Let P(B)=0.55, P(A|B)=0.60, and P(A|B¯)=0.20. Calculate P(B|A).

The measure of angle <B = 140

A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle

Also, It is also sometimes called an inscribed quadrilateral and the circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle or circumscribed circle

In a cyclic quadrilateral, opposite angles are supplementary

that is x + 4x -20 = 180

Collecting like terms

5x = 180+20

5x = 200

Dividing by x we have

x = 200/5

x= 40

Therefore the measure of angle B is

4x - 20

4(40) -20

160 - 20

Therefore <B = 140

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The measure of angle of the quadrilateral inscribed in a circle is 140 degrees.

For a quadrilateral inscribed in a circle, oppsosite sides are supplementary.

Supplementary angles adds up to 180 degrees.

From the diagram;

Angle D and angle B are opposite angle of a quadrilateral inscribed in a circle.

First, we determine the value of x.
Since supplementary angles adds up to 180 degrees.

Angle D + Angle B = 180

x + 4x - 20 = 180

Solve for x

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 200/5

x = 40

Now, the measure of angle B will be:

Angle B = 4x - 20

Plug in x = 40

Angle B = 4( 40 ) - 20

Angle B = 160 - 20

Angle B = 140 degrees.

Therefore, angle B has a measure of 140°.

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The number line model is a useful tool for representing mathematical expressions, such as 3x > 6, 2x + 7 ≥ 5, and 4x ≤ -3. By plotting points and drawing lines.

A number line is a visual representation of numbers in a linear sequence. It consists of an infinitely long line that is usually marked with a ruler and divided into equal intervals. The numbers are placed along the line in their numerical order starting from the left side.

The expression 3x > 6 can be represented by the number line model shown below. The line is drawn to the left of 6 showing that the value of 3x is greater than 6. The line is labelled with the point 3x to illustrate that the value of 3x is greater than 6. This number line model is an accurate representation of the expression 3x > 6.

The expression 2x + 7 ≥ 5 can be represented by the number line model shown below. The line is drawn to the right of 5 showing that the value of 2x + 7 is greater than or equal to 5. The line is labelled with the point 2x + 7 to illustrate that the value of 2x + 7 is greater than or equal to 5. This number line model is an accurate representation of the expression 2x + 7 ≥ 5.

The expression 4x ≤ -3 can be represented by the number line model shown below. The line is drawn to the left of -3 showing that the value of 4x is less than or equal to -3. The line is labelled with the point 4x to illustrate that the value of 4x is less than or equal to -3. This number line model is an accurate representation of the expression 4x ≤ -3.

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Answer:

Step-by-step explanation:

(1). [tex]x^{-5}[/tex] = [tex]\frac{1}{x^{5} }[/tex]  

(2). [tex]x^{0}[/tex] [tex]x^{4}[/tex] [tex]x^{5}[/tex] = [tex]x^{0+4+5}[/tex] = [tex]x^{9}[/tex]

(3). [tex]\frac{x^4 y^3}{x^2y^4}[/tex] = [tex]\frac{x^{4-2} }{y^{4-3} }[/tex] = [tex]\frac{x^2}{y}[/tex]

(4). [tex]\frac{x^{5} x^{-2} }{x^{4} x^{-1} }[/tex] = [tex]\frac{x^{5-2} }{x^{4-1} }[/tex] = [tex]\frac{x^3}{x^3}[/tex] = 1

A cubic functiοn can be either οne οr twο, and the number οf minimum and/οr maximum pοints οn the graph οf a quartic functiοn can be zerο, οne, twο, οr three.

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.

The x² term is written first, then the x term, and finally the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm. In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.

Fοr a quadratic functiοn, which has degree ², there is always οne minimum οr maximum pοint. This is because the graph οf a quadratic is a parabοla, which has a vertex that is either a minimum οr maximum pοint, depending οn whether the leading cοefficient is pοsitive οr negative.

Fοr a cubic functiοn, which has degree 3, there can be either οne οr twο minimum and/οr maximum pοints. This is because the graph οf a cubic is a curve that can have οne hump οr twο humps, depending οn the cοefficients οf the terms.

Hence a cubic functiοn can be either οne οr twο, and the number οf minimum and/οr maximum pοints οn the graph οf a quartic functiοn can be zerο, οne, twο, οr three.

