Which expression is equivalent to 1/4-3/4x

Answer:

a) Entries of A are non negative, that is ai,j ≥ 0 for all 1 ≤ i ≤ n and all 1 ≤ j ≤ n.

c) yes MS is stochastic

Step-by-step explanation:

a) A stochastic matrix is a square matrix whose columns are probability vectors. A probability vector is a numerical vector whose entries are real numbers between 0 and 1 whose sum is 1.

B)

a) Now, suppose Sx=λx for some λ>1. Since the rows of S are nonnegative and sum to 1, each element of vector Sx is a convex combination of the components of x, which can be no greater than maximum of x the largest component of x. On the other hand, at least one element of λx is greater than maximum of x, which proves that λ>1 is impossible and Hence  λ = 1.

b) Then [tex]S^{2}[/tex] =[tex]P^{2}_{ij}[/tex] is also stochastic; it is the two-step transition matrix for the chain {Xn, n = 0,1,…}. To every stochastic matrix S, there corresponds a Markov chain {Xn} for which S is the unit-step transition matrix.

However, not every stochastic matrix is the two-step transition matrix of a Markov chain.

c) Let A and B be two row-stochastic matrices and suppose we know the product of column stochastic matrices is column-stochastic. Observe that,

MS = [tex]((MS)^{T})^{T} = (S^{T}M^{T})^{T}[/tex]

by properties of transpose of a matrix. Let us consider [tex]S^{T} M^{T}[/tex]. It is easy to see that the transpose of a row-stochastic matrix is column-stochastic by definition (and vice versa). Thus, [tex]S^{T}[/tex]and [tex]M^{T}[/tex] are column stochastic and by our assumption, it must then be the case that [tex]S^{T} M^{T}[/tex] is column-stochastic. Since  [tex]S^{T} M^{T}[/tex]  is column-stochastic, then it's transpose [tex](S^{T} M^{T})^{T}[/tex]=MS is row stochastic.

Answer:

b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost.

Step-by-step explanation:

The p value that is corresponding in line with the slope of regression line is 0.345, which is quite above the significance level of 0.05. as a result, we failed to discard the null hypothesis that there is no important association or connection between x and y variables.

Going by the above explanation we can then conclude that there's no statistically significant linear relationship between the number of miles driven and the maintenance cost.

Answer:

[tex]t=\frac{30.8-30}{\frac{1.5}{\sqrt{32}}}=3.017[/tex]    

[tex]p_v =2*P(t_{(31)}>3.017)=0.0051[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the treu mean is different from 30 minutes at 1% of significance

Step-by-step explanation:

Data given and notation  

[tex]\bar X=30.8[/tex] represent the sample mean

[tex]s=1.5[/tex] represent the sample standard deviation

[tex]n=32[/tex] sample size  

[tex]\mu_o =30[/tex] represent the value that we want to test

[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

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

1) State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is equal to 30 minutes, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 30[/tex]  

Alternative hypothesis:[tex]\mu \neq 30[/tex]  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

2) Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{30.8-30}{\frac{1.5}{\sqrt{32}}}=3.017[/tex]    

3) P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=32-1=31[/tex]  

Since is a two sided hypothesis test the p value would be:  

[tex]p_v =2*P(t_{(31)}>3.017)=0.0051[/tex]  

4) Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the treu mean is different from 30 minutes at 1% of significance

Answer:

18

Step-by-step explanation:

Answer:

Unknown 1: -OH group at 3400-3600

Unknown 2: Ketone and alkene group

Step-by-step explanation:

Unknown 1:

This compound has a strong IR absorption at 3400 - 3600cm-¹; this indicates that it is an alcoholic group (OH)

No absorption between 1600 and 2900cm-¹: this rule out the presence of ketone (C = O)

Hence the unknown compound is OH group

Unknown 2:

This has strong IR absorption at 1680cm-¹: this indicates the presence of (C=O) group.

No absorptions above 3100cm-¹: this indicates the presence of C = C - H

So therefore, unknown 2 is most likely to be Ketone and alkene group

Answer:

The​ p-value for this​ test is 0.22065.

Step-by-step explanation:

We are given that a national study report indicated that​ 20.9% of Americans were identified as having medical bill financial issues.

A news organization randomly sampled 400 Americans from 10 cities and found that 90 reported having such difficulty.

Let p = proportion of Americans who were identified as having medical bill financial issues in 10 cities.

