three points x1, x2, x3 are selected at random on a line l. what is the probability that x2 lies between x1 and x3?

a) The luminosity of Alpha Centauri A is 3.817 × \(10^26\)Watts.

b) The light bulb must be placed at a distance of 1.9×\(10^17\)m away.

a) To calculate the luminosity of Alpha Centauri A, we can use the inverse square law for light. This law states that the luminosity of a light source is equal to the apparent brightness divided by 4π times the square of the distance. The apparent brightness of Alpha Centauri A is given as 2.7×\(10 ^−8\)Watts/m2 and its distance is 4.4 light-years, which is equal to 4.05 × \(10^16\)m. Thus, the luminosity of Alpha Centauri A is equal to 2.7 × \(10^-8\)Watts/m2 divided by (4π ×(4.05 × \(10^16\) m)2), which is equal to (4π×(4.05 × \(10^16\)m)2) Watts.

b) To calculate the distance at which a light bulb must be placed in order to have the same apparent brightness as Alpha Centauri A, we can again use the inverse square law for light. This time, we will use the given luminosity of the light bulb (100 Watts) and the given apparent brightness of Alpha Centauri A (2.7 × \(10^-8\)Watts/m2). Rearranging the equation, we get the distance equal to the square root of (100 Watts divided by 4π times 2.7 × \(10^-8\)Watts/m2), which is equal to 1.9 ×\(10^17\)m. Thus, the light bulb must be placed at a distance of1.9 × \(10^17\)m away in order to have the same apparent brightness as Alpha Centauri A in our sky.

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Answer:

center: (-3, 4)

radius: 4

Explanation:

The equation of a circle with radius r and center (h, k) is equal to

In this case, the given equation is

This equation can also be written as

Therefore, (h, k) = (-3, 4 and r = 4. It means that the answers are

center: (-3, 4)

radius: 4

Answer:(3,0) , (-2,0)

Step-by-step explanation:To find the x-intercept, substitute in  0 for y and solve for x

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\(f(x) = {x}^{2} - x - 6 \)

\(f(x) = (x - 3)(x + 2)\)

\(0 = (x - 3)(x + 2)\)

_________________________________

Hint :

\(a \times b = 0\)

\(a = 0 \: \: \: or \: \: \: b = 0\)

_________________________________

Thus ;

\( x - 3 = 0\)

Add sides 3

\(x - 3 + 3 = 0 + 3\)

\(x = 3\)

Or

\(x + 2 = 0\)

Subtract sides 2

\(x + 2 - 2 = 0 - 2\)

\(x = - 2\)

Thus the x-intercepts are (( - 2 )) and (( 3 )) .

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Answer:

y+9 = -7 (x-5)

Step-by-step explanation:

The point-slope form of the equation of a line is

y-y1=m(x-x1)

y-(-9)= -7(x-5)

y+9= -7(x-5) <---This is the answer

A model that would predict the population after m months is 714(0.9792)^m.

The population declines by 25% every month, in order to determine the monthly rate of decline, divide 25% by 12.

Monthly rate of decline = 25% / 12 = 2.08%

The equation that can be used to determine the population after m months is:

P( 1 - r)^m

Where:

The model : 714( 1 - 0.0208)^m

714(0.9792)^m

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The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.

It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.

A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.

A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.

For the Z-test, the test statistic is computed as

z = (x - μ) / (σ / √n)

where x = sample mean,

μ = population mean,

σ= population standard deviation,

and n = sample size.

The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.

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Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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You didn't give a graph but I will visualize what it looks like for you.

The line is going through (0,-2) because that is the y-intercept.

The line has a slope of 3.

So, the line goes through:

(1,1)

(2,4)

(3,7)

(4,10)

(5,13)

Since there is no picture provided, I can't give you the answer, but I can help you solve it.  

To solve this you have to first look at the b part of the formula y=mx+b, so -2.

Then, you can find -2 on the y-axis (the vertical axis)

and then you could move upwards 3 spaces, then right 1 space.

You would do this as the slope is 3/1 (the mx part of the equation).

Finally, you continue to move up 3, and right 1 until there are enough points on the graph to make a line, and that will help you see what graph is correct.

It should look something like this:

Answer:

8(h)=96

Step-by-step explanation:

Remember when you are writing a multiplication equation, it's a division backwards.

96/8=h

h×8=96

hope this helps you

goodluck

Answer: 8x=96

Step-by-step explanation:

8X = 96

X = 96/8

X = 12 hours

Answer:

I think 2 and 3

Step-by-step explanation:

The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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I already answered this question to this student today. Student unresponsive.

Given:

Where the Mean (μ ) and Standard Deviation (σ) for a Normal Distribution, you need to find:

Where "X" is the number of hours worked per worker.

In order to calculate that probability, you should approximate to a Standard Normal Distribution. Therefore, you need to find z-statistic:

The value of "X" you must use is:

Then, substituting values and evaluating, you get:

Therefore, now you need to find:

Now you need to use the Standard Normal Distribution Table in order to find the value of the probability. Then, you get:

Hence, the answer is:

The law of motion for the unemployment rate is given by the equation: Δu = fu - s(1 - u). The correct option is (a) Δu = fu - s(1 - u).

