Let AA and BB be two mutually exclusive events, such that P(A)=0.2272P(A)=0.2272 and P(B)=0.4506P(B)=0.4506. Find the following probability:

Answer:

Hello!

David spends a total of $35.65 for both the Spanish and Mexican coffee

Step-by-step explanation:

5.25 × 3 = 15.75

9.95 × 2 = 19.90

15.75 + 19.90 = 35.65

Hope this helps!!

Answer:

my rate is a 2

Step-by-step explanation:

Developers determine the specifics of how to build a system in the design phase. b

The design phase and its importance:
Define Objectives:

The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.

The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:

During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.

This architectural design provides a high-level view of the system's organization.
Design System Components:

With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:

The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:

The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.

Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.

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a. The number of different routes from A to C is 7 + 2*4 = 15.

b. The number of different routes from A to C and back to A is 15 * 15 = 225.

c. The number of different routes from A to C and back to A in which town B is visited at least once can be calculated using the formula below: total number of routes from A to C and back to A - number of routes from A to B and back to A - number of routes from A to C and back to B + number of routes from A to B and back to C = 225 - 7*7 + 4*2 + 2*4 = 196.

d. The number of different routes from A to C and back to A that do not use any road twice is equal to the total number of permutations of all routes which can be arranged without repetition. This can be calculated using the formula below: 15P15 = 15!/(15-15)! = 1,307,674,368,000.

4. The number of nonempty collections of letters that can be formed from four As and eight Bs can be calculated using the formula below: total number of collections - number of collections with only As - number of collections with only Bs = 2^12 - 1 - 1 = 4095.

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Answer: D

Step-by-step explanation:

The first term is 3 and the common difference is 2.

Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.

The problem is to find two numbers that satisfy two conditions: their sum is 23, and their product is maximized. In other words, we need to determine two numbers that maximize their product while their sum remains constant.

To solve this problem, we can use algebraic reasoning. Let's assume the two numbers are x and y. We know that their sum is 23, so we have the equation x + y = 23. To maximize their product, we can express one variable in terms of the other. Solving the equation for y, we have y = 23 - x. Substituting this value of y in terms of x into the equation for the product, we get P = x(23 - x). This is a quadratic equation in terms of x. To find the maximum product, we can determine the vertex of the parabola represented by the quadratic equation. The x-coordinate of the vertex represents the value of x that maximizes the product. By solving for x, we can then find the corresponding value of y.

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When diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

Step 1: Create an equation that connects a sphere's volume to radius as the first step.

V = 4/3*π*r³

Step 2: Calculate each side's derivative in respect to time (Let the time be "t").

(d/dt)V = (d/dt)(4/3*π*r³)

dV/dt = 4πr²*dr/dt

Step 3: The problem description informs us that the diameter is 600 m, hence r must be 30 mm.

Additionally, it is stated that now the radius of a sphere is expanding at a rate of 2 mm/s; as a result, dr/dt must equal 2 mm/s.

We are interested in dV/dt, or the rate of change of the sphere's volume.

dV/dt = 4π(30mm)²*(2mm/s)

dV/dt = 22,620 mm³/s

So, when diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

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The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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Answer:

$3.25

Step-by-step explanation:

To get the price of one cup of coffee without including Dax's two dollar tip, the first step is to subtract 2 from 18.25.

18.25 - 2= 16.25

16.25 is price of the five cups of coffee that Dax bought without the two dollar tip. The final step is to get the price of one cup of coffee which is basically:

16.25 ÷ 5 = 3.25

The cost of each cup of coffee is $3.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

To get the price of one cup of coffee without including Dax's two-dollar tip, the first step is to subtract 2 from 18.25.

18.25 - 2= 16.25

16.25 is the price of the five cups of coffee that Dax bought without the two-dollar tip. The final step is to get the price of one cup of coffee which is basically:

16.25 ÷ 5 = $3.25

Hence, the cost will be $3.25.

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Answer:

1. First choice

2. Image C

3. Fourth chioice

4. Third choice

5. First choice.

Step-by-step explanation:

Solve the equation.

\( {x}^{2} - 9 = 0\)

Use the difference of two squares formula.

\( {x}^{2} - {y}^{2} = (x + y)(x - y)\)

\((x + 3)(x - 3) = 0 \\ x = 3, - 3\)

A linear relationship already says it all. Find the graph that is NOT a curve. The only image that is not a curve and the graph straight forwards is the Image C aka A choice.

A nonlinear function is a function that does not have a straight line graph. All linear functions are linear, except for Quadratic and up. Every polynomial function with the degree greater than one wont be a linear.

\(y = x + 3\)

If we change the constant from 3 to 5 then we would get

\(y = x + 5\)

The graph would shift up 2 units.

The second and third graph both are function. We can tell by doing a line test. Simply draw a vertical line first. Then we check if the line intercepts the graph more than a point or not.

If the line intercepts more than a point then it is not a function.

If the line intercepts only a point then it is a function.

The probability that out of four residential fires who independently reported on a single day, two are in family homes, one is in an apartment, and one is in another type of dwelling is 0.0895 or 8.95%.