SO, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 20.9%   {means that % of Americans who were identified as having medical bill financial issues in these 10 cities is less than or equal to 20.9%}

Alternate Hypothesis, [tex]H_A[/tex] : p > 20.9%   {means that % of Americans who were identified as having medical bill financial issues in these 10 cities is more than 20.9% and is more severe}

The test statistics that will be used here is One-sample z proportion statistics;

                                  T.S.  = [tex]\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of 400 Americans from 10 cities who were found having such difficulty =  [tex]\frac{90}{400}[/tex] = 0.225 or 22.5%

            n = sample of Americans = 400

So, test statistics  =  [tex]\frac{0.225-0.209}{{\sqrt{\frac{0.225(1-0.225)}{400} } } } }[/tex]

                               =  0.77

Now, P-value of the test statistics is given by the following formula;

         P-value = P(Z > 0.77) = 1 - P(Z [tex]\leq[/tex] 0.77)

                                            = 1 - 0.77935 = 0.22065

Testing the hypothesis, using the information given, it is found that the p-value is of 0.2148.

At the null hypothesis, it is tested if the proportion for these cities is of 20.9% = 0.209, hence:

[tex]H_0: p = 0.209[/tex]

At the alternative hypothesis, it is tested if the proportion for these cities is greater than 0.209, hence:

[tex]H_1: p > 0.209[/tex].

The test statistic is given by:

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

In which:

For this problem, the parameters are: [tex]p = 0.209, n = 400, \overline{p} = \frac{90}{400} = 0.225[/tex].

Then, the value of the test statistic is:

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

[tex]z = \frac{0.225 - 0.209}{\sqrt{\frac{0.209(0.791)}{400}}}[/tex]

[tex]z = 0.79[/tex]

The p-value for this test is the probability of finding a sample proportion above 0.225, which is 1 subtracted by the p-value of z = 0.79.

Looking at the z-table, z = 0.79 has a p-value of 0.7852.

1 - 0.7852 = 0.2148.

The p-value for this test is of 0.2148.

A similar problem is given at https://brainly.com/question/24166849

Answer:

[tex]430-1.943\frac{26.9}{\sqrt{7}}[/tex]    

[tex]430+1.943\frac{26.9}{\sqrt{7}}[/tex]    

And the best option would be:

e. 430 ± 1.943 (26.9/√7)

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".

[tex]\bar X=430[/tex] represent the sample mean

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

s=26.9 represent the sample standard deviation

n=7 represent the sample size  

Solution to the problem

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=7-1=6[/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 table to find the critical value. The excel command would be: "=-T.INV(0.05,6)".And we see that [tex]t_{\alpha/2}=1.943[/tex]

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

[tex]430-1.943\frac{26.9}{\sqrt{7}}[/tex]    

[tex]430+1.943\frac{26.9}{\sqrt{7}}[/tex]    

And the best option would be:

e. 430 ± 1.943 (26.9/√7)

For 90 percent confidence interval for the mean weight of all baby orca whales is,

[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Thus option e is the correct option.

Given-

Mean [tex]X[/tex] of the random sample is 430 pounds.

Standard deviation [tex]s[/tex] of the sample is 26.9 pounds.

Confidence interval is 90 percent.

The degree of freedom is sample size n-1. Thus,

[tex]D_f=7-1[/tex]

[tex]D_f=6[/tex]

The critical value for 90 percent confidence level is,

[tex]t_{\frac{a}{2} }=1.943[/tex]

The confidence interval of a mean can be given by,

[tex]X\pm t_{\frac{a}{2}}\dfrac{s}{\sqrt{n} }[/tex]

Put the value in above equation we get,

[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Taking positive sign,

[tex]430+1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Taking negative sign,

[tex]430-1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Hence, For 90 percent confidence interval for the mean weight of all baby orca whales is,

[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Thus option e is the correct option.

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Answer:

(6+2)/(-4+8)= 8/4= 2

y+2=2(x+8)

y+2=2x+16

y=2x+14

Step-by-step explanation:

To estimate the product 137 multiplied by 18, we can round the numbers to the nearest ten. 137 is approximately 140, and 18 is approximately 20. The estimated product of 137 x 18 is 2800.

To estimate the product 137 multiplied by 18, we can round the numbers to the nearest ten. 137 is approximately 140, and 18 is approximately 20. Then, we multiply the rounded numbers: 140 x 20 = 2800. Therefore, the estimated product of 137 x 18 is 2800.

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The ASA and AAS are methods of proving triangle congruence. ASA requires two angles and the included side in one triangle to match the respective parts in the other triangle. AAS requires two angles and a non-included side in one triangle to match the respective parts in the other triangle.