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Therefore, when one angle is specified as 44°, the length of the absent side (base) is approximately 11.8.

Three straight edges and three angles make up the closed, two-dimensional shape of a triangle. Three non-collinear elements are connected to create it. A triangle's three sides add up to a constant 180 degrees. The longest side in a right triangle, also known as the hypotenuse, is the side that faces the greatest angle. Triangles can be categorized into different types depending on how long their sides are and how much inclination they have, including equilateral, isosceles, scalene, acute, right, and obtuse triangles. In order to learn shapes and angles, triangles are frequently used in geometry and trigonometry.

given

The length of the missing side can be determined using the trigonometric formula cosine (cos).

adjacent / hypotenuse = cos(44°)

cos(44°) = x / 17

x = 17 cos(44°)

x ≈ 11.8 (rounded to the closest tenth) (rounded to the nearest tenth)

Therefore, when one angle is specified as 44°, the length of the absent side (base) is approximately 11.8.

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If AD = 2/3 AB, the ratio of the length BC of to the length of DE is 3/4.

In Mathematics and Geometry, an arc simply refers to a trajectory that is generally formed when the distance from a given point has a fixed numerical value.

Based on the diagram representing the arcs, we have the following:

Arc DE = π(AD)(2.36/2π) = (2/3)(AB)(2.36/2)

Arc DE = (2/3)(AB)(1.18 radians)

Arc BC = (π) (AB)(1.18/2π)

Arc BC = (AB)(0.59 radians)

Arc BC/Arc DE = (AB)(0.59 radians)/(2/3)(AB)(1.18 radians)

Arc BC/Arc DE = (3/2)(0.59 radians/1.18 radians)

Arc BC/Arc DE = 3/4

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Answer: 3/4

Step-by-step explanation: correct on plato

Answer:

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According to the proof, the option C which has ∠WXY ≅ ∠YZW statement is used within the proof.

Given rectangle WXYZ.

Asked to prove the statement: ΔWXY ≅ ΔYZW

According to the SAS postulate, two sides of one triangle and the angle that connects them are congruent if they are also congruent with two sides and the included angle of a second triangle.

According to given rectangle:

XW ≅ YZ (opposite side of rectangle)

∠WXY ≅ ∠YZW (opposite angle of rectangle)

XY ≅ WZ (opposite side of rectangle)

Hence, ΔWXY ≅ ΔYZW according to SAS Postulate.

Therefore, the statement ∠WXY ≅ ∠YZW is used within this proof. So option C is correct.

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FE = 15 units as per the Pythagoras theorem.

∠D = 65°

A right-angled triangle is another situation in which the right angle is applied.

A triangle is referred to as a right-angled triangle if one of its three angles is 90 degrees.

A right-angled triangle's three interior angles all add up to 180 degrees, thus if one angle is always 90 degrees, the other two must also always add up to 90 degrees.

Now in the triangle given,

DF = 8, DE = 17

Using Pythagoras theorem, we can get FE.

FE² = DE² - DF²

FE ² = 289 - 64

FE² = 225

FE = 15

Now using the principles of angles in a right angle triangle:

∠D + ∠F + ∠E = 180°

∠D = 180 - 90 - 25

∠D = 65°

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Therefore , the solution of the given problem of unitary method comes out to be it will cost $27.00 to purchase enough sand to fully fill the sandbox.

The job can be finished by combining the data obtained that use this nanosection method throughout all additional variable data of two people who used a single method. Simply put, this indicates that when a desired result manifests, either equation  the stated entity would be known or, in actuality, the colour by both enormous operations would be skipped. A changeable fee of Rupees ($1.01) may well be necessary for forty pens.

Here,

The playground has the following size:

=> 3 m x 2 m x 1 m = 6 cubic meters

We require 6 cubic metres of sand to fully fill the sandbox.

Sand will cost $4.50 per cubic metre in total, which equals:

=> $4.50 per cubic metre times 6 cubic metres equals $27.00.

Therefore, it will cost $27.00 to purchase enough sand to fully fill the sandbox.

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The value fοr x that maxes the twο ratiοs equivalent is (C) 15/4.

In mathematics, a prοpοrtiοn is an equatiοn that states that twο ratiοs are equal. A ratiο is the relatiοnship between twο numbers indicating hοw many times the first number cοntains the secοnd.

