how many ways are there to seat 6 people around a circular table where two sections are considered the same when everyone has the same immediate left and immediate right neighbor?

The mean is 11.9 while the median is 10.5

Here, we want to calculate the mean and the median

Mathematically, the mean is the average of the numbers

We proceed as follows to find the mean;

To get the median, we simply re-arrange the values in the data set from the lowest to the highest

That will be;

6,7,9,10,11,16,16,20

The median term refers to the middle number

Since the number of terms here is even, then the median would be the average of the two 4th terms counting from both ends

Thus, the median is;

The median is 10.5

The length of arc EG is approximately 7.35 units.

To find the length of arc EG, we need to use the formula:

length of arc = (central angle/360°) × 2πr

where r is the radius of the circle and the central angle is in degrees.

We are given that m∠EFG = 58°, and EF = 6 units. Since EF is a chord of the circle, we can use the chord-chord angle theorem to find that m∠EGF = ½(180° - 58°) = 61°.

Now, we can use the Law of Cosines to find the length of GE:

GE² = EF² + FG² - 2(EF)(FG)cos(∠EGF)

GE² = 6² + FG² - 2(6)(FG)cos(61°)

Since FG = 2r (because it is the diameter of the circle),

GE² = 36 + (2r)² - 12r cos(61°)

We can simplify this to:

GE² = 4r² - 12r cos(61°) + 36

GE² = 4(r² - 3r cos(61°) + 9)

Now, we can use the formula for the length of the arc:

length of arc EG = (m∠EGF/360°) × 2πr

length of arc EG = (61/360) × 2πr

length of arc EG = (61/180) × πr

Substituting the expression for GE² in terms of r, we get:

length of arc EG = (61/180) × π √[4(r² - 3r cos(61°) + 9)]

We can now use a calculator to find the approximate value of the length of arc EG.

Rounded to the nearest hundredth, the length of arc EG is approximately 7.35 units.

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first one is easy money

right angle = 90, and we also have 42 so:

90+42=132

180-132=48

2nd one is weird, why is there a 150 down there? triangles add up to 180 nso right angle already gets 90 degrees.--oh wait I just got it, so that is the angle of the outer. we know a line is 180 degrees, so 180-150=30 so we found that degree

So now 90+30=120, 180-120=60

Answer:

\(b = 8\)

Step-by-step explanation:

First, cross multiply across the equal sign. Note that what you do to one side, you do to the other:

\((b+10)(2b-7)(\frac{8}{b+10}) = (\frac{4}{2b -7})(b+10)(2b-7)\\ \\(2b -7)(8) = (4)(b+10)\)

Next, distribute 8 and 4 to their corresponding parenthesis:

\(8(2b -7) = 16b - 56\\4(b + 10) = 4b + 40\)

\(16b - 56 = 4b + 40\)

Next, isolate the variable, b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, add 56 and subtract 4b from both sides:

\(16b (-4b) - 56 (+56) = 4b (-4b) + 40 (+56)\\16b - 4b = 40 + 56\\12b = 96\)

Isolate the variable, b. Divide 12 from both sides:

\(12b = 96\\\frac{12b}{12} = \frac{96}{12} \\b = \frac{96}{12} \\b = 8\)

\(b = 8\) is your answer.

~

Answer:

Sonnet 18. One of Shakespeare's best known and most loved sonnets, this reading explains that the stability of love will immortalize a partners beauty and youth. 'Shall I compare three to a summers day? And summers lease hath all too short a date.

Step-by-step explanation:

Answer:

-4 degrees C

Step-by-step explanation:

-9 + 5 = -4

Answer and Step-by-step explanation:

The answer is 5 and 17.

I first started with 2 and 14, and tried to see if it worked.

This is how you find the second number.

You input the smaller value in the first part, and the bigger number in the second part:

(_ × 2) + (_ × 3)

I kept increasing each number by 1 until I got to the numbers 5 and 17.

I saw that 17 - 5 is 12.

Then, I plugged it into the expression I made.

(5 × 2) + (17 × 3)

10 + 51 = 61.

So, the answer is 5 and 17.

#teamtrees #PAW (Plant And Water)

(a) For an F-distribution with degrees of freedom q₁ = 4 and q₂ = 9, the probability of observing an F-value less than a certain value is 0.0112.

