Volcanic eruptions of Mt. Vesuvius follow a Poisson distribution with an average of 2.5 eruptions every 100 years. Use that to answer the following:
a) Find the probability that there will be exactly 3 eruptions in the next 200 years. (6 points) (Round your answer to 4 decimal places)
b) Find the probability the next eruption occurs between 25 and 50 years. (6 points) (Round your answer to 4 decimal places)

The scale factor is 2 if the two triangles are similar to each other after applying the property of a similar triangle.

The ratio among comparable dimensions of an object and a model with that object, known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

It is given that:

Two triangles are shown in the picture

From the definition of the similar triangle.

Scale factor = 6/3 = 2

Thus, the scale factor is 2 if the two triangles are similar to each other after applying the property of a similar triangle.

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Answer:

21 meters

Step-by-step explanation:

you can see it goes 21 meters before it hits the ground

Answer:

21 is the answer

When the null hypothesis is rejected possible a Type i error has occurred.

Let's Understand what is null hypothesis?

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a set of provided observations. Using sample data, hypothesis testing is used to judge a hypothesis' veracity. It is sometimes referred to as just "the null" and its symbol is [tex]H_{0}[/tex].

We have total 4 cases:

[tex]H_{0}[/tex]  accepted when  [tex]H_{0}[/tex] is true ->  Correct decision

[tex]H_{0}[/tex] rejected when [tex]H_{0}[/tex] is true -> Type i Error  when null hypothesis is  present and we have rejected

[tex]H_{0}[/tex] accepted when [tex]H_{0}[/tex] is false -> Type ii Error when null hypothesis is not  present but we have accepted

[tex]H_{0}[/tex] rejected when [tex]H_{0}[/tex] is false -> Correct decision.

So according to question null hypothesis is rejected so we have two options Either Null hypothesis is present or not present.

if it is present  then it is Type i Error.

if it is not present then it is Correct decision.

So when the null hypothesis is rejected possible a Type i error has occurred.

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3456

Step-by-step explanation:

2x2=4 3456 67867789990

A 96% confidence interval for the mean difference in textbook prices at the two online bookstores is (3.22,8.38).

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

The mean and standard deviation are M = 5.8 and s = 4.658

To calculate the estimated standard error, we apply

S = [tex]\sqrt{s^2/n}[/tex]

 =[tex]\sqrt{4.658^2/5}[/tex]

= 2.08

The 96% confidence interval is :

CI = x ±t₉₆s/√n

= 5.8 ±2.7764× 2.08/√5

= 5.8±2.58

= (3.22,8.38)

Hence, a 96% confidence interval for the mean difference in textbook prices at the two online bookstores is (3.22,8.38).

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Answer:

-4/5 (fraction)

Step-by-step explanation:

add the numbers:

25x^2-16=0

use quadratic formula

simplify -40/50

-4/5

Answer:

no

Step-by-step explanation:

Using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

The characteristics of normal distributions are as follows: Bell-like in its symmetry.

The distribution's mean and median, which are both at its center, are equal.

68 percent of the data, or approximately, falls within one standard deviation of the mean.

So, the formula is used to determine the Z score for a data point x in a normal distribution:

Z = z - mean/standard deviation

Now, use the formula to calculate the z value as follows:

Z = z - mean/standard deviation

Z = 25 - 16/6

Z = 9/6

Z = 3/2

Z = 1.5

Therefore, using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.

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Answer:

larysa got a larger drawing because 1 in 5 is bigger then 1 in 8 yards so that makes her area way larger

Answer:

15%

Step-by-step explanation:

i hope i got this right

Answer:

15% is the answer to your question

A complex number is represented on a complex plane. The number [tex]z = 3-5i[/tex] is represented in a smilar manner as real numbers but y axis cosidered a imaginary axis.

What is a complex plane?

A complex plane is formed by complex numbers in a similar manner as the Cartesian coordinate system. But the x axis is made up of real numbers and y axis is made up of imaginary numbers.

A complex number is plotted on a complex plane. In the complex plane the x axis is known as the real axis and the y axis is known as the imaginary axis.

Consider the given complex number.

[tex]z = 3-5i[/tex]

Here, 3 is real number and -5 is imaginary number.

Since 3 is real number hence, move 3 steps in the right direction on x axis. Now, -5 is the imaginary number hence, move 5 steps in the downward direction parallel to the y axis.

The final position is [tex]z = 3-5i[/tex].  

Hence, a complex number is represented on a complex plane.

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The acceleration of the truck when it has a mass of 5000 kg and the truck driver presses on the brakes is 1.2m/s².

The rate of change of an object's velocity with respect to time is defined as acceleration. Vector quantities are accelerations.

The orientation of an object's acceleration is determined by the orientation of the net force acting on that object's acceleration, which is the rate at which velocity changes over time in terms of both speed and direction. A point or object moving in a straight line is accelerated if it accelerates or decelerates.

