in how many ways can we seat 6 people at a round table if john and sam insist on sitting next to each other? (two seatings are equivalent if one is a rotation of the other.)

For given study the sample would be - The number of pixies over Mermaid Lagoon on the 16 days observed.

Here, peter pan is studying the migration patterns of pixies. as part of this research, he counts the number of pixies over mermaid lagoon on 16 randomly selected days.

We need to find the sample of this study.

We know that, a sample is nothing but a group of elements chosen from the population. It is a small data set that you obtain from a larger set of data to represent the population.

In this case ths sample would be - The number of pixies over Mermaid Lagoon on the 16 days observed.

Therefore, sample for this situation - The number of pixies over Mermaid Lagoon on the 16 days observed.

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The options for given question:

1) The number of pixies over Mermaid Lagoon on the 16 days observed.

2) Peter Pan

3) The number of pixies in Neverland

4) The number of pixies over Mermaid Lagoon on any day.

There are 300 number of ways in which committee can be formed. It can be solved by the fomula of combination.

What is the formula of combination?

Following is the fomula of combination:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Here, n is the total objects available and r is the number of object need to choose from n objects.

Consider no man refuses to serve together. Now, number of ways in which 4 men and 3 women committee can be formed from a group of 7 men and 6 woman.

[tex]^7C_4\times\ ^6C_3[/tex]

Now, consider a goup in which the two persons who do not want to serve togather are togather. Consider these person as a single person. Now, we need to choose 3 men (two individual men and one group of 2 men will make 4 men in the group) from 6 men (7 converts into 6 because group of two person is considerd as 1.).

[tex]\ ^6C_3\times\ ^6C_3[/tex]

Now, subtract [tex]\ ^6C_3\times\ ^6C_3[/tex] from [tex]^7C_4\times\ ^6C_3[/tex] to get the actual answer.

[tex]^7C_4\times\ ^6C_3-\ ^6C_3\times\ ^6C_3\\=\frac{7!}{4!3!}\times \frac{6!}{3!3!}-\frac{6!}{3!3!}\times\frac{6!}{3!3!}\\=35\times20-20\times20\\=20\times15\\=300[/tex]

Hence, there are 300 number of ways in which committee can be formed. It can be solved by the fomula of combination.

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As per the Pythagoras theorem, there are totally 4 triangles possible.

Pythagoras theorem:

In geometry, Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs.

Given,

Here we need to find how many (non-congruent) isosceles triangles exist which have a perimeter of 10 and integer side lengths.

As per the Pythagoras theorem, we know that the sum of two sides should be greater than the third.

And here we have the isosceles triangles, then the value of two side of the triangle is equal.

Here the perimeter of the triangle is 10.

Then the values must be the sum of 10,

=> 2, 6, 2

=> 1, 1, 8

=> 3, 3, 4

=> 4, 4, 2

These are the possible combinations.

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The area of the largest rectangle that can be inscribed in the right triangle is calculated to be 6 cm^2

As we know that for a rectangle of width W and length L the area is given as;

A = L × W

Now let's say that L is along the 8 cm side and W is along the 3 cm side, let's find a relation between these two.

When we inscribe the rectangle in the larger triangle the quotient between the catheti of the right triangle must be equal to the quotient of the catheti of the right triangle that is generated.

Therefore that new triangle will have legs equal to the;

8cm - L and W.

Then we have that:

8cm - L / W = 8 cm / 3 cm

L = 8 cm - 8/3 × W

Now we can write L in terms of W so that we can replace that in the area equation to get

A = (8cm - (8/3)×W)×W = 8cm×W - (8/3)×W^2

This is the equation we have to maximize, also this is a quadratic polynomial of negative leading coefficient, which means that the maximum is at the vertex.

As we know the vertex of the general quadratic polynomial;

a × x^2 + b × x + c

is at:

x = -b / 2a

Then, in this scenario, the vertex is at;

W = (-8 cm) / (2 × 8/3) = 1.5 cm

Then the length is given by:

L =  8cm - (8/3) × 1.5cm = 4 cm

Therefore the area of the largest rectangle that can be inscribed in the given right triangle is;

A = 1.5 cm × 4 cm = 6 cm^2

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The probability of type ii error at the 5% significance level is 49.5%

Probability:

In statistics, the number of possible way of occurring an particular event is referred as probability.

