If A and B are mutually exclusive, then P(A\capB) = 0.
A and B are independent if and only if P(A\capB) = P(A)P(B)
If A and B are two events with P(A) = 0.4, P(B) = 0.2, and P(A B) = 0.5. Find the following:
(a) P(A\capB) (b) P(A?\capB) (c) P(A?\cupB?) (d) P(A|B)
If A and B are independent events with P(A) = 0.4 and P(B) = 0.2. Find the following:
Roll a die once. The event of getting a "2" and the event of getting a "5" are (a) independent;
(b) mutually exclusive;
(c) Neither

Roll a die twice. The event of getting a "2" on the first roll and the event of getting a "5" on the second roll are
(a) independent;
(b) mutually exclusive;
(c) Neither

Answer:

219.96

Step-by-step explanation:

Do you mean the product? The term quotient is for division.

Solving the provided question we can say that the  algebraic equation the value of 'y' is 19.

The difference is that expressions, which are essentially mathematical "phrases," do not contain an equal sign. Equations have an equal sign and demonstrate that two mathematical expressions are equivalent. An algebraic equation is 2x + b = 14, but 2x + b is an algebraic expression. Complete addition and subtraction from left to right after working from left to right to complete multiplication and division.

Expressions, which are essentially mathematical "phrases," are distinguished by the lack of the equal sign. Equations have an equal sign, which indicates that two mathematical expressions are equal.

3x+2y =  -4

15x +42y =  588

32y = 608

y = 608/32

y= 19

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Distance is a measure of how far an object has traveled from a starting point. Displacement is the change in position from the starting point.

It is the total distance an object has moved and is the sum of all the displacements an object has made. The formula for calculating distance is distance = speed x time. For example, if a car has traveled at a speed of 50 km/h for 4 hours, then the distance traveled is 200 km (50 km/h x 4 h = 200 km).

Displacement is the change in position from the starting point. It is the shortest distance between the starting point and the final point and does not take into account the direction of motion. The formula for calculating displacement is displacement = final position – initial position. For example, if a car starts at point A and travels to point B, the displacement is the distance between A and B (B – A).

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a). The sequence as represented in question a). is not an arithmetic sequence and hence, does not have a common difference.

b). The sequence formed by recording the daily odometer reading of a car after driving 15 miles each day does not have a negative common difference.

It follows from the task content that the sequence which has a negative common difference be determined.

It follows that the common difference, by definition is the difference between successive terms a (n) of the sequence.

Therefore, common difference is usually given by; a (n) - a (n-1).

a). Since the given sequence is; 64, 32, 16, 8, ....

Since The common difference is; 32 - 64 ≠ 16 - 32 ≠ 8 - 16.

Hence, the sequence does not have a common difference and hence, is not an arithmetic sequence.

b). For a sequence involving the daily odometer reading of a car after driving 15 miles every day.

It follows that the recursive function for such a sequence would take the form; a (n) = a (n-1) + 15.

By comparison with the standard recursive function for arithmetic sequences, a (n) = a (n-1) + 15, it follows that the common difference, d = 15.

On this note, the common difference for the sequence is not a negative number.

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Answer:

Solution: Sine is a trigonometric function of an angle defined as the ratio of the length of the perpendicular(opposite) side to the hypotenuse. Thus, the value of sin 2A = √3 / 2.

r is called as radius in the formula  A=πr^2

A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.

Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).

A model is, for example, the method for the area of a circle, πr2.

Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

Α= pi r^2

Divide each side by pi

A / pi = r^2

Take the square root of each side

sqrt( A / pi ) = sqrt(r^2)

sqrt( A / pi ) =r

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Answer: you learn more, and it looks good on job applications, but you have to go to more school and use up more of your time

Step-by-step explanation:

The descriptions with the correct rule of transformation are given above.

Rotation 90° counterclockwise

(x, y) → (-x, y)

Reflection over the x-axis

(x, y) → (x, -y)

Translation 2 left and 2 up

(x, y) → (x - 2, y + 2)

Translation 2 right and 2 down

(x, y) → (x + 2, y - 2)

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

(x, y) is in the first quadrant.