Acceleration will be:

= Force / mass

= 6000 / 5000

= 1.2 m/s²

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With a 95% confidence interval, the proportion of all shrubs of this species that will resprout after a fire is between 0.17 and 0.67.

What is a confidence interval?

An area surrounding a measurement that indicates how accurate it is called a confidence interval.

Here, we have

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means the probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 14

x = 6

p = 6/14 = 0.42

q = 1 - 0.42 = 0.58

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail.

Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 2.05. Thus, Thus, the z score for a confidence level of 95% is 1.96

Therefore, the 95% confidence interval is

0.42 ± 1.96√(0.58)(0.42)/14

The lower limit of the confidence interval is

0.42 - 0.25 = 0.17

The upper limit of the confidence interval is

0.42 + 0.25 = 0.67

Hence, with a 95% confidence interval, the proportion of all shrubs of this species that will resprout after a fire is between 0.17 and 0.67.

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The area between one standard deviation and either side of mean is 34%

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

In particular, the empirical rule predicts that 68% of observations falls within the first standard deviation (µ ± σ)

95% within the first two standard deviations (µ ± 2σ)

99.7% within the first three standard deviations (µ ± 3σ).

According to the question,

If we place the flag 1 standard deviation on either side of the mean

which means flag is placed either on (µ + σ) or ( (µ - σ)

and Using Empirical rule,

68% of area lie under (µ ± σ)

Therefore , Area between either  (µ + σ) or ( (µ - σ) = 68 / 2

=> 34%

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I don't know for certain if you are trying to write this in standard form, graph it, or so forth. However, here is the standard form.

Standard Form:

[tex](x+2)^2+(y-2)^2=36\\[/tex]

Hope this helps you!

The worth of the stock after the increase is $14.375.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Based on the information given, the addition expression will be:

= Original value + Increase

= $11.50 + (1/4 × $11.50)

= $11.50 + $2.875

= $14.375

The value is $14.375.

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Expression [tex]\frac{x^7y^5}{x^2y^3}[/tex] can be simplified as x⁵y² by applying laws of components.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

[tex]\frac{x^7y^5}{x^2y^3}[/tex]

Simplify the expression by using law of exponents [tex]a^n/a^m =a^{(n-m)[/tex],

The expression can be rewritten as,

= [tex]x^{(7-2)}{y^{(5-3)}[/tex]

= x⁵ y²

The expression can be simplified as x⁵y².

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Answer:

$747.50

Step-by-step explanation:

There is a 0.044% probability of having exactly 8 boys in a sample of 10 births.

Simply put, the probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2 (a head or tail).

P(heads) = 1/2 is what we write.

So, X is the proportion of boys among n particular births. Let p represent the likelihood of having a boy at a certain birth.

Here n=10.

Additionally, because male and female births are equally likely, there is a 50% chance of having a boy or a girl.

P(Boy) = P(girl) = 0.5

p = 0.5

Based on the information provided, there will be a defined number of trials (n) of 10, with a constant chance of success (p).

Furthermore, every trial stands alone from the others.

So, with n=10 and p=0.5, X follows a binomial distribution.

The following is the probability function of the binomial distribution for the k number of successes, where x = k.

[tex]\mathrm{P}(\mathrm{X}=\mathrm{k})=(10 C k) 0.5^k(1-0.5)^{10-k}[/tex]

Finding the likelihood of 8 boys in n=10 births is necessary.

P(X=8) = (10C8)0.5⁸(1-0.5)¹⁰⁻⁸

= 45 × 0.0039 × 0.25

P(X = 8) = 0.0438

Therefore, there is a 0.044% probability of having exactly 8 boys in a sample of 10 births.

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The probability of rolling a 3 the first time and a 3 the second time is 1/36.

Given that,

There are two rolls of one die.

We have to determine the probability of receiving a 3 both the first and second times.

We know that,

There are 6 faces on a die.

Of these 6 faces, one of them is 3 and one of them is 3

So, the probabilities of rolling a 3 and a 3 are:

P(3) = 1/6

P(3) = 1/6

The probability of rolling a 3 the first time and a 3 the second time is calculated as follows:

Pr=P(3)×P(3)

This gives

Pr=1/6×1/6

Multiply

Pr=1/36

Therefore, the probability of rolling a 3 the first time and a 3 the second time is 1/36.

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The weekly goal of 150 minutes of moderate exercise or 75 minutes of intense exercise has increased by 22.9 percent.

The intensity of exercises depends on mostly the amount of energy you have to spend. But the time spent also differs. Intense exercises are basically exercises that require you to expend more energy than how much you spend on normal exercise. Any exercise becomes intense when you spend 70 to 85 percent of your maximum heart rate working out. It is vigorous but you get the same amount of calories burned.

