An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (An ordinary (fair) coin is tossed 3 times. Ou) and "tails" () which we write , , etc. For each outcome, let be the random variable counting the number of tails in each outcome. For example, if the outcome is , then . Suppose that the random variable is defined in terms of as follows: . The values of are thus:Outcome Value of Calculate the probability distribution function of , i.e. the function . First, fill in the first row with the values of . Then fill in thevalue x of X Px(X)

Answer:

A= 69

Step-by-step explanation:

A= h*b/2= (6*23)/2=69

Answer:

A = 69 [tex]ft^{2}[/tex]

Step-by-step explanation:

The formula utilised to determine the area of a triangle is:

A = [tex]\frac{1}{2}[/tex] * b * h

The base and height are given, and thus, can easily be substituted for in the formula to find the area.

A = [tex]\frac{1}{2}[/tex] * 23 * 6

A = 69 [tex]ft^{2}[/tex]

Answer:

60

Step-by-step explanation:

15cubes assuming 3rows of 5 cubes in one layer so volume of first layer is 3x5x1 =15

4 layers means 4 times or 4 inch in height, either way 4x15 = 60

Answer:

75

Step-by-step explanation:

Answer:

d. No, because the two populations from which the samples are selected do not appear to be normally distributed.

Step-by-step explanation:

First, the assumptions of an independent-measures t test are as follows:

1. The data is continuous

2. Only two groups are compared

3. The two groups should be independent

4. The groups should have equal variance

5. The data should be normally distributed

In this case, the 5th assumption has been violated because scores in the two samples are distributed in different ranges in two samples. So the outliers in the scores may be exist. Therefore, it would not be valid for the professor to use the independent-measures t test because the two populations from which the samples are selected do not appear to be normally distributed.

Answer:

better golf scores

Step-by-step explanation:

i did the quiz just a few secs ago

According to the excerpt, seeing the "hole as bigger" has the benefit of improving gold scores. The right answer is D.

Visualization is the capacity to create mental images of situations and things using one's imagination.

Visualization enhanced results in the excerpt provided.

Golfers typically earned better gold scores when they saw the golf hole as larger circles.

The result of seeing the "hole as greater" is that you will receive better gold scores.

Learn more about visualization at:

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Answer:

x = 1/2( ln(4) -5)

Step-by-step explanation:

e ^ 2x+5 =4

Take the natural log of each side

ln(e ^ 2x+5) =ln(4)

2x+5 = ln(4)

Subtract 5 from each side

2x = ln(4) - 5

Divide by 2

2x/2 = (ln(4) -5)/2

x = 1/2( ln(4) -5)

Answer:

its c on edge.

Answer:

2/15 cups of cheese

Step-by-step explanation:

Because you are eating 2/5 of the recipe you have to multiply the values

2/5*1/3 = 2/15

Answer: $350 because you multiply 140 and 100 then divide 40

Answer:

The hourly growth rate is of 3.15%

Step-by-step explanation:

The population of bacteria after t hours can be modeled by the following formula:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial population and r is the hourly growth parameter, as a decimal.

A sample of 3000 bacteria selected from this population reached the size of 3145 bacteria in one and a half hours. Find the hourly growth rate parameter.

This means that [tex]P(0) = 3000, P(1.5) = 3145[/tex]

We use this to find r.

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]3145 = 3000e^{1.5r}[/tex]

[tex]e^{1.5r} = \frac{3145}{3000}[/tex]

[tex]\ln{e^{1.5r}} = \ln{\frac{3145}{3000}}[/tex]

[tex]1.5r = \ln{\frac{3145}{3000}}[/tex]

[tex]r = \frac{\ln{\frac{3145}{3000}}}{1.5}[/tex]

[tex]r = 0.0315[/tex]

The hourly growth rate is of 3.15%

Step-by-step explanation:

= 5- 2 + 12 /4

= 5 -2 + 3

= 8- 2

= 6

Answer:

6

Explanation:

What you do is you take 12 divided by 4 and you get 3. The equation is now 5-2+3, you subtract 2 from 5 and get 3. Now you have 3 plus 3 which gets you 6.

Answer:

Arlin has to give lauren 1.37

Step-by-step explanation:

9.37 + 6.63 / 2 = 16 / 2 = 8

9.37 - 8 = 1.37

Answer:

$1.37

Step-by-step explanation:

I would start by adding up the total money between them. $9.37 + $6.63 = $16.00. They want the same amount of money, so divide the total by two.

$16.00/2 = $8.00.

Now take the difference between how much Arlin had ($9.37) and how much she has now ($8.00).

$9.37 - $8.00 = $1.37

Answer:

The significance level α is 0.02.

Step-by-step explanation:

A hypothesis test for single mean can be performed to determine whether the average starting salary for a 21-25 year old college grad exceeds $52,000 per year.

The hypothesis is defined as follows:

H₀: The average starting salary for a 21-25 year old college grad does not exceeds $52,000 per year, i.e. µ ≤ 52,000.

Hₐ: The average starting salary for a 21-25 year old college grad exceeds $52,000 per year, i.e. µ > 52,000.

The information provided is:

σ = $5,745

n = 65

Also, if [tex]\bar X>\$53,460[/tex] then the null hypothesis will be rejected.

Here, we need to compute the value of significance level α, the type I error probability.

A type I error occurs when we reject a true null hypothesis (H₀).

That is:

α = P (type I error)

α = P (Rejecting H₀| H₀ is true)

   [tex]=P(\bar X>53460|\mu \leq 52000)[/tex]

   [tex]=P[\frac{\bar X-\mu_{0}}{\sigma/\sqrt{n}}>\frac{53460-52000}{5745/\sqrt{65}}][/tex]

   [tex]=P(Z>2.05)\\=1-P(Z<2.05)\\=1-0.97982\\=0.02018\\\approx0.02[/tex]

*Use a z-table for the probability.

Thus, the significance level α is 0.02.

Answer:

Each notebook costs $2

Step-by-step explanation:

We have to find the amount she spent on each notebook.

22-10=12

We know she spent $12 on six notebooks

We need to divide to find the answer

12/6=2

Each notebook costs $12

Answer:

$2

Step-by-step explanation:

First subtract 10 from 22 to get the price she spent on notebooks which is $12.

Then divide 12 by 6 to get the price she spent on each which is, $2

Answer:

The t-test for one mean can be safely used for this situation.

Step-by-step explanation:

A statistical experiment is conducted to determine if a particular training program would improve physical fitness.

The objective of the experiment was to determine if there is some evidence that the maximum oxygen uptake of the sample of students differed from the general population of untrained subjects, whose maximum oxygen uptake is known to be 45 ml/kg/min on average.

The hypothesis is defined as:

H₀: The population mean is 45 ml/kg/min, i.e. μ = 45.

Hₐ: The population mean is different from 45 ml/kg/min, i.e. μ ≠ 45.

The test for single mean can be either using the z-distribution or the t-distribution.

The z-distribution is used if it provided that:

The t-distribution is used if :

To use a t-distribution for a single mean test the following assumptions are to made:

In this case we will use a t-distribution since there is no information about the population standard deviation.

The sample of 35 students are randomly selected for the training program.

The maximum oxygen uptake of every student is independent of the others.

Thus, the t-test for one mean can be safely used for this situation.

Answer:

The correct option is 16.041 ounces.

Step-by-step explanation:

A single mean test can be used to determine whether the average amount of shampoo per bottle is 16 ounces.

The hypothesis can be defined as:

H₀: The average amount of shampoo per bottle is 16 ounces, i.e. μ = 16.

Hₐ: The average amount of shampoo per bottle is different from 16 ounces, i.e. μ ≠ 16.

The information provided is:

[tex]n=64\\\sigma=0.20\\\alpha =0.10[/tex]

We can compute a 90% confidence interval to determine whether the population mean is 16 ounces or not.

Since the population standard deviation is known we will compute the z-interval.

The critical value of z for 90% confidence interval is:

[tex]z_{0.05}=1.645[/tex]

*Use a z-table.

Compute the 90% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\\[/tex]

Since the sample size is quite large, according to the law of large numbers the on increasing the sample size, the mean of the sample approaches the whole population mean.

So, the 90% confidence interval estimate for sample mean is:

[tex]CI=\mu\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\\=16\pm 1.645\times \frac{0.20}{\sqrt{64}}\\=16\pm0.041125\\=(15.958875, 16.041125)\\\approx (15.959, 16.041)[/tex]

Thus, the correct option is 16.041 ounces.

Answer:

y = -x+3

Step-by-step explanation:

We have two points so we can find the slope

m =(y2-y1)/(x2-x1)

    (1-2)/(2-1)

    -1/1

 The slope is -1

We can use the slope intercept form of the equation

y = mx+b where m is the slope and b is the y intercept

y = -x+b

Substitute a point into the equation to find b

2 = -1 +b

Add 1 to each side

2+1 =-1+1 +b

3 =b

y = -x+3

D : 2350

Step-by-step explanation:

Given,

The grocery price: 350

The amount lady gave: 2000

The amount returned to the lady: 1650

Also, given that the shopkeeper of the next shop comes with the Rs.2000 note saying "duplicate" *and takes his money back.

Therefore, the loss would be the sum of two items:

1) The shopkeeper have to return the 2000 rupees to the next shopkeeper. Therefore, he suffers the loss of 2000.

2) He also sold the grocery worth 350 rupees. Therefore, it would be the extra loss of 350 rupees.

Hence, the shopkeeper faced the loss of 2000 + 350 = 2350 rupees.  

Answer:

4 sisters

Step-by-step explanation:

-This is a logic question.

-Given that she has 3 sisters, it only means that the 4 are siblings of the same family.

-As such, eaxh sister can correctly claim to have 3 sisters.

Hence, there is a total of 4 sisters.

See the attached picture

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

Let [tex]\mu[/tex] = true average writing lifetime under controlled conditions

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 10 hr   {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 hr    {means that the true average writing lifetime under controlled conditions is less than 10 hr}

The test statistics that is used here is one-sample t test statistics;

                           T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean

             s = sample standard deviation

             n = sample size of pens = 18

          n - 1 = degree of freedom = 18 -1 = 17

Now, the decision rule based on the critical value of t is given by;

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as  -1.74 < 0.57, so we fail to reject our null hypothesis.

Answer:

a) 0.75

b) 0.4375

c) 0.5714

Step-by-step explanation:

Solution:-

- The events are defined as follows:

Event A : The Asian project is successful

Event B : The European project is successful

- The two given events are independent. Their respective probabilities are:

 P ( A ) = 0.25

 P ( B ) = 0.25

- The conditional probability for European project to fail given that asian project also failed.

- The probability can be expressed as:

            P ( B ' / A ' ) = P ( A' & B' ) / P ( A' )

- According to the property of independent events we have:

            P ( A ' & B ' ) = ( 1 - P ( A ) )* ( 1 - P ( B ) )

Therefore,

            P ( B ' / A ' ) = [ ( 1 - P ( A ) )* ( 1 - P ( B ) ) ] /  ( 1 - P ( A ) )

            P ( B ' / A ' ) = 1 - P ( B )

Answer: The probability is simply the failure of event (B) : The european project fails = 0.75.

b) The probability that at-least one of the two projects will successful consists of (either A or B is successful) or  ( Both are successful). We can mathematically express it as:

          P ( At-least 1 project is success ) = P ( A U B ) + P ( A & B )

          P ( At-least 1 project is success ) = P ( A )*(1 - P ( B )) + P ( B )*(1 - P ( A )]+ P ( A ) * P ( B )

                                                                = 2*0.25*0.75 + 0.25^2

                                                                = 0.4375

c ) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful?

