Find the 3rd cumulant of a discrete random variable that has
probability generating function G(z) = z^3 /z^3−8(z−1) .
Find the 3rd cumulant of a discrete random variable that has probability generating function G(2) = 23-8(2-1) z³–8(z−1) ·

To determine which plan offers Benito the better rate, let's compare the costs of both plans based on the given information.

Plan Y:

Monthly fee: $44

Cost per text message: $0.02

To calculate the total cost of Plan Y, we need to consider the monthly fee plus any additional charges for text messages.

Let's compare this to an alternative plan, Plan Z, which we'll define:

Monthly fee: $50

No additional charges for text messages

With Plan Z, Benito has a fixed monthly fee of $50 and does not incur any additional charges for text messages.

To determine which plan offers a better rate, we need to consider Benito's text messaging habits. If Benito sends a large number of text messages per month, Plan Y's additional charge of $0.02 per text message could quickly accumulate and result in a higher overall cost compared to Plan Z.

On the other hand, if Benito sends only a few text messages per month, the additional charge for text messages in Plan Y might not significantly impact the total cost.

Ultimately, the better rate depends on Benito's text messaging usage. If Benito sends a high volume of text messages, Plan Z with its fixed monthly fee of $50 may be more cost-effective. However, if Benito sends very few text messages, Plan Y could potentially offer a better rate.

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Answer:

A. 183 meters

Step-by-step explanation:

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters

Find distance BC

Cos (60°)=BC / AB (Adjacent divided by the hypotenuse)

Cos (60°)=1/2

BC=a

AB=500

Cos (60°)=BC / AB

1/2=a/500

1/2 * 500=a

250=a

a=250m

Find distance AC

Sin(60°)=AC/AB (opposite side divided by hypotenuse)

Sin(60°)=√3/2

AC=b

AB=500

Sin(60°)=AC/AB

√3/2=b/500

√3/2 * 500=b

250√3=b

b=433m

Distance AC and BC=AC+BC

433m+250m=683m

Subtract the distance AB from AC+BC

= 683m - 500m

=183m

Answer is A. 183 meters

Answer:

A. 183 meters

Step-by-step explanation:

sin(60) = x/500

= 433

tan(60) = 433/x

= 250

This is the driving distance. 433+250= 683. Directly walking (using hypotenuse distance) is 500.

683-500=183!

According to the given statement The probability that the sum equals Erika's age in years is 2/12, which simplifies to 1/6.

To find the probability that the sum of the numbers equals Erika's age of 14, we need to consider all possible outcomes and calculate the favorable outcomes.
First, let's consider the possible outcomes for flipping the coin. Since the coin has sides labeled 10 and 20, there are 2 possibilities: getting a 10 or getting a 20.
Next, let's consider the possible outcomes for rolling the die. Since a standard die has numbers 1 to 6, there are 6 possibilities: rolling a 1, 2, 3, 4, 5, or 6.
To find the favorable outcomes, we need to determine the combinations that would result in a sum of 14.
If Erika gets a 10 on the coin flip, she would need to roll a 4 on the die to get a sum of 14 (10 + 4 = 14).
If Erika gets a 20 on the coin flip, she would need to roll an 8 on the die to get a sum of 14 (20 + 8 = 14).
So, there are 2 favorable outcomes out of the total possible outcomes of 2 (for the coin flip) multiplied by 6 (for the die roll), which gives us 12 possible outcomes.
Therefore, the probability that the sum equals Erika's age in years is 2/12, which simplifies to 1/6.

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Answer:

256

Step-by-step explanation:

65% is 208

15% is 48

15% + 65% is 80%

So, just add 48 and 208 together:

48 + 208 = 256

Therefore, 80% of that number is 256.

Answer:

256

Step-by-step explanation:

We know that 65% of a number is 208 and 15% is 48, so we can simply add 208 + 48 to get 256.

If the ratio of flamingos to monkeys was 6:7, then in present the number of monkeys is 18 and number of flamingo is 12.

Let "6x" be the number of flamingos and "7x" be the number of monkeys,

After the 4 monkeys were born, the number of monkeys became 7x + 4, and the ratio of flamingos to monkeys became 2:3.

This means that the number of flamingos is now 2/3 of the total number of monkeys,

Which is : 2/3(7x + 4) = 6x,

Simplifying further,

We get,

⇒ 2(7x + 4) = 18x,

⇒ 14x + 8 = 18x

⇒ 8 = 4x

⇒ x = 2

So, there were 6x = 12 flamingos and 7x = 14 monkeys in the safari park before the 4 monkeys were born.

After the 4 monkeys were born, the number of monkeys became 14 + 4 = 18, and the new ratio of flamingos to monkeys is 2:3,

Which means the number of flamingos is 2/5 of total-number of animals.

⇒ 2/5(12 + 18)

⇒ 12

Therefore, there are currently 12 flamingos and 18 monkeys in the safari park.

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The estimated value of the infinite sum [infinity] (2n + 1)−9 n = 1 is 0.00253, correct to five decimal places.

To estimate the sum, we can use the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio.

In this case, the first term is (2(1) + 1)−9 = 1/512, and the common ratio is 2/3. Therefore, the sum can be estimated as (1/512)/(1-(2/3)) = 1/2560 = 0.000390625.

However, since this only gives us two decimal places of accuracy, we need to add more terms to the sum to get a more accurate estimate. By adding more terms using a calculator or computer program, we find that the sum converges to approximately 0.00253, correct to five decimal places.

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The questions are all illustrations of conditional probabilities, and they can be solved using the general conditional probability formula; P(A|B) = P(A and B)/P(B)

The conditional probability P(A|B) is calculated using:

P(A|B) = P(A and B)/P(B)

Using the above formula, we have:

P(has at least 4 sides| not a hexagon) = 38/50

P(has at least 4 sides| not a hexagon) = 0.76

P(not a square | has less than 7 sides) = 30/45

P(not a square | has less than 7 sides) = 0.67

P(not an octagon | not a triangle) = 39/51

P(not an octagon | not a triangle) = 0.76

P(octagon | sum of interior angle measures is at least 600) = 9/25

P(octagon | sum of interior angle measures is at least 600) = 0.36

The conditional probability is calculated using:

P = P(perfect attendance and honor roll)/P(Honor roll)

So, we have:

P = 25%/38%

Evaluate

P = 0.66

Hence, the probability that a student has a perfect attendance, given that he made the honor roll is 0.66

The conditional probability is calculated using:

P = P(Home has a pool and at least 3 bedrooms)/P(at least 3 bedrooms)

So, we have:

P = 25%/70%

Evaluate

P = 0.36

Hence, the probability that a home has a pool, given that it has at least 3 bedrooms is 0.36

Using the conditional probability formula in (a), we have:

P(uses Ins tag ram| does not use Sna pch at) = 45/(20 + 45)

P(uses Ins tag ram| does not use Sna pch at) = 0.69

P(does not use Ins tag ram| uses Sna pch at) = 25/(30 + 25)

P(uses Instag ram| does not use Sna pch at) = 0.45

Using the conditional probability formula in (a), we have:

P(plays sport| has a part-time job) = 22/68

P(plays sport| has a part-time job) = 0.32

P(has a part-time job| plays sport) = 22/40

P(has a part-time job| plays sport) = 0.55

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To estimate the true proportion of contaminated aluminum cans with 90% confidence and within a margin of error of 0.02, a sample size needs to be determined.

The formula for sample size determination is: n = \((Z^2 * p * q) / E^2\) Where n is the required sample size, Z is the z-score associated with the desired confidence level (90% in this case), p is the estimated proportion of contaminated cans, q is the complement of p (1 - p), and E is the desired margin of error (0.02 in this case). As the true proportion of contaminated cans is unknown, an initial estimate is required. Based on the information provided, it is not clear what this estimate is, so we will assume it to be 0.5 (i.e., the most conservative estimate). Therefore, the required sample size is: n = (1.645^2 * 0.5 * 0.5) / 0.02^2

n = 426.38 Rounding up to the nearest whole number, the minimum sample size required is 427 aluminum cans.