(b) For an F-distribution with degrees of freedom q₁ = 5 and q₂ = 8, the probability of observing an F-value less than a certain value is 0.9512.

(c) The probability of observing an F-value less than 6.16 for an F-distribution with degrees of freedom q₁ = 6 and q₂ = is not provided.

(a) To find the probability for an F-distribution, you can use statistical tables or software. In this case, with q₁ = 4 and q₂ = 9, the probability of observing an F-value less than a certain value is 0.0112.

(b) Similarly, for q₁ = 5 and q₂ = 8, the probability of observing an F-value less than a certain value is 0.9512.

(c) The probability of observing an F-value less than 6.16 for an F-distribution with degrees of freedom q₁ = 6 and q₂ = is not provided in the given information. To calculate this probability, you would need to refer to the appropriate statistical tables or use software.

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(a) For an F-distribution with degrees of freedom q1 = 4 and q2 = 9, the value of f for a probability of 0.0112 is approximately 0.388.

(b) For an F-distribution with degrees of freedom q1 = 5 and q2 = 8, the value of f for a probability of 0.9512 is approximately 2.715.

(c) The probability P(F < 6.16) for an F-distribution with degrees of freedom q1 = 6 and q2 = 16 is approximately 0.995.

(a) To find the value of f for a given probability, we can use statistical tables or software. For q1 = 4 and q2 = 9, the f-value for a probability of 0.0112 is approximately 0.388.

(b) Similarly, for q1 = 5 and q2 = 8, the f-value for a probability of 0.9512 is approximately 2.715.

(c) To find the probability P(F < 6.16), we can use statistical tables or software. For q1 = 6 and q2 = 16, the probability is approximately 0.995, indicating that the F-value is less than 6.16 in about 99.5% of the cases.

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Answer:

Below

Step-by-step explanation:

It's 66

To find a percentage of a number just multiply it by 0.whatever the percentage if that makes sense...

In this case you would do 55 x 1.2 = 66

Hope this helps!

\(\huge\text{Hey there!}\)

\(\huge\boxed{\mathsf{120\% \ of\ 55}}\\\huge\boxed{= \dfrac{120}{100}\times55}\\\huge\boxed{= \dfrac{6}{5}\times\dfrac{55}{\bf 1}}\\\huge\boxed{= \dfrac{6\times55}{5\times 1}}\\\\\\\huge\boxed{6\times55=\bf 330}\\\boxed{5\times1=\bf 5}\\\\\\\huge\boxed{= \dfrac{330\div5}{5\div5}}\\\huge\boxed{=\dfrac{66}{1}}\\\huge\boxed{= \bf 66}\)

\(\huge\boxed{\textsf{Therefore, your ANSWER is: 66}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\huge\boxed{\frak{Amphitrite1040:)}}\)

Answer:

The number 51.243 is bigger than 5.1243.

Step-by-step explanation:

To compare two decimal numbers, we start by looking at the digits to the left of the decimal point. In this case, both numbers have the same digit in the tens place, which is 5. So we need to look at the next digit to the right of the decimal point.In 51.243, the digit to the right of the decimal point is 2, which is larger than the digit to the right of the decimal point in 5.1243, which is 1. Therefore, we can conclude that 51.243 is bigger than 5.1243.

Answer:

51.243

Step-by-step explanation:

because 51 is greater than 5.1

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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Answer:

yes

Step-by-step explanation:

why not

Because the transformations don't change the size, we can see that B'C' = 24 units.

Here we know that we have a triangle ABC, and we apply some transformations to it.

First, the original side BC has a length of 24 units, then we apply a reflection and a translation to get the triangle A'B'C'.

Notice that we didn't use a dilation/contraction, then the dimensions do not change.

This means taht the length of BC and B'C' must the same ones, then we can conclude that B'C' = 24 units.

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Answer:

1.73 pounds of strawberries per gallon of ice cream

Step-by-step explanation:

9 1/2 and 5 1/2 can be converted into decimals

9.5 pounds of strawberries for 5.5 gallons of ice cream

9.5 / 5.5 = 1.73 pounds of strawberries per gallon of ice cream

The family of functions P = C1e^t / (1 + C1e^t) is a solution to the differential equation dP/dt = P(1 - P) on an appropriate interval of definition.

