"Events A1, A2 and A3 form a partiton of the sample space S with probabilities P(A1) = 0.3, P(A2) = 0.5, P(A3) = 0.2.If E is an event in S with P(E|A1) = 0.1, P(E|A2) = 0.6, P(E|A3) = 0.8, computeP(E) =P(A1|E) =P(A2|E) =P(A3|E) ="

Answer:

Multicollinearity

Step-by-step explanation:

Answer:

There are 795 combinations.

Step-by-step explanation:

The number of ways or combinations in which we can select k element from a group of n elements is given by:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

So, if Miriam want to choose 3 movies with at least two comedies, she have two options: Choose 2 comedies and 1 foreign film or choose 3 comedies.

Then, the number of combinations for every case are:

1. Choose 2 Comedies from the 10 and choose 1 foreign film from 15. This is calculated as:

[tex]10C2*15C1=\frac{10!}{2!(10-8)!}*\frac{15}{1!(15-14)!}[/tex]

[tex]10C2*15C1=675[/tex]

2. Choose 3 Comedies from the 10. This is calculated as:

[tex]10C3=\frac{10!}{3!(10-3)!}=120[/tex]

Therefore, there are 795 combinations and it is calculated as:

675 + 120 = 795

Answer:

The answer to your question is: 800.4 km

Step-by-step explanation:

Data:

111 km to east

444 km to north

555 km to east

How far is from her starting position?

See the picture please

To do this problem, we must to find the hypotenuse of a right triangle where one cathetus is 444 km and the other one is the sum of 111 and 555km.

them the pythagorean theorem says c² = a² + b²

                                                              c² = 444² + (111+555)²

                                                               c² = 444² + 666²

                                                                c² = 197136  + 443556

                                                               c² = 640692

                                                                c = 800.4 km

Answer: 7.211

Step-by-step explanation:

TRUST ME, IF IT"S WRONG YOU CAN GIVE ME 1 STAR, IF YOU GET IT RIGHT PLEASE SUBSCRIBE TO ICONIC COOKING, THANK YOU, LUV YOU

Answer:

Step-by-step explanation:

For the first two parts, you need to know the number of hours in a day, and the number of days in 30 days (!?). No doubt, these numbers are familiar to you.

Part A.

The distance traveled in 24 hours (1 day) is 24 times the distance traveled in one hour.

  distance per day = (27,600,000 m/h)×(24 h/day) = 662,400,000 m/day

Since you are familiar with place value and powers of 10, you know you can write this as ...

  662,400,000 m/day = 6.624×100,000,000 m/day = 6.624×10⁸ m/day

__

Part B.

Using the result from Part A, we know that 30 days' travel will be 30 times one day's travel:

  distance in 30 days = (30 days)×6.624×10⁸ m/day = 198.72×10⁸ m

     = 1.9872×10¹⁰ m

__

Part C.

Your judgment is required to determine a "suitable unit." I might choose gigameters, abbreviated Gm. "giga-" is a prefix meaning 10⁹, so the distance traveled in 30 days could be written as ...

  1.9872×10¹⁰ m = 19.872×10⁹ m = 19.872 Gm = 1.9872×10¹ Gm

_____

Comment on "suitable unit"

In my engineering career, I would often choose units from the list of SI prefixes, so that exponents were a multiple of 3. That means any given measurement or calculation result ranged from 1 to 999, multiplied by some suitable choice of units. Here, the distance traveled in 30 days would be left as (about) 19.9 Gm. The choice of units is intended to avoid the need for scientific notation.

The meaning of "a more suitable unit in scientific notation" is unclear in this context. I would say a "more suitable unit" is Gm, whose value in scientific notation is 10^9 m or 10^6 km.

Answer:

A. simpson's paradox

Step-by-step explanation:

The Simpson's paradox was named after Edward Simpson, the person who described this paradox for the first time in 1951. In this paradox, you find two contrary patterns. For example, a positive and a negative correlation, depending on how data is analyzed. The differences in the analyses are how data are grouped. This paradox is observed often in social researches. Most of the times, results are affected by the sample on each group or additional information related to the data.

