"We keep tossing a fair coin n = 10^6 million times, write down the outcomes: it gives a Heads-and-Tails-sequence of length n. We call an integer i special, if the i, i + 1, i + 2, i + 3, . . . , i + 18-th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the i-th element of the sequence. Let X denote the number of special integers i. What is the expected value of X? I also want the numerical value. 5. We rand

Answer:

21 sq ft

Step-by-step explanation:

The formula is 0.5bh; b is the length of the base (6) and h is the height (7). So if you plug in those values, you have 0.5(6)(7). Multiply those and you get 21!

Answer:

The area of the triangle is 21 ft (640.08 centimeters)

The area of the rectangle is 120 ft (3657.6 centimeters)

The area of the whole figure is 141 ft (4297.68 centimeters)

Step-by-step explanation:

The area of a triangle is:

[tex]A = \frac{1}{2}bh[/tex]  b is the base and h is the height.

Plug in what you have

[tex]A= \frac{1}{2}(6)(7)[/tex] multiply 6 by 7

[tex]A = \frac{1}{2} (42)[/tex] divide 42 by 2

[tex]A = \frac{42}{2}[/tex]

[tex]A = 21[/tex]

Now you have to find the area of the rectangle

The area of a rectangle is:

A = bh

Plug in what you have

A = (10)(12)

A = 120

Now add both areas together to get the area of the whole figure

120 + 21 = 141

Answer:

1. 0.869 = 86.9% probability that an average American adult watches more than 300 minutes of television per day.

2. 100% probability that an average American adult watches more than 2,000 minutes of television per week.

Step-by-step explanation:

To solve this question, we need to understand the poisson distribution and the normal distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.

Normal distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

To approximate the Poisson to the normal, we use [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]

1. Find the probability that an average American adult watches more than 300 minutes of television per day.

The mean is 320 minutes per day, so [tex]\lambda = 320, \mu = 320, \sigma = \sqrt{320} = 17.89[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 300. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{300 - 320}{17.89}[/tex]

[tex]Z = -1.12[/tex]

[tex]Z = -1.12[/tex] has a pvalue of 0.131.

1 - 0.131 = 0.869

0.869 = 86.9% probability that an average American adult watches more than 300 minutes of television per day.

2. Find the probability that an average American adult watches more than 2,000 minutes of television per week.

A week has 7 days, so [tex]\lamda = 7*320 = 2240, \mu = 2240, \sigma = \sqrt{2240} = 47.33[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 2000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2000 - 2240}{47.33}[/tex]

[tex]Z = -5.07[/tex]

[tex]Z = -5.07[/tex] has a pvalue of 0

1 - 0 = 1

100% probability that an average American adult watches more than 2,000 minutes of television per week.

Answer:[tex](g,h)=(-2,2)[/tex]

Step-by-step explanation:

Given

Midpoint is [tex](-2,3)[/tex]

Endpoints are [tex]G(g,4)[/tex] and [tex]H(-2,h)[/tex]

Mid point of any two point is given by

[tex]x=\frac{x_1+x_2}{2}[/tex]

and [tex]y=\frac{y_1+y_2}{2}[/tex]

So,[tex]-2=\frac{g+(-2)}{2}[/tex]

[tex]-4=g-2[/tex]

[tex]g=-2[/tex]

Also

[tex]3=\frac{4+h}{2}[/tex]

[tex]6=4+h[/tex]

[tex]h=2[/tex]

Therefore [tex](g,h)=(-2,2)[/tex]

Answer:

- The integral of arctan(x)/x =

C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).

- The radius of convergence is R = 1/x

Step-by-step explanation:

First note that

tan^(-1)x = arctan(x)

And

arctan(x) = Σ [(-1)^n. x^(2n+1)]/(2n+1). From n = 0 to infinity

arctan(x)/x = Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity

∫arctan(x)/x dx = ∫{Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity}dx

= ∫{Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.∫x^(2n)dx

= {Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.x^(2n+1)/(2n+1) + C

= C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).