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Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

Answer:

D

Step-by-step explanation:

It is exponential decay if it was growth then it would say 1+0.12 not 1-0.12

Answer:

A - (-6,12)

B - (  -12,9

Step-by-step explanation:

Answer:

13/4

Step-by-step explanation:

We do reciprocal of 1/13 it will be 13/1 after we multiply last answer 13/4

Answer:

3 1/4

Step-by-step explanation:

\( \frac{1}{4} \div \frac{1}{13} \\ \\ = \frac{1}{4} \times \frac{13}{1} \\ \\ = \frac{1 \times 13}{4 \times 1} \\ \\ = \frac{13}{4} \\ \\ = 3 \frac{1}{4} \\ \)

Answer:

s = \(\frac{19}{4}\)

Step-by-step explanation:

substitute the given values into the equation

s = (10 × \(\frac{1}{2}\) ) + ( \(\frac{1}{2}\) × - 2 × (\(\frac{1}{2}\) )² )

  = 5 + (- 1 × \(\frac{1}{4}\) )

  = 5 - \(\frac{1}{4}\)

  = 4 \(\frac{3}{4}\)

  = \(\frac{19}{4}\)

Thomas considers cohesion to be the presence of strong positive bonds between members of a group. In his perspective, cohesion represents a sense of unity, attachment, and solidarity among individuals within the group.

Cohesion, according to Thomas, goes beyond mere cooperation or coordination of activities. It encompasses the emotional and social aspects of group dynamics, emphasizing the quality and strength of the relationships between members. The existence of strong positive bonds implies that individuals feel connected, trust each other, and have a shared sense of identity and purpose.

Thomas likely believes that cohesive groups are characterized by mutual support, collaboration, and a sense of belonging. Members are more likely to work together effectively, communicate openly, and have a higher level of commitment to group goals. Cohesion may also contribute to increased satisfaction, motivation, and overall well-being within the group.

Thomas's perspective aligns with the socio-emotional aspect of group cohesion, emphasizing the interpersonal connections and social dynamics that contribute to the cohesiveness of a group.

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Answer:

His confidence is transformed by the crowd’s response.

Step-by-step explanation:

Scotty is described as being a "quavering husk...just moments before." This shows his lack of confidence and anxiety about being on stage.

The value of x is 3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

As, we know that The median (also called a midline or midsegment) is a line segment half-way between the two bases.

median = (a+ b ) / 2

So, 12.5 = (3x+1 + 15) / 2

12.5 = 3x + 16 / 2

25 = 3x + 16

3x = 9

x= 3

Hence, the value of x is 3.

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Answer:y = 1.5

Therefore, the cost of one ounce of Sumatra $3.00 and the cost of one ounce of Celebes Kalossi would be $1.50

not sure if its same problem but

...

The answer is c) 50%. A random sample means that each member has an equal chance of being selected. This means that out of a sample size of any number, the percentage of members selected will always be 50%.

For example, if we have a random sample of 100 members, 50 of them will be selected. This principle applies to any population size, regardless of whether it's 10 or 10,000. It's important to note that this applies only to random samples, as non-random samples can have a biased selection process which affects the percentage of members selected. In summary, the percent of members in a random sample that have an equal chance of being selected is always 50%.

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Answer:

Step-by-step explanation:

The parenthesis can cancel because the lack of anything you can do in them, so that will leave you with 7m + 3 + 7m + 6

Next step is to add like numbers, you should start by adding 7m + 7m, which would be 14m.

Next would be to add 3 + 6, which is nine.

To end this equation, simply put 14m + 9

There is no one-number answer because we do not know what m is. So the equation 14m + 9 is the final answer.

Answer:

\((3\, y + 2\, z)^{2} - (3\, y - 2\, z)^{2} = 24\, y\, z\)

Step-by-step explanation:

Make use of the fact that for any \(a\) and \(b\):

\(\begin{aligned}& (a + b)\, (a - b) \\ =\; & a^{2} - a\, b + a\, b - b^{2} \\ =\; & a^{2} - b^{2}\end{aligned}\).

In other words, the difference \((a^{2} - b^{2})\) between two squares could be written as the product of \((a + b)\) and \((a - b)\).

Apply this identity to rewrite and simplify the expression in this question. In this example, \(a = 3\, y + 2\, z\) whereas \(b = 3\, y - 2\, z\).

\(\begin{aligned} & \underbrace{(3\, y + 2\, z)^{2}}_{a^{2}} - \underbrace{(3\, y - 2\, z)^{2}}_{b^{2}} \\ =\; & \underbrace{((3\, y + 2\, z) + (3\, y - 2\, z))}_{(a + b)}\\ &\times \underbrace{((3\, y + 2\, z) - (3\, y - 2\, z))}_{(a - b)} \\ =\; &6\, y\, (3\, y + 2\, z - 3\, y + 2\, z) \\ =\; & 24\, y \, z \end{aligned}\).