Answer:

L=13.715

Step-by-step explanation:

Given that

x=t + cos t

y= t - sin t

0 ≤ t ≤ 3π

[tex]\dfrac{dx}{dt}=1-sin\ t[/tex]

[tex]\dfrac{dy}{dt}=1-cos\ t[/tex]

We know that length of parametric curve given as

[tex]L=\int_{a}^{b}\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2}dt[/tex]

[tex]\left(\dfrac{dx}{dt}\right)^2=1+sin^2 t-2t\ sint[/tex]

[tex]\left(\dfrac{dy}{dt}\right)^2=1+cos^2 t-2t\ cost[/tex]

Now by putting the values

[tex]L=\int_{0}^{3\pi}\sqrt{3-2sin\ t-2cos\ t}\ dt[/tex]

Now by using calculator

L=13.715

To find the curve length for ( x = t + cos t ) and ( y = t - sin t ) over [tex]\( 0 \le t \le 3\pi \):[/tex]

1. Calculate derivatives:

[tex]\[ \frac{dx}{dt} = 1 - \sin t, \quad \frac{dy}{dt} = 1 - \cos t \][/tex]

2. Set up integral:

 [tex]\[ L = \int_0^{3\pi} \sqrt{(1 - \sin t)^2 + (1 - \cos t)^2} \, dt \][/tex]

3. Simplify integrand:

  [tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]

4. Calculate numerically:

 [tex]\[ L \approx 21.2694 \][/tex]

The curve length is approximately ( 21.2694 ).

To find the length of the curve given by the parametric equations ( x = t + cos t ) and ( y = t - sin t ) for[tex]\( 0 \le t \le 3\pi \)[/tex] , we use the formula for the arc length of a curve defined by parametric equations:

[tex]\[ L = \int_a^b \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt \][/tex]

1. **Find the derivatives of ( x ) and ( y ) with respect to ( t ):**

  For [tex]\( x = t + \cos t \):[/tex]

 [tex]\[ \frac{dx}{dt} = 1 - \sin t \][/tex]

  For[tex]\( y = t - \sin t \):[/tex]

 [tex]\[ \frac{dy}{dt} = 1 - \cos t \][/tex]

2. **Set up the integral for the arc length:**

[tex]\[ L = \int_0^{3\pi} \sqrt{\left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2} \, dt \][/tex]

3. **Simplify the integrand:**

[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 \][/tex]

  Expand both terms:

[tex]\[ \left(1 - \sin t\right)^2 = 1 - 2\sin t + \sin^2 t \][/tex]

  [tex]\[ \left(1 - \cos t\right)^2 = 1 - 2\cos t + \cos^2 t \][/tex]

  Add the expressions together:

[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 = (1 - 2\sin t + \sin^2 t) + (1 - 2\cos t + \cos^2 t) \][/tex]

[tex]\[ = 1 - 2\sin t + \sin^2 t + 1 - 2\cos t + \cos^2 t \][/tex]

  [tex]\[ = 2 - 2\sin t - 2\cos t + \sin^2 t + \cos^2 t \][/tex]

  Recall that[tex]\( \sin^2 t + \cos^2 t = 1 \):[/tex]

[tex]\[ = 2 - 2\sin t - 2\cos t + 1 \][/tex]

[tex]\[ = 3 - 2(\sin t + \cos t) \][/tex]

  So the integrand becomes:

[tex]\[ \sqrt{3 - 2(\sin t + \cos t)} \][/tex]

4. **Set up the integral for the arc length:**

[tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]

5. **Calculate the integral:**

  This integral is complex and generally requires numerical methods or a calculator to evaluate.

  Using a calculator:

[tex]\[ L \approx \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \approx 21.2694 \][/tex]

Thus, the length of the curve, correct to four decimal places, is approximately ( 21.2694 ).

Answer:

No.

Step-by-step explanation:

The equation does not match the form of any conic section.

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

Answer:

Step-by-step explanation:

Let's get this in a form we can better recognize.  we'll rearrange it until we have y by itself.

x^2 + xy = 1

xy = 1 - x^2

y = 1/x - x

There, much better.  Now,  just looking at the graph you can tell there's no symmetry along the x or y axis.  If you do not know how to check for symmetry along x=y or origin symmetry let me know.  But checking for those does show that there is no symmetry along y = x but there is origin symmetry.  

To determine that you just make all x and ys negative, and then see if you can get back to the original.  Again, let me know if you don't get determining symmetry through algebra and I'd be happy to explain each of the variations; x ais, y axis, y=x and origin.

There were 100 total students surveyed.

There are 41 freshman students that have an ATM card.

The probability is the number of freshman that have an ATM card over the total number of students.

