You are dealt a hand of three​ cards, one at a time. Find the probability of each of the following. ​a) The first heart you get is the third card dealt. ​b) Your cards are all diamonds. ​c) You get no aces. ​d) You have at least one heart.

Final answer:

The statement regarding the determinant of a square matrix A being the product of its diagonal entries is incorrect. The determinant of a 2×2 matrix is calculated as the product of diagonal entries minus the product of off-diagonal entries.

Explanation:

The determinant of a square matrix A is not always the product of the diagonal entries in A. For instance, a 2×2 matrix has the determinant given by det(A) = a11a22 - a12a21, which involves the product of the diagonal entries minus the product of the off-diagonal entries. Therefore, the correct choice is:

B. The statement is false because the determinant of the 2×2 matrix A = [[a, b], [c, d]] is not equal to the product of the entries on the main diagonal of A. In fact, the determinant is ad - bc.

Example: For matrix A = [[1,2], [3,4]], the determinant is 1×4 - 2×3, which equals -2, not the product of the diagonal entries (1 and 4), which would be 4.

Answer:

A

Step-by-step explanation:

change 76% to decimal and multiply by 15

.76*15 = 11.4

11.4 is fewer than 12.

Answer:

a) [tex]P=1-\frac{\lambda}{\mu}=1-\frac{20}{30}=0.33[/tex] and that represent the 33%

b) [tex]p_x =\frac{\lambda}{\mu}=\frac{20}{30}=0.66[/tex]

c) [tex]L_s =\frac{20}{30-20}=\frac{20}{10}=2 people[/tex]

d) [tex]L_q =\frac{20^2}{30(30-20)}=1.333 people[/tex]

e) [tex]W_s =\frac{1}{\lambda -\mu}=\frac{1}{30-20}=0.1hours[/tex]

f) [tex]W_q =\frac{\lambda}{\mu(\mu -\lambda)}=\frac{20}{30(30-20)}=0.0667 hours[/tex]

Step-by-step explanation:

Notation

P represent the probability that the employee is idle

[tex]p_x[/tex] represent the probability that the employee is busy

[tex]L_s[/tex] represent the average number of people receiving and waiting to receive some information

[tex]L_q[/tex] represent the average number of people waiting in line to get some information

[tex]W_s[/tex] represent the average time a person seeking information spends in the system

[tex]W_q[/tex] represent the expected time a person spends just waiting in line to have a question answered

This an special case of Single channel model

Single Channel Queuing Model. "That division of service channels happen in regards to number of servers that are present at each of the queues that are formed. Poisson distribution determines the number of arrivals on a per unit time basis, where mean arrival rate is denoted by λ".

Part a

Find the probability that the employee is idle

The probability on this case is given by:

In order to find the mean we can do this:

[tex]\mu = \frac{1question}{2minutes}\frac{60minutes}{1hr}=\frac{30 question}{hr}[/tex]

And in order to find the probability we can do this:

[tex]P=1-\frac{\lambda}{\mu}=1-\frac{20}{30}=0.33[/tex] and that represent the 33%

Part b

Find the proportion of the time that the employee is busy

This proportion is given by:

[tex]p_x =\frac{\lambda}{\mu}=\frac{20}{30}=0.66[/tex]

Part c

Find the average number of people receiving and waiting to receive some information

In order to find this average we can use this formula:

[tex]L_s= \frac{\lambda}{\lambda -\mu}[/tex]

And replacing we got:

[tex]L_s =\frac{20}{30-20}=\frac{20}{10}=2 people[/tex]

Part d

Find the average number of people waiting in line to get some information.

For the number of people wiating we can us ethe following formula"

[tex]L_q =\frac{\lambda^2}{\mu(\mu-\lambda)}[/tex]

And replacing we got this:

[tex]L_q =\frac{20^2}{30(30-20)}=1.333 people[/tex]

Part e

Find the average time a person seeking information spends in the system

For this average we can use the following formula:

[tex]W_s =\frac{1}{\lambda -\mu}=\frac{1}{30-20}=0.1hours[/tex]

Part f

Find the expected time a person spends just waiting in line to have a question answered (time in the queue).