Answer:

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

The Distributive Property tells us that we can remove the parentheses if the term that the polynomial is being multiplied by is distributed to, or multiplied with each term inside the parentheses.

If a number outside the parentheses has a negative sign then the first and simplest way is to change each positive or negative sign of the terms that were inside the parentheses. Negative or minus signs become positive or plus signs. Similarly, positive or plus signs become negative or minus signs.

Step-by-step explanation:

Since the derivative is negative in the interval x > 0, the function y = 3x/(6x - 1) is decreasing on that interval.

To find the critical point(s) and determine if the function is increasing or decreasing on the given interval for the function y = 3x/(6x - 1), we need to first find the derivative of the function and then locate any values of x where the derivative is equal to zero or undefined.

Taking the derivative of y with respect to x:

y' = (d/dx)(3x/(6x - 1))

To simplify the derivative, we can use the quotient rule:

y' = [(6x - 1)(3) - (3x)(6)] / (6x - 1)^2

y' = (18x - 3 - 18x) / (6x - 1)^2

y' = -3 / (6x - 1)^2

To find the critical point(s), we set the derivative equal to zero:

-3 / (6x - 1)^2 = 0

Since the numerator is constant and nonzero (-3), the fraction can only be equal to zero if the denominator is equal to zero:

6x - 1 = 0

Solving for x:

6x = 1

x = 1/6

The critical point is at x = 1/6.

To determine if the function is increasing or decreasing on the interval x > 0, we can examine the sign of the derivative in that interval.

For x > 0, the denominator (6x - 1)^2 is always positive, and the numerator (-3) is negative. Dividing a negative number by a positive number gives a negative result. Therefore, the derivative y' = -3 / (6x - 1)^2 is negative for x > 0.

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The required simplified solution of the given expression is 4√15i.

A simplified solution of the given expression √-240 is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

The square root of the negative value induces the property of the complex number. (a complex number is a number that contains both the real and imaginary parts of the number)

Simplifying,
√-240= √4×4×-15
         = 4 √-15
         = 4√15i   {∵ √-1 = i}

Thus, 4√15i is the required simplified solution to the provided expression.

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The question seems to be incomplete,
The complete question could be as,

Simplify the complex number √-240 ?

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

the answer must be ±6

Step-by-step explanation:

√36 = ±6

Answer:

6 is the correct answer because✓36 is 6

Answer:

65 = <JKL

Step-by-step explanation:

There are two expressions that represent the same thing.

The diagram shows that <JKL = 45 + x

The question states that JKL = 3x + 5

The two expressions must be equal since they represent the same thing.

3x + 5 = x + 45

Subtract 5 from both sides

3x + 5 -  5 = x + 45 - 5

3x = x + 40                     Subtract x from both sides

3x - x = x - x + 40

2x = 40                          Divide by 2

2x/2 = 40/2

x = 20

So x + 45 = 20 + 45 = 65

or

3x + 5 = 3*20 + 5 = 60 + 5 = 65

Answer:

Step-by-step explanation:

According to the graph, the range of f(x) is:

g(x) = 4f(x), so its range is 4 times greater:

Correct choice is D

Answer:

(0,7)

Step-by-step explanation:

domain = (0,50)

g(x) = 4f(x)

x = 0 × 4

x = 0

y = 1.75 × 4

y = 7

(x,y) => (0,7)

The probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

The symbol "∩" represents the intersection of two events.

For example, "a ∩ d" means the event where both "a" and "d" occur together.

The symbol "~" means "not" or "complement." So, "~ (a ∩ d)" means the event where "a ∩ d" does NOT occur, or in other words, where "a" OR "d" does not occur.

Now, onto the question.

We are given that p(a ∩ d) = 2/5, which means that the probability of both events "a" and "d" occurring together is 2/5.

We want to find the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur.

To find this probability, we need to use some basic probability rules.

One of these rules is that the probability of an event happening (let's call it "E") is equal to 1 minus the probability of the complement of that event not happening (~E).

In other words, p(E) = 1 - p(~E).

So, if we apply this rule to the event "~ (a ∩ d)", we get:
p(~ (a ∩ d)) = 1 - p(a ∩ d)

Now we can substitute in the value we were given for p(a ∩ d):
p(~ (a ∩ d)) = 1 - 2/5

Simplifying this gives:
p(~ (a ∩ d)) = 3/5

Therefore, the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

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