Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use ???? = 0.01.

Answer:

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

Step-by-step explanation:

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.

This means that [tex]\mu = 192723, \sigma = 42000[/tex]

Sample of 75:

This means that [tex]n = 75, s = \frac{42000}{\sqrt{75}}[/tex]

What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?

1 subtracted by the p-value of Z when X = 190000. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}[/tex]

[tex]Z = -0.56[/tex]

[tex]Z = -0.56[/tex] has a p-value of 0.2877

1 - 0.2877 = 0.7123

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

Answer:

C

Step-by-step explanation: just C-

Answer: Its not c

Step-by-step explanation: It is A

Answer:

Step-by-step explanation:

Given:

Substitute x= -3:

Answer:

A FORMULA is an expression that uses variables to state a rule.

Answer:

y=1/2x+1/2

Step-by-step explanation:

In order to find the slope, you can use rise/run, in this case, the slope is 1/2 and the y-intercept is at (0, 0.5)

The line in the middle is half the length of the line on the outside. Multiply the middle line by 2 and set it equal to the outside line.

2(x-3) = x + 6

Simplify:

2x -6 p x + 6

Add 6 to both sides

2x = x + 12

Subtract x from both sides:

X = 12

The answer is B) 12

Answer:

Coefficient of skewness = 0.5785

Population standard deviation = 88.154

Step-by-step explanation:

Given the data:

Month Jan Feb Mar Apr May Jun Jul

Unit Sales 314 285 158 482 284 310 281

Reordered data : 158, 281, 284, 285, 310, 314, 482

The population mean of the data :

Mean, μ = Σx / n = 2114 / 7 = 302

The median :

1/2(n+1)th term

n = 7

1/2(8)th term

Median = 4th term = 285

The population standard deviation, s :

s = √(Σ(x - μ)²/n)

s = √[(158-302)^2 + (281-302)^2 + (284-302)^2 + (285-302)^2 + (310-302)^2 + (314-302)^2 + (482-302)^2] / 7

s= √(54398 / 7)

s = √7771.1428

s = 88.154

The Pearson Coefficient of skewness :

[3(μ - median)] / s

3(302 - 285) / 88.154

3(17) / 88.154

51 / 88.154

= 0.5785

Answer:

x=2pi/3 +2pi n, 4pi/3 +2pi n for all integar of n.

Step-by-step explanation:

Answer:

Answer = √(0.301 × 0.699 / 83) ≈ 0.050

A 68 percent confidence interval for the proportion of persons who work less than 40 hours per week is (0.251, 0.351), or equivalently (25.1%, 35.1%)

Step-by-step explanation:

√(0.301 × 0.699 / 83) ≈ 0.050

We have a large sample size of n = 83 respondents. Let p be the true proportion of persons who work less than 40 hours per week. A point estimate of p is  because about 30.1 percent of the sample work less than 40 hours per week. We can estimate the standard deviation of  as . A  confidence interval is given by , then, a 68% confidence interval is , i.e., , i.e., (0.251, 0.351).  is the value that satisfies that there is an area of 0.16 above this and under the standard normal curve.The standard error for a proportion is √(pq/n), where q=1−p.

Hope this answer helps you :)

Have a great day

Mark brainliest

Explanation:

It's most effective to use a contingency table because we have two variables here: 1) the responses, and 2) the party affiliation.

We can have the responses along the rows and the party affiliation along the columns, or vice versa.

See the example below. The values are completely random simply for the purpose of the example (and not drawn from any real life data source).

As per the given options, the appropriate for the displaying these data will be contingency table. Hence, option D is correct.

A pie chart is a visual depiction of information in the shape of a pie, where the pieces of the pie represent the magnitude of the data. To depict data as a pie chart, you need a list of quantitative variables as well as categorical variables.

As per the given information in the question,

A contingency table in statistics is a particular kind of matrix-style table that shows the frequency of the variables. They are extensively utilized in scientific, engineering, business intelligence, and survey research.

To know more about Pie charts:

https://brainly.com/question/24207368

#SPJ5

↦ [tex]\huge\underline{ \underline{Answer:-}}[/tex]

[tex]5x = 3x + 12 \\ 5x - 3x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Step-by-step explanation:

hope it is h helpful to you

Answer:

5/11.... you put the 5 which is yellow over the others which is 12 but remember she removed 1 so it would be equal to 11

Answer:

ok so if she takes a red apple out that means

2 red

5 yellow

4 green

11 in total

so 5/11

The answer is D

Hope This Helps!!!