Rotation 90° counterclockwise (x, y) will be in the II quadrant.

So,

(x, y) → (-x, y)

(x, y) is in the first quadrant.

Reflection over the x-axis (x, y) will be in the IV quadrant.

(x, y) → (x, -y)

(x, y) is in the first quadrant.

Translation 2 left and 2 up we get,

(x, y) → (x - 2, y + 2)

(x, y) is in the first quadrant.

Translation 2 right and 2 down we get,

(x, y) → (x + 2, y - 2)

Thus,

The descriptions with the correct rule of transformation are given above.

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Answer:

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Let the number of quarters be x, then the number of dimes is x - 10.

We know that quarter is $0.25 and dime is $0.10.

The total amount is $10.90.

Set up equation and solve for x:

Najee has 34 quarters and 34 - 10 = 24 dimes.

Therefore ,the solution of the given problem of circle comes out to be as a result, the answer to the given circle problem is 6 + π cm

Each spot on a circle's plane is evenly spaced from the core and is a sealed, double object. The development of a ribbon of reflective symmetry is aided by each arc tracing the circle. Each angle also has an axis of symmetry centered on it.

Here,

The central angle of a 9 Pi sq millimeter circle is 60 degrees.

R² = 9 for the area of a circle.

Circumference = 2πR

=> = 6π cm = 2π*3 

(60/360)*6 cm is the length of an arc.

Following are the calculations for arc's perimeter: Radius + Arc Length + Radius = +3 + 3 = 6 + cm

Therefore ,the solution of the given problem of circle comes out to be as a result, the answer to the given circle problem is 6 + π cm

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The value of CE in the segment is 30 units.

The value of x in the segment is 1 units.

A line segment is bounded by two distinct points on a line. Therefore, point D is located on the segment CE. Hence,

CD = 24 and DE = x

CE = 5x

Therefore, the measurement of the segment CE can be found as follows:

CE = CD + DE

5x = 24 + x

5x - x = 24

4x = 24

divide both sides of the equation by 4

x = 24 / 4

x = 6

Finally,

CE = 5(6) = 30

The segment XZ is bisected by the point Y. Hence,

XY = 12x

XZ = 18x - 6

Hence, let's find x

Therefore,

2XY = XZ

2(12x) = 18x - 6

24x = 18x - 6

24x - 18x = -6

-6x = -6

x = -6 / -6

x = 1

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But to see one’s own face essential that the light emitted by it is either bounced back into our eyes (intimate a mirror - or something very much like it) - or that the light is recorded, captured and then played back into our eyes.

Did you know that shapes have a face? No, this face does not mean a face with two eyes, a nose, and a mouth. I mean a face of a shape, or the flat surface of a shape that you can trace and see. This face is known as a face in math.

Plane shapes in math mean any closed, flat, two-dimensional shape. All plane shapes have a face, because you can trace the shape of all plane shapes.

A triangle has a triangle face.

A rectangle has a rectangle face.

A diamond has a diamond face.

A circle has a circle face.

A square has a square face.

An oval has an oval face.

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In the given set of data, 4/5 is the constant of proportionality in the proportional relationship.

When two or more parameters are either directly or indirectly proportional to one another, the relationship is written as a = kb or a = k/b, where k denotes the direction of the relationship between the two variables. The proportionality constant, k, is defined as follows.

The ratio of two proportional values at a constant value serves as the definition of the proportionality constant. When the product or ratio of two variables yields a constant, the relationship between the two is proportional. By comparing the ratio of the two specified quantities, we can calculate the value of the proportionality constant. A direct variation or an inverse variation of this relationship are both possible.

Given

2 : 5/2

2 = (k)5/2

also

3 : 15/4

3 = (k)15/4

This gives us

k = 2 × 2/5

k = 4/5

k = 3 × 4/15

k = 4/5

Thus, In the given set of data, 4/5 is the constant of proportionality in this proportional relationship.

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The additive inverse of -13 7/8 is +13 7/8.

The additive inverse of a number is the number that, when added to the original, equals zero. The additive inverse of -13 7/8 can be found by turning the sign of the original number into its opposite, which would be +13 7/8. This can be expressed mathematically using the formula a + (-a) = 0, where a is the original number.