We can set up a prοpοrtiοn tο sοlve fοr x:

1/5 : 3/4 = x : 1

Crοss-multiplying, we get:

4x = 5(3)

4x = 15

x = 15/4

Hence, the answer is (C) 15/4.

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The equation  [tex]\frac{x-70}{2}[/tex] = 60° and by solving the equation, arc-x is 190°

The chord-chord power theorem provides an explanation for the connection that exists between arcs and cords. The theorem states that the product of the lengths of the two segments of one chord and the product of the lengths of the two segments of the other chord is the same if two chords intersect inside a circle. In circle geometry, problems involving chords and arcs can be solved using this theorem.

According to the Circle identity rule,

⇒ [tex]\frac{x-70}{2}[/tex] = 60°

⇒ x - 70 = 120°

⇒ x = 120° + 70°

Then x = 190°

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Answer:

D

Step-by-step explanation:

We can use the units-of-production depreciation method to calculate the depreciation in year 3, since we know the estimated life of the machine in terms of units produced.

First, we need to calculate the depreciation per unit:

Depreciation per unit = (Cost - Residual value) / Expected number of units

Depreciation per unit = ($30,200 - $4,000) / 150,000 units

Depreciation per unit = $0.176 per unit

Next, we can calculate the total depreciation for year 3 based on the number of units produced:

Depreciation for year 3 = Depreciation per unit x Units produced in year 3

Depreciation for year 3 = $0.176 per unit x 40,000 units

Depreciation for year 3 = $7,040

Therefore, the depreciation in year 3 would be $7,040. This corresponds to option D.

Answer:

1/45

Step-by-step explanation:

Let A be the event that the applicant has a Master's degree and B be the event that the applicant does not have work experience.

Then, we are given:

P(A) = 1/3

P(not B) = 4/9

P(at least one characteristic) = P(A or B) = 1/5

We want to find P(A and not B), which is the probability that the applicant has a Master's degree but no work experience.

Using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

We can rearrange to solve for P(A and B):

P(A and B) = P(A) + P(B) - P(A or B)

P(B) = 1 - P(not B) = 1 - 4/9 = 5/9

Substituting in the given probabilities:

1/5 = 1/3 + 5/9 - P(A and B)

Solving for P(A and B):

P(A and B) = 1/3 + 5/9 - 1/5

P(A and B) = 1/45

Therefore, the probability that the applicant will have both characteristics (a Master's degree and no work experience) is 1/45.

The only possible value of ∠P in ΔNOP

∠P ≈ 59°

P must be less than 180 degrees because it is an angle in a triangle. As a result, the value of P to the nearest degree can only be:

∠P ≈ 59°

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is where the term "angle" originates. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign " is used to denote angles.

from the question:

Using the Law of Cosines, which states that the following formula holds for any triangle with sides a, b, and c and opposite angles A, B, and C, we can determine all possible values of P in NOP.

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

Extending this to NOP, we can use the angle and existing side lengths to determine the length of side n:

cos(28°) = o/n

n = o / cos(28°) = 51 / cos(28°) ≈ 59.87 inches

The Law of Cosines can now be used once more to determine the potential values of P. We are aware of:

[tex]p^2 = n^2 + o^2 - 2no cos(P)[/tex]

Substituting the values we know, we get:

[tex]56^2 = (59.87)^2 + 51^2 - 2(59.87)(51) cos(P)[/tex]

Simplifying this expression and solving for cos(P), we get:

[tex]cos(P) = (59.87^2 + 51^2 - 56^2) / (2(59.87)(51))[/tex]

cos(P) ≈ 0.506

Taking the inverse cosine of this value, we get:

P ≈ 59.3° or P ≈ 300.7°

P must, however, be smaller than 180° because it is an angle in a triangle. As a result, the value of P to the nearest degree can only be:

∠P ≈ 59°

Hence, in NOP, P can only have one potential value.

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The only possible value of ∠P in ΔNOP

∠P ≈ 59°

P must be less than 180 degrees because it is an angle in a triangle. As a result, the value of P to the nearest degree can only be:

∠P ≈ 59°

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is where the term "angle" originates. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign " is used to denote angles.

from the question:

Using the Law of Cosines, which states that the following formula holds for any triangle with sides a, b, and c and opposite angles A, B, and C, we can determine all possible values of P in NOP.