Answer:

we conclude that population mean is not 11.5

Step-by-step explanation:

The hypothesis :

H0 : μ = 11.5

H1 : μ ≠ 11.5

The test statistic :

(xbar - μ) ÷ (s/√(n))

Test statistic = (12 - 11.5) ÷ (2/√(16))

Test statistic = (0.5) ÷ (2 ÷ 4)

Test statistic = 0.5 / 0.5

Test statistic = 1

The Pvalue from test statistic value, df = n - 1 = 16 - 1 = 15

Pvalue = 0.333

Pvalue > α ; we fail to reject the null ; Hence, we conclude that population mean is not 11.5

Answer:

1. +30

2. +64

3. 0

4. -3

5. +24

6. +18

7. -48

8. -64

9. +21

10. -30

11. +12

12. 0

13. -4

14. +56

15. +2

Step-by-step explanation:

When multiplying integers:

two negatives = positive

two positives = positive

one negative x one positive = negative

So, if the signs are the same, the answer is positive.

If you have two different signs, the answer is negative.

You multiply the integers like normal.

Anything multiplied by zero = 0.

Anything multiplied by one = itself (just be careful of the sign).

Answer:

0.001831055

Step-by-step explanation:

Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14

As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 14)

P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2

               = 120 * 0.5^14 *(1-0.5)^2

= 0.001831055

Step-by-step explanation:

[tex]\dfrac{2x^2+x-6}{x+x-6} = \dfrac{(2x-3)(x+2)}{2(x-3)}[/tex]

9514 1404 393

Answer:

  $500

Step-by-step explanation:

Bruno's fraction of the total contribution was ...

  Bruno / Total = $20/($25 +20 +35) = 20/80 = 1/4

Then Bruno's share of the earnings is this same fraction, so is ...

  (1/4) × ($2000) = $500

Step-by-step explanation:

let y = x+5/4

Interchanging x and y , we get ;

x = y+5/4

or, 4x = y+5

or, 4x-5 = y

or, g(x) -1 = 4x-5

Answer:

In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:

4x-5

Answer:

Solution given:

B.g(x)=[tex]\frac{x+5}{4}[/tex]

let

g(x)=y

y=[tex]\frac{x+5}{4}[/tex]

Interchanging role of x and y

we get:

x=[tex]\frac{y+5}{4}[/tex]

doing crisscrossed multiplication

4x=y+5

y=4x-5

So

g-¹(x)=4x-5

Answer:

The appropriate answer is "0.9803".

Step-by-step explanation:

According to the question,

The probability of sample proportion differs from population proportion by les than 4% will be:

= [tex]P(-\frac{0.04}{\sqrt{\frac{0.23\times 0.77}{602} } }<z<\frac{0.04}{\sqrt{\frac{0.23\times 0.77}{602} } } )[/tex]

= [tex]P(-\frac{0.04}{\sqrt{\frac{0.1771}{602} } }<z<\frac{0.04}{\sqrt{\frac{0.1771}{602} } } )[/tex]

= [tex]P(-2.33<z<2.33)[/tex]

= [tex]0.9803[/tex]

Answer:

The standard deviation is of 8.586.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have a genetic mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

About 9% of the population has a particular genetic mutation.

This means that [tex]p = 0.09[/tex]

900 people are randomly selected.

This means that [tex]n = 900[/tex]

Find the standard deviation for the number of people with the genetic mutation in such groups of 900.

[tex]\sqrt{V(X)} = \sqrt{900*0.09*0.91} = 8.586[/tex]

The standard deviation is of 8.586.

Answer:

Bunny Hill Ski Resort:

y = 10x + 35

Diamond Ski Resort:

y = 5x + 40

Point where the cost is the same:

(1, 45)

Step-by-step explanation:

The question tells us that:

$35 and $40 are initial fees

$10 and $5 are hourly fees

This means that x and y will equal:

x = number of hours

y = total cost of ski rental after a number of hours

So we can form these 2 equations:

y = 10x + 35

y = 5x + 40

Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.

Because they both equal y, we can set the equations equal to each other:

10x + 35 = 5x + 40

And we use basic algebra to solve for x:

10x + 35 = 5x + 40

(subtract 5x from both sides)

5x + 35 = 40

(subtract 35 from both sides)

5x = 5

(divide both sides by 5)

x = 1

Remember, x equals the number of hours.

