assume x and y are two independent binary random variables, and p (x) and p (y ) are given as the followings: X P(X)
0 0.3
1 0.7
Y P(X)
0 0.6
1 0.4
calculated the mutual information

Answer:

you would be able to pull out $1,933.33 each month for 20 years if you have $400,000 saved for retirement and it earns 7% interest.

The answer is 1) V = [tex]2\pi\int\limits(2)+ {x} \, dx[/tex]; 2) V = [tex]2\pi \int\limits(1 - 2x) - 2x dx[/tex]; 3) V =[tex]2\pi \int\limits {\sqrt{2} } \, dx[/tex] ; 4) V = [tex]2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx[/tex] .

1) The volume of the shell is then given by the product of the area of its curved surface and its height. The height is equal to 2 - (-2) = 4, and the radius is equal to the minimum of the distances from x = 2 to the two curves, which is x = 2 - () = 2 + . The volume of the solid is then given by the definite integral:

V = [tex]2\pi\int\limits(2)+ {x} \, dx[/tex] = [tex]2\pi [(/3) + 2x][/tex] evaluated from 0 to 1 = (4/3)π.

2) The height of the region is equal to  - (2x) =  -2x, and the radius is equal to the minimum of the distances from x = 1 to the two curves, which is x = 1 - (2x) = 1 - 2x. The volume of the solid is then given by:

V = [tex]2\pi \int\limits(1 - 2x) - 2x dx[/tex]=[tex]2\pi [/5 - 2/3 + /2][/tex] evaluated from 0 to 1 = (8π/15).

3) The height of the region is equal to (2-x) -  = 2-x. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = The volume of the solid is then given by:

V =[tex]2\pi \int\limits {\sqrt{2} } \, dx[/tex] = [tex]2\pi [(x^4/4)][/tex] evaluated from 0 to √2 = (π/2).

4) The height of the region is equal to () - (2-) = 2 - 2. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = √((2-)/2). The volume of the solid is then given by:

V = [tex]2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx[/tex] = [tex]4\pi [(2/3)\± (2\sqrt{2} /3)][/tex]

The complete Question is:

Use the shell method to find the volumes of the solids generated by revolving the regions bounded by the curves and lines in about the

1.  y = x, y = -x/2, and x = 2

2. y = 2x, y = x/2, and x = 1

3. y = x/2, y = 2-x, and x = 0

4. y = 2-x/2, y = x/2, and x = 0

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i believe its  a+2b

Step-by-step explanation:

plssss telll me if im wrong

Ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.

A function’s initial value is its value when x equals zero. This is equivalent to the y-intercept. The graph shows that our line crosses the y-axis at point zero, eight. As a result, the starting value is eight. We’ll use SymPy’s solution() function to solve the two equations for the two variables x and y. The solution() method accepts two arguments: a pair of equations (eq1, eq2) and a pair of variables to solve for (x, y). A Python dictionary serves as the SymPy solution object.

The initial value, also known as the y-intercept, is the output value of a linear function when the input is 0.

The continuous solution to the initial value issue given by the linear equation with a forcing component q1x2 is one that meets the starting conditions and holds true across the whole range of x values. The equation's answer is provided by:

C1e(q1x2) + C2x + C3 = y(x).

Where C1, C2, and C3 are starting conditions-determined constants. To obtain the answer, use the beginning conditions to solve for C1, C2, and C3.

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The complete question is: What is the continuous solution to the initial value problem given by the linear equation with a forcing term q1x2?

The function with the greater rate of change will have the greater output value for every input value which is true.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

Let m₁ > m₂ and c₁ > c₂. Then the equations are given as,

y = m₁x + c₁

y = m₂x + c₂

The function with the greater rate of change will have the greater output value for every input value which is true.

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Answer:

x = 127°

x = 36

Step-by-step explanation:

The sum of interior angles for the given geometrical figure is calculated with the following formula:

(s-2) × 180

3 × 180 = 540

90 + 143 + 77 + 103 + x = 540

413 + x = 540

x = 127°

The given is a hexagon. The sum of its exterior angles is equal to 360.

80 + 59 + 2x + 59 + 54 + x = 360

252 + 3x = 360

3x = 108

x = 36

As a result, the third side's length might be any value higher than 0 and less than 12, or any number bigger than 12 and less than 24.

