Suppose we have the following joint probabilities. A A2 A3 B1 .15 .20 10 B2 25 .25 .05 Compute the following probabilities (to 3 decimals) a. P(A2B2)= c. P(B11A2) 

The center of the circle is (6,7) and the radius of the circle is 1.414 units

The diameter with endpoints = (5, 8) and (7, 6)

The mid point of the diameter = The center of the circle

The center of the circle = \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

Substitute the values in the equation

The center of the circle = ( (5+7)/2 , (6+8)/2 )

= (12/2 , 14/2)

= (6, 7)

The radius of the circle = The distance between (6, 7) and (7, 6)

The distance between two points = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The distance between (6, 7) and (7, 6) = \(\sqrt{(7-6)^2+(6-7)^2}\)

= \(\sqrt{1^2+(-1)^2}\)

= \(\sqrt{1+1}\)

= \(\sqrt{2}\)

= 1.414 units

Hence, the center of the circle is (6,7) and the radius of the circle is 1.414 units

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The value of the Arrow-Debreu security is calculated as the present value of its expected payoff, discounted at the risk-neutral rate. As a result, the premium of the Arrow-Debreu security can be computed using the following formula: \($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$,\)

where π=0.4, R=1.05, n=6, and t=2 (expiry node).

By substituting the values, we obtain:

\($P_{2}=\frac{1}{(1+1.05)^{6-2}}\times 0.4 = \frac{0.4}{(1.05)^4} \approx 0.3058$.\)

Therefore, the premium of the Arrow-Debreu security is approximately $0.3058.

Arrow-Debreu securities are typically utilized in financial modeling to simplify the pricing of complex securities. They are named after Kenneth Arrow and Gerard Debreu, who invented them in the 1950s. An Arrow-Debreu security pays $1 if a particular state of the world is realized and $0 otherwise.

They are generally utilized to price derivatives on numerous assets that can be broken down into a set of Arrow-Debreu securities. The value of an Arrow-Debreu security is calculated as the present value of its expected payoff, discounted at the risk-neutral rate. In other words, the expected value of the security is computed using the risk-neutral probability, which is used to discount the value back to the present value.

The formula is expressed as:

\($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$\),

where P_t is the price of the Arrow-Debreu security at time t, π is the risk-neutral probability of the security’s payoff, R is the risk-free rate, and n is the total number of time periods.However, Arrow-Debreu securities are not traded in real life. They are used to determine the prices of complex securities, such as options, futures, and swaps, which are constructed from a set of Arrow-Debreu securities.

This process is known as constructing a complete financial market, which allows for a more straightforward pricing of complex securities.

The premium of the Arrow-Debreu security is calculated by multiplying the risk-neutral probability of the security’s payoff by the present value of its expected payoff, discounted at the risk-neutral rate.

The formula is expressed as

\($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$,\)

where P_t is the price of the Arrow-Debreu security at time t, π is the risk-neutral probability of the security’s payoff, R is the risk-free rate, and n is the total number of time periods. Arrow-Debreu securities are not traded in real life but are used to price complex securities, such as options, futures, and swaps, by constructing a complete financial market.

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Answer:

to find perimeter we add all sides so you have to add

area you have to × first box and second box .

-28 is the standard form of the equation.

Ax+By=C is the formula for a linear equation. You must place the x and y on the same side of the equal sign and the constant on the other side in order to convert an equation in slope-intercept form (y=mx+b) to standard form. Terms can be moved using inverse procedures.

The standard form of a linear equation is

Ax+By=C A x + B y = C .

y=-3/4x+7 in standard form

Multiply both sides by 4  .

4y=4(3.4x+7) 4 y = 4 ( 3 4 x + 7 ).

3x - 4y = -28

-28 is the standard form of the equation.

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A logarithmic graph has a curved shape, with its vertical axis increasing exponentially, and its horizontal axis increasing in a logarithmic scale. The graph is useful for plotting data with a wide range of values, as it can be used to compress the data into a smaller range.

A logarithmic graph is a type of graph that is used to represent data with a wide range of values. It has a curved shape, with its vertical axis increasing exponentially and its horizontal axis increasing in a logarithmic scale. This scale compresses the data into a smaller range, which makes it easier to visualize and compare values that span a large range. It is useful for plotting data that grows or decreases exponentially, such as population growth or exponential decay. Logarithmic graphs are also used to graph values that have a very large range, such as the size of galaxies. The graph helps to compress the data into a smaller range, making it easier to visualize and compare values.

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Answer:

Please provide a question to be answered.

Answer: 14/40 or 7/20

Step-by-step explanation: We need to set the fraction's denominators equal to each other and their LCM is 40 so Andrea ran 1/8 which =5/40. Billie ran 1/5 which =8/40. 5/40+8/40=13/40/ Carol ran both Andrea's and Billie's length combined so that's another 13/40 = 26/40. The whole length is 40/40 so 40/40-26/40=Dana's length which =14/40 or 7/20

The times that the ball is 34 feet high to the nearest tenth of a second is equal to 4.61 and 0.39 seconds.