[tex]c^2=a^2+b^2-2abcos(C)[/tex]

Extending this to NOP, we can use the angle and existing side lengths to determine the length of side n:

cos(28°) = o/n

n = o / cos(28°) = 51 / cos(28°) ≈ 59.87 inches

The Law of Cosines can now be used once more to determine the potential values of P. We are aware of:

[tex]p^2=n^2+o^2-2ncos(P)[/tex]

Substituting the values we know, we get:

[tex]56^6=(59.87)^2+51^2-2(59.87)(51)cos(P)[/tex]

Simplifying this expression and solving for cos(P), we get:

[tex]cos(P)=(59.87^2+51^2+-56)/(2(59.87)(51))[/tex]

cos(P) ≈ 0.506

Taking the inverse cosine of this value, we get:

P ≈ 59.3° or P ≈ 300.7°

P must, however, be smaller than 180° because it is an angle in a triangle. As a result, the value of P to the nearest degree can only be:

∠P ≈ 59°

Hence, in NOP, P can only have one potential value.

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Answer: 61

Step-by-step explanation:

Each dinner guest ate 1/12 fraction of the whole pan of cornbread.

What do you mean by fraction?

In mathematics, a fraction is a way to represent a part of a whole or a ratio between two quantities. A fraction consists of a numerator, which is the number above the line, and a denominator, which is the number below the line. The numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole or the ratio. Fractions are often expressed as a/b, where a is the numerator and b is the denominator.

Calculate the fraction :

To calculate the fraction of a whole pan of cornbread each guest ate, we need to divide the amount of cornbread shared among the guests (i.e., 1/2 of the pan) by the number of guests (i.e., 6). Dividing a fraction by a whole number involves multiplying the numerator of the fraction by the reciprocal of the whole number.

To find out what fraction of the whole pan of cornbread each guest ate, we can divide the amount of cornbread shared among the guests (1/2 of the pan) by the number of guests (6):

(1/2) ÷ 6 = (1/2) x (1/6) = 1/12

Therefore, each dinner guest ate 1/12 of the whole pan of cornbread.

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a.  The value of the annuity is $7,735.42. b. The interest is  -$1,735.42 (rounded to the nearest dollar).

Interest is the cost of borrowing money or the amount earned on deposited funds over a certain period of time. It is typically expressed as a percentage of the principal amount, also known as the interest rate. When someone borrows money, they usually pay interest to the lender as compensation for the use of the funds. On the other hand, when someone saves or invests their money, they may earn interest on their deposits or investments. The amount of interest earned or paid depends on factors such as the interest rate, the principal amount, the duration of the loan or deposit, and the compounding frequency. Interest is an important concept in personal finance, investing, and economics in general.

a. To find the value of the annuity, we can use the formula for the present value of an annuity:

PV = (PMT x (1 - (1 + r)^(-n))) / r

where PV is the present value of the annuity, PMT is the periodic payment, r is the interest rate per period, and n is the total number of periods.

In this case, PMT = $100, r = 5.5% / 2 = 0.0275 (since interest is compounded semiannually), and n = 30 years x 2 = 60 periods (since there are two semiannual periods in a year).

Substituting these values into the formula, we get:

PV = (100 x (1 - (1 + 0.0275)^(-60))) / 0.0275 = $7,735.42

Therefore, the value of the annuity is $7,735.42.

b. The total interest earned on the annuity over the 30-year period is simply the difference between the total amount deposited and the present value of the annuity. Since the total amount deposited is $100 x 2 x 30 = $6,000 (since there are two semiannual deposits of $100 for each of the 30 years), we can find the interest as:

Interest = Total amount deposited - Present value of annuity

= $6,000 - $7,735.42

= -$1,735.42 (rounded to the nearest dollar)

Since the interest is negative, this means that the annuity earned less interest than the total amount deposited. This is likely because the interest rate of 5.5% is relatively low, and the semiannual compounding may also have contributed to a lower overall interest earned.

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The answer of the given question based on percentage of the no. of officers that are male are approximately 21.3% of the police officers are male.

Multiply the number by the percentage you want to find, expressed as a decimal. For example, if you want to find 20% of 100, you would multiply 100 by 0.20.

