Let A1, A2, A3, and A4, be events from a common sample space. these events are pairwise mitially exclusive, with the exception tha A1 and A2 occur simultaneously with a probability of 0.1. if events A1, A2, and A3 each occur with probability 0.3, what is the largest possible value for the probability of A4?

this is my work:
P(A1) = P(A2) = P(A3) = 0.3
sum of the probabilities of all events must be equal to 1, so we have:
P(A1) + P(A2) + P(A3) + P(A4) = 1
the probability of both A1 and A2 is 0.1
P(A1 and A2) = 0.1
the probability of the intersection of two events is given by P(AnB) = P(A) + P(B) - P(AuB)
So, we can write:
P(A1) + P(A2) - P(A1 and A2) = 0.3 + 0.3 - 0.1 = 0.5
we have:
P(A1) + P(A2) + P(A3) + P(A4) = 1
0.3 + 0.3 + 0.3 + P(A4) = 1
P(A4) = 1 - 0.9 = 0.1

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out

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The expression that correctly shows 6 x 6 in exponential notation is 6²

From the question, we have the following parameters that can be used in our computation:

6 * 6

Next, we apply the law of indices/exponent

So, we have the following representation

6¹⁺¹

Evaluate the sum

6²

Hence, the correct expression of 6 * 6 is 6²

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Answer:

It will be straight line on x equal zero and y equal 6 horizontal straight line

Note that where the diameter of the bicycles are 60 inches and 9 inches respectively, the rotation of each tire after traveling 600 feet would be:

Small Tire (9in Diameter ) =   188.4 Rotations.

Big Tire (60 in Diameter) = 3.2 rotations

Note that the above were arrived at using the knowledge of Circumference.

Note that the circumference in geometry is the perimeter of a circle or ellipse.

This is calculated using the formula:

C = 2πr

or

C = πD

Where C = Circumference

R = radius

D = Diameter which is 2r

π = 3.14

To arrive at how many rotations each tire did, we'd have to divide the distance traveled by the circumference of each tire.

For the Small Tire, the diameter is 9 feet.

Thus, the circumference of Small Tire = 3.14 * 9

= 28.26 feet

Thus, the rotations by the small tire is:

600/28.26

= 21.2314225053

[tex]\approx[/tex] 21.2feet

Applying the same process to the big tire, we have:

C =  3.14 * 60

C = 188.4

The rotations by the big tire =
600/188.4

= 3.1847133758

[tex]\approx[/tex] 3.2 feet.

Thus, the rotations  by each tire over 600ft is given as:

Big Tire = 3.2

Small Tire =  188.4 .

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Full Question:

See attached image.

Answer:

[tex]\dfrac{-8y}{y-3}[/tex]

Step-by-step explanation:

[tex]\sf \dfrac{49 - y^2}{6y^2 +42y}=\dfrac{7^2-y^3}{6y^2 +6*7y}\\\\[/tex]

                 [tex]\sf =\dfrac{(7+y)(7-y)}{6y(y + 7)}=\dfrac{(7+y)(7-y)}{6y(7+y)}\\\\\\=\dfrac{7-y}{6y}[/tex]

y² - 10y + 21

sum = -10

Product = 21

Factors = (-7) , (-3)   {(-7)*(-3) = 21  & (-7)+ (-3) = -10}

y² - 10y + 21 = y² - 7y - 3y + 21

                    = y(y - 7) - 3(y - 7)

                   = (y - 7) ( y - 3)

[tex]\sf \dfrac{49 -y^2}{6y^2 + 42y}*\dfrac{48y^3}{y^2 - 10y + 21}=\dfrac{7-y}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\[/tex]

                                         [tex]\sf = \dfrac{(-1)(y-7)}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\=\dfrac{(-1)*8y^2}{y-3}\\\\\\=\dfrac{-8y^}{y-3}[/tex]

The rate of the jet in still air is 741 mph, and the rate of the wind is 150 mph.

What is rate ?

A rate is a ratio of two quantities, typically a change in one quantity over a corresponding change in another quantity, often over a specific time period. For example, the interest rate on a loan is the ratio of the interest paid to the amount of the loan. A speed is a rate at which an object covers distance, velocity is a rate of change of position, etc.

To find the rate of the jet in still air:

Rate = Distance / Time

The distance is 2964 miles, and the time is 4 hours. So the rate of the jet in still air is:

Rate = 2964 / 4 = 741 mph

To find the rate of the wind, you can use the formula:

Wind Rate = (Distance with wind - Distance against wind) / Time

The distance with the wind is 3564 miles, the distance against the wind is 2964 miles, and the time is 4 hours. So the rate of the wind is:

Wind Rate = (3564 - 2964) / 4 = 600 / 4 = 150 mph

So the rate of the jet in still air is 741 mph, and the rate of the wind is 150 mph.

