates of the point set on Cartesian plane, then the coordinates of the image are defined by the following expression:

P'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where θ is the angle of rotation, in degrees.

If we know that P(x, y) = (- 6, 4) and θ = 180°, then the coordinates of the image are, respectively:

P'(x, y) = (- 6 · cos 180° - 4 · sin 180°, - 6 · sin 180° + 4 · cos 180°)

P'(x, y) = (6, - 4)

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The area of the region that meets the given conditions is 1.

To find the area of the region that meets the given conditions, we need to calculate the definite integral of the curve y = e^x within the specified limits.

First, we need to find the intersection point between the strip and the curve. Setting y = 2 in the curve equation, we have:

2 = e^x

Taking the natural logarithm of both sides, we get:

ln(2) = x

So the intersection point is (ln(2), 2).

To find the area, we integrate the curve y = e^x from the y-axis to the intersection point (ln(2), 2):

A = ∫[0, ln(2)] e^x dx

Evaluating the integral, we have:

A = [e^x] from 0 to ln(2)

A = e^(ln(2)) - e^0

A = 2 - 1

A = 1

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The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2/3x + 5/2y = 15

4x + 15y = 12

Multiply the first equation by 6, to eliminate the fractions.

6 * (2/3x + 5/2y = 15)

This gives

4x + 15y = 90

Subtract the equation 4x + 15y = 90 from 4x + 15y = 12

4x - 4x + 15y - 15y = 12 - 90

Evaluate the difference

0 + 0 = -78

Evaluate the sum

0 = -78

The above equation is the same equation as option (b) 0 = 26

This is so because they both represent that the system of equations have no solution

Hence, the equation that could represent a linear combination of the system is 0 = 26

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Complete question

The system of equations below has no solution.

2/3x + 5/2y = 15

4x + 15y = 12

Which equation could represent a linear combination of the system?

Answer:

x=2

Step-by-step explanation:

7x=14

divide by 7 on each side to get x by itself

x=14/7

x=2

a. The tree diagram that summarizes the given probabilities is attached.

b.  The probability that the individual does not participate in sports, given that he graduate sis  0.2 =  20%.

We apply Bayes' theorem to calculate:

Probability (Does not participate in sports if graduates)  = (P(Does not participate in sports) * P(Graduates | Does not participate in sports)) / P(Graduates)

The given data include: probability of not participating in sports = 0.02 probability of graduating given no participation in sports = 0.82 probability of graduating  = 0.18

Probability (Does not participate in sports if graduates)  = (0.02 * 0.82) / 0.18 = 0.036 / 0.18=  0.2

| Sports | No Sports |

                          |-------|--------|

Student participates | 0.18  | 0.62  |

                          |-------|--------|

Student does not participate | 0.02  | 0.78  |

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It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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A sample distribution with n = 20 and a five-number summary of 2, 4, 6, 8, and 10 can be generated by arranging the values in increasing order as follows: 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10.

To construct a sample distribution with a specific five-number summary, we need to determine the arrangement of values within the dataset. The five-number summary consists of the minimum value (2), the first quartile (Q1, 4), the median (Q2, 6), the third quartile (Q3, 8), and the maximum value (10).

Since the dataset has 20 observations, we need to arrange these values in increasing order while ensuring that they match the given five-number summary. In this case, we can start by placing the minimum value of 2 at the beginning of the dataset. Next, we need to include additional values between 2 and 4 to represent the first quartile. We can add two 2's, a 3, and two 4's to achieve this.

Moving forward, we continue adding values to match the remaining quartiles. For Q2, we include values 5 and 6, and for Q3, we include three 8's and four 9's. Finally, we add four 10's to represent the maximum value.

By arranging the values in this manner, we obtain a sample distribution with n = 20 and a five-number summary of 2, 4, 6, 8, and 10.

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The percent change in the number of card collected from last month to the this month is 24%.

What is percentage of a number?

A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Given that, Evita collected 25 cards in the last month.

He collects 19 cards in the this month.

The difference between the number of cards  in the last month and the this month is ( 25 - 19) =6.

The percent change in the number of card collected from last month to this month is

=[(The difference of the number of cards)/(the number cards in last month)] × 100

= (6/25)× 100

= 24%

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Answer:

76

Step-by-step explanation:

Let x = number of pages

Since Charmaine had 16 pages left, subtract 16 from x to indicate that is the number of pages read like this: x - 16

Divide that by 3 like this: (x - 16)/3

Do the same for Bernice: (x - 36)/2

Make them equal to each other

(x - 16)/3 = (x - 36)/2

Cross multiply

2(x - 16) = 3(x - 36)

Distribute

2x - 32 = 3x - 108

Move like terms to the same side by subtracting 2x from both sides

2x - 32 = 3x - 108

- 2x         - 2x

-32 = x - 108

Add 108 to both sides

-32 = x - 108

+ 108    + 108

x = 76

This means there are 76 pages in the book.

a. The value of h'(3) is 45.

b. The value of H'(1) is 36.

The complete table is in the attachment. h' and H are derivates from function h(x) and H(x). Using the Chain Rules to derivate the function.

Calculate the h'(x) function

h(x) = f(g(x))

h'(x) = d/dx {f(g(x))}

h'(x) = f' (g(x)) × g'(x)

h'(3) = f' (g(3)) × g'(3)

h'(3) = f'(2) × 9

h'(3) = 5 × 9

h'(3) = 45

Calculate the H'(x) function

H(x) = g(f(x))

H'(x) = d/dx {g(f(x))}

H'(x) = g' (f(x)) × f'(x)

H'(1) = g' (f(1)) × f'(1)

H'(1) = g'(3) × 4

H'(1) = 9 × 4

H'(1) = 36

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SOLUTION:

Case: Parallelograms

Method:

Sketch the parallelogram

The angles mHence the angle J is 45 degrees

The angles mHowever,

Final answers:

1. J= 45 degrees {Opposite angles are equal in a parallelogram}

2. K= 135 degrees {Adjacent angles sum up to 180 degrees in a parallelogram}

Answer:

127 from 35

127 - 35

92

Step-by-step explanation:

Answer:

The pattern is plus 3, then plus 5

Step-by-step explanation:

1. 1 + 3= 4

2.  4 + 5= 9

So, the pattern is, plus 3 then plus 5

The prοbability that there will be fewer than 2 arrivals in a given minute \(P(X < 2) = e^{(-\lambda)} + \lambda * e^{(-\lambda)\)

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο determine the prοbability that there will be fewer than 2 arrivals in a given minute, we need tο knοw the arrival rate οr average number οf arrivals per minute. Withοut this infοrmatiοn, we cannοt calculate the exact prοbability.

Hοwever, we can make an assumptiοn οr use a hypοthetical scenariο fοr illustratiοn purpοses. Let's assume that the average number οf arrivals per minute is λ, where λ represents the rate parameter fοr a Pοissοn distributiοn. The Pοissοn distributiοn is cοmmοnly used tο mοdel the number οf events οccurring in a fixed interval οf time when the events happen independently and at a cοnstant average rate.

The prοbability οf having fewer than 2 arrivals in a given minute can be calculated as the sum οf the prοbabilities οf having 0 arrivals and having 1 arrival.

P(X < 2) = P(X = 0) + P(X = 1)

In a Poisson distribution, the probability of having x events occur is given by the formula:

\(P(X = x) = (e^{(-\lambda)} * \lambda ^x) / x\)

Using the assumption of λ, we can calculate the probability as:

P(X < 2) = P(X = 0) + P(X = 1) =\((e^{(-\lambda)} * \lambda^0) / 0! + (e^{(-\lambda)} * \lambda^1) / 1!\)

Simplifying further:

\(P(X < 2) = e^{(-\lambda)} + \lambda * e^{(-\lambda)\)

Please note that the value of λ is required to compute the probability accurately. Without knowing the specific value of λ, we cannot provide a numerical probability.

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Answer:

5.83 = CD

Step-by-step explanation:

We can use the pythagorean theorem to solve

The legs are the x and y distances

x = (1- -4) = 5 units and y = 3 units

a^2+ b^2 = c^2

5^2 + 3^2 = c^2

25+9 = c^2

34 = c^2

Taking the square root of each side

sqrt(34) = c  which is the distance from C to D

5.830951895 = CD

5.83 = CD

Answer:

C. 5.83

Step-by-step explanation:

This is the correct answer I took the exam

Answer:

Step-by-step explanation:

Area of the larger circle:

The shaded area:

Area of the larger circle:

Answer:

13.50h+75

Step-by-step explanation:

I believe this is the answer because 13.50 would be the "per" of the expression and the 75 bonus would be added. I hope this helps :)

Answer:

40 + 75x = 125 + 25x

Step-by-step explanation:

t takes 5 hours of work for each to cost the same.

The anti derivative of the function eˣ² is eˣ²/2x.

The given function is;  eˣ².

To find the anti derivative of the function, integrate the function with respect to x.

Let y = eˣ²

Integration of exponential function remains same but applying the chain rule, the derivative of the power of exponent comes at the denominator.

∫y. dx = ∫eˣ² .dx.

∫eˣ² .dx. = eˣ²/(d/dx)x²

∫eˣ² .dx. =  eˣ²/2x

Thus, the anti derivative of the function is found as eˣ²/2x.

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The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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