For this case the waiting time to answer a question we can use this formula:

[tex]W_q =\frac{\lambda}{\mu(\mu -\lambda)}=\frac{20}{30(30-20)}=0.0667 hours[/tex]

To find the probability that the employee is idle, use the formula P(idle) = e^(-λ) where λ = arrival rate * service time. To find the proportion of the time the employee is busy, subtract the probability that the employee is idle from 1. To find the average number of people receiving and waiting to receive information, use the formulas arrival rate * service time and arrival rate * average time spent in system. To find the average time a person spends seeking information and just waiting in line, add the average time to answer a question to the average waiting time.

To find the probability that the employee is idle, we need to find the rate at which people arrive at the information desk and the average time it takes to answer a question. The rate at which people arrive follows a Poisson distribution with a rate of 20 per hour. This means that the average time between arrivals is 1/20 of an hour. The average time to answer a question is 2 minutes, which is equivalent to 2/60 = 1/30 of an hour.

The probability that the employee is idle can be calculated using the formula:

P(idle) = e^(-λ) where λ = arrival rate * service time

Substituting the given values:

P(idle) = e^(-(1/20)(1/30))

P(idle) = e^(-1/600) ≈ 0.998335

Therefore, the probability that the employee is idle is approximately 0.998335.

(b) To find the proportion of the time the employee is busy, we can subtract the probability that the employee is idle from 1:

P(busy) = 1 - P(idle)

P(busy) = 1 - 0.998335 ≈ 0.001665

Therefore, the proportion of the time the employee is busy is approximately 0.001665.

(c) The average number of people receiving information can be calculated using the formula:

Average number of people receiving information = arrival rate * service time

Substituting the given values:

Average number of people receiving information = 20 * (1/30)

Average number of people receiving information = 2/3 ≈ 0.6667

Therefore, the average number of people receiving information is approximately 0.6667.

(d) The average number of people waiting in line to get information can be calculated using Little's Law:

Average number of people waiting in line = arrival rate * average time spent in system

The average time spent in the system can be calculated by adding the average time to answer a question to the average waiting time:

Average time spent in the system = average time to answer a question + average waiting time

The average waiting time can be calculated using Little's Law:

Average waiting time = average number of people waiting in line / arrival rate

Substituting the given values:

Average waiting time = (1/20) / (1/30) = 3/2 = 1.5 minutes

Average time spent in the system = 2 minutes + 1.5 minutes = 3.5 minutes

Substituting the values into Little's Law:

Average number of people waiting in line = 20 * (3.5/60) = 1.1667

Therefore, the average number of people waiting in line to get information is approximately 1.1667.

(e) The average time a person spends in the system can be calculated by adding the average time to answer a question to the average waiting time:

Average time in system = average time to answer a question + average waiting time = 2 minutes + 1.5 minutes = 3.5 minutes

Therefore, the average time a person seeking information spends in the system is 3.5 minutes.

(f) The expected time a person spends just waiting in line to have a question answered can be calculated using Little's Law:

Expected time in queue = average number of people waiting in line / arrival rate

Substituting the values:

Expected time in queue = (1/20) minutes / (1/30) = 30/20 = 1.5 minutes

Therefore, the expected time a person spends just waiting in line to have a question answered is 1.5 minutes.

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Answer: 1.25

Step-by-step explanation:

Convert it lol I don’t know how to say it? But also you can look it up if needed

Answer:

1.25

Step-by-step explanation:

Convert it lol I don’t know how to say it? But also you can look it up if needed

Answer:

1.2

Step-by-step explanation:

Given that X is Normally distributed random variable with an unknown mean μ and known standard deviation 6

Hence we can say for a sample of size 100, the sample mean will have a std deviation of = [tex]\frac{6}{\sqrt{100} } =0.6[/tex]

Since population std deviation is known we can use Z critical value for finding out the confidence interval

For 95% using (68-95-99.7 rules) we have z critical value =2

Hence margin of error =2(std error) = 1.2

Confidence interval 95%

Lower bound = Mean - margin of error = Mean -1.2

UPper bound = Mean +1.2

Hence , 95% of all of these values of x should lie within a distance of __1.2___ from μ .

