Let A and B be two events. Suppose that P (A)=0.45 and P(B)=0.16.
(a) Find ,P(A or B) given that and are independent.

(b) Find ,P(A or B) given that and are mutually exclusive.

Answer:

We can start by drawing a diagram that shows the relations between the variables:

x

|

|

2x²+3y²=z w = 3x²+2y²-z

|

|

z

a. To find ( ∂y/∂w )z, we need to differentiate z with respect to y, and then differentiate w with respect to y, and divide the two derivatives:

∂z/∂y = 6y

∂w/∂y = 4y

Therefore, ( ∂y/∂w )z = (∂z/∂y)/(∂w/∂y) = (6y)/(4y) = 3/2

b. To find ( ∂z/∂w )x, we need to differentiate z with respect to w, and then differentiate x with respect to w, and divide the two derivatives:

∂z/∂w = -6x

∂x/∂w = 6x

Therefore, ( ∂z/∂w )x = (∂z/∂w)/(∂x/∂w) = (-6x)/(6x) = -1

c. To find ( ∂z/∂w )y, we need to differentiate z with respect to w, and then differentiate y with respect to w, and divide the two derivatives:

∂z/∂w = -6x

∂y/∂w = 4y

Therefore, ( ∂z/∂w )y = (∂z/∂w)/(∂y/∂w) = (-6x)/(4y) = (-3x)/(2y)

Hence, ( ∂y/∂w )z = 3/2, ( ∂z/∂w )x = -1, and ( ∂z/∂w )y = (-3x)/(2y).

Answer:

\(-8f(0) +4g(-8)=-32\)

Step-by-step explanation:

Given

See attachment

Required

\(-8f(0) +4g(-8)\)

From the attachment;

\(f(0) = 1\)

and

\(g(-8) = -6\)

Substitute these values in \(-8f(0) +4g(-8)\)

\(-8 * 1 + 4 * -6\)

\(-8 -24\)

\(-32\)

Hence:

\(-8f(0) +4g(-8)=-32\)

Step-by-step explanation:

this is solved like this

\( log_{3}(6) \: - log_{3}(4) \\ = log_{3}( \frac{6}{4} ) \\ = log_{3}( \frac{3}{2} ) \\ = log_{3}(1.5) \\ \)

Managers and other decision makers are urged to be creative during step 2, which involves the process of establishing numerous alternative goals.

Numerous indicates a big amount. Despite the fact that you only have two feet, the word "many" might be used to describe the limitless number of pairs of shoes you own. The terms choice, election, option, preference, and selection can also be used to describe alternatives.

The report contains many of errors. The book contains numerous examples of plagiarism. All around the country are his innumerable progeny.

The numerous awards that are hung on the walls serve as visual proof of his huge accomplishment. She has proven her worth on numerous occasions. Alternative and alternate are phrases that are essentially synonymous.

Both expressions, which date from the middle of the 16th century, provide possibilities in addition to those that are initially suggested: an alternative perspective or proposal.

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Answer:

3x10=30   30x178=5,430

Step-by-step explanation:

\(3 \times 10 \times 178 \\ 30 \times 178 \\ 5340 \: \: answer\)

Answer:

Step-by-step explanation:

4⁻²/4³ = 1/(4²×4³) = 1/4⁵ = 1/1024

Answer: it is proportional

Step-by-step explanation: Because the y and the x numbers equal are the same

Answer:

It is proportional

Step-by-step explanation:

Both x and y increases at a constant rate

The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

Given that

In a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal. Calculate a 90% confidence interval for the percentage of all U.S. adults who support the proposal based on the results of this poll (at the time of the poll). Complete the table below after that. Carry your calculations to a minimum of three decimal places.

We have to find the lower limit of 90%.

We know that

In a poll of 200 randomly selected U.S. Among adults, 104 expressed support for the novel idea.

p-hat = 104/200 = 0.52

ME = z×√[pq/n] = 2.5758×√[0.52*0.48/200] = 0.091

Now, the lower limit of the 90% confidence interval well be

p-hat-ME = 0.52-0.091 = 0.429

Therefore, The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

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Answer:

1/2

Step-by-step explanation:

The numerator in 8/15 has to be closer to 0 to be closer to 0.

The numerator in 8/15 has to be closer to 15 to be closer to 1.

Ther numerator in 8/15 has to be closer to the middle, which it is, to be closer to 1/2.

Answer: 1/50

Step-by-step explanation:

Step 1: We need to multiply the numerator and denominator by 100 since there are 2 digits after the decimal.

0.02 = (0.02 × 100) / 100

= 2 / 100 [ since 0.02 × 100 = 2 ]

Step 2: Reduce the obtained fraction to the lowest term

Since 2 is the common factor of 2 and 100 so we divide both the numerator and denominator by 2.