The question refers to two of the many methods to prove that triangles are congruent: Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS). In triangle congruence, congruent means that two triangles have the same size and shape.

For the ASA congruence, two angles and the included side in one triangle must be congruent to the corresponding two angles and the included side in another triangle. For example, if we have two triangles, Triangle ABC and Triangle DEF, if angle A is congruent to angle D, angle B is congruent to angle E, and side AB is congruent to side DE, then the two triangles are congruent by ASA.

For AAS congruence, two angles and a non-included side in one triangle must be congruent to the corresponding two angles and the non-included side in another triangle. For instance, in Triangle ABC and Triangle DEF, if angle A is congruent to angle D, angle B is congruent to angle E, and side BC is congruent to side EF, then the two triangles are congruent by AAS.

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Final answer:

Different materials exhibit varying degrees of thermal expansion when subjected to a temperature change. Polymers such as polyethylene expand the most, followed by soft metals like lead and aluminum, with hard metals like platinum and minerals like quartz showing much less expansion.

Explanation:

When materials undergo a change in temperature, they typically experience a change in size, known as thermal expansion or contraction. This phenomenon happens because the kinetic energy of the particles within the material changes, consequently changing the distances between particles. The amount by which a material expands or contracts is dependent on its coefficient of thermal expansion, which varies widely among different materials. Polymers such as polyethylene show significant thermal expansion, more so than soft metals like lead and aluminum, and much more than hard materials like platinum and quartz. When temperature increases, thermal stress may arise in materials that are constrained and cannot freely expand, leading to deformation or even damage. Platinum, being a metal, would deform more than quartz due to its higher thermal expansion, but less than softer metals and polymers.

To rank the items based on the total change in length along the long axis of beams with a temperature change of 20 degrees, we would expect polyethylene to have the greatest change due to its high coefficient of thermal expansion, followed by soft metals like lead and aluminum. Platinum would have some expansion but considerably less than softer metals and polymers, and quartz would experience the least amount of expansion given its low thermal expansion characteristic.

Answer:

The P-value for this test is P=0.2415.

Step-by-step explanation:

We have to perform an hypothesis testing on the mean of alla account balances.

The claim is that the mean of all account balances is significantly greater than $1,150.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1150\\\\H_a: \mu>1150[/tex]

The sample size is n=20, with a sample mean is 110 and standard deviation is 125.

We can calculate the t-statistic as:

[tex]t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{1170-1150}{125/\sqrt{20}}=\dfrac{20}{27.95}=0.7156[/tex]

The degrees of freedom fot this test are:

[tex]df=n-1=20-1=19[/tex]

For this one-tailed test and 19 degrees of freedom, the P-value is:

[tex]P-value=P(t>0.7156)=0.2415[/tex]

Answer:

185

Step-by-step explanation:

sorry. had to do something but im bsck :)

Answer:

400nanometers

Step-by-step explanation:

Based on Margot measurement, the distance for 6wavelengths of visible light is 2400nanometers. To calculate the resulting distance for 1wavelength we have:

6wavelength = 2400nanometers

1wavelength = x

6wavelength × x = 2400nanometers × 1wavelength

x = 2400nanometres/6

x = 400nanometres

The researchers conducted an experiment to test the effectiveness of a placebo in reducing pain. A statistical test called the paired t-test can be used to analyze the data and determine if the mean BOLD measurements are higher in the first session than in the second. The results of this test will provide evidence to confirm or refute the effectiveness of the placebo.

The researchers conducted an experiment to test the effectiveness of a placebo in reducing pain. They measured the blood oxygen level-dependent (BOLD) signal during two consecutive sessions with electric shocks applied to the volunteers' arms. In the second session, a cream that was actually a placebo was applied to the volunteers. The mean and standard deviation of the differences in BOLD measurements were calculated to determine if there was evidence to confirm that the placebo was effective.

To test if the mean BOLD measurements were higher in the first session than in the second, a statistical test can be used. The paired t-test is suitable for this scenario, as it compares the means of two related samples. The t-test calculates a t-value which can be compared to a critical value to determine if there is evidence of a significant difference. In this case, with a significance level of α = 0.05, if the t-value is greater than the critical value, it would indicate evidence that the mean BOLD measurements are higher in the first session than the second.

If the calculated t-value is greater than the critical value, there is evidence to confirm that the placebo is effective in reducing pain. Conversely, if the calculated t-value is not greater than the critical value, there is not enough evidence to confirm that the placebo is effective. It is important to note that statistical significance does not necessarily imply practical significance, so further investigation may be required to understand the magnitude of the effect.