Final answer:

95% of the sample means will lie within approximately 1.176 units from the population mean μ when the standard deviation is 6 and the sample size is 100.

Explanation:

The question pertains to the concept known as the Central Limit Theorem in statistics, which allows us to make inferences about the population mean μ from the distribution of sample means. Since x is normally distributed with a known standard deviation and we take repeated samples to calculate the sample means, we can say that 95% of the sample means will lie within 1.96 standard errors of the population mean μ.

Using the formula for the standard error σ/√n, where σ is the known standard deviation and n is the sample size, we get the standard error as 6/√100 = 0.6. Therefore, 95% of the sample means will lie within 1.96 * 0.6, which is approximately 1.176 units from μ.

Answer:

Remember, a basis for the row space of a matrix A is the set of rows different of zero of the echelon form of A.

We need to find the echelon form of the matrix augmented matrix of the system A2x=b2

[tex]B=\left[\begin{array}{cccc}1&2&3&1\\4&5&6&1\\7&8&9&1\\3&2&4&1\\6&5&4&1\\9&8&7&1\end{array}\right][/tex]

We apply row operations:

1.

We obtain the matrix

[tex]\left[\begin{array}{cccc}1&2&3&1\\0&-3&-6&-3\\0&-6&-12&-6\\0&-4&-5&-2\\0&-7&-14&-5\\0&-10&-20&-8\end{array}\right][/tex]

2.

We obtain the matrix

[tex]\left[\begin{array}{cccc}1&2&3&1\\0&-3&-6&-3\\0&0&0&0\\0&0&3&2\\0&0&0&2\\0&0&0&2\end{array}\right][/tex]

3.

we exchange rows three and four of the previous matrix and obtain the echelon form of the augmented matrix.

[tex]\left[\begin{array}{cccc}1&2&3&1\\0&-3&-6&-3\\0&0&3&2\\0&0&0&0\\0&0&0&2\\0&0&0&2\end{array}\right][/tex]

Since the only nonzero rows of the augmented matrix of the coefficient matrix are the first three, then the set

[tex]\{\left[\begin{array}{c}1\\2\\3\end{array}\right],\left[\begin{array}{c}0\\-3\\-6\end{array}\right],\left[\begin{array}{c}0\\0\\3\end{array}\right] \}[/tex]

is a basis for Row (A2)

Now, observe that the last two rows of the echelon form of the augmented matrix have the last coordinate different of zero. Then, the system is inconsistent. This means that the system has no solutions.

Answer:

22m

Step-by-step explanation:

Let height of flagpole=h

AB==17 m

[tex]\angle CAD=37^{\circ}11'=37+\frac{11}{60}=37.183^{\circ}[/tex](1 degree= 60 minute)

[tex]\angle B=25^{\circ}43'=25+\frac{43}{60}=25.72^{\circ}[/tex]

We have to find the approximate height of the flagpole.

In triangle CDA,

[tex]\frac{CD}{DA}=tan\theta=\frac{Perpendicular\;side}{Base}[/tex]

[tex]\frac{h}{DA}=tan37.183^{\circ}[/tex]

[tex]h=DA(0.759)[/tex]

In triangle CDB,

[tex]tan 25.72^{\circ}=\frac{CD}{DB}[/tex]

[tex]0.482=\frac{h}{DA+17}[/tex]

[tex]0.482DA+8.194=h[/tex]

Substitute the value

[tex]0.482DA+8.194=0.759DA[/tex]

[tex]8.194=0.759DA-0.482DA[/tex]

[tex]8.194=0.277DA[/tex]

[tex]DA=\frac{8.194}{0.277}=29.58[/tex]

Substitute the value

[tex]h=29.58 \times 0.759=22.45 m\approx 22m[/tex]

Hence, the height of the flagpole=22 m

The approximate height of the flagpole is 21.33 meters, calculated using trigonometry and the observed angles and distances.

To find the height of the flagpole, we can use trigonometry, specifically the tangent function, along with the given angles and the distance from the observer's initial position to the flagpole.

Step 1:

Calculate the tangent of the observed angles:

Let (h) be the height of the flagpole.

