A binomial probability experiment is conducted with the given parameters compute the probability of X successes in the N independent trials of the experiment an equals 10P equals 0.35 and X equals 3​

Answer:

See explanation below

Step-by-step explanation:

1. 12x - 18 = 6(2x -3)

2. 15x + 25 = 5(3x + 5)

3. 14x + 21 = 7(2x + 3)

4. 5x - 5 = 5(x - 1)

5. 12x - 30 = 6(2x - 5)

6. 10x + 8 = 2(5x + 4)

7. 27x + 18 = 9(3x + 2)

8. 4x - 20 = 4(x - 5)

9. 20x + 30 = 10(2x + 3)

10. 4(x + 5) = 4x + 20

11. 3(x - 2) = 3x - 6

12. 5(2x + 4) = 10x + 20

13. 5(x - 1) = 5x - 5

14. 1/2(10x + 12) = 5x + 6

15. 4(2x + 4) = 8x + 16

16. 2(5x - 2) = 10x - 4

17. 2(x - 8) = 2x - 16

18. 4(2x + 1) = 8x + 4

The 95% confidence interval for the proportion in the adult population who would say “Yes” of asked is 0.51 and 0.57.

To find the 95% confidence interval for the proportion in the adult population who would say "Yes," we can use the following formula

CI = p ± z × sqrt((p × (1 - p)) / n)

where

p = proportion of the sample who answered "Yes"

z = the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96)

n = sample size

Plugging in the values given in the question, we get

p = 0.54

z = 1.96

n = 1019

CI = 0.54 ± 1.96 × sqrt((0.54 × (1 - 0.54)) / 1019)

CI = 0.54 ± 0.030

CI = (0.51, 0.57)

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I have solved the question in general, as the given question is incomplete,

The complete question is:

Overall, 54% of the sample (550 of 1019 people) answered “Yes.” Find a 95% confidence interval for the proportion in the adult population who would say “Yes” if asked.?

the probability of the complement of (A ∪ B) is 0.3.

How to find and what is Morgan's law?

Since A and B are mutually exclusive, we have:

P(A ∩ B) = 0

The complement of (A ∪ B) is the set of outcomes that are not in A or B. So:

(A ∪ B)′ = A′ ∩ B′

Using De Morgan's law, we have:

A′ ∩ B′ = (A ∪ B)′

We can now use the formula for the probability of the complement:

P((A ∪ B)′) = 1 - P(A ∪ B)

Since A and B are mutually exclusive, we have:

P(A ∪ B) = P(A) + P(B)

So:

P((A ∪ B)′) = 1 - (P(A) + P(B))

Substituting the given probabilities, we get:

P((A ∪ B)′) = 1 - (0.2 + 0.5)

P((A ∪ B)′) = 1 - 0.7

P((A ∪ B)′) = 0.3

Therefore, the probability of the complement of (A ∪ B) is 0.3.

De Morgan's laws are a pair of fundamental laws in Boolean algebra and set theory that describe the relationship between the intersection and union of sets and their complements. The two laws are:

The complement of the union of two sets is equal to the intersection of their complements.

Symbolically: (A ∪ B)′ = A′ ∩ B′

The complement of the intersection of two sets is equal to the union of their complements.

Symbolically: (A ∩ B)′ = A′ ∪ B′

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The variance of a sample is equal to n - 1 degrees of freedom, the appropriate chi-square distribution for a sample of n observations taken from a normal population is n - 1 degrees of freedom.