- We can mathematically express the required conditional probability as follows with help of  part b):

           P ( A / At-least 1 project is success ) = P ( A & any at-least 1 is success) / P ( At-least 1 project is success )

- The probability of P ( A & any at-least 1 is success), consists of event A success and event B fails or both are a success:

          P ( A & any at-least 1 is success) = P ( A )*( 1 - P ( B ) ) + P ( A )*P ( B )

                                                                 = 0.25*0.75 + 0.25^2

                                                                 = 0.25

- The conditional probability can now be evaluated:

          = P ( A & any at-least 1 is success) / P ( At-least 1 project is success )

          = 0.25 / 0.4375

          = 0.5714

Answer: The minimum reliability for the second stage be 0.979.

Step-by-step explanation:

Since we have given that

Probability for the overall rocket reliable for a successful mission = 97%

Probability for the first stage = 99%

We need to find the minimum reliability for the second stage :

So, it becomes:

P(overall reliability) = P(first stage ) × P(second stage)

[tex]0.97=0.99\times x\\\\\dfrac{0.97}{0.99}=x\\\\0.979=x[/tex]

Hence, the minimum reliability for the second stage be 0.979.

Using probability of independent events, it is found that the minimum reliability for the second stage must be of 97.98%.

If two events, A and B, are independent, the probability of both events happening is the multiplication of the probability of each happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this problem:

Then:

[tex]P(A \cap B) = P(A)P(B)[/tex]

[tex]0.97 = 0.99P(B)[/tex]

[tex]P(B) = \frac{0.97}{0.99}[/tex]

[tex]P(B) = 0.9798[/tex]

Hence, the minimum reliability for the second stage must be of 97.98%.

A similar problem is given at https://brainly.com/question/24174994

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16[/tex]  

And rounded up we have that n=385

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

We can use as an estimator for p [tex]\hat p =0.5[/tex]. And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16[/tex]  

And rounded up we have that n=385

Answer:

the answer to the question is 3/5

Answer:

What does this mean 31>28

Step-by-step explanation:

Final answer:

The expression 31>28 means that 31 is greater than 28, which is a basic mathematical comparison used widely across various contexts, from simple arithmetic to data analysis and the mnemonic for remembering the number of days in each month.

Explanation:

The expression 31>28 is a mathematical comparison indicating that the number 31 is greater than the number 28. This can be applied in various contexts, such as comparing quantities, ages, temperatures, or even the number of days in different months. For example, using the knuckle mnemonic, months with 31 days are more than those with 28 days (February, typically), illustrating a practical application of this comparison.

In statistics and data analysis, understanding comparative values like this is crucial. It helps in analyzing data intervals, as in the provided reference, where different age intervals are being compared based on the number of data values they contain. This fundamental concept of comparison underpins much of mathematical reasoning and data analysis.

Answer:

12

Step-by-step explanation:

3x4=12

Answer:

12

Step-by-step explanation:

Multiply the number of bags times the apples per bag

4*3 = 12

He needs 12 apples

If no other money is added or withdrawn from the account how much will be in the account after 10 years is $4,440.73.

Using this formula

Amount=Principla(1+Interest rate)^ Time

Let plugm in the formula]

Amount=$3,000(1+0.04)^10

Amount=$3,000(1.04)^10

Amount-$3,000(1.4802442849)

Amount=$4,440.73

Therefore how much will be in the account after 10 years is $4,440.73.

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Polynomials are classified by their degree and number of terms. x³-8 is a 3rd degree binomial, 24 is a 0th degree monomial, 2x⁴-x³+5x²+x-7 is a 4th degree quintic, and 10x is a 1st degree monomial.

Polynomials can be classified by their degree (the highest power of the variable) and by the number of terms they contain. This classification is done as follows:

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Polynomials are classified by degree and number of terms: [tex]x^3[/tex]- 8 is a cubic binomial, 24 is a zero-degree monomial, [tex]2x^4 - x^3 + 5x^2[/tex] + x - 7 is a quartic quintic, and 10x is a linear monomial.