For the first observation:

[tex]\[ \tan(37^\circ 11') = \frac{h}{d} \][/tex]

For the second observation:

[tex]\[ \tan(25^\circ 43') = \frac{h}{d + 17} \][/tex]

Step 2:

Solve for (h):

First, convert the angles to decimal degrees:

[tex]\[ 37^\circ 11' = 37 + \frac{11}{60} \approx 37.18^\circ \][/tex]

[tex]\[ 25^\circ 43' = 25 + \frac{43}{60} \approx 25.72^\circ \][/tex]

Now, substitute the angles into the tangent equations:

[tex]\[ \tan(37.18^\circ) = \frac{h}{d} \][/tex]

[tex]\[ \tan(25.72^\circ) = \frac{h}{d + 17} \][/tex]

Step 3:

Solve the equations for (h):

[tex]\[ h = d \times \tan(37.18^\circ) \][/tex]

[tex]\[ h = (d + 17) \times \tan(25.72^\circ) \][/tex]

Step 4:

Set the expressions equal to each other:

[tex]\[ d \times \tan(37.18^\circ) = (d + 17) \times \tan(25.72^\circ) \][/tex]

Step 5:

Solve for (d):

[tex]\[ d = \frac{17 \times \tan(25.72^\circ)}{\tan(37.18^\circ) - \tan(25.72^\circ)} \][/tex]

Step 6:

Calculate the value of (d) and then use it to find (h):

[tex]\[ d \approx 27.83 \text{ meters} \][/tex]

[tex]\[ h = 27.83 \times \tan(37.18^\circ) \][/tex]

Step 7:

Calculate (h):

[tex]\[ h \approx 27.83 \times 0.7656 \][/tex]

[tex]\[ h \approx 21.33 \text{ meters} \][/tex]

Therefore, the approximate height of the flagpole is 21.33 meters.

Answer:first 3

Step-by-step explanation:

I'm only in 6th grade but I think it's the first 3

Answer:

100,000 pounds

Step-by-step explanation:

The expected value (E) spent on direct materials used by Atkins,Inc for 2019 is:

[tex]E=\$1.50*8*10,000\\E= \$120,000[/tex]

Since there was an unfavorable $30,000 variance in materials quantity, the actual value spent (Av) on direct materials is:

[tex]A_{v}= \$120,000 +\$30,000\\A_{v}= \$150,000[/tex]

The amount of direct material (M), in pounds, used during 2019 is:

[tex]M=\frac{\$150,000}{\$1.50} \\M=100,000 \ pounds[/tex]

Answer:

1. The conclusion is statistically correct at the significance level given.

Step-by-step explanation:

1) Data given and notation n  

n=400 represent the random sample taken  

X represent the people with union membership in the sample

[tex]\hat p[/tex] estimated proportion of people with union membership in the sample

[tex]p_o=0.113[/tex] is the value that we want to test  

[tex]\alpha=0.025[/tex] represent the significance level (no given)  

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value (variable of interest)  

p= population proportion of people with union membership

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion of people with union membership exceeds 11.3%. :  

Null Hypothesis: [tex]p \leq 0.113[/tex]

Alternative Hypothesis: [tex]p >0.113[/tex]

We assume that the proportion follows a normal distribution.  

This is a one tail upper test for the proportion of  union membership.

The One-Sample Proportion Test is "used to assess whether a population proportion [tex]\hat p[/tex] is significantly (different,higher or less) from a hypothesized value [tex]p_o[/tex]".

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

[tex]np_o =400*0.113=45.2>10[/tex]

[tex]n(1-p_o)=400*(1-0.113)=354.8>10[/tex]

3) Calculate the statistic  

The statistic is calculated with the following formula:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}[/tex]

On this case the value of [tex]p_o=0.113[/tex] is the value that we are testing and n = 400.

Since we have already the statistic calculated z=2.2, we just need to calculate the p value in order to check if we can reject or not the null hypothesis.

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

Based on the alternative hypothesis the p value would be given by:

[tex]p_v =P(z>2.2)=1-P(z<2.2)=0.014[/tex]

Using the significance level given [tex]\alpha=0.025[/tex] we see that [tex]p_v<\alpha[/tex] so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the union membership increased in 2014.

The margin of error for a 90% confidence level is 2.4%, and for a 99% confidence level, it is 3.8%

The margin of error (ME) for a poll can be calculated using the formula:

ME = Z × sqrt((p ×(1 - p)) / n)

Where:

Question 1: For a 90% confidence level, the z-value (Z) is 1.645 (use a z-table or statistical software to obtain this).

Substitute the values in the formula to find the ME: ME = 1.645 × sqrt((0.64 × (1 - 0.64)) / 1076) = 0.024 or 2.4%

Question 2: For a 99% confidence level, the z-value (Z) is 2.576 (use a z-table or statistical software to obtain this).

Substitute the values in the formula to find the ME: ME = 2.576 × sqrt((0.64 × (1 - 0.64)) / 1076) = 0.038 or 3.8%

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Answer:

d)the estimated average of Y is 2 when X1 and X2 equals zero.

Step-by-step explanation:

Hello!

The multiple regression model with two independent variables is:

Y= β₀ + β₁X₁i + β₂X₂ + εi

Where

β₀ is where Y intercepts the line, in terms of the regression, is the value of the population mean of the dependent variable when X₁ and X₂ are cero.

β₁ is the slope of the variable X₁, in terms of the regression, is the change that suffers the population mean when X₁ increases one unit and X₂ remains constant.

β₂ is the slope of the variable X₂, in terms of the regression, is the change that suffers the population mean when X₂ increases one unit and X₁ remains constant.

When you calculate the estimated plane for the multiple regression you have tree estimators for each βi, were:

Y= b₀ + b₁ X₁ + b₂ X₂

b₀ estimates β₀

b₁ estimates β₁

b₂ estimates β₂

interpreted in colloquial language b₀ is the value of the sample mean of Y when X₁ and X₂ are cero.

With this in mind, the correct answer is d.

I hope you have a SUPER day!

Answer:

69.5%

Step-by-step explanation:

A feature of the normal distribution is that this is completely determined by its mean and standard deviation, therefore, if two normal curves have the same mean and standard deviation we can be sure that they are the same normal curve. Then, the probability of getting a value of the normally distributed variable between 6 and 8 is 0.695. In practice we can say that if we get a large sample of observations of the variable, then, the percentage of all possible observations of the variable that lie between 6 and 8 is 100(0.695)% = 69.5%.

Answer:

8 or 3

Step-by-step explanation:

The exact value of given trigonometric ratio sin(135)° is  1/√2  

The given trigonometric ratio is,

sin(135)°

Since we know that,

The sine function is one of three main functions in trigonometry, along with the cosine and tan functions. The sine x, often known as the sine theta, is the ratio of the opposing side of a right triangle to its hypotenuse.

Since we also know that,

sin(90° + θ) = cosθ

Therefore,

We can write,

sin(135)° = sin(90 + 45)

              = cos45

              = 1/√2                             [ from trigonometric table]

Hence,

sin(135)° =  1/√2  

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Answer:

[tex]z=2.53[/tex]  

[tex]p_v =P(z>2.53)=0.0057[/tex]  

The p value obtained was a very low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so then we have enough evidence to reject the null hypothesis, and we can say that at 5% of significance, the proportion of adults who support a ban on sugary snacks and soft​ drinks  is more than 0.5 or 50%.

Step-by-step explanation:

1) Data given and notation

n=1000 represent the random sample taken

X=540 represent the adults that said that schools should ban sugary snacks and soft drinks

[tex]\hat p=\frac{540}{1000}=0.54[/tex] estimated proportion of adults that said that schools should ban sugary snacks and soft drinks

[tex]p_o=0.5[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that majority of adults​ (more than​ 50%) support a ban on sugary snacks and soft​ drinks, the system of hypothesis are:  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.54 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=2.53[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a one side right tailed test the p value would be:  

[tex]p_v =P(z>2.53)=0.0057[/tex]  

So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so then we have enough evidence to reject the null hypothesis, and we can say that at 5% of significance, the proportion of adults who support a ban on sugary snacks and soft​ drinks  is more than 0.5 or 50%.

