A man is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet, all from different wineries. a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? (2 points) b) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (4 points) c) If 6 bottles are randomly selected, what is the probability that all of them are the same variety?

Answer:

0.62% probability that the mean of our sample is greater than $70.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 65, \sigma = 20, n = 100, s = \frac{20}{\sqrt{100}} = 2[/tex]

What is the probability mean of our sample is greater than $70.

This is 1 subtracted by the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{70 - 65}{2}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a pvalue of 0.9938

1 - 0.9938 = 0.0062

0.62% probability that the mean of our sample is greater than $70.

Answer:

a) The size of each of the two samples(equal), n = 518

b) Sample size, n = 439

Step-by-step explanation:

For clarity and easiness of expression, the complete solution to this question is handwritten and attached as files. Check the attached files below for the explanations.

Answer:

y = 12 + 6x

y = 12x

Step-by-step explanation:

From the information provided, the following equations are derived:

y = 12 + 6x    ------- Eqn 1

y = 12x          ------- Eqn 2

Since Eqns 1 and 2 have the same subject, we equate them to solve for x. We have:

12x = 12 + 6x

Putting like terms together, we have:

12x - 6x = 12 ⇒ (12 - 6)x = 12

6x = 12 ⇒ x = 2

x = 2

Substitute x into Eqn 1 or 2

Eqn 1

y = 12 + 6x

y = 12 + 6(2) = 12 + 12

y = 24

Eqn 2

y = 12x

y = 12(2)

y = 24

It means that it will take Ms. Ironperson and Mr. Thoro 2 days apiece to produce the same number of posters at the current rate (which is 24 posters). Both Ms. Ironperson and Mr. Thoro will individually take 2 days to produce 24 Avenger posters apiece.

Answer:

The amount of heat lost by the aluminum is 31,500 J

Step-by-step explanation:

Given;

mass of aluminum, m =  500 g

initial temperature of the aluminum, θ₁ = 100° C

final temperature of the aluminum, θ₂ = 30°C

specific heat capacity of water, C = 4.18 J/g °C

specific heat capacity of aluminum , C = 0.90 J/g

Heat lost by the aluminum is equal to heat gained by the water.

The amount of heat lost by the aluminum, is calculated as;

Q = MCΔθ

Q = 500 x 0.9 (100 - 30)

Q = 500 x 0.9 x 70

Q = 31,500 J

Therefore, the amount of heat lost by the aluminum is 31,500 J

Answer:

[tex] E(100 Y^2) =100 E(Y^2)[/tex]

And we have that :

[tex] E(Y^2) =\sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(Y^2) =0^2 *0.6 + 1^2 *0.25 +2^2*0.10 +3^2 *0.05 = 1.1[/tex]

And finally we have:

[tex] E(100 Y^2) =100 *1.1 = 110[/tex]

Step-by-step explanation:

For this case we have the following probability masss function given:

Y         0           1              2             3

p(Y)    0.6        0.25      0.10         0.05

And we can define the surcharge with this expression [tex] 100Y^2[/tex]

We want to find the expected value for the last expression and we can do it on this way:

[tex] E(100 Y^2) =100 E(Y^2)[/tex]

And we have that :

[tex] E(Y^2) =\sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(Y^2) =0^2 *0.6 + 1^2 *0.25 +2^2*0.10 +3^2 *0.05 = 1.1[/tex]

And finally we have:

[tex] E(100 Y^2) =100 *1.1 = 110[/tex]

Answer:

[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]

And we can find this probability with this difference

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]

And we can find the difference with the normal standard distirbution or excel:

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]

Step-by-step explanation:

Let X the random variable that represent the hotel room cost of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(202,70)[/tex]  

Where [tex]\mu=202[/tex] and [tex]\sigma=70[/tex]

We are interested on this probability

[tex]P(210<X<290)[/tex]

The z score formula is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the formula we got:

[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]

And we can find this probability with this difference

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]

And we can find the difference with the normal standard distirbution or excel:

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]

Answer:

For the given data, the mean is 50.8, the median is 51, and the mode is 52.

For the sample with this error, the mean is 48.7, the median is 51, and the mode is 52.

For the sample with this value removed, the mean is 43.2, the median is 50, and the mode is 52.

Step-by-step explanation:

We are given the following set of sample data below;

18, 26, 30, 42, 50, 52, 52, 76, 78, 84.

The formula for calculating mean is given by;

         Mean  =  [tex]\frac{\text{Sum of all data values}}{\text{Total number of observations}}[/tex]

                     =  [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 76+ 78+ 84}{10}[/tex]  

                     =  [tex]\frac{508}{10}[/tex]  =  50.8

For calculating median, we have to observe that the number of observations (n) in our data is even or odd, i.e;

                    Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                    Median  =  [tex]\frac{(\frac{n}{2})^{th}\text{ obs.} +(\frac{n}{2}+1)^{th}\text{ obs.} }{2}[/tex]

Now, here in our data the number of observations is even, i.e. n = 10.