The multinomial distribution deals specifically with events that have multiple discrete outcomes. The multinomial distribution is not limited to events with only discrete outcomes.

We have given that

The National Fire Incident Reporting Service stated, among all residential fires.

Let consider the number of events ,

X₁---> fires residential who are in home

X₂--> fires residential who are in appartment

X₃--> fires residential who are in another type of dwelling

The probability of ae X₁ occured (p₁)

= 73% = 0.73

The probability of event X₂ occured (p₂) = 20% =0.20

The probability of event X₃ occurred (p₃) = 7% = 0.07

Four residential fires are independently reported on a single day.

we have to calculate probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?

Now, Using the Multinomial distribution,

X₁= 2 , X₂= 1, X₃ = 1 and n = 4

P( X₁, X₂,-----,Xₙ ) =( n!/(X₁! X₂! ----Xₙ!) )( p₁ˣ₁ × p₂ˣ₂ × ----× pₙˣₙ)

P( 2,1,1) = 4!/2! 1! 1! ( 0.73² × 0.2× 0.07¹)

= 12 ( 0.014 × 0.5329)

= 0.0895272

Hence, the required probability is 0.089..

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Complete question:

The National Fire Incident Reporting Service stated that, among residential fires, 73% are in family homes, 20% are in apartments, and 7% are in other types of dwellings.

a) If four residential fires are independently reported on a single day, what is the probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?

The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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Answer:

80 cm^3

Step-by-step explanation:

The computation of the number of cubic centimeters rounded up to 10 cubic centimeter is shown below

For any type coin,

r = d ÷ 2

= 2 ÷ 2

= 1 cm

l = 0.5cm

For making 1 coin, the plastic required would be = Volume of coin

= πlr^2

= 3.14 × 0.5 × 1 × 1

= 1.57cm^3

Now For 50 coins,

Plastic needed is

= 50 × 1.57

= 78.5cm^3

= 80 cm^3

the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.

94.68 cm

The formula for circumference of a circle is C = 2πr, where r is the radius of the circle. Therefore, to find the circumference of the circle, we need to first calculate the radius.

The area of the circle is given as A = πr2.

Therefore, we can rearrange this equation to solve for the radius, which is

r = √(A/π)

Plugging in the given area, A = 3.14, we get

r = √(3.14/π) = √(3.14/3.14) = 1

Now, we can use the circumference formula to calculate the circumference, which is

C = 2πr = 2π(1) = 2π × 3.14 = 6.28 × 3.14 = 19.4568

Therefore, the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.

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It will take Thoriso 30 minutes to walk to school.

what is speed ?

Speed is a measure of how quickly an object is moving. It is defined as the distance traveled by an object in a given amount of time. The formula for speed is:

Speed = distance / time

The unit of speed depends on the units of distance and time used. Common units of speed include meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph).

Given by the question:
We can use the formula:

time = distance / speed

to calculate the time it will take Thoriso to walk to school.

Let d be the distance from Thoriso's home to school. Since the distance is the same whether she walks or rides her bicycle, we have:

distance walked = distance biked = d

Let's first calculate how long it takes Thoriso to bike to school:

time biked = distance biked / biking speed

time biked = d / 15 km/h

We are given that it takes her 10 minutes (0.167 hours) to bike to school, so we can set up the following equation:

0.167 hours = d / 15 km/h

Solving for d, we get:

d = 2.5 km

Now, we can calculate how long it will take Thoriso to walk to school:

time walked = distance walked / walking speed

time walked = d / 5 km/h

time walked = 2.5 km / 5 km/h

time walked = 0.5 hours or 30 minutes

Therefore, it will take Thoriso 30 minutes to walk to school.

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\(\huge\fcolorbox{blue}{aqua}{Answer:}\)

════════════════════

1.

\(kx^{2} + kx + \frac{25}{4}\)

All you need to do is factor out \( \frac{1}{4}\)

=\( \frac{4kx^{2 +} + 4kx + 25 } {4} \)

if you evaluate it it will become

\(kx^{2} + kx + \frac{25}{4} \)

────────────────────

2.

\( \frac{3y² + 1}{4} - \frac{y}{2} = 6\)

\(3y² + 1 - 2y = 24\)

\(3y² - 23 - 2y = 0\)

\(3y² - 2y - 23 = 0\)

\(y=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 3\left(-23\right)}}{2\times 3} \)

\(y=\frac{-\left(-2\right)±\sqrt{4-4\times 3\left(-23\right)}}{2\times 3} \)

\(y=\frac{-\left(-2\right)±\sqrt{4-12\left(-23\right)}}{2\times 3} \)

\(y=\frac{-\left(-2\right)±\sqrt{4+276}}{2\times 3} \)

\(y=\frac{-\left(-2\right)±\sqrt{280}}{2\times 3}\)

\(y=\frac{-\left(-2\right)±2\sqrt{70}}{2\times 3}\)

\(y=\frac{2±2\sqrt{70}}{6}\)

\(y=\frac{2\sqrt{70}+2}{6}\)

\(y=\frac{\sqrt{70}+1}{3}\)

\(y=\frac{2-2\sqrt{70}}{6}\)

\(y=\frac{1-\sqrt{70}}{3}\)

\(y=\frac{\sqrt{70}+1}{3}\)

So the answer is

\(y=\frac{\sqrt{70}+1}{3}\)

════════════════════

Explanation:

#Carry on learning

The distance between each pair of points using the Pythagorean Theorem for (1) (-7,1), (-8,2) is 1.4 and for (2) (-4, -7), (-1, -1) is 6.7.