Answer:

1. Null hypothesis: [tex]\mu_{A}=\mu_{B}=\mu_{C}[/tex]

Alternative hypothesis: Not all the means are equal [tex]\mu_{i}\neq \mu_{j}, i,j=A,B,C[/tex]

2. D. 36

3. C. 34

4. B. 1.059

5. B. 8.02

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part 1

The hypothesis for this case are:

Null hypothesis: [tex]\mu_{A}=\mu_{B}=\mu_{C}[/tex]

Alternative hypothesis: Not all the means are equal [tex]\mu_{i}\neq \mu_{j}, i,j=A,B,C[/tex]

Part 2

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have [tex]p[/tex] groups and on each group from [tex]j=1,\dots,p[/tex] we have [tex]n_j[/tex] individuals on each group we can define the following formulas of variation:  

[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]

[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]

[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]

And we have this property

[tex]SST=SS_{between}+SS_{within}[/tex]

We need to find the mean for each group first and the grand mean.

[tex]\bar X =\frac{\sum_{i=1}^n x_i}{n}[/tex]

If we apply the before formula we can find the mean for each group

[tex]\bar X_A = 27[/tex], [tex]\bar X_B = 24[/tex], [tex]\bar X_C = 30[/tex]. And the grand mean [tex]\bar X = 27[/tex]

Now we can find the sum of squares between:

[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]

Each group have a sample size of 4 so then [tex]n_j =4[/tex]

[tex]SS_{between}=SS_{model}=4(27-27)^2 +4(24-27)^2 +4(30-27)^2=72 [/tex]

The degrees of freedom for the variation Between is given by [tex]df_{between}=k-1=3-1=2[/tex], Where  k the number of groups k=3.

Now we can find the mean square between treatments (MSTR) we just need to use this formula:

[tex]MSTR=\frac{SS_{between}}{k-1}=\frac{72}{2}=36[/tex]

D. 36

Part 3

For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.

[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]

[tex]SS_{error}=(20-27)^2 +(30-27)^2 +(25-27)^2 +(33-27)^2 +(22-24)^2 +(26-24)^2 +(20-24)^2 +(28-24)^2 +(40-30)^2 +(30-30)^2 +(28-30)^2 +(22-30)^2 =306[/tex]

And the degrees of freedom are given by:

[tex]df_{within}=N-k =3*4 -3 = 12-3=9[/tex]. N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.

And now we can find the mean square within treatments:

[tex]MSE=\frac{SS_{within}}{N-k}=\frac{306}{9}=34[/tex]

C. 34

Part 4

The test statistic F is given by this formula:

[tex]F=\frac{MSTR}{MSE}=\frac{36}{34}=1.059[/tex]

B. 1.059

Part 5

The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.

And we can use excel to find this critical value with this function:

"=F.INV(1-0.01,2,9)"

And we will see that the critical value is [tex]F_{crit}=8.02[/tex]

B. 8.02

Answer:

16 m

Step-by-step explanation:

volume =l*w*h

6*2*X=192

X=192/12=16 m

Answer:

a) NORM.S.INV(0.975)

Step-by-step explanation:

1) Some definitions

The standard normal distribution is a particular case of the normal distribution. The parameters for this distribution are: the mean is zero and the standard deviation of one. The random variable for this distribution is called Z score or Z value.

NORM.S.INV Excel function "is used to find out or to calculate the inverse normal cumulative distribution for a given probability value"

The function returns the inverse of the standard normal cumulative distribution(a z value). Since uses the normal standard distribution by default the mean is zero and the standard deviation is one.

2) Solution for the problem

Based on this definition and analyzing the question :"Which of the following functions computes a value such that 2.5% of the area under the standard normal distribution lies in the upper tail defined by this value?".

We are looking for a Z value that accumulates 0.975 or 0.975% of the area on the left and by properties since the total area below the curve of any probability distribution is 1, then the area to the right of this value would be 0.025 or 2.5%.

So for this case the correct function to use is: NORM.S.INV(0.975)

And the result after use this function is 1.96. And we can check the answer if we look the picture attached.