The appropriate chi-square distribution for a sample of n observations taken from a normal population is n - 1 degrees of freedom. This is because the chi-square distribution measures the variance of a population, which is the squared sum of the differences between the observed values and the expected values. Since the expected value for a sample of n observations is equal to the mean of the population, the variance of the sample is equal to the sum of the squared differences between the observed values and the mean of the population. This gives us the formula for the chi-square distribution:

Chi Square = [tex](Sum of (Observed - Mean)^2) / (Mean)[/tex]

For a sample of n observations, the mean is equal to the sum of the observations divided by n, so we can rewrite the formula as follows:

Chi Square = [tex](Sum of (Observed - (Sum of Observations/n))^2) / (Sum of Observations/n)[/tex]

Since the sum of the observations is a constant, we can move it to the other side of the equation, giving us:

We can simplify this equation further by noting that the sum of the [tex](Observed - (Sum of Observations/n))^2[/tex] terms is equal to the variance of the sample. This gives us the final equation:

Chi Square = Variance / (Sum of Observations/n)

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The fractiοn οf students whο chοse card as their favοrite game type is: 1/6. Thus, option D is correct.

A circle is a clοsed twο-dimensiοnal shape that is defined as the set οf all pοints in a plane that are equidistant frοm a single fixed pοint called the center οf the circle. The distance frοm the center οf the circle tο any pοint οn the circle is called the radius οf the circle.

A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane such that its distance frοm a fixed pοint (the center) remains cοnstant.

A circle is a very impοrtant and cοmmοn geοmetric shape that has many practical applicatiοns in mathematics, physics, engineering, and οther fields.

Tο determine the fractiοn οf students whο chοse card as their favοrite game type, we need tο find the pοrtiοn οf the circle graph that represents the card categοry.

Frοm the graph, we can see that the card categοry cοvers 16.66% οf the entire circle graph.

i.e.

16.66/100 = 1/6

Therefore, the fraction of students who chose card as their favorite game type is:

1/6

So, the answer is option D: 1/6.

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Complete question:

The circle graph shows the favourite game type of students in Ms. Hunter's class.

What fraction of the students chose card?

a. 2/3

b. 5/9

c. 3/10

d. 1/6

Answer:

You need to know that the ratio of their sides are congruent

if we  that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:

100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.

If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.

So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:

On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.

However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.

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The real estate tax on Brianna Wallen's home is $37,934.83.

Property owners, including homeowners, are subject to a tax based on the assessed value of their properties. It is often collected by local governments and used to pay for amenities like public transportation, roads, and security.

The assessed value of the property and the tax rate are used to determine the amount of property tax due. The assessed value of a property is its worth as established by a government assessor and may be based on a number of variables, including recent sales prices of nearby properties, the price to replace the property, and the property's condition.

The tax is calculated using the given formula:

Tax = (Assessment Rate x Market Value) x (Tax Rate / 1000)

Substituting the given values we have:

Tax = (0.29 x $438,300) x (81.16 / 1000)

Tax = $37,934.83

Hence, the real estate tax on Brianna Wallen's home is $37,934.83.

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Answer:

x = 21

Step-by-step explanation:

Given the angle measurements of two angles, we can deduce that this is a 30-60-90 triangle. The formula for side lengths of this type of triangle is given by s → s√3 → 2s with s being the shortest side (the side opposite the 30° angle).

We are looking for the side length represented by s[tex]\sqrt{3}[/tex]. We can see that the hypotenuse is represented by 2s, so...

2s = 24

s = 12

The side length of the shortest side is 12. Therefore, we can say that

x = s  [tex]\sqrt{3}[/tex]

x = 12 * [tex]\sqrt{3}[/tex]

x = 20.785

The question asks for our answer to the nearest whole number, so

x = 21

To show that the properties of a probability distribution for a discrete random variable are satisfied, we need to verify that the probability distribution function (PDF) satisfies, The PDF must be non-negative for all values of the random variable and The sum of the probabilities for all possible values of the random variable must be equal to 1.

Let X be a discrete random variable taking values x1, x2, ..., xn, and let P(X) be the probability distribution function for X, such that P(X = xi) = pi for all i.

The PDF must be non-negative for all values of the random variable. This means that for any value xi of the random variable, the probability pi must be greater than or equal to zero. That is,

pi ≥ 0 for all i.

This property ensures that probabilities are never negative, which is a necessary condition for a valid probability distribution.

The sum of the probabilities for all possible values of the random variable must be equal to 1. That is,

∑ pi = 1 for all i.

This property ensures that the total probability of all possible outcomes is equal to 1, which is a necessary condition for a valid probability distribution.

Therefore, if the PDF satisfies these two properties, we can conclude that it represents a valid probability distribution for the given discrete random variable.

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Answer:

hello!!!!

Payment per year

1,000×12months=12,000

total payment over the lifetime of the loan.

12,000×10years=120,000

Answer:

$120,000

Step-by-step explanation:

If you make monthly payments of $1,000 for 10 years, the total payment over the lifetime of the loan would be $1,000 x 12 months x 10 years = $120,000

Using a system of equations, 32 lbs of the $3.40/lb chocolate and 12.8 lbs of the $9.00/lb chocolate will be needed to obtain the desired mixture.

Let x be the amount of the $3.40/lb chocolate needed, and y be the amount of the $9.00/lb chocolate needed to make 44.8 lbs of a $5.00/lb mixture.

We can set up the following system of equations:

x + y = 44.8 (total amount of mixture)

3.4x + 9y = 5(44.8) (total cost of mixture)

Solving this system of equations, we get:

x = 32 lbs of the $3.40/lb chocolate

y = 12.8 lbs of the $9.00/lb chocolate

Therefore, to obtain the desired mixture, 32 lbs of the $3.40/lb chocolate and 12.8 lbs of the $9.00/lb chocolate will be needed.

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Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.

Having three straight sides and three angles where they intersect, a triangle is a closed, two-dimensional shape. It is one of the fundamental geometric shapes and has a number of characteristics that can be used to study and resolve issues that pertain to it. The triangle inequality theory states that the sum of a triangle's interior angles is always 180 degrees, and that the longest side is always the side across from the largest angle. Triangles can be used to solve a wide range of mathematical issues in a variety of disciplines and can be categorised based on the length of their sides and the measurement of their angles.

given

We can use the following congruence theories or postulates based on the data in the diagram:

A. ASA

B. AAS

C. LL (corresponding angles hypothesis)

F. SAS

Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.

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Answer:

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).

In this case, we know that P = $10,000, r = 6.5% = 0.065, and we want to find t when A = $29,500. We also know that the interest is compounded annually, so n = 1.

Substituting these values into the formula, we get:

$29,500 = $10,000(1 + 0.065/1)^(1t)

Dividing both sides by $10,000, we get:

2.95 = (1.065)^t

Taking the natural logarithm of both sides, we get:

ln(2.95) = ln(1.065)^t

Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the right side as:

ln(2.95) = t ln(1.065)

Dividing both sides by ln(1.065), we get:

t = ln(2.95)/ln(1.065) ≈ 18.2

Therefore, the person must leave the money in the bank for about 18.2 years to reach $29,500. To the nearest tenth of a year, the answer is 18.2 years.

Answer:

Jika 16,5% dari suatu jumlah adalah 891, kita dapat menggunakan persamaan:

0,165x = 891

di mana x adalah jumlah aslinya. Kita ingin menyelesaikan persamaan ini untuk x.

Kita dapat memulai dengan membagi kedua sisi dengan 0,165:

x = 891 / 0,165

x = 5400

Jadi, jumlah aslinya adalah 5400.
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Answer:

61°

Step-by-step explanation:

∠4 is the vertical angle to the 61° angle. This means they will have the same measure, so ∠4 is 61°.

The distance Jamie will run is equal to half of the rate in kilometers per hour, the equation is d = r (1/2)

Speed is a scalar number that represents the rate of movement of an item. It is described as the distance covered in a certain amount of time, regardless of direction. In contrast, velocity is a vector quantity that accounts for both speed and direction. It is characterised as the pace at which an item shifts in a certain direction. In physics, the idea of velocity is crucial since it aids in explaining how an object's location varies over time and is used to compute other crucial variables like acceleration and momentum.

