A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 9 faculty members and 10 students eligible to serve on the committee. In how many ways can the committee be formed

Answer:

8.1 moles

Step-by-step explanation:

Given parameters: Mass of water to be decomposed = 29.2g Unknown: Number of moles of oxygen. Solution: To solve this problem, we first write the balanced reaction equation :                 2H₂O    →     2H₂    +    O₂ Now convert the given mass of the water to number of moles;   Number of moles of water =      Molar mass of water = 2(1) + 16 = 18g/mol   Number of moles of water =   = 16.2moles     From the balanced reaction equation:     2 moles of water produced 1 mole of oxygen gas;     16.2 mole of water will produce     = 8.1moles of oxygen gas

Hope this helps you :3

We have been given that a sprinkler is designed to rotate 360∘ clockwise, and then 360∘ counterclockwise to water a circular region with a radius of 11 feet. The sprinkler is located in the middle of the circular region. The sprinkler begins malfunctioning and is only able to rotate 225∘ in each direction.

We are asked to find the area of the sector to nearest square foot.

We will use area of sector formula to solve our given problem.

[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex], where,

[tex]\theta[/tex] = Central angle of sector,

[tex]r[/tex] = Radius.

For our given problem [tex]\theta = 225^{\circ}[/tex] and [tex]r=11[/tex].

[tex]\text{Area of sector}=\frac{225^{\circ}}{360^{\circ}}\times \pi (11)^2[/tex]

[tex]\text{Area of sector}=0.625\times 121\pi[/tex]

[tex]\text{Area of sector}=237.5829444277281137[/tex]

[tex]\text{Area of sector}\approx 238[/tex]

Therefore, the sprinkler can water approximately 238 square feet.

To find the area of the sector, we need to find the central angle, find the fraction of the circle covered by the sector, and then multiply it by the area of the entire circle with a radius of 11 feet.

To find the area of the sector, we need to find the central angle first. Since the sprinkler can only rotate 225∘ in each direction, the total angle covered is 225∘+225∘=450∘.

Next, we need to find the fraction of the circle covered by the sector. We can do this by finding the ratio of the central angle to the total angle of a circle, which is 360∘. This can be calculated as (450/360).

Finally, we multiply the fraction by the area of the entire circle with a radius of 11 feet, which is π(11)^2, to find the area of the sector.

Plugging in the values and calculating, we find that the 98% confidence interval is approximately (0.5847, 0.6553).

To construct a 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders, we can use the formula:

CI = p ± z * √(p * (1-p) / n)

Where:

Using a standard normal distribution table or a calculator, we can find that the z-score for a 98% confidence level is approximately 2.33.

Plugging in the values into the formula:

CI = 0.62 ± 2.33 * √(0.62 * (1-0.62) / 3100)

Calculating the values:

CI = 0.62 ± 2.33 * √(0.62 * 0.38 / 3100)

CI = 0.62 ± 2.33 * √(0.235 / 3100)

CI = 0.62 ± 2.33 * 0.01516

CI = 0.62 ± 0.03535

CI ≈ (0.5847, 0.6553)

Therefore, the 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders is approximately (0.5847, 0.6553).

https://brainly.com/question/34700241

#SPJ3

Answer:

The series is absolutely convergent.

Step-by-step explanation:

By ratio test, we find the limit as n approaches infinity of

|[a_(n+1)]/a_n|

a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)

a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)

[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]

= |-3n³/2(n+1)³|

= 3n³/2(n+1)³

= (3/2)[1/(1 + 1/n)³]

Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity

= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity

= 3/2 × 1

= 3/2

The series is therefore, absolutely convergent, and the limit is 3/2

Answer:

1.53

Step-by-step explanation:

Find the attachment for explanation

The z-value corresponding to the probability of 0.937 using the standard normal distribution table is 1.53 and this can be determined by using the given data.

Given :

Assuming that the distribution is normal so the probability for being within the maximum limit is given by:

[tex]\rm P=1-\dfrac{6.3}{100}[/tex]

P = 0.937

Now, the z-value corresponding to the probability of 0.937 using the standard normal distribution table is 1.53.

Therefore, the correct option is D) 1.53.

For more information, refer to the link given below:

https://brainly.com/question/23044118

Answer:

1/4 of his income.

Step-by-step explanation:

If Wilbur spends 2/3 of his income, 1/3 or 4/12 of it is left for other purposes (It is easier if everything has a common denominator of 12). And if he shares 1/12 of that remaining amount, there is 3/12 left. And when we simplify 3/12, we get 1/4.

*Mark me brainliest!*

Answer:

260

Step-by-step explanation:

A = bh

Answer:

Event 4, Event 2, Event 1, Event 3 (least to most likely)

Step-by-step explanation:

Let's take a look at each event:

Event 1- Spinner B lands on a black slice.

2 black slices, 8 total slices

2/8=1/4=25% probability

Event 2- Spinner A lands on a black slice.

3 black slices, 15 total slices

3/15=1/5=20%

Event 3- Spinner B lands on a black or purple slice.

8 black or purple slices, 8 total slices

8/8=1=100%

Event 4- Spinner A lands on a green slice.

0 green slices, 15 total slices

0/15=0=0%

So, in order of least to most likely, we have Event 4 (0%), Event 2 (20%), Event 1 (25%), and event 3 (100%).

Answer:

[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]

[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]

And in order to obtain the confidence interval for the deviation we just take the square root and we got:

[tex] 0.541 \leq \sigma \leq 2.595[/tex]

Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim

Step-by-step explanation:

Data provided

1.9, 2.4, 3.0, 3.5, and 4.2

We can calculate the sample mean and deviation from this data with these formulas:

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

[tex] s=\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}[/tex]

And we got:

[tex]\bar X= 3[/tex]

s=0.903 represent the sample standard deviation

n=5 the sample size

Confidence=95% or 0.95

Confidence interval

We need to begin finding the confidence interval for the population variance is given by:

[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]

The degrees of freedom given by:

[tex]df=n-1=5-1=4[/tex]

The Confidence level provided is 0.95 or 95%, the significance is then[tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical values for this case are:

[tex]\chi^2_{\alpha/2}=11.143[/tex]

[tex]\chi^2_{1- \alpha/2}=0.484[/tex]

And the confidence interval would be:

[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]

[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]

And in order to obtain the confidence interval for the deviation we just take the square root and we got:

[tex] 0.541 \leq \sigma \leq 2.595[/tex]

Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim

Answer:

82.8 centimeters

Step-by-step explanation:

Chandler has 828 millimeters of fabric.

Expressing as a ratio

[tex]\dfrac{1}{x}= \dfrac{10}{828}\\10x=828\\x=828\div 10\\x=82.8 cm[/tex]

Therefore, Chandler has 82.8 centimeters of fabric.

Answer:

82.8 centimeters of fabric

Step-by-step explanation:

1 centimeters= 10 millimeters;

828mm x 1cm ÷10 mm=82.8cm ;centimeters of fabric

The exercise is performed by conversion factor and a smaller unit is transferred to a larger unit that is centimeters.

Answer:

x= 3,1

Step-by-step explanation:

-b ±  √b²-4(ac)/2a

4 ±  √(-4)² - 4 · (1·3)/2·1

x = 2 ± 1

x = 3,1

The equation of the hyperbola with vertices at[tex](0,±\sqrt{54}) and foci at (0,±\sqrt{89}) is \(\frac{y^2}{54} - \frac{x^2}{35} = 1\).[/tex]

To write the equation of a hyperbola, you need to know the values of a (which determines the distance from the center to the vertices) and c (which determines the distance from the center to the foci). The general equation for a hyperbola centered at the origin (h, k) with a vertical transverse axis is:

[tex]\(\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1\)[/tex]

Since the hyperbola is centered at the origin (0,0), this simplifies the equation:

[tex]\(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\)[/tex]

For this hyperbola, the vertices are at [tex](0,\(\pm\sqrt{54}\)), so a is \(\sqrt{54}\)[/tex]. The foci are at [tex](0,\(\pm\sqrt{89}\))[/tex], so c is [tex]\(\sqrt{89}\)[/tex]. To find b, we use the relationship [tex]c^2 = a^2 + b^2 (since e > 1)[/tex].

Calculating b, we have:

[tex]\(c^2 = a^2 + b^2\)[/tex]

[tex]\(89 = 54 + b^2\)[/tex]

[tex]\(b^2 = 35\)[/tex]

Thus, the equation of the hyperbola is:

[tex]\(\frac{y^2}{54} - \frac{x^2}{35} = 1\)[/tex]

The equation of the hyperbola is : [tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

To write the equation of the hyperbola given its vertices and foci, we need to determine the major axis, minor axis, and eccentricity.

The vertices of the hyperbola are at [tex]\( (0, \pm \sqrt{54}) \)[/tex] and the foci are at [tex]\( (0, \pm \sqrt{89}) \).[/tex]

The distance from the center to a vertex is [tex]\( \sqrt{54} \)[/tex], which is the length of the semi-major axis, [tex]\( a \)[/tex]. The distance from the center to a focus is [tex]\( \sqrt{89} \),[/tex] which is the length of [tex]\( c \)[/tex], the distance from the center to a focus.