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Answer:

The steps to finding the upper and lower quartiles are given in the first choice.

1.  Order the data from least to greatest. If you don't do this, the data is random.

2.  Find the median - you will do this so that you can find the midpoint of the data set (half of of the data is smaller and half of the data is larger).

3.  Find the lower quartile - this is the half of the lower half of numbers; think of it as breaking the lower half of the data into 2 sections.  

4.  Find the upper quartile - this is the half of the greater half of numbers; this will break the upper half of the data into 2 sections.  

Answer:

A.

Step-by-step explanation:

Just took the test:)

Step-by-step explanation:

Here given

6x - 2y = 12

2y = 6x - 12

2y = 6(x - 2)

y = 6( x - 2)

2

y = 3(x - 2)

y = 3x - 6

Comparing with y = mx + c

so slope (m) = 3

Hope it will help you :))

Answer:

b

Step-by-step explanation:

Null hypothesis: mean of valence for all metal song is equal to mean of valence of blues song.

Null hypthesis tests the claim

Altenate hypothesis: mean of valence for all metal songs is not equal to mean of valence of blues song.

Alternate hypothesis rejects the claim.

Answer:

(A) Since Sample 1 comes from the population of Metal songs only and Sample 2 comes from the population of Blue songs only,

The 90% confidence interval for mean valence for Metal songs is (0.2224 , 0.6797)

The 90% confidence interval for mean valence for Blue songs is (0.3063 , 0.8557)

All intermittent and final answers were rounded up to four decimal places.

(B) The option (b) is correct. This is because the question says that the research group suspects a difference between both means, not that one mean is greater or less than the other.

Step-by-step explanation:

(A) Using a 90% confidence level, the true mean is within 1.645 standard deviations of the sample mean

For METAL SONGS,

Lower limit = 0.451 - (1.645)(0.139)

= 0.451 - 0.2287 = 0.2224

Upper limit = 0.451 + (1.645)(0.139)

= 0.451 + 0.2287 = 0.6797

For BLUE SONGS,

Lower limit = 0.581 - (1.645)(0.167)

= 0.581 - 0.2747 = 0.3063

Upper limit = 0.581 + (1.645)(0.167)

= 0.581 + 0.2747 = 0.8557

(B) The null hypothesis is:

Mean valence of Metal songs is equal to the mean valence of Blue songs

Alternative hypothesis:

Mean valence of Metal songs is NOT equal to the mean valence of Blue songs.

The population of deer will double when the growth rate exceeds the mortality rate, and the net effect is a 4% growth rate. It will take approximately 17.3 years for the population to double.

The population of deer will double when their growth rate exceeds the mortality rate and the net effect is a 4% growth rate. We can calculate the time it takes for the population to double using the formula for exponential growth:

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As per the given data in the question, Emil's monthly PMI payment is $28.81.

A mortgage is a loan used to finance the purchase or upkeep of a home, land, or other types of rental properties.

The lender agrees to repay the loan over time, usually in regular installments divided into principal and interest. Loans are protected by the property.

To determine Emil's monthly PMI payment, we first need to determine the loan-to-value (LTV) ratio.

Emil is making a 15% down payment on a $175,000 home, which means his loan amount is $148,750. To calculate the LTV ratio, we divide the loan amount by the property value:

LTV ratio = loan amount / property value

LTV ratio = $148,750 / $175,000

LTV ratio = 0.85

Since Emil's LTV ratio is between 85.01% and 90%, his PMI rate for a 15-year fixed-rate loan is 0.23% according to the table.

To calculate Emil's monthly PMI payment, we multiply the loan amount by the PMI rate and divide by 12 (for the 12 months in a year):

Monthly PMI payment = (loan amount x PMI rate) / 12

Monthly PMI payment = ($148,750 x 0.23%) / 12

Monthly PMI payment = $28.81

Therefore, Emil's monthly PMI payment is $28.81.

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Given:

Given that the measurements of the triangle.

We need to determine the value of x.

Value of x:

The value of x can be determined using by angle bisector theorem.

The angle bisector theorem states that "if the angle that bisects the triangle will divide the opposite sides into two segments that are proportional to the remaining two sides of the triangle".

