call a positive real number special if it has a decimal representation that consists entirely of digits $0$ and $7$. for example, $\frac{700}{99}

Thus, 45% of timely payments will not be made by under 100 - (165/200)*100% = 17.5% of clients.

what is binomial distribution?

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial can result in either a success or a failure.

The distribution is characterized by two parameters: the number of trials n and the probability of success in each trial p. The probability of exactly k successes in n trials can be calculated using the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

(1) To find the probability that over 10% of the clients will not make timely payments, we need to use the binomial distribution. Let X be the number of clients out of 200 who do not make timely payments. Then X has a binomial distribution with parameters n = 200 and p = 0.08. We want to find P(X > 0.1*200) = P(X > 20).

Using the normal approximation to the binomial distribution, we can approximate X with a normal distribution with mean μ = np = 2000.08 = 16 and standard deviation σ = sqrt(np(1-p)) = sqrt(2000.08*0.92) = 3.36.

P(X > 20) can be approximated as P(Z > (20 - 16)/3.36) = P(Z > 1.19), where Z is a standard normal variable. Using a standard normal table or a calculator, we can find that P(Z > 1.19) = 0.1179.

Therefore, the probability that over 10% of the clients will not make timely payments is approximately 0.1179.

(2) Let Y be the number of clients out of 200 who make timely payments. Then Y has a binomial distribution with parameters n = 200 and p = 0.92 (since 8% of clients do not make timely payments, 92% do). We want to find the smallest k such that P(Y < k) > 0.45.

We can use a table of the cumulative binomial distribution or a calculator to find that P(Y < 164) = 0.4443 and P(Y < 165) = 0.4658. Therefore, the smallest k such that P(Y < k) > 0.45 is 165.

Thus, 45% of timely payments will not be made by under 100 - (165/200)*100% = 17.5% of clients.

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The probability that over 10% of these clients will not make timely payments is approximately 0.03.

What exactly is probability?

Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. It is used to quantify the likelihood or chance of an event occurring, and is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

Now,

(1) Let X be the number of clients who will not make timely payments out of 200 loans approved. We are given that the probability of not making timely payments is 8%, or 0.08. Since X follows a binomial distribution with n = 200 and p = 0.08, we can use the normal approximation to the binomial distribution to find the probability that over 10% of these clients will not make timely payments:

First, we need to calculate the mean and standard deviation of X:

mean = n * p = 200 * 0.08 = 16

standard deviation = sqrt(n * p * (1 - p)) = sqrt(200 * 0.08 * 0.92) = 3.19

Now we can use the normal distribution with a continuity correction to find the probability:

P(X > 0.1 * 200) = P(X > 20) = P((X - mean) / standard deviation > (20 - mean) / standard deviation)

= P(Z > 1.88) ≈ 0.03

Therefore, the probability that over 10% of these clients will not make timely payments is approximately 0.03.

(2) Let Y be the number of clients who make timely payments out of 200 loans approved. We are given that 45% of the timely payments will not be made, so the probability of making a timely payment is 1 - 0.45 = 0.55. Since Y also follows a binomial distribution with n = 200 and p = 0.55, we need to find the largest value of k such that the probability of at least k clients making timely payments is at least 0.45.

We can use a cumulative binomial distribution to find the probability:

P(Y ≥ k) = 1 - P(Y < k) = 1 - binom.dist(k - 1, n, p, TRUE)

We can then use trial and error to find the largest value of k such that P(Y ≥ k) ≥ 0.45:

P(Y ≥ 127) ≈ 0.455 > 0.45

P(Y ≥ 128) ≈ 0.426 < 0.45

Therefore, the largest value of k such that the probability of at least k clients making timely payments is at least 0.45 is 127. This means that under 63.5% of clients (127/200) will make timely payments.