So, Median  =  [tex]\frac{(\frac{n}{2})^{th}\text{ obs.} +(\frac{n}{2}+1)^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{(\frac{10}{2})^{th}\text{ obs.} +(\frac{10}{2}+1)^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{5^{th}\text{ obs.} +6^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{50+52 }{2}[/tex]  =  51

A Mode is a value that appears the maximum number of times in our data.

In our data, the value 52 is appera]ing maximum number of times, i.e. 2 times which means that mode of our data is 52.

Now, suppose the value 76 in the data is mistakenly recorded as 55 instead of 76. For the sample with this error,

            New Mean  =   [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 55+ 78+ 84}{10}[/tex]  

                                =  [tex]\frac{487}{10}[/tex]  =  48.7

Now, suppose the value 76 in the original sample is inadvertently removed from the sample. For the sample with this value removed,

            New Mean  =   [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 78+ 84}{9}[/tex]  

                                =  [tex]\frac{432}{10}[/tex]  =  43.2

            So, Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                                 =  [tex](\frac{9+1}{2})^{th} \text{ obs.}[/tex]

                                 =  [tex]5^{th} \text{ obs.}[/tex] = 50

Answer:

  x = -1/5, x = 1

Step-by-step explanation:

Maybe you want to find x.

Subtract the right side and collect terms.

  6x^2 +4x^2 -6x -4 -(2x -2) = 0

  10x^2 -8x -2 = 0

  5x^2 -4x -1 = 0 . . . . . . divide by 2

  (5x +1)(x -1) = 0 . . . . . . factor

Solutions are the values of x that make these factors zero:

  5x +1 = 0   ⇒   x = -1/5

  x -1 = 0   ⇒   x = 1

Solutions are x = -1/5, x = 1.

Answer:

Step-by-step explanation:

[tex]y = f(x) =\frac{1}{\sqrt{3 \pi} } e^{-x^{2/3}}[/tex]

y = 0, x = 0 and x = 3

Consider an element of thickness dx at a distance x from the origin. By Cylindirical Shell Method, the volume of the element is given by

[tex]dV=(2\pi rdr)h=(2\pi xdx)f(x) => dV=(2\pi xdx) \frac{1}{\sqrt{3\pi}}e^{-x^{\frac{2}{3}}}[/tex]

[tex]dV=2\sqrt{\frac{\pi}{3}}xe^{-x^{\frac{2}{3}}}dx[/tex]

Integrate the above integral over the limits x=0 to x=3 which implies

[tex]\int_{0}^{V}dV=2\sqrt{\frac{\pi}{3}}\int_{0}^{3}xe^{-x^{\frac{2}{3}}}dx[/tex]

Solve by subsititution

[tex]Let,\\ -x^{\frac{2}{3}}=y => \frac{-2}{3}x^{\frac{-1}{3}}dx=dy => x^{\frac{-1}{3}}dx=\frac{-3}{2}dy[/tex]

Also, apply the new limits

[tex]At,\\\\ x=0, y=0 \ and \ At, x=3, y=-\sqrt[3]{9}[/tex]

This implies,

[tex]\int_{0}^{V}dV=2\sqrt{\frac{\pi}{3}}\int_{0}^{3}x^{\frac{4}{3}}e^{-x^{\frac{2}{3}}}x^{\frac{-1}{3}}dx=2\sqrt{\frac{\pi}{3}}\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}(\frac{-3}{2})dy[/tex]

[tex]V=-\sqrt{3\pi}\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}dy[/tex]

Let,

[tex]I=\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}dy[/tex]

Integrate by parts the above integral

[tex]u=y^2 \ and \ dv=e^ydy => du=2y \ and \ v=e^y[/tex]

Integrate by parts formula

[tex]\int udv=uv-\int vdu => y^2e^y-\int 2ye^ydy[/tex]

Again integrate by parts

[tex]u=y \ and \ dv=e^ydy => du=1 \ and \ v=e^y[/tex]

Integrate by parts formula

[tex]\int udv=uv-\int vdu => y^2e^y-2[ye^y-e^y]=e^y[y^2-2y+2][/tex]

Therefore,

[tex]I=[e^y(y^2-2y+2)]_{0}^{-\sqrt[3]{9}}\\\\=e^{-2.0802}[(2.0802)^2+2(2.0802)+2]-e^{0}[0-0+2]\\\\\frac{(4.3272+4.1604+2)}{8.0061}-2\\\\=\frac{10.4876}{8.0061}-2\\\\=1.3099-2\\\\=-0.6901[/tex]

This implies, the volume is

[tex]V=-\sqrt{3\pi}I\\\\=-\sqrt{3\times 3.142} \times (-0.6901)\\\\=3.0701 \times 0.6901\\\\=2.1186[/tex]

That is, up to three decimal places

[tex]V\approx 2.118[/tex]

[tex]answer \\ = 2 , 4 , 5 \\ additional \: information \\ let \: r \: be \: a \: relation \: a \: to \: b. \: then \: the \: set \\ of \: first \: components \: or \: the \: set \: of \: \\ elements \: of \: a \: are \: called \: domain \\ and \: the \: set \: of \: second \: components \\ or \: the \: set \: of \: elements \: of \: b \: are \: called \: the \: range. \\ hope \: it \: helps[/tex]

Answer: 20% of 500= 100

So 500-100 = 400

4x100= 400

Step-by-step explanation:

Answer:

a sultan

Step-by-step explanation:

i looked it up on quizlet after thinking it was sultan and i was right

anyways the answer is sultan and its correct

have a good day!

Answer

the answer is sultan

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area = area of rectangle 1 + area of rectangle 2 + area of rectangle 3 +area of triangle

= 8*12 +  12*9 + 19 *5 +  (1/2) * 4 *12

= 96 + 108 + 95 + 24

= 323 sq. cm

Answer:

Step-by-step explanation:

Perhaps you're factoring ...

  2x² +3x -54

  = 2x² +12x -9x -54 . . . . rewrite 3x appropriately

  = 2x(x +6) -9(x +6) . . . . factor pairs of terms

  = (2x -9)(x +6) . . . . . . . . finish the factoring

The factors are (2x -9) and (x +6).

Answer:

The width or range of the confidence interval with sample size 200 will be about half of that of the confidence interval with sample 50.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)

- For the two random samples, of sizes 50 and 200, the Central limit theorem allows us to say that the sample mean is approximately equal to the population mean as this random sample satisfies the condition of being a simple random sample and a distribution obtained from a normal distribution.

- Making the right assumption that population standard deviation is known and z-distribution is used to find the critical value

Critical value for 95% = 1.96

The critical value for both samples are the same then.

- Standard Error of the mean = σₓ = (σ/√n)

where σ = population standard deviation

n = sample size

For the two distributions

Confidence Interval = (Sample mean) ± [(Critical value) × (Standard Error of the mean)

(Sample mean)₅₀ = (Sample mean)₂₀₀

(Critical value)₅₀ = (Critical value)₂₀₀

(Standard Error of the mean)₅₀ = (σ/√50) = 0.1414σ

(Standard Error of the mean)₂₀₀ = (σ/√200) = 0.0707σ

0.1414σ = 2 × 0.0707σ

(Standard Error of the mean)₅₀ = 2 × (Standard Error of the mean)₂₀₀

(Standard Error of the mean)₅₀ > (Standard Error of the mean)₂₀₀

Hence,

(Margin of Error)₅₀ > (Margin of Error)₂₀₀

(Margin of Error)₅₀ = 2 × (Margin of Error)₂₀₀

Confidence Interval = (Sample mean) ± (Margin of error)

Hence, the width or range of the confidence interval with sample size 50 will be about two times larger than the confidence interval with sample 200.

Hope this Helps!!!

Answer:

480

Step-by-step explanation:

Answer: [tex]2x^2+3x-2[/tex]

Step-by-step explanation:

You can do long division, which is very very hard to show with typing on a keyboard. You essentially want to divide the leading coefficient for each term. Ill try my best to explain it.

Do [tex]\frac{2x^3}{x}=2x^2[/tex]. Write 2x^2 down. Now multiply (x - 3) by it. Then subtract it from the trinomial.

[tex]2x^2*(x-3)=2x^3 -6x^2\\(2x^3 -3x^2-11x+6)-(2x^3-6x^2) = 3x^2-11x+6[/tex]

Now do [tex]\frac{3x^2}{x} =3x[/tex]. Write that down next to your 2x^2. Multiply 3x by (x - 3) to get:

[tex]3x(x-3)=3x^2-9x\\(3x^2-11x+6)-(3x^2-9x)=-2x+6[/tex]

Your final step is to do [tex]\frac{-2x}{x} =-2[/tex]. Write this -2 next to your other two parts

Multiply -2 by (x - 3) to get:

[tex]-2(x-3)=-2x+6\\(-2x+6)-(-2x+6)=0[/tex]

Our remainder is 0 so that means (x - 3) goes into that trinomial exactly:

[tex]2x^2+3x-2[/tex] times

Answer:

2x² + 3x -2

Step-by-step explanation:

2x³ - 3x² - 11x + 6 : (x - 3)

2x³ - 6x² from (x - 3) * 2x²

-------------------------- —

3x² - 11x + 6

3x² - 9x from (x - 3) * 3x

-------------------------- —

- 2x + 6

- 2x + 6 from (x - 3) * (-2)

-------------------------- —

0

so 2x³ - 3x² - 11x + 6 : (x - 3) = 2x² + 3x -2

Answer:

[tex]2043.67[/tex]

Step-by-step explanation:

Hundredths is at 2 decimal places.