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The required mean of the table is 32.71.

Mean: The formula is E(X)=μ=∑xP(x). where x represents the value of the random variable X, P(x) represents the corresponding probability, and the symbol Σ represents the sum of all products xP(x). Here we use the symbol μ for mean, since it is a parameter. Represents the population mean.

Mean=Total of household/Total number of dogs

⇒ [tex]\frac{(323+176+87+51+32+8+10)}{(0+1+2+3+4+5+6)}[/tex]=[tex]\frac{687}{21}[/tex]=32.71

Standard Deviation: Standard deviation is calculated as the square root of variance by determining the deviation of each data point from the mean. If the data points are far from the mean, there will be more variation within the data set. Therefore, the wider the data, the higher the standard deviation.

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False claims do not have to engage with previous theories in order to be effective. So it must contradict previous theories. So the option d is correct.

A tentative, verifiable explanation for a natural world phenomenon is what is known as a scientific hypothesis. The scientific method's foundational element is it.

It's sometimes referred to as a "informed guess" that was made using past knowledge and observation. Despite the fact that this is true, a hypothesis is a better guess.

Creating a hypothesis calls for active observation and background research, in contrast to making a "informed guess," which implies a random prediction based on one's expertise. A hypothesis is predicated on the fundamental tenet that no outcome is predetermined.

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American household size According to government statistics, a family is defined as two or more people who live together and are related by blood or marriage, whereas a household is defined as all the residents of a dwelling unit.

A housing unit, also known as a dwelling unit or a housing unit, is a building, a portion of a building, or a space that is used as a home, a place to live, or a place to sleep by one or more people who maintain a common household.

Size of American households In contrast to a household, which is defined as all the occupants of a dwelling unit, a family is defined as two or more people who live together and are related by blood or marriage.

As a result, although all families are part of households, some households do not.

Therefore, American household size According to government statistics, a family is defined as two or more people who live together and are related by blood or marriage, whereas a household is defined as all the residents of a dwelling unit.

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The total amount spent by John is $37.78.

Given is that John goes to a restaurant and has a bill of 32.57. He uses a 10% off coupon on the cost of the meal. The tax is 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied.

Amount left as a tip -

{t} = 18% of 32.57

{t} = 18/100 x 32.57

{t} = 5.87

Amount included in tax -

8% of 32.57

8/100 x 32.57

2.61

Billed amount after coupan is applied -

10% of 32.57

10/100 x 32.57

$3.26

Amount spend -

(32.56 - 3.26) + 2.61 + 5.87

$37.78

Therefore, the total amount spent by John is $37.78.

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The correct solution for the following system of Inequalities is (-1, 1) because it is on the darker region.

An equation is an expression that shows the relationship between numbers and variables.

Inequalities is used for the non equal comparison of these numbers and variables.

Let x represent the x axis and let y represent the y axis.

The solution to the system of linear equalities is the intersection of both inequalities which is the darker region.

The point that satisfies both inequalities as shown on the graph is (-1, 1) because it is on the darker region.

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Answer:

Start at 1 on y-intercept and go down 2 units and right 1 unit

Step-by-step explanation:

First you have to graph your y-intercept (1) *which is the red dot in the graph I made for you*

Then you must use your slope (-2) to graph the rest

Since your slope is negative you have to go down from your y-intercept. In your case you are going down 2 units from your intercept. And since your slope is a whole number instead of a fraction you just go to the right 1 unit to make the coordinate (1,-1).

That is how you graph your equation.

I hope this helped!

A. The variable is qualitative because it is a numerical measure is correct answer.

Any variable that isn't numerical is referred to as a qualitative variable or a category variable. It describes information that falls into a category. for instance: Eye color (variables include: blue, green, brown, hazel).

In statistics, qualitative variables are given nominal scales since they cannot be ordered on a numerical scale. Qualitative variables are exactly what the word "nominal" means: names. No ordering is either conceivable or inferred on a nominal scale (except for alphabetical ordering like New York, Washington, West Virginia or Chelsea, Edinburgh, London). In other words, data are classified according to a category on the nominal scale.

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I have been working 1004 days at the job as a student

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, and division among others.