2/100 = (2 ÷ 2) / (100 ÷ 2) = 1/50

Answer:

Tomatoes = 11.5

Onions = 2

Step-by-step explanation:

Andre wants to purchase some onions and tomatoes to make tomato soup. The recipe states that four times the number of tomatoes, , plus five times the number of onions, x, should produce 56 bowls of tomato soup. A different recipe states that two times the number of tomatoes used minus the number of onions used should produce 21 bowls of tomato soup. What is the resulting recipe for the number or tomatoes and onions used in the soup when Andre adds the two recipes together?

Let

Tomatoes = x

Onions = y

Recipe 1:

4x + 5y = 56

Recipe 2:

2x - y = 21

4x + 5y = 56 (1)

2x - y = 21 (2)

Multiply (2) by 5

4x + 5y = 56 (1)

10x - 5y = 105 (3)

Add

10x + 4x = 105 + 56

14x = 161

x = 161 / 14

= 11.5

Substitute x =11.5 into

2x - y = 21

2(11.5) - y = 21

23 - y = 21

-y = 21 - 23

-y = -2

y = 2

Tomatoes = 11.5

Onions = 2

Answer:

720)))

Step-by-step explanation:

A polynomial can have as many real zeros as its degree, hence one with three degrees can have as many as three zeros.

The roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

A polynomial with n degrees can have as many variables as n in total.

For example, a quadratic equation ax² + bx + c = 0 is a two-degree equation so it has a maximum of two roots or zeros.

A polynomial with the given degree structure will have exactly 3 roots because it has 3 degrees.

Hence "The maximum number of real zeros in a polynomial will be same as its degree thus 3 degrees will have 3 zeros".

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Answer:

a)\(a_{n}\) =−2n+14

b)\(a_{n}\)  = − 5 n + 30

Answer:

Considers each unit is equal to one my answers are bellow.

Step-by-step explanation:

D: -4,3

E: 2, 0

F: -2 ,-7

G: -6 , -5

Correct me if I'm wrong

The equation of a plane that passes through a point and is parallel to the YZ plane can be written as:

x = constant

When a plane is parallel to the YZ plane, it means that its normal vector is perpendicular to the X-axis. Since the normal vector is perpendicular to the X-axis, the X-coordinate of any point on the plane remains constant.

To find the equation of the plane, we need a point that lies on the plane. Let's assume the point (a, b, c) lies on the plane.

Since the plane is parallel to the YZ plane, the X-coordinate of any point on the plane will remain constant. Therefore, we can say that x = a.

The equation of the plane becomes:

x = a

The equation of a plane that passes through a point and is parallel to the YZ plane is given by the equation x = a, where a is the constant X-coordinate of any point on the plane. This equation represents all points where the X-coordinate remains constant, while the Y and Z coordinates can vary freely.

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Answer:8/9 is the answer as the resulting quotient you get is 0.88.... And so on

Answer:

it is 0.888888.... is 8/9 or \(\frac{8}{9}\)

Answer:

B and C

Step-by-step explanation:

A general way to know this is, if the answer can be given as a rate, percentage, or probability, then this is a statistical question

If the answer is yes, no, true, false, or something exact, then the question is not statistical.

Let's analyze the given questions:

a) "How many cups are in a gallon?"

There is an exact number of cups in a gallon (16) so this is not an staistical question.

b) "Which measure spoon do home backers use most frequently?"

While here the answer may be something like "teaspoon", the root of the answer is a percentage, here we actually would see the percent of home backers (so we need to find a sample, study that sample, etc) that use each spoon, and based on that, we could conclude what is the correct answer, then this is a statistical question.

c) "On average, how much salt do professional pastry chefs use in pie crust?"

Here we need to find a mean value, so we would need to do a survey and etc, then this is a statistical question.

d) "Which is larger, 17 ounces or 2 cups?"

Here we have an exact solution, so this is not a statistical question.

e) "Did a specific store sell more measuring cups or measuring spoons on a given day?"

Here we just need to compare the two numbers:

number of measuring cups sold = k

number of measuring spoons sold = m

And we need to see which one is larger, so the answer is exact, thus, this is not a statistical question.

This may be similar to option B, the difference is that in option B we are talking about all home backers, so we need to find a sample and do statistics, while in this case, we are talking about a specific store.

Then the correct options are: B and C

The state income tax owed on a $90,000 per year salary is $5,175.

Tax is a compulsory amount that is levied by the government on the income of individuals or on certain goods and services. Progressive tax is when the amount of tax paid by individuals increases as the amount of income earned increases. The amount paid as tax can be determined by multiplying the appropriate tax rate by the total income.

Tax paid = income x tax rate

$90,000 x 5.75%

$90,000 x 0.0575 = $5,175

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The state income tax owed on an $90,000 per year salary is  $5,175.

Taxes are mandatory contributions levied on individuals or corporations by a government entity

Given,

A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 3000 2% 3001 - 5000 3% 5001 - 17,000 5% 17,001 and up 5.75%

We need to find the state income tax owed on an $90,000 per year salary.

Tax paid = income x tax rate

$90,000 x 5.75%

5.75% should be converted to decimal by dividing with 100.

