activity 2: normal-based inference from summarized data (banding and survival over ten-year period.5.what is the 95% confidence interval for this difference? based on this interval, what is a possible conclusion about the true difference in proportions?

Answer:

28 horses

Step-by-step explanation:

336/12=28

because every 12 miles they change the horse.

Answer:

n = 36

Step-by-step explanation:

Hope this helps! :)

Answer: n>17

Step-by-step explanation:

Answer:

You forgot the rest of the function, but if x is -2, then the function is represented by f(x)=-2x

If you supply more information the equation would be different.

Step-by-step explanation:

Answer:

1/3 is the slope

Step-by-step explanation:

Use this formula \(\frac{y2 - y1}{x2 - x1}\)

Plug in (-1, -6) and (5, -4)

\(\frac{-4 - -6}{5 - -1} = \frac{2}{6}/2 = \frac{1}{3}\)

Hope this helps ya!!!

Answer:

Step-by-step explanation:

By using the principle of counting, it can be calculated that

Total number of ways to arrange the four face cards in a 52-card deck =  11880

What is principle of counting?

Principle of counting states that if there are m ways to do one job and m ways to do another job after that job, there are m \(\times\) n ways to do both the jobs together.

There are three face cards of hearts, three face cards of diamonds, three face card of clubs and three face cards of spade

Total number of face cards = 3 + 3 + 3 + 3 = 12

We can arrange the four face card in  \({12 \choose 4}\) ways = 495 ways

The four cards should be arranged in a row.

Number of choices for the first card = 4

Number of choices for the second card = 3

Number of choices for the third card = 2

Number of choices for the fourth card = 1

Total number of ways  to arrange the four cards in a row = 4 \(\times\) 3 \(\times\) 2 \(\times\) 1 = 24

Total number of ways to arrange the four face cards in a 52-card deck =

495 \(\times\) 24 = 11880

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Answer:

10x-4

Step-by-step explanation:

(ii) The median of X is ±√(-ln(0.5)).

(iii) The 95th percentile of X is ±√(-ln(0.05)).

(iv) E(X) = -x * \(e^(-x^2)\)+ √π/2

(v) MGF is not possible in this case.

Let's work through the parts of the problem one by one:

(a) First, let's determine which part of the function represents a valid cumulative distribution function (CDF).

(i) F(x) = 1 - \(e^(-x^2)\); -∞ ≤ x < 0

(ii) F(x) = 1 - \(e^(-x^2)\); 0 ≤ x < ∞

To be a valid CDF, the function F(x) must satisfy the following conditions:

1. F(x) is non-decreasing.

2. F(x) is right-continuous.

3. lim(x→-∞) F(x) = 0 and lim(x→∞) F(x) = 1.

Both parts (i) and (ii) satisfy these conditions, so both can represent valid CDFs. We'll continue with part (ii) for the subsequent calculations.

(i) Derive the probability density function of X:

To derive the probability density function (PDF), we need to take the derivative of the cumulative distribution function (CDF) with respect to x.

f(x) = d/dx [F(x)]

f(x) = d/dx [1 - \(e^(-x^2)\)]

To find the derivative, we'll use the chain rule:

f(x) = -2x * \(e^(-x^2)\)

(ii) Derive the median of X:

The median of a distribution is the value of x for which F(x) = 0.5.

Setting F(x) = 0.5 and solving for x:

0.5 = 1 - \(e^(-x^2)\)

\(e^(-x^2)\) = 0.5

-x² = ln(0.5)

x² = -ln(0.5)

x = ±√(-ln(0.5))

The median of X is ±√(-ln(0.5)).

(iii) Derive the 95th percentile of X:

The pth percentile of a distribution is the value \(x_p\) such that F\((x_p)\) = p.

Setting \(F(x_p)\) = 0.95 and solving for \(x_p\):

0.95 = 1 - \(e^(-x_p^2)\)

\(e^(-x_p^2)\) = 0.05

\(-x_p^2\) = ln(0.05)

\(x_p^2\) = -ln(0.05)

\(x_p\)= ±√(-ln(0.05))

The 95th percentile of X is ±√(-ln(0.05)).

(iv) Derive the expectation of X:

The expectation of X, denoted as E(X), is given by the integral of x times the PDF over its entire range.

E(X) = ∫x * f(x) dx, where the integral is taken from -∞ to ∞.