The probability becomes 41/100

Now divide the fraction to get the decimal answer:

41/100 = 0.410

Answer:

A) 0.3

B) 0.2

Step-by-step explanation:

We are given the following in the question:

P(Industry in Shanghai) = P(A) = 0.7

P(Industry in Beijing) = P(B) = 0.4

P(Industry in Shanghai or Beijing)  = P(A∪B) = 0.8

a)We need to find the probability that the industry is located in both Shanghai and Beijing that is we need to find P(A∩B)

Formula:

P(A∪B) = P(A) + P(B) - P(A∩B)

Putting the values we get,

0.8 = 0.7 + 0.4 - P(A∩B)

P(A∩B) = 0.3

Thus, the probability that the industry is located in both Shanghai and Beijing is 0.3.

b)Now, we need to find the probability that it is not in either cities

Probability = 1 - Probability(Industry in Shanghai or in Beijing)

                 = 1 - P(A∪B)

                 = 1 - 0.8

                 = 0.2

The probability that the industry will locate in both Shanghai and Beijing is 0.3, while the probability that it will locate in neither of the cities is 0.2.

This problem is solved using the concept of probability in Mathematics. Let's denote A as the event that an industry with locate in Shanghai and B is the event that it will locate in Beijing.

The probability of A, P(A), is given as 0.7 and the probability of B, P(B), is given as 0.4. The probability it will locate in either of the cities, P(A U B), is given as 0.8.

We know, P(A U B) = P(A) + P(B) - P(A ∩ B), where P(A ∩ B) represents the probability the industry will locate in both cities. Using the given probabilities:

0.8 = 0.7 + 0.4 - P(A ∩ B), so P(A ∩ B), the probability the industry will locate in both cities, is equal to 0.3. (a)

The probability the industry will not locate in either of the cities, denoted as P'(A U B), is equal to 1 - P(A U B) = 1 - 0.8 = 0.2. (b).

This means there is a 30% chance the industry will locate in both Shanghai and Beijing, and a 20% chance it will locate in neither city.

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Answer:

Yes

Step-by-step explanation:

Yes it is possible, if the equations are equivalent. For example in one variable, we have x=2 and if we add the equation 2x=4 both considered on the Real numbers, then the system has two equations and one variable, more equations than variables and yet the solution is unique x=2.

Answer:

Yes, it's possible.

Step-by-step explanation:

We know that a linear system has a unique solution if it has the same number of equations than variables (but remember that you musn't have a linear combination of equations).

So it is possible to create a system with more equations than variables, with a unique solution.

Example:

1)  X + Y + Z = 3

2) 2X + 2Y + 2Z = 6

3) X + Y = 2

4) X + Z = 2

This is a 4 equation and 3 variable system.  Pay attention to equation number 1) and 2). They are a linear combination (number 2 is the number 1 multiplied by 2). So, for this system you can basically ignore one of them.

If you do that, you will have 3 equations and 3 variables, with a unique solution. In this case solution is X = 1, Y = 1, Z = 1.

Now, let's see if equation number 2 satisfies:

2x1 + 2x1 + 2x1 = 6

                     6 = 6

With this simple example we proved that you can have a linear system with a unique solution if it has more equations than variables.

Final answer:

Explanation on how to calculate the APR for a mortgage loan based on provided information.

Explanation:

To calculate the APR on the loan, we first need to determine the total amount paid over the life of the loan. The total payment per month is $18,300, and the loan term is 25 years. So, the total payment over 25 years would be $18,300 x 12 months x 25 years = $5,220,000.

Next, calculate the total interest paid by subtracting the loan amount from the total payments: $5,220,000 - 75% of $4,200,000 = $5,220,000 - $3,150,000 = $2,070,000.

Finally, use the formula for APR: APR = (Total Interest Paid / Loan Amount) x 100%. Therefore, APR = ($2,070,000 / $3,150,000) x 100% ≈ 65.71%. So, the APR on this loan is approximately 65.71%.

Answer:

1,2,3,4,6,9,12,18,36 Is correct one

Answer:

1, 2, 3, 4, 6, 9, 12, 18, 36

Step-by-step explanation:

Answer:

The term used to describe this type of survey is - voluntary response sample or self elected sample.

The thing that is wrong with this type of sampling is that only those people will respond who have a strong interest in the particular topic.

Also, it is quite possible that only 38% responses do not reflect the opinions of the whole general population.

Answer:

4b - 3s = 40

4b = 40 + 3s

b = 40 - 3s/4

4b - 3s = 40

4b - 40 =3s

4b - 40 /3 = s

The age of the brother b = 40 - 3s/4, and the age of the sister is s = 4b - 40/3

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let the age of the brother be b and the age of the sister be s

If four times the brother's age is subtracted from three times the sister's age, the difference is 40.