Pythagoraan theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

(1) To calculate the distance between the points (-7,1), (-8,2), using Pythagorean theorem, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equawtion 1

(2) Similarly, For points (-4, -7), (-1, -1), to calculate the distance between the points, we use the formula ablove

Given:

Substitute these values into equation 1

Hence, the distance between each pair of points is 1.4 and 6.7 respectively.

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Answer:

1) x = 50 m

2) Max area = 22500 m²

3) Max area of each pen = 1500 m²

4) y = 150 m

5) dimensions of pen are 50m and 30m

6) Graph is attached

Step-by-step explanation:

Area of a rectangle is length × width

Let length be y and let width be x

Thus;

A = xy

Fencing material is 600m

Thus,perimeter = 600

Perimeter is; P = 6(length) + 2(width)

Thus;

600 = 6x + 2y

y = (600 - 6x)/2

y = 300 - 3x

Thus,

A = x(300 - 3x)

A = -3x² + 300x

We can see that the coefficient of x² is negative. This means that the parabola will open downward and has a maximum value at the vertex.

The vertex formula is;

x = -b/2a

a = -3

b = 300

Thus;

x = -300/(2 × -3)

x = 50 m

Since y = 300 - 3x, then;

y = 300 - 3(50)

y = 150 m

Maximum area of entire garden = xy = 50 × 150 = 7500 m²

There are 5 pens, thus;

Max area of each pen = max area of entire garden/5 = 7500/5

Max area of each pen = 1500 m²

Dimensions of each pen will be;

x and y/5

>> x = 50 m and y/5 = 150/5 = 30m

A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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Answer:

by SAS congruence rule

Step-by-step explanation:

WX=ZY (given) (side)

angle X =angle Z (given) (angle)

XZ=XZ. (common side) (side)

the picture isnt that clear but i hope that this is right..

hope this helps u :)

The linear equation with undefined slope and an x-intercept of -13 is:

x = -13

The general linear equation is written as:

y = a*x + b

Where a is the slope and b is the intercept of the y-axis.

And undefined slope is used only for vertical lines, where the slope (technically) tends to infinite.

These lines are of the form x = K, where K is a real number. (so we have x = constant)

And we know that the x-intercept is at x equal -13, with that we can conclude that the constant will be equal to -13, then the equation of the line is:

x = -13.

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5 Households. To determine the number of households included in the histogram representing the number of television sets per household for a sample of U.S. households, follow these steps:

1. Identify the bars on the histogram, which represent the number of television sets per household.
2. Find the height of each bar, which represents the number of households with that specific number of television sets.
3. Add up the heights of all the bars in the histogram.

The total sum represents the number of households included in the histogram.

The x-axis displays the total number of TVs owned by households, while the y-axis displays the number of homes utilising a specific number of TVs.

There are only 5 households total, and each one has 5 televisions. This is the lowest proportion of homes with the same number of televisions, which makes sense given that having five televisions in a single home is unusual.

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The type of sample that a store prints a request on each receipt asking customers to fill out a satisfaction survey online if they are willing is a voluntary response sample.

In the statistics world, a voluntary response sample is a research sample that relies on individual self-selection. This is in opposition to random sampling, in which the samples are gathered in a way that ensures everyone in a particular population has an equal chance of being chosen. This method of self-selection is also known as self-selection bias or sampling bias.Voluntary response samples are subject to a variety of flaws. The responses may not be representative of the population as a whole, and they may be skewed by numerous factors, such as which individuals are most likely to volunteer, how these volunteers differ from the population as a whole, and how the survey questions are phrased.The results of a voluntary response survey may be useful in generating hypotheses or gaining a general sense of how individuals feel about a particular subject. However, they are not reliable enough to draw any conclusions or to be taken seriously in the scientific sense.

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The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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Answer:

the answers is D.Sample space

Answer:

\(15^4\)

Step-by-step explanation:

Given the following question:

\(15\times15\times15\times15\)

In order to find the exponent of the given expression we count how many times the number is being multiplied by itself, that number would then be the exponent.

\(15\times15\times15\times15\)
They're four 15's
\(15^4\)

To prove the answer:
\(15\times15\times15\times15=50625\)
\(15^4=50625\)
\(15^4\)

Hope this helps.

Answer:

im pretty sure its A bc he just got a 5.0 rating and a thanks also i just got a 100% so thx to you for letting me get a try and thx to you above with a 5.0 rating

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The axes labels give you a clue as to the variables: time, volume.

__

The graph is a plot of volume versus time. That is, each point is the volume at a particular time.