The relationship between [tex]\( a \), \( b \)[/tex] (the length of the semi-minor axis), and [tex]\( c \)[/tex] for a hyperbola is given by the equation [tex]\( c^2 = a^2 + b^2 \).[/tex]

Substituting the given values, we get:

[tex]\[ 89 = 54 + b^2 \][/tex]

[tex]\[ b^2 = 89 - 54 \][/tex]

[tex]\[ b^2 = 35 \][/tex]

So, [tex]\( b = \sqrt{35} \)[/tex].

The standard form equation of a hyperbola centered at the origin with vertices on the y-axis is:

[tex]\[ \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \][/tex]

Substituting [tex]\( a = \sqrt{54} \) and \( b = \sqrt{35} \),[/tex] we get:

[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

Therefore, the equation of the hyperbola is:

[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

This equation represents a hyperbola centered at the origin with vertices at [tex]\( (0, \pm \sqrt{54}) \) and foci at \( (0, \pm \sqrt{89}) \).[/tex]

Answer:

f(x)=-3+14x

Step-by-step explanation:

its the opposite

The inverse of the following function f(x)=3-14x will be [tex]f^-(x)[/tex] = [3 -f(x)]/14.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

A function is basically a relationship between which one variable will be dependent and another will be independent.

For example, let's say y = sinx then here x will be independent but y will be dependent.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +9 like that.

Given that the function

f(x)=3-14x

⇒ f(x) + 14x =3

⇒ 14x = 3 -f(x)

⇒ x =  [3 -f(x)]/14 hence, it will be the correct answer.

For more about the function

brainly.com/question/23712366

#SPJ5

Answer:

3n + 2

Step-by-step explanation:

-n + 4n -4 + 6

3n + 2

Answer:

The 99% of confidence limits for the proportion that plan to vote for the incumbent.

(0.6473 ,0.7527)

Step-by-step explanation:

Explanation:-

Given data the election of a local construction union involves 2,000 union members. Among them, 500 members are randomly selected.

Given large sample size 'N' = 2000

Given sample size 'n' = 500

Given data Of the 500 surveyed, 350 said they would vote for the incumbent.

The sample Proportion

                        [tex]p = \frac{x}{n} = \frac{350}{500} =0.7[/tex]

                       q = 1-p = 1 - 0.7 = 0.3

Confidence intervals:-

The 99% of confidence intervals are determined by

[tex](p-Z_{\alpha } \sqrt{\frac{pq}{n} } , p+Z_{\alpha }\sqrt{\frac{pq}{n} } )[/tex]

The z- score of 0.99 level of significance =2.576

[tex](0.7-2.576\sqrt{\frac{0.7X0.3}{500} } , 0.7+2.576\sqrt{\frac{0.7X0.3}{500} } )[/tex]

on using calculator, we get

(0.7 - 0.0527 ,0.7+0.0527)

(0.6473 ,0.7527)

Conclusion:-

The 99% of confidence limits for the proportion that plan to vote for the incumbent.

(0.6473 ,0.7527)

Answer: 320°

Step-by-step explanation:

This is a circle geometry.

The arc length of the circle is given to be 8πcm and the radius is 4.5cm.

Now the length of an arc of a circle is

Arc length = πr0°/180° or 2πr0°/360°

To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go

πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.

πr0° = 8π × 180

0°. = 8π × 180

-----------

π × r

= 8 × 180. 8 × 180

-------- or ---------

9/2. 4.5

= 8 × 180 × 2

------------

9

= 8 × 20 × 2

= 320°

or 8 × 180/4.5

= 1440/4.5

= 320°

Answer:

The minimum score required for the scholarship is 644.

Step-by-step explanation:

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.

In this problem, we have that:

[tex]\mu = 488, \sigma = 111[/tex]

What is the minimum score required for the scholarship?

Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.

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

[tex]1.405 = \frac{X - 488}{111}[/tex]

[tex]X - 488 = 1.405*111[/tex]

[tex]X = 644[/tex]

The minimum score required for the scholarship is 644.

Answer:

She drove [tex]\frac{147}{2} miles/ hour[/tex]

Step-by-step explanation:

We are given that Lydia drove 441 miles in 6 hours.

We are supposed to find how fast did she drive in miles per hour

Distance covered by Lydia in 6 hours = 441 miles

Distance covered by Lydia in 1 hour =[tex]\frac{441}{6}[/tex]

Distance covered by Lydia in 1 hour =[tex]\frac{147}{2} miles/ hour[/tex]

Hence She drove [tex]\frac{147}{2} miles/ hour[/tex]

Using the concept of stratified sampling, it is found that 10 people will be selected from those who responded yes.

