Suppose two independent events A and B have the following probabilities: P(Aᶜ = 0.40 and P(B∣A) = 0.80. Compute the probability that either avent A accurs, or Boccurs, or both occur.

Answers

Answer 1

Answer:

Answer:

neither A nor B will occur simultaneously, as they are mutually exclusive.

Step-by-step explanation:

To compute the probability that either event A occurs, or B occurs, or both occur, you can use the principle of the union of events. The probability of the union of two events A and B (denoted as A ∪ B) can be calculated as:

�

(

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∪

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)

�

(

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)

�

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)

−

�

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∩

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)

P(A∪B)=P(A)+P(B)−P(A∩B)

In this case, you're given:

�

(

�

∁

)

0.40

P(A

∁

)=0.40, which means the probability of the complement of A (i.e., the probability that A does not occur).

�

(

�

∣

�

)

0.80

P(B∣A)=0.80, which is the conditional probability of B occurring given that A has occurred.

Let's break it down:

�

(

�

∁

)

P(A

∁

) is the probability that event A does not occur, which is

−

�

(

�

)

1−P(A).

�

(

�

∣

�

)

P(B∣A) is the conditional probability that event B occurs given that A has occurred.

So, you can calculate

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)

P(A) and

�

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�

)

P(B) as follows:

�

(

�

)

−

�

(

�

∁

)

−

0.40

0.60

P(A)=1−P(A

∁

)=1−0.40=0.60

Now, you can use the formula for the union of events to calculate

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∪

�

)

P(A∪B):

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∪

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)

�

(

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)

�

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)

−

�

(

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∩

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)

P(A∪B)=P(A)+P(B)−P(A∩B)

But before we calculate

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(

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∩

�

)

P(A∩B), note that events A and B are independent, so

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∩

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)

�

(

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)

⋅

�

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∣

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)

P(A∩B)=P(A)⋅P(B∣A).

�

(

�

∩

�

)

�

(

�

)

⋅

�

(

�

∣

�

)

0.60

⋅

0.80

0.48

P(A∩B)=P(A)⋅P(B∣A)=0.60⋅0.80=0.48

Now, plug this value into the formula:

�

(

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∪

�

)

0.60

�

(

�

)

−

0.48

P(A∪B)=0.60+P(B)−0.48

Solve for

�

(

�

)

P(B):

�

(

�

)

�

(

�

∪

�

)

0.48

−

0.60

P(B)=P(A∪B)+0.48−0.60

�

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)

�

(

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∪

�

)

−

0.12

P(B)=P(A∪B)−0.12

Now, you have the equation:

�

(

�

∪

�

)

0.60

�

(

�

∪

�

)

−

0.12

−

0.48

P(A∪B)=0.60+P(A∪B)−0.12−0.48

Simplify:

�

(

�

∪

�

)

0.60

−

0.12

−

0.48

P(A∪B)=0.60−0.12−0.48

�

(

�

∪

�

)

0.00

P(A∪B)=0.00

So, the probability that either event A occurs, or B occurs, or both occur is 0.00. This means that neither A nor B will occur simultaneously, as they are mutually exclusive.

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What is the name of the relationship between ∠1 and ∠8 ?A. adjacent angles

B. alternate interior angles

C. alternate exterior angles

D. corresponding angles

Answers

Answer:

∠1 and ∠8 are alternate exterior angles.

Step-by-step explanation:

We are given two parallel lines and one transversal line which cuts both parallel line and makes two 8 angles.

We need to find the relation between them

As we know total 8 angles form when two parallel line cut by one line.

Name of angles (relation of angles)

Alternate interior angles
Adjacent angles
Corresponding angles
Alternate exterior angles

Alternate Exterior Angles are a pair of angles on the inside of each of those two parallel lines but on opposite sides of the transversal.

Alternate Exterior Angles are a pair of angles on the outer side of each of those two parallel lines but on opposite sides of the transversal.

Adjacent angles are a pair of angles whose a common side and a common vertex.

Corresponding angles are a pair of angles whose one out side and one inside of those parallel lines but on same side of the transversal.

Here, ∠1=∠8 because ∠1 and ∠8 are alternate exterior angles.

Thus, ∠1 and ∠8 are alternate exterior angles.

Answer:

Alternate exterior angles

If cos θ -sin θ =1, find θ cos θ +sin θ?