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Answer:

5√3

Step-by-step explanation:

Thanks to the given information we can say that the smallest leg is 5 because the triangle is half of an equaliteral one.

for the same reason we can say that x is 5√3 that is the simplest from of the result of the Pytaghorean theorem

Answer:

63

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

example

length of R = 2

width of R = 3

Area = 3*2 = 6

length of T = 2 * 4 = 8

widht of T = 3 * 4 = 12

Area = 12 * 8 = 96

96 : 6 = 16

The scores, in order from least to greatest, are:

-7.2, -5 3/4, 3 1/8, 9. Therefore, the final order is: -7.2, -5 3/4, 3 1/8, 9

A decimal form is a way of expressing numbers in the base-10 number system, which is the number system we use in everyday life. In decimal form, a number is represented by a combination of digits, where the rightmost digit represents units (ones), the next digit represents tens, the next represents hundreds, and so on. Each digit is multiplied by a power of 10, determined by its position in the number.

-7.2 , -5 3/4 , 3 1/8, 9

The numbers are already in decimal form, so we can compare them directly.

-7.2 is less than -5.75

-5.75 is less than 3.125

3.125 is less than 9

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Answer:

8 people

Step-by-step explanation:

3 people to do the job in 16 hours so each of the people will mow 1/3 of the lawn during the 16 hours.

So if was a single person was mowing the lawn would take them 3 times longer 16*3 =48 hours

To mow the lawn in 6 hours will need 48 hours to be split in 6 hours so will get 48/6 = 8 people.

It is not possible for the graph of a height function of a car on a roller coaster to be a step function. Hence Amy is wrong.

A sort of function called a step function is one that only varies at discrete, isolated places in its domain and is constant everywhere else. A step function is one that "steps" down to the next integer at each integer input while remaining constant in between. An example of this is the floor function, which rounds down any input to the nearest integer.

On the other hand, it is doubtful that the height of a roller coaster car as a function of time is a step function because it is anticipated to fluctuate continually as opposed to hopping from one value to another at certain moments. Instead of abrupt increases in height that would be consistent with a step function, roller coasters often entail smooth, continuous curves and elevation changes.

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The problem entails calculating the probability for a scenario in which the IRS audits 30% of tax returns at random and a married pair has filed separate returns. Calculate the chances of both husband and wife being audited, just one of them being audited, neither of them being audited, and at least one of them being audited.

a) Probability that both the husband and the wife will be audited: (0.3)² = 0.09 or 9%

b) Probability that only one of them will be audited:

c) Probability that neither one of them will be audited: (0.7)² = 0.49 or 49%

d) Probability that at least one of them will be audited: This is the complement of the probability that neither one of them will be audited. So, the probability that at least one of them will be audited is 1 - 0.49 = 0.51 or 51%.

The relevant terms in this question are probability and statistics. To solve for the probability of each scenario, we used the formulas for independent probabilities and complements.

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An argument can be invalid even if the premises are true and the conclusion is false.This statement is actually false.

Invalidity refers to the structure of the argument, not the truth value of the premises or conclusion. An invalid argument fails to establish the truth of its conclusion even if its premises are true. In contrast, a valid argument guarantees that the conclusion follows from the premises, regardless of the truth or falsity of the premises. Therefore, an argument can be valid with false premises, and an argument can be invalid with true premises.

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Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid

argument.

If an argument is invalid, then whenever the premises are all false, the conclusion must also be false.

An invalid argument is one where the conclusion does not necessarily follow from the premises, even if the premises

are all true.

In other words, it is possible for the premises to be true, but the conclusion to be false. However, in the scenario you

described, all the premises are false. In an invalid argument, there is no guarantee that the conclusion will also be false.

Identify the argument as invalid.

Recognize that all the premises are false.

Understand that in an invalid argument, the conclusion does not necessarily follow from the premises.

Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid

argument.

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The Central Limit Theorem is a fundamental concept in statistics that states that the sampling distribution of the mean of a random sample approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To validate the Central Limit Theorem, you can follow these steps in any computation language of your choice:

1. Define the population distribution: Choose a probability distribution, such as a uniform, exponential, or binomial distribution, to represent the population from which samples will be drawn.

2. Generate random samples: Use the chosen distribution to generate random samples of different sizes. For example, you can generate 100 samples of size 10, 100 samples of size 30, and so on. Make sure to record the means of these samples.

3. Calculate the sample means: For each sample, calculate the mean by summing up all the values in the sample and dividing by the sample size.

4. Plot the sampling distribution: Create a histogram or a density plot of the sample means. This plot will show the distribution of the sample means.

5. Compare with the theoretical distribution: Overlay the theoretical normal distribution on the plot of the sample means. The mean of the sample means should be close to the mean of the population, and the shape of the distribution should resemble a normal distribution.

6. Repeat the process: Repeat steps 2-5 with different sample sizes to observe how the shape of the sampling distribution changes as the sample size increases. The Central Limit Theorem predicts that the distribution of the sample means will approach a normal distribution as the sample size increases.

By following these steps and comparing the distribution of the sample means with the theoretical normal distribution, you can validate the Central Limit Theorem in your chosen computation language.

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To check that data follows a continuous distribution using the goodness-of-fit procedure you can change the continuous variable into categorical.

In this question we need to describe how would the goodness-of-fit procedure be modified to check that data follows a continuous distribution.

We know that the Chi - square goodness of fit test can be applied to discrete distributions such as binomial, Poisson, etc.

For continuous distributions we can use Kolmogriv - Smirnov test, t-test ( the single-sample, paired t-test, and the two-sample, unpaired t-test)

A goodness-of-fit test is concerned with the question whether a data set may have been generated by a certain distribution.

Therefore, to check that data follows a continuous distribution we need to change the continuous variable into categorical.

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The perimeter of the rectangle is 174 meters.

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The length of a rectangle is 6 meters more than twice the width. This is expressed as

L = 2W + 6    ------1

The area of the rectangle is expressed as L x W. The area of the rectangle is given as 1620 meters. It is expressed as

L x W = 1620   -------2

Putting the value of L in equation 2

(2W + 6) x W = 1620

\(2W^{2} + 6W = 1620\\\)

Dividing 2 both side

\(W^{2} + 3W = 810\)

\(W^{2} +(30-27)W -810 = 0\)

\(W^{2} + 30W - 27W -810 =0\)

\(W(W+30) - 27(W+30)=0\)

\((W+30)(W-27)=0\)

\(W = -30, 27\)

Width cannot be negative, so, W = 27

From equation 1

L = 2W + 6

  = 2*27 + 6

  = 60

The perimeter of the rectangle is expressed as 2(L + W).

2(L + W) = 2 (60 + 27)

             = 174 meters

Therefore, the required perimeter is 174 meters.

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

The inequality that express the relationship between -2 and -5 is : " greater than " or " > "

\(\qquad \tt \dashrightarrow \: - 2 > - 5\)

Answer:

50$

Step-by-step explanation:

$1.25x40= 50 so she would have to pay 50$

Mariana has to pay $50 for a monthly subscription and 40 downloaded songs

Given that,
Mariana signed up for a streaming music service that costs $7 per month.
If she wants to download songs for offline listening, the service charges $1.25 per song.
To determine how much total money would Mariana have to pay in a month in which she downloaded 40 songs.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Mariana signed up for a streaming music service that costs $7 per month.
The service charges $1.25 per song.
Now,
Total cost of month and 40 downloaded songs = 7 + 1.25 * 40
= 57

Thus, Mariana has to pay $50 for a monthly subscription and 40 downloaded songs.

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Two numbers differ by 7.If their product is 120, find the number​

Let

x and y the numbers

we have

x-y=7 ------> x=7+y -----> equation A

x*y=120 ----> equation B

solve the system

substitute equation A in equation B

(7+y)*y=120

solve for y

y^2+7y-120=0

solve the quadratic equation by graphing

the solutions are

y=8 and y=-15

Find out the value of x

For y=8

x=7+8=15

For y=-15

x=7+(-15)

x=-8

therefore

Problem N 2

we have that

EF=9 cm ----> given

EF=EH+HF ----> by addition segment postulate

substitute given values

9=x+HF

HF=(9-x) cm

step 1

In the right triangle EDH

Applying the Pythagorean Theorem

ED^2=EH^2+DH^2-----> DH^2=ED^2-EH^2

DH^2=(x+3)^2-x^2 ------> equation A

step 2

In the right triangle DHF

Applying the Pythagorean Theorem

DF^2=HF^2+DH^2 -----> DH^2=DF^2-HF^2

DH^2=(2x)^2-(9-x)^2 ------> equation B

step 3

equate equation A and equation B

Simplify

x^2+6x+9-x^2=4x^2-(81-18x+x^2)