That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)

Hope it helps (●'◡'●)

Answer: 10

Step-by-step explanation:

4 x 2 x 5 = 40

9 + 2 + 7 + 8 + 4 = 30

40 - 30 = 10

= 10

Answer:

Step-by-step explanation:

If the triangles given in the picture are similar,

ΔVUT ~ ΔVLM

By the property of similarity of two triangles, their corresponding sides will be proportional.

[tex]\frac{TV}{VM}= \frac{VL}{VU}[/tex]

[tex]\frac{49}{14}=\frac{28}{8}[/tex]

[tex]\frac{7}{2}=\frac{7}{2}[/tex]

True.

Therefore, ΔVUT and ΔVLM will be similar.

Answer:

The answer is 40 chocolates in the box in total

Answer:

[tex]37 \frac{7}{12}[/tex] inches.

Step-by-step explanation:

Let's start by converting all of these mixed numbers to improper fractions to handle them a little better.

56 × 4 = 224 ⇒ 224 + 1 = [tex]\frac{225}{4}[/tex]

18 × 3 = 54 ⇒ 54 + 2 = [tex]\frac{56}{3}[/tex]

So, we have our improper fractions. Now, we need to convert each to twelfths so we can subtract.

225 × 3 = 675

56 × 4 = 224

[tex]\frac{675}{12} - \frac{224}{12}[/tex] = [tex]\frac{451}{12}[/tex]

[tex]\frac{451}{12} = 37 \frac{7}{12}[/tex]

So, the answer is [tex]37 \frac{7}{12}[/tex] inches.

Answer:

The probability of observing between 43 and 64 successes=0.93132

Step-by-step explanation:

We are given that

n=100

p=0.50

We have to find the probability of observing between 43 and 64 successes.

Let X be the random variable  which represent the success of population.

It follows binomial distribution .

Therefore,

Mean,[tex]\mu=np=100\times 0.50=50[/tex]

Standard deviation , [tex]\sigma=\sqrt{np(1-p)}[/tex]

[tex]\sigma=\sqrt{100\times 0.50(1-0.50)][/tex]

[tex]\sigma=5[/tex]

Now,

[tex]P(43\leq x\leq 64)=P(42.5\leq x\leq 64.5)[/tex]

[tex]P(42.5\leq x\leq 64.5)=P(\frac{42.5-50}{5}\leq Z\leq \frac{64.5-50}{5})[/tex]

[tex]=P(-1.5\leq Z\leq 2.9)[/tex]

[tex]P(42.5\leq x\leq 64.5)=P(Z\leq 2.9)-P(Z\leq- 1.5)[/tex]

[tex]P(42.5\leq x\leq 64.5)=0.99813-0.06681[/tex]

[tex]P(43\leq x\leq 64)=0.93132[/tex]

Hence, the probability of observing between 43 and 64 successes=0.93132

Answer: 3 years

Step-by-step explanation:

Interest is calculated as:

= (P × R × T) / 100

where

P = principal = 150,000

R = rate = 2.5%.

I = interest = 11250

T = time = unknown.

I = (P × R × T) / 100

11250 = (150000 × 2.5 × T)/100

Cross multiply

1125000 = 375000T

T = 1125000/375000

T = 3

The time taken will be 3 years

Answer:

-3a+3bx+2ab

Step-by-step explanation:

Answer:

[tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex]

The graph is shown below.

=========================================================

Explanation:

Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.

This is close to 5x-7, except we're off by 2 units.

In other words,

5x-7 = (5x-5)-2

since -7 = -5-2

Based on that, we can then say,

[tex]g(x) = \frac{5x-7}{x-1}\\\\g(x) = \frac{5x-5-2}{x-1}\\\\g(x) = \frac{(5x-5)-2}{x-1}\\\\g(x) = \frac{5(x-1)-2}{x-1}\\\\g(x) = \frac{5(x-1)}{x-1}+\frac{-2}{x-1}\\\\g(x) = 5+\frac{-2}{x-1}\\\\g(x) = \frac{-2}{x-1}+5[/tex]

This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).

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

Compare the equation [tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex] to the form [tex]g(x) = \frac{a}{x-h}+k\\\\[/tex]

We can see that

The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.

The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.

The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.

The graph is shown below. Some points of interest on the hyperbola are

Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.

Answer:

x = 4/3

Step-by-step explanation: