f(x) = 4/5x - 2
Find f(3)

The expected number of tosses needed to obtain hth in a row is h^2/2. For example, the expected number of tosses needed to obtain HTH in a row is 4^2/2 = 8.

Let E be the expected number of tosses needed to obtain hth in a row. We can approach this problem recursively by considering the expected number of additional tosses needed given the outcome of the previous toss.

If the previous toss was tails, then we are back to the starting point and need E tosses to obtain hth in a row.

If the previous toss was heads, then we need to obtain h-1 more heads in a row to complete the hth sequence. The expected number of additional tosses needed to obtain h-1 heads in a row is E, by the same reasoning as above. In addition, we need one more toss to obtain the next head in the hth sequence.

Thus, we have the recurrence relation E = 1/2(E+1) + 1/2(E+h), which simplifies to E = E/2 + (h/2) + 1/2. Solving for E, we obtain E = h^2/2.

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1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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Answer:

u = j+k/y

Step-by-step explanation:

Solve for  u  by simplifying both sides of the equation, then isolating the variable.

Answer:

2)vertical angles

3)alternate interior angles

Step-by-step explanation:

yeah thats all i got

The line p || r as, the alternate interior angle are equal.

The basic qualities listed below make it simple to identify parallel lines.

We have to prove that p || r

and, we have given <1 = <5

<4 = <1 by (Vertically Opposite Angle).

and, <4 = <5 (Transitive Property)

So, the line p || r as, the alternate interior angle are equal.

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Answer:

4200000

Step-by-step explanation:

Answer:

4,200,000

Step-by-step explanation:

Answer:

3rd one

Step-by-step explanation:

Answer:

0.0

Step-by-step explanation:

0.019 or 0.0

Answer:

y=-3x+3

Step-by-step explanation:

Answer:

x = 330 and y = 40

Step-by-step explanation:

Answer:

\(\huge\boxed{y-3=\dfrac{1}{2}(x-1)}\)

Step-by-step explanation:

The point-slope form of an equation of a line:

\(y-y_1=m(x-x_1)\)

\(m\)- slope

\((x_1;\ y_1)\) - point on a line

We have

\(m=\dfrac{1}{2};\ (1;\ 3)\to x_1=1;\ y_1=3\)

Substitute:

\(y-3=\dfrac{1}{2}(x-1)\)

Answer:

The simplified answer to the given equation is 6√2

Step-by-step explanation:

First, we must simplify the radicals in the equation.

√2 = 1.414213562

∛2 = 1.25992105

Now, we divide these numbers. You can divide it this way or you can divide it using a calculator.

√2 ÷ ∛2 = 1.122462048

Now, let;s look at our answer choices. We can immediately cross out A because 1/4 equals 0.25. Let's look at the others.

6√2 = 1.22462048

So, our answer here is answer choice B.

Answer:

Its option one!!!

Step-by-step explanation: In a function, EACH X only has ONE Y.

Since the first set has -6 matched to both -4 AND 1, it is not a function.

(ordered pairs are set up like this by the way, (X,Y)

Hope I helped ! ^^

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem \(A^2 = B^2 + C^2\) => AC = \(\sqrt{115}\)

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

\(A^2 = B^2 + C^2\)

AC = \(\sqrt{14^2 - 9^2}\)

AC  = \(\sqrt{196 - 81}\)

AC = \(\sqrt{115}\)

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Answer: GH = 12

Step-by-step explanation:

Don't panic! Remember that a perpendicular bisector divides a segment equally in half. (If you're writing a proof, cite the "Definition of a perpendicular bisector)

It breaks down to: GH = HI

HI = 12

By the transitive property of segment congruence: GH = 12

Good luck!

Answer:

im sorry but i really cant see the image

Step-by-step explanation:

You have the following expression:

If the values of x and y are:

x = 9

y = 1

when you replace these values into the polynomial expression you obtian:

Hence, the answer is 73

9514 1404 393

Answer:

  EL/EF and OS/OJ

Step-by-step explanation:

In the similar triangles, angle F and angle J have the same measure, so will have the same tangent. The tangent is the ratio of the opposite side to the adjacent one.