Hence, option (c) is correct choice.

The length of a triangle's third side must meet the triangle inequality theorem, which says that the total of the lengths of the triangle's two sides must be higher than the length of the triangle's third side.

As a result, the length of the third side of a triangle with two sides of length 12 must be between 0 and 24, omitting 12.

The third side can have the following lengths:

0 < length < 12

12 < length < 24

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The missing option may be:

(a)  6 < length < 12

(b) 2 < length < 4

(c) 12 < length < 24

(d) 15 < length < 30

Answer: dedicated or consecrated to God or a religious purpose; sacred.

or used in exclamations of surprise or dismay.

For the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).

Given is that a point is rotated 90 degrees about the origin.

Assume the point to be -

P(x, y)

For the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).

Therefore, for the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).

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Written without exponents, you'd have

   abbbcc   and    aabbc

Both have one a, two b's, and one c.

The GCF is [tex]ab^2c[/tex], since those are the greatest factors they all have in common.

The probability of getting someone who is a woman or a heavy drinker is,

0.546 to three decimal places.

None of the above is the correct option.

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

Given:

The table lists the drinking habits of a group of college students.

If a student is chosen at random,

then the probability of getting someone who is a woman or a heavy drinker,

=P(woman) + P(heavy drinker) - P(woman and heavy drinker)

= 216/405 + 13/405 - 8/405

= 221/405

= 0.546 to three decimal places.

Therefore, the probability is 0.546.

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The sine function is  y = 4 sin[ (π/6)x ] + 1.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

1) The parent function is sin(x)

2) sin(x) has:

Middle line: y = 0

Amplitude: 1 because the function goes from 1 unit up to 1 unit down the midddle line.

Period: 2π because sine function repeats every 2π units.

y-intercept: (0,0) because sin(0) = 0.

Now look how these changes in the function reflect on the parameters:

A sin (ωx + B) + C:

That function will have:

amplitude A, becasue the amplitude is scaled by that factor

Period: 2π / ω, because the function is compressed horizontally by that factor.

It will be translated B units to the left

It will be translated C units up.

And you need

Period = 12 => 2π / ω = 12 => ω = π/6

A = 4

Translate the midline from y = 0 to y = 1 => shift the function 1 unit up => = 1.

Translate the y-intercept from y = 0 to y = 1, which is already accomplished when you translate the function 1 unit up.

So, the is the function searched>

y = A sin (ωx + B) + C = 4 sin[ (π/6)x ] + 1

Now you can check the amplitude, the period, the middle line and the y-intercept of that y = 4 sin[ (π/6)x ] + 1.

Hence, the sine function is  y = 4 sin[ (π/6)x ] + 1.

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The values for k for which the given curve y = (k + 1) x² - 3x + (k + 1) lies below the X axis are k < -5/2 and k > 1/2.

Quadratic functions are defined as the kind of polynomial functions with the greatest degree of the independent variable equals 2.

A quadratic function can be generally represented as f(x) = ax² + b x + c.

The given function is y = (k + 1) x² - 3x + (k + 1), which is quadratic.

The graph of a quadratic function is a parabola.

If the curve lies below the X axis, then the curve will not touch the X axis.

Then the graph will be an inverted parabola, which does not touch the X axis.

So the function will not have values equal to zero.

That is y ≠ 0

So the function does not have real roots.

So the discriminant of the function f(x) = ax² + b x + c, which is [tex]\sqrt{b^2-4ac}[/tex]  will be negative.

Discriminant of the given function is [tex](-3)^2-[4 (k+1)(k+1)][/tex]. [tex](-3)^2-[4 (k+1)(k+1)][/tex] < 0

9 - 4(k + 1)² < 0

9 - 4(k² + 2k + 1) < 0

9 - 4k² - 8k - 4 < 0

-4k² - 8k + 5 < 0

Dividing throughout by -1,

4k² + 8k - 5 > 0

Let 4k² + 8k - 5 = 0

k = [ -8 ± √[(8)² - (4 × 4 × (-5)] / (2 × 4)

  = [ -8 ± √144 ] / 8

  = [-8 ± 12] / 8

Zeroes are k = 4/8 = 1/2 and k = -20/8 = -5/2

4k² + 8k -5 = 0 when k = 1/2 and k = -5/2

4k² + 8k -5 > 0, when k > 1/2 and k < -5/2

Hence the set of values of k are k > 1/2 and k < -5/2 for which the given function lies below the X axis.