When -13 7/8 is added to +13 7/8, the result is 0. This can be seen by calculation: -13 7/8 + 13 7/8 = -13 7/8 + 8/8 + 5/8 = -5/8 + 8/8 = 3/8 + 8/8 = 11/8 + 8/8 = 19/8 + 8/8 = 27/8 + 8/8 = 35/8 + 8/8 = 43/8 + 8/8 = 51/8 + 8/8 = 59/8 + 8/8 = 67/8 + 8/8 = 75/8 + 8/8 = 83/8 + 8/8 = 91/8 + 8/8 = 99/8 + 8/8 = 107/8 = 0.

Therefore, the additive inverse of -13 7/8 is +13 7/8.

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Answer:

The correct answer is that X < 0.

Step-by-step explanation:

Now that all the important information is covered, let's take a look at the number line.

Please let me know if this helped!!!

A function example table is a tool used to organize and present information about a specific function or set of functions.

It typically includes the following columns:

Input: This column lists the inputs or arguments that the function accepts.

Output: This column lists the outputs or return values that the function produces.

Description: This column provides a brief explanation of what the function does and how it works.

Example: This column provides one or more examples of how the function can be used, along with the corresponding inputs and outputs.

Function example tables are a useful tool for documenting and understanding code, as they provide a clear and concise summary of a function's behavior.

They can also be helpful for testing and debugging code, as they can be used to quickly check that a function is behaving as expected.

In conclusion, A function example table can be used to organize and present information about a specific function or set of functions, it typically includes the following columns: Input, Output, Description and Example.

This table is a useful tool for documenting and understanding code, as they provide a clear and concise summary of a function's behavior which can also be helpful for testing and debugging code.

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The product of r and s to the fourth power is written as

In math, the term exponent refers to the number of times a certain number multiplies it self.

The number that is being multiplies is referred to as the base number while the number of times it multiplies itself is the exponents

In the problem, the multiplication of r and s is done as follows

= r * s

= rs

In this case, the base number is rs and raise to the fourth power implies that rs multiplies it self four times

= rs * rs * rs * rs

= (rs)⁴

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Answer:

(rs)^4

Step-by-step explanation:

When there are 25 students in the group, the number of people who not like non-fiction will be A. 15 people.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, three fifths of the students in the reading group like non-fiction books. If there are 25 students in the group, the number of people who not like non-fiction will be:

= 3/5 × 25

= 15

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Answer:

A step to step solution

Step-by-step explanation:

The measure of all these angles is just adding up the remote interior angles (the 2 angles that are shown in every triangle in this worksheet)

Find the sum, and that is your answer.

The first solution is 49+80 = 129

Therefore, the answer for #1 is 129 degrees

The number 9550000 can be arranged in a total of 8!/(4!4!) = 70 different ways.

Digits are numerals or numbers used for counting, measuring, and representing quantities. They are the building blocks of mathematics, and are used to express amounts, relationships, and orders of magnitude. Digits are also used in computers and other digital devices to store and communicate information.

The 8 digits of 9550000 can be arranged using the formula for permutation: nPr = n!/(n-r)!

In this case, n = 8 and r = 8. So, the number of permutations of the 8 digits of 9550000 will be 8!/(8-8)! = 8!/(0!) = 8! = 40320.

However, we need to account for the fact that there are 4 zeros in the number 9550000. To do this, we need to divide the number of permutations by 4! (factorial of 4) to account for the 4 identical digits.

Therefore, the total number of ways the digits in the number 9550000 can be arranged is 40320/4! = 70.

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Answer:

triangle angle sum theorem

Calculating the total VMT or VKT for all road segments during a certain time period by multiplying the daily traffic volume on each segment by its length.

The average automobile is around 15 feet long, so if you multiply 5280 by this number, you get about 350 cars, assuming they are all touching. Just over 284 million automobiles were on the road in the second quarter of 2022 in the United States. Though estimating the overall number of automobiles on the planet is not a precise science, the number is rising quickly.