In order to determine the time or times for this ball at a height of 34 feet, we would simply substitute the value of the height into the function h(t) as follows;

h(t) = -16t² + 80t + 5

34 = -16t² + 80t + 5

Re-arranging the equation, we have:

16t² - 80t + 34 - 5 = 0

16t² - 80t + 29 = 0

Next, we would solve the quadratic equation by using the quadratic formula:

\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-80)\; \pm \;\sqrt{-80^2 - 4(16)(29)}}{2(16)}\\\\x = \frac{80\; \pm \;\sqrt{6400 - 1856}}{32}\\\\x = \frac{80\; \pm \;\sqrt{4544}}{32}\)

x = (80 ± 8√71)/32

x = (80 + 8√71)/32  and  x = (80 - 8√71)/32

x = 4.61 and 0.39 seconds.

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The correct answer is D. more than 70,000 books.

Let's denote the number of books sold by x.

The total earnings from the first publisher will be:

200,000 + 1x

The total earnings from the second publisher will be:

60,000 + 3x

We want to find the range of x values where the earnings from the second publisher will be greater than the earnings from the first publisher:

60,000 + 3x > 200,000 + x

2x > 140,000

x > 70,000

Therefore, Dr. Lewis will make more from the deal with the second company than he will from the deal with the first when he sells more than 70,000 books.

The correct answer is D. more than 70,000 books.

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Answer: Lin needs to drink 27 ounces of water to reach her goal.

Step-by-step explanation: 1 cup = 8 fluid ounces.

8 cups = 8 x 8 = 64 ounces.

As of now Lin has drank 37 ounces of water. So, this means till now she has drank 37/8 = 4.625 cups of water.

In terms of ounces, she needs to drink 64-37=27 ounces of water to reach her goal.

Hence, the answer is 27 ounces or 8-4.625=3.375 cups.

Answer:

6

Step-by-step explanation:

6

Answer:

.85

Step-by-step explanation:

Compound interest formula

\(PV(1+\frac{i}{n})^{nt}\)

Melanie:

\(3800(1+\frac{.02}{4})^{(6*4)\\}\\=3800(1+.005)^{24}\\3800*1.1272=4283.21\)

Sebastian:

\(3800(1+\frac{.02}{12})^{12*6}\\3800(1.0017)^{72}\\3800*1.1274=4284.06\)

4824.06-4283.21= .85

We now have three equations, so we can solve them.

Let's define the length of the 3 boards in terms of x:

F=x

S=2x-3

T=2

F+S+T =26

x+2x-3+2 =26

3x =26+1=27

x =27/3 = 9 feet for First section

2x-3 =18-3 = 16 feet = Second

2 = Third

9+16+2 = 27

27 is the length of the shortest piece.

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Using the z table, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

In the given question,

We have to find the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82%.

The confidence interval is 82%.

We can write 82% as 82/100 and 0.82.

Now the value of

\(\alpha\)=1−0.82

\(\alpha\)=0.18

Now finding the value of \(\alpha\)/2

\(\alpha\)/2=0.18/2

\(\alpha\)/2=0.09

Now finding the value of \(z_{a/2}\).

\(z_{0.82}\) = 1.34

Hence, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

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Answer:

Step-by-step explanation:

A x - 2

B x + 2

C x - 2

D x - 2

Option B is not equivalent

Answer:

283 m^2

Step-by-step explanation:

To find the area of a circle, you need to times pi, in this case 3.14, by the radius,9.5 here, squared.

A= π (r^2)

The most important details are that the vector y belongs to the subspace of R4 spanned by the columns of A if it can be written as a linear combination of the columns of A. This is equivalent to solving a system of linear equations using Gaussian elimination or matrix inversion. If a solution exists, then y is in the subspace of R4 spanned by the columns of A.

We are given a matrix A whose columns span R4. We are required to find out if the vector y belongs to the subspace of R4 spanned by the columns of A. Let's begin:We know that a vector y belongs to the subspace of R4 spanned by the columns of A if it can be written as a linear combination of the columns of A. That is,y = a1c1 + a2c2 + a3c3 + a4c4where c1, c2, c3 and c4 are the columns of A. Let's plug in the values given in the question:y = (10 -8 7 4) a1 + (16 7 -5 -7) a2 + (4 -7 4 -5) a3 + (-5 0 6 -2) a4We need to check if there exists a1, a2, a3 and a4 such that the above equation is true. This is equivalent to solving a system of linear equations as follows:10a1 + 16a2 + 4a3 - 5a4 = y1-8a1 + 7a2 - 7a3 + 0a4 = y216a1 - 5a2 + 4a3 + 6a4 = y34a1 - 7a2 - 5a3 - 2a4 = y4where y1, y2, y3 and y4 are the components of vector y. We can solve this system of equations using Gaussian elimination or matrix inversion. If a solution exists, then y is in the subspace of R4 spanned by the columns of A. Otherwise, y is not in the subspace of R4 spanned by the columns of A.