Given,

The manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the capital district. in order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2. the hypotheses to be tested are: h subscript 0 : mu equals 9 h subscript 1 : mu not equal to 9 assume that the actual average is $8.8.

Here we need to find the probability of type ii error at the 5% significance level.

While we looking into the give question, we have identified the following,

Semi skilled worker hourly wages = $9

Number of samples = 100

sample mean = $8

Standard deviation = $2

Hypotheses

H₀ : μ = 9

H₁ : μ ≠ 9

Significance level = 5%

Therefore, the type II error is calculated as,

=> P [(100 - 9/(2/√100)) ≥ (9 - 8)/(2/√100))] = 1 - 5

When we simplify this one then we get, the probability as 49.5%.

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70 + 60 + 8x + 2 = 180

132+8x= 180

8x= 180-132

8x=48

x= 6

plug in x

8(6)+2 = 50

Answer:

x = 6

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

To find the value of x, we can use the following equation:

70 + 60 + 8x + 2 = 180

132 + 8x = 180

8x = 48

x = 6

Answer:

9

Step-by-step explanation: 8 - 4m = - 10 - 2m

collect the like terms, calculate

-2m = -18 divide both sides,

m = 9

Answer:

wwwwwwwwwwww upper guy

Step-by-step explanation:

The probability that at least one number occurs exactly 6 times is 0.01303 and the probability that at least one number occurs exactly once is 0.323.

In the given question, roll a fair die 10 times.

(a) We have to compute the probability that at least one number occurs exactly 6 times.

At least one number occurring exactly 6 times.

From Binomial distribution

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

As we roll a dice 10 times. So n=6

As we know that a dice have six faces. Each faces are mark from the number 1 to 6.

That means if we rolled a dice then there is possibility of coming six numbers.

So the probability of coming number in one time is

p=1/6

The probability of not coming the same number is

q=1-p

q=1-1/6 = 5/6

x=6

Now putting the value

[tex]P(X=6) = 6\times^{10}C_{6}(\frac{1}{6})^{6}(\frac{5}{6})^{10-6}[/tex]

[tex]P(X=6) = 6\times^{10}C_{6}(\frac{1}{6})^{6}(\frac{5}{6})^{4}[/tex]

After solving, at least one number occur exactly 6 times

Probability = 0.01303

(b) We have to compute the probability that at least one number occurs exactly once.

[tex]P(X=1)= ^{10}C_{1}(\frac{1}{6})^{1}(\frac{5}{6})^{10-1}[/tex]

[tex]P(X=1) = ^{10}C_{1}(\frac{1}{6})^{1}(\frac{5}{6})^{9}[/tex]

After solving, the probability that at least one number occurs exactly once is

Probability = 0.323

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The approximate percentage training hours are delivered online is 30%

What is percentage ?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.

10%, a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. (Value/Total Value)100% is the formula used to calculate percentages.

The amount of hours remitted online are 25.6% in 2018 reports

It has reduced from last year , it has been reported 28.6% in 2017 and 30.4% in 2016

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Answer:

5≥17

Step-by-step explanation:

The size of the sample that she would have to get a margin of error less than 0.03 is 752

We have the margin of error E = 0.03

The confidence interval C I = 90 percent

p = 1 - p = 0.5

z α / 2 = 1.645

The formula for the sample size is given as

(z α / 2 / E)² * p * (1 - p)

(1.645 /  0.03)² * 0.5 * 0.5

= 54.833² * 0.5 *0.5

= 752

Hence n is given as 752. The size of the sample would have to be 752.

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The standard error of the sample mean of a given sample of 43 observations with standard deviation 8.85 is equal to 1.35 ( round to 2 decimal places).