5.75/100=0.0575

So $90,000 x 0.0575 = $5,175

Hence the state income tax owed on an $90,000 per year salary is  $5,175.

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AR(1) model has a stationary, Zero-mean process with exponentially decaying autocorrelation and a variance that depends on the variance of the noise term. The variance of the model is \(\sigma ^2e / 0.36.\)

The AR(1) model given is:

yt = 0.8yt-1 + et

where {et: t = 1, 2, ...} is an i.i.d. sequence with a mean of zero and variance of σ^2e.

To better understand this model, we can look at its properties:

Stationarity: For this AR(1) model to be stationary, we require that the absolute value of the AR(1) coefficient, 0.8, be less than 1. Since 0.8 < 1, the model is stationary.

γk = Cov(yt, yt-k)

Using the formula for the covariance of an AR(1) model, we have\(γk = (0.8)^k * σ^2e / (1 - (0.8)^2)\)

Thus, the ACF for this model decays exponentially with lag k, indicating that past values of y are highly correlated with each other.

Mean: Since the model is stationary, we can calculate its mean by setting yt = yt-1 = ... = y0 = μ, and solving for μ:

μ = 0.8μ

Solving for μ, we get μ = 0, indicating that the mean of the model is zero.

Variance: We can calculate the variance of the model by using the formula for the variance of an AR(1) model:

\(Var(yt) = \sigma ^2e / (1 - (0.8)^2)\)

Thus, the variance of the model is σ^2e / 0.36.

Overall, this AR(1) model has a stationary, zero-mean process with exponentially decaying autocorrelation and a variance that depends on the variance of the noise term.

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The average tax rate for a firm with taxable income of $311,360 is approximately 33.61%.

To find the average tax rate for a firm with taxable income of $311,360, we need to calculate the total tax paid and then divide it by the taxable income. Here's a step-by-step explanation:

1. Determine the tax brackets applicable to the taxable income: The firm's taxable income falls into the first four tax brackets.

2. Calculate the tax for each bracket:
  a. For the first bracket ($0-$50,000): 15% of $50,000 = $7,500
  b. For the second bracket ($50,001-$75,000): 25% of $25,000= $6250    
  c. For the third bracket ($75,001-$100,000): 34% of $25,000 = $8,500
  d. For the fourth bracket ($100,001-$335,000):

The firm's taxable income falls within this bracket at $311,360. So, we calculate the tax for the income in this bracket, which is $311,360 - $100,000 = $211,360.

Thus, 39% of $211,360 = $82,430.40

3. Calculate the total tax paid:

$7,500 + $6,250 + $8,500 + $82,430.40 = $104,680.40

4. Calculate the average tax rate: Total tax paid divided by taxable income = $104,680.40 / $311,360 ≈ 0.3361 or 33.61%

The average tax rate for a firm with taxable income of $311,360 is approximately 33.61%.

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If the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces, then the sample space would not change.

It would still contain the same six possible outcomes. However, the probability of rolling an odd number would change to 4/7, as the face with the 3 would come up twice as often.

The sample space for this experiment is {1,1,1,2,2,3}, which is all the possible outcomes when the die is rolled. The probability of rolling an odd number is 2/3, as there are two faces with a 1 and one face with a 3.

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Two teams have the same number of played games.

What is pigeonhole Principle?

Suppose that there are n football teams in the tournament.

The number of games for a team is either 1 or 2 or 3 . . . or (n – 1). These (n – 1) numbers correspond to (n – 1) pigeonholes in which the n teams are to be housed. So at least two of them should be in the same pigeonhole.

Therefore, At some moment, two teams have the same number of played games.

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Answer:

Step-by-step explanation:

A=bh A=7*8 A=56units^2

Answer:

34

Step-by-step explanation:

i think its 34

The features of function g if g(x)=f(x+4)+8 are

The equation of function f is given as:

\(f(x)= \log_2(x)\)

The function g is given as:

g(x) = f(x + 4) + 8

This means that:

\(g(x)= \log_2(x + 4) + 8\)

Set the radicand to 0 to determine the domain and the vertical asymptote

x + 4 = 0

Solve for x

x = -4

This means that the domain is (-4, inf) and the vertical asymptote is x = -4

The function can output any real number.

So, the range is (-inf, inf)

Set x to 0 to determine the y-intercept

\(g(0)= \log_2(0 + 4) + 8\)

Evaluate the sum

\(g(0)= \log_2(4) + 8\)

Apply the law of logarithm

g(0)= 2 + 8

g(0) = 10

Hence, the y-intercept is (0,10)

Set g(x) to 0 to determine the x-intercept

\(\log_2(x + 4) + 8 = 0\)

Subtract 8 from both sides

\(\log_2(x + 4) = -8\)

Express as exponents

\(x + 4 = 2^{-8\)

This gives

x + 4 = 0.00390625

Subtract 4 from both sides

x = -3.99609375

Approximate

x = -4

Hence, the x-intercept is (-4,0)

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Answer:

c

Step-by-step explanaticcon: