What is the Inequality for this graph?

Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is

1 - 1.9287 x 10⁻²².

It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.

We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.

Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.

Poisson distribution gives the probability of occurrence of any event in a given time interval.

Let the average number of event per year in 30 years of period is λ.

\(\lambda = \frac{1500}{30}\)

λ = 50

Let, the occurrence of an earthquake is a random variable x.

Then the probability that at least an earthquake occur in next 30 years is calculated as:

P(x ≥ 1) = 1 - P(x<1)

P(x ≥ 1) = 1- P(x=0)   -----(1)

PDF of Poisson distribution with parameter λ is given as:

\(P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}\)

So, in this case

\(P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}\)

\(P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}\)

\(P(x=0)={1.9287 \times 10^{-22}\)

Substitute this value in equation (1)

P(x ≥ 1) = 1 - 1.9287 x 10⁻²²

Hence, the probability of an earthquake in next 30 years is

1 - 1.9287 x 10⁻²².

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To determine the three angles in a triangle, we can use the Law of Cosines or the Law of Sines. However, since we are not given any side lengths, we will use the dot product formula to find the angles between the sides.

Then, we can compute the magnitudes of these vectors using the Pythagorean theorem:

|AB| = sqrt((Bx - Ax)^2 + (By - Ay)^2)
|AC| = sqrt((Cx - Ax)^2 + (Cy - Ay)^2)
|BC| = sqrt((Cx - Bx)^2 + (Cy - By)^2)

where (Ax, Ay), (Bx, By), and (Cx, Cy) are the coordinates of points A, B, and C, respectively.

Finally, we can use the dot product formula above to compute the cosines of angles A, B, and C, and then take the inverse cosine to find the angles in radians:

A = acos((AB · AC) / (|AB| · |AC|))
B = acos((AB · BC) / (|AB| · |BC|))
C = acos((AC · BC) / (|AC| · |BC|))

where acos denotes the inverse cosine function.

Therefore, we can determine all three angles in the triangle (in radians) using the above formulae.
It seems that the three points of the triangle were not provided in your question. To help you determine the angles of the triangle, please provide the coordinates of the three points (A, B, and C).

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The equation that gives total savings y as a function of the number of months x is y = $300x

Given that Mrs. White started saving $300 a month. After 3 months, she had $1200. Now, we need to write an equation that gives total savings y as a function of the number of months x
Let us consider that the total savings Mrs. White saved after x months = y
From the given data, we can see that the amount of saving she does each month = $300
So, at the end of 3 months, she had saved an amount of= $300 × 3 = $900
Total savings after 3 months, y = $1200
Thus, we can say that; the total amount she saves, increases every month by $300$300$300 ×x= $y (total savings)
We can write this equation as the function of total savings y as a function of the number of months
x:y = $300x

Thus, the equation that gives total savings y as a function of the number of months x is y = $300x.

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Answer:

Unknown

Step-by-step explanation:

You need to reduce the fractions the best you can and solve from there :) not to sure tho I am only 13

The solution of x for the equation \(\sqrt{3x - 4} = 2\sqrt{x-5}\) is x = 16.

Given,

The equation; \(\sqrt{3x-4} =2\sqrt{x-5}\)

We have to solve this equation to get the value of x.

That is,

\(\sqrt{3x-4} =2\sqrt{x-5}\)

Square both sides to remove square root.

\(\sqrt{3x-4} ^{2} = (2\sqrt{x-5} )^{2}\)

We get,

3x - 4 = 4 (x - 5)

That is,

3x - 4 = 4x - 20

Here,

20 - 4 = 4x - 3x

Then,

x = 16

That is,

The solution of x for the equation \(\sqrt{3x - 4} = 2\sqrt{x-5}\) is x = 16.

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Answer:

<     (less than)

Step-by-step explanation:

4.7*0.001 ___ 4

0.0047___4

0.0047 < 4

The example for a discrete sample space among the options given is option c, which is the number of possible values of heights of students. A discrete sample space refers to a set of possible outcomes that can be counted or listed, and this is the case with the possible values of heights of students.

On the other hand, options a, b, and d do not represent a discrete sample space because they involve continuous variables that can take on any value within a range, such as the number of outcomes when 100 coins are tossed or the maximum temperature recorded on a day. Overall, it is important to understand the concept of sample space in probability theory and how it relates to the nature of variables and possible outcomes.
a. Number of outcomes when 100 coins are tossed together.

Discrete sample spaces consist of a finite or countable number of outcomes, whereas continuous sample spaces have an infinite number of possible outcomes. In this case, tossing 100 coins results in a finite number of outcomes (2^100), making it a discrete sample space.

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The diameter of the pizza to the nearest inch is 11 inches.

Let's call the diameter of the pizza "d". The circumference of the pizza can be calculated using the formula:

C = πd

And since the outer edge of the crust from one piece measures 5.5 inches, that length is equal to 1/8 of the circumference of the pizza:

5.5 = (1/8)C

So we can substitute the formula for the circumference into this equation:

5.5 = (1/8)(πd)

Solving for d, we can multiply both sides by 8/π:

d = (5.5)(8/π)

Calculating the approximate value of π as 3.14, we get:

d ≈ (5.5)(8/3.14) = 11 inches

So the diameter of the pizza is approximately 11 inches, rounded to the nearest inch.

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The vector a with the same direction as (-10, 3, 10) and a length of 5 is approximately (-7.65, 2.29, 7.65).

To find a vector with the same direction as (-10, 3, 10) but with a length of 5, we can scale the original vector by dividing each component by its magnitude and then multiplying it by the desired length.

The original vector (-10, 3, 10) has a magnitude of √((-10)^2 + 3^2 + 10^2) = √(100 + 9 + 100) = √209.

To obtain a vector with a length of 5, we divide each component of the original vector by its magnitude:

x-component: -10 / √209

y-component: 3 / √209

z-component: 10 / √209

Now, we need to scale these components to have a length of 5. We multiply each component by 5:

x-component: (-10 / √209) * 5

y-component: (3 / √209) * 5

z-component: (10 / √209) * 5

Evaluating these expressions gives us the vector a:

a ≈ (-7.65, 2.29, 7.65)

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Answer:

f(x) = x² - 13x + 42

Step-by-step explanation:

given zeros are x = 6 and x = 7 then the corresponding factors are

(x - 6) and (x - 7)

the quadratic function is then the product of the factors , that is

f(x) = (x - 6)(x - 7) ← expand using FOIL

     = x² - 13x + 42

Step-by-step explanation:

The height of your chair can be described as 29 - 10 1/4.

We can do this math mentally to get an answer of 18 3/4, or we can write this in decimal form; 18.75 inches.

The height of your chair is 18.75 inches

The value of z* to construct a 99% confidence interval is 2.58.

The value of z* that can be used to construct confidence interval can be calculated or find out in many ways. But, usually and the easiest way is by look the value in T table.

The value of z* is equal to the value of critical value in t table. So, to find it we search the column of 99% confidence level or if use the one tail is equal to 0.005 or if use the two tail is equal to 0.01. Then, we search the row of z, after that we get the value of 2.576.

Attached image for t table.

Thus, the value of z* for 99% confidence interval is 2.58.

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Answer

ANGLE SIDE SIDE

Step-by-step explanation: Because you have an angle side side hope this helps

Answer:

5

Step-by-step explanation:

Answer:

8 weeks

Step-by-step explanation:

Answer:

No, but my friend's name is amber

Step-by-step explanation:

In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

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The 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

To find the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers, we can use the formula for the confidence interval for a proportion.

The formula for the confidence interval is:

CI = p1 ± Z * √((p1 * (1 - p1)) / n)

Where:

CI is the confidence interval,

p1 is the sample proportion (proportion of accidents involving teenage drivers),

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z ≈ 1.96),

n is the sample size (number of accidents checked).

Given:

Number of accidents checked (sample size), n = 582

Number of accidents involving teenage drivers, x = 91

First, we calculate the sample proportion:

p1 = x / n = 91 / 582 ≈ 0.1566

Now we can calculate the confidence interval:

CI = 0.1566 ± 1.96 * √((0.1566 * (1 - 0.1566)) / 582)

Calculating the standard error of the proportion:

SE = √((p1 * (1 - p1)) / n) = √((0.1566 * (1 - 0.1566)) / 582) ≈ 0.0184

Substituting the values into the formula:

CI = 0.1566 ± 1.96 * 0.0184

Calculating the values:

CI = 0.1566 ± 0.0361

Finally, we can simplify the confidence interval:

CI = (0.1205, 0.1927)

Therefore, the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

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The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

The final cost after the discount and tax is $179.76

Step-by-step explanation:

Since the discount is 30%, she only pays 70% of the price of the ticket.

Discounted price before tax:

70% of $240 = 0.7 × $240 = $168

Now think of the price $168 as a new price.

The price is $168 which is 100% of the price. Tax is 7% of the price, so you must pay 107% of the price.