Hence, applying the theorem, we have;

[tex]\frac{x}{20-x}=\frac{14}{11}[/tex]

Cross multiplying, we get;

[tex]11x=14(20-x)[/tex]

Simplifying, we get;

[tex]11x=280-14x[/tex]

[tex]25x=280[/tex]

   [tex]x=11.2[/tex]

Thus, the value of x is 11.2

Answer:

2y^2+18x

Step-by-step explanation:

4y^2 + 6x -2y^2 + 12x

=4y^2-2y^2+6x+12x

=2y^2+6x+12x

=2y^2+18x

Answer:

2y^2+18x

Step-by-step explanation:

4y^2+6x-2y^2+12x

=4y^2-2y^2 6x+12x

=2y^2+18x

Answer:

[tex]z=\frac{0.556 -0.5}{\sqrt{\frac{0.5(1-0.5)}{836}}}=3.238[/tex]  

[tex]p_v =2*P(z>3.238)=0.0012[/tex]  

The p value is a reference value and is useful in order to take a decision for the null hypothesis is this p value is lower than a significance level given we reject the null hypothesis and otherwise we have enough evidence to fail to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

n=836 represent the random sample taken

[tex]\hat p=0.556[/tex] estimated proportion of interest

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

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

z would represent the statistic (variable of interest)

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

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that ture proportion is equal to 0.5 or no.:  

Null hypothesis:[tex]p=0.5[/tex]  

Alternative hypothesis:[tex]p \neq 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].

Calculate the statistic  

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

[tex]z=\frac{0.556 -0.5}{\sqrt{\frac{0.5(1-0.5)}{836}}}=3.238[/tex]  

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 next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z>3.238)=0.0012[/tex]  

The p value is a reference value and is useful in order to take a decision for the null hypothesis is this p value is lower than a significance level given we reject the null hypothesis and otherwise we have enough evidence to fail to reject the null hypothesis.

Given:

Given that the radius of the circle is 3 units.

The arc length is π.

The central angle is θ.

We need to determine the expression to find the measure of θ in radians.

Expression to find the measure of θ in radians:

The expression can be determined using the formula,

[tex]S=r \theta[/tex]

where S is the arc length, r is the radius and θ is the central angle in radians.

Substituting S = π and r = 3, we get;

[tex]\pi=3 \theta[/tex]

Dividing both sides of the equation by 3, we get;

[tex]\frac{\pi}{3}=\theta[/tex]

Thus, the expression to find the measure of θ in radians is [tex]\theta=\frac{\pi}{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

a. The probability of getting an specific sequence would be

[tex](1/20)*(1/19)*(1/18)*(1/17)*(1/16)[/tex]

b. The probability  of having an specific sequence would be.

[tex]5/20 = 1/4[/tex]

Step-by-step explanation:

a. If you draw 5 marbles without replacement, the probability of getting an specific sequence would be

[tex](1/20)*(1/19)*(1/18)*(1/17)*(1/16)[/tex]

b. If you draw 5 marbles all at once without replacement, the probability  of having an specific sequence would be.

[tex]5/20 = 1/4[/tex]

Answer:

24 cm

Step-by-step explanation:

Answer:

See down below.

Step-by-step explanation:

Theoretical probability is what we expect to happen. For example, we do a test of flipping a coin. You know that its either gonna be heads or tails.

Experimental probability is what actually happens when we try it out. It occurs when we are doing an experiment and then something happens.

Hope this helps!

Theoretical probability is calculated based on assumptions and mathematical calculations, while experimental probability is based on actual data and observations.

Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is based on assumptions and mathematical calculations. For example, if you flip a fair coin, the theoretical probability of getting heads is 1 out of 2, or 0.5.

Experimental probability, on the other hand, is calculated by conducting an actual experiment and observing the outcomes. It is based on actual data and observations. For example, if you flip a coin 10 times and get heads 6 times, the experimental probability of getting heads is 6 out of 10, or 0.6.

In summary, theoretical probability is based on calculations and assumptions, while experimental probability is based on actual data and observations.

Final answer:

To calculate a 95% confidence interval for the true average CO2 level in the population of all homes, we use the sample mean and sample standard deviation to calculate the margin of error and determine the lower and upper bounds of the confidence interval.

Explanation:

To calculate a 95% confidence interval for the true average CO2 level in the population of all homes, we can use the sample mean and sample standard deviation provided.

First, we calculate the margin of error using the formula: Margin of Error = Critical Value x (Sample Standard Deviation / sqrt(Sample Size)). The critical value for a 95% confidence interval is 1.96.

Next, we calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error to the sample mean respectively.

Therefore, the 95% confidence interval for the true average CO2 level in the population of all homes is (589.17, 719.15).

This means that we can be 95% confident that the true average CO2 level in the population of all homes falls within this range.

Answer:

See the attached file for the answer.

Step-by-step explanation:

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