The equation represents the change in the unemployment rate (Δu) over time. Let's break down the components of the equation:

- fu represents the job finding rate (f) multiplied by the current unemployment rate (u). This term represents the number of unemployed individuals who find jobs and transition into employment, which decreases the unemployment rate.

- s(1 - u) represents the separation rate (s) multiplied by the difference between one and the current unemployment rate (1 - u). This term represents the number of individuals who become separated from their jobs and enter unemployment, which increases the unemployment rate.

Therefore, the equation Δu = fu - s(1 - u) combines the effects of job finding and separation rates on the change in the unemployment rate.

Thus, the correct option is (a) Δu = fu - s(1 - u)

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In a normal distribution, the mean represents the center of the distribution and the standard deviation represents the spread of the distribution.

The higher the standard deviation, the more spread out the data is. The probability of a specific outcome occurring is given by the area under the curve of the normal distribution that corresponds to that outcome.

For example, if we wanted to find the probability of x being between 45 and 55, we would find the area under the normal curve between those two values. This can be done using a table of standard normal probabilities or by using a calculator or statistical software.

In general, if we know the mean and standard deviation of a normally distributed random variable, we can use that information to find probabilities for specific outcomes or ranges of outcomes.

you'll need to provide a specific range or value of X. Once you have that, you can use the Z-score formula or a standard normal distribution table to determine the probability.

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The area enclosed by the curve, x - t² - 3t, y - vt and the y-axis is (9/2)v - 13.5 square units.

The area enclosed by the curve, x - t² - 3t, y - vt and the y-axis is obtained as follows:

1. The curve x = t² - 3t, y = vt intersects the y-axis when x = 0, which occurs when t = 0 and 3.

Therefore, the value of t lies between 0 and 3. Thus, the limits of integration are 0 and 3.S

2. Using A = ∫[a, b] ydx or A = ∫[c, d] xdy, where a, b, c, and d are the limits of integration, we have A = ∫[0, 3] xt - (t² - 3t)dv

3. Substituting x = t² - 3t and y = vt in the above equation, we have: A = ∫[0, 3] (t² - 3t)vt - (t² - 3t)dt

4. A = ∫[0, 3] (v - 1)(t² - 3t)dt

5. A = ∫[0, 3] v(t² - 3t)dt - ∫[0, 3] (t² - 3t)dt

6. Using integration by substitution, let u = t² - 3t. Then, du/dt = 2t - 3dt = 0.5(2t - 3)dt.

7. ∫v(u) du = v(u) * du/dt * dt. Thus, A = ∫[0, 3] v(2t - 3) (0.5dt) - ∫[0, 3] u(0.5dt)

8. Therefore, A = 0.5∫[0, 3] v(2t - 3)dt - 0.5∫[0, 3] udt

9. A = 0.5[(2v/3)(3³ - 0³) - 3v(3² - 0²)] - 0.5[(3² - 0²)(3 - 0)]

10. Simplifying, we get A = (9/2)v - 13.5 square units.

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For function represented as "f(x) = 3x(x+5)", the value of f(-2) is -18.

The 'Function" is a rule which assigns unique output value for each input value for given set. A function takes one or more inputs, and produces a "single-output", The "input-values" are called domain, and "output-values" are named as range.

In order to find the value of function at "-2", we substitute x as "-2" in the given function f(x) and then evaluate the expression:

We get,

⇒ f(x) = 3x(x+5),

⇒ f(-2) = 3(-2)(-2+5),

⇒ f(-2) = 3(-2)(3),

⇒ f(-2) = -18,

Therefore, the value of f(-2) is -18.

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The given question is incomplete, the complete question is

For the function f(x) = 3x(x+5), find the value of f(-2).

The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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Answer:

Step-by-step explanation:

Use the formula to find the z-score, then go to the table that will give you the probability that the value is less than this z-score.

\(z=\frac{53-50}{3}=1\)

The probability that the value lies to the left of 1 on a standard bell curve is 84.1345%, or 84%, the third choice down.

The value of  P(x≤53) is 0.84, the correct option is C.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Mean=50

Now,

To find P(x≤53), you can use a normal distribution calculator1234 or a normal distribution table. You need to convert the raw score of 53 into a standard score (or z-score) by using the formula:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation. In this case, x = 53, μ = 50, and σ = 3. So,

z = (53 - 50) / 3

z = 1

Then, you can enter the z-score and the mean and standard deviation of the normal distribution into the calculator or look up the z-score in the table. The calculator or table will give you the cumulative probability of getting a z-score less than or equal to 1. This is the same as P(x≤53).

Therefore, by probability the answer will be 0.84.

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No fallacy is committed in the given immediate inference, as it follows the rules of the square of opposition.

The immediate inference presented in the statement is valid and can be categorized as a particular affirmative proposition (I-type) of the square of opposition.According to the square of opposition, a particular affirmative proposition can be inferred from a universal affirmative proposition (A-type) when the subject is distributed.

In the given statement, the universal affirmative proposition is "All advocates of school prayer are individuals who insist on imposing their views on others," which distributes the subject "advocates of school prayer."

Therefore, the particular affirmative proposition "Some advocates of school prayer are individuals who insist on imposing their views on others" can be inferred from the universal affirmative proposition.

No fallacy is committed in the given immediate inference, as it follows the rules of the square of opposition. However, it should be noted that the validity of the inference does not necessarily imply the truthfulness of the statement, as it is possible for some advocates of school prayer to not insist on imposing their views on others.

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Answer: Elise's number is 37

Step-by-step explanation:

-5(x-19)=-90

-5x+95=-90

-5x=-185

x=37

Answer:

Step-by-step explanation:

First find the slope of the line

(4 , 3) ; x₁ = 4 ; y₁ = 3

(-4,-1) ; x₂ = -4 ; y₂ = -1

slope \(= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\)

        \(=\frac{-1-3}{-4-4}\\\\=\frac{-4}{-8}\\\\=\frac{1}{2}\)

m = 1/2 , and take any one point (4 , 3)

y -y1 = m(x - x1)

\(y - 3 = \frac{1}{2}(x - 4)\\\\y -3 = \frac{1}{2}x-4*\frac{1}{2}\\\\y - 3 =\frac{1}{2}x - 2\\\\y = \frac{1}{2}x - 2 + 3\\\\y =\frac{1}{2}x + 1\)

Answer:

3x-2y=0

Step-by-step explanation:

Using two point form for finding the equation:

\(y-y_{1} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} }(x-x_{1} )\)

Since the line is starting from origin then A(0,0) andpassing point B(8,12):

\(y-0=\frac{12-0}{8-0} (x-0)\)

\(y=\frac{12}{8}(x)\)

\(y=\frac{3}{2} (x)\)

\(2y=3x\)

\(3x-2y=0\)

Put the value of B(8,12) in the equation:

\(3x-2y=0\)

\(3(8)-2(12)=0\)

\(24-24=0\)

\(0=0\)

Hence the equation is correct

Hope it helps.

The probability that at most a fifth of the buyers would prefer green is approximately 0.0198

This problem can be solved by using the binomial distribution. Let X be the number of buyers out of 15 who prefer green. Then X follows a binomial distribution with parameters n = 15 and p = 0.6.

We want to find the probability that at most a fifth of the buyers would prefer green. This means we want to find P(X ≤ 3), since a fifth of 15 is 3.

Using the binomial probability formula, we have

P(X ≤ 3) = Σ P(X = k) for k = 0 to 3

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (15 choose 0) (0.6)⁰ (0.4)¹⁵ + (15 choose 1) (0.6)¹(0.4)¹⁴ + (15 choose 2) (0.6)² (0.4)¹³ + (15 choose 3) (0.6)³ (0.4)¹²

= 0.0000265 + 0.000397 + 0.00312 + 0.0163

Add the number

= 0.0198

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Answer:

x = -3 or x = 4

Step-by-step explanation:

\(x^2-x-12=0\)

\((x+3)(x-4)=0\)

\(x + 3 = 0\)

\(x = -3\)

\(x - 4 = 0\)

\(x = 4\)

Answer:

x=-3 or x=4

Step-by-step explanation:

x2−x−12=0

Step 1: Factor left side of equation.

(x+3)(x−4)=0

Step 2: Set factors equal to 0.

x+3=0 or x−4=0

x=−3 or x=4

Answer:

the price is 4 dollars

Step-by-step explanation:

Answer:

$0.63 per unit

Step-by-step explanation:

you divide 3.78 by 6 and you get 0.63 if rounded 0.60

srry if it's incorrect

Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

Answer:

1241

Step-by-step explanation:

∴

L.C.M. of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260

∴

the required number is 1260 - 19 = 1241

Hence, if we add 19 to 1241 we will get 1260 which is exactly divisible by 28, 36 and 45.

Answer:

Story

Jane is 1.7 m tall.  She stands 250 m away from the base of the Eiffel tower and looks up at the top of the building.  The angle of elevation from her eyeline to the top of the building is 45°.

Question

Calculate an estimate of the height of the building. Give your answer to the nearest meter.

Calculation

Label the sides of the triangle O, A and H (where O is the side opposite to the angle, A is the side adjacent to the angle and H is the hypotenuse).

In the triangle, the angle and side A is known, and O must be calculated.

Therefore, use the trig ratio tan(x) = O/A:

⇒ tan(40) = O/250

⇒ 250tan(40) = O

⇒ O = 209.7749078...

Assume Jane's eye-level is approximately 1.5 m above the ground.

Therefore, the Eiffel tower is approximately:

209.7749078... + 1.5 = 211.2749078.. meters tall

Rounding to the nearest meter ⇒ 211 m