107% of $168 = 1.07 × $168 = $179.76

Answer: The final cost after the discount and tax is $179.76

Answer:

42.6 degrees

Step-by-step explanation:

A supplementary angle is one that adds to the other one so the sum is 180 degrees. So 180-137.4=42.6

Answer:

-30, 210 and 330 degrees

Step-by-step explanation:

Given the expression Sin x = - 1/2

x = arcsin(-1/2)

x = -30 degrees

Since sin is negative in the third and fourth quadrant

x = 180 + 30

x = 210 degrees

In the fourth quadrant

x = 360 - 30

x = 330

Hence the value of x within the interval -360 < x < 360 are -30, 210 and 330 degrees

In this investigation, the dependent variable is the number of fish in the stream and the independent variable is the amount of pollution.

Variables are symbols or names that are used to represent values in a mathematical or scientific investigation. They allow us to describe and analyze patterns and relationships in data.

There are two main types of variables:

1. Independent variables are variables that are manipulated or controlled in an experiment to determine their effect on the dependent variable. The independent variable is also referred to as the predictor variable or the explanatory variable.

2. Dependent variables are variables that are being measured in an experiment and are dependent on the independent variable. The dependent variable is also referred to as the response variable or the outcome variable. It is the variable that is being affected by the independent variable.

The dependent variable is dependent on the independent variable, as changes in the amount of pollution are expected to affect the number of fish in the stream. The goal of the investigation is to determine the relationship between the two variables and see how changes in the amount of pollution affect the number of fish in the stream.

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Answer:

central angle ( θ) = 1.91875radians

central angle ( θ) in degrees = 109.92degree

Step-by-step explanation:

Given:

diameter of 320 millimeters

Then the Radius of the circular

brake drum can be calculated as

Radius =Diameter/2

Radius = 320 millimeters/ 2

Radius= 160 millimeters

central angle ( θ) = arc/r

central angle ( θ) = 307 millimeters /160 millimeters

central angle ( θ) = 1.91875radians

Than to convert it to degrees we have

1rad × 180/π = degree

Where π =3.142

central angle ( θ) = 1.91875radians * 180/π

Therefore,central angle ( θ) in degrees = 109.92degree

Answer:

if point bearing of k-l is 084 degree so the bearing of point l-k is 84 degree

The bearing of a point L from a point K is 264 degrees.

What is Addition?

A process of combining two or more numbers is called addition.

Given that;

The bearing of a point K from a point L is 084 degrees.

Now,

Since, The bearing of a point K from a point L is 084 degrees.

Hence, The bearing of a point L from a point K = 180° + 84°

                                                                         = 264°

Thus, The bearing of a point L from a point K is 264 degrees.

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Answer:

Use slope formula,m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, to find the slope of a line that passes through the points (–3, 8) and (4, –6).

m =

✔ -2

Use slope-intercept form, y = mx + b, to find the y-intercept (b) of the line.

b =

✔ 2

What is the new equation written in slope-intercept form, y = mx + b?

✔ y = -2x + 2

Step-by-step explanation:

MidPoint that \($PQ/FH = 1+1 = \boxed{2}$\)

Since M is the midpoint of EF, we have EM = FM.

Similarly, since N is the midpoint of EH, we have EN = HN.

Since EFGH is a parallelogram, we have FG || EH, so by the parallel lines proportionality theorem, we have

\(FP/FH\) = \(GM/GH\) and \(HQ/FH\)

​ = \(GN/GH\)

​Adding these two equations, we get

\((FP+HQ)/FH\)

​ = \((GM+GN)/GH\)

​But \($GM+GN\) = MN = \(\frac{1}{2}EH = \frac{1}{2}FG$\), since EFGH is a parallelogram.

\((FP+HQ)/FH\) = \(\frac{1}{2} FG / GH\)

That \($\triangle FGH$ and $\triangle FGP$\) are similar (since \($\angle FGP = \angle FGH$ and $\angle GPF = \angle HFG$\)), so we have \($GP/GH = FG/FH$\). Similarly, we have\($HQ/GH = EH/FH = FG/FH$\) (since EFGH is a parallelogram).

Therefore,

\({(FP+HQ)}/FH\)= \({(\frac{1}{2} FG)}/GH\) = \({(GP+HQ)} /GH\)

Implies that \($PQ/FH = FP/GP + HQ/HQ$\). But \($FP/GP = 1$\) (since \($\triangle FGP$\) is isosceles with \($FG = GP$\)), and \($HQ/HQ = 1$\) as well.

we have \($PQ/FH = 1+1 = \boxed{2}$\).

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