To solve this problem we must perform the following algebraic operations with the given information

Calculate the days from 08/21/2019 to 08/21/2022, we get:

Days 1 = (08/21/2022 - 08/21/2019) * (365 days/1 year)

Days 1 = 3 years * (365 days/1 year)

Days 1 = 1095 days

Calculate the days from 05/21/2019 to 08/21/2019, we get:

Days 2 = (08/21/2019 - 05/21/2019) * (30 days / 1 month)

Days 2 = 3 months * (30 days / 1 month)

Days 2 = 90 days

Calculating the days from 05/20/2019 to 05/21/2019, we get:

Days 3 = 05/21/2019 - 05/20/2019

Days 3 = 1 day

Calculate the total days from 08/21/2019 to 05/20/2022, we get:

Total days = Days 1 - days 2 - days 3

Total days = 1095 days - 90 days - 1 day

Total days = 1004 days

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The volume of the cuboid is 16 cubic yards.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

Given:

A cuboid with height 2 yards, length 2 yards and width 4 yards.

The volume of the cuboid,

= length x width x height

= 4 x 2 x 2

= 16 cubic yards.

Therefore, the volume is  16 cubic yards.

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The set of mobile gaming apps in which the number of monthly users was greater than 12 million is {A, B}

A set is a collection of distinct objects, called elements or members, that are brought together by a common property or rule.

Sets can be represented using set notation, which uses curly brackets {} to enclose the elements of the set. For example, the set of natural numbers less than 5 can be represented as {1, 2, 3, 4}.

The set of mobile gaming apps in which the number of monthly users was greater than 12 million can be determined by checking given the table for mobile gaming apps with value greater than 12 million.

You will notice that only A and B have values greater than 12 million. That is 23 million and 13 million for A and B respectively.

Thus, the set will be {A, B}

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John will be able to meet the goal of practicing piano for mentioned time on Saturday and Sunday.

Required amount of practice = [tex]2 \frac{1}{2} [/tex] hours

Required amount of practice = (2×2)+1/2

Required amount of practice = 5/2 hours

Required amount of practice = 2.5 hours

Practice performed on Saturday = [tex]1 \frac{1}{6} [/tex]

Practice performed on Saturday = (6×1)+1/6

Practice performed on Saturday = 7/6 hours

Practice performed on Sunday = [tex]1 \frac{1}{4} [/tex]

Practice performed on Sunday = (4×1)+1/4

Practice performed on Sunday = 5/4 hours

Combined practice performed = 7/6 + 5/4

Combined practice performed = 1.2 + 1.3

Performing addition

Combined practice performed = 2.5 hours

The performed practice is equal to the goal and hence he will meet the goal.

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The probability of selecting sticks with a boy's name is 8/13 and the probability of selecting sticks with a girl's name is 2/5.

Now, According to the question:

Formula to find the probability of an event:

"P(A) = n(A) / n(S)

where, n(A) is the number of favorable outcomes of an event A

n(S) is the total number of outcomes for an experiment"

"Information available from the question"

Total number of students are,

n(S) = 10 + 16

n(S) = 26

Let event A: selecting first stick with a boy name

n(A) = 16

So, the probability of a boy is,

P(A) = n(A)/n(S)

P(A) = 16/26

P(A) = 8/13

if the first stick is not replaced, then n(S) would be,

26 - 1 = 25

Let event A: selecting first stick with a boy name

n(B) = 10

So, the probability of a boy is,

P(B) = n(B)/n(S)

P(B) = 10/25

P(B) = 2/5

Therefore, the probability of selecting sticks with a boy's name is 8/13 and the probability of selecting sticks with a girl's name is 2/5.

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The lines that are perpendicular to 3x – y = 10, are y = –1/3x + 17 and x + 3y = 27.

The correct option is B and C.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

We have a linear equation,

3x – y = 10.

Arranging to the slope-intercept form.

y = 3x - 10.

The slope of the lines that are perpendicular to line y = 3x - 10,

= negative reciprocal of 3

= -1/3

Therefore, the required lines are y = –1/3x + 17 and x + 3y = 27.

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Answer: x = -8

Step-by-step explanation:

12 ( x + 10 ) = 24

First we divide the two sides of the exercise by 12.

[tex]\boldsymbol{\sf{x+10=\dfrac{24}{12} }}[/tex]

We divide 24 by 12..

x + 10 = 2

Subtract 10 from both sides.

x = 2 - 10

Subtract 10 from 2 to get. Since the number 10 is greater than 2, the result will be negative.

x = -8

Answer:

[tex] \sf \: x = - 8[/tex]

Step-by-step explanation:

Given equation,

→ 12(x + 10) = 24

Now the value of x will be,

→ 12(x + 10) = 24

→ 12(x) + 12(10) = 24

→ 12x + 120 = 24

→ 12x = 24 - 120

→ 12x = -96

→ x = -96 ÷ 12

→ [ x = -8 ]

Hence, the value of x is -8.