In a stratified sample, the population is divided into groups, and the same number of elements of each group is surveyed.

In this problem:

A similar problem is given at https://brainly.com/question/24188753

To decide how many participants who answered 'yes' to include in a stratified random sample of 20, use the proportion of 'yes' answers out of 300 to calculate the sample from that stratum.

In a stratified random sample, the population is divided into groups, or strata, and a sample is taken from each group to ensure that each subgroup of the population is adequately represented. To determine the number of people that will be selected from those who responded yes in a stratified random sample, we need to find the proportion of 'yes' responses among the 300 respondents and then apply that proportion to the sample size of 20.

Assuming we know the exact number of people who responded 'yes', let's call that number 'Y'. The number of 'yes' responses in the stratified sample would then be (Y/300) * 20. Without the actual number of 'yes' responses, we cannot compute the exact number of people that should be selected from the 'yes' group. However, this formula demonstrates how you would calculate it once the value for 'Y' is known.

https://brainly.com/question/29852583

#SPJ3

Answer:

The null hypothesis is rejected.

There is  enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.

P-value=0.0036 (two tailed test).

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women that vote is differs from the proportion of men that vote.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

Being π1: proportion of men that vote, and π2: proportion of women that vote.

The significance level is 0.05.

The sample 1 (men), of size n1=(2744+1599)=4343 has a proportion of p1=0.6318.

[tex]p_1=X_1/n_1=2744/4343=0.6318[/tex]

The sample 2 (women), of size n2=(3733+1924)=5657 has a proportion of p2=0.6599.

[tex]p_2=X_2/n_2=3733/5657=0.6599[/tex]

The difference between proportions is (p1-p2)=-0.0281.

[tex]p_d=p_1-p_2=0.6318-0.6599=-0.0281[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{2744+3733}{4343+5657}=\dfrac{6477}{10000}=0.6477[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.6477*0.3523}{4343}+\dfrac{0.6477*0.3523}{5657}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00004}=\sqrt{0.00009}=0.0096[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.0281-0}{0.0096}=\dfrac{-0.0281}{0.0096}=-2.913[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=2\cdot P(t<-2.913)=0.0036[/tex]

As the P-value (0.0036) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.

Answer:

[tex]P=0.4737[/tex]

Step-by-step explanation:

First, we need to know that nCx give as the number of ways in which we can select x elements from a group of n. It is calculated as:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

Then, to select 3 fish in which at least one a them is a black goldfish we can:

1. Select one black goldfish and 2 yellow goldfish: There are 9 different ways to do this. it is calculated as:

[tex]3C1*3C2 =\frac{3!}{1!(3-1)!}* \frac{3!}{2!(3-2)!}=9[/tex]

Because we select 1 black goldfish from the 3 in aquarium and select 2 yellow goldfish from the 3 in the aquarium.

2. Select 2 black goldfish and 1 yellow goldfish: There are 9 different ways. it is calculated as:

[tex]3C2*3C1 =\frac{3!}{2!(3-2)!}* \frac{3!}{1!(3-1)!}=9[/tex]

3.  Select 3 black goldfish and 0 yellow goldfish: There is 1 way. it is calculated as:

[tex]3C3*3C0 =\frac{3!}{3!(3-3)!}* \frac{3!}{0!(3-0)!}=1[/tex]

Now, we identify that just in part 2 (Select 2 black goldfish and 1 yellow goldfish), two yellow goldfish and a black goldfish remain in the tank after the customer has left.

So, the probability that two yellow goldfish and a black goldfish remain in the tank after the customer has left given that the customer purchased a black goldfish is equal to:

[tex]P=\frac{9}{9+9+1} =0.4737[/tex]

Because there are 19 ways in which the customer can select a black fish and from that 19 ways, there are 9 ways in which two yellow goldfish and a black goldfish remain in the tank.

25

Step-by-step explanation:

25

Answer:

Here, we have:

P(5 days snow in this 8 days) = 8C5 x (0.85)^5 x (1 - 0.85)^3 = 0.084

P(6 days snow in this 8 days) = 8C6 x (0.85)^6 x (1 - 0.85)^2 = 0.238

P(7 days snow in this 8 days) = 8C7 x (0.85)^7  x (1 - 0.85)^1  = 0.385

P(8 days snow in this 8 days) = 8C8 x (0.85)^8 x (1 - 0.85)^0 = 0.272

Add up those above, then the probability that it will snow AT LEAST five of those days in February:

P = 0.084+ 0.238 + 0. 385 + 0.272 = 0.979

Hope this helps!