As given in the question,

Population mean of the random variable 'μ' = 141

Standard deviation 'σ' = 8.85

Sample size 'N' = 43 observations

Standard error of the sample mean

= σ / √N

= 8.85 / √43

= 8.85 / 6.56

= 1.349

= 1.35 (round to 2 decimal places )

Therefore, for the given standard deviation and sample size the standard error of the sample mean is equal to 1.35.

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Answer:

The top speed of a cheetah is around 69 to 75 mph. However, the cat can only sprint a short distance of around 0.28 miles. A cheetah is about 2.7 times faster than the fastest human runner. A cheetah accelerates very quickly, allowing it to overtake prey at close range. The fastest cheetah on record is Sarah. Sarah lives at the Cinncinati Zoo in Ohio.

Step-by-step explanation:

Answer:

35.7632

Step-by-step explanation:

multiply the value in miles per hour by the conversion factor '0.44704'.=35.7632 meters per second

The missing measures of the angles are as follows:

The figure that completes the question is added as an attachment

From the figure of the rectangle, we have:

m∠BDC = 16°

A rectangle has four (4) interior angles that are 90 degrees each.

This means that

m∠ADE = 90 - 16

m∠ADE = 74°

Also, we have:

m∠ABD = m∠BDC = 16° by the alternate interior angles

By the complementary angle, we have:

m∠CBE = 90 - 16 = 74°

By the alternate interior angles, we have

m∠ADE = m∠CBE = 74°

Solving further, we have the following equations:

m∠AEB = 180 - 2(16)

m∠AEB = 148°

m∠DEA = 180 - m∠AEB

m∠DEA = 180 - 148

m∠DEA = 32°

Hence, the measure of the angle DEA is 32 degrees

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The correct option regarding how many times stronger the wave amplitude A of the earthquake was than the standard wave Ao is given by:

A = 39,811 Ao.

To find the ratio of A and Ao, which states how many times a earthquake measuring R in the Richter scale was stronger than the standard intensity Ao, we have to solve the following logarithmic function:

R = log(A/Ao)

The Richter scale of the earthquake in this problem is given as follows:

R = 4.6.

Hence the ratio of the measures is obtained as follows:

4.6 = log(A/Ao)

The power of 10 is the inverse function of the logarithm, hence if it is applied to both sides of the equation, then we can isolate the ratio A/Ao as follows:

A/Ao = 10^4.6

A/Ao = 39,811.

Applying cross multiplication, the ratio is given as follows:

A = 39,811 Ao.

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Answer:

2/10

Step-by-step explanation:

add the numbers and minus

Answer:

a I dont have a explanation but its a

6000FT, is the shortest length of fence that the rancher can use.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Let the rectangular field's length be x.

rectangle field width = y

square feet of a rectangular field's area

Because length is always positive, it is always positive.

Once more, discriminate with respect to x

replace x=1500

Therefore, at x=1 500, fencing is minimal.

Change x to 1 500.

the rectangular field is 1500 feet long.

rectangle field's width is 1000 feet.

Replace the values

shortest used fence length =6000ft

Hence, 6000FT, is the shortest length of fence that the rancher can use.

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The probability that the shipment will be accepted anyway is 0.0885.

Given,

In the question:

A random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that 8% of the apples on the truck do not meet the desired standard.

To find the probability that the shipment will be accepted anyway.

Now, According to the question:

The sample size, n = 150.

The population proportion, p = 0.08.

The shipment is accepted of the sample proportion is less than 5%.

Now, to find the required probability the listed conditions to verified.

Randomization: It was stated that a random sample is chosen.

Independence: It can be supposed that the fact that a sample is satisfactory is independent of the other apple's condition.

10% condition: It can be supposed that the population size is larger than 150 (sample size).