Answer:

97 inches

Step-by-step explanation:

Using law of sines, we know that y/sin∠Y = z/sin∠Z.

Solve:

[tex]\frac{500}{sin117}[/tex] = [tex]\frac{z}{sin10}[/tex]

Therefore, z = (500/sin117)(sin10)

Enter this into a calculator to get:

z = 97.44495296, which rounds to 97 inches.

I hope this helps! :D

The rate of change in this context refers to the change in the value of p, specifically between the peak and closing.This allows us to understand how much p changes on average between these two points in time.

It is a measure of how quickly or slowly the value of p is changing over time.

By calculating the average rate of change, we can understand the overall trend of the value of p and whether it is increasing or decreasing at a steady rate or if there are fluctuations.

This information can be useful for understanding the performance of a stock or investment, as well as predicting future trends.

Additionally, the rate of change can also help to identify any potential issues or opportunities within the market.

Overall, the rate of change provides a clear picture of the stock's performance over a certain period of time.

To calculate the average rate of change of p between peak and closing, we need to find the difference in p values (p(14) - p(8)) and divide that by the difference in time (14 - 8).

p(14) - p(8) = ? - ? = ?

(14 - 8) = ?

The average rate of change of p is ?/6.

The meaning of the rate of change in the context of this problem is the average change in the value of p per unit of time.

In this case, we are looking at the average change in p between the peak and closing, and expressing that change as a ratio of p(14) - p(8) to (14 - 8). This allows us to understand how much p changes on average between these two points in time.

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The final cost of the laptop be if jamal buys it on saturday is $695.79

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

The new laptop is currently priced at $859

On saturday the store is giving a 25% discount off all laptops

Sales tax on final purchase=8.5%

Now, the final value on saturday be x

x*100/859=25

x=25*859/100

x=214.75

The value will be 859-214.75=644.25

8% of 644.25

x*100/644.25=8

x=8*644.25/100

x=51.54

Final cost= 644.25+51.54

=695.79

Therefore, the final cost after 8 percent sales tax will be $695.79

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A   Are they are limited to the amount of paint they have?      80g / 1 g/mile  = 80 miles       using all of the paint

         50 trucks /2 trucks/mile  = 25 miles     using all of the  trucks of asphalt

B    25 miles of bridge =  =    25 trucks   leaving 25 trucks of asphalt         25 trucks/2 trucks/mile = 12.5 miles of land highway  possible

      25 miles of bridge =       25 miles x 3 gal/mile = 75 gallons of paint    leaving only 5 gallons of paint for 5 add'l land miles

         25 miles of bridge + 5 land miles = 30 miles total highway .

The equations of the lines are

The parallel lines

We have the points to be

(3, 6) and (0, 2)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 2

Using the points, we have

6 = 3m + 2

So, we have

3m = 4

Divide

m = 4/3

So, the equation is

y = 4/3x + 2

For the other parallel line, we have

y = 4/3x - 2

Perpendicular line

The slopes of parallel and perpendicular lines are opposite reciprocals

So, we have

m = -3/4

This gives

y = -3/4x + c

We have the point to be (0, 8.5)

So, we have

y = -3/4x + 8.5

y = -0.75x + 8.5

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The numerical value of x and the measure of segment BC are 1 and 5 respectively.

Given that; B is a point between A and C.

Since B is between A and C

AC = AB + BC

8 = 3x + 5x

Solve for x

8 = 8x

8x = 8

x = 8/8

x = 1

Next, determine the measure of BC,

BC = 5x

Plug in x = 1

BC = 5( 1 )

BC = 5

Therefore, x equal 1 and the measure of BC is 5.

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Mary's Tuesday distance is 1/8 times her Monday distance

On Monday Mary ran 1 3/5 miles

= 8/5

On Tuesday Mary ran 1/5 miles

Therefore the number of times her Tuesday distance was her Monday distance can be calculated as follows

1/5 ÷ 8/5

= 1/5 ×5/8

= 1/8

Hence her Tuesday distance was 1/8 times her Monday distance

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The expression for the perimeter of the triangle will be 6x + 22.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

A workmanship class is making a painting for their school which has a triangle attracted the center. The length of the lower part of the triangle is x. Another side is 11 a larger number of than 4 times the length of the lower part of the triangle. The last side is 11 a greater number of than the lower part of the triangle.

Then the dimension of the triangle will be x, 4x + 11, and x + 11. Then the perimeter isgiven as,

P = x + 4x + 11 + x + 11

P = 6x + 22

The expression for the perimeter of the triangle will be 6x + 22.

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