Given that the ACS estimated there were 150 million workers in 2016, there are at least 115 million automobiles and trucks on American roads every day. Congestion is expected to be so bad during morning and afternoon rush hours. A balance between the demand for using the system and the infrastructure's capabilities can be achieved by creating digital twins of the transportation system and using them to optimise flows.

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The other addend is from the arithmetic operation is 14

The act of combining two or more objects is known as an addition. The process of computing the sum of two or more integers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently utilized in daily life.

The addends are the figures that are added. Between the addends is the plus sign (+), which represents addition.

Given that:

7 + x = 21

Then;

x = 21 - 7

x = 14

Therefore, we can conclude that if one addend is 7, the other will be 14 to make a sum of 21.

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The graph shows the different combinations of loaves of bread and rolls that the baker can sell in order to reach a total revenue of $27.

What is the slope-intercept form?

The slope-intercept form is a way of expressing a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept is the point at which the line crosses the y-axis, meaning the point at which the line intersects the y-axis when x = 0.

The given equation is in the form of y = mx + b where y =27, m = 3 and b = 1, is a linear equation and it can be represented as a straight line in a coordinate plane.

To graph this equation, we can use the following steps:

The graph shows the different combinations of loaves of bread and rolls that the baker can sell in order to reach a total revenue of $27.

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Answer:

[tex]\boxed{47.089 \;meters} \\\\[/tex]

Step-by-step explanation:

For any function f(x), the maximum or minimum value can be determined by 1. Finding the first derivative f(x) with respect to x i.e. f'(x)

2. Setting this first derivative to 0, solving for x

3. Substituting for x in the original function to get the maximum/minimum value

[tex]\textrm{The equation for the function f(t) is }\\f(t) = -4.9t^2 + 20.58t + 25.48\\\\[/tex]

[tex]\textrm{The first derivative of this function with respect to t is }\\\\f'(t) = - 2\cdot 49t + 20.58\\= -9.8t + 25.48\\\\[/tex]

[tex]\textrm{Setting this first derivative equal to 0 gives:}\\\\-9.8t + 20.58 = 0\\\\-9.8t = -20.58 \;\;\;\;\;\textrm{(Subtracting 20.58 from both sides)}\\\\9.8t = 20.58 \;\;\;\;\;\; \textrm{ (Multiplying both sides by -1)}[/tex]

[tex]\textrm{Therefore }\\\\t = \dfrac{20.58}{9.8}\\\\t= 2.1 \textrm{ seconds}[/tex]

[tex]\textrm{Therefore, at = 2.1 seconds, the ball will reach its maximum height.}[/tex]

To find what this maximum height is, substitute t = 2.1 in the original equation and solve for h(t)

[tex]h(t)\;at\;t=2.1 \\h(2.1) = 4.9\cdot \:2.1^2+20.58\cdot \:2.1+25.48=47.089 \;meters\\\\[/tex]

[tex]\textrm{ The maximum height the ball achieves before landing is } \boxed{47.089 \;meters} \\\\[/tex]

[tex]\textrm {This occurs 2.1 seconds after launch }[/tex]

Answer:

Step-by-step explanation:

just do - x + = -

- x - = +

so the answer is + i think

We Proven that AB is congruent to BC in the given triangle.

Two sets of points are said to be congruent if and only if one set of points can be transformed into the other by an isometry, or a combination of rigid motions like translation, rotation, and reflection.

This indicates either object might be precisely aligned with other object by moving & reflecting it, but not by resizing it. The ability to cut out and then perfectly match up two separate plane figures on a piece of paper indicates that they are congruent. I'm allowed to turn the paper over.

Given that

BD ≅ BE

DE bisects AB

DE bisect BC

If DE bisects AB it means

BD = DA

2BD = 2DA

2BD = AB

BD ≅ AB

Also DE bisect BC meaning

BE = EC

2BE= 2EC

2BE = BC

BE ≅ BC

As it already given that BD ≅ BE, we have,

⇒ AB ≅  BD ≅ BE ≅  BC

⇒ AB ≅ BC

Hence, Proven that AB is congruent to BC in the given triangle.

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