E(X) = ∫x * (-2x * \(e^(-x^2)\)) dx

To solve this integral, we can use integration by parts:

Let u = x, dv = -2x * \(e^(-x^2)\)dx

Then, du = dx, v = \(-e^(-x^2)\)

Using the integration by parts formula:

∫u * dv = uv - ∫v * du

E(X) = [-x * \(e^(-x^2)\)] - ∫\((-e^(-x^2))\)dx

E(X) = -x * \(e^(-x^2)\) + ∫\(e^(-x^2)\) dx

To evaluate the integral ∫\(e^(-x^2)\)dx, we can use the Gaussian integral, which does not have a simple

closed-form solution. The result of this integral is √π/2.

E(X) = -x * \(e^(-x^2)\)+ √π/2

(v) Derive the moment generating function of X:

The moment generating function (MGF) of a random variable X is defined as the expected value of \(e^(tX)\), where t is a parameter.

M(t) = E\((e^(tX)\))

To find the MGF, we substitute the expression for X into the MGF formula:

M(t) = E\((e^(tX)\))

M(t) = ∫\(e^(tx)\) * f(x) dx

Using the PDF derived earlier:

M(t) = ∫\(e^(tx) * (-2x * e^(-x^2))\) dx

We can simplify this expression by multiplying the terms:

M(t) = -2 ∫x * \(e^(tx - x^2)\) dx

Finding the integral in closed form is challenging due to the combination of exponential and quadratic terms. However, we can still compute the MGF numerically or approximate it using techniques like Taylor series expansion.

Note: Due to the complexity of the integral involved, finding a closed-form solution for the expectation and MGF is not possible in this case.

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It is a trinomial because it follows the pattern of x^2 + bx + c. In this case, x^2 - 10x + 25. Also, it only has three numbers and two operation symbols, signifying a trinomial (three = tri).

Answer:

3x^2 + x - 6 = 0

Step-by-step explanation:

x - 6 = -3x^2

step 1: add 3x^2 to both sides

x - 6 + 3x^2 = 0

step 2: put the terms in order from greatest degree (exponent) to least.

3x^2 + x - 6 = 0

done! :)

A standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.

The probability is calculated by dividing the total number of outcomes by the total number of events.

Odds and probability are two different concepts.

Divide the probability of an event occurring by the probability that it won't happen to calculate chances.

The four main types of probability that mathematicians study are axiomatic, classical, empirical, and subjective.

So, the probability that a standard normal random variable will occur with a probability ranging from 0.3 to 3.2 must therefore be calculated.

First, a mean and standard deviation are introduced for a standard normal random variable.

The probability that a standard normal random variable will fall between 0.3 and 3.2 needs to be calculated.

Therefore, it should be more likely that:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using the usual value of z:

P(0.3<z<3.2)=0.9993−0.6179

Justify by saying:

P(0.3<z<3.2)=0.3814

Therefore, a standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.

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The triangle that has the maximum area among the given options of isosceles triangle, right-angle triangle, equilateral triangle, and none of these, is the equilateral triangle.

An equilateral triangle has all three sides equal in length and all three angles equal to 60 degrees.

For a given perimeter, the equilateral triangle will have the maximum area compared to other types of triangles. This is due to the fact that among all triangles with a fixed perimeter, the equilateral triangle has the largest area.

The isosceles triangle has two sides of equal length, but the third side can vary. The right-angle triangle has one angle of 90 degrees, and the remaining two angles can vary. Both of these types of triangles may have smaller areas compared to an equilateral triangle with the same perimeter.

Therefore, among the options provided, the equilateral triangle will have the maximum area for a given perimeter.

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Answer:

D.

Step-by-step explanation:

x + 6 ≤ 8

subtract 6 on both sides.

x ≤ 2

Option D is the correct answer.

Answer:

3 raise to power -100

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

a) 0

b) 1

c) 0

Step-by-step explanation:

These are common values from the unit circle but you could also just check with your calculator. Just be sure to set it to degree mode and not radian mode.

Answer:

40,30,80,60,80,30,50,40,60,90,30

The maximum distance between them is the diameter of the circle, which is of 44 units.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

The diameter is twice the radius, and is the maximum distance between two points on the same circle.

They are running on a circular path, modeled by:

\(x^2 + y^2 - 10x - 18y = 378\)

Completing the squares, the equation is:

\((x - 5)^2 + (y - 9)^2 = 378 + 5^2 + 9^2\)

\((x - 5)^2 + (y - 9)^2 = 378 + 25 + 81\)

\((x - 5)^2 + (y - 9)^2 = 484\)

Then, the radius is: \(\sqrt{484} = 22\), which means that the maximum distance between the runners at any given time is of 44 units.

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The rate of growth of revenue when 420 units have been sold is R'(420) = R'(350)..