Moderate exercises are the normal ones. These require normal intake of heart rate and energy but take more time. The walk from your house to your college/school or the normal crunches and all you do are perfect examples of moderate exercises.

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Answer: A

Step-by-step explanation: To solve this problem, we need to use the properties of triangles and the given information to determine the measure of angle C.

First, we can use the fact that angle A is opposite angle C to deduce that angles A and C are congruent (i.e. they have the same measure). This means that the measure of angle C is 25 degrees.

Next, we can use the fact that triangle AABC is isosceles (i.e. it has two sides of equal length) to deduce that angle B is also 25 degrees. This is because the sum of the interior angles of a triangle is 180 degrees, so if angle A is 25 degrees and angle C is 25 degrees, then the remaining angle, angle B, must be 180 - (25 + 25) = 130 degrees.

We can also use the fact that triangle AEFG is isosceles to deduce that angle F is also 100 degrees. This is because the sum of the interior angles of a triangle is 180 degrees, so if angle E is 100 degrees, then the remaining angle, angle F, must be 180 - 100 = 80 degrees.

Finally, we can use the given information that the measure of angle Z is 25 degrees and the measure of angle F is 100 degrees to deduce that the measure of angle X is 180 - (25 + 100) = 55 degrees. This is because the sum of the interior angles of a triangle is 180 degrees, and we have already determined the measures of two of the angles (angles Z and F).

Therefore, the measure of angle C is 25 degrees, which means the correct answer is A) 125 degrees.

Answer:

y = 3 cos (π (0-3) + 2)

y = 3 cos (-2π + 2)

y = 3 cos (-2)

y = 3(-1)

y = -3

Answer:

y - 8 = -1/11(x - 7)

Step-by-step explanation:

Answer:

has to be c other wise it would make sense

Answer: The glass of water has inertia

Step-by-step explanation: The trick works no matter how heavy an object is since friction is weaker for lighter objects. Provided you pull quickly enough, this trick can even be done with glasses or plate

If we live on the moon, a day on the Moon is about a lunar month long

The correct answer is an option (c)

We know that a day is the length of time between two noons or sunsets. A day is of 24 hours on Earth and 708.7 hours (which is 29.53 Earth days) on the moon.

We know that a lunar month is nothing but the time the Moon takes to go around the Earth.

A lunar month is of approximately 29.53 days.

This means, a day on the Moon is about a lunar month.

Therefore, a day on the Moon is of 708.7 hours i.e., about a lunar month.

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Step-by-step explanation:

the table was filled correctly already by somebody yesterday.

the important thing to remember is that an arc angle is always measured at the center point of the circle. that is the difference to angles between the intersecting lines of arc segments.

it would be really important that you start doing these things yourself. this hands-on experience of these (really basic) questions is designed to help you get a feeling how these things work together, which makes later topics much easier for you.

please tell me what you don't understand here. you only need to apply common sense. no magic voodoo math formulas or strategies.

FAR = 100° FR = 140° VO = 60° FR+VO = 200°

FAV = 80° FV = 60° RO = 100° FV+RO = 160°

OAV = 100° VO = 60° FR = 140° VO+FR = 200°

OAR = 80° RO = 100° FV = 60° RO+FV = 160°

how did we get the measures of the intercepted arcs ? by counting the 20° segments on the arc. the full circle arc represents 360°. always, for every circle. one time around is one time around and therefore 360°, no matter the size of the circle.

when you stand directly on the south pole of the Earth for 24 hours, you will have rotated the full 360° in that time (one rotation per day). if you stand on the equator for 24 hours, the Earth has taken you on one spin of the full 360°. the difference is the absolute arc length and the necessary speed at which we cover the distance of a full arc length.

every 250 million years our whole sogar system rotates once (by the full 360°) around the center of our galaxy.

the degrees have nothing to do with radius, diameter, area, ... of a circle. only with the relative parts of the circumference. when the minute arm of a clock moved for 15 minutes, then it went 90° around the clock's face. after 60 minutes it went the full 360°, and the cycle starts anew.

so, minutes on a clock or hours of the day are just another way of counting degrees around a circle.

what have we noticed with the sum of the measures of the intercepted arcs ?

many things.

e.g.

they are exactly twice as large as the line angles. 100 to 200. 80 to 160.

the sum of 2 pairs of opposing arc angles is always 360°.

...

so, how will we get the line angles based on the sum of the angles of the intersected arcs ?

we cut the sum of the intersected arc angles in half. 200 to 100. 160 to 80.

Adjacent angles of a parallelogram are supplementary.

[tex]y+3y=180 \\ \\ 4y=180 \\ \\ y=\boxed{45} \\ \\ \\ \\ 3(45)+3x=180 \\ \\ 45+x=60 \\ \\ x=\boxed{15}[/tex]