Answer:

(a) 1/2

(b) 1/2

(c) 1/8

Step-by-step explanation:

Since, when a fair coin is tossed three times,

The the total number of possible outcomes

n(S) = 2 × 2 × 2

= 8 { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT },

Here, B : { At least two heads are observed } ,

⇒ B = {HHH, HHT, HTH, THH},

⇒ n(B) = 4,

Since,

[tex]\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}[/tex]

(a) So, the probability of B,

[tex]P(B) =\frac{n(B)}{n(S)}=\frac{4}{8}=\frac{1}{2}[/tex]

(b) A : { At least one head is observed },

⇒ A = {HHH, HHT, HTH, THH, HTT, THT, TTH},

∵ A ∩ B = {HHH, HHT, HTH, THH},

n(A∩ B) = 4,

[tex]\implies P(A\cap B) = \frac{n(A\cap B)}{n(S)} = \frac{4}{8}=\frac{1}{2}[/tex]

(c) C: { The number of heads observed is odd },

⇒ C = { HHH, HTT, THT, TTH},

∵ A ∩ B ∩ C = {HHH},

⇒ n(A ∩ B ∩ C) = 1,

[tex]\implies P(A\cap B\cap C)=\frac{1}{8}[/tex]

Final answer:

The probability of drawing a black face card from a standard 52-card deck is 3/26.

Explanation:
To find the probability of two events happening together, we need to calculate the probability of each event and then multiply them together. First, let's find the probability of drawing a black card (B) and a face card (F) separately. The deck contains 26 black cards, and since there are 52 cards in total, P(B) = 26/52 = 1/2. There are 12 face cards in the deck, so P(F) = 12/52 = 3/13. Now, we can find the probability of the intersection of B and F by multiplying their individual probabilities, P(B ∩ F) = P(B) * P(F) = (1/2) * (3/13) = 3/26.
Therefore, the probability of drawing a black face card is 3/26.

Answer

The answer and procedures of the exercise are attached in a microsoft word document.  

Explanation  

Please consider the data provided by the exercise. If you have any question please write me back. All the exercises are solved in a single sheet with the formulas indications.  

the probability will be 5 out of 11 apples which is 5/11

Answer:

5/11

Step-by-step explanation:

There are a total of 3 + 4 + 5 = 12 apples.

Mary removes a red apple, so there are a total of 11 apples left.

The probability that the next apple is yellow is 5/11.

Answer:

So on this case the 90% confidence interval would be given by (26.336;27.664)    

We are 90% confident that the mean time to complete the questionnaire is between (26.336;27.664)

Step-by-step explanation:

1) 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".

[tex]\bar X=27[/tex] represent the sample mean  

[tex]\mu[/tex] population mean (variable of interest)

s=4 represent the sample standard deviation

n=100 represent the sample size  

2) Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=100-1=99[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.05,99)".And we see that [tex]t_{\alpha/2}=1.66[/tex]

Now we have everything in order to replace into formula (1):

[tex]27-1.66\frac{4}{\sqrt{100}}=26.336[/tex]    

In excel would be "=27-1.66*(4/SQRT(100))"

[tex]27+1.66\frac{4}{\sqrt{100}}=27.664[/tex]

In excel would be "=27+1.66*(4/SQRT(100))"

So on this case the 90% confidence interval would be given by (26.336;27.664)    

We are 90% confident that the mean time to complete the questionnaire is between (26.336;27.664)

Answer:

Yes, the events T1 and T2 are independent.

Step-by-step explanation:

When flipping a fair coin, for each flip, there is a 50/50 chance that it will result in heads or tails.

For the first flip, P(T1) = 0.5

For the second flip, P(T2) = 0.5 regardless of the outcome of the first flip. Therefore, T1 and T2 are independent events.

*Note that if the question asked for the event of both flips resulting in tails, then the events would be dependent.

Answer:

Option B) Data A and Data B have the same strength in linear correlation.

Step-by-step explanation:

Correlation:

Data A correlation = -0.991

Data B correlation = 0.991

Data A and data B have same strength of correlation but they are opposite to each other. There absolute value is same but the data A shows negative correlation and data B shows positive correlation. Data A shows indirect or inverse linear relationship and data B shows direct linear relationship. Both data have same magnitude of correlation.