6x+9=4x^2-81+18x-x^2

6x+9=3x^2+18x-81

3x^2+18x-81-6x-9=0

3x^2+12x-90=0 -------> quadratic equation

step 4

Solve for x

Complete the square

3x^2+12x=90

Factor 3

3(x^2+4x)=90

simplify

(x^2+4x)=30

x^2+4x+4=30+4

rewrite as perfect squares

(x+2)^2=34

take the square root both sides

The value of x must be a positive value

therefore

Answer: x=-3, y=-8

Step-by-step explanation:

you will leave the first equation alone for now

the second, we will subtract 2y from both sides

5x-2y=1

now you system is

4x-y=-4

5x-2y=1

we will multiply the first equation with -2

-8x+2y=8

5x-2y=1

add both equations, we get -8x+5x=9,  -3x=9,  

x=-3

we will replace x with -3 in any equation, lets use 4x-y=-4,

-12-y= -4,         -y=12-4,                -y=8,         y=-8

In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.

The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.

Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.

Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.

By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.

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Answer:

The leading coefficient is 4

Step-by-step explanation:

Answer:

x > - 7

Step-by-step explanation:

Given

- 3x < 21

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

x > - 7

The solution of inequality - 3x < 21 is,

⇒ x > - 7

We have to given that,

The inequality is,

⇒ - 3x < 21

We can simplify the inequality as,

⇒ - 3x < 21

Divide 3 both side,

⇒ - 3x /3 < 21 / 3

⇒ - x < 7

Take - 1 as common,

⇒ - x < 7

⇒ x > - 7

Therefore, The solution of inequality - 3x < 21 is,

⇒ x > - 7

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The maximum number of spheres that can be made through ice will be 60.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

As per the given,

Number of ice portions = 40

Weight of one ice portion = 3 ounce

Since, 1 lb = 16 ounce

3 ounce = 3/16 lb

Weight of 40 portion = 120/16 lb

The weight of one sphere of ice = 1/8 lb

Number of possible sphere = (120/16)/(1/8)

⇒ 120/16 x 8/1

⇒ 60 sphere

Hence "60 spheres are the most that can be produced by ice".

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The complete question is :

What statistical tests and analysis can be conducted to determine whether there is a significant association between being banded and penguin survival rates, given a dataset with information on the number of banded and non-banded penguins that survived and did not survive?

                                   Banded           Not Banded

Survived                  75                          100

Did Not Survive         25                          50

To determine if there is a significant association, statistical tests such as chi-squared test or Fisher's exact test can be used, to compare the observed proportions of survival and non-survival in banded and non-banded penguins to the expected proportions under the assumption of no association.

To answer the question of whether there is an association between being banded and survival rate, we can calculate the proportions of penguins that survived or did not survive in each group:

                                     Banded                           Not Banded

Survived                         0.75                                0.67

Did Not Survive         0.25                                0.33

From this table, it seems that a higher proportion of banded penguins survived compared to non-banded penguins. However, we cannot conclude that there is a definite association between being banded and survival rate based on this limited data. To make more definitive conclusions, we would need to conduct statistical tests and analysis.

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In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n          

                                                                                                                        In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n            

In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n                                                                                                                                                                        we need to perform the inverse Z-transform. The inverse Z-transform converts a function in the Z-domain back into the time domain.

The general form of the inverse Z-transform is given by:

f(n)= \(\frac{1}{2\pi j}\) ∮ \(_{C}\) \(F(z)z^{n-1} dz\)

​ where

F(z) is the function in the Z-domain, f(n) is the corresponding time-domain sequence, j is the imaginary unit, and ∮\(_{c}\)

​represents integration around a closed path in the Z-plane.