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The estimated probability that it would take at least three questions for Mary to need additional clues is 0.0014.

To calculate this probability, we can use the formula P(X≥3) = 1 - P(X<3). P(X<3) is the probability of Mary needing additional clues for fewer than three consecutive questions, which is equal to the sum of all the probabilities of Mary needing additional clues for zero, one, and two consecutive questions. This sum is equal to 0.9986. Therefore, P(X≥3) = 1 - 0.9986 = 0.0014.

The estimated probability that Mary needed additional clues to answer two consecutive questions is 0.0166. This is because there are six instances of two consecutive questions requiring additional clues (the 99 and 10 in the last row, the 20 and 20 in the second row, the 39 and 36 in the third row, the 13 and 51 in the fourth row, the 52 and 52 in the fifth row, and the 10 and 55 in the last row).

To calculate this probability, we can use the formula P(X=2) = 1 - P(X<2) - P(X>2). P(X<2) is the probability of Mary needing additional clues for less than two consecutive questions, which is equal to the sum of all the probabilities of Mary needing additional clues for zero and one consecutive questions.

This sum is equal to 0.9850. P(X>2) is the probability of Mary needing additional clues for more than two consecutive questions, which is equal to the probability of Mary needing additional clues for three or more consecutive questions. This probability is equal to 0.0014.

Therefore, P(X=2) = 1 - 0.9850 - 0.0014 = 0.0166.

Therefore, the estimated probability that it would take at least three questions for Mary to need additional clues is 0.0014.

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Answer:

\(m<-\frac{185}{k};\quad \:k>0\)

Step-by-step explanation:

\(-mk-110>75\\\\\mathrm{Add\:}110\mathrm{\:to\:both\:sides}\\\\-mk-110+110>75+110\\\\Simplify\\\\-mk>185\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-mk\right)\left(-1\right)<185\left(-1\right)\\\\Simplify\\\\mk<-185\\\\\mathrm{Divide\:both\:sides\:by\:}k;\quad \:k>0\\\\\frac{mk}{k}<\frac{-185}{k};\quad \:k>0\\\\Simplify\\\\m<-\frac{185}{k};\quad \:k>0\)

Answer:

the correct answer is c........

The function that has a restricted domain is k(x) = (x + 3) . Option C

A function is defined as an expression that is used to show the relationship between two variables.

These variables are called;

Then, we can say that;

Examining the expressions for each function will reveal this.

The division by x + 3 in the function k(x) says that the value of x cannot be -3 because division by zero is undefined.

As a result, the domain of k(x) is restricted to all real numbers except -3.

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Answer:

M= ([-1],[1/2])

The number in the green box is -1

Step-by-step explanation:

M= ([x1+x2/2], [y1+y2/2])

M= ([2+(-4)/2], [5+1/2])

M= ([-2/2, 6/2])

M= ([-1, 3])

Answer:

1/2

Step-by-step explanation:

Answer: divided by 3

Step-by-step explanation: x is rise y is run

Answer:

The answer is 1/3

Step-by-step explanation:

y2 - y1 0 - (-1)

_______ = ______ = 1/3

x2 - x1 0 - (-3)

The diagonals of a square are congruent and perpendicular.

A square is a polygon that has 4 sides. All four sides of the square are equal in length and perpendicular to each other which means the angle between the two adjacent sides is 90°.

Given:

ABCD is a square.

By the property of square,

AD = BC (all sides are equal)

∠BAD = ∠ABC (right angle)

AB = BA (reflexive property)

△ADB ≅ △BCA, by SAS criterion.

AC = BD.

In △AOB and △AOD

OB = OD (diagonals of a square bisect each other)

AB = AD (all sides are equal)

AO = AO (same side)

△AOB ≅ △ AOD, by SSS criterion.

So, ∠AOB = ∠AOD

By the property of linear pair,

∠AOB + ∠AOD = 180°

∠ AOB = ∠AOD = 90°

⇒ AO ⊥ BD

⇒ AC ⊥ BD.

Therefore, AC = BD and AC ⊥BD.

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Answer:

i think its the same thing

Step-by-step explanation:

Angle-Angle (AA) similarity postulate,  if two angles of one triangle are congruent to two angles of another, then the triangles are similar.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

As per the diagram,

Triangles RPQ & RST are similar since

∠P = ∠S & ∠Q = ∠T

Side - side - side (SSS) similarity theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Triangles RPQ & RST are similar since

RP/RS = RQ/RT = ST/PQ

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Answer:

-453/15 = -30.2

Answer:

-30.2 or -30 1/5

Step-by-step explanation:

The length of the garden is 99 m.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the area of the rectangle is 8811 \(m^{2}\) and the width is 89 m. Substituting these values into the formula, we get:

8811 \(m^{2}\) = Length x 89 m

To solve for the length, we can divide both sides of the equation by 89 m:

Length = 8811 \(m^{2}\) / 89 m

Simplifying, we get:

Length = 99 m

Therefore, the length of the garden is 99 m.

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