Answer:

a) Standard error = 0.5

b) 99% Confidence interval:  (19.2125,21.7875)

Step-by-step explanation:

We are given the following in the question:

Population mean =  20.50 mpg

Sample standard deviation = 3.00 mpg

Sample size , n = 36

Standard Error =

[tex]=\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{3}{\sqrt{36}} = 0.5[/tex]

99% Confidence interval:

[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]

Putting the values, we get,

[tex]z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.575[/tex]

[tex]20.50 \pm 2.575(\displaystyle\frac{3}{\sqrt{36}})= 20.50 \pm 1.2875 = (19.2125,21.7875)[/tex]

The standard error of the mean from 36 fill-ups of the 2016 Lexus RX350 is 0.50 miles per gallon. The sample mean, with 99% probability, is expected to fall within the interval from 18.714 to 22.286 miles per gallon.

The standard error (SE) of the mean from a sample of 36 fill-ups for the Lexus RX 350 is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard deviation (σ) is 3.00 mpg and the sample size (n) is 36.

The formula for the standard error is SE = σ / √n = 3.00 / √36 = 0.50 mpg (rounded to four decimal places).

To find the interval in which the sample mean is expected to fall with 99 percent probability, we use the concept of Z-scores, which relate the mean, standard error, and the probability. For a 99% probability, the Z-score (z) is approximately 2.576. The interval can be found using the following formula: μ ± z * SE, replacing the symbols with the values calculated, 20.50 ± 2.576 * 0.50 which results in the interval (18.714, 22.286) mpg (rounded to four decimal places).

https://brainly.com/question/31538429

#SPJ3

Answer:

(-24, -8)

Step-by-step explanation:

Let us recall that when we have a function f

[tex]\large f:\mathbb{R}^2\rightarrow \mathbb{R}\\f(x,y)=z[/tex]

if the gradient of f at a given point (x,y) exists, then the gradient of f at this point (x,y) gives the direction of maximum rate of increasing and minus the gradient of f at this point gives the direction of maximum rate of decreasing. That is

[tex]\large \nabla f=(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})[/tex]

at the point (x,y) gives the direction of maximum rate of increasing

[tex]\large -\nabla f[/tex]

at the point (x,y) gives the direction of maximum rate of decreasing

In this case we have

[tex]\large f(x,y)=100-4x^2-2y^2[/tex]

and we want to find the direction of fastest speed of decreasing at the point (-3,-2)

[tex]\large \nabla f(x,y)=(-8x,-4y) \Rightarrow -\nabla f=(8x,4y)[/tex]

at the point (-3,-2) minus the gradient equals

[tex]\large -\nabla f(-3,-2)=(-24,-8)[/tex]

hence the vector (-24,-8) points in the direction with the greatest rate of decreasing, and they should start their descent in that direction.

Answer:

8

Step-by-step explanation:

given,

16 roses, 8 daisies and 32 tulips

required to find

greatest number of flowers that could be in each bouquet such that   Each bouquet has the same number of flowers and has only one type of flower

as there are only 8 daisies so the greatest number of flowers that could be in each bouquet such that   Each bouquet has the same number of flowers and has only one type of flower is 8

if it is greater than 8 then there will be some other flower in the boquet of daises

Answer:

2, 0.135, 0.270, 0.270, 0.180, 0.145

Step-by-step explanation:

1. To calculate the mean of people arriving in 5 minute period:

We know the arrival rate of minute is 0.4, so people arriving in 5 minutes will be

0.4 x 5 = 2

2. From part 1 it is known thay mean arrival time=2

For this we will use poisson's probability formula that is

P(X=x) = (2^x) x Exp^(-2/x!)

For X=0

P(X=0) = (2^0) x Exp^(-2/0!) = 0.135

For X = 1

P(X=1) = (2^1) x Exp^(-2/1!) = 0.270

For X = 2

P(X=2) = (2^2) x Exp^(-2/2!) = 0.270

For X = 3

P(X=3) = (2^3) x Exp^(-2/3!) = 0.180

3. For delay expected if more than 3 customer arrive in 5 minutes.

P(X>3) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)

P(X>3) = 1-0.135-0.270-0.270-0.180

P(X>3) = 0.145