In ΔFEL, the desired ratio is ...

  tan(F) = EL/EF . . . . . 2nd choice

In ΔJOS, the equivalent ratio is ...

  tan(J) = tan(F) = OS/OJ . . . . . 7th choice

Answer:

IT'S TWOOOOOOOOOOOOOOOO 222222222222222

Answer:

4

Step-by-step explanation:

an=-4+3(n-1)=-4+3n-3=3n-7

a1=3×1-7=3-7=-4

a5=3×5-7=15-7=8

a1+a5=-4+8=4

Answer:

yes!! finally a question i can solve:
so,

Step-by-step explanation:

Exact Form:

x = − 3/2

Decimal Form:

x = −1.5

Mixed Number Form:

x = -1  1/2

Answer: 16.308

Step-by-step explanation:brainiest please

The set of ordered pairs {(-2,0), (3, 1), (3,2), (1,3)} that is a function. The correct answer would be an option (C).

A function is a set of ordered pairs such that for every unique input, there is only one unique output.

A set A {(9,0), (9, 1), (9,2), (9,3)} contains multiple outputs for the same input, so it's not a function.

B set B [(-1,0), (-2, 0), (2,0), (1,0)] contains multiple outputs for the same input, so it's not a function.

C set C {(-2,0), (3, 1), (3,2), (1,3)} contains only one output for every unique input, so it's a function.

D set D {(9,5), (9,5), (9,5), (9,5)} all the ordered pair has the same inputs and outputs, it's not a function.

Therefore, the set of ordered pairs that is a function is C set C {(-2,0), (3, 1), (3,2), (1,3)}.

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Answer:

B) H, N, K, I

Step-by-step explanation:

Collinear points are points that are on the same line. Therefore, the answer is B.

The points H, N, K, and I are collinear which is the correct answer that would be an option (B).  

Collinear points are defined as points that are along a straight line represented by a collinear. Because a straight line may be drawn continuously between any two points, they are always collinear. There can be a collinear relationship from three or more points, although it is not necessary.

A group of points that are coplanar, or a planar surface that extends endlessly in all directions, are all located on the same plane. Four or more points may or may not be coplanar, however, any two or three points are always coplanar.

We have given a line and a planar surface with points H, N, K, I, M, N, O, J, K, and L.

At the line, points H, N, K, and I are collinear.  

Hence, the points H, N, K, and I are collinear which is the correct answer that would be an option (B).  

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The triangle is obtuse. The sum of the measures of the angles is 25 + 87 + x = 180 degrees, where x is the measure of the third angle. So, x = 68 degrees.

The sum of the measures of the angles in any triangle is always 180 degrees. Let's find out the measure of the third angle of the triangle:Acute the measure of the third degree angle is 68 degrees so all three angles are acute.The sum of the measures of the angles is 25 + 87 + 68 = 180 degrees, which shows that all angles are acute.Acute the measure of the third triangle is 78 degrees so all three angles are acute.

The sum of the measures of the angles is 25 + 87 + 78 = 190 degrees, which shows that all angles are not acute. Therefore, option B can be eliminated.Obtuse 25 degrees +87 degrees =112 degrees and 112 degrees is an obtuse angle.The sum of the measures of the angles is 25 + 87 + x = 180 degrees, where x is the measure of the third angle. So, x = 68 degrees. Therefore, the triangle is obtuse. The answer is C.Right 25 degrees +87 degrees = 112 degrees and 202 degrees - 112 degrees = 90 degrees. Therefore, the triangle is not right. So, option D can be eliminated.

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Answer:

r = 5

Step-by-step explanation:

To find r, you have to isolate it by adding 1 to both sides.

If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

What is a logarithmic function?

A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: \(f(x) = log_b(x),\) where b is the base of the logarithm.

To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.

In the case of logarithmic functions, the derivative of \(f(x) = log_b(x)\) is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.

Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

What is a logarithmic function?

A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: \(f(x)=log_b(x)\). where b is the base of the logarithm.

To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.

In the case of logarithmic functions, the derivative of \(f(x)=log_b(x)\). is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.

Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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