Answers

$cos\theta-sin\theta=1\ \ \ \ |square\ both\ sides\n\n(cos\theta-sin\theta)^2=1\n\ncos^2\theta-2sin\theta cos\theta+sin^2\theta=1\n\n1-2sin\theta cos\theta=1\n\n-2sin\theta cos\theta=1-1\n\n-2sin\theta cos\theta=0\iff sin\theta=0\ or\ cos\theta=0\n\n\theta=k\pi\ or\ \theta=(\pi)/(2)+k\pi\ \ \ \ (k\in\mathbb{Z})$

$For\ \theta=k\pi\to cosk\pi-sink\pi=\pm1-0=\pm1\to conclusion:\theta=2k\pi\n\nFor\ \theta=(\pi)/(2)+k\pi\to cos((\pi)/(2)+k\pi)-sin((\pi)/(2)+k\pi)=0-(\pm1)=\mp1\to\n\to conclusion:\theta=(3\pi)/(2)+2k\pi\n\n============================\n\ncos\theta+sin\theta=(*)\n\nfor\ \theta=2k\pi\to(*)=1+0=1\n\nfor\ \theta=(3\pi)/(2)+2k\pi\to(*)=0-1=-1$

According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 60x4 + 86x3 – 46x2 – 43x + 8?x – 6
5x – 8
6x – 1
8x + 5

Answers

the answer is (6x-1)

Answer: The answer is (B) $(8)/(5)$ and (C) $(1)/(6)$ .

Step-by-step explanation: The given polynomial is

$f(x)=60x^4+86x^3-46x^2-43x+8.$

We are to select the correct option that could be a factor of the polynomial f(x) according to the Rational Root Theorem.

The Rational Root Theorem states that:

If the polynomial $P(x)= a_nx^n+a_(n-1)x^(n-1)+\cdots+a_2x^2+a_1x+a_0$ has any rational roots, then they must be of the form $\pm\frac{\textup{factors of }a_0}{\textup{factors of }a_n}.$

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only $(8)/(5)$ and $(1)/(6)$ can be written in the form $\pm\frac{\textup{factors of }a_0}{\textup{factors of }a_n}.$ , because

$(8)/(5)=\frac{\textup{a factor of 8}}{\textup{a factor of 60}},\n\n(1)/(6)=\frac{\textup{a factor of 8}}{\textup{a factor of 60}}.$

Thus, (B) and (C) are the correct options.

The data set gives the number of bottles filled by each of the workers in a bottling plant in one day. {36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}

Answers

Answer:

The best measure of center is median = 37.50.

Step-by-step explanation:

The complete question is:

The data set gives the number of bottles filled by each of the workers in a bottling plant in one day.

{36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}

The best measure of center for this data set is the , and its value expressed up to one decimal place is?

Solution:

The three measures of center are:

Mean
Median
Mode

The mean is the average value of the data set and uses all the values of the data set.

The median is the middle value of the data set.

Mode is the value of the data st with the highest frequency or number of occurrence.

Compute the mean, median and mode of the data set provided as follows:

$\text{Mean}=(1)/(n)\sum X=(1)/(14)* [36+18+....+72+29]=40.57$

So, the mean is 40.57.

The data set in ascending order is:

{16, 18, 28, 29, 35, 36, 37, 38, 40, 41, 44, 66, 68, 72}

There are 14 values in the data set. That is an even data set.

The median for an even data set is the average of the middle two values.

The middle two values are: 37, 38

Average of {37, 38} = $(37+38)/(2)=37.50$

So, the median is 37.50.

None of the values are repeating itself. Thus, the data does not have a mode.

For the provided data:

Mean > Median

Implying that the data set is right-skewed.

For a skewed distribution or data set the median is the measure of center.

Thus, the best measure of center is median = 37.50.

Verify the identity
Cos^2x-Sin^2x=1-2sin^2x

Answers

$cos^2x-sin^2x=1-2sin^2x\n\n\nR=1-2sin^2x=cos^2x+sin^2x-2sin^2x=cos^2x-sin^2x=L\n\n\n\n\nsin^2x+cos^2x=1$

If eric practiced the piano 8hrs a week, if he practices 1/4 of that how many hours is that?

Answers

divide 8 by 4 and you get 2 hours

Work:

It is fourths, so divide
8 ÷ 4
That gives you 2

Answer:

2 hours

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