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Answer:

The exterior of a triangle is the sum of two of its interior angles except the one adjacent to it. The angle x is evaluated as 135°.

What is a triangle?

A triangle is a two dimensional shape bounded by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.

Given that,

There is a triangle shown in the figure with following angles,

∠y = 102°  and ∠Z = 57°.

Angle x is the exterior angle of the given triangle. Use the property of exterior angle to get,

∠x  = ∠B + ∠Z

    = (180° - y) + 57°

    = (180° - 102°) + 57°

    = 135°

Hence, the angle x has been worked out as ∠x = 135°.

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The least positive integer N such that the set of 1000 consecutive integers beginning with 1000 N is 282.

Let x² appear before 1000N so:

(x+1)² − x² >1000⟹ x ≥ 500

Let A = [1000N, 1000(N+1)]

So I let x=500

then, x²=250000

, obviously this is impossible since the set has a square already.

So now I need to set some number, k² ≥ 5012 = 0 (mod1000)

So I need to solve the quadratic residue:

Lets see: 500²=250000

and 501²=251001

and 502²=252004

501²=500²+1000+ ∑ (12k−1)

502²=500²+2(1000)+∑ (12k−1)

The final answer is: N=282

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043.

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.

The functions can be simplified and ordered as follows (from smallest to largest):

1. O(1) = constant functions

2. O(log n) = logarithmic functions

3. O(√n) = square root functions

4. O(n log n) = log-linear functions

5. O(n²) = quadratic functions

6. O(n² / log n) = "quasi-quadratic" functions

This is a description of the concept of big-O notation and asymptotic analysis in computer science. Big-O notation is used to describe the upper bound of the growth rate of a function. It provides a way to classify functions based on how quickly they grow relative to the input size. Asymptotic analysis, on the other hand, is the study of the behavior of functions as the input size approaches infinity.

The purpose of this analysis is to determine which algorithms are the most efficient for a given problem. By understanding the asymptotic behavior of functions, we can make informed decisions about the trade-offs between different algorithms and choose the one that is best suited for a particular problem.

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Approximately 68% of housing prices are between a low price of $144,000 and a high price of $160,000.

The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Given that the mean of housing prices is $152,000 and the standard deviation is $8,000, we can use the Empirical Rule to determine that approximately 68% of housing prices fall within one standard deviation of the mean. This means that the range of prices that contains 68% of the data is between:

$152,000 - $8,000 = $144,000 and $152,000 + $8,000 = $160,000.

So, approximately 68% of housing prices are between a low price of $144,000 and a high price of $160,000.

Answer: Negative two times z plus eight.

Step-by-step explanation:

The expression $-2z + 8$ represents "negative two times the quantity of z plus 8". To interpret this as a phrase, we can say "8 increased by the negative of two times the quantity of z."

The probability in each case is:

The probabilities provided are the probabilities of each value of X. For example,

Similarly,

When finding probabilities for a range of X values, you need to add up the individual probabilities of all the values in the range. For example, if you are looking for

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(a) The likelihood function for this sample is given by:

L(λ) = λ^2 * exp(-λ * (5 + 3 + x))

where x is the third observation, X₃, which is larger than 10.

(b) To find the MLE for λ, we take the derivative of the log-likelihood with respect to λ and set it equal to zero:

d/dλ ln(L(λ)) = 2/λ - (5 + 3 + x) = 0

Solving for λ, we find that the MLE for λ is λ = (2) / (5 + 3 + x).

Since x is greater than 10, the MLE for λ is positive and less than 2/(5 + 3 + 10) = 2/18

Therefore, the correct answer is as given above

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When dividing two exponential functions with the same base, the second law states that the exponents must be subtracted

f(4) = (6)⁴ = 1296

According to the first law, adding the exponents will multiply two exponential functions with the same base. According to the second law, we must subtract the exponents when dividing two exponential functions with the same base. The third law indicates that we must multiply the exponents in order to increase a power to a new power.