To obtain the radius of convergence, we apply the ration test

R = Limit as n approaches infinity |a_n/a_(n+1)|

a_n = (-1)^n.x^(2n+1)]/(2n+1)²

a_(n+1) = (-1)^(n+1).x^(2(n+1)+1)]/(2(n+1)+1)²

|a_n/a_(n+1)| = (2(n+1) + 1)²/(2n+1)².x

= (1/x)[1 + 2/(2n+1)]

R = Limit as n approaches infinity |a_n/a_(n+1)|

= R = Limit as n approaches infinity (1/x)[1 + 2/(2n+1)]

R = 1/x

The integration of the arctan (x)/x is C + Σ [(-1)^n x^(2n+1)]/(2n+1)² where n is from 0 to ∞. The radius of convergence is R = 1/x

It is the reverse of differentiation.

The indefinite integral is a power series that will be

[tex]\rm \int \dfrac{\tan^{-1}x }{ x} \ dx[/tex]

We know that the arctan is given as

[tex]\rm \tan^{-1} x = \dfrac{\sum [(-1)^n \ x^{2n+1}]}{(2n+1)}\\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ x^{2n})]}{(2n+1)}\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n}[/tex]

Then we have

[tex]\rm \int \dfrac{\tan^{-1} x }{x}\ dx= \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n} dx\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \int x^{2n}\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)^2} x^{2n + 1} + C[/tex]

To obtain the radius of convergence, then the ration test

[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{a_n}{a_{n+1}}\\\\\\a_n = \dfrac{(-1)^n \ x^{2n+1} }{(2n+1)^2}\\\\\\a_{n+1} = \dfrac{(-1)^{n+1} \ x^{2(n+1)+1} }{(2(n+1)+1)^2}\\\\\\ \dfrac{a_n}{a_{n+1}} = \dfrac{1}{x}(1+\dfrac{2}{2n+1})[/tex]

Then we have

[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{1}{x}(1+\dfrac{2}{2n+1})\\\\\\R = \dfrac{1}{x}[/tex]

More about the integration link is given below.

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Answer:

WHAT IS THE QUESTION WHAT IS X IN WHAT EQUATION!!!!!!!!

Step-by-step explanation:

Answer:

plzz i asked for brainliest on ur other question

Step-by-step explanation:

Answer:

$780 to $1100

Step-by-step explanation:

A confidence interval has two bounds. A lower bound and an upper bound. They are dependent of the sample mean and of the margin of error M.

In this problem:

Sample mean: $940

Margin of error: $160

The lower end of the interval is the sample mean subtracted by M. So it is 940 - 160 = $780

The upper end of the interval is the sample mean added to M. So it is 940 + 160 = $1100

So the answer is

$780 to $1100

Answer:

[tex]940-160=780[/tex]

[tex]940+160=1100[/tex]

So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100

Step-by-step explanation:

For this case we can define the following random variable X as the monthly rent and we know the following properties given:

[tex]\bar X= 940 [/tex] represent the sample mean

[tex] ME = 160[/tex] represent the margin of error

n = 10 represent the sample size

The confidence interval for the true mean is given by:

[tex] \bar X \pm z_{\alpha/2} \sqrt{\frac{\sigma}{\sqrt{n}}}[/tex]

And is equivalent to:

[tex]\bar X \pm ME[/tex]

And for this case if we replace the info given we got:

[tex]940-160=780[/tex]

[tex]940+160=1100[/tex]

So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100

Answer:

Step-by-step explanation:

The question is incomplete because the data is missing, i.e. the probability that you will score 5, 4, 3, 2, 1.

But it is resolved as follows:

[tex]P(x\geq 3) = P(\frac{x - m}{\frac{sd}{\sqrt{n} } } \geq \frac{3 - m}{\frac{sd}{\sqrt{n} }})\\\\[/tex]

where m is the mean and sd is the standard deviation.

the m is calculated by the sum of the multiplication of the score by the probability of this  

that is to say,  

score   probability

  5           0.2

  4           0.3

  3            0.1

  2           0.3

  1             0.1

m = 5*0.2 + 4*0.3 + 3*0.1 + 2*0.3 + 1*0.1

m = 3.2  

However, the standard deviation will be calculated by

sd = [tex]\sqrt{\\}[/tex]∑[tex](x - m)^{2}*p[/tex]

that is, knowing the mean already, we can calculate the standard deviation, following the example:

sd =[tex]\sqrt{[(5-3.2)^2] *0.2 + [(4-3.2)^2] *0.3 + [(3-3.2)^2] *0.1 + [(2-3.2)^2] *0.3 + [(1-3.2)^2] *0.1 }[/tex]

sd = [tex]\sqrt{1.76}[/tex]

sd = 1.327

And also n = 5, because it's 5 scores. We replace in the initial equation:

[tex]P(x\geq 3) = P(Z \geq \frac{3 - 3.2}{\frac{1.327}{\sqrt{5} }})\\\\[/tex]

[tex]P(x\geq 3) = P(Z \geq -0.337)\\\\\\[/tex]

Therefore for the example the number z is -0.337, which if in the normal distribution table corresponds to 0.3520, that is the probability that the average is at least 3, for the example is 35.20 %.

The requried, Il. The voluntary response makes it likely that the most dissatisfied people were the ones to respond. Ill. The response suffers from under coverage. are true. Option A is correct.

The survey is defined as an activity that took the participation of the public in order to improve the service by taking feedback from the targeted public.

here,
As of the given conditions,
The number of people that returned the voluntaries is not a very large number, while the voluntary response increases the likelihood that the most dissatisfied people responded, the response also suffers from under coverage

.

Thus, Both II and III are correct statements. Option A is correct.

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A minimum sample size of 64 business students must be randomly selected to estimate the mean monthly earnings with 95% confidence within $140 of the true population mean, given the population standard deviation of $569.

To find the minimum sample size required to estimate an unknown population mean μ with a certain level of confidence, we can use the formula:

n = (Z*σ/E)^2

Where:

For a 95% confidence level, the Z-score is approximately 1.96. The population standard deviation σ is given as $569. The margin of error E is $140.

Plugging these values into the formula, we get:

n = (1.96*569/140)^2

n = (1114.44/140)^2

n = (7.96)^2

n = 63.4

Since the sample size must be a whole number, we would round up to the next whole number which gives us a minimum sample size of 64 business students that must be randomly selected to estimate the mean monthly earnings of business students at one college with the desired precision and confidence level.

Final answer:

To estimate the population mean with a 95% confidence level and a margin of error of $140, we use the formula n = (Z*σ/E)^2 with σ = $569. Using the z-score for 95% confidence (1.96), the calculation yields 119.44, which we round up to 120 business students needed for the sample.

Explanation:

Calculating Minimum Sample Size for Estimating a Population Mean

To determine the minimum sample size needed to estimate the mean monthly earnings of business students at one college with 95% confidence and a margin of error of $140, we use the formula for the sample size (n). The formula is derived from the properties of a normal distribution and the central limit theorem and is as follows:
n = (Z*σ/E)^2
where:
Z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence),
σ (sigma) is the population standard deviation, and
E is the desired margin of error.

Plugging in the given values of σ = $569 and E = $140, we find:
n = (1.96 * 569 / 140)^2
n ≈ (10.924)^2
n ≈ 119.44

Since we cannot survey a fraction of a person, we round up to the nearest whole number. Therefore, 120 business students must be randomly selected to achieve the desired precision.

Answer:

22%

Step-by-step explanation:

Answer:

22% tax bracket

Step-by-step explanation:

Answer:

The next score he needs to have an overall average of 79 is 89.

Step-by-step explanation:

Gary earned an average score of 77 on his 5 quizzes . The number of score he needs to have an average of 79 can be calculated below.

average score = 77

number of quizzes = 5

sum of Garry score = a

a/5 = 77

cross multiply

a = 77 × 5

a = 385

let

the next score he needs be  b to score an average of 79

average = 79

number of quizzes = 6

385 + b/6 = 79

cross multiply

385 + b = 474

b = 474 - 385

b = 89

The next score he needs to have an overall average of 79 is 89.

Answer:

That should be pentagon, irregular

(5 sides which are not equal)

Hope this helps!

:)

Answer:

(2.5,5)

Step-by-step explanation:

The x coordinate of the midpoint is found by averaging the x coordinates

(-1+6)/2 = 5/2 = 2.5

The y coordinate of the midpoint is found by averaging the y coordinates

(5+5)/2 = 10/2 = 5

Answer:

I believe it is standard form?

Step-by-step explanation:

Answer:  y= - 2(x - 3)(x+5)​  is Factored form

Step-by-step explanation: Quadratic equation forms

Vertex form is y = a(x -h)² + k

Standard form is   y = ax² + bx + c

Factored form is [tex]y = a(x + r_{1} )(x + r_{2} )[/tex]

Answer:

Expected value of company loss = $99.01

Standard deviation = $226.91

Step-by-step explanation:

We first obtain the probability mass function of the company's losses based on the chances of the possible various number of refurbished computers in the customers order.

There are 15 total computers in stock.

There are 4 refurbished computers in stock.

There are 11 new computers in stock

The customer orders 2 computers. If there are no refurbished computers in the order, there are no losses on the company's part.

Probability of no refurbished computers in the order = (11/15) × (10/14) = 0.5238

The customer orders 2 computers. If there is only 1 refurbished computer in the order, there is a loss of $100 on the company's part.

Probability of 1 refurbished computers in the order = [(11/15) × (4/14)] + [(4/15) × (11/14)]

= 0.4191

The customer orders 2 computers. If there are 2 refurbished computer in the order, there is a loss of $1000 on the company's part.

Probability of 2 refurbished computers in the order = [(4/15) × (3/14)] = 0.0571

So, the Probabilty function of random variable X which represents the possible losses that the company can take on is given as

X | P(X)

0 | 0.5238

100 | 0.4191

1000 | 0.0571

Expected value of company loss is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable or sample space

pᵢ = probability of each variable

E(X) = (0 × 0.5238) + (100 × 0.4191) + (1000 × 0.0571) = $99.01

Standard deviation is obtained as the square root of variance.

Variance = Var(X) = Σx²p − μ²

where μ = E(X) = 99.01

Σx²p = (0² × 0.5238) + (100² × 0.4191) + (1000² × 0.0571) = 0 + 4191 + 57,100 = 61,291

Var(X) = Σx²p − μ²

Var(X) = 61291 − 99.01² = 51,488.0199

Standard deviation = √(51,488.0199) = $226.91

Hope this Helps!!!

Answer:

A) 0.015

B) 4 bous6

Step-by-step explanation:

That at most 2 of the selected children are male means that number of male must be less than or equal to 2

Pr (male) = 0.506

Pr (female) = 0.494

Pr (at most 2 males) = 0.506 x 0.506 x 0.494 x 0.494 x 0.494 x 0.494 = 0.015

Expected number of boys in a randomly selected number of 6 is

0.506 x 6 = 3.03

We round off to 4 boys

Answer:

No

Step-by-step explanation:

I got it right on Instruction

Answer:

its No trust me

Step-by-step explanation:

Answer:

x=±√7 -2

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

The required value of the quadratic function which is determined by the using quadratic formula would be [tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex]   which is the correct answer would be an option (B).

The quadratic function is defined as a function containing the highest power of a variable is two.

We have been given that quadratic function as

5x = 6x² – 3

⇒ 6x² - 5x  - 3 = 0

Compare the given function to the standard quadratic function

f(x) = ax² + b x + c = 0.

We get a = 6, b = -5 and c = -3

Using the quadratic formula to solve the above quadratic function

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of a = 6, b = -5 and c = -3 in the quadratic formula

[tex]x = \dfrac{-(-5)\pm\sqrt{-5^2-4\times6\times-3}}{2\times6}[/tex]

[tex]x = \dfrac{5\pm\sqrt{25+72}}{12}[/tex]

[tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex]

Therefore, the correct answer would be an option (B).

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Answer:

The correct answer is option (d).

Step-by-step explanation:

From the given example, the statement that is correct is, this confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.

This is because, In this scenario or setup, all the students are already part of the data. This is not a sample from a l population that is larger, but probably, the population itself.

Answer: A, D, E

Step-by-step explanation

Solving the equation p = 2(a + b) for b involves two steps: first dividing each side by 2, then subtracting 'a' from each side. This results in the final equation 'b = (p/2) - a'.

To solve the equation p = 2(a + b) for b, you would first divide each side by 2 to isolate 'a + b'.

This gives you p/2 = a + b. Next, to isolate 'b', you would subtract 'a' from each side of the equation.

This gives you b = (p/2) - a, which is your final, simplified expression for 'b' in terms of 'p' and 'a'.

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Answer:

506.58

Step-by-step explanation:

Your welcome ;w;

Answer:

Mean = sum of elements/number of elements = (9 + 8 + 12 + 6 + 10)/5 = 9

Hope this helps!

:)

Answer:

9

Step-by-step explanation:

The mean is also called the average

Add up all the number

(9+8+ 12+ 6+ 10)

45

Then divide by the number of numbers

45/5 = 9

Answer:

The probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.

Step-by-step explanation:

Let the random variable X represent the lengths of the classes.

The random variable X is uniformly distributed within the interval 49.0 and 54.0 minutes.

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

Compute the probability that a given class period runs between 50.75 and 51.25 minutes as follows:

[tex]P(50.75<X<51.25)=\int\limits^{51.25}_{50.75}{\frac{1}{54-49}}\, dx\\\\=\frac{1}{5}\times [x]^{51.25}_{50.75}\\\\=\frac{51.25-50.75}{5}\\\\=0.10[/tex]

Thus, the probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.

Answer: 0.050

I just did it and i got it right.

Answer:

E. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y

Step-by-step explanation:

Confidence interval formula is given as

CI = \bar{x} \pm z*(\sigma/\sqrt{n})

Here, we can see that the width of confidence interval is z*(\sigma/\sqrt{n}) , which is dependent only on z critical value, standard deviation (sigma) and sample size (n)

This simply entails that either z or n or both are greater for x as compared to y.

Option E is correct answer because x and y can have sample sizes, but if the z critical is greater for x, then the width will be larger.

The confidence interval tells about the probability where a value falls between a range. The interval constructed from X is greater than that of Y because the z value for X is greater than Y.  

[tex]CI = \bar{x} \pm z\times (\dfrac {\sigma}{\sqrt{n}})[/tex]

Where,

[tex]CI[/tex] = confidence interval

[tex]\bar{x}[/tex] = sample mean

[tex]z[/tex] = confidence level value

[tex]{s}[/tex] = sample standard deviation

[tex]{n}[/tex] = sample size

From the formula, confidence interval is the the directly proportional to the confidence level value, standard deviation, and population.

Since the standard deviation, and the population is constant,

Therefore, the interval constructed from X is greater than that of Y because the z value for X is greater than Y.  

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Answer:

Each friend would receive Half (1/2) of an apple.

Each friend receives 1/2 apple.

The unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Total number of friends = 6

Total number of apples = 3

The apple gets each friend is determined in the following steps given below.

[tex]\rm Each \ friend =\dfrac{Total \ Apple}{Total \ frineds}\\\\Each \ friend = \dfrac{3}{6}\\\\Each \ friend =\dfrac{1}{2}[/tex]

Hence, each friend receives 1/2 apple.

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Answer:

y=2x+1

Step-by-step explanation:

A(1;3)  and m=2

y-yA=m(x-xA)

y-3=2(x-1)

y-3=2x-2

y=2x+1; or 2x-y+1=0

Answer:

0.104 (10.4%)

Step-by-step explanation:

[tex]UCL = \bar{p}+z(\sigma)[/tex]

[tex]\sigma = p(1-)) Vn = 1.02(1-202)) 5[/tex] = 0.028

[tex]\thereforeUCL = .02+(3x0.028)[/tex] = 0.104

[tex]\thereforeUCL[/tex]= 10.4%