So the equation that represents this statement is:

⇒ 4b - 3s = 40

⇒ 4b = 40 + 3s

Divided by 3 into both sides and solve for b,

⇒ b = 40 - 3s/4

Now solve for b,

⇒ 4b - 3s = 40

⇒ 4b - 40 =3s

Divided by 3 into both sides

⇒ s = 4b - 40/3

Hence, the age of the brother b = 40 - 3s/4, and the age of the sister is s = 4b - 40/3

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For this case we have that by definition, the equation of a line in the point-slope form is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

[tex](x_ {0}, y_ {0})[/tex]: It is a point through which the line passes

m: It's the slope

We have according to the graph, that the line goes through:

[tex](x_ {1}, y_ {1}): (- 2, -1)\\(x_ {2}, y_ {2}) :( 2,1)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {1 - (- 1)} {2 - (- 2)} = \frac {1 +1} {2 + 2} = \frac {2} {4} = \frac {1} {2}[/tex]

Thus, the line is of the form:

[tex](y-y_ {0}) = \frac {1} {2} (x-x_ {0})[/tex]

We substitute a point:

[tex](y-1) = \frac {1} {2} (x-2)[/tex]

Answer:

[tex](y-1) = \frac {1} {2} (x-2)[/tex]

The Expression  [tex]\((\frac{p^4q}{p^8})^2\)[/tex] simplifies to [tex]\(\frac{1}{p^8}\)[/tex].

The correct option is D.

To simplify the expression (p⁴q/p⁸)², we can simplify the numerator and denominator separately, and then simplify the exponent:

Numerator: p⁴q

Denominator: p⁸

To simplify the numerator, we divide the exponents of p:

[tex]\(p^4q = \frac{p^4}{p^8}\)[/tex]

Now, we can simplify the expression [tex]\((\frac{p^4}{p^8})^2\)[/tex]:

[tex]\((\frac{p^4}{p^8})^2 = \frac{p^4}{p^8} \cdot \frac{p^4}{p^8} = \frac{p^4 \cdot p^4}{p^8 \cdot p^8}\)[/tex]

Simplifying the numerator and denominator further:

[tex]\(\frac{p^4 \cdot p^4}{p^8 \cdot p^8} = \frac{p^{4+4}}{p^{8+8}} = \frac{p^8}{p^{16}}\)[/tex]

Finally, we can simplify the expression to:

[tex]\(\frac{p^8}{p^{16}} = p^{8-16} = p^{-8} = \frac{1}{p^8}\)[/tex]

Therefore, [tex]\((\frac{p^4q}{p^8})^2\)[/tex] simplifies to [tex]\(\frac{1}{p^8}\)[/tex].

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Final answer:

Jimmy earned $190 for working on 500 parts. This includes $37.50 for the first 150 parts, $52.50 for the next 150 parts, and $100 for the 200 parts beyond the initial 300.

Explanation:

Jimmy's earnings can be calculated by dividing the parts he worked on into three segments that correspond to different pay rates.

The first 150 parts at $0.25 each.

The next 150 parts (from part 151 to 300) at $0.35 each.

Any parts above 300 at $0.50 each.

So the calculation would be as follows:

First segment: 150 parts × $0.25 = $37.50

Second segment: 150 parts × $0.35 = $52.50

Third segment: 200 parts (500 - 300) × $0.50 = $100.00

Adding these amounts together will give us the total earnings:

$37.50 + $52.50 + $100.00 = $190.00

Therefore, Jimmy earned a total of $190 yesterday.

Answer:

  f(x) = -1/3x² -2x

Step-by-step explanation:

For vertex (h, k) and scale factor "a", the vertex form of a quadratic is ...

  y = a(x -h)² +k

For the given vertex, the vertex form function with scale factor "a" is ...

  f(x) = a(x +3)² +3

If that goes through the point (-6, 0), then we have ...

  f(-6) = a(-6 +3)² +3 = 0

  9a = -3 . . . . . . . subtract 3

  a = -1/3 . . . . . . . divide by 9

In standard form, the equation is ...

  f(x) = (-1/3)x² -2x

Answer:

1.28 or 128

Step-by-step explanation:

you would take 32 and divide it by.25

Answer:

The probability is 0.9993

Step-by-step explanation:

This situation follows a Binomial distribution in which we have:

So, the probability that x of the n elements are success is given by:

[tex]P(x)=nCx*p^{x}*(1-p)^{n-x}[/tex]

That means that the probability that x adults from the 66 use their smartphone in meeting or classes is:

[tex]P(x)=66Cx*0.52^{x}*(1-0.52)^{66-x}[/tex]

Where 66Cx is calculated as:

[tex]66Cx=\frac{66!}{x!(66-x)!}[/tex]

Then, the probability that at least 22 of them use their smartphone in meeting or classes is:

P = P(22) + P(23) + P(24) +... + P(64) + P(65) + P(66)

Therefore, replacing x for each number from 22 to 66 on the equation of P(x), and making a sum with all the probabilities, we get that:

P = 0.9993

Answer: x= - 3, y = 7

Step-by-step explanation:

Answer:

  If production is to be maximized, Jerry should build fences and Tom should make dishes.

Step-by-step explanation:

Tom can build more fences per day than Jerry, and Jerry can make more dishes per day than Tom. Each has his special skill, and production will be maximized when that special skill is utilized.

Answer:

Step-by-step explanation:

1) The greatest common factor of 72 and 112 is 8, so the least common multiple is ... 72×112/8 = 1008.

The least common multiple of 72 and 112 is 1008.

__

2) The house number will be a multiple of 1008 between 3000/1008 = 2.98 and 4000/1008 = 3.96. The only integer in that range is 3, so Peter's house number is ...

  3 × 1008 = 3024

Peter's house number is 3024.

Answer:

[tex]1.486*10^8[/tex]

[tex]9.118*10^3[/tex]

Step-by-step explanation:

By definition, the form of Scientific notation is:

[tex]a*10^n[/tex]

Where the base is 10, "a" is any number from 1 to 10 but not including 10,  and "n" is an integer.

Therefore to write a number in Scientific notation, the decimal point must be after the first digit and the power "n" must indicate how many places the decimal point is moved.

We know that:

[tex]148.6\ million=148,600,000\ millions[/tex]

Then, we need to move the decimal point 8 places to the left:

[tex]=1.486*10^8[/tex]

To write $9,118 in scientific notation, we need to move the decimal point 3 places to the left:

[tex]=9.118*10^3[/tex]

Answer: 2 hours

Step-by-step explanation:

Given : Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively.

Let t be the time taken by both of them working together.

Then, according to the question, we have

[tex]\dfrac{1}{t}=\dfrac{1}{3}+\dfrac{1}{6}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{2+1}{6}\ \ [\because\ L.C.M. (3,6)=6]\\\\\Rightarrow\dfrac{1}{t}=\dfrac{3}{6}=\dfrac{1}{2}\\\\\Rightarrow t=2[/tex]

Hence, it will take 2 hours by the two machines .

Answer:

A neuropsychologist​ is most likely to be administering the tests.

Step-by-step explanation:

Mr. Spindero periodically visits a hospital clinic where he takes various paper and pencil tests that document the progression of his dementia.

A neuropsychologist​ is most likely to be administering the tests.

Certain disorders within the brain and nervous system can alter the normal  behavior and cognitive function of a person.

So, a neuropsychologist deals with such patients. He specializes in understanding the relationship between the physical brain and behavior.

Answer:

x=-y/g

Step-by-step explanation:

m-y=m+gx

m-m-y=gx

-y=gx

x=-y/g

Answer:

  A.  $16,079

Step-by-step explanation:

You are given the income of a married couple and the tax table applicable to married couples. To find the amount of tax owed, you first find the applicable line in the table, then do the computation it tells you.

The applicable line for an income of $110,000 is the one that says ...

  "77,401 to 165,000"

The left (Tax Rate) column of that line has "22%", and the right (Tax Owed) column tells you the computation you need to make.

You find "the excess over $77,400" by subtracting that amount from the $110,000 income:

  the excess over $77,400 = $110,000 -77,400 = $32,600

__

Then the tax owed is 22% of this amount plus $8907:

  tax owed = $8,907 + 0.22 × 32,600

  = $8,907 + 7,172

  tax owed = $16,079

Answer:

20,000,000,000 or 200

Step-by-step explanation:

depending on which 2 you are asking for

The place value of 2 in the number 24,398,407,268 is 20 billion, as it is in the ten billion place.

The place value of 2 in the number 24,398,407,268 refers to the position of 2 in the number and its corresponding value. In this case, the 2 is in the ten billion place. To find the value of 2 in that position, we multiply it by 10 billion (109). Therefore, the place value of 2 in this number is 20 billion (2 x 10^9).

Answer:7

Step-by-step explanation:

Answer: $61 because you have to do 10 x3 to get 30 then + $1 because $1 is equal to 5 pounds