Normality: This condition requires that np and n (1 − p) must be at least 10, so it can be verified as,

np = (150 x 0.08)

np = 12 [tex]\geq[/tex] 10

The mean of the sample proportion can be estimated as:

μ[tex]_p[/tex] = p

    = 0.08

Similarly, The standard deviation of the sample proportion can be estimated as:

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

    =  [tex]\sqrt{\frac{0.08(1-0.08)}{150} }[/tex]

    =  0.02215

Thus, the sampling distribution of sample proportion can be approximated as,

p ~ N(0.08 ~ 0.0222)

The required probability is given as:

P(p < 0.05) = P (p - μ[tex]_p[/tex] /σ[tex]_p[/tex]  < 0.05 - 0.08/ 0.0222)

                  = P(Z < -1.35)

                 = 1 - P (Z < 1.35)

                  = 0.0885

Note: The probability value corresponding to the Z score is obtained from the unit normal table.

Thus, the probability that the shipment will be accepted anyway is 0.0885.

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The probability of getting 3 twice in a row is 1/36

A spinner has 6 equal parts labeled from 1 to 6.

The spinner is spun twice.
First time what is the conditions {1,2,3,4,5,6}

Second time choices are

{1,1} {1,2} {1,3} {1,4} {1,5} {1,6}

{2,1} {2,2} {2,3} {2,4} {2,5} {2,6}

{3,1} {3,2} {3,3} {3,4} {3,5} {3,6}

{4,1} {4,2} {4,3} {4,4} {4,5} {4,6}

{5,1} {5,2} {5,3} {5,4} {5,5} {5,6}

{6,1} {6,2} {6,3} {6,4} {6,5} {6,6}

So we have total 6*6 = 36 choices

{3,3} comes only 1 times.

We know the formula for probability:

Probability(Event) = Favorable Outcomes/Total Outcomes.

Favorable Outcomes = 1.

Total Outcomes=36.

So the probability of getting a 3 twice in a row is 1/36.

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Answer:

yass

queen

Step-by-step explanation:

Answer:

v = 15

Step-by-step explanation:

By exterior angle theorem:

9v° = 31° + (4v + 44)°

9v° = (4v + 44 + 31)°

9v = 4v + 75

9v - 4v = 75

5v = 75

v = 75/5

v = 15

It is false that when two variables are highly correlated, a change in the value of one will cause a change in the value of another.

What is the variable of an equation?

An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 = 10. "X" in this case is a variable.

The fact that two variables are correlated does not mean that one causes the other.

False

If there is a causal relationship between two variables, then variables are correlated but it is not always true that if variables are correlated then there is a causal relationship.

Hence, it is false that when two variables are highly correlated, a change in the value of one will cause a change in the value of another.

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Using the exponential growth formulas, we get the population at 10 years would be 2593.

What is exponential growth?

A process called exponential growth sees a rise in quantity over time. It happens when the derivative of a quantity's instantaneous rate of change with respect to time is equal to the original quantity.

Given Initial population is Pt= 1725.

The doubling time of the population is D=17

Now we need to find the population at time t=10

Using the formula,

[tex]P_{t}=P_{0} (2)^{\frac{t}{D} } \\P_{t}=1725 (2)^{\frac{10}{17} } \\P_{t}=1725 (2)^{0.588}\\P_{t}=1725 \space\ . \space\ 1.503\\P_{t}=2593[/tex]

Hence the population of the island in 10  years would be 2593.

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Answer:

1/14 ; 1/35

Step-by-step explanation:

A

6/10 x 5/9 x 4/8 x 3/7

3/5 x 5/9 x 1/2 x 3/7

1 x 1/3 x 3/14

1/14

B

4/10 x 3/9 x 2/8 x 6/7

2/5 x 1/3 x 1/4 x 6/7

2/15 x 3/14

1/5 x 1/7

1/35

The probability that  4 creature cards is pulled is 1/14 and the probability that 3 land cards and 1 creature card is pulled is 4/35

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here there are 4 land cards and 6 creature cards

thus selecting four cards at random from 10 cards is  ¹⁰C₄=210

and the event of selecting 4 creature cards from a total of 6 cards is ⁶C₄ =15

Therefore probability of pulling 4 creature cards is = 15/210

                                                                                     = 1/14

The probability of pulling 3 land cards and 1 creature cards is    

= ⁴C₃ × ⁶C₁   /  ¹⁰C₄

= 4/35

Hence 1/14 and 4/35 are the respective probabilities.