:)

Answer:

[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]

[tex] |62-78.9| = 16.9[/tex]

[tex] |63-78.9| = 15.9[/tex]

[tex] |68-78.9| = 10.9[/tex]

[tex] |72-78.9| = 6.9[/tex]

[tex] |79-78.9| = 0.1[/tex]

[tex] |80-78.9| = 1.1[/tex]

[tex] |83-78.9| = 4.1[/tex]

[tex] |93-78.9| = 14.1[/tex]

[tex] |94-78.9| = 15.1[/tex]

[tex] |95-78.9| = 16.1[/tex]

[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]

And replacing we got:

[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]

And the best anwer is

10.12

Step-by-step explanation:

We have the following data given:

62 63 68 72 79 80 83 93 94 95

And we need to begin finding the mean with the following formula:

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

And replacing we got:

[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]

Now we can find the mean absolute deviation like this:

[tex] |62-78.9| = 16.9[/tex]

[tex] |63-78.9| = 15.9[/tex]

[tex] |68-78.9| = 10.9[/tex]

[tex] |72-78.9| = 6.9[/tex]

[tex] |79-78.9| = 0.1[/tex]

[tex] |80-78.9| = 1.1[/tex]

[tex] |83-78.9| = 4.1[/tex]

[tex] |93-78.9| = 14.1[/tex]

[tex] |94-78.9| = 15.1[/tex]

[tex] |95-78.9| = 16.1[/tex]

And finally we can find the mean abslute deviation with the following formula:

[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]

And replacing we got:

[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]

And the best anwer is

10.12

Answer:

a. For n=25, the mean and standard deviation of the prices of the mobile homes all possible sample mean prices are ​$63,800 and ​$1,580​, respectively.

b. For n=50, the mean and standard deviation of the prices of the mobile homes all possible sample mean prices are ​$63,800 and ​$1,117​, respectively.

Step-by-step explanation:

In this case, for each sample size, we have a sampling distribution (a distribution for the population of sample means), with the following parameters:

[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{n}[/tex]

For n=25 we have:

[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{25}=7,900/5=1,580[/tex]

The spread of the sampling distribution is always smaller than the population spread of the individuals. The spread is smaller as the sample size increase.

This has the implication that is expected to have more precision in the estimation of the population mean when we use bigger samples than smaller ones.

If n=50, we have:

[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{50}=7,900/7.07=1,117[/tex]

For samples of size 25 and 50, the mean of x bar is $63,800. The standard deviation of x bar is $1580 for a sample size of 25 and $1117 for a sample size of 50.

a. For samples of size 25, the mean of x bar is equal to the population mean, which is $63,800. The standard deviation of x bar is equal to the population standard deviation divided by the square root of the sample size. So, the standard deviation of x bar is $7900/sqrt(25) = $1580.

b. For samples of size 50, the mean of x bar is still $63,800. The standard deviation of x bar is $7900/sqrt(50) = $1117. Note that as the sample size increases, the standard deviation of x bar decreases.

https://brainly.com/question/14747159

#SPJ11

Answer:

1.4

Step-by-step explanation:

4.6 + (- 3.2)

A plus sign and a minus sign results in a minus sign

Re-write the expression without the parenthesis

4.6 - 3.2

Subtract

1.4

Hope this helps :)

Answer:

the answer is attached to the picture

Answer:

Step-by-step explanation:

if x= -2

and P(x)=x^4+4x^3+6x^2-8

then P(-2)=(-2)^4+4*(-2)^3+6*(-2)^2-8=16-32+24-8=0

so P(x)=(x+2)* Q(x)   and P(x) is divisible by x+2

Given Information:

Probability of super event = P(S) = 0.0023

Number of suppliers = n = 3

Probability of unique event = P(U) = 0.014

Required Information:

Probability that all three suppliers will be disrupted = ?

Answer:

P(3) = 0.0023

Step-by-step explanation:

We want to find out the approximate probability that all three suppliers will be disrupted at the same time at some point during the next five years.

The required probability is given by

P(n) = P(S) + (1 - P(S))*P(U)ⁿ

Where P(S) is the probability of super event that will disrupt all suppliers, P(U) is the probability of unique event that would disrupt one of the suppliers and n is the number of suppliers.

P(3) = 0.0023 + (1 - 0.0023)*(0.014)³

P(3) = 0.0023 + (0.9977)*(0.014)³

P(3) = 0.0023

The correct option is C = 0.0023

Therefore, there is 0.23% probability that all three suppliers will be disrupted at the same time at some point during the next five years.