The result of step 1 is the percentage of the number you're looking for. In the example above, 20% of 100 is 20.

If you want to express the result as a percentage, simply multiply the result by 100 and add the percent sign. In the example above, 20 times 100 is 2000, so 20% of 100 is equivalent to 2000%.

To summarize, the formula to find the percentage of any number is:

Percentage of a number = (percentage expressed as a decimal) x (the number)

To find the percentage of police officers who are male, we need to add up the number of male officers and divide it by the total number of officers, then we multiply by 100 to convert to percentage.

From the table, we can see that there are 170 officers in total who are male. Therefore:

Percentage of officers who are male = (number of male officers / total number of officers) x 100

= (170 / 800) x 100

= 21.25%

Rounding to the nearest tenth of a percent gives us:

Percentage of officers who are male = 21.3% (rounded to one decimal place)

Therefore, approximately 21.3% of the police officers are male.

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Answer:

1/2

Step-by-step explanation:

3 odd and 3 even on a die

Therefore, none of the statements could be true for g except for g(0) = -2 and g(-9) = 6, which we already know are true based on the given information.

In mathematics, a function is a relationship between a set of inputs (called the domain) and a set of possible outputs (called the range), with the property that each input is associated with exactly one output. Functions are used to model real-world situations and to describe relationships between variables. They are an important concept in many branches of mathematics, as well as in fields such as physics, engineering, and economics. Functions play a central role in calculus, where they are used to study rates of change, derivatives, and integrals. A function can be represented using an equation, formula, or graph. The notation "f(x)" is often used to denote a function of the input variable "x".

Here,

Since the function g has a domain of -20 ≤ x ≤ 5, any input value outside of this range is not defined for g. Similarly, since the range of g is -5 ≤ g(x) ≤ 45, any output value outside of this range is not attainable by g.

Given that g(0) = -2 and g(-9) = 6, we can use this information to eliminate the statements that are not possible:

A. g(0) = 2 is not possible, since we know that g(0) = -2.

B. g(-4) = -11 is not possible, since -4 is not in the domain of g.

C. g(7) = -1 is not possible, since 7 is not in the domain of g.

D. g(-13) = 20 is not possible, since -13 is not in the domain of g.

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The number of times that Greg chooses a yellow pebble is 22 times.

To find the number of possible choices, calculate the number of chances in the total number of outcomes.

Since we need to find the number of choices that are expecting a yellow pebble, find the total number of yellow pebbles in the number of pebbles in both Claire and Laura's cases and find the total number of yellow pebbles.

Here we have

A table below shows the number of painted pebbles by Claire and Laura

From the table,

Number of pebbles that Laura painted = 8 yellow, 7 green, 10 blue

Number of pebbles that Claire painted = 14 yellow, 5 green, 6 blue

Total number of yellow pebbles = 8 + 14 = 22

Given that

Greg chooses a pebble at random from the box 75 times, and each time replaces the pebble  

Hence, the number of time that Greg get yellow pebble = number of yellow pebbles

Therefore,

The number of times that Greg chooses a yellow pebble is 22 times.

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The equation represented by the attached graph is

Quadratic equation in standard vertex form is

y = a(x - h)² + k     where a = 1/4p

The vertex

v (h, k) = (0, 0) from the graph

h = 0

k = 0

substitution of the values into the equation gives

y = a(x - h)² + k

y = a(x - 0)² + 0

y = ax²

Using point (1, 3) form the graph to solve for a

y = ax²

3 = a(1)²

a = 3

plugging in to the equation

y = ax²

y = 3x²

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Answer:

Yes, (3,8) is a solution to this system of inequalities

Step-by-step explanation:

y > x +4                               Is (3,8) a solution to this system of inequalities?

y < 6x + 10

Let's put the number in and check!

8 > 3 + 4

8 > 7

This is true

8 < 6(3) + 10

8 < 28

This also true

So, Yes, (3,8) is a solution to this system of inequalities

Answer: 2,400

Step-by-step explanation: Multiply the mass value by 2000

Answer:

2400 pounds

Step-by-step explanation:

1 ton is 2000 pounds

So we can multiply the number of tons by 2000 to get the answer.

1.2 * 2000 = 2400 pounds

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