The distance is calculated using the given formula:

Distance = rate (time)

Given that, the time is 1/2 hour thus:

d = r (1/2)

Thus, the distance Jamie will run is equal to half of the rate in kilometers per hour, and the equation is d = r (1/2).

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The statements below describe the graph of y > mx, where m > 0

The inequality is given as:

y > mx

Where m > 0

The inequality symbol implies that:

The condition m > 0 implies that:

Next, we assume that:

m = 5

So, we have:

y > 5x

See attachment for the graph of y > 5x

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Step-by-step explanation:

B) 20:23

C) 6,0375

hope this helps

The value of a is 2.

the vertex form of the graph : y = 2 ( x + 1 )² - 9,

the standard form of the graph : y = 2x² + 4x - 7,

the factored form of the graph : y = 2 ( x + 1) ( x + 1 ) - 9.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The equation of the parabola in vertex form:

The vertex v is at v ( -1, -9 ) this is equivalent to v ( h, k )

the equation of parabola in vertex form is y = a ( x- h )² + k

y = a ( x - (-1) )² + (-9)

substituting point ( -3, -5 ) from the graph we have:

-5 = a ( -3 + 1 )² - 9

-5 = 2a - 9

a = 2

substituting the known values to y = a ( x- h ) + k

y = 2 ( x + 1 )² - 9

the equation of the parabola in factored form

y = 2 ( x + 1) ( x + 1 ) - 9

the equation of the parabola in standard form

y = 2 ( x + 1) ( x + 1 ) - 9

y = 2 ( x² + 2x + 1 ) - 9

y = 2x² + 4x - 7

Hence, the value of a is 2

the vertex form of the graph : y = 2 ( x + 1 )² - 9

the standard form of the graph : y = 2x² + 4x - 7

the factored form of the graph : y = 2 ( x + 1) ( x + 1 ) - 9

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The correct sampling technique for the given case is C. Simple random sampling

Each person in a population has an equal probability of being chosen to be a member of specific sample when using simple random sampling as a statistical sampling technique. With this technique, a random sample is picked at random from a wider population, giving each person a fair chance of being chosen. This indicates that there is no bias in selection process and that any person or object in overall population has same likelihood of getting chosen.

Simple random sampling is frequently employed in research investigations because it is an easy-to-use and objective sampling technique. Given that 100 names were randomly chosen from a list of all registered voters, simple random sampling is appropriate sampling technique in this particular case.

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The returned value would be 70 which is the missing value in the data set. Hence, option D is correct. We have some X values; we called these numeric inputs and some Y value that we are trying to predict.

This set of data would yield a result of 70 if a median imputer were run on it. In regression, we have some X values that are referred to as independent variables and some Y values that are referred to as dependent variables (this is the variable we are trying to predict). Several Y values are possible, but they are uncommon.

Learning a function that can predict Y given X is the fundamental concept behind a regression. Depending on the data, the function may be linear or non-linear.

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Complete question is:

Imagine X in the below is a missing value. If I were to run a median imputer on this set of data. What would the returned value be? 50 , 60 , 70 , 80 , 100 , 60 , 5000 , x (It's okay to have to look up how to do this!)

50

An error

80

70

100

The basic idea of a regression is very simple. We have some X values, we called these ______ and some Y value (this is the variable we are trying to _______.

We could have multiple Y values, but that is not but that is not re-ordered ordinals intercepts features numeric inputs.

Answer:

Step-by-step explanation:

D is it

The correct answer is C. This is not a probability model because the sum of the probabilities is not 1.Therefore, the sum of the probabilities must be equal to 1 for a set of probabilities to be considered a probability model.

Probability is a measure of the probability of an event, expressed as a number between 0 and 1.

For example, the probability of rolling a 6 on a fair six-sided die is 1/6 or approximately 0.17.