Revenue from selling x units = R(x). Also, sales are increasing at a rate of 70 per day. That means if x units are sold today, then tomorrow, the units sold would be (x + 70) units. Rate of increasing sales = 70 per day. Now, when 420 units have been sold:

Initial units sold = x = 420 - 70 = 350 units

Total units sold = 420 units

Number of units sold today = 420 - 350 = 70 units

Now, Revenue generated from 350 units of the item = R(350)

Revenue generated from 420 units of the item = R(420)

Rate of growth of revenue when 420 units have been sold = R'(420)\

From the definition of the derivative:

R'(x) = lim_ {h→0} {R(x+h) - R(x)}/{h}

R'(420) = lim_ {h→0} {R(420+h) - R(420)}/{h}

R(420) = R(350 + 70) = R(350) + R'(350) * (70)And, R(420 + h)

= R(350 + 70 + h) = R(350) + R'(350) * (70 + h), Using these equations,

R'(420) = lim_ {h→0} {R(350) + R'(350) * (70 + h) - R(350) - R'(350) * (70)}/{h}

= lim_ {h→0} {R'(350) * h}/{h}

= R'(350)

Thus, the rate of growth of revenue when 420 units have been sold is R'(420) = R'(350).

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Answer:

x = - 1

Step-by-step explanation:

- 15 = 22x + 7 ( subtract 7 from both sides )

- 22 = 22x ( divide both sides by 22 )

- 1 = x

Answer:

\(x^{2} - 14 = 50\)

Step-by-step explanation:

Let x = Unknown number

Number squared = \(x^{2}\)

Difference between the number squared and 14 is 50:

= \(x^{2} - 14 = 50\)

= \(x^{2} = 14 + 50\)

= \(x^{2} = 64\)

(NOTE: It cannot be \(14 - x^{2} = 50\) since:

\(x^{2} = 14 - 50\) which would mean \(x^{2} = -36\) and a square of a number CANNOT be a negative number)

Taking the square root of both sides to get rid of the square:

= \(x = \sqrt{64}\)

= x = ±8

For #8, two lines in the same plan that never intersect and are equidistant at all points are parallel lines.

Answer:

931 Days

Step-by-step explanation:

Answer:

931 days pls brainliest

Step-by-step explanation:

Answer:

4 is the answer to the 1st question

The count of turtles, T, along a randomly chosen stretch of 1 kilometer of the river follows a Poisson distribution with a parameter λ of 3, while the count of platypus, P, follows a Poisson distribution with a parameter λ of 0.4.

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. It is appropriate in this case because the count of turtles and platypus along the river can be considered as a series of independent events.

For turtles, the average number of turtles per kilometer is given as 3. The Poisson distribution is characterized by a single parameter λ, which represents the average rate or intensity of the events. In this case, λ = 3, indicating that on average, there are 3 turtles per kilometer. The Poisson distribution describes the probability of observing a specific number of turtle sightings within the interval of 1 kilometer.

Similarly, for platypus, the average number of platypus per kilometer is given as 0.4. Using the same reasoning as above, the count of platypus follows a Poisson distribution with λ = 0.4.

The independence assumption is crucial for the Poisson distribution to be appropriate in this context. It implies that the presence or absence of turtles does not affect the presence or absence of other turtles, and the same applies to platypus.

Additionally, the independence between turtles and platypus means that the presence or absence of one species does not influence the presence or absence of the other species.

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Answer:

Step-by-step explanation:

Earnings = 16.75 hours × $8.25/hour = $138.1875

Deductions = 6.5% + 1.45% = 7.95%

net = 92.05% of $138.1875 ≈ $127.20

The probability that at least one of the three randomly selected people has been vaccinated is approximately  961/1000 as a fraction.

Percent of vaccinated people = 66%

Number of people randomly selected = 3

The probability that a person has been vaccinated is

= 66%

=  0.66 as a decimal.

The probability that at least one of three people has been vaccinated

= Total probability - Probability that none of them have been vaccinated

Total probability = 1

The probability that the first person selected has not been vaccinated is

1 - 0.66 = 0.34.

The probability that the second person selected has not been vaccinated is also 0.34.

And the same goes for the third person.

So, the probability that none of the three people have been vaccinated is,

= 0.34 x 0.34 x 0.34

= 0.039304

The probability that at least one of the three people has been vaccinated is ,

= 1 - 0.039304

= 0.960696

= 0.961

= 961/1000 as a fraction.

Therefore, the probability that at least one of the three people has been vaccinated is approximately  961/1000 as a fraction.

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