The thousandths place is higher than 5, so add 1 to the hundredths place.

Answer:

2043.67

Step-by-step explanation:

If you’ve ever rounded a number, you would know that if it’s 5 or higher, round it up, and if it’s 4 or lower, round it down. In this case, the second decimal place reads ’6’ which is higher that 5, so we round up. The rest of the numbers stay the same

2043.67

Answer:

a) Median amount of time that is spent is around 2.3, rounded to 2.

b) 4 unit time

c) Mean amount of time is bigger than the median.

Step-by-step explanation:

Find the given attachment.

Note: Complete Question, along with the diagram is added

Answer:

Sqrt(13)

Step-by-step explanation:

d = sqrt(3^2 + 2^2) = sqrt (13)

Answer:

Brainelist~~~!!!

Step-by-step explanation:

4c=3

c=3/4

c=0.75

The solution of the linear equation 4·c = 3, obtained by solving for the variable c is; c = 3/4

A linear equation is an equation that can be expressed in the form; y = m·x + c

The equation 4·c = 3 is a linear equation

In order to solve the equation 4·c = 3 for the variable c, the variable c needs to be isolated to one side of the equation, by dividing both sides of the equation by 4 as follows;

4·c = 3

(4·c)/4 = 3/4

c = 3/4

Therefore, the solution of the equation, 4·c = 3 is; c = 3/4

Learn more on linear equations here: https://brainly.com/question/30338252

#SPJ6

9514 1404 393

Answer:

  £2272.54

Step-by-step explanation:

An equation for the value is ...

  v = £2300(0.998^t)

Then for t=6, the value is ...

  v = £2272.54

_____

Additional comment

The growth factor (0.998) is (1 - decay rate) = (1 -0.002).

Answer:

the answer is 2272.54

Step-by-step explanation:

:))

Answer:

[tex]105.13ft^2[/tex]

Step-by-step explanation:

Rectangle

[tex]A=lw\\=10*8\\=80ft^2\\[/tex]

Semicircle

[tex]A=\frac{1}{2} \pi r^2\\=\frac{1}{2}* \pi *4^2\\=25.13ft^2[/tex]

Add both values together

[tex]80+25.13\\=105.13ft^2[/tex]

Answer: 105.13

Step-by-step explanation:

Answer:

618

Step-by-step explanation:

l x w

34x5

14x27

5x14

618

Answer:

(B) Centers: The crocodiles have a greater median length than the alligators

(C) Spreads: The lengths of the alligators are more spread out

Step-by-step explanation:

The question is incomplete without the diagram. Find attached the diagram used in solving the question

Centers: this is the median of the distribution

Spread: this is the variation of the data distribution. The range can be used to find the spread. If the range is large, the spread is larger and If the range is small, the spread is smaller.

Range = highest value - lowest value

From the diagram:

Median of crocodile = 17

Median of the alligator = 9

Therefore, for Centers: The crocodiles have a greater median length than the alligators (option B)

Spread for crocodile data = from 15 to 19

Range = 19-15 = 4

Spread for alligator data = from 7 to 15

Range = 15-7 = 8

For Spreads: The lengths of the alligators are more spread out.

Answer: b and c

Step-by-step explanation:

Answer:

Geometric Sequence.

Step-by-step explanation:

Geometric sequence. If you take a close look at the graph, it never touches the x - axis. If you use division in a geometric sequence, you will get a very small number, but you will never touch the axis.

uhh there is no such thing because -1 isn't a perfect square.

Answer:

[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]

And replacing we got:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=2, p=1-0.16=0.84)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

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

And we can find this probability:

[tex] P(X \geq 1)[/tex]

And we can solve this probability like this:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)[/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]

And replacing we got:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]

Answer:

746 mi^2

Step-by-step explanation:

The top rectangle has an area of

A = 22*23 =506

The bottom rectangle has an area of

A =10 *24 = 240

Add the areas together

506+ 240 =746

Answer:

746

Step-by-step explanation:

22*23= 506

24*10= 240

506+240= 746

plz mark brainliest

Answer:

[tex]9\dfrac{5}{6}[/tex]

Step-by-step explanation:

[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]

Hope this helps!