In order for a set of probabilities to represent a probability model, the sum of all the probabilities must be equal to 1. This ensures that there is a 100% chance that one of the possible outcomes will occur.

If the sum of the probabilities is less than 1, then there is a possibility that none of the outcomes will occur.

If the sum of the probabilities is greater than 1, then there is a possibility that more than one outcome will occur, which is not possible in a probability model.

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The cardinality of set from the given vein diagram is found as 2.

Think about set A. The set A is said to be finite and so its cardinality is same to the amount of elements n if it includes precisely n items, where n  ≥  0. |A| stands for the cardinality of such a set A.

It turns out that there are two kinds of infinite sets that we need to determine between since one form is much "bigger" than the other. Particularly, one type is referred to as countable and the other as uncountable.

From the given figure

Set A = {8 , 8, 3, 6}

Compliment of Set B (elements not present in set B):

Set [tex]B^{c}[/tex] = {8, 8, 6(pink), 3(white)}

Thus,

(A∩ [tex]B^{c}[/tex] ) = {8, 8} (present in both set)

n (A∩ [tex]B^{c}[/tex] ) = 2 (cardinal number)

Thus, the cardinality of the set from the given vein diagram is found as 2.

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The quadratic function, x2 + 14x + 49 f, would have 7 as the lone zero.

Any subset of a Cartesian product is a relation.

For instance, a subset of is known as a "binary relation from A to B," and in specifically, a subset of is known as a "relation on A."

These ordered pairs (a,b) with first components from A and second components from B make up a binary relation from A to B.

A function is a relation that links every item in a set X to a single item in a different set Y. (possibly the same set).

A graph, which is the collection of all ordered pairs (x, f (x)), serves as the sole representation of a function.

As you can see from these definitions, every function is a relation from X to Y, but not vice versa .

(x - 7)(x - 7)

⇒ (x - 7)²

⇒ x² + 7²+ 2 × 7 × x

⇒ x² + 49 + 14x

⇒ x² + 14x + 49

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Answer:

Step-by-step explanation:

To find the number of students who studied in the library or cafeteria (including both), we need to add the number of students who studied in the library and the number of students who studied in the cafeteria, but we need to subtract the number of students who studied in both the library and cafeteria to avoid counting them twice.

So, the number of students who studied in library or cafeteria is:

170 + 135 - 76 = 229

Therefore, 229 students studied in the library or cafeteria (including both).

Answer:

Step-by-step explanation:

8.35 times 105 is 876.75

1.6 times 10 is 16

  Hope this helps

If the probability distribution is f(x) = 2(1/3)ˣ for x = 1,2,3,... then the moment generating function is Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].

The moment generating function (MGF) of a random variable is defined as a mathematical function that is used to determine expected values of the random variable.

It is a way to characterize the entire probability distribution of the random variable by generating a sequence of moments from the function.

The probability distribution is  f(x) = 2(1/3)ˣ for x = 1,2,3,... ;

The MGF will be ⇒ Mₓ(t) = [tex]\[ \sum_{x=1}^{\infty} e^{tx} .2(\frac{1}{3})^{x}[/tex]

⇒ [tex]2 \[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] ;

This expression [tex]\[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] represents an infinite geometric series.

So, [tex]\[ \sum_{x=1}^{\infty}(\frac{e^{t} }{3} )^{x}[/tex] = [tex]\frac{e^{t}/3 }{1-e^{t}/3 }[/tex] = [tex]\frac{e^{t} }{3-e^{t} }[/tex]

We get, Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].

Therefore, the Moment generating Function for the given Probability Distribution is Mₓ(t) = [tex]\frac{2e^{t} }{3-e^{t} }[/tex].

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The given question is incomplete, the complete question is

Find the moment-generating function of the discrete random variable X that has the probability distribution f(x) = 2(1/3)ˣ for x = 1,2,3,....