In the first paragraph, we summarize that the family of functions P = C1e^t / (1 + C1e^t) is a solution to the differential equation dP/dt = P(1 - P). This equation represents the rate of change of the variable P with respect to time t, and the solution provides a relationship between P and t. In the second paragraph, we explain why this family of functions satisfies the given differential equation.

To verify the solution, we can substitute P = C1e^t / (1 + C1e^t) into the differential equation dP/dt = P(1 - P) and see if both sides are equal. Taking the derivative of P with respect to t, we have:

dP/dt = [d/dt (C1e^t / (1 + C1e^t))] = C1e^t(1 + C1e^t) - C1e^t(1 - C1e^t) / (1 + C1e^t)^2

      = C1e^t + C1e^(2t) - C1e^t + C1e^(2t) / (1 + C1e^t)^2

      = 2C1e^(2t) / (1 + C1e^t)^2.

On the other hand, evaluating P(1 - P), we get:

P(1 - P) = (C1e^t / (1 + C1e^t)) * (1 - C1e^t / (1 + C1e^t))

        = (C1e^t / (1 + C1e^t)) * (1 - C1e^t + C1e^t / (1 + C1e^t))

        = (C1e^t - C1e^(2t) + C1e^t) / (1 + C1e^t)

        = (2C1e^t - C1e^(2t)) / (1 + C1e^t)

        = 2C1e^t / (1 + C1e^t) - C1e^(2t) / (1 + C1e^t).

Comparing the two sides, we see that dP/dt = P(1 - P), which means the family of functions P = C1e^t / (1 + C1e^t) is indeed a solution to the given differential equation.

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Among the given options, (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements.

An outlier is defined as a measurement that significantly deviates from the other measurements in a data set.

In this case, one of the measurements among the 10 is identified as an outlier.

When comparing the remaining 9 measurements with the entire set of 10 measurements, the maximum value of the 9 measurements cannot exceed the maximum value of the 10 measurements because the outlier, by definition, exceeds the upper quartile or lower quartile by at least 1.5 times the interquartile range.

It is important to note that the median of the 9 measurements can be either greater than or less than the median of the 10 measurements, depending on the specific values of the measurements.

The presence of the outlier does not necessarily determine the relationship between the medians of the two sets.

Similarly, the standard deviation of the 9 measurements may or may not be less than the standard deviation of the 10 measurements.

The inclusion or exclusion of the outlier can have an impact on the standard deviation calculation, but it is not guaranteed to be lower or higher in either case.

Therefore, among the given options, the only statement that must be true is (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements.

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Answer:

224

Step-by-step explanation:

200*0.12=24

200+24=224

The amount to be paid for the loan is $248.

'Simple interest is the interest amount for a particular principal amount of money at some rate of interest.

According to the given problem,

Principal amount (P) = $200

Rate of interest (r) = 12%

Time period (t) = 2 years

We know,

Final amount to be paid with interest (A) = P( 1 + rt )  

                                                                   = 200{ 1 + ( 0.12 × 2 )

                                                                   = 200( 1 + 0.24 )

                                                                   = 200 × 1.24

                                                                   = $248

Hence, we can conclude, we have to pay $248 for the loan.

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The probability that 45 or more people in this sample have consumed alcoholic beverages is 0.0516, or about 5.16 percent.

The probability that 45 or more people in a sample have consumed alcoholic beverages can be determined using normal distribution, as the sample size is sufficiently large. The distribution is also normal because of the large sample size. Using the normal distribution table or a calculator, the probability can be determined. The formula is:

P(X > 44.5) = 1 - P(X ≤ 44.5) = 1 - 0.9484 = 0.0516, approximately.

(Note: We use 44.5 because it is the midpoint of the interval 44.5 to 45.5, which is the one that includes 45.)

Therefore, the probability that 45 or more people in this sample have consumed alcoholic beverages is 0.0516, or about 5.16 percent.

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Answer:

130 and 211

Step-by-step explanation:

15+17= 32

17+32=49

32+49=81

49+81=130

81+130=211

Answer:

130 and 211

Step-by-step explanation:

15,17,32,49,81 _ _

15+2=17+15=32+17=49+32=81

that mean 81+ 49=130

and 81+130= 211

Hence, the answer is 130 and 211.