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As per the given standard deviation, the confidence interval is 495.84, upper bound is $65,495.8 and the lower bound is $64,504.2

Confidence interval

Confidence interval means a range of values, bounded above and below the statistic's mean, that likely would contain an unknown population parameter.

Given,

A student at another business school surveys 100 of 1000 graduates from last year and asks about their salaries. the researcher finds that the average income is $65, 000, with a standard deviation of $8000.

Here we need to find the confidence interval lower and upper bounds if you wanted to be 95% sure that the real mean of all 1000 students is within a range of the sample mean.

While we looking into the given question, we have identified the following values,

standard deviation = $8,000

Average income = $65,000

Sample size = 1000

Confidence level = 95%

Then the value of confidence interval is calculated by the formula,

Then we get the value of

Lower bound = 64504.2

Upper bound = 65495.8

Confidence interval (±) = 495.84

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The parameters of the rectangle in the question  can be presented as follows;

(A) The lengths of the opposite sides found using Pythagorean Theorem are the same, therefore, the opposite sides of the rectangle are congruent

(B) The lengths of the diagonals of the rectangle are both 5·√2, therefore, the diagonals are congruent

(C) The slopes of the sides of the rectangle are 1/3 and -3, therefore, the sides are perpendicular, and the and the re are 4 right angles on the rectangle.

A rectangle is a quadrilateral that has congruent opposite sides and each of the 4 interior angles of the rectangle are right angles.

(A) The lengths of the sides of the  rectangle are;

Top side; √(6² + 2²)

Opposite to the top √(6² + 2²)

Left side; √(3² + 1²)

Right side; √(3² + 1²)

The lengths of the opposite side are the same

Therefore;

The opposite sides are congruent

(B) The lengths of the diagonals are as follows;

Length of first diagonal=  √((2 - 1)² + (1 - 8)²) = √(1² + 7²) = √(50) = 5·√2

Length of the second diagonal = √((4 - (-1)² + (7 - 2)²) = √(50) = 5·√2

The length of the first and second diagonal are the same, therefore, the diagonals of the rectangle are congruent.

(C), Slope of the top side = (4 - 2)/(7 - 1) = 2/6 = 1/3

Slope of the opposite to the top side = (1 - (-1))/(8 - 2) = 1/3

Slope of the left side = (2 - (-1))/(1 - 2) = -3

Slope of the right side = (4 - 1)/(7 - 8) = -3

The slope of the top side are the negative inverse of the slope of the left and right sides of rectangle

Therefore, the sides of the rectangle are perpendicular, and the rectangle consists of 4 right angles

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Using the concept of midpoint of a line segment, the length of BD is 9 units

A midpoint is a point lying between two points and is in the middle of the line joining the two points. If a line is drawn joining the two points, then the midpoint is a point at the middle of the line and is equidistant from the two points. Given any two points, say A and C, the midpoint is a point B which is located halfway between points A and C. Therefore, to calculate the midpoint, we can simply measure the length of the line segment and divide by 2.

In the question given;

AE = 18, DE = 5

But D is the midpoint of CE

CE = 2DE

CE = 2 * 5 = 10

The line CE IS 10

But AE is the total length of the line segment and it equals 18

AE = AC + CE

AC = AE - CE

AC = 18 - 10

AC = 8

If AC = 8, BC = 1/2(AC)

BC = 1/2 (8)

BC = 4

The line BD = BC + CD

BE = 4 + 5 = 9

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it might not be possible to carry out a randomized controlled experiment, even when the aim is to investigate causality in the collected data  the researcher should be worried about potential g idiographic

Type of causal reasoning is an idiographic explanation  

we know that there are 2 types of  approach for understanding the social life

Idiographic  

nomothetic  

and here idiographic approach use for understanding single or individual type case or event but a nomothetic approach that is used for understanding large scale social pattern

so here also cause of the single situation is exhaustively examined  

so correct answer is an idiographic explanation

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