To classify polynomials by degree and number of terms, we check its highest exponent and count its terms:

[tex]x^3[/tex] - 8: This is a binomial (two terms) and its degree is 3 because the highest exponent of x is 3.

24: This is a monomial (one term) and its degree is 0 since it is a constant.

[tex]2x^4 - x^3 + 5x^2[/tex] + x - 7: This is a polynomial of five terms, so it's called a quintic. Its degree is 4 because the highest exponent of x is 4.

10x: This is a monomial (one term) and its degree is 1 because x is to the first power.

The classification is based on the degree of the polynomial, which is determined by the highest power of the variable x present in the equation, and the number of terms present in the polynomial (monomial for one term, binomial for two terms, and so on).

Answer:

The probability that the mean is less than 110

P(x⁻<110) =0.5

Step-by-step explanation:

Explanation:-

Given the standard deviation of the Population' σ' = 1250

Given sample size 'n' = 350

The standard error of the mean determined by

                                                                             [tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]

                                             Standard error = [tex]\frac{1250}{\sqrt{350} } = 66.8153[/tex]

  by using normal distribution    [tex]z = \frac{x -mean}{S.E}[/tex]

                                         [tex]z = \frac{x^{-} -110}{66.8}[/tex]

                                   cross multiplication  66.8z = x⁻-110

                                                                         x⁻  =  66.81Z+110

P(x⁻<110)=P(66.81Z+110<110)

             = P(66.81Z < 110-110)

            = P(66.81Z<0)

           = P(Z<0)

           = 0.5- A(z₁)

          = 0.5 - A(0)  (here z₁=0)

         = 0.5 -0.00

        =0.5

Conclusion:-                            

The probability that the mean is less than 110

P(x⁻<110) =0.5

Answer:

90% confidence interval: (22.35,23.45)

Step-by-step explanation:

We are given the following in the question:

Sample mean, [tex]\bar{x}[/tex] = 22.9 years

Sample size, n = 20

Alpha, α = 0.10

Population standard deviation, σ = 1.5 years

90% Confidence interval:

[tex]\bar{x} \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]

Putting the values, we get,

[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.64[/tex]

[tex]22.9 \pm 1.64(\dfrac{1.5}{\sqrt{20}} )\\\\ = 22.9 \pm 0.55 \\\\= (22.35,23.45)[/tex]

(22.35,23.45) is the required 90% confidence interval for population mean age.

The 90% confidence interval for the population mean age, from the given data, is approximated to be between 22.46 years and 23.34 years.

To construct a 90% confidence interval of the population mean age, we will use the formula for the confidence interval, which is sample mean ± Z-score * (Standard deviation/ sqrt (sample size)), where the Z-score is based on the confidence level. For 90%, the Z-score is 1.645.

So in this case, the sample mean is 22.9 years, the known standard deviation is 1.5 years, and the sample size (n) is 20. Plugging these values into the formula gives:

22.9 ± 1.645 * (1.5 / sqrt (20))

When you calculate, it will give an interval of about 22.46 years to 23.34 years. Hence the 90% confidence interval for the population mean age is 22.46 years to 23.34 years.

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Answer:

1 cm cubed

Step-by-step explanation:

The volume of a rectangular prism is found by the equation: [tex]V=lwh[/tex] , where [tex]l[/tex] is the length, w is the width, and h is the height.

Here, our dimensions are 2 by 1/4 by 2. So: [tex]l=2,w=1/4,h=2[/tex].

Substituting these into the equation, we have:

[tex]V=2*(1/4)*2=1[/tex]

Thus, the volume is 1 cm cubed.

Hope this helps!

Answer:

1

Step-by-step explanation:

2*2=4

4*1/4=1

multiplying 1/4 is the same as dividing by 4