Answer:

6

-

5

Step-by-step explanation:

You can do there are multiple ways but the easiest is rise over run so

so -4 to 2 is 6 and -2 to 3 is 5 so the answer is

6

--

5

You can also do the much harder way of

Y2-Y1   (-2,-4)     2-(-4)    6

---------    x  y       --------= --

X2-X1    (3,2)      3-(-2)    5

Answer:

43/20  or 2 3/20

Step-by-step explanation:

11/4-3/5

Convert to common denominator

55/20-12/20

43/20 or 2 3/20

Hope this helps!

Step-by-step explanation:

y = 123° (vertically opposite angle)

x = 123° (Alternate Exterior angle)

z = 123 + z = 180 ( as all sum of all angles on a sprint line is 180°)

→ z = 180 - 123 = 57°

→ z = 57°

therefore,

y = 123°

x = 123°

z = 57°

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

btw great handwriting! (◔‿◔)

Answer:

infinitely many solutions

Step-by-step explanation:

please make me as brainlies

Answer:

x = -1, y = -6

Step-by-step explanation:

\($$A system of equations, also known as a set of simultaneous equations can be solved using several commonly used methods.$$\)

\(\text{Let} \\ \\y \ = \ 6x \quad $-----$ \; (1) \\ \\2x \ + \ 3y \ = \ -20 \quad $-----$ \; (2). \\ \\ \\ 1. \quad \text{The Substitution Method} \\ \\\\\text{Substitute equation (1) into equation (2), yielding} \\ \\\\2x \ + \ 3(6x) \ = \ -20 \\ \\2x \ + \ 18x \ = \ -20 \\ \\20x \ = \ -20 \\ \\x \ = \ -1 \\ \\\text{Since} \ \ x \ = -1, \text{using equation (1) to find the value of } y, \\ \\y \ = \ 6 (-1) \\ \\y \ = \ -6\)

\(2. \quad \text{The Elimination Method} \\ \\ \text{First, multiply each term of equation (1) by 3, giving} \\ \\ y \ \times \ 3 \ = \ (6x) \ \times \ 3 \\ \\ 3y \ = \ 18x \\ \\ \text{Rearrange the equation such that the one side of the previous equation becomes 0.} \\ \\ 18x \ - \ 3y \ = \ 0 \qquad $-----$ \; (3) \\ \\ \text{Add equation (2) and equation (3) together,} \\ \\ (2x \ + \ 3y) + (18x \ - \ 3y) \ = \ -20 + 0 \\ \\ 2x \ + \ 18x \ + \ 3y \ - \ 3y \ = \ -20 \\ \\ 20x \ = \ -20 \\ \\ x \ = \ -1\)

\(\text{When} \ \ x \ = \ -1, \ \ \text{according to equation (1),} \\ \\ y \ = \ 6(-1) \\ \\ y \ = \ -6\)

There are total of 152 students in 5th grade, then the number of pencils altogether will be equal to 2,736 pencils.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total number of students in 5th grade = 152

Amount of pencil each student have = 18

Then, the total number of pencils altogether,

= 152 × 18

= 2,736 pencils.

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Answer: No Triangle: 30 , 85 , 60, and 2, 8, 10

One Triangle: 7, 24, 25

Many Triangles: 45, 45, 90           5, 15, 160

Answer: Your answer will be Option three

Step-by-step explanation: Because she ate 1/3 the rest of the cake.

Have a brilliant day- your friend Lily ^_^

Answer:

k=5

Step-by-step explanation:

15-8k+15k-8=42

15+7k=50

7k=35

k=5

The inverse of the function is y = ( 1/5 )x - 6.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Consider the function,

y = 5x + 30

To find the inverse of the function we interchange x and y then find the equation for y.

Therefore, after interchanging x and y:

x = 5y + 30

Subtracting 30 from each side of the equation.

x - 30 = 5y + 30 - 30

x - 30 = 5y

Now, dividing the whole equation by 5

( x - 30 ) / 5 = 5y / 5

y = ( 1/5 )x - 30/ 5

y = ( 1/5 )x - 6

Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.

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Answer: The answer is D