Here,

Given :

=>f(2) = 36

=> f(3) = 216

So,

=> f(x) = (6)ˣ

=>f(4) = (6)⁴ = 1296

If f(x) = , where b > 0 and b 1, is the formula for an exponential function. B is referred to as the base and x is referred to as the exponent, just like in any exponential expression. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by two folds per hour.

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The limit of x + x2 divided by 1 - 4x2 as x approaches infinity is 0. To solve this limit, we can use l'Hospital's Rule.

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The Constant of proportionality is [tex]\frac{1}{2}[/tex].

What is constant of proportionality?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

Here to find constant of proportionality we need to divide y by x. Then,

=> constant of proportionality = [tex]\frac{y}{x}[/tex]

Here put x=10 and y=5 then

=> [tex]\frac{5}{10} = \frac{1}{2}[/tex]

Now put x=20 and y=10 then

=> [tex]\frac{10}{20} = \frac{1}{2}[/tex]

Hence the constant of the proportionality is [tex]\frac{1}{2}[/tex].

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The slopes I found are (A) equivalent. This means that the slope triangles are (B) similar and no matter what (C) two points I pick on the line the slope will be the (A)same.

The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Mathematically, the slope is the change in y divided by the change in x. That is:

Slope = y2-y1 / x2-x1

The slope of the line between points A and B:

A (x1 = -5, y1 = -2) and B (x2 = -2, y2 = 0)

Slope = [(0-(-2) )]/ [-2-(-5)] = 2/3

The slope of the line between points B and C:

B (x1 = -2, y1 = 0) and C (x2 = 4, y2 = 4)

Slope = [4-0]/ [4-(-2)] = 4/6 = 2/3

The slope of the line between points A and C:

A (x1 = -5, y1 = -2) and C (x2 = 4, y2 = 4)

Slope = [(4-(-2))]/ [4-(-5)] = 6/9 = 2/3

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The rule for the translation is  (x, y) Right-arrow (x + 2, y – 3).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Given;

A triangle has coordinates F(−2, 3), G(−4, 1), and H(−2, −2)

. The triangle is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5).

If a point A(x, y) is translated a units right and b units down, the new point is at A'(x + a, y - b)

Therefore, the translation of FGH to F'G'H' will be (x + y) ⇒ (x + 2, y - 3).

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12 inches is equal to one foot. 12 inches seems like more because 12>1, but they are really equal.

The number of miles the business person can travel with 110 dollars is 290 miles.

Value Rent-A-Car rents a luxury car at a daily rate of $37.33 plus 25 cents per mile. A business person is allotted $110 for car rental each day.

Therefore, the number of miles the business person can travel on 110 dollars can be calculated as follows;

Using equations,

Therefore,

y = 0.25x + 37.33

where

Therefore, let's find the distance he can travel for 110 dollars.

110 = 0.25x + 37.33

110 - 37.33 = 0.25x

72.67 = 0.25x

x = 72.67 / 0.25

x = 290.68

Therefore,

number of miles he can travel = 290 miles

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For, the given differential equation, 1) For  800 < P < 10000, the population will increase and 2) For 0 < P < 800, the population will decrease.

                               dP/dt = kP (1- (P/K)) (1-(m/P))   -(1)

where k is a constant and K is the carrying capacity.

Here, K = 10000, m = 800 and k = 0.05

Putting these values in Equation 1 we get,

                      dP/dt = 0.05P (1- (P/10000)) (1-(800/P))

1.) If dP/dt > 0 then P is increasing

As dP/dt > 0

So, 0.05P (1- (P/10000)) (1-(800/P)) > 0

Both ((10000- P)/10000) > 0 and ((P-800)/P) > 0

=> P < 10000 and P > 800

So, for  800 < P < 10000, the population will increase.

2.)  If dP/dt < 0 then P is decreasing

As dP/dt < 0

So, 0.05P (1- (P/10000)) (1-(800/P)) < 0

Both ((10000- P)/10000) > 0 and ((P-800)/P) > 0

=> P > 10000 and P < 800

So, for  0 < P < 800, the population will decrease.

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Answer: she will save 40$

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