In this case, the function F(z) is a rational function, and we can find its inverse Z -transform using partial fraction decomposition. Let's find the inverse Z-transform step by step:

Step 1: Express F(z) in partial fraction form.

\(F(z)=\frac{1}{z^2} + \frac{3}{z} +4\)

Step 2: Find the roots of the denominator The roots of \(z^{2} =0\) and

z=0 (a double pole at the origin).

Step 3: Perform partial fraction decomposition.

We can write \(F(z)=\frac{A}{z} +\frac{B}{z^2} ​\)

​Multiplying through by \(z^{2}\) to clear the fractions we get,\(1+3z^{-1} +4z^{-2} = A+Bz^{-1}\)                                                                                                        Comparing coefficients, we get:

A=1

B=4

Step4: Apply the inverse Z transform for each term

Inverse Z transform for A/z is \(a^{n}\), where a is the root of corresponding term in the denominator. In this case a=0, so the inverse Z transform of A/z=1

The inverse Z transform of \(\frac{B}{z^2}\) is n.\(a^{n}\), where a is the root of the corresponding term in denominator. In this case a=0. So the inverse Z transform of \(\frac{B}{z^2}\) is n.\(a^{n}\)=0

therefore the time domain of function f(z) is

f(n)=1+0=1

So the sampled time domain representation of the function F(z)=\(1+3z^{-1} +4z^{-2}\) is f(n)=1 for all the values of n

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Answer:

900 ml of milk

Step-by-step explanation:

the scale is 1:1 so just multiply by 3

Answer:

Candy canes are a classic Christmas treat, traditionally white with red stripes and flavored with peppermint. They have been popular since the 1600s and are thought to have originated in Germany. Today, 90 percent of all candy canes are sold between Thanksgiving and Christmas.

In a bag of Christmas treats, there are 3 red candy canes for every 5 gingerbread men. If there total is 40 treats, then the number of candy canes will be 24. This can be calculated by taking 40 divided by 8 (5+3) which equals 5, and then multiplying this by 3 which equals 15. Therefore, 24 candy canes are included in the bag of 40 Christmas treats.

Step-by-step explanation:

The best method for Carlos to find his five most popular cooking demonstrations from his database would be to sort the demonstrations based on the number of times each demonstration has been viewed or purchased.

Carlos can use the data from his database to determine which cooking demonstrations are the most popular by looking at the number of times each demonstration has been viewed or purchased. By sorting the demonstrations in descending order based on this metric, Carlos can easily identify his top five most popular demonstrations.

Carlos can use various methods to find his five most popular cooking demonstrations from his database. One way is to analyze customer feedback and reviews for each demonstration to determine which ones are the most well-received. However, this method may not be the most accurate as not all customers leave feedback or reviews. Another way is to use data analytics tools to track the number of times each demonstration has been viewed or purchased. This data can be easily obtained from Carlos's database, and he can sort the demonstrations in descending order based on this metric. By doing this, he can easily identify his top five most popular demonstrations and offer them for the next month's cooking demonstrations. In conclusion, Carlos can use data analytics to find his five most popular cooking demonstrations from his database. Sorting the demonstrations based on the number of times each demonstration has been viewed or purchased is the best method for him to use as it is easy to obtain and provides accurate results.

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With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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Answer:

13.9

Step-by-step explanation:

So the average can be defined as: \(average=\frac{sum}{amount}\) and in this context, the sum is the sum of ages on the team, and the amount is the amount players, which is 10.

So to find the sum of people, we simply multiply the average by the amount: \(13.5*10=sum\implies135=sum\)

Since a 15 year old joined, the new sum is now: \(135+15=150\) and the new amount is: \(10+1=11\)

An 11 year old quit, so now the sum is: \(150-11=139\) and the new amount is: \(11-1=10\)

Now let's take the new sum and amount to find the average: